reference collection book RC kansas city public library kansas city, missouri W HUT ^-/ V^ From the collection of the n m V 0 Prejinger library t P San Francisco, California 2008 • • • • • . • • • • . e « • ? • • " • . ^ - . • ' » _ »!••»»• • « # ^ « t . V ' * • 4 «> ' « w » * A • « THE BELL St St fi iVI Jecnnical ournai :^^^ AN DEVOTED TO THE SCIENTIFIC ND ENGINEERING ASPECTS OF ELECTRICAL COMMUNICATION ADVISORY BOARD A. B. GoETZE M. J. Kellt E. J. McNeely EDITORIAL COMMITTEE B. McMillan, Chairman K. E. Gould S. E. Brillhart A. J. Busch L. R. Cook A. C. DiCKIESON R. L. DiETZOLD »^NSAS CITY A PUBLIC Lm. ^RM E. I. Green R. K. HONAMAN H. R. HUNTLET F. R. Lack J. R. Pierce f'EB 5 1958 EDITORIAL STAFF W. D. Bulloch, Editor R. L. Shepherd, Production Editor INDEX VOLUME XXXVI 1957 AMERICAN TELEPHONE AND TELEGRAPH COMPANY NEW YORK LIST OF ISSUES IN VOLUME XXXVI No. 1 January Pages l-"48 2 March 349-592 3 May 593-830 4 July 831-1046 5 September 1047-1318 6 November 1319-1514 S - ' I THE BELL SYSTEM Jechnical lournal {^^^ AN DEVOTED TO THE SCIENTIFIC ^^^ AND ENGINEERING \SPECTS OF ELECTRICAL COMMUNICATION i^OLUME XXXVI JANUARY 1957 NUMBER 1 Transatlantic Communications — An Historical Restime-' 1 6 1^57 MERVIN J. KELLY AND SIR GORDON RADLBY 1 Transatlantic Telephone Cable System — Planning and Over- All Per- formance E. T. MOTTRAM, R. J, HALSEY, J. W. EMLING AND R. G, GRIFFITH 7 System Design for the North Atlantic Link H. A. LEWIS, R. S. TUCKER, G. H. LOVELL AND J. M. ERASER 29 Repeater Design for the North Atlantic Link T. F. GLEICHMANN, A. H. LINCE, M. C. WOOLEY AND F. J. BRAGA 69 Repeater Production for the North Atlantic Link H. A. LAMB AND W. W. HEFFNER 103 Power Feed Equipment for the North Atlantic Link G. W. MESZAROS AND H. H. SPENCER 139 Electron Tubes for the Transatlantic Cable System J. O. McNALLY, G. H. METSON, E. A. VEAZIE AND M. F. HOLMES 163 Cable Design and Manufacture for the Transatlantic Submarine Cable System a. w. lebert, h. b. fischer and m. c. biskeborn 189 I System Design for the Newfoundland-Nova Scotia Link R. J. HALSEY and J. F. BAMPTON 217 Repeater Design for the Newfoundland-Nova Scotia Link R. A. BROCKBANK, D. C. WALKER AND V. G. WELSBY 245 Power-Feed System for the Newfoundland-Nova Scotia Link J. F. p. THOMAS AND R. KELLY 277 Route Selection and Cable Laying for the Transatlantic Cable System j. s. jack, capt. w. h. leech and h. a. lewis 293 Bell System Technical Papers Not Published in This Journal 327 Recent Bell System Monographs 335 Contributors to This Issue 338 COPYRIGHT 1957 AMERICAN TELEPHONE AND TELEGRAPH COMPANY THE BELL SYSTEM TECHNICAL JOURNAL ADVISORY BOARD A. B. GOETZE, President, Western Electric Company M. J. EELiiT, President, BeU Telephone Laboratories E.J. McNEBLY, Executtve Vice President, American Telephone and Telegraph Company EDITORIAL COMMITTEE B. McMillan, Chairman S. E. BBILLHABT E. I. GBEEN A. J, BUSCH E, K. HONAMAN L.B.COOK H.B.HUNTLEY A. C. DICKIESON F. B. LACK B. L. DIETZOLD J. B. PIEKCE K. E. GOULD Q. N. THAYEB EDITORIAL STAFF J. D. TEBO, Editor E. L. 8HEPHEED, Production Editor T. N. POPE, Circulation Manager THE BELL SYSTEM TECHNICAL JOURNAL is published six times a year by the American Telephone and Telegraph Company, 195 Broadway, New York 7, N. Y. F. R. Kappel, President; S. Whitney Landon, Secretary; John J. Scan- Ion, Treasurer. Subscriptions are accepted at $5.00 per year. Single copies $1.25 each. Foreign postage is 65 cents per year or 11 cents per copy. Printed in U. S. A. THE BELL SYSTEM TECHNICAL JOURNAL VOLUME XXXVI JANUARY 1957 number 1 Copyright 1957, American Telephone and Telegraph Company Transatlantic Communications — An Historical Resume By DR. MERVIN J. KELLY* and SIR GORDON RADLEYf (Manuscript received Jul}' 30, 1956) The papers that follow describe the design, manufacture and installa- tion of the first transatlantic telephone cable system with all its com- ponent parts, including the connecting microwave radio-relay system in Nova Scotia. The purpose of this introduction is to set the scene in which this project was undertaken, and to discuss the technical contribution it has made to the development of world communications. Electrical communication between the two sides of the North At- lantic started in 1866. In that year the laying of a telegraph cable be- tween the British Isles and Newfoundland was successfully completed. Three previous attempts to establish transatlantic telegraph communi- cation by submarine cable had failed. These failures are today seen to be the result of insufficient appreciation of the relation between the mechanical design of the cable and the stresses to which it is subjected as it is laid in the deep waters of the Atlantic. The making and laying of deep sea cables was a new art and designers had few experiments to guide them. During the succeeding ninety years, submarine telegraph communi- cation cables have been laid all over the world. Cable design has evolved from the simple structure of the first transatlantic telegraph cable — a * Bell Telephone Laboratories, f British Post Office. 1 2 THE BELL SYSTEM TECHNICAL JOUllNAL, JANUARY 1957 stranded copper conductor, insulated with gutta-percha and finished off with servings of jute yarn and soft armoring wires — to the relatively complex structure of the modern coaxial cable, strengthened by high tensile steel armoring for deep sea operation. The coaxial structure of the conducting path is necessary for the transmission of the wide fre- quency band width required for many telephone channels of communi- cation. The optimum mechanical design of the structure for this first transoceanic telephone cable has been determined by many experiments in the laboratory and at sea. As a result, the cable engineer is confident that the risk of damage is exceedingly small even when the cable has to be laid and recovered under conditions which impose tensile loads approaching the breaking strength of the structure. The great difference between the transatlantic telephone cable and all earlier transoceanic telegraph cables is, however, the inclusion of submerged repeaters as an integral part of the cable at equally spaced intervals and the use of two separate cables in the long intercontinental section to provide a separate transmission path for each direction. The repeaters make possible a very large increase in the frequency band width that can be transmitted. There are fifty-one of these submerged repeaters in each of the two cables connecting Clarenville in Newfound- land with Oban in Scotland. Each repeater provides 65 db of amplifi- cation at 164 kc, the highest transmitted frequency. The working frequency range of 144 kc will provide thirty-five telephone channels in each cable and one channel to be used for telegraph traffic between the United Kingdom and Canada. Each cable is a one-way traffic lane, all the "go" channels being in one cable and all the "return" in the other. The design of the repeaters used in the North Atlantic is based on the use of electron tubes and other components, initially constructed or selected for reliability in service, supported by many j^ears of research at Bell Telephone Laboratories. Nevertheless, the use of so many re- peaters in one cable at the bottom of the ocean has been a bold step forward, well beyond anj^thing that has been attempted hitherto. There are some 300 electron tubes and 6,000 other components in the sub- merged repeaters of the system. Many of the repeaters are at depths exceeding 2,000 fathoms (2j miles) and recovery of the cable and re- placement of a faulty repeater might well be a protracted and expensive operation. This has provided the incentive for a design that provides a new order of reliability and long life. On the North Atlantic section of the route, the repeater elements are housed in flexible containers that can pass around the normal cable TRANSATLANTIC COMMUNICATIONS 3 laying gear without requiring the ship to be stopped each time a repeater is laid. The advantages of this flexible housing have been apparent dur- ing the laying operations of 1955 and 1956. They have made it possible to continue laying cable and repeaters under weather conditions which would have made it extremely difficult to handle rigid repeater housings with the methods at present available. A single connecting cable has been used across Cabot Strait between Newfoundland and Nova Scotia. The sixteen repeaters in this section have been arranged electronically to give both-way amplification and the single cable provides "go" and "return" channels for sixty circuits. "Go" and "return" channels are disposed in separate frequency bands. The design is based closely on that used by the British Post Office in the North Sea. Use of a single cable for both-way transmission has many attractions, including that of flexibility in providing repeatered cable systems, but no means has yet been perfected of laying as part of a continuous operation the rigid repeater housings that are required because of the additional circuit elements. This is unimportant in rela- tively shallow water, but any operation that necessitates stopping the ship adds appreciably to the hazards of cable lajdng in very deep water. The electron tubes used in the repeaters between Newfoundland and Scotland are relatively inefficient judged by present daj^ standards. They have a mutual conductance of 1,000 micromhos. Proven reliability, lower mechanical failure probability and long life were the criteria that determined their choice. Electron tubes of much higher performance with a mutual conductance of 6,000 micromhos are used in the New- foundland-Nova Scotia cable, and it is to be expected that long re- peatered cable systems of the future will use electron tubes of similar performance. This will increase the amplification and enable a wider frequency band to be transmitted; thus assisting provision of a greater number of circuits. If every advantage is to be taken of the higher performance tubes, it will be necessary to duplicate (or parallel) the amplifier elements of each repeater, in the manner described in a later paper, in order to assure adquately long trouble-free performance. This has the disadvantage of requiring the use of a larger repeater housing. During the three years that have elapsed since the announcement in December, 1953 by the American Telephone and Telegraph Company, the British Post Office, and the Canadian Overseas Telecommunication Corporation, of their intention to construct the first transatlantic telephone cable system, considerable progress has been made in the development and use of transistors. The low power drain and operating voltage required will make practicable a cable with many more sub- 4 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 merged repeaters than at present. This will make possible a further widening of the transmission band which could provide for more tele- phone circuits with accompanying decrease in cost per speech channel or the widened band could be utilized for television transmission. Much work, however, is yet to be done to mature the transistor art to the level of that of the thermionic electron tube and thus insure the constancy of characteristics and long trouble-free life that this transatlantic service demands. The present transatlantic telephone cable whose technical properties are presented in the accompanying papers, however, gives promise of large reduction in costs of transoceanic communications on routes where the traffic justifies the provision of large traffic capacity repeatered cables. The thirty-six, four-kilocycle channels which each cable of the two-way system provides, are the equivalent of at least 864 telegraph channels. A modern telegraph cable of the same length without repeaters would provide only one channel of the same speed. The first transat- lantic telegraph cable operated at a much slower speed, and transmitted only three words per minute. The greater capacity of future cables will reduce still further the cost of each communication circuit provided in them. Such considerations point to the economic attracti\'eness, where traffic potentials justify it, of providing broad band repeatered cables for all telephone, telegraph and teletypewriter service across ocean barriers. The new transatlantic telephone cable supplements the service now provided by radio telephone between the European and North American Continents. It adds greatly to the present traffic handling capacity of this service. The first of these radio circuits was brought into operation between London and New York in 1927. As demands for service have grown, the number of circuits has been increased. We are, however, fast approaching a limit on further additions, as almost all possible frequency space has now been occupied. The submarine tele- phone cable has come therefore at an opportune time; further growth in traffic is not limited by traffic capacity. Technical developments over the years by the British Post Office and Bell Telephone Laboratories have brought continuing improvement in the quality, continuity and reliability of the radio circuits. The use of high freciuency transmission on a single side band with suppressed carrier and steerable receiving antenna are typical of these developments. Even so, the route, because of its location on the earth's surface, is particularly susceptible to ionospheric disturbances which produce quality deterioration and at times interrupt the service completely. TRANSATLANTIC COMMUNICATIONS 5 Cable transmission will be free of all such quality and continuity limita- tions. In fact, service of the quality and reliability of the long distance service in America and Western Europe is possible. This quality and continuity improvement may well accelerate the growth in transatlan- tic traffic. The British Post Office and Bell Telephone Laboratories are contin- uing vigorous programs of research and development on submarine cable systems. Continuing technical advance can be anticipated. Broader transmission bands, lower cost systems and greater insurance of con- tinuous, reliable and high quality services surely follow. Transatlantic Telephone Cable System — Planning and Over-All Performance By E. T. MOTTRAM,* R. J. HALSEY,t J. W. EMLING* and R. G. GRIFFITHJ (Manuscript received October 10, 1956) The transatlantic telephone cable system was designed as a link connecting communication networks on the two sides of the Atlantic. The technical planning of the system and the objectives set up so that this role would be fidfilled, are the principal subjects of this paper. Typical performance char- acteristics illustrate the high degree with which the objectives have been realized. Optimum application of the experience of the British Post Office with rigid repeaters and the Bell System with flexible repeaters, together with close cooperation among three administrations, have played a large part in achieving the objectives. INTRODUCTION The transatlantic telephone cable system was planned primarily to connect London to New York and London to Montreal, and thus serve as an interconnection between continent-wide networks on the two sides of the Atlantic. Thus, the system has to be capable of serving as a link in wire circuits as long as 10,000 miles, connecting telephone instruments supplied by various administrations and used by peoples of many nations. This role as an intercontinental link has, therefore, been a controlling consideration in setting the basic objectives for the system. The end sections of the system utilize facilities which are integral parts of the internal networks of the United States, Great Britain and Canada, but the essential new connecting links, extending between Oban, Scotland, and the United States-Canada border, and forming the greater part of the system, were built under an Agreement between the joint owners — the American Telephone and Telegraph Company and its subsidiary the Eastern Telephone and Telegraph Company (oper- ating in Canada), the British Post Office, and the Canadian Overseas * Bell Telephone Laboratories, t British Post Office. % Canadian Overseas Telecommunication Corporation. PLANNING AND OVER-ALL PERFORMANCE 9 Telecommunication Corporation. It is thus the joint effort of three nations. In planning the system, the main centres of interest were, naturally, the two submarine cable sections, Scotland to Newfoundland, and New- foundland to Nova Scotia, each of which had to meet a unique combina- tion of requirements imposed by water depth, cable length and trans- mitted bandwidth. OVER-ALL VIEW OF THE SYSTEM The transatlantic system provides 29 telephone circuits between Lon- don and New York, six telephone circuits between London and Mont- real, and a single circuit split between London — New York and Lon- don — Montreal ; this split circuit is available for telegraph and other narrow band uses. There are also 24 telephone circuits available for local service between Newfoundland and the Mainland of Canada, and there is considerable excess capacity over the radio-relay link that crosses the Maritime Provinces of Canada. A map of the system is shown in Fig. 1 ; the facilities used, together with the approximate route distances are shown in Fig. 2. It will be seen that the over-all lengths of the London to New York and London to ]\Iontreal circuits are 4,078 and 4,157 statute miles respectively. Seven of the New York to London circuits are permanently extended to Euro- pean Continental centres — Paris, Frankfurt (2), Amsterdam, Brussels, Copenhagen and Berne. The longest circuit is thus New York to Copen- hagen, 4,948 miles. Starting at London, which is the switching centre for United Kingdom and Continental points, 24-circuit carrier cables provide two alternative routes to Glasgow and thence to Oban by a new coaxial cable. Between London and Oban the two routes are fed in parallel at the sending ends, so a changeover can be effected at the receiving ends only. At a later date, an alternative route out of Oban will be provided by a new coaxial cable to Inverness. From Oban a deep-sea submarine link connects to Clarenville, New- foundland. This link is in fact two parallel submarine cables, one vised for east-to-west transmission, the other for transmission in the reverse direction. Each cable is roughly 1,950 nautical-miles in length and lies at depths varying between a few hundred fathoms on the continental shelf and about 2,300 fathoms at the deepest point. Each cable incorpo- rates 51 repeaters in flexible housings which compensate for the cable attenuation of about 3,200 db at the top frequency of 164 kc. These z < ? > 00 n < Q Z <5 z o X 't t < I U i/i en Z '.h- to < < to o -i2 z o tL UJ -10 t7 to H h- --^ 1- t =5 o 7" 7 U< CO UJ ^ o n if) in O OBJECTIVE LIMITS FOR VOICE CHANNEL V — 100 200 300 400 500 600 800 1000 FREQUENCY IN CYCLES PER SECOND 2000 3000 4000 Fig. 3 — C.C.I.F. objectives for frequency characteristic of voice channel. No specific objectives were agreed upon for the frequency characteris- tics of the 12-channel groups as such, but there was an expectation that ±2db could be achieved except for frequencies adjacent to the filters in the split group. For program channels, the C.C.I.F. recommendations were also adopted in respect of the two-band (6.4 kc) and three-band (10 kc) arrangements. To meet the requirements of these channels and of teleg- raphy, an overall frequency stability objective of ±2 cycles was adopted. Noise and Crosstalk Noise objectives were established to be reasonably consistent both with Bell System and C.C.I.F.* objectives for circuits of transatlantic length. The objective for the rms circuit noise at a zero level point in the * The methods specified by these two bodies for the assessment of circuit noise differ in three respects, the units employed, the frequency weighting employed, and the fraction of the busy hour for which the specified noise may occur. The meters concerned are the Bell System 2B noise meter (FIA weighting network) reading in dba and the C.C.I.F. psophometer (1951 weighting network) reading in millivolts across 600 ohms. The relationship between readings on the two meters is discussed in a later paper and it will suffice here to note that, for white noise dbm (COIF) = dba (Bell) - 84. 20 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 Table II — RMS Xoise Objectives in Busy Hour Link Approx. mileage Noise dba New York-Sydnej^ Minesl 1,000 400 2,000 500 31 Montreal -bydney Mines J Sydney Mines-Clarenville Clarenville-Oban Oban-London 28 36 28 Total New York-Londonl 38 Montreal-London / busy hour was agreed as 38 dba (i.e. —46 dbm or 3.9 mv). This was allocated between the various links as in Table II. For the program channels, the agreed noise objective was —50 dbm as measured on a C.C.I.F. psophometer with a 1951 program weighting network. Statistical data on probable speech le^'els and distributions at London and New York terminals were provided as a basis for repeater loading studies. Early planning studies indicated that these objectives would probably be met on all, or nearly all channels without resort to compandors. If, as the system aged, the noise increased owing to increasing misalign- ment, the use of compandors would offer a means for reducing message circuit noise below the objectives. The minumum equal-level crosstalk loss between any two telephone channels was set at 56 db for any source of potentially intelligible cross- talk. For channels used for VF telegraph, the eciual-level crosstalk loss between go and return directions was set as a minimum of 40 db; for all program channels the minimum crosstalk attenuation would be 55 db. Restrictions of Telegraph and Other Services Since the system was being designed primarily for message telephone service, it was agreed that a channel used for any other service should not contribute more to the system rms or peak load than if this channel were used for message telephone, except by prior agreement between Post Office, Bell System and Canadian Overseas Telecommunication Corporation engineering representatives. Signalling Objectives In order to conserve frequenc.y space, it Avas decided to transmit all calling and supervisory signals within the telephone channel bands and, PLANNING AND OVER-ALL PERFORMANCE 21 to avoid transmission degradation, it was agreed that the signahng power and duration would not amount to more than 9 milliwatt-seconds in the busy hour at a zero level point; this would not contribute unduly to the loading of the system. It was agreed that, for initial operation, ringdown signaling would be employed, but the system design should be such as to permit the use of dialing at a later date. Echo Suppressors Echo control was considered essential, since the via net loss of the transatlantic circuits would be only 0.5 db, with a one-way transmission time of 35 milliseconds. Echo suppressors would be provided initially at New York and Montreal only, and arrangements made in London to cut out such suppressors as may be fitted there on Continental circuits, when these are used for extension of the transatlantic circuits. It was recognized, however, that other suppressors might be encountered in the more remote parts of Continental and United States extensions. The general problem of how best to arrange and operate echo suppressors on very long switched connections is one which remains for consideration later. Maintenance and Operating Services Telephone Speaker and Telegraph Printer Circuits The need for telephone and telegraph circuits for maintenance and administration was recognized, and it was agreed to provide the fol- lowing circuits on the submarine links at frequencies immediately out- side the main transmission bands where inferior and somewhat uncer- tain characteristics might be expected (Fig. 4) : (a) A 4-kc band, possibly sub-standard in regard to noise, equipped with band splitting equipment (EB Banks) to provide two half-band- width telephone (speaker) circuits, and (b) two frequency-modulated telegraph (printer) circuits. These circuits would be extended over the land circuits to the terminal stations by standard arrangements as needed and would be used to pro- ^'ide the following facilities: (I) An omnibus speaker circuit connecting the principal stations on the route, including Montreal. (II) A speaker circuit for point-to-point communication between the principal stations — i.e., non-continuous. (III) A direct printer circuit between London and White Plains. (IV) An omnibus printer circuit as (I) above. 22 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 o o o o y o z (O o in in-»H o in '.^^^^^^' 01 (\J in 1- If! [I z 0(n o-o in 8 in Ul z ^LU HLU <2 <3 — o o in ujO uJO ^- r: N^-^ ■J lllllllllll o in rf) ■^ / 't o o Qjin -iiiJ Zo z < z — o 8 LU in o ct 1— ( U o LU <0 tr < -J o a z in Ul z ?::] M a iT) (0 z < ^5 1- < in lii < 13 1 U I I I Ul x: LU(^ UjU UJU LU -J o C3 (\j U U ,,i o o o 01 1 '^ 1 <0 L^ z *i ujcr z^ rf z ^? UJ I z < a o <<) $ 1 "^ u zu- t-0- Z LU i: 1 2^1 03 1- 1 u 1 ^ 1 ^-* 1 aj ffWfflfflfl to K- <^ 1 (O CM < LU *( LU 5i- 2i- < LU 2i- z o >. o CM < 1 1 -^ LU a 1 'O D a a> 1 LU LU cr _l 0) o _l O ^ tH o (\1 o (\J i^H u > liJK ,^ u :«: H- ^ 1 ^, ^2 I !3 < UJ ?- rf< :^:;;v.v:v:.;:;- ;v./-:v:;V:- bC o in ID y in LU o LUuj -'o o o o ^ -Jo UJ lO ^^ o< z -l< Q >in > zin LU UUUJ o 1' 5^ o in in u u U ^i i i o o 1 ^^ o (\J t\j r~i "" r~\ PLANNING AND OVER-ALL PERFORMANCE 23 Repeater Test Frequencies In each submarine cable link, test freciuency bands were required for monitoring repeater performance; and these are indicated in Fig. 4. Pilot Frequencies It was agreed to provide pilot facilities throughout the route for line-up maintenance and regulation purposes. In addition to the usual pilots on the inland networks, there would be provided: (a) a 92-kc pilot in each 12-channel group, continuous only in a par- ticular section of the route and fitted with a recording voltmeter at the receiving end of that section, and (b) an 84.08-kc overall pilot in each 12-channel group as recommended by the C.C.I.F. This would transmit continuously over the entire route and would be monitored and recorded at every main station. Connections between Component Links At the time that the objectives were being established, a far-reaching decision was made to employ channel equipment at London, New York, and Montreal only, and to adopt the frequency band 60-108 kc as the standard frequency for connecting the various parts of the over-all system. By adopting this band as standard for the transatlantic system, it also became possible to interconnect readily with land systems at each end. This agreement also facilitated decisions on responsibihty for design and manufacture of equipment. For example, it became logical to define each submarine system as the equipment between points where the 60-108-kc band appeared, i.e., the group connecting frames. Thus, these systems would include not only the cable, repeaters, and power supplies, but also the terminal gear to translate between 60-108 kc and line frequency of the submarine sj^stem. It also became logical to assign responsibility for manufacture of all of this equipment to the administra- tion responsible for the specific system design, i.e., responsibility for the Oban-Clarenville Hnk to the Bell System and the Clarenville-Sydney Mines link to the Post Office. THE REALIZATION OF THE SYSTEM With decisions reached on the system objectives and interconnecting arrangements, it became possible to lay out jointly a detailed over-all plan and for each administration to proceed with developing and engi- neering the links under its jurisdiction. 24 THE BELL SYSTEIVI TECHNICAL JOUKXAL, JANUARY 1957 There was an understanding that there should be no deliberate attempt to make the characteristics of one link compensate for those of another, and so it would be incumbent on the administrations to produce the best possible group characteristic on each link. The overall plan for the system, as finally developed, is shown in Fig. 2. Except for the necessity to split one of the three transatlantic groups in each direction to provide 6^ circuits to Montreal and 5| to New York, which required specially designed crystal filters, no unusual circuit facilities were required. Special equipment arrangements were called for at Sydney Mines and Clarenville to provide security for the Montreal-London circuits where they appeared in the same office with White Plains-London circuits. In these cases, a special locked room was constructed to house the equipment associated with the channel group containing the Canadian circuits. The details of how the two all-important submarine cable links were designed and engineered to meet their indi\'idual objectives are given in companion papers. The efficiency and integrity of these two links are the highest that could be devised by engineers on both sides of the Atlantic. Finally, each section of the connecting links was lined-up and tested individually before bringing them all together as an integrated system. OVER-ALL PERFORMANCE OF THE SYSTEM The system went into service on September 25, 1956, so soon after completion of some of the links that it was not possible to include all the final equalizers. Nevertheless, after completion of the initial overall line-up, the performance has been found to meet very closely the orig- inal objectives. The system went into service without the use of com- pandors on any of the telephone circuits, but compandors are included in the program equipment. At the time of writing, onlj^ the 2-channel program equipment is available for use. Frequency Characteristics of 12-channel groups Fig. 5 shows the frequency characteristic of one of the 12-channel groups, link b}' link and over-all, measured at group frequencies corre- sponding to 1,000 cycles on each channel. In both of the complete London-New York groups the deviation from flat transmission is within ±1.5 db, and some further improvement is to be expected when the equalization is finalized. For the split group, the characteristics are similar except for the effect of the splitting filters. PLANNING AND OVER-ALL PEFRORMANCE 25 Variation of Over-all Transmission Loss The system has, of course, only been completed for a short time, but the indications so far are that the standard deviation of the transmission loss, as indicated by the 84.08-kc group pilots is well within the objective of 1.5 db. Alarms operate when the received pilot level deviates by ±4 db and, so far, these alarms have not operated under working conditions. Frequency Characteristics of Telephone Circuits Fig. () shows the measured frecjuency characteristic of a typical circuit in the two directions of transmission as measured in the through and terminated conditions. Half the C.C.I.F. limits are met on most circuits. CHANNEL 5 6 107 103 99 95 91 87 83 79 75 71 67 FREQUENCY IN KILOCYCLES PER SECOND LONDON TO WHITE PLAINS WEST HAVEN TO WHITE PLAINS PORTLAND TO WEST HAVEN SYDNEY MINES TO PORTLAND CLARENVILLE TO SYDNEY MINES OBAN TO CLARENVILLE LONDON TO OBAN Fig. 5 — Frequency characteristic of typical London-New York channel group. (Measured at group frequencies corresponding to 1,000 cycles.) 26 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 UJ - z < CD a. O u 1- V- o O 3 J 5 W CL tr CC Q. Ul 1- cr UJ UJ 3 > a o. t- u 5 2 —' cr \- z UJ H" < z UJ oc s Ul 13 cr q: u. Z > O a. rW c A \ / UJ UJ /\ \ / UJ -I a: F^ / \ Y o < cr C3 z I UJ < • fH < 1 cr O o tu II II II ^ / oS o o A Y a. \- o CL (0 o <3 o Q ,£3 H m icuj CD -u z < _l z UJ 15 UJ 1- z UJ O 5 _l Z UJ 2 Q. 1 I (X A \ "7 s 1- 3 o /\ \ / Q. z O '-fi / \ Y 3 a UJ 2 UJ 03 O s z 1 UJ Q. < OJ _i 3 Z .A t — '■■■/ A \ / < a o / \ \/ z UJ 5 CK / \ V UJ < U. o z 2 cr UJ 1- UJ -I _l < z 2 cc UJ 1- cr UJ h- cr UJ a. cr 1-H — 1' bio < u < o O a. a — DC o 1- UJ _l < a. 1— z z tu 10 1- 1- 15 _I Q 2 _1 Q. 5 CO > 5 CO > t- (J 8 z < Ul o z < z UJ o 1- UJ tr cc 1- o: < II II II II o o U. 1- a. \- CO o o o o IJOU. o T o £Dl- a a. cr UJ H CC UJ cr tt UJ^ CC z z u nh J2 UJh- u rr < _l n -iF^ -^ i-z H -i UJ o i^ii t^ (/)0 Ol o> <. _i 1- s o II II 11 II II II o + Q. 5 AA LU (f> to to o _J UJ w z 1 z cr 1 u UJ o o CL ^ lY ^i^ Y BAND FOR 12 4 LITTING FILTER cr < _i D Q ct o 1- < _i =) Q O CL 3 cc o 1- < _l Q o < _l a o LU Q CL -) 1- UJ 1- V u z mO cr Q. II U CL U C) Ill O 1 z Z in > cr Q cr _jO CL rr CL rr I'^fl n -5 D III _> III UOm III o (> CL C) n "'LU (T cr cr -) DC -) 0^7 O? 0. o O m O lO II II II II II II II f) u_ ^ ? Q Q X ,-^, '^ n n 10 lO o (/) 10 32 DESIGN OF SYSTEM — NORTH ATLANTIC LINK 33 Proven Integrity Assurance of reliability dictated use of elements whose integrity had actually been proved by successful prior experience in the laboratory or in the Bell System. This resulted in adoption of a coaxial cable struc- ture explored by the Laboratories soon after the war, field tested in the Bahamas area in 1948 and applied commercially on the USAF Missile Test Range project^^ in 1953. It also resulted in specification of a basic flexible repeater design which had been imder test in the Laboratories since before the war and had been in use on the Key West-Havana submarine cable telephone system'* since 1950. Cable The cable adopted was the largest which had actually been success- fully laid in deep water, and its size afforded an important benefit in the form of reduced unit attenuation. The structure and characteristics of this cable are covered in detail in a companion paper.' Suffice it to point out here that by its adoption for the North Atlantic link, there were specified for the system designers (a) the attenuation characteris- tic of the transmission medium, (b) the influence on this of the pressure and temperature environments, (c) the unit contribution of the cable to the resistance of the power loop, and (d) the impedances faced by the repeaters. Re'peater The adaptation of the basic Key West-Havana repeater design to the present project hkewise presented the system designers with cer- tain restrictions. Most important, the space and form of the long, tubu- lar structure limited the size of the high voltage capacitors in the power separation filters, and thus their voltage rating, to the extent that this determined the maximum permissible number of repeaters. Likewise the performance of the repeater circuit was at least partially defined because of several factors. One was the effect of the physical shape on parasitic capacitances in the circuit, which in turn reacted on the feed- back and hence on modulation performance, gain-bandwidth and the aging characteristic. Use of the Key West-Havana electron tube in- fluenced the above factors and also tended to fix the input noise figure and load capacity. System Design In similar respects, the principle of proven integrity reacted into the broad consideration of system design. For instance, in a long system 34 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 having many repeaters in tandem, automatic gain control (gain regu- lation) in the repeaters provides an ideal method for minimizing the amount of the total system margin which must be allocated to environ- mental loss variations. However, this would have required adoption of elements of unproved integrity which might have increased the proba- bility of system failure. So the more simple and reliable alternative was adopted — • fixed gain repeaters with built-in system margins. System Inaccessibility The inaccessibility of the undersea system for periodic or seasonal adjustment and the decision to avoid automatic gain regulation were major factors in the allocation of system margins between undersea and shore locations. To avoid wasting such a valuable commodity as margin, required the most careful consideration of means of trimming the system during laying. Equalization for control of misalignment in the undersea link is a function of the match between cable attenuation and repeater gain. Generally speaking, these are fixed at the factory. Very small unit deviations from gain and loss objectives could well add to an impressive total in a 3,200-db system. Accordingly, it was neces- sary to plan for periodic adjustment of cable length during laying, and where necessary, insertion of simple mop-up undersea equalizers at the adjustment points, DESIGN OF HIGH-FREQUENCY LINE Terminology The high-frequency line, as the term is used here, includes the cable, the undersea repeaters, the undersea equalizers, and the shore-station power separation filters, transmitting and line-frequency receiving amplifiers, and associated equalizers. Repeater Spacing and System Bandwidth As in most transmission media, the attenuation of the cable increases with increasing frequency. Hence the greater the bandwidth of the sys- tem, the greater the number of repeaters needed. In this system, powered only from its ends, the maximum permissible number of repeaters and thus the repeater spacing is determined by a dc voltage limitation, as explained in a later section. With the repeater spacing fixed, and the type of cable fixed, the re- quired repeater gain versus frequency is known to the degree of ac- curacy that the cable attenuation is known. The frequency band which DESIGN OF SYSTEM — NORTH ATLANTIC LINK 35 can be utilized then depends on repeater design considerations, includ- ing gain-bandwidth limitations, signal power capacity and signal-to- noise requirements. The early studies of this transatlantic system were based on "scaling up" the Havana-Key West system/ In these studies, consideration was given to extending the band upward as far as possible by using com- pandors^ on the top channels, thus lightening the signal-to-noise re- quirements on these channels by some 15 db provided they are re- stricted to message telephone service. As the repeater design was worked out in detail, however, it became evident that a rather sharp upper frequency limit existed. This resulted from the parasitic capacitances imposed by the size and shape of the flexible repeater, the degree of precision required in matching repeater gain to cable loss in such a long system, and the feedback requirements as related to the requirement of at least 20 years' life. These limitations resulted in the decision to develop a system with 36 channels of 4-kc carrier spacing, utilizing the frequency band from 20 to 164 kilocycles per second. Signal-to-Noise Design Scaling-up of Key West-Havana System The length of the North Atlantic cable was to be about 16 times that of the Havana-Key West system. The number of channels was to be increased as much as practicable. The length increase entailed an in- creased power voltage to ground on the end repeaters. Increase in length and in number of channels entailed increased precision in control of variations in cable and repeaters. Work on these and other aspects was carried on concurrently, to determine the basic parameters of the ex- tended system. Increasing cable size decreases both the attenuation and the dc re- sistance, and in turn the voltage to ground on the end repeaters. It was soon decided that the largest cable size which could be safely adopted was the one used in the Bahamas tests. This has a center-conductor sea- bottom resistance of about 2.38 ohms per nautical mile. It consumes about 28 per cent of the total potential drop in cable plus repeaters. Number of Repeaters As indicated earlier, the factor which emerged as controlling the number of repeaters was the dc voltage to ground on the end repeaters. Considerations which entered into this were: voltage which blocking capacitors could safely withstand over a life of at least 20 years; volt- 36 THE BELL SYSTEM TECHNICAL JOTJRNAL, JANUARY 1957 age which other repeater elements such as connecting tapes between compartments could safely hold without danger of breakdown or corona noise; initial power potential and possible need for increasing dc cable current later in life to combat repeater aging; allowance for repair re- peaters; and a reasonable allowance for increased power potential to offset adverse earth potential. Let R = dc resistance of center conductor (ohms/nautical mile) L = length of one cable* (nautical miles) Erep = voltage drop across one repeater at current I / = ultimate (maximum) line current (amperes) N = ultimate number of submerged repeaters, in terms of equivalent regular repeaters n = allowance for repair repeaters, in terms of number of regular submerged repeaters using up same voltage drop. Em = maximum voltage to ground at shore-end repeaters at end of life, and in absence of earth potential. S = spacing of working regular repeaters (nautical miles) Then for the ultimate condition 2E^ = LIR - 2SIR + NErep (1) in which the term 2SIR accounts for the sum of the cable voltage drops on the two shore-end cable sections; the sum of their lengths is assumed, for simplicity, to equal 2S. This equation also neglects a small allow- ance (less than 0.6 volt per mile) for the voltage drop in cable added to the system during repair operations. Also S(N - n + 1) = L (2) because the repeater spacing is determined by the number of working regular repeaters. From (1) and (2), 2Em = LIR + NErep " 2LIR/(N - n -|- 1) (3) The allowance n for repair repeaters was determined after studies of cable fault records of transoceanic telegraph cables, including average number of faults per year and proportion of faults occurring in shallow water. If the fault occurs in shallow water — as is true in most casesf • — • the net length of cable added to the system and the resulting attenua- tion increase, are small. Several shallow-water faults might be permis- * The length of a cable is greater than the length of the route because of the need to pay out slack. The slack allowance, which averages 5 per cent in deep water on this route, helps to assure that tlie cable follows the contour of the bottom. t Because of trawler activity, ship anchors and icebergs. DESIGN OF SYSTEM — NORTH ATLANTIC LINK 37 sible without adding a repair repeater. Therefore it was decided to let n = 3. Since the repair repeater is a 2-tube repeater while the regular repeater has 3 vacuum tubes, ?i = 3 corresponds to about 5 repair re- peaters per cable. To determine the maximum voltage E„i , it was necessary to consider blocking capacitors and earth potentials. Based on laboratorj^ life tests, the blocking capacitor developed has an estimated minimum life of 36 years at 2,000 volts. It is estimated that life varies inversely as about the fourth power of the voltage. The po- tential actually appearing on these capacitors is determined by the dis- tance of the repeater from shore, the power potential applied to the sys- tem, and the magnitude and polarity of any earth potential. Earth potential records on several Western Union submarine tele- graph cables were examined. These covered a continuous period from 1938 to 1947, including the very severe magnetic storms of April, 1938, and jNIarch, 1940. It was judged rea.sonable to allow a margin of 400 volts (200 volts at each shore station) for magnetic storms during the final years of life of the system. With an assumed maximum voltage of 2,300 volts on the end repeaters due to cable-current supply eciuipment, and 200 volts per end as allow- ance for the maximum opposing earth potential which the system would be permitted to offset without automatic reduction of the cable current, the voltage across the end repeater in late years of life (i.e., after line current had been increased to offset aging) would normally be 2,300 and would infrequently rise to 2,500. On the rare occasions where earth po- tential would rise above twice 200 volts, the cable current would be some- what reduced and the transmission affected to a reasonably small extent. In the early years of life when the cable-current supply voltage would normally be about 2,000 volts, an opposing earth potential of twice 500 volts could be accommodated without affecting cable current; according to the telegraph cable records this would practically never occur. With conditions changing in this way over the years, the life of the blocking capacitors in the end repeaters was calculated to be satisfactory. Accordingly E^ was established as 2,300 volts. The system length L was estimated as about 1 ,985 nautical miles and the ultimate current I was estimated as 0.250 amperes, with a correspond- ing ultimate Erep of about 62.8 volts. Substituting in (3), A^ = 55 N-n = 52 working repeaters S = 37.4 nautical miles. 38 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 From a later estimate of L = 1,955 nautical miles, S calculates to be 36.9. The repeater design was based on this spacing in the deep sea tem- perature and pressure environment. Subsequently, after better knowl- edge had been obtained of the cable attenuation in deep water, the actual repeater spacing for the main part of the crossing was changed to about 37.4 nautical miles for the eastbound (No. 1) cable and 37.6 for the west- bound. Only 51 repeaters were required in each cable. Number of Channels The number of channels which could be transmitted was determined by the upper and lower boundary frequencies. In this system, the bot- tom frequency was established at 20 kc, primarily because of the loss characteristics of the power separation filters.^ Preliminary studies were made to estimate the usable top frequency. For a system having a fixed number of repeaters, this frequency falls where the maximum permissible repeater gain equals the loss of a re- peater section of the cable — which varies approximately as the square root of frequency. The repeater gain is the difference between the re- peater input and output levels. The minimum permissible transmission level at the repeater input depends on the random noise (fluctuation noise) contributed by cable and repeaters, and on the specified require- ment for random noise. The maximum permissible transmission level at the repeater output may depend on the modulation noise contributed by the repeaters below overload, or on overload from the peaks of the multi-channel signal complex. In this system, overload was found to be the controlling factor. An important consideration was to provide enough feedback in the repeater so that at the end of 20 years the accumulated gain change (Mu-Beta effect) in all the repeaters would not cause the signal-to-noise performance to fall outside limits. The usable feedback voltage was scaled from the Havana-Key West design according to the relation that this voltage varies inversely as the f power of the top frequency. Electron tube aging was estimated from laboratory life tests on Key West-Havana type tubes. Concurrently, detailed theoretical and experimental studies were be- ing conducted on the transmission design of a repeater suited to trans- atlantic use with the chosen type of cable, as discussed in a companion paper.' Intimate acquaintance with the repeater limitations led to a de- cision in 1953 to develop a system with a working spectrum of 144 kc (36 channels) and a top frequency of 164 kc. Use of compandors would not increase this top frequency appreciably. DESIGN OF SYSTEM — NORTH ATLANTIC LINK 39 Computed Noise When the repeater design was estabhshed, the remaining theoretical work on signal-to-noise consisted in refining the determination of the repeater output and input levels; computations of system noise, and com- parison of this with the objectives to establish the margin available for variations; and determination of the necessary measures in manufactur- ing and cable laying so that these margins would not be exceeded by the deviations from ideal conditions which would occur. These deviations assumed great importance, because they tended to accumulate over the entire length of the system, and because many of them were unknown in magnitude before the system was actually laid. The repeater levels and the resultant system noise were computed as follows : It was recognized that the output levels of different repeaters would differ somewhat at any given frequency. The maximum allowable output level of the highest-level repeater was computed by the criterion that the instantaneous voltage at its output grid would be expected to reach the load-limit voltage very infrequently. This is the system load criterion estabhshed by Holbrook and Dixon. ^ It premises that in the busy hour, the load-limit voltage (instantaneous peak value) should be reached 0.001 per cent of the time, or less. It is probable that the level could be raised 2 db higher than the one computed in this way without notice- able effect on intermodulation noise. An important factor in the Holbrook-Dixon method is the talker volume distribution. Because of the special nature of this long circuit, a careful study was made of the expected United States talker volumes. First, recent measurements of volumes on long-distance circuits were examined for the relation between talker volume and circuit length. They showed a small increase for the longer-distance circuits. This rela- tion was extrapolated by a small amount to reach the 4000-mile value appropriate to the New York-London distance. Second, an estimate was made of the probable trends in the Bell Sys- tem plant in the next several years, which might affect the United States volumes on transatlantic cable calls. The result of this was a "most probable U. S. volume distribution". This distribution, which had an average value of —12.5 vu at the zero level point, with a standard deviation of 5 db, agreed very well with one furnished by the Post Office and based on calls between London and the European continent. A further small allowance was then made for the contribution of signaling tones and system pilots which brought the resultant distribution to an average value of — 12 vu at zero level of the 40 THE BELL SYSTEM TECHNICAL JOUHXAL, JANUARY 1957 system (the \q\q\ of the outgoing New York or London or Montreal switchboard), and a standard deviation of 5 db. It is approximately a normal-law distribution (expressed in vu), except that the very infre- quent high volumes are reduced by load limiting in the inland circuits. The other data needed for system load computations are the number of channels, and the "circuit activity", i.e., the per cent of time during the busy hour that the circuit is actually carrying voice in a given direc- tion (eastbound or westbound) . The circuit activity value used in design- ing United States long-distance multi-channel circuits is 25 per cent; for the transatlantic system, 30 per cent waS used. The peak value of the computed system multi-channel signal is the same as the peak value of a sine wave having an average powder of -t-17.4 dbm at the zero transmission level point of the system. This ^'alue, together with the measured sine-wave load capacity of the undersea repeater, determines the maximum permissible output trans- mission level of the repeater. The measured sine-wave load capacity is about +1.3.5 dbm at 164 kc. Hence the maximum permissible output transmission level for the 164-kc channel is +13.5 — 17.4 = —3.9 db. If the relati\'e output levels of the various submarine repeaters were precisely known, the highest-level repeater could have an output trans- mission level of —3.9 db at 164 kc. An allowance of about 2 db was made for uncertainty in knowledge of repeater levels, giving — 6 db as the de- sign value for the maximum repeater output level at 164 kc* The repeater has frequency shaping in the circuit between the grid of its output tube and the cable. The maximum repeater output at lower frequencies is smaller than at 164 kc, but the maximum voltage on the output grid, from an overload standpoint, is approximately constant over the 20 to 164 kc band. The transmission level of the maximum level repeater output is thus determined, based on load considerations. Another factor which might limit this level is modulation noise. This was found to be less of a re- striction than the load limitation, however. With the output level determined, the random noise and the modula- tion noise for the system can be computed. The random noise computa- tion is made on the assumption that all repeaters are at the same level, and then a correction is made for the estimated difTerences in levels of the various repeaters. The equation is No = Nin-^G - TL + 10 log n + dr * At the time of writing, the No. 1 cable (eastbound) is setup with a somewhat lower maximum output level than this; the safe increase in level will be deter- mined later. DESIGN OF SYSTEM NORTH ATLANTIC LINK 41 where A^o = system random noise, in dba,* referred to zero transmis- sion level Nin — random noise per repeater in dba, referred to repeater input level G — repeater gain in db TL — transmission level of repeater output n = number of undersea repeaters dr = db increase in noise due to differing output levels of the various repeaters as compared to the highest level repeater. At the top frequency of 164 kc, TL = — 6 db as seen above, G = 60.7 db, and Nin is about —55.5 dba, which corresponds to a noise figure of about 2 db. Hence for 52 repeaters, ATfl ■55.5 + 60.7 - (-6) + 10 log 52 + ck = 28.4 + dr At lower frequencies, the noise power referred to repeater input is greater because part of the equalization loss is in the input circuit; the repeater gain is less, to match the lesser loss of a repeater section of cable; and the repeater output level is lower on account of the equaliza- tion loss from output grid to repeater output. This is shown in Table I. Table 1 Channel Nin = Approx. Input Noise, dba G = Approx. Repeater Gain, db TL = Approx. Output Trans Level, db A^o = Resulting Noise dba Top Freq -55.5 -53 -46 60.7 45 22 -6 -11 -19 28.4 + dr Middle 20.2 + dr Bottom Freq 12.2 + dr In order to estimate dr (which is a function of frequency) before the cable was laid, the factors were studied which might contribute to differ- ences between the levels of the various repeaters. Estimates were made of probable total misalignment — by which is meant the level difference between highest-level and lowest-level repeaters. These values together with estimates of the resulting noise increases, are shown in Table II. This is based on the assumption that the repeater levels would be dis- tributed approximately uniformly between highest and lowest. The posi- tion of a repeater along the cable route is not significant. * "dba" is a term used for describing the interfering effect of noise on a speech channel. Readings of the 2B noise meter with FIA weighting may be converted to dba b,y adding 7 db. dba may be translated to dbm (unweighted) by noting that flat noise having a power of 1 milliwatt over a 3,000-cycle band equals approxi- mately -(-82 dba, and that 1 milliwatt of 1,000-cycle single-frequenc}' power equals -t-85 dba. 42 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 Table II Channel M = Estimated Misalignment dr = Resulting Noise Increase No — Resulting System Random Noise (Approx.) Top Middle 12 db 10 db 6db 7.4 db 6.0 db 3.4 db 36 dba 26 dba Bottom 16 dba A study was made of the expected intermodulation noise. This noise is affected by repeater level differences, by talker volumes, and by circuit activity. It has a time distribution, the most attention being given to the root-mean-square modulation noise in the busy hour. Modulation noise was computed in two ways: by the Bennett method,^ and by the Brockbank-Wass method.^ Results by the two methods are in fairly good agreement. The values computed by the Bennett method are shown in Table III. Because noise powers, not dba, are additive, these values of modula- tion noise would contribute only a very small amount to the total noise in the deep-sea cable system, as previously stated.* Other possible contributory sources of noise in the deep-sea cable sys- tem are noise in the terminals, noise picked up in the shore lead-in cables, and corona noise in the repeaters. The system has been designed so that the expected total of these is small. Hence the estimate of total deep- sea cable system noise, made before cable-laying, gave the values shown in Table IV, to the nearest db. Misalignment Control Objective Since the noise objective for the deep sea cable link was set as 36 dba in the joint meetings of the British Post Office and Bell System Repre- sentatives^, the above estimate of system noise led in turn to the objec- tive that the system be manufactured and laid in such a way that the misalignment, including effects of seasonal temperature change, should be no greater in the top channel than the value assumed in the estimate, which was 12 db. Half of this was alloted to initial misalignment and half to effects of temperature change. Greater misalignments were per- missible at lower frequencies. * The following table for adding two noises expressed in dba shows the magni- tudes of the increases: db difference lietween larger and smaller 2 4 6 8 10 15 20 noises Resulting db to be added to larger noise to 2.1 1.4 1.0 0.6 get sum of the two 0.4 0.1 0+ DESIGN OF SYSTEM XORTH ATLAXTIC LINK 43 Table HI Weighted Noise in dba at Zero Transmission Level Channel Second Order Products Third Order Products Total Top Middle Bottom 8.2 0.2 -1.8 8.5 3.8 2.5 11.3 5.4 3.9 Table IV Channel Estimated System RMS Noise at 0 db Transmission Level Top dba 36 26 16 dbm (Psophometert) -48 Middle Bottom -58 -68 t The psophometer is the C.C.I.F. circuit noise meter. On message telephone circuits, dbm (psophometer) + 84 = dba using C.C.I.F. 1951 weighting and Bell System FIA weighting. Control of this misalignment required extensive consideration in the equalization design of the system. Causes of Misalignment The basic causes of misalignment can be grouped as follows: those producing unequal repeater levels when the system is first laid; those resulting from changes in cable loss produced by changes in sea-bottom temperature; and those from aging of the cable or repeaters. There are a large number of possible causes of initial misalignment. While the cable and repeaters were manufactured within very close tolerances to their design objectives, they covild not exactly meet those objectives. In addition, the cable loss as determined in the factory must be translated to the estimated loss on sea-bottom, and the length of each repeater section must be tailored in the factory so that its expected sea- bottom loss will best match the repeater gain. Possible sources of error in this process include: uncertainty in temperature of the cable when it is measured in the factory, and in its temperature on the sea-bottom; uncertainty in temperature and pressure coefficients of attenuation; changes in cable loss between factory and sea-bottom conditions, not accounted for by pressure and temperature coefficients. These latter changes in cable loss were called "lajing effect". The determination of the magnitude of laying effect, and its causes, are dis- 44 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 cussed in the paper on cable design. ^ Suffice it to say here that after meas- uring the loss of a length of cable in the factory and computing the sea- bottom loss, the computed result was a little greater than the actual sea-bottom loss. The difference, i.e., the laying effect, was approxi- mately proportional to frequency, and was greater for deep-sea than for shallow-water conditions. Its existence was confirmed by precise mea- surements on trial lengths of cable, made early in 1955 in connection with cable-laying tests near Gibraltar. Laying effect had been suspected from statistical analysis of less pre- cise tests of repeater sections of cable generally similar to transatlantic cable, as measured in the factory and as laid in the vicinity of the Baha- mas. However, the repeater design had of necessity been estabhshed before the Gibraltar test results were known. The consequence was a small systematic excess of repeater gain over computed cable loss, ap- proximately proportional to frequency, and amounting at the top frequency to about 0.04 db per nautical mile on the average, for deep- sea conditions, and about 0.025 db per mile for shallow-water condi- tions. While this difference appears small, it would accumulate in a transatlantic crossing of some 1,600 miles of deep sea and 350 miles of relatively shallow sea, to about 75 db at the top frequency. This would be enough to render almost half of the channels useless if no remedial action were taken. After the system is laid, changes in cable loss or repeater gain may occur. These may be caused by temperature effects and by aging of cable or repeaters. Comprehensive studies* of the expected amounts of temperature change were made both before and after the 1955 laying. These gave an estimate of 0 to ±1 degree F annual variation in sea-bottom temperature in the deep-sea part of the route (about 1,600 nautical miles) and per- haps ±5° F on the Continental shelves (about 330 nautical miles). Use of these figures leads to a db5-db variation in system net loss at 164 kc from annual temperature changes. If the deep-sea bottom temperature did not change at all, the estimated net loss variation due to temperature would be about half of this. Control of Misalignment The first line of defense against variations leading to misalignment was the design and production of complementary repeaters and cable. This is discussed in companion papers. * Factual data on deep sea bottom temperatures are elusive. Many of the exist- ing data were acquired by unknown methods vmder unspecified circumstances, using apparatus of unstated accuracies. Statistical analj'sis of selected portions of the data leads to the quoted estimates. DESIGN OF SYSTEM — NORTH ATLANTIC LINK 45 Signal-to-noise changes from undersea temperature variations were minimized by providing adjustable temperature equalizers at both the transmitting and the receiving terminals, and devising a suitable method of choosing when and how to adjust them. Partial compensation for laying effect was carried out at the cable factory by slightly lengthening the individual repeater sections. In the 1955 cable, where the factory compensation was based on early data, the increased loss compensated for about two-fifths of the laying effect at the top frequency. In the 1956 cable, which had the benefit of the 1955 transatlantic experience, the compensation was increased to nearly twice this amount. Since the loss of the added cable is approximately proportional to the square root of frequency and the laying effect is approximately directl}" proportional to frequencj^ the proportion of laying effect compensated varied with frequency, and a residual remained which had a loss deficiency rising sharply in the upper part of the trans- mitted band. The remainder of the laying effect, which was not compensated for in the factory, as well as other initial variations, were largely compensated by measures taken during cable laying at intervals of 150 to 200 miles. The whole length of the cable was divided into eleven "ocean blocks", each either four or five repeater sections long. At each junction between successive ocean blocks, means were provided to compensate approxi- matel}^ for the excess gain or loss which had accumulated up to that point. These means were twofold. The first means was adjustment of the length of the repeater section containing the junction. For this purpose, the beginning of each block, except the first, was manufactured with a small excess length of cable. This was to be cut to the desired length as determined by shipboard transmission measurements. The second means was a set of undersea equalizers. These equalizers were fixed series networks, encased in housings similar to the repeater housings but shorter. Before the nature of the laying effect was known, it had been planned to have equalizers with perhaps several shapes of loss versus frequency; but to combat laying effect, nearly all were finally made with a loss curve sloping sharply upward at the higher frequencies, as shown in Fig. 3.* Because the equalizer components had to be manufactured many months in advance and then sealed into the housings, last minute designs of undersea equalizers were not practical. The proven-integrity principle prevented use of adjustable units. Because the equalizers were series- * This characteristic was based on a statistical analj-sis of the data on some similar cable laid for the Air Force project. 46 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 type, each block junction was located at approximately mid-repeater section to minimize the effects of reflections between equalizer and cable impedances. The actual adjustments at block junctions were determined by a series of transmission measurements during laj'ing, as described in the com- panion paper on cable laying.^ Six equalizers were used at block junctions in the 1955 (No. 1) cable, and eight in the 1956 (No. 2) cable. The result of all the precautions taken to control initial misalignment was, in the 1955 cable, to hold the initial level difference between highest and lowest-level repeaters to about 6 db near the top frequency and to values between 4 and 9 db at lower frequencies, the 9 db value occurring in the range 50 to 70 kc where there is noise margin. In the 1956 cable, the level difference was about 4 db at the top freciuency, and from 2 to 7 db elsewhere in the band. Shore Equalization The equalization to be provided at the transmitting and receiving ends of the North Atlantic link had these primary functions: 1. For signal to noise reasons, to provide a signal level approximately flat with frequency on the grid of the third tube of the undersea repeaters. 2. To equalize the system so that the received signal level is approxi- mately constant over the transmitted band. 3. To keep the system net loss flat, regardless of temperature varia- tions in the ocean. (A change of 1° F in sea-bottom temperature would cause the cable loss to change by 2.8 db at 160 kc and less than this at lower frequencies. The amplifiers are relatively unaffected by small temperature changes.) 4. To provide overload protection for the highest level repeater. 5. To incorporate some adjustment against possible cable aging. <«^ / HI m O / / / z / (0 _ (0 2 o _J / / z o , y p ' cr UJ ^ 20 40 60 80 100 120 140 FREQUENCY IN KILOCYCLES PER SECOND 160 180 Fig. 3 • — Undersea equalizer — loss-frequency characteristic. DESIGN OF SYSTEM — NORTH ATLANTIC LINK 47 TRANSMITTING AMPLIFIER TEMP EQ TRANS EQ LOW PASS FILTER DEVIATION EQUALIZER TO INPUT OF CABLE Fig. 4 — Transmitting equalizers — block schematic. A portion of the transmitting terminal is shown in block schematic form in Fig. 4. All of the equalizers are constant resistance, 135 ohm un- balanced bridged-T structures. Their functions are as follows: Transmitting Temperature Equalizer — It was estimated that the cable loss change from temperature variations would not exceed ±5 db at the top of the transmitted band. The change in cable loss versus frequency due to temperature variations is approximately the same as if the cable were made slightly longer or shorter, and so the temperature equalizer was designed to match cable shape. Temperature equalizers are used both in the transmitting and receiving terminals to minimize the signal- to-noise degradation caused by temperature misalignment. Each equal- izer provides a range of about ±5 db at the top of the band, the loss being adjustable in steps of 0.5 db by means of keys. See Fig. 5. This range might appear to be more than necessary, but it must be borne in mind that the sea bottom temperature data left much to be desired in precise knowledge of both average and range. Transmittiiig Equalizer — The transmitting equalizer was so designed that with the temperature equalizer set at mid-range and with repeaters that match the cable loss, the signal level on the grid of the output tube of the first repeater would be flat with frequency. The loss-frequency characteristic is shown on Fig. 6. L.P. Filter — This filter transmits signals up to 164 kc and suppresses by 25 db or more, signals in the frequency range from 165 to 175 kc. Its purpose is to prevent an accidentally applied test tone from overloading the deep sea repeaters should such a tone coincide with the resonance Fig. 5 — Transmitting temperature equalizer. 48 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 28 P4 (/I O _i z o U1 z 20 12 10 20 30 40 50 60 80 100 200 300 FREQUENCY IN KILOCYCLES PER SECOND Fig. 6 — Transmitting equalizer — loss-frequencj' characteristic. of the crystal used in a repeater for performance checking. The gain of a repeater to a signal applied at the resonance frequency of its crystal is about 25 db greater than at 164 kc. Deviation Equalizer ■ — • The transmitting deviation equalizer is used to protect the highest level repeater from overload. The design is based on data obtained during the lajdng indicating which repeater was at the highest level at the various frequencies. The characteristic of this equal- izer is shown on Fig. 7. A portion of the receiving terminal is shown in block schematic form on Fig. 8. The generalized function of the equalizers is to make the signal level flat versus frequency at the input to the receiving amplifier No. 2. The specific functions of the various equalizers are as follows: 6 4 2 0 20 40 60 80 100 120 140 FREQUENCY IN KILOCYCLES PER SECOND 160 180 Fig. 7 — Transmitting deviation equalizer — loss-frequency characteristic. DESIGN OF SYSTEM — NORTH ATLANTIC LINK 49 Cable Length Equalizer — In planning the system, an estimate was made of how far the last repeater (receiving end) would be from the shore. Considerations of interference and level dictated a maximum dis- tance not exceeding approximately 32 miles. For protection against wave action, trawlers and similar hazards, the repeater should be no closer than about five miles. To take care of this variation, a cable length equal- izer was designed that is capable of simulating the loss of 10 miles of cable, adjustable in 0.5 db steps at the top of the frequency band. Two of these could be used if needed. Once the system is laid, this equalizer should require no further adjustment unless it is used to take care of cable aging or a cable repair near shore. Receiving Fixed Equalizer — This is the mop-up equalizer for the sys- tem. A final receiving equalizer, Fig. 9, has been constructed for the first crossing. Another, tailored to the No. 2 cable, will be designed on the basis of data taken after completion. PAD \. PAD TEMPERATURE EQUALIZER LENGTH BUILD-OUT RECEIVING AMPLIFIER N0.1 RECEIVING FIXED EQUALIZER RECEIVING AMPLIFIER NO. 2 Fig. 8 — Receiving equalizers — block schematic. Receiving Temperature Equalizer — The receiving temperature equal- izer is identical with the transmitting temperature unit. OPERATIONAL DESIGN General The operational design of a transmission system considers the supple- mentary facilities which are needed for operation of the main transmis- sion facility, for its supervision and for its maintenance. In the present instance, these facilities include the cable station power plants for driving the carrier terminals and high frequency line, the carrier terminals them- selves and their associated carrier supply bays, the telephone and tele- graph (speaker and printer) equipments needed for maintenance, super- vision and administration of the overall facility, the pilots, protection devices and alarms and the maintenance and fault locating equipment. Power Supplies With the exception of the plants for cable current supply, the power plants at Clarenville and Oban are relatively conventional, and follow telephone office techniques which are standard for the telephone adminis- 50 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 tration of the particular side of the Atlantic on which they are located. They will not be discussed here, although it might be well to point out that the equipment supply for the Bell equipment is direct current, ob- tained from floated storage batteries, while the supply for the Post Office equipment is alternating current from rotary machines driven normally from the station ac supply, with storage battery back-up. The cable current supplies for the North Atlantic Hnk^" are complex and highly special. It is pertinent to discuss here briefly the requierments which beget this complexity. To assist in this, an elementary schematic of the cable power loop is shown in Fig. 10. The following main requirements governed the design of these plants: 1. Constant maintenance of uniform and known current in the power loop. 2. Protection of HF line against faults induced by failures in power bays. 3. Protection of HF line against damage from power voltage surges caused by faults in the line itself. Maintenance of constant and known operating current in the line is very important from the standpoint of system life because of the de- pendence of the rate of electron tube aging on the power dissipated in the heaters. ^^ The principal factor which tends to cause variations in the line current is the earth potential which may appear between the terminals of the system. This potential may be of varying magnitude and of either po- „ 14 _l LU u UJ 12 Q Z 01 10 O -J z ^B cr UJ if) z ~ 6 4 /I 1 \ r^ V y ^ \ / \-«^ \ ^ ^ k 20 40 60 80 100 120 140 160 FREQUENCY IN KILOCYCLES PER SECOND 180 Fig. 9 — Receiving fixed equalizer — loss-frequency characteristic. DESIGN OF SYSTEM — NORTH ATLANTIC LINK 51 OQ >> C 5 a. 60 80 100 120 140 LINE FREQUENCY IN KILOCYCLES PER SECOND 160 Fig. 13 — Group to group frequencj' response — Xo. 1 cable. DESIGN OF SYSTEM NORTH ATLANTIC LINK 61 if any net change in the cable temperature averaged over the whole cable length. The greatest possibility of change would be in the shallow-water sections, and crystal measurements indicate that at the end of a year the average temperature of the shallow-water sections returned nearly to its initial value. Hence about 5 db seems chargeable to one year's aging. Extrapolation into the future, however, is uncertain. Theoretical considerations lead to the idea that the rate of cable aging should decrease. Information on long-term change in transmission loss of previous cables is very limited. The Havana-Key West cables were accurately measured just after laying, and again five years later. The change in that system due to aging is very small, if indeed there is a change. That cable is generally like the transatlantic, though it is smaller and has a perhaps significant difference in construction of the central conductor. The above applies to the net loss of the undersea part of the system only. The group-to-group net loss variation with time of the Clarenville- Oban link has been held within a much smaller range by temperature equalizer adjustments. Practices have been worked out which it is be- lieved will hold the in-service variation with time to a fraction of a db. Net Loss versus Carrier Frequency Power Level Single-frequency tests of carrier frequency output power versus input power were made, up to a test power a little below the estimated overload of the highest-level repeater. An increase of 0.1 db in system net loss oc- curs at a power 2 to 3 db below the load limit of the transmitting am- plifier. This is about 15 or 16 db above the expected rms value of the in-service system busy hour load. The 0.1 db change is presumably due to the cumulative effect of smaller changes in several of the undersea amplifiers. mo ■* ^5 3 LU< Dai 2 -J 15 el' ^ ^ — 160 KC / 90 KC / 0 ^ ^ /> X - ■ "^C )KC ••~~ ^ . — ■^ 4 6 8 10 MONTHS FROM OCTOBER 1,1955 12 Fig. 14 — Change in system gain in first eleven months. 62 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 2.4 2.0 1.6 I/) m 1.2 5 o S 0.8 Z 0.4 -0.4 1-0.8 -1.2 -1.6 -2.0 A / o 215 MILS f \ A Y ^ A •f MILS \ i \ ^^ k r r 225 MILS v •^ H [^ 1/ p^ 1 \ X — / \ ^^ y 20 40 60 80 100 120 140 FREQUENCY IN KILOCYCLES PER SECOND 160 180 Fig. 15 — Effect of cable current on system gain — No. 1 cable. Nel Loss versus DC Cable Current Changes in cable current affect the repeater gain to a shght extent, the amount depending on the magnitude and phase of the feedback in the repeater as a function of frequency. Measured changes in the loss of the 2,000-mile system, for currents of 5 and 10 milliamperes less than the normal value of 225 milliamperes, are shown in Fig. 15. Under normal conditions the automatic control will hold the cable current variation within ±0.5 milliampere. The shape of the curve on Fig. 15 is almost the same as that computed in advance from laboratory measurements on model repeaters. System Noise Shown in Fig. 16 are values of noise on the No. 1 cable system meas- ured in the Fall of 1955 and again in the Spring of 1956. The noise increase is compatible with the decrease in undersea system net loss during this period. To prevent overload, the loss in the transmitting temperature equalizer has to be increased as the undersea loss decreases; this lowers the levels of the various parts of the undersea system by various amounts. The noise shown in the top channel exceeds the 36 dba objective by a small amount. The excess can be recovered, if necessary, by certain changes in the terminals without recourse to compandors. Fig. 16 shows also the noise on the No. 2 cable system shortly after DESIGN OF SYSTEM — NORTH ATLANTIC LINK 63 36 34 32 30 28 26 d i^ / / 7 NO.t CABLE r MARCH 31,1956__/ >^ / / H ^ J y NO.l CABLE OCTOBER 13,1955 ~~-^ r f J A y y^ A ->^N0.2 CABLE AUGUST 17, 1956 24 22 f1^ ) ^ n "^^ ^A^/1 ^ 9 /^ / i w^ y =<^ ^ 20 18 16 14 -n_nd /ctC V xy^ '^ y z-' cr^ 20 40 60 80 100 120 140 LINE FREQUENCY IN KILOCYCLES PER SECOND 160 180 Fig. 16 — System noise. completion of laying. The noise is lower than on the No. 1 cable. This is because results of experience on the No. 1 cable were utilized in better choice of cable repeater section lengths and in better equalization while laying the 1956 cable. Modulation Tests Two-tone modulation tests of second and third order products were made, using a large number of successive frequency combinations. The highest level modulation products were at least 60 db below the 1 -milli- watt test tones, at zero transmission level. This is approximately the value computed before the system was laid. Most of the modulation products were down substantially more than 60 db. Probably various causes contributed to the good performance, including the effect of mis- alignment in lowering repeater levels, and small propagation-time dif- ferences which minimize in-phase addition of third-order products from successive repeaters. Telegraph Transmission Tests At present writing, telegraph tests have been made only on the printer (telegraph order wire) channels, and without a system multi-channel 64 THE BELL SYSTEM TECHNICAL JOUllNAL, JANUARY 1957 load. With the proposed specific telegraph level (STL) of —30 db (i.e. telegraph signal of —30 dbm per telegraph channel at 0 db telephone transmission level), the telegraph distortion was too low to measure reliably ; it was possible to send clear messages under test conditions with a signal 36 db weaker than this. Crystal Tests All of the peaks of noise at the crystal resonance frequencies were easily discernible. The crystal gain values all lay in the range from 23.6 to 27.2 db, with 60 per cent of them lying in the range from 25 to 26 db. Crystal gain, as used here, is the difference between the system gain at a repeater crystal frequency and the average of the gains at 50 cycles above and below this frequency; the latter value is approximately the gain if the crystal were absent. No significant changes in crystal gain have occurred in eleven months of system life, and none were expected. These measurements are to be continued over the years, as an indication of electron tube aging, as explained in the companion paper on the repeater.' A series of measurements of the frequency of each of the 51 repeater crystals versus time has been made. (Any of these frequency determina- tions can be checked on the same day within ±0.1 cycle with the special test apparatus and techniques used.) The crystals were designed to be extremely stable in frequency, so that measurements on one repeater, made at the land terminal, would not be affected by the combined effect of 50 other crystals at 100-cycle spacings. The crystal frequency varies only about — | cycle per degree Fahrenheit increase in sea-bottom uj 173.403 tr UJ Q. UJ 173.401 > 173.399 173.397 O z UJ O UJ tr u. 170.702 170.700 ^ -V ^ -^ EASTERNMOST REPEATER (NO.Sl) ^ y 1 1 1 1 1 1 1 1 MID-OCEAN REPEATER (N0.26) -^ 20 40 60 80 100 120 140 DAYS AFTER COMPLETION 160 180 200 Fig. 17 — Resonant frequency versus time — shore and deep sea crj^stals. DESIGN OF SYSTEM — NORTH ATLANTIC LINK 65 temperature. The change in frequency due to crystal aging in 11 months under the sea is considered to He in the range 0 to —0.4 cycle. Although the crystals were not designed as sea-bottom temperature indicators and are within a repeater housing, it seems likely that with precise techniques and, after some further stabilization, some uniquely accurate information on change of sea-bottom temperature will be ob- tainable. In accordance with previous oceanographic knowledge of sea-bottom temperature, the frequency changes have been larger in the crystals near shore. The greatest change has been in the repeater nearest Oban. This is about 17 miles from shore and in water only about 50 fathoms deep. Its freciuency change, and that of a typical deep-sea repeater, are shown in Fig. 17. FUTURE CONSIDERATIONS Spare Equipment for Cable Stations In a system as far-flung geographically as this one, and as important, much thought must be given not only to the supplies needed for routine replacement of expendable items, but also to major replacements neces- sitated by fire or other causes. Accordingly, a schedule of spare equip- ment has been established, divided into two groups — "shelf" and "casualty". Shelf spares are carried in the station itself, and include items such as dial lights, electron tubes and dry cell batteries, which have limited life in normal service. These are maintained in the cable station in quantity estimated as adequate for two years of operation. Casualty spares embrace those major, essential frames and equip- ments without which the system cannot be operated. There are two sub- divisions: those which are in common use in the telephone plant and are, therefore, available by "cannibalization", and those which are special to the project, like the cable current supplies and the cable terminating bays. The common-use items are not stocked as casualty spares. Spares of the special items have been built and are stored in locations remote from the cable stations. In event of catastrophe, these can be drawn out and flown as near the point of need as possible, for onward-shipment by available means. Spare Equipment for the Undersea Link Although every effort has been made to produce a trouble-free system, the underwater link is still subject to the hazards of trawlers, icebergs. 66 THE BELL SYSTEM TECHNICAL JOUKNAL, JANUARY 1957 anchors and submarine earthquakes or land slides. There must be con- sidered, too, the possibility of fault from human failure. So it is necessary to contemplate the replacement of a length of cable, or a repeater or equalizer. For such contingency, spare cable of the vari- ous armor types has been stored on both sides of the Atlantic. Spare repeaters and equalizers are also available. In addition, a spare called a "repair repeater" has been stocked. Need for this arises from the fact that except in very shallow water, a repair cannot be effected without the addition of cable over and above the length which was in the circuit initially. The amount of cable which must be added is a function of water depth, condition of the sea at the time of the repair, and the amount of cable slack available in the im- mediate vicinity of the point in question. When excess cable is introduced in amount sufficient to significantly reduce the system operating margins, its loss must be compensated. Hence, the repair repeater. A repair repeater is a two-tube device, essentially like a regular re- peater although its impedances are designed to match the cable im- pedances at input and output ends. However, its gain is sufficient to offset only about 5.3 miles of cable. A second type of repair repeater is under consideration, to compensate for about 15 miles of cable. Long-Term Aging General In a system with some 3,200-db gross loss at its top frequency between points which are accessible for adjustment, a long-term change in loss of only one per cent would have a profound effect on system performance. For this reason, the repeater design included careful consideration of net gain change over the years.^ The degree of control over aging is such that in a period of at least 20 years, and perhaps much longer, the esti- mated change in 51 repeaters might total 8 db added gain at the top frequency. The gain variation with frequency would be proportional to either curve of Fig. 15, and the rate of aging would be slower in earlier than in later years. Estimates of cable aging are discussed in the section on "Net Loss Tests." Means of Combatting Aging The effects of aging would become important on the top channels first. Remedial measures to improve signal-to-noise, especiall}^ in the top DESIGN OF SYSTEM — NORTH ATLANTIC LINK 67 channels, include: possible increase of transmission level at input of the final transmitting and load limiting amplifier in the transmitting termi- nal; pre-distortion ahead of this amplifier; compandors; increase of dc current; and undersea re-equalization in later years. This last would be very expensive, and so it is necessary to examine fully the possibilities of the other measures. The penalty for increasing the transmission level at the input of the transmitting amplifier is more peak-chopping and modulation-noise peaks. The improvement that could be realized in this way is probably fairly small. Pre-distortion is accomplished by inserting ahead of the transmitting amplifier a suitable shaping network adjusted for gain in the top part of the band and loss at lower frequencies. A complementary network (restoring network) is placed at the receiving terminal. This measure would improve signal-to-noise in the uppermost part of the band and reduce it in lower channels which have less noise. Some 3-db improve- ment might be thus realized in the top channel. Compandors would give an effective signal-to-noise improvement of up to about 15 db for message telephone service, but none for services such as voice-frequency telegraph. Compandors would be applied only to those channels needing them. They halve the range of talker volume, but also double the transmission variations between compressor and expandor, and thus tend to require some increase in the overall channel net loss. The program (music) channels are already equipped with com- pandors which use up a part of the obtainable advantage. If the combination of such measures netted an effective message sig- nal-to-noise improvement of 20 db in the top channel, this would counter- balance aging of some 28 db in this channel, if the aging were uniformly distributed along the system length. Thus considerable aging could be handled without undersea modification. ACKNOWLEDGEMENTS A system of the complexity of the one described obviously results from teamwork by a very large number of individuals. However, no paper on this subject could be written without acknowledgement to Dr. 0. E. Buckley and J. J. Gilbert and O. B. Jacobs, now retired from Bell Telephone Laboratories. All of the early and fundamental Bell System work on repeatered submarine cable systems, and the concept of the flexible repeater, came from these sources and from their co- workers. Messrs. Gilbert and Jacobs have also contributed to the present project. 68 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 REFERENCES 1. E. T. Mottram, R. J. Halsey, J. W. Emling and R. G. Griffiths, Transatlantic Teleplione Cable System — Planning and Over-All Performance. See page 7 of this issue. 2. A. W. Lebert, H. B. Fischer and M. C. Biskeborn, Cable Design and Manu- facture for the Transatlantic Submarine Cable System. See page 189 of this issue. 3. T. F. Gleichmann, A. H. Lince, M. C. Wooley and F. J. Braga, Repeater De- sign for the North Atlantic Link, See page 69 of this issue. 4. J. J. Gilbert, A Submarine Telephone Cable with Submerged Repeaters. B.S.T.J., 30, p. 65, Jan., 1951. 5. C. W. Carter, Jr., A. C. Dickieson and D. Mitchell, Application of Com- pandors to Telephone Circuits, A.I.E.E. Trans., 65, pp. 1079-1086, Dec. Supplement, 1946. 6. B. D. Holbrook and J. T. Dixon, Load Rating Theory for Multi-Channel Amplifiers. B.S.T.J., 18, p. 624, July, 1939. 7. W. R. Bennett, Cross Modulation in Multi-Channel Amplifiers, B.S.T.J., 19, pp. 587-610, Oct., 1940. 8. R. A. Brockbank and C. A. Wass, Non-Linear Modulation in Multi-Channel Amplifiers, Jl.I.E.E., March, 1945. 9. J. S. Jack, Capt. W. H. Leech and H. A. Lewis, Route Selection and Cable Laying for the Transatlantic Cable System. See page 293 of this issue. 10. G. W. Meszaros and H. H. Spencer, Power Feed Equipment for the North Atlantic Link. See page 139 of this issue. 11. J. O. McNally, G. H. Metson, E. A. Veazie and M. F. Holmes, Electron Tubes for the Transatlantic Cable System. See page 163 of this issue. 12. H. A. Lamb and W. W. Heffner, Repeater Production for the North Atlantic Link. See page 103 of this issue. 13. P. T. Haury and L. M. Ilgenfritz, Air Force Submarine Cable System, Bell Lab. Record, 34, pp. 321-324, Sept., 1956. Repeater Design for the North Atlantic Link T. F. GLEICHMANN,* A. H. LINCE,* M. C. WOOLEY* and F. J. BRAGA* (Manuscript received October 8, 1956) Some of the considerations governing the electrical and mechanical de- sign of flexible repeaters and their component apparatus are discussed in this paper. The discussion includes description of the feedback amplifier and the sea-pressure resisting container that surrounds it. Examples are given of some of the extraordinary measures taken to ensure continuous per- formance in service. INTRODUCTION Repeaters for use in the transatlantic submarine telephone cable sys- tem had to be designed to resist the stresses of laying, and to withstand the great pressures of water encountered in the North Atlantic route. In anticipation of the need for such a long telephone system in deep water, development work was started over 20 years ago on the design of a flexible repeater that could be incorporated in the cable and be handled as cable by conventional cable ship techniques. Successful com- pletion, in 1950, of the design and construction of the 24-channel Key West, Florida-Havana, Cuba system,^ led to the adoption of similar repeaters designed for 36 channels for the North Atlantic link discussed in companion papers.^- ^ Repeater transmission characteristics determine, to a large extent, the degree to which system objectives can be met. In this repeater, sig- nificant characteristics are: (a) Noise and Modidation. These were established by the circuit con- figuration and by the use of the conservative electron tube^ developed for the Key West-Havana project. (b) Initial Misalignment, or mismatch of repeater gain and cable loss throughout the transmitted band of frequencies. A match within 0.05 db was the objective. This affected both the design and the precision required in manufacture. * Bell Telephone Laboratories. 69 70 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 a u CO o o3 a, bC FLEXIBLE REPEATER DESIGN 71 (c) Aging. As electron tubes lose mutual conductance with age, re- peater feedback decreases, repeater gain changes, and misalignment is affected. Decrease in feedback increases the gain at the higher frequen- cies so that the signal input must be reduced to prevent overloading, resulting in a signal-to-noise penalty. Gain increase is inversely propor- tional to the amount of feedback; in these repeaters, 33 to 34 db of feed- back was the objective to keep this source of misalignment in bounds. Because repeaters are inaccessible for maintenance, facilities are pro- vided to enable the individual repeater performance to be checked from the shore end. This feature also permits a defective repeater to be identi- fied in the event of transmission failure. REPEATER UNIT The repeater, for the sake of discussion, may be divided into two parts, (1) the repeater unit, which contains the electron tubes and other cir- cuit components and (2) the water-proof container and seals Avhich house the repeater unit. Circuit The circuit of the repeater unit is sho^vn in Fig. 1. It is a three-stage feedback amplifier of conventional design with the cathodes at ac ground. The amplifier is connected to the cable through input and output cou- pling networks. Each coupling network consists of a transformer plus gain-shaping elements and a power separation inductor. The coupling networks directly affect the insertion gain as do the two feedback networks. The design of these networks controls the insertion gain of the amplifier. The required gain (inverse of cable loss) is shown in Fig. 2. The 39 db shaping required between 20 and 164 kc is divided approximately equally among the input and output coupling networks and the feedback networks. The interstage networks are of conventional design. The gain of the first interstage is approximately flat across the band. The second inter- stage has a sloping characteristic, the gain increasing with frequency. The gain shaping of these networks offsets the loss of the feedback net- works so that the feedback is approximately flat across the band. Plate and heater power is supplied to the repeater over the cable.'* The plate voltage (approximately 52 volts) is obtained from the drop across the heater string. The dc circuits are isolated from the container by the high voltage blocking capacitors Ci , C2 and C3 . 72 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 ^ 60 _) LU (D \^ 50 a z Z 40 < O a ^30 Z) a ai °= 20 10 ^ ■^ "^ ■^ / X / 20 40 60 80 100 120 140 FREQUENCY IN KILOCYCLES PER SECOND Fig. 2 — Required insertion gain. 160 180 Gain Formula The circuit of Fig. 1 may be represented by a simplified circuit con- sisting of an input coupling network, a three stage amplifier, an output network and a feedback impedance Z^ as shown in Fig. 3. From this figure it can be shown that the insertion gain of the repeater is given by:« e = 2e'e'Z, Pil^iifJmTZlZiZ^ — PiPogmTZlZ2Z0_ (1) when Zp « QmTZpZgZxZi » (Zo + Z^ and where Pi = Zi + Zg and po = Zo + Zp are "potentiometer terms". The gain of the input network is defined as e*i = Y lEi ; where Y is the open circuit voltage of the input network with Ei as the source, and the gain of the output network is defined as e' = ill\. This expression may be put in familiar form by recognizing that pip^gmrZxZiZ^ is jUjS, the feedback around the loop. Hence 2i'e'Z [r M^ - M/3J (2) Equation (2) shows that the insertion gain of the I'epeater is the prod- uct of five factors, namel}': FLEXIBLE REPEATER DESIGN 73 (1) e^ — the gain of the Input Network (2) e- — the gain of the Output Network (3) Zc — the cable impedance (4) Z^ ■ — the feedback impedance (5) (m/S/I - /i|8) — the M^ effect term It should be noted that a number of simplifj'ing assumptions have been made. For example, the effect of grid plate capacitance has been neglected. In addition the /3 circuit has been assumed to be a two termi- nal impedance whereas it is actually a four terminal network. However, in the pass band and over a large part of the outband of the repeater these simplifications give a very good approximation to the true gain of the repeater. In the pass band (n^/1 — ju/3) is very nearly unity so that the gain con- trolhng factors are e\ e^, and 1/Z^ assuming that Zc is fixed. Coupling Networks The input and output networks are essentially identical. The net- works are of unterminated design and therefore do not present a good termination to the cable at all frequencies which results in some ripple in the system transmission characteristic at the lower edge of the band and makes the repeater insertion gain sensitive to variations in the cable impedance. However, this arrangement has the advantage of maximum 1 — Z-»oo— 1 1 1 1 gmT Z1Z2 ] I I, L INPUT COUPLING NETWORK > ' OUTPUT COUPLING NETWORK »2 ' t c -L 1-^. 1 -*-r c^ Zg~^ *— Zp Zo— * < '\jj Zy3 ? ^T^ 1 V = OPEN CIRCUIT VOLTAGE OF INPUT COUPLING NETWORK WITH El, AS THE SOURCE ©, = GAIN OF INPUT COUPLING NETWORK DEFINED AS 6*' = V/Ej, ©2= GAIN OF OUTPUT COUPLING NETWORK DEFINED AS 6*2 = L/I, Z,Z2= INTERSTAGE IMPEDANCES gf^-p = PRODUCT OF g^ OF THREE AMPLIFIER TUBES Fig. 3 — Simplified amplifier circuit. 74 THE BELL SYSTEM TECHNICAL JOUKKAL, JANUARY 1957 TO HEATER CIRCUIT TO GRID OR PLATE TO BETA CIRCUIT Fig. 4 — Coupling network. signal to noise performance, highest gain, and most effective shaping with a minimum of elements. A minimum of elements is important in view of the space restrictions imposed by the flexible repeater structure. The sensitivity of the gain to variation in impedance is minimized by close manufacturing control of the cable and networks. The schematic of a coupling network is shown in Fig. 4 and the equiva- lent circuit in Fig. 5. Capacitor Ci and inductor L4 are part of the power separation circuit. The effect of L4 in the transmission band is negligible and it has been omitted from the equivalent circuit. However Ci is in the direct transmission path and has a small effect at the lower edge of the band so that it becomes a design parameter. The combination R2 , L2 controls the low-frequency gain shaping of the network. Inductor L3 R, C, Rj^ L3 L3I, ■a ^im^^^^ C1-HIGH VOLTAGE BLOCKING CAPACITOR Cr GRID CATHODE CAPACITANCE C3 - HIGH SIDE CAPACITANCE Zc -CABLE IMPEDANCE R, -RESISTANCE OF C, R,l^ R3t^ L31 Lm - MUTUAL Gm - CONDUCTANCE OF MUTUAL G-HIGH SIDE CONDUCTANCE L3 -LEAKAGE BUILD-OUT T - IDEAL TRANSFORMER R: -RESISTANCE OF LEAKAGE --LEAKAGE (LOW SIDE) LOW FREQUENCY SHAPING "ELEMENTS Fig. 5 — Eqviivalent circuit of coupling network. FLEXIBLE REPEATER DESIGN 75 builds out the leakage inductance of the transformer and together with capacitor Cs controls the shaping at the top end of the band. These ele- ments are adjusted during manufacture of the networks to provide the desired shaping. The equivalent circuit is an approximation to the true transformer circuit. By standard network analysis techniques the ratio V/Ei , the gain of the network, can be obtained. The agreement between measure- ments and computation is sufficiently close, several hundredths of a db, to insure that the representation is good. Each coupling network is designed to provide approximately one- third of the total shaping required, or 13 db. While these networks are 32 30 26 26 ^24 U ai Q 22 ? 20 < 18 16 3 14 12 / \ / \ / ' \ 1/3 CABLE SLOPE V / \ * r \ ^ / \ ^ ^f^ \ '^ < — TRANSMISSION BAND — >| \ 1 1 1 10 20 40 60 80 100 200 400 600 1000 FREQUENCY IN KILOCYCLES PER SECOND Fig. 6 — Gain of input coupling network. outside the feedback path, the impedances which they present to the amplifier are important factors in the feedback design. It can be seen from Fig. 3 that at the amplifier input the proportion of the feedback voltage which will be effective in producing feedback around the loop is dependent upon the potentiometer division between the grid-cathode impedance of the first tube and the impedance looking back into the coupling network. The greater the gain shaping of the network, the greater the potentiometer loss. The maximum gain which can be ob- tained from the coupling network is limited by the capacitance across the circuit. This capacitance cannot be reduced without increasing the 'G THE BELL SYSTEM TECHXICAL JOIRXAL, JANUARY 1957 z < 2 1 0 -1 HI u LU Q if) -3 O -6 4 6 8 10 20 40 60 80 tOO 200 400 600 FREQUENCY IN KILOCYCLES PER SECOND Fig. 7 — Input potentiometer term. potentiometer loss, and seriously limiting feedback. In this design an acceptable compromise is made when the ratio of network capacitance to grid-cathode capacitance has been fixed at 1.2 as suggested b}" Bode.^ The gain through the input network and the deviation from one-third cable shape is shown in Fig. 6. A typical potentiometer term is shown in Fig. 7 Similar considerations apply to the output network with the further restriction that the impedance presented to the output tube should be about 40,000 ohms at the top edge of the band for optimum modulation performance. The coupling networks have a temperature characteristic which must be taken into account in the insertion gain of the repeater. The charac- teristic is due to variations in the resistance of Ci and R2 with tempera- ture. This amounts to 0.005 db per degree F at 20 kc, decreasing with frequency, becoming negligible above 80 kc. Beta Circuit The beta or feedback network is designed to complement the combined characteristics of the input and output coupling networks and mop-up residual effects, such as those due to mjS effect and coupling network temperature coefficients. The network also provides the dc path for the output tube plate current. FLEXIBLE REPEATER DESIGN 77 The configuration of the beta circuit is shown in Fig. 8. In the pass band it is a two terminal network whose impedance varies from about 300 ohms at 20 kc to 70 ohms at 164 kc. It consists of essentially two parts. The elements to the left of the dotted line provide the major por- tion of the shaping. With these the repeater is within ±0.7 db of the required gain. The series resonant circuits to the right of the dotted line reduce this to the ±0.05 db set as the objective. The mopping up elements are connected to the main portion of the beta circuit through a resistance potentiometer Ri , R2 and R3 • This scales the elements of the resonant circuits to values which would meet mounting space and component restrictions. Built-in Testing Features The crystal Y and capacitor C, Fig. 1, in the feedback path provide the means for checking the repeater from the shore station. The crystal is a sharply tuned series-resonant shunt on the feedback path which reduces the feedback at the resonant frequency and produces a narrow peak in the insertion gain characteristic of the repeater. The feedback reduction, and hence the peak gain, is controlled by the potentiometer divider formed by the reactance of the capacitor and the series resonant resist- ance of the crystal. The crystal and capacitor are chosen so that sub- stantially all the feedback is removed from the repeater. With no feed- TO V3 HEATER l+B) V3 PLATE FILTER 1 1 AND DC BLOCKING | I CAPACITOR TO CATHODES OF V„V2,V3 TO GRID OF V, THROUGH HIGH SIDE OF INPUT COUPLING NETWORK AAAq^V\A— ^ 1— r -wv TO PLATE OF V3 THROUGH HIGH SIDE "of OUTPUT COUPLING NETWORK Fig. 8 — Beta network. 78 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 back the peak gain is proportional to the mutual conductance of the three tubes. At frequencies well off resonance the impedance of the crystal is high so that no reduction in feedback results. Periodic measurements of gain at the resonant frequency relative to measurements made at a frequency off resonance will show any changes in the tubes. The crystal frequency is different for each repeater so that by measuring the gain from the shore stations at the various crystal frequencies it is possible to monitor the performance of the individual repeaters. The increase in gain at the peak is approximately 25 db. The crystal frequencies, spaced at 100-cycle intervals, are placed above the normal transmitted band between 167 and 173.4 kc. Thermal noise always present at the input to the repeater, is also am- plified over the narrow band of frequencies corresponding to the peak gain in each repeater so that at the receiving end of the line there are a series of noise peaks, one for each repeater. Should a repeater fail, the noise peaks of all repeaters between the faulty repeater and the receiving end will be present and those from repeaters ahead will be missing. By determining which peaks are missing the location of the failed repeater can be determined. It is obvious that to locate a faulty repeater the power circuit must be intact. To guard against power interruption owing to an open electron-tube heater, a gas tube V4, Fig. 1, is connected across the heater string as a bypass. Loop Feedback The design of the feedback loop follows conventional practice. The restrictions that limit the amount of feedback that can be obtained in the transmitted band are well known. ^ Broadly speaking, the figure of merit of the electron tubes and the incidental circuit capacitances de- termine the asymptotic cutoff which limits the amount of feedback that can be obtained in the band. With the flexible repeater circuit, capaci- tances are rather large because of the severe space restrictions and physi- cal length of the structure. Transit time of 1.8° per megacj^cle per tube and a like amount for the physical length of the feedback loop reduced the available feedback by 2 db. Margins of 10 db at phase cross-over and 30° at gain cross-over were set as design objectives. While these may seem to be ultraconservative in view of the tight controls placed on components and the mechanical assembly, it should be borne in mind that the repeaters are inaccessible and repairs would be costly. Modulation and tube aging considerations require a minimum feed- FLEXIBLE REPEATER DESIGN 79 ■ ■ ■ ■ ■- ( ■:d 2 -HI 4 4 ^ 6 « 7 • 8 < 9 '10-11 ' 12 ■ 13 ■ 14 ■ 15 ■ 16 ^^ 1 1 INPUT TERMINAL 2 INPUT BLOCKING CAPACITOR 3 GROUNDING CAPACITOR 4 CRYSTAL 5 INPUT NETWORK 6 VACUUM TUBE (FIRST STAGE) 7 FIRST INTERSTAGE NETWORK 8 VACUUM TUBE (SECOND STAGE) 9 SECOND INTERSTAGE NETWORK 10 VACUUM TUBE (THIRD STAGE) 11 OUTPUT NETWORK 12 BETA NETWORK (1) 13 BETA NETWORK (2) 14 GAS TUBE 15 DRYER 16 OUTPUT BLOCKING CAPACITOR 17 OUTPUT TERMINAL Fig. 9 — Repeater make-up. back of 33-3-i db. With the restrictions noted above and the effect of the potentiometer terms on the available feedback, the top edge of the band is limited to about 165 kc with the desired feedback. Mechanical Design To provide a flexible structure the repeater unit is assembled in a number of longitudinal sections mechanically coupled by helical springs and electrically interconnected by means of bus tapes. The assembly is composed of 17 sections. Figs. 9 and 10 show the repeater make-up and an assembled unit. The sections consist of the circuit component, or components, mounted in machined plastic forms and enclosed in a plastic container w^hich in turn is enclosed in a housing of the same material.* The sections contain circuit components grouped functionally such as input coupling net- work, interstage, electron tube, or high \'oltage blocking capacitor. In the case of the feedback network it was necessary to mount the network in two sections because of the large numbers of components involved. A typical network, container and housing are shown in Fig. 11. The bus tapes are placed in grooves milled in the outer surfaces of the * The material used is methyl methacrj-late which was chosen for its ph.ysical and chemical stability and good machinability. f|i mippMlli)— H.iMIUc Fig. 10 — Overall view of the repeater unit. 80 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 Fig. 11 — Network section. section containers. Wiring spaces are machined into the ends of the con- tainers for connecting network leads to the bus tapes. The housing is placed over the container and the buses and is closed by a plastic coupler plate which also forms part of the intersection couplers. The coupler plates are fastened to the housing with plastic pins. Between sections the bus tapes are looped toward the longitudinal axis of the repeater unit. The dimensions of the loop are rigidly con- trolled so that as the unit is flexed during bending of the repeater, the loops always return to their original location between sections and do not short to each other or the metal outer container. The bus tapes have either an electrical connection or lock at one end of each section to eliminate any tendency of the tapes to creep as the repeater unit is flexed. The buses consist of two copper tapes in parallel to guard against opens should one tape break. The design of the connections to the buses is such that once the section is closed there can be no disturbance of the tapes or network leads in the vicinity of the electrical connections. The bus-type wiring plan was chosen as the best arrangement for the long structure in keeping with the stringent transmission requirements. Elec- trically adjacent but physically remote components can thus be inter- FLEXIBLE REPEATER DESIGN 81 connected with careful control of the parasitic capacitances and cou- plings to insure reproducibility from unit to unit in manufacture. COMPONENTS The development of passi^•e components for use in the flexible repeater presented a number of unusual problems, the most important being: (1) the extreme reliability^ (2) the high degree of stability, (3) the limita- tions on size and shape and, (4) an environment of constant low tempera- ture. The repeaters for the transatlantic system contain a total of approxi- mately 6,000 resistors, capacitors, inductors and transformers. If we are to be 90 per cent certain of attaining the objective of 20 years service without failure of any of these components, the effective average annual failure rate for the components must be not more than 1 in a million. To assure this degree of reliability by actual tests would require more than 400 years testing on 6,000 components. Obviously some other ap- proach to insure reliability is required. The most obvious avenue, that of providing a large factor of safety, was not open because of space limitations. Fortunately, with only one exception, the passive components do not wear out. Thus the approach to reUability could be made by one or more of the following: 1 . The use of constructions and materials which have been proved by long use, particularly in the Bell System. 2. The use of only mechanically and chemically stable materials. 3. The use of extreme precautions to avoid contamination by materials which might promote deterioration. 4. Special care in manufacture to insure freedom from potentially hazardous defects. The philosophy of using only tried and proved types of components dictated the use of wire wound resistors, impregnated paper and silvered mica capacitors and permalloy cores for inductors and transformers. While newer and, in some ways, superior materials are known, none of these possessed the necessary long record of trouble-free performance. In some cases, particularly in resistors, this approach resulted in more difficult design problems and also in physically larger components. While the ambient conditions in the repeater, i.e., low temperatures and ex- treme dryness, are ideal from the standpoint of minimizing corrosion or other harmful effects of a chemical nature, the materials used in the fab- rication of components were nevertheless limited to those which are in- 82 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 100 90 H 80 in 70 60 50 LU a. z LU cn LU 0- 20 10 K ^ ^ \ l^.. ■LIQUIDS AND SOFT WAX V \ \ \ y \ \ \ V \ \ ^ ~~~ ^ V -HARDER' WAXES \ ^ "^ -^ ^ ' 1/2 1 V/2 TIME IN YEARS 21/2 Fig. 12 — • Accelerated life tests on paper capacitors with various impregnants at room temperature (60° to 80°F). herently stable and nonreactive. In addition, raw materials were care- fully protected from contamination from the time of their manufacture until they were used, or, wherever possible, they were cleaned and tested for freedom from contaminants just prior to use. Unusually detailed specifications were prepared for all materials. The effort to achieve extreme reliability also influenced or dictated a number of design factors such as the minimimi wire diameters used in wound apparatus, the use of as few electrical joints as possible and the use of relati\'ely simple structures. These limitations resulted in the use of unencased components in most instances. Wherever possible, the ends of windings were used as terminal leads to avoid imnecessary soldered connections. This injected the additional hazard of lead breakage owing to handling during manufacture and inspection. This hazard was mini- mized in most instances by providing the windings with extra turns which were removed just before the component was assembled in the network. Thus, the lead wires in the final assembly had never been sub- jected to severe stress. Where this technique was impracticable, special fixtures and handling procedures were used to prevent imdue flexing or stressing of lead wires. As mentioned above there was one type of passive component in which life is a function of time and severity of operating conditions. These are the capacitors, especially those subject to high voltages. Because of this FLEXIBLE REPEATER DESIGN 83 and the fact that the physical and electrical requirements dictated the use of relatively high dielectric stress in these capacitors, a program of study covering a wide range of dielectric materials was undertaken about 1940. This study showed that none of the usual solid or semisolid materi- als used to impregnate paper capacitors were suitable for continuous use at sea bottom temperatures. Typical results of this program are shown in Figs. 12 and 13. These curves show the performance of capacitors operating at approximately 1.8 times normal dielectric stress at both sea bottom and room temperatures. It is evident that even semisolid im- pregnants are inferior to liquids at the lower temperature. The need for the maximum capacitance in a given space restricted the field still fur- ther, so that the final choice was a design using castor-oil-impregnated kraft paper as the dielectric. It is well established that the life of impregnated paper capacitors is inversely proportional to the fourth to sixth power of the voltage stress ; or h = where p ranges from 4 to 6. This fact permits the accumulation of a large amount of life information in a relatively short time. In order to insure in lij I- z o z z < LU a. t- z UJ o a. LU a 100 90 SO 70 60 50 40 30 20 10 I X \ LIQUIDS k X ^-. l\ \ SOFT WAX . u \ \ \ >- 1 y' . HARDER-' WAXES / ^ It £ \ " ■ 1/2 1 n/2 TIME IN YEARS 21/2 Fig. 13 — Accelerated life tests on paper capacitors with various impregnants at 40°F. 84 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 that the capacitor design selected would provide the degree of reliability required, a number of capacitors were constructed and placed on test at voltage stresses ranging from 1^ to 2j times the maximum stress ex- pected in service. From the performance of these samples, a prediction of performance vmder service conditions can be made as follows: The total equivalent exposure in terms of capacitor years at the maxi- mimi ser^qce voltage can be computed for the samples under test by the following summation : T = N.T. (I;)' + N.T. g)' +---+N,T. (.0' (1) where Ni , N2 , • • • Nr are the number of samples on test at voltage stresses Vi , V2 and Vr , Ti , T2 , ■ • • Tr are the total times of the individ- ual tests and Vs is the maximum voltage stress under service conditions. If, as has been the case in the tests described above, there has been only one failure in the total exposure T, we can estimate from probability equations the limits or bounds within which the first failure will occur in a system involving a given number of capacitors operating at a volt- age stress Vs . These equations are: probability of no failures in exposure T = e" '^'^ (2) probability of more than one failure in exposure time T = l-(i + T)e-"' (3) where T is obtained from (1) and L is the total exposure in the same units as T for the service conditions. The solutions of (2) and (3) for L using any desired probability give the maximum and minimum ex- posures in capacitor-years, within which the first failure may be ex- pected to occur under service conditions. However, since the voltage on the capacitors varies from repeater to repeater, it is necessary to determine the equivalent exposure of the sys- tem in terms of capacitor-years per year of operation at the maximum service voltage in order to estimate the time to the first failure in the system. This is obtained from (1) for one-half of one cable by substitut- ing the supply voltage at each repeater for Fi , y2 , etc., the maximum service voltage for Vs and the number of capacitors per repeater for A^. The total exposure for a two cable system is then 4 times this figure. With the data which has been accumulated and the number of capacitors and voltages of the transatlantic system, we estimate with a probability of being correct nine times in ten that the first "wear-out" failure of a FLEXIBLE REPEATER DESIGN 85 capacitor in the transatlantic system will not occur in less than 16 years nor more than 600 years. There is, of course, the possibility of a catastrophic or early failure due to mechanical or other defects not associated with normal deterioration of the dielectric. Such potential failures are not always detected by the commonly used short-time over-voltage test. Thus, for submarine cable repeaters, all capacitors subjected to dc potentials in service are sub- jected to at least 1| times the maximum operating voltage for a period of four to six months before they are used in repeaters. Experience indi- cates that this is adequate to detect potential early failures. The results of this type of testing on submarine cable capacitors is an indication of the care used in selecting materials and manufacturing the capacitors. Only one failure has occurred in more than 3,000 capacitor-years of testing. An important aspect of the control of quality of components is the control of the raw materials used in their manufacture. For the trans- atlantic project, this was accomplished by rigid specifications, thorough inspection and testing, supplemented in some cases by a process of se- lection. This can be illustrated by the procedure used for selecting the paper used as the dielectric in capacitors. The Western Electric Company normally inspects many lots of capacitor paper during each year. Those lots which were outstanding in their ability to stand up under a highly accelerated voltage test were selected from this regular inspection proc- ess. These selected lots were then subjected to a somewhat less highly accelerated life test. Paper which met the performance requirements of this test was slit into the proper widths for use in capacitors. Sample capacitors were then prepared with this paper and so selected that they represented a uniform sampling of the lot at the rate of one sample for approximately each three pounds of paper. These samples were impreg- nated with the same lot of oil to be used in the final product. Satisfactory completion of accelerated life and other tests on these samples consti- tuted final qualification of the paper for production of capacitors. Rela- tively few raw materials were adaptable to such tests or required such detailed and exhaustive inspection as capacitor paper. But the attitude in all cases was that the material be qualified not only as to its primary constituents or characteristics but also as to its uniformitj^ and freedom from unwanted properties. To a considerable extent, stability of components is assured by the practice of using only those types of structures which have long records of satisfactory field performance. However, in some cases, a product far 86 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 more stable than usual was required. This was true of the high voltage capacitors where other requirements dictated the use of impregnated paper as the dielectric but where the degree of stabiUty required was comparable to that expected of more stable types of capacitors. In so far as possible, stabiUty was built into the components by appropriate design but, where necessary, stabiUzing treatments consisting of re- peated temperature cycles were used to accelerate aging processes to reach a stable condition prior to assembly of the repeaters. Temperature cycling or observation over periods up to six months were used also to determine that the components' characteristics were stable. Exceptional inspection procedures followed to insure reliability and stability are described in detail in a companion paper.^ As mentioned earlier, the design and construction of components was simplified by omitting housings or containers, except for oil impregnated paper capacitors. Adequate mountings for the components were obtained in several ways. Mica capacitors were cemented to small bases of methyl methacrylate which were in turn cemented in suitable recesses in net- work structures. Inductors and transformers were cemented directly into recesses in the network housings. Fig. 14 illustrates some of these structures and their mounting arrangements. On the bottom is a molyb- denum permalloy dust core coil in which a mounting ring of methyl Fig. 14 — Mounting for molybdenum permalloy dust core coils. FLEXIBLE REPEATER DESIGN 8^ Fig. 15 — Capacitor and resistor capacitor combinations. methacrylate provided with radial fins is secured around the core by tape and the wire of the winding. Such inductors were mounted by ce- menting the projecting fins into slots arranged around a recess in the network housing. On top is an inductor which, for electrical reasons, required a core of greater cross-section than could be accommodated in the network when made by the usual toroidal construction. In this case, the effective cross-section of two cores M^as obtained by cementing the cores in a "figure-8" position and by applying the winding so that it threads the hole in both cores. With these constructions, the cement used to secure the inductors does not come into contact with the wire of the winding which is thereby not subject to strains produced by curing of the cement. For economy of space and also to reduce the number of soldered con- nections, many of the components' structures contain two or more ele- ments. Inductors and resistors were combined by winding inductors with resistance wire. Separate adjustment of inductance and resistance were obtained by adjusting turns for inductance and the length of wire in a 88 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 small "non-inductive" winding for resistance. The inductor on the bot- tom in Fig. 14 illustrates one type in which the non-inductive part of the winding is placed on one of the separating fins. In some cases, capaci- tors and resistors were also combined. Fig. 15 shows two of these. The capacitor at the bottom right contains three capacitances and a single re- sistance in the same container. This construction requires that the re- sistor parts be capable of withstanding the capacitor drying and impreg- nation process and also that the resistor contain nothing which would be harmful to the capacitor. The capacitor on the left in this figure is housed in a ceramic container on which is wound a resistor. The capaci- tor at the top is a high-voltage type Avhich, aside from electron tubes, represents the largest single component used in the repeater. In this ca- pacitor, the tape terminals which contact the electrodes are brought out through the ceramic cover and are made long enough to reach an ap- propriate point so as to avoid additional soldered connections. Such special designs introduced many problems in the manufacture of the components. However, the improved performance of the repeater and the increase in the inherent reliability of the overall system fully justified the greater effort which was required for the production of such special- ized apparatus. POWDER BY-PASS GAS TUBE* The fault locating means, referred to previously, requires that the power circuit through the cable be continuous. To protect against an open circuit in the repeater, such as a heater failure, an additional de- vice is required to bypass the line current. This bypass must be a high resistance under normal operating conditions since anj' current taken b}^ this device must be supplied through preceding repeaters. If an open circuit occurs the bypass must carry the full cable current. At full cur- rent, the voltage drop should be small to avoid excessive localized power dissipation in the repeater. The de^'ice should recover when power is removed so that false operation by a transient condition will not perma- nently bypass the repeater. A gas diode using an ionically heated cathode has been used to meet these requirements. By making the breakdown voltage safely greater than the drop across the heater string, no power is taken by the tube under normal repeater operation. In the event of an open circuit in the repeater, the voltage across the tube rises and breakdown occurs. Full cable current is then passed through the gas discharge. Removal of power Material contributed by Mr. M. A. Townsend. FLEXIBLE REPEATER DESIGN 89 from the cable allows the tube to deionize and recover in the event of false triggermg by transients. The cathode is a coil of tungsten wire coated with a mixture of barium and strontium oxide. A cold cathode glow dis- charge forms when the tube is first broken down. This discharge has a sustaining voltage of the order of 70 volts. The glow discharge initially covers the entire cathode area. Local heating occurs and some parts of the oxide coating begin to emit electrons thermionically. This local emis- sion causes increased current density and further increases the local heating. The discharge thus concentrates to a thermionic arc covering only a portion of the coil. The sustaining voltage is then of the order of 10 volts. Mechanically the tube was designed to minimize the possibility of a short circuit resulting from structural failure of tube parts. Fig. 16 shows the construction of the tube. The glass envelope and stem structure which had previously been developed for the hot cathode repeater tubes were used as a starting point for the design. The anode is a circular disk of nickel attached to two of the stem lead wires. To provide shock resistance the supporting stem leads are crossed and welded in the center. To pro- tect against weld failure, a nickel sleeve is used at each end of the cathode Fig. 16 — The power by-pass gas tube. 90 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 coil. It is crimped to hold the coil mechanically in place and then welded at the end for electrical connection. At the end of the coil as well as in all other places where it is possible, a mechanical wrap is made in addi- tion to spot welding. An additional precaution is taken by inserting an insulated molybdenum support rod through the center of the cathode coil. The filling gas is argon at a pressure of 10 mm Hg. To provide ini- tial ionization, 1 microgram of radium in the form of radium bromide was placed on the inside of the tube envelope. All materials were pro- cured in batches of sufficient size to make the entire lot of tubes and care- fully tested before being approved for use. The tubes were fabricated in small groups and a complete history was kept of the processing of each lot. For detailed study of tube performance, a number of electrical tests were made. These involved measurements of breakdown voltage, operat- ing voltage as a glow discharge at low current, current required to cause the transition to a thermionic arc, the time required at the cable current to cause transition to the low voltage arc, and the sustaining voltage at the full cable current. All tubes were aged by operating at 250 milliamperes on a schedule which included a sequence of short on-off periods (2 min. on, 2 min. off) followed by periods of continuous operation. A total of 150 starts and 300 hours of continuous operation were used. Following this aging schedule the tubes were allowed to stabilize for a few days and then sub- jected to a 2-hour thermal treatment or pulse at 125°C. It was required that no more than a few volts change in breakdown voltage occur during this thermal pulse before a tube was considered as a candidate for use in repeaters. After aging and selection as candidates for repeaters, tubes were stored in a light-tight can at 0°C. Measurements were made to assure stability of breakdown voltage and breakdown time. The quality of each group of 12 tubes was further checked by continu- ous and on-off cycling life tests. The fact that none of these tubes has failed on the cycling tests at less than 3,500 hours and 1,500 starts and no tube on continuous operation has failed at less than 4,200 hours gives assurance that system tubes will start once and operate for the few hours necessary to locate a defective repeater. Long-term shelf tests of repre- sentative samples at 70°C and at 0°C give assurance of satisfactory behavior in the system. CONTAINER AND SEALS The design of the flexible enclosure for the flexible repeater unit is basically the same as it emerged from its development stages in the FLEXIBLE REPEATER DESIGN 91 1930's. It is virtually identical to the structure of the repeaters manu- factured by the Bell Telephone Laboratories for the cables laid in 1950 between Key West and Havana.' The functions of the enclosure are to protect the repeater unit from the effects of water at great pressure at the ocean bottom; to provide means of connecting the repeater to the cable before laying; and to be slender and flexible enough to behave like cable during laying. How these functions are met in the design may be more readily understood by refer- ence to Fig. 17. The repeater unit, described earlier, is surrounded by a two-layer carcass of steel rings, end to end. The rings are surrounded in turn by a copper tube If inches in diameter and having a ^-inch wall. When a repeater is bent during laying by passing onto the cable-ship drum, the steel rings separate at the outer periphery of the bend and the copper tube stretches beyond its elastic limit. As the repeater leaves the drum under tension the rings separate and the copper stretches on the opposite side, leaving the repeater in a slightly elongated state. At the ocean bottom, hydraulic pressure restores the repeater to its original condition with rings abutted and the copper tube reformed. The system of seals in each end of the tube consists of (1) a glass-to- Kovar seal adjacent to the repeater unit, (2) a rubber-to-brass seal sea- ward from the glass seal, and (3) a core tube and core sleeve seal sea- ward from the rubber seal. The glass seal, although capable of withstanding sea bottom pressures, is primarily a water vapor barrier and a lead-through for electrical con- nection to the repeater circuit. In service it is normally protected from exposure to sea pressures by the rubber seal. The rubber seal, capable of withstanding sea bottom pressures, is in- deed exposed to these pressures for the life of the repeater, but is not exposed to sea water. It is likewise a lead-through for electrical connec- tion from the cable to the glass seal. The core sleeve seal is an elastic barrier betw^een sea water on the out- side and a fluid on the inside. This fluid, polyisobutylene, is a viscous honey-like substance, chemically inert, electrically a good insulator, and a moderately good water vapor barrier. It fills the long thin annular space outside the cable core and inside a copper core tube and thus becomes the medium of transmitting to the rubber seal the sea pressure exerted on the core sleeve. It can be seen that the core sleeve seal has nominally no pressure resisting function and no electrical function. The same fluid is also used to fill the space between the glass and rub- ber seals. Voids at any point in the s^^stem of seals are potential hazards to long, trouble-free life. Empty pockets, for instance, lying between the 7i 73 o o 92 FLEXIBLE REPEATER DESIGN 93 central conductor and the outer conductor, or container, are capable of becoming electrically conducting paths if filled with water vapor. As pointed out in companion papers,^' ^ the voltage between the repeater (and cable) central and outer conductors is in the neighborhood of 2,000 volts at the ends of the transatlantic system. The filling of the seal interspace with a liquid would defeat one func- tion of the rubber seal if special features were not provided in the rubber seal design. Very slight displacement of the rubber seal toward the glass seal because of sea pressure, or resulting from reduction in volume owing to falling temperature, would otherwise build up pressure in the liquid and on the glass seal. We avoid this by providing a kind of resihence in the interspace chamber. Three small brass bellows, partly compressed, occupy fixed cavities in the chamber. They can compress readily and maintain essentially constant conditions independent of external pres- sures and temperatures. The entire repeater assembly enclosed in copper is approximately 23 feet long. Tails of cable at each end make the total length about 80 feet before splicing. The central conductor of each cable tail is joined to the rubber seal central conductor, with the insulation molded in place in generally the same manner as in cable-to-cable junctions elsewhere in the system. The outer-conductor copper tapes of the cable tails are electrically connected to the copper core tubes. The copper region is coated with asphalt varnish and gutta percha tape to minimize corrosion. Over this coating bandage-Hke layers of glass fabric tape are built up to produce an outer contour tapering from cable diameter at one end up to repeater diameter and back down to cable diameter at the opposite end. The tape covering is saturated with asphalt varnish. This tape is primarily a bedding for the armor wires that are laid on the outside of both cable tails and repeater to make the repeater cable-like in its tensile properties and capable of being spliced to cable. In the region of the repeater proper where the diameter is double that of cable, extra armor wires are added to produce a layer without spaces. Also, to avoid subjecting the repeater to the torque characteristically present in cable under the tensions of laying, a second layer of armor wires of opposite lay is added over the first layer. This armoring process is so closely related to the armoring of cable core in a cable factory that it is performed there. Materials Following the same design philosophy applied to the repeater compo- nents, the materials of construction of the repeater container and seals 94 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 were chosen for maximum life, compatibility with each other, and for best adaptability to the design intent. Specifications particularly adapted to this use were set up for all of the some 50 different metals and non- metals employed in the enclosure design. In general, the methods es- tablished for proving the integrity of the materials are more elaborate than usual commercial practice. In most instances, such as that of cop- per container tubes, the extraordinary inspection for defects and weak- nesses with its resulting rejection rate, resulted in high cost for the usable material. TESTING A substantial part of the development work on the repeater enclosure was concerned with devising tests that give real assurance of soundness and stability. It is beyond the scope of this paper to discuss how each part is tested before and after it is assembled but certain outstanding tests deserve mention. Steel Ring Tests Each of the inner steel rings, before installation, is required to pass a magnetic particle test to find evidence of hidden metallurgical faults. Each ring is later a participant in a group test under hydraulic pressure simulating the crushing effect of ocean bottom service but exceeding the working pressures. The magnetic particle test is repeated. Helium Leak Tests Both glass and rubber seal assemblies, before being installed in re- peaters, are required to undergo individual tests under high-pressure helium gas. Helium is used not only because its small molecules can pass through smaller leaks than can water molecules but because of the ex- cellent mass spectrometer type of leak detectors commercially available for this technique. While helium is applied at high pressure to the outer wall of the seal, the inner wall is maintained under vacuum in a chamber joined with the leak detector. The passage of helium through a faulty seal at the rate of 10~^ milliliters per second can be detected. Stated differently, this is 1 milliliter of helimn in 30 years. The relation of water-leak rate to helium-leak rate is dependent on the physical na- ture of the leak, but if they were assumed to be equal rates, the amount of water which might enter a tested repeater in 20 years would be 0.66 grams. A desiccant within the repeater cavity is designed to keep the FLEXIBLE REPEATER DESIGN 95 relative humidity under 10 per cent if the water intake were five times this amount. After glass seals are silver brazed into the ends of the copper tube of the repeater the helium test is repeated to check the braze and to re- check the seal. For this test the entire repeater must necessarily be sub- merged in high pressure helium. Obviously, in order to sense a possible passage of the gas from the outside to the inside, the leak detector vac- uum system must be connected to the internal volume of the repeater. For this and other reltsons a small diameter tube that by-passes the seal is provided as a feature of the seal design. After the leak integrity of the repeater is established by this means for all but the access tube, this tube is then used as a means of vacuum drying the repeater and then filling it with extremely dry nitrogen. Following this, the tube is closed by welding and brazing. This closure is then the only remaining leak possibility and is checked by a radioisotope leak test. Radioisotope Leak Test Of various methods of detecting the passage of very small amounts of a liquid or a gas from the outside to the inside of a sealed repeater, a scheme using a gamma-emitting radioisotope appeared to be the most applicable. The relatively small region of the welded tube referred to above is surrounded by a solution of a soluble salt of cesium^^^. With the entire repeater in a pressure tank, hydraulic pressure in excess of service pres- sures is applied for about 60 hours. The repeater is removed from the tank, the radioactive solution is removed and the test region is washed by a special process so as to be essentially free from external radioac- tivity. A special geiger counter is applied to the region. If there has been no leak the gamma radiation reads a low value. If an intake has occurred of as much as one milligram of the isotope solution, the radiation count is about four to five times greater than that of the no-leak condition. The rate of leak indicated is an acceptable measure of soundness of the repeater closure. The helium and subsequent isotope leak tests are made on a repeater not only when its glass seals are installed but are performed again on each rubber seal after it is brazed in place. Electrical Tests Prior to assembly into the repeater the various networks are tested under conditions simulating as nearly as is feasible the actual operating 96 THE BELL SYSTEM TECHNICAL JOUKXAL, JANUARY 1957 50 40 30 20 ^ 10 u liJ Q 0 z -10 < o -20 -30 -40 -50 0 s 's. / ^ y / \ 1 \ GAIN / vA / ^-j ^; — •> PHASE \ 1 / ^ V \ \ \ — ..-'' — ^, \ \ \ PHASE \ \ \ \ 160 120 80 40 -40 -80 LU LU a. UJ Q UJ _l z < UJ If) < I Q. -120 -160 5 1.0 2 5 10 20 50 100 200 500 1000 2000 5000 10,000 FREQUENCY IN KILOCYCLES PER SECOND Fig. 18 — • Mu Beta gain and phase. conditions of the particular network. The input and output coupling networks and the beta networks enter directly into the insertion gain and hence are held to very close limits. To ensure meeting these limits elements which go into a particular network are matched and adjusted as a group before assembly into the network. Repeater units are tested for transmission performance both before and after closing. These tests consist of; mu-beta measurements (simul- taneous measurements of gain and phase of the feedback loop); noise; modulation; insertion gain at many frequencies; exact f requeue}^ of the fault location crystal and crystal peak gain. Modulation and crystal frequency measurements are made with the repeater energized at 225 milliamperes cable current and also at 245 milliamperes as a check on the ultimate performance of the whole sj^stem initially and after aging. PERFORMANCE OF REPEATERS The phase and gain characteristics of the feedback loop of the repeater are shown in Fig. 18. It will be noted that at the upper edge of the band the feedback is a little less than the 33-34 db set as the objective. Addi- tional elements could have been used in the interstages to increase the feedback but the return per element is small. Since an}' element is a potential hazard, the lower feedback is acceptable. FLEXIBLE REPEATER DESIGN 97 <3 0.1 U LU a z o 5 -0.1 lU D < -0.2 J^ /_^ -^ r V ^ N \ \ \ I 1 20 40 60 80 100 120 140 FREQUENCY IN KILOCYCLES PER SECOND 160 180 Fig. 19 — Repeater deviation from 36.9 NM design cable. The deviation of the insertion gain of the repeater from the loss of 36.9 nautical miles of design cable^ at sea bottom is shown in Fig, 19. This is well within the objective of =t0.05 db. It has been pointed out that the repeater input and output impedance do not match the cable impedance. This results in ripples in the system frequency characteristic due to reflections at the repeater. These are shown in Fig. 20. The noise performance of the repeater is determined by the input tube and the voltage ratio of the input coupling network. Amplifier noise referred to the input is shown in Fig. 21. At the upper frequencies the 10 15 20 25 30 35 40 45 FREQUENCY IN KILOCYCLES PER SECOND 65 60 Fig. 20 — Interaction ripple for TAG sj'stem. 98 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 repeater contribution to cable noise is very small. At the lower frequen- cies, while the repeater noise is considerably greater than thermal noise, this does not degrade performance because of the lower cable attenua- tion at these frequencies. MANUFACTURING DRAWINGS Because of the extraordinary nature of many of the manufacturing problems associated with undersea repeaters it was determined at the outset that a so-called single-drawing system would be used. For this reason, considerably more information is supplied than is normal. The effect is illustrated best in the rather large number of drawings that consist of text material outlining in detail a specific manufacturing technique. Such drawings specify the devices, supplies and work ma- terials needed to perform an operation, and the step-by-step procedure. Of course, these papers are by no means a substitute for manufacturing skill. Primarily they insure the continuance of practices proved to be effective with the Havana-Key West project. REPAIR REPEATER The "repair repeater," used to offset the attenuation of the excess cable which must be added in making a repair, is basically the same general design as the line repeater. It employs a two-stage amplifier, designed to match the loss of 5.3 nautical miles of cable to within ±0.25 db. The larger deviation compared to the line repeater is permissible since few repair repeaters are expected to be added in a cable. The input 1,0 a. LJ I > o m ^ 6 1/1 _l lil UJ ^ Q z UJ 2 in o z 0 V \ \ \, \ \^ "^ -\ "~~^ 20 40 60 80 100 120 140 FREQUENCY IN KILOCYCLES PER SECOND 160 Fig. 21 — Repeater noise. FLEXIBLE REPEATER DESIGN 99 and output impedances match the cable. As in regular repeaters a crys- tal and gas tube are provided for maintenance testing. The crystals give approximately 25 db increase in gain and are placed between 173.5 and 174.1 kc so as not to duplicate any frequencies used in the line repeaters. The crystal frequency spacing is 100 cycles. Wherever possible the same components and mechanical details are used in the repair repeaters as in the line repeaters. When changes in design were necessary, these were modifications in the existing designs rather than new types. Capacitors are like those of line repeaters. Ex- cept for the length of the container, the enclosure is identical to the line repeater. Noise and overload considerations restrict the location of a repair repeater to the middle third of a repeater section. UNDERSEA EQUALIZERS Even though the insertion gain of the line repeater matches the nor- mal loss characteristic of the cable rather closely, uncertainties in the knowledge of the attenuation of the laid cable can lead to misalignment which, if uncorrected, would seriously affect the performance of the system. Misalignment which has cable loss shape can be corrected by shortening or lengthening the cable between repeaters at intervals as the cable is laid. Other shapes, however, require the addition of networks or equalizers in the line. With these factors in mind a series of undersea equalizers were de- signed. The loss shapes were chosen on the basis of a power series analy- sis of expected misalignments. The designs were restricted to series im- p- -^ ^V\A/ 1 ^^wr- (a) ^/vV 4'- -^ (b) Fig, 22 — (a) Schematic of Type IV equalizer, (b) Schematic of Tj-pe V equalizer 100 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 CO _l UJ o LU a > \ TYPE EZ / /^ \ \ / / \ y / \ /^ z ^ ft in 33 2 1 TYPE 31 / / > A y / 0 - ^ ^ 20 40 60 80 100 120 140 160 FREQUENCY IN KILOCYCLES PER SECOND 160 200 Fig. 23 — Equalizer loss characteristics. pedance type equalizers to avoid the necessity for shunt arms and the accompanying high-voltage blocking capacitor required to isolate the cable power circuits. This restriction confines the ultimate location of the equalizers to the middle portion of repeater sections to minimize the reaction of the poor repeater impedance on the equahzer characteristic. The dc resistance of equalizers is low so that material increase of the system power supply voltage is not required. The configuration of two of the equalizers are shown in Fig. 22. The loss characteristics are shown in Fig. 23. Each equahzer has a maxi- mum loss spread in the pass band of about 4 db which represents a com- promise between keeping the number of equaUzers low and at the same time keeping the misalignment within tolerable hmits. The components used are modifications of the repeater components. The mechanical construction is identical to the repeater except that with the smaller numljer of elements, the container is materially shorter than a repeater. ACKNOWLEDGMENTS Scores of individuals have contributed to the development of these repeaters, some leading to basic decisions, some creating, adapting and FLEXIBLE REPEATER DESIGN 101 perfecting both electrical and mechanical designs. Many of these people have furnished the continuing drive and enthusiasm that are so essential for a team of engineers and scientists having divergent interests. It is nearly impossible to assign relative importance to the work of trans- mission engineers, apparatus designers, mathematicians and research scientists in the fields of materials and processes. Equally difficult is any realistic appraisal of the work of all of the technical aides and shop personnel whose contributions are so significant to the final product. The authors of this paper, in reporting the results, therefore acknowl- edge this large volume of effort without listing the many individuals by name. REFERENCES 1. E. T. Mottram, R. J. Halsey, J. W. Emling and R. G. Griffith, Transatlantic Telephone Cable S3^stem — Planning and Over-All Performance. Page 7 of this issue. 2. H. A. Lewis, R. S. Tucker, G. H. Lovell and J. M. Fraser, Sj\stem Design for the North Atlantic Link. See page 29 of this issue. 3. J. J. Gilbert, A Submarine Telephone Cable with Submerged Repeaters, B.S.T.J., 30, p. 65, 1951. 4. G. W. Meszaros and H. H. Spencer, Power Feed Equipment for the North At- lantic Link. See page 139 of this issue. 5. A. W. Lebert, H. B. Fischer and I\L C. Biskeborn, Cable Design and Manu- facture for the Transatlantic Submarine Cable System. See page 189 of this issue. 6. H. W. Bode, Network Analysis and Feedback Amplifier Design, D. Van Nos- trand Co., Inc. 7. H. A. Lamb and W. W. Heffner, Repeater Production for the North Atlantic Link. See page 103 of this issue. 8. J. O. McNally, G. H. Metson, E. A. Veazie and M. F. Holmes, Electron Tubes for the Transatlantic Cable Sj'stem. See page 163 of this issue. Repeater Production for the North Atlantic Link By H. A. LAMB* and W. W. HEFFNER* (Manuscript received September 20, 1956) Production of submarine telephone cable repeaters, designed to have a minimum trouble-free life of twenty years, required many new and refined manufacturing procedures. Care in the selection and training of personnel, manufacturing environment, inspection, and testing, were of great impor- tance in the successful attainment of the idtimate objective. Although quality of product has always been of major significance in Western Electric Company manufacture, building electronic equipment for use at the bottom of the ocean, where maintenance is impossible and replacement of apparatus extremely expensive, required unusual manufacturing methods. MANUFACTURING OBJECTIVE Late in 1952, the manufacture of flexible repeaters for the North Atlantic Link of the transatlantic submarine telephone cable S3"stem was allocated to the Kearny Works of Western Electric Compan3\ hi accordance with established practice in initiating radically new products and processes, production of these repeaters was assigned to the Engineer of Manufacture Organization rather than to regular manu- facture in the telephone apparatus shops. The job — to produce 122 thirty-six channel carrier repeaters and 19 eciualizers capable of operat- ing satisfactorih^ at pressures up to 6,800 pounds per square inch on the ocean floor, with minimum maintenance, for a period of at least twentj^ years. Initial delivery of repeaters was required for March, 1954, less than a year and a half after the project started. GENERAL PHILOSOPHY QuaUty has always been the prime consideration in producing appara- tus and equipment for the Bell Sj^stem. There is an economical breaking point, however, beyond which the return does not warrant the abnormal * Western Electric Company. 103 104 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 expenditures required to approach theoretical perfection. The same philosophy applies to all manufactured commodities, be they auto- mobiles, airplanes or telephone systems. In general, all of these products are physically available for preventive and corrective maintenance at nominal cost. With electronic repeaters at the bottom of the ocean, main- tenance is impossible and replacement would be extremely expensive. The general philosophy adopted at the inception of the project was to build integrity into the product to the limit of practicability. To do this, a number of fundamental premises were established, which form the foundation of all operations involved: 1 . Manufacturing environment would be provided which, in addition to furnishing a desirable place to work, could be kept scrupulously clean and free from contamination. 2. The best available talent would be screened and selected for the particular work involved. 3. Wage payments would be based on day work, rather than on an incentive plan basis, because production schedules and the complexity of the operations did not permit the high degree of standardization essential to effective wage incentive operation. 4. A sense of individual responsibility would be inculcated in every person on the job. 5. Training programs would be established to thoroughly prepare supervisors, operators, and inspectors for their respective assignments before doing any w^ork on the project. 6. Inspection, on a 100 per cent basis, would be established at every point in the process which could, conceivably, contribute to, or affect the integrity of the product. PREPARATION FOR MANUFACTURE Manufacturing Location It appeared desirable to set up manufacture in a location apart from the general manufacturing area. Experience gained to date has satisfied us that this was the correct approach, since it provided a number of advantages : 1 . Administration has been greatly facilitated by having all necessary levels of supervision located in the immediate vicinity of the work. 2. It was necessary for the people on the job to acquire and maintain a new philosophy of perfection in product, rather than a high output at an "acceptable cjuality level." This was easier at a separate location, since only one philosophy was followed throughout the plant. FLEXIBLE REPEATER MANUFACTURE 105 3. Engineering, production control, service and maintenance organi- zations were located close to actual production and had no assignments other than the project. 4. The small plant, due to its semi-isolation, tends to produce a \'ery closely knit organization and good teamwork. A large number of manufacturing locations were examined and the one selected was a one-story modern structure in Hillside, New Jersey, which provided a gross area of 43,700 square feet. The entire plant was air conditioned; in most cases, the temperature was controlled to minimum 73 degrees F, maximum 77 degrees F. The air was filtered through two mechanical and one electrostatic filters. Relative humidity was maintained at maximum 40 per cent in all but one area — the capacitor winding room — in which it was necessary to maintain maximum 20 per cent humidity to avoid mechanical difficulty with capacitor paper. While most of the air was recirculated, the air from the cafeteria, cleaning room, locker and toilet rooms was exhausted to the OUTDOOR ENCLOSURE FOR --■ COMPRESSED GASES EMPLOYEES' PARKING CAPACITY 125 CARS A,B,C,D,E INDICATE CLASSIFICATION OF AREA Fig. 1 — Plant laj'out. 106 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 outside atmosphere. Two separate air conditioning systems were in use. One, of 300 tons capacity, provided for most of the plant, while a smaller unit of 30 tons capacity served the capacitor winding, testing, and im- pregnating rooms. Each installation had its own air filtering and condi- tioning equipment. Plant Layout The plant layout is illustrated in Fig. 1. All working areas, with the exception of the repeater enclosure area, were individually enclosed, and walls from approximately four feet above the floor were almost entirely of reinforced glass. This arrangment facilitated supervision by other than first-line supervisors, who were located with the groups, and provided a means of viewing the operations by the many visitors at Hillside, without contaminating the critical areas or disturbing the operators. Analysis of Design for Facilities and Operations In analyzing the design for manufacture there were, of course, numer- ous instances where conventional methods and facilities were entirely adequate for the job. Since their inclusion would contribute little to this article, we shall confine the description to those cases which are new or unusual. Collaboration with Bell Telephone Laboratories in Preparation of Manu- factoring Informatio7i Early in 1953 a coordination committee was established, consisting of representatives from the various Laboratories design groups and Western engineers, which met on a bi-weekly basis during the entire period preceding initial manufacturing operations. These meetings provided a clearing house for questions and policies of a general nature for this particular project and served to keep all concerned informed as to the progress of design and the preparations for manufacture. It is customary, during the latter stages of development of any project at the Laboratories, for Western engineers to participate in the prepara- tion of manufacturing information as an aid in pointing the design to- ward the most economical and satisfactory production methods and facilities. Since the decision to use the Bell System repeater in the Trans- atlantic system was based on the performance of the Key West-Havana installation, and the fact that changes in design would require further FLEXIBLE REPEATER MANUFACTURE 107 trials over an extended period of time, only minor changes to facilitate manufactm'e were made. Further, since some experience had been gained by the Laboratories in producing repeaters for that installation, it was decided to "pool" effort in preparing the manufacturing process informa- tion, which is normally Western's responsibility. Close cooperation of the two groups, therefore, has resulted in the production of repeaters which are essentially replicas of those in the initial installation except for the internal changes necessary to increase transmission capacity from 24 to 36 channels. Other Western Electric Locations and Outside Suppliers During the development work on the Key West-Havana repeaters, the Hawthorne Works of Western Electric had furnished the molyb- denum-permalloy cores for certain inductors, the Tonawanda Plant had furnished mandrelated resistance wire, and the Allentown Plant had fabricated the glass seal subassemblies. Since the experience gained in this development work was extremely valuable in producing the additional material required for the Transatlantic system and since the facilities for doing the work were largely available, these various locations were asked to furnish similar material for the project. Although the Kearny Crystal Shop had not been involved in the Key West-Havana project, arrangements were made there to make the crystals for this project, since facilities were available, along with considerable experience in producing precision units. Subcontracted Operations While it was believed, initially, that all component parts for repeaters should be manufactured by Western Electric, critical analysis indicated that it was neither desirable nor economical in certain cases. One of the outstanding examples in this category is the hardened and ground chrome-molybdenum steel rings that constitute the strength members in the repeater and sustain the pressures developed on the ocean bottom. Purchasing the many large and varied machine tools and associated heat treating equipment necessary to produce these parts would have required a substantial capital expenditure and additional manufacturing space. Arrangements, therefore, were made with a highly qualified and well equipped supplier to produce the rings, using material furnished by Western, which had been previously inspected and tested to \'ery strin- gent requirements. 108 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 The situation attending the manufacture of a relatively small number of comparatively large copper parts used in the rubber and core tube seals was much the same. Here, again, the large size machine tools and additional manufacturing space, required for only a short time, would have increased the over-all cost of the project considerably. These parts, therefore, were subcontracted in the local area and inspection was per- formed by Hillside inspectors. A safeguard, in so far as integrity is concerned, was provided by the fact that these were individual parts that could be reinspected at the time of delivery. No subassembly operations that might possibly result in oversight of a defect, were subcontracted. Manufacturing Conditions Two major problems confronted us in planning the manufacture of repeaters. First, to produce units that were essentially perfect; and second, to prevent the contamination of the product b}^ any substance that might degrade its performance over a long period of time. In ap- proaching both of these objectives, it was realized that the product had a definite economic value which the cost of production should not exceed. In many cases, therefore, it was necessary to rely on judgment, backed by considerable manufacturing experience, in determining when the "point of no return" had been reached in refining processes and practices. The initial approach to this phase of the job was to classify, with the collaboration of Bell Telephone Laboratories, all of the manufacturing operations involved as to the degree of cleanliness required. In setting up these criteria, it was necessary to evaluate the importance of contami- nation in each area and the practicability of eliminating it at the source or to insure that whatever foreign material accumulated on the product was removed. A representative case is the machining of piece parts. While the shop area is cleaner, perhaps, than any similar area in industry, the \evy nature of the work is such that immediate contamination cannot be avoided since material is being removed in the form of chips and turn- ings, and a water soluble oil is used as a coolant. In this instance, however, the parts can be thoroughly cleaned and their condition observed before leaving the area. Conversely, in the case of an operation such as the assembly of paper capacitors into a container which is then hermetically sealed, it is vitally necessary to insure that both the manufacturing FLEXIBLE REPEATER MANUFACTURE 109 area and the processes are free from, and not conducive to producing, particles of material which are capable of causing trouble. The various classifications established for the production areas include specific requirements as to temperature, relative humidity, static pres- sure with respect to adjacent areas, cleanliness in terms of restrictions on smoking and the use of cosmetics and food, and the type and use of special clothing. Special Clothing Employees' clothing was considered one of the most important sources of contamination for two reasons; first, for the foreign material that could be collected upon it and carried into the manufacturing areas, and second, that various types of textiles in popular use are subject to con- siderable raveling and fraying. After considerable study of many types of clothing for use in critical areas, the material adopted was closely woven Orion, which has proved to be acceptably lint-free. The complete uniform — supplied at no cost to employees — consists of slacks and shirts for both male and female employees, Orion surgeon's caps for the men and nylon-visored caps for the women. In addition shoes, without toecap seams, were provided. Nylon smocks were furnished to protect the uniforms while employees moved from locker rooms to the entrance vestibule. Two changes of clothing were provided each week, and the laundering was done by an outside concern. Employees to whom this special clothing was issued were paired for locker use. Both kept their uniforms and special shoes in one locker and their own clothes and shoes in the other. This prevented the transfer to the uniforms of any foreign material that might exist on the street clothing. At the entrance vestibule to the A, B, and C areas (Fig. 1) the employees were required to clean their shoes in the specially designed facilities provided and to wash their hands in the wash basins installed for this purpose. Smocks were then removed and hung on numbered hooks that line the walls at the end of the vestibule. Employees were then permitted to go to their work positions within the inner areas. At any time that it was necessary for employees to leave the work areas for any purpose, they were required to put on their smocks in the vesti- bule and upon their return, to go through the cleaning procedure again. Employees in the other areas were provided only with smocks, mainly for the protection of their clothes since the work invoh-ed could soil or stain them but could not be contaminated from the clothing. 110 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 Cleaning Schedules were established for cleaning the areas at regular intervals, the frequency and methods depending upon the type of manufacturing operations and the activity. Usually, the vinyl plastic floors were ma- chine scrubbed and vacuum dried. Walls, windows and ceilings were cleaned by hand with lint-free cloths. Manufacturing facilities such as bench tops, which were linoleum covered, were washed daily. Test sets, cabinets, test chambers and bench fixtures W'Cre also cleaned daily. Hand tools were cleaned at least once a week by scrubbing with a solu- tion of green soap, rinsing in distilled water, followed by alcohol and then dried in an oven. Dust Cou7it Since it was impossible to determine what contaminating material in the form of air-borne particles might be encountered from day to day, and what the effect might be during the life of the repeaters, the general approach to this problem was to control, so far as possible, the amount of dust within the plant. In order to verify, continuously, the over-all effectiveness of the vari- ous preventive measures, dust counts were made in each classified area at daily intervals, using a Bausch and Lomb Dust Counter. This device combines, in one instrument, air-sampling means and a particle-counting microscope. Over a two-year period it has been possible to maintain, in certain areas, a maximum dust count of between 2,000 and 3,500 particles per cubic foot of air with a maximum size of 10 microns. Control checks, taken outside the building at the employees' entrance, generally run upwards of 25,000 particles per cubic foot, a good portion of which are of comparatively large size. PRODUCTION AND PERSONNEL Equipping the plant, obtaining and installing facilities, and selecting and training personnel proceeded on a closely overlapped basis with receipt and analysis of Bell Telephone Laboratories' product design information. Because of the critical nature of the product, provisions were made not only for the most reliable commercially available utilities and services, but also for emergency lighting service in some areas. Maintenance and service staffs had to be built up rapidly as the super- visory and manufacturing forces were being developed. FLEXIBLE REPEATER MANUFACTURE 111 "Qualification" of All Personnel Before employees were assigned to production work the^^ were re- quired to pass a qualification test estaljlished by the inspection organi- zation to demonstrate satisfactory performance. Programs were, there- fore, set up for "vestibule" training and qualification of new employees. This activity was carried on by full-time instructors who had been trained by Western and Bell Laboratories engineers. Training was carried out in two stages: 1. (a) The employee received instruction and became acquainted with equipment and requirements, (b) A practice period in which the employee developed technic{ues and worked under actual operating conditions, with all work submitted to regular inspection. 2. A qualification period in which the employee was required to demonstrate that work satisfactory for project use could be produced. The main objective during stage 1 was progressive quality improve- ment and in stage 2 the maintenance of a satisfactory quality level over an extended period of time. Employees made a definite number of units at acceptable quality levels in order to qualify. The number of units required for training varied with the type of work and the ease with which it was mastered. All personnel were required to pass qualification tests before being assigned to production work and were restricted to that work unless trained and qualified for other work. Employees trained on more than one job were requalified before being returned to a previous assignment. Records of the performance of individual operators started in the training stage were continued after the employees were assigned to production work. The performance record of the operators was based on results obtained during the inspection of their work, while that of the inspectors was based on special quality accuracy checks of their work. Personnel Selection It was apparent that the new manufacturing techniques, including the cleanliness and quality demands, would necessitate that all shop supervisors and employees be very carefully selected. It also appeared (and this was subsequently confirmed) that after the careful selection and training of supervisors, long training periods would be required for specially selected shop emploj^ees. In selecting first line shop supervisors, such factors as adaptability, personality, and ability to work closely with the engineers were of para- mount importance. For the parts and apparatus included in their re- 112 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 sponsibility, they were required to thoroughly learn the design, the operations to be performed, the facilities to be used, the data to be recorded, the cleanliness practices to be observed ■ — and in most cases, prepare themselves to be able to do practically all of the operations, be- cause subsequently they had to train selected operators to perform criti- cal operations to very high quality standards under rigidly controlled manufacturing conditions. As shop supervisors and employees were assigned to the manufacture of repeaters, they were thoroughly indoc- trinated in the design intent and the new philosophy of manufacture. Standard ability and adaptability tests were used in a large number of cases to assist in proper selection and placement of technicians. Tests for finger and hand dexterity; sustained attention; eyes, including per- ception and observation; and reaction time of the right foot after a visual stimulus. (The latter test was relatively important for induction brazing operations.) Other requisite considerations were a high degree of de- pendability and integrity, involving intellectual honesty and conscien- tious convictions; capability of performing tedious, frustrating, and exasperating operations against ultra-high quality standards, verifying their own work; perseverance and capability to easily adapt to changes in assignment and occupation or the introduction of design changes. We considered whether or not they would stand up under "fishbowl" operations, wherein they would receive a considerable amount of ob- servation from high levels of Western Electric Company and Bell Sys- tem management and other visitors. Also, could they duplicate high quality frequently after quahfying for a particular operation? During the period of repeater manufacture, the number of employees rose from less than 50 in January, 1954, to a maximum of 304 by Feb- ruary, 1955, after which there was a gradual reduction to a level of about 265 employees for six months and then a gradual falling off as we were completing the last of the project. In the period from May to December, 1954, between 30 and 45 employees were constantly in training prior to being placed on productive work. During 1955 this decreased to prac- tically no employees in training during the midpart of the year and there- after training was required merely to compensate for a small labor turn- over and employee reassignment. It is significant that labor turnover was very low and attendance was exceptionally good during the life of the Hillside operations. Personnel Training The original plan, which was generally followed, was to prove in the tools for each phase of the job, followed by an intensive program of train- FLEXIBLE REPEATER MANUFACTURE 113 ing. Indoctrination of laboratory technicians could be considered as "vestibule training" in that they were acclimated to the area and con- ditions, given oral instruction in the work, then given practice materials and demonstrations and, when qualified, were started on making project material. To do this, extra supervisors were required at the beginning of the job. A supervisor trained a few employees, qualified some of them, and began work on the project. Another supervisor was then required to train additional employees who, as they became cjualified, were trans- ferred to the supervisor responsible for making project apparatus. Addi- tional testing of the employees, instruction and reinstruction and, in some cases, retraining were required. In practically all cases, we were able to fit an employee selected for work at Hillside into some particular group of operations. The extra emphasis on selection and training cre- ated a well-balanced team that later resulted in considerable flexibility. During all of this training our supervisors worked closely with engineers and inspectors who understood the design intent and the degree of per- fection required. At the beginning, each technician was trained for only one operation of a particular job, such as (1) winding Type X capacitors or (2) im- pregnating all paper capacitors or (3) winding Type Y transformers and so became an expert on this one operation. Later, the tours of duty for many technicians were broadened to cover several operations. Communications To keep employees informed, we occasionally assembled the entire group, presenting informative talks on current production plans and our future business prospects. Motion pictures were shown of the cable laying ships and the operations of cable splicing and cable laying. A dis- play board, showing all of the repeater components, was mounted on the wall of the cafeteria. This informed the operators just where the parts were used in apparatus; also, just where their products went into the wired repeater unit, and how all electrical apparatus was enclosed against sea pressure in the final repeater. In small groups, all of the em- ploj^ees at Hillside were gi\'en a short guided tour of the plant to see the facilities and hear a description of the operations being performed in each area. These communications were extended to everyone at the Hillside Plant, including those who did not work directly on the product. It was our conviction that the maintenance men, boiler operators, oilers, station wagon chauffeur, janitors, and clerical workers in the office were all interested and could do a better job if kept informed of the needs and progress of the project. 114 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 Scheduling Capacity was provided at the Hillside Shop to manufacture a max- imum of 14 repeaters in a calen(hir month. This envisioned 6-day opera- tion with some second and thii'd shift operations; due allowance was made for holidays and vacations, so that the annual rate would be ap- proximately 160 enclosures per year. (An enclosure is either a repeater or an equalizer.) Some of the facilities and raw materials were ordered late in 1953. This ordering expanded early in 1954 and continued through 1955 to include parts to be made by outside suppliers and the parts and appara- tus to be made at Hillside. Apparatus designs were not all available at the beginning of the job, and the ultimate quantities required were also subject to sharp change as the project shaped up, thus further compli- cating the scheduling problem. Because of the time and economic factors involved, coupled with the developmental nature of the product and processes, one of the most difficult and continuing problems was the balancing of production to meet schedules. For this task, we devised "tree charts" for the apparatus codes and time intervals in each type of repeater or equalizer for each project. Each chart was established from estimates of the time required to accomplish the specified operations and the percentage of good prod- uct each major group of operations was expected to produce. RAW MATERIALS Many of the specifications were written around the specific needs of the job and embodied requirements that were considerably more strin- gent than those imposed on similar materials for commercial use. As a result, it was necessary for many suppliers to refine their processes, and, in some cases, to produce the material on a laboratory basis. One example is the container, or repeater enclosure, which consists, in part, of a seamless copper tube approximately If inches in diameter having a ^-inch wall and approximately 8 feet long. This material was purchased in standard lengths of 10 feet. The basic material was re- quired to be phosphorous deoxidized copper of 99.80 per cent purity. The tubing, as delivered, had to be smooth, bright, and free from dirt, grease, oxides (or other inclusions including copper chips), scale, voids, laps, and slivers. Dents, pits, scratches, and other mechanical defects could not be greater than 0.003 inch in depth. The tubing had to be concentric within 0.002 inch and the curvature in a 10-foot length not exceed | inch to facilitate assembly over the steel rings. FLEXIBLE REPEATER MANUFACTURE 115 Only one supplier was willing to accept orders for the tubes, and only on the basis of meeting the mechanical requirements on the outside sur- face. To establish a source of supply, it was necessary to accept the sup- plier's proposal on the basis that some of the tubes produced could be expected to meet requirements on the inside as well as the outside sur- face. Inspection of the inside surface was performed with a 10-foot Bore- scope. The supplier then set aside, overhauled, and cleaned a complete group of drawing facilities for this project. In addition, a number of refinements were made in lubrication and systematic maintenance of tools. After all refinements were made and precautions taken, however, the yield of good tubes in the first 400 produced was less than 1.0 per cent. Consulta- tions with Western and Bell Laboratories' engineers, and with the sup- plier's cooperation, raised the yield to approximately 50 per cent. Procurement of satisfactory mica laminations for capacitors intro- duced an unusual problem. The best grade of mica available in the world market was purchased which the supplier, under special plant condi- tions, split and processed into laminations. Despite care in selection and processing, only 50 per cent of the 250,000 laminations purchased met the extremely rigid recjuirements for microscopic inclusions and delam- inations, and less than 8 per cent survived the capacitor manufacturing processes. A large number of the parts, and the most complex, are made from methyl-methacrylate (Plexiglass). At the time manufacture began, there was little, if anj^, experience or information available on machining this material to the required close tolerances and surface finish. Consequently, considerable pioneering effort was expended in this field before satis- factory results were obtained. The methacrylate parts cover a wide range of size and complexitj^ — from l|-inch diameter by 4|-inch long tubular housing to tiny spools |-inch diameter and j^-inch long. Most of the parts are cylindrical in shape with some semicylindrical sections that must mate with other sections to form complete cylinders. Others have thin fins, walls, flanges and projections. Five representative parts are shown in Fig. 2. Methyl-methacrylate has a tendency to chip if tools are not kept sharp and care is not used in entry or exit of the tool in the work, particularly in milling. In some cases, it is necessary, with end-milling, to work the cutter around the periphery of the area for a slight depth so that sub- sequent cuts will not break out at an unsupported area. Normall}^, with a sharp cutter and a 0.010-inch finish cut, and a slow feed, chipping will not result. High-speed steel tools with zero rake were used for turning 116 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 O cc 01 o FLEXIBLE REPEATER MANUFACTURE 123 that the glass seal contain a minimum of residual tensile stress. These two problems were resolved collectively by performing the sealing opera- tion on a single spindle glass sealing machine. Accurate positioning of the glassware and sealing fires, together with precise timing and tem- perature controls, achieved the desired results. Evaluation of residual stresses were made by inspections using a polarimeter and by a thermal shock test. The maximum safe stress was established at 1 .74 KG/mm^. The thermal shock test required successive immersion of the unit in boiling water and ice water. The electrical char- acteristics of these units exceeded all others made previously by Western Electric. The ratio of reactance to effective resistance ("Q") was greater than 175,000 — twice that ever previously produced and 17 times that required in the average filter crystal. Stabilit}^ for frequency and resistance was assured by a 28-day aging test. During this period, precise daily resonant frequency and resistance measurements were recorded against temperature within 0.1° C. The maximum permissible change was 0.0005 per cent in frequency and -f5 per cent to — 10 per cent in resistance. GLASS SEALS MANUFACTURED AT ALLENTOWN The glass seal used to close each end of the container for the repeaters and equalizers is manufactured at the Allentown Works of the Western Electric Gompany. The unit is essentially a glass bead-type seal. It insulates the central conductor of the repeater from the container and serves as a final vapor barrier between the cable and the interior of the repeater. As such, it backs up several other rubber and plastic barriers as shown in Fig. 3. Fig. 4 shows the various components, subassemblies, and a cross-sec- tion of the unit. The unit consists of the basic seal brazed in the Kovar outer shell, to which is brazed a copper extension provided with two brazing-ring grooves. One of these grooves is used in brazing the seal, along with support members, into a length of container tubing in the same manner as the seal is ultimately brazed into the repeater. Packaging of the seal in this manner was necessary to pressure test the seal. Under test, in a specially constructed chamber 10,000 psi of helium gas pressure was applied to the external areas of the packaged glass seal and a mass spectrometer type leak detector was connected through the tubulation to the internal cavity of the packaged unit. In this manner, the interface of the glass to metal seal, the brazed joints, and the porosity of the metal were checked for leakage. The unit is left in this package for delivery to provide protection during shipment. Before the seal could be used. 124 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 it was machined from the package by cutting the copper extension to length, leaving the second groove for use in brazing the seal to the re- peater and removing the container tubing and the support members. The basic seal consists of the cup, central conductor and glass. The cup (smaller cylindrical item in the upper lefthand corner of Fig. 4) was machined from Kovar rod. The wall of the cup is tapered from a thickness of 0.025 inch at the base to 0.002 inch at the lip. The last O.OOG inch of the lip is further tapered from this 0.002 inch to a razor edge. The internal surface is better than a 63-micro-inch turned finish and was also liquid honed to give it a uniform matte finish. The central con- ductor (slim piece in the upper right-hand corner of Fig. 4) was also machined from Kovar rod. Both the cup and central conductor were further processed by pickling, hypersonically cleaning in deionized water, and decarburizing. The glass, a borosilicate type of optical quality, was cut from heavy walled tubing. The glass tubing was hand polished, lapped and etched to remove surface scratches, and to arrive at the spe- cified weight. It was also fire polished and hypersonically cleaned to remove all traces of surface imperfections and to assure maximum clean- liness. In order to make the basic glass seal, the metal parts had to be oxidized under precisely controlled conditions. For the oxidizing operation, a suitable fixture was loaded with brazed shell-cup assemblies, central conductor assemblies, and a Kovar disc, which had been prepared in precisely the same manner as the cups and central conductors. The disc was carefully weighed before and after oxidizing and the increase in weight divided by the area involved yields the weight gain due to oxida- tion for each run. Limits of 1.5 to 2.5 milligrams per square inch of oxide were set. This operation was performed by placing the loaded, sealed retort, through which passed a metered flow of dried air, into a furnace for a specified time-temperature cycle. In the glassing operation the oxidized shell assembly, the carbon mold and the central conductor were placed in a fixture and held in the proper relationship. The carbon mold served to support the glass, while it was being melted, in that section between the cup and central conductor where the glass was normally unsupported. The prepared cut glass tubing was loaded into the Kovar cup and the fixture was sealed into the retort. During the glassing cycle, a constant flow of nitrogen passed through the retort to provide an atmosphere Avhich minimized any reduction or further oxidation of the already carefully oxidized parts. After the proper purging period, the retort was placed in the furnace. In the furnace, the glass melted and formed a bond with the oxidized Kovar of the cup and FLEXIBLE REPEATER MANUFACTURE 125 central conductor to form the seal. After the specified temperature-time cycle, the retort was removed from the furnace, allowed to partially cool and then placed into an annealing oven. Vertical furnaces and retorts were used for brazing, decarburizing, oxidizing and glassing. By varying the type of gases flowing into the retorts, atmospheres which are reducing, oxidizing, or neutral were ob- tained. To provide maximum uniformity of process, separate retorts and holding fixtures were provided for operations involving hydrogen and for air-nitrogen operations, so that a retort or a fixture used for hydrogen treatments was never used for oxidizing or glassing. PILOT AND REGULAR PRODUCTION We called our first efforts Practice Parts and Training; the next we called Pilot Production. Next, certain items identified as Trial Laying Repeaters and Oscillators were manufactured for use in "proving in" the ship laying gear. To prove in manufacturing facilities, a few un- equipped housings were made without the usual electrical components normally in a repeater. Similarly, each of the apparatus components and parts required exploratory and pilot effort before regular production could be undertaken. As might be expected, the manufacturing yield of components meeting all requirements was very low during the early stages of the undertaking. However, substantial improvement was brought about as experience was gained. Comments on some of the production problems, highlights, and yield results, follow. Paper Capacitors were manufactured only after painstaking qualifying trials and tests had been performed on each individual roll of paper. Cycling and life testing, procurement of acceptable ceramic parts and gold-plated tape and cans, selection and matching of rolls of paper for winding characteristics, and similar problems, all had to be completely resolved to a point of refinement previously unattempted for telephone apparatus. Composite percentage yield for all operations on paper capacitors is shown in Fig. 5. Yield is shown as the ratio of finished units of acceptable quality to the number of units started in manufacture. Mica Capacitors were made from only the most meticulously selected laminations, as mentioned earlier. Even the best mica is particularly susceptible to damage in processing. In spite of experience and knowl- edge of this, the multiple handling of the laminations contributed an unusually high material shrinkage as each separate lamination needed to be cleaned, then handled individually many times through the proc- 126 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 80 75 70 65 60 Q m 55 >- £50 LLI U tr 45 40 35 30 25 20 JFMAMJJASONOJFMAMJJASONDJFMAMJJASOND 1954 1955 1956 Fig. 5 — Paper capacitor yield. esses. The art of silk screening was applied to deposit silver paste in a specific area or areas on each side of a lamination. A sharply defined rectangular area was required so that when superimposed one over an- other the desired capacitance would be obtained. Cementing of mica laminations onto machined methacrylate forms presented some addi- tional problems through the bowing of the mica laminations as the ce- ment cured. Obtaining screens that would give the proper length and width dimensions for the coated area, was another problem. A silk screen woven of strands of silk obviously limits, by the diameter of the threads, the extent to which the dimensions of an opening may be increased or decreased. Beryllium copper U-shaped terminals were used to clamp the layers of mica together into a stack. Control of the pressure used in crimping these terminals was found to be very critical in view of the exceptionally tight limits on capacitance and stability. Fig. 6 shows the composite yield at various times for all mica capacitors. Resistors. There were three designs of ceramic resistors, which were resistance-wire wound on ceramic spools. These were intended to be assembled into the hole inside the core tube on which the paper capaci- tors were wound. Special winding machines equipped with binocular FLEXIBLE REPEATER MANUFACTURE 127 80 75 70 65 60 ^ 55 V ^50 LU o CL 40 35 30 25 20 1 / » i\/ / ^ N / \ / ^ — ^ I \l NO PRODUCTION Al 1 1 1 1 1 »i' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 JFMAMJJA5ONDJFMAMJJASONDJFMAMJJASON0 1954 1955 1956 Fig. 6 — Mica capacitor yield. attachments were necessary to wind these resistors. Other resistors were hand wound on methyl-methacrylate forms, or on the outside of the ceramic containers, for certain types of paper capacitors. Rough adjust- ments were required of the lengths of resistance wire prior to winding, and close adjustments to resistance values were made after the windings were completed and before leads were attached to resistors. Again it was necessary to provide periodic samples that could be placed on life test by the Laboratories to ascertain that the manufacturing processes were under control. These samples, in all possible cases, were taken from prod- uct that would normally be rejected because of some minor defect, but which would not in any way detract from the validity of the life tests. The making of hard solder splices between nichrome resistance wire and gold-plated copper leads, and keeping ceramic parts from coming in contact with metal surfaces and thereby being contaminated because of the ceramic's abrasive characteristics, were two major problems on resistors. Fig. 7 indicates resistor jdelds. Inductors comprised 20 different designs, most of which were air core, but there were some for which it was necessary to cement permalloy dust cores into pockets of the methacrylate form, and thereafter using 128 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 90 85 80 75 70 a y 65 >- 5 60 uj u (r 55 LU Q. 50 45 40 35 30 » r-^ / \A /CURRENT / M A / / M A r / -I lA --, J — —"^CUMULATIVE 1 - -' V 1 f\A / / V ^ k^ / ' \ \ r 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 JFMAMJJASONO JFMAMJJASONO 1954 1955 JFMAMJJASONO 1956 Fig. 7 — Resistor yield. wire on a shuttle, wind by hand the turns required to produce an in- ductor. These varied from a very small inductor, smaller in diameter than a pencil, to a fairly large "figure eight" inductor with turns having a major diameter of about Ij inches. Each layer of a winding was in- spected with a microscope to insure that the wire had not been twisted or kinked, or that the insulation was damaged or uneven. Some of the shuttles became fairly long so that they could hold the amount of wire required to make a continuous winding. The operator's handling of this shuttle, as she moved it down around the openings in the methacrylate part, or placed it on a bench to proceed with the interleaving tape, de- manded considerable dexterity and concentration to insure that the shuttle was not turned over — which in effect would put a twist in the wire. Although best known means were used to sort cores for their mag- netic properties prior to the time a winding was made, the limits on the inductors themselves were so close that subsequently a large number of windings were lost. The best cores that could be selected, plus the best winding practice, could not produce 100 per cent of the inductors within the required limits. Crazing of the insulation on the wire; cementing together of two methacrylate parts or of permalloy cores into pockets of FLEXIBLE REPEATER MANUFACTURE 129 90 85 M;^ ^_^^/\cuRRENT / \ \ / \ 80 ji .1 \l Xj . / ^ rr^-'T' ^ \l ^-CUMULATIVE 75 70 65 60 55 50 45 40 35 \r \ 1 1 \ f V \\ A .^0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 J FMAMJJASONDJFMAMJJASONO 1954 1955 JFMAMJJASOND 1956 Fig. 8 — Inductor yield. methaciylate parts, and handling those inductors having long delicate leads, were the most troublesome items on this apparatus. Fig. 8 shows manufacturing yield for inductors. Networks combined several codes of component apparatus, such as a mica and a paper capacitor, resistor and an inductor. Six networks were used in each repeater unit consisting of two interstage networks, an input, an output, and two beta networks. They demanded a most delicate wiring job in that stranded gold-plated copper wires had to be joined in a small pocket in methyl methacrylate, where a minimum amount of heat can be applied; otherwise the methacrylate is affected. After soldering, a minimum amount of movement of the stranded wire was permitted, inasmuch as the soldered gold-plated copper wire be- comes quite brittle. Repeater Units, are wired assemblies consisting of seventeen sections in which there are six networks, three electron tubes, one gas tube, one crystal, three high voltage capacitors, one dessicator and two terminal sections. The successive build-up of these materials left little chance to make a repair because a splice in a lead was not permissible. It is during this assembly stage that a repeater received its individual identitj^ be- 130 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 cause of the frequency of the particular crystal assembled into the unit. A manufacturing yield of 100 per cent was achieved in the assembly and wiring of repeater units. It was necessary to calibrate the test equipment for this job very closel3^ Bell Telephone Laboratories and Western Electric worked at length to calibrate the testing details and the test sets for individual net- works. Adjustments in components apparatus to bring the network to the fine tolerances required were accomplished by minute scraping of the silvered mica on a mica capacitor or removing turns from wire- wound inductors. The cementing of methacrylate parts, which was a troublesome item on mica capacitors and inductors, also had to be con- tended with on networks. PACKING AND SHIPPING COORDINATION Repeaters were packed in Western Electric specially designed 34-foot long aluminum containers, weighing 1,000 pounds. Forty of these con- tainers were made by an outside firm. Fig. 9 shows two containers tied down in a truck trailer. The repeaters were nested in a pocket of polj^- ethylene bags containing shaped rubberized hair sections in order to cushion the repeaters during their subsequent handhng and transporta- tion. The instrumentation required with each case was tested, properly set, and inspected prior to its use on each outgoing case. The instruments were a shock recorder to register shocks in three planes, and a thermome- ter to register the minimum and maximum temperatures to which the repeater had been exposed. Arrangements were made with a commercial trucking company to provide three specially equipped truck trailers, which could be cooled by dry ice during hot weather and warmed by burning bottled gas during cold weather so as to control temperature within the 20-degree F. to 120-degree F. called for in the repeater spe- cification. Appointment of a shipping coordinator supervisor added tremendously to the smooth functioning of services and provided the continuing vigi- lance required to protect repeaters and deliver them to the right place at the right time. His responsibility was to coordinate all the shipping information and arrangements from the time the item was ready for packing at the Hillside plant, through all trucking arrangements to the armoring factory, to the airport, to England, and to follow, with sta- tistical data and reports, each enclosure until we were able to record the date on which the repeater was laid or stored in a depot. FLEXIBLE REPEATER MANUFACTURE 131 Fig. 9 — Shipping containers. INSPECTION PLAN AND PROCEDURES Ge7ieral It is axiomatic that quality is not obtained by inspection but must be built into the product. However, the Inspection Organization does have the responsibility of certifying that the desired quality exists. Our eval- uation indicated that the ordinary inspection "screening" would be inadequate to insure the high degree of integrity demanded and that additional safeguards would have to be provided. These controls were achieved, in a practical way, by: (1) Selective placement, intensive training and subsequent qualifica- tion testing of all personnel. (2) Inspection during manufacturing operations in addition to in- 132 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 spection of product after completion, and regulating inspection so that critical characteristics received repetitive examination during the process of manufacture and assembly. (3) A maintenance program for inspection and testing facilities which provided checks at considerably shorter intervals than is considered normal. (4) Inspection and operating records and reports that point out areas for corrective measures. (5) Records of quality accuracy for all inspection personnel as an aid in maintaining the high quality level. (6) Verification of all data covering process and final inspection as a certification of the accuracy of these data and that the apparatus satis- factorily meets all requirements. Selection and Training of Inspection Personnel The quality of a product naturally depends upon the skills, attitude, and integrity of the personnel making and inspecting it. It was realized that in order to develop the high degree of efficiency in the inspection organization necessary to insure the integrity of the product, personnel of very high caliber would be required. These employees would have to be (1) experienced in similar or comparable work, (2) they would have to be precise, accurate and, above all, dependable, (3) in order to reduce the possibility of contamination and damage they would have to be neat and careful, and (4) they w^ould require the ability to work in harmony with other employees, often as a member of a "team," in an environ- ment where their work would be under constant scrutiny. Most of the inspection employees selected to work at Hillside were transferred from the Kearny Plant and had an average Western Electric service of twelve years. They were hand-picked for the attributes out- lined above, and the "screening" was performed by supervision through personal interviews supplemented by occupational tests given by the personnel department. These tests, which are in general use, are designed to evaluate background and pl^sical characteristics, and they were given regardless of whether the emploj^ee had or had not previously taken them. The following group of tests is an example of those given inspectors and testers of apparatus components: (1) Electrical — ac-dc theory and application. (2) Ortho-Rater — Eye test for phoria, acuity, depth, and color. (3) Finger Dexterity — Ability and ease of handling small parts. FLEXIBLE REPEATER MANUFACTURE 133 (4) Special — Legibility of handwriting, ability to transcribe data and to use algebraic formulae in data computations. Inspection Plan The general plan of visual and mechanical inspection consisted of: (1) Inspection of every operation performed — ^ and in many cases partial operations — during the course of manufacture. This is of par- ticular importance where the quality characteristics are hidden or inac- cessible after completion of the operation. (2) Repeated inspection at subsequent points for omissions, damage and contamination. (3) Rejection of product at any point where there was failure to ob- tain inspection or where the results of such inspection had not been recorded. Most of the visual inspection was performed at the operators' posi- tions to reduce, to a minimum, the amount of handling that could result in damage and contamination. Visual inspection covered three general categories: (1) Inspection of work after some or all operations had been com- pleted, such as the machining of parts. (2) Inspection at those points where successive operations would co^•er up the work already performed. An example of this is the hand winding of toroidal inductors where each layer of wire was examined under a mi- croscope for such defects as twists, cracks, and crazes in enamel insula- tion, spacing and overlapping of turns, and contamination before the op- erator was allowed to proceed with another layer. While being inspected, the work remained in the holding fixture, which was hinged in such a man- ner as to permit inspection of both top and bottom of the coil. Inductors received an average of 13 and a maximum of 26 visual inspections during winding. (3) Continuous "over-the-shoulder" inspection, where strict adher- ence to a process was required or where it was impossible to determine, by subseciuent inspection, whether or not specific operations had been performed. In these cases, the inspector checked the setup and facilities, observed to see that the manufacturing layouts were being followed, that the operations were being performed satisfactorily, and that spe- cifications were being met. ELECTRICAL TESTING The electrical testing, in itself, was not unusual for carrier apparatus and runs the gamut from dc resistance through capacitance, inductance, 134 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 and effective resistance, to transmission characteristics in the frequency band 20-174 kc. What was unusual were the extremely narrow limits imposed and the number and variety of tests involved as compared to those usually specified for commercial counterparts. The following two examples will serve to illustrate the extreme meas- ures taken to prove the integrity of the product: (A) One type of Resistor was wound with No. 46 mandrelated nichrome wire to a value of 100,000 ohms plus or minus 0.3 per cent. This resistor received six checks for dc resistance, five for instantaneous stability of resistance and two for distributed capacitance, at various steps in the process which included six days' temperature cycling for mechanical stabilization. This resistor was considered satisfactory, after final anal- ysis of the test results, if: (a) The difference in any two of the six resist- ance readings did not exceed 0.25 per cent, (b) The change in resistance during cycling was not greater than 0.02 per cent, (c) The "instantaneous stability" (maximum change during 30 seconds) did not vary more than 0.01 per cent. In addition, it was required that the distributed capaci- tance, minimum 7, maximum 10 mmf, should not differ from any other resistor by more than 2 mmf. (B) For high voltage paper capacitors, the 0.004-inch thick Kraft paper, which constitutes the dielectric, was selected from the most promising mill lots which the manufacturers had to offer. This selection was based on the results obtained from tests that involve examination for porosity, conducting material and conductivity of water extractions. These tests were followed by the winding and impregnation in Halowax of test capacitors. The test capacitors were then subjected to a direct voltage endurance test at 266 degrees F for 24 hours. Samples of prospective lots of paper, which have passed the above test, were then used to wind another group of test capacitors that were subsequently impregnated with Aroclor and sealed. 1,500-volt dc was then applied to the capacitors at 203° F for 500 hours. In case of failure, a second sampling was permitted. After the foregoing tests had been passed, the supplier providing the particular mill lot was authorized to slit the paper. Upon receipt, six special capacitors were wound, using a group of six rolls of the paper being qualified. These capacitors were then impregnated, checked for dielectric strength at 3,000-volt dc, and measured for capacitance and insulation resistance. The capacitors were then given an accelerated life test at 2,000-volt dc, temperature 150° F, for 25 days. Each lot of six satisfactory test capacitors qualified six rolls of paper for use. Product capacitors were then wound from approved paper, and the dry units checked for dielectric strength at 300-volt dc. Capacitance FLEXIBLE REPEATER MANUFACTURE 135 was checked and units were then assembled into cans and ceramic covers soldered in place. Assemblies were pressurized with air, through a hole provided for the purpose, while the assembly was immersed in hot water to determine if leaks were present. Capacitors were then baked, vacuum dried, impregnated, pressurized with nitrogen, and sealed off. The com- pletely sealed units were then placed in a vacuum chamber at a tem- perature of 150° F, 2 mm. mercury, for 3 hours to check for oil leaks. Capacitance was rechecked and insulation resistance measured. After seven days, capacitors were unsealed to replenish the nitrogen that had been absorbed by the oil, resealed and again vacuum leak tested. An X-ray examination was then made of each individual unit to verify internal mechanical conditions. Capacitors were then placed in a tem- perature chamber and given the following treatment for one cycle : 16 hours at 150°F; 8 hours at 75°F; 16 hours at 0°F; 8 hours at 75°F. At the end of ten days, or 5 cycles, the insulation resistance and con- ductance was measured and a norm established for capacitance. Capacitors were then recycled for ten days, and, if the capacitance had not changed more than 0.1 per cent, they were satisfactory to place on production life test. If the foregoing conditions had not been met, the capacitors were recycled for periods of ten days until stabilized. At that time, 10 per cent of the capacitors in every production lot were placed on "Sampling Life Test", which consisted of applying 4,000- volt dc in a temperature of 150°F for 25 days. At the same time, the balance of the capacitors in the lot were placed on production life test at 3,000-volt dc in a temperature of 42°F for 26 weeks. At the end of this time, the insulation resistance was measured and the capacitance checked at 75°F and at 39°F. The difference in capacitance at the two temperatures could not exceed -|-0.001, —0.005 mf, and the total ca- pacitance could not exceed maximum 0.3726, minimum 0.3674 mf. The capacitance from start to finish of the life test could not have changed more than plus or minus 0.1 per cent. If all of the preceding requirements had been satisfied, the particular lot of capacitors described was considered satisfactory for use. The foregoing examples are typical of the procedures evolved for insuring, to the greatest degree possible, the long, trouble-free life of all apparatus used in the repeater. Radioisotope Test There were many new and involved tests which were developed and applied to the manufacture of repeaters. One of the most unique is the use of a radioisotope for the detection of leaks under hydraulic pressure. 136 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1057 Tlie initial closure operatiuiis consisted of brazing into each end of the repeater housing a Kovar-to-glass seal. These seals are equipped with small diameter nickel tubulations which were used to flush and pressurize the repeaters with nitrogen. After these operations had been performed, one of the tubulations was pinch welded, overb razed and coiled down into the seal cavity. The repeater was then placed in a pres- sure cylinder with the open tubulation extending through and sealed to the test cylinder. A mass spectrometer was then attached to the tubula- tion and the test cylinder pressurized with helium at 10,000 psi. At the conclusion of this test the repeater was removed from the test cylinder and, after breaking the desiccator diaphragm, the remaining open tubu- lation was pinchwelded and overbrazed. At this point, it became neces- sary to determine whether the final pinchweld and overbrazing would leak under pressure. Since there was no longer any means of access to the inside of the repeater, all testing had to be done from the outside. This was accom- plished by filling the glass seal with a solution of radioisotope cesium 134, which was retained by a fixture. The repeater was then placed in a test cylinder and hydraulic pressure applied, which was transmitted to the radioisotope in the fixture. After 60 hours under pressure, the re- peater was removed from the cylinder and the seal drained and washed. An examination was then made Avith a Geiger counter to determine if any of the isotope had entered the final weld. The washing procedure, after application of the isotope solution, in- volved some sixty operations with precise timing. In the case of the re- peater at the rubber seal stage where both ends were tested, it was desirable that these operations be performed concurrently. This was accomplished by recording the entire process on magnetic tape which, when played back, furnished detailed instructions and exact timing. RAW MATERIAL INSPECTION As might be expected, raw materials used in the project were very carefully examined and nothing left to chance. Every individual bar, rod, sheet, tube, bottle or can of materials was given a serial number and a sample taken from each and similarly identified. Each sample was then given a complete chemical and physical analysis before each corre- sponding piece of material was certified and released for processing. In many cases, the cost of inspection far exceeded the cost of the material. However, the discrepancies revealed and the assurance provided, more than justify the expense. Detailed records of all raw material inspection were compiled and furnished to the responsible raw material engineer who examined them, FLEXIBLE REPEATER MANUFACTURE 137 critically, as an additional precaution before the material was released to the shop. INSPECTION RECORDS To eliminate, as much as possible, the human element in providing assurance that all prescribed operations had been performed satisfac- torily, inspected properly and the results recorded, means were estab- lished to compile a complete history of the product concurrent with manufacture. This was accomplished through the provision of permanent data books of semilooseleaf design, which require a special machine for removing or inserting pages. Each of these books covered a portion of the work involved in pro- ducing a piece of apparatus and contained a sequential list of pertinent operations and requirements prescribed in the manufacturing process specifications. Space was provided, adjacent to the recorded information, for both the operator and inspector to affix their initials and the data. A reference page in the front of each book identified the initials with the employees' names. All apparatus was serially numbered and the data were identified accordingly. If a unit was rejected, that serial num- ber was not reused. These data books, in addition to establishing a complete record of manufacture, provided a definite psychological advantage in that people were naturally more attentive to their work when required to sign for responsibility. QUALITY ACCURACY As pointed out previously, every precaution was exercised in selecting and training inspection personnel assigned to the project. However, it was realized at the outset that human beings are not infallible and that insurance, to the greatest degree possible, would have to be provided against the probability of errors in observation and jugment. Quality accuracy evaluation procedures were, therefore, established for deter- mining the accuracy of each inspector's performance. Quality accuracy checking was performed by a staff of five Inspection Representatives and in^'olved an examination of the work performed by inspectors to determine how accurately it was inspected. Materials which the inspector accepted and those which had been rejected were both examined. VERIFICATION AND SUMMARY OF DATA As an added measure of assurance as to the integrity of the product, procedures were established for verifying and summarizing the inspec- tion records for each serially numbered component, up to an including complete repeaters, 138 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 Verification involved a complete audit of the inspection records to provide assurance that all process operations were recorded as having been performed satisfactorily, that the prescribed inspections had been made, and that the recorded results indicated that the product met all of the specified requirements. This work was performed by a group of six Inspection Representatives who had considerably experience in all phases of inspection and inspection records. As the verification of a particular piece of apparatus proceeded, a verification report was prepared which, when completed, contained the most pertinent inspection data, such as: (1) Recorded measurements of electrical parameters. (2) Values calculated from measurements to determine conformance. (3) Confirmation that all process and inspection operations had been verified. (4) Identification (code numbers and serial or lot numbers) of mate- rials and components entering into the product at each stage of manu- facture. The verification report usually listed the data for twenty serial num- bers of a particular code of apparatus along with the specified require- ments. Included, also, was a cross-reference to all the inspection data books involved so that the original data could be located easily. These verification reports were prepared for all apparatus up to and including the finally assembled and tested repeaters. The following gives an indication of the number of items examined in the verification of one complete repeater: Items verified in data books 17 , 593 Items verified on recorder charts 1 , 142 Calculations verified 1 , 580 20,315 Number of entries on verification reports 4 , 070 Verification reports, in addition to presenting the pertinent recorded data, provided a "field" of twenty sets of measurements from which it was easily possible to spot a questionable variation. For example, it was the adopted practice on this project to examine, critically, any charac- teristic of a piece of apparatus, in a universe of twenty, which varied considerably from the rest, despite the fact that it was still within limits. While the number of cases turned up in the verification process which have resulted in rejection of product are relatively few, we believe that the added insurance provided, and the psychological value obtained, considerably outweigh the cost. Power Feed Equipment for the North Atlantic Link By G. W. MESZAROS* and H. H. SPENCER* (Manuscript received September 20, 1956) Precise regulation of the direct current which provides power for the undersea repeaters in the new transatlantic telephone cable is necessary to maintain proper transmission levels and to assure maximum repeater tube life. The highest possible degree of protection is needed against excessive currents and voltages under a wide variety of possible faidt conditions. Furthermore, to minimize the dielectric stresses, a double-ended series-aiding power feed must be used and the balance of these applied voltages must be maintained in spite of substantial earth potentials. This paper describes the design features which were employed to attain these objectives simulta- neously, while eliminating, for all practical purposes, any possibility of even a brief system outage due to power failure. INTRODUCTION The principal objectives in the power plant design for the Trans- atlantic cable system were as follows: 1. To stress reliabilit}^ in order to guarantee continuous dc power to the electron tubes that form an integral part of the submerged repeaters. This is essential, not only to be able to maintain continuous service, but to prevent cooling and contraction of the repeater components, especially the tubes. 2. To provide close dc cable current control to ensure constant cathode temperature and regulated plate and screen potentials for the repeater tubes. These operating conditions are essential both for ob- taining maximum life from these tubes and for maintaining constant transmission level. 3. To control and limit the applied dc cable potentials in order to minimize the dielectric stresses. The life of certain capacitors in the re- peaters is critically dependent upon these stresses. Moreover, momen- * Bell Telephone Laboratories. 139 140 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 tary high potentials increase the chances of corona formation and insu- lation breakdown . 4. To protect the cable repeaters from the excessive potentials or cur- rents to which they might be subjected after an accidental open or short circuit in the cable. 5. To compensate for earth potentials up to 1,000 volts, of either po- larity, that may develop between the grounds at Oban and Clarenville during the magnetic storms accompanying the appearance of sun spots and the aurora borealis. 6. To provide adequate alarms and automatic safety features to en- sure safe current and voltage conditions to both the cable and the operating personnel. DESIGN REQUIREMENTS Reliable Cable Power The first basic problem of design was to select a reliable source of dc power for energizing the cable repeaters. Although a string of batteries, on continuous charge, is perhaps the most dependable source of direct current, such an arrangement is not attractive here. A complex set of high-potential switches would be required for removing sections of bat- teries for maintenance and replacement purposes. Protection of the repeater tubes from damage during a cable short circuit would be dif- ficult. Facilities to accommodate changing earth potentials would be cumbersome. Furthermore, the problem of hazards to personnel w^ould be serious. The use of commercial ac power with transformers and rectifiers to convert to high potential dc would expose the cable to power inter- rviptions even with a standby diesel-driven alternator, because of the time required to get the engine started. A diesel plant could be operated on a continuous basis, but this prime power source would also present a considerable failure hazard even with the best of maintenance care. The two-motor alternator set, used so successfully in the Bell System's type "L" carrier telephone system, was adopted as representing the most reliable continuous power source available. This set normally operates on commercial ac power, but when this fails, the directly-coupled battery-operated dc motor quickly and automatically takes over the drive from the induction motor, to prevent interruption of the alter- nator output. Here the storage battery is still the foundation for con- tinuity, but at a more reasonable voltage. As described later, the possibility of a system outage resulting from fail- TRANSATLANTIC CABLE POWER SYSTEM 141 ure of this two-motor alternator set has been essentially eliminated by using two such sets, cross-connected to the rectifiers supplying power to the two cables, with a continuously operating spare for each set, auto- matically switched in upon failure of the regular set. The regulating features of the rectifiers will be described in a later section. In the present discussion of reliability it is sufficient to note that series regulating tubes are used, which are capable of acting as high- speed switches, through which two rectifiers can be paralleled. Thus either rectifier can accept instantaneously the entire load presented by the cable. In each regulator the series tubes carrying the cable current are furnished in duplicate and connected in parallel to share the cable load, a single tube being capable of carrying the entire load. These cur- rent regulators are operated from separate ac sources to protect against loss of cable power because of failure of one of the sources of ac power. Cable Potentials To minimize the cable potentials, half of the dc power is supplied at each end of each cable, the supplies being connected in series aiding. With this arrangement, as shown in Fig. 1, the dc cable potential at one end of each cable is positive with respect to ground while at the other end the potential is negative. This places the maximum potential and risk on the repeaters near the shore ends, which are more readily re- trieved, while the repeaters in the middle of the cable, in deeper water, have potentials very near to ground. The power equipment would be simpler with a single-ended arrangement, but at the penalty of doubling the dielectric stresses in the entire system, which would be prohibitive. A balanced power feed could have been attained at the expense of power separation filters in the middle of the cable or a shunt impedance of appropriate size at the midpoint. The resulting complications, in- CLARENVILLE 1950 VOLT DC SUPPLY 1950 VOLT DC SUPPLY RECEIVING ^ I TRANSMISSION DC POWER a SUBMARINE CABLE TRANSMITTING -3900 VOLTS TRANSMITTING s SUBMARINE CABLE RECEIVING -* — DC POWER TRANSMISSION OBAN Fig. 1 — Cable voltage supplj', 142 THE BELL SYSTEM TECHNICAL JOURXAL, JANUARY 1957 IT cr < o — CO lO luj KT a: Dlibz LLIl- CL O O > u (0 I— 'Wv UJZO _nija: UJ ' a.uj z I- >(fl z o2 ot Hj >. N— ■ r^ \ ^— — — r- , __. •— — _ ^-« \ K ^^ GAIN -^, f--'^ N ^< N '1 \ N s. N K \ \, V. \ s \N , \ \^ PHASE \ \\ X MARGIN* \ \ \i\ 1 \ .\ WITHOUT R-C NETWORK ""^^ ...^^^-f \ \ WITH R-C NETWORK : \ a \ \ NJ\ >\ 180 140 (0 LU LU tr 100 o LU Q 60 UJ z < LU in < I Q. 20 - 0 -20 -60 01 0.02 0.05 0.1 0.2 0.5 1 2 5 10 20 50 100 200 500 FREQUENCY IN KILOCYCLES PER SECOND Fig. 6 — DC amplifier gain and phase, experimental model. data were obtained by opening the feedback loop at the control grid of the first stage, applying normal dc bias plus a A'ariable frequency ac signal to the grid of the tube, and measiu'ing the magnitude and relative phase of the return signal. The corresponding characteristics with the compensating network in place are also shown in Fig. 6. The compensating network effectively puts a relatively low-impedance shunt across the interstage network at the higher frequencies, resulting in a "step" in the gain characteristic. A secondary effect is the phase shift in the transition region. The calcu- lated "corner frequencies" are 2,800 and 195 cps, respectively, chosen on the basis of the criteria (1) little effect on regulator gain at 100 or 120 cps, the most prominent rectifier ripple frequency, and (2) a gain step of something above 20 db with no appreciable contribution to the phase shift at frequencies above 30 kc. The calculated loss at 120 cps is 1.2 db with a maximum phase shift of about 60 degrees at the median frequency. These results agree quite well with the measured data plotted in Fig. 6. As indicated in Fig. 6, the phase margin at the gain crossover frequency of 55 kc was somewhat over 100 degrees for the experimental model on which these measurements were made. The gain margin could not be measured readily but is clearly substantial. On production units, larger wire sizes and longer lead lengths resulted in lesser, but still satisfactory stability margins, as shown in Fig. 7, the phase margin being somewhat 154 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 DU - ■V X s S^:: PHASE V N, 30 \ 20 10 0 -10 -■ -• "^ ^ ■^^ N \ s \ •^, '-> V "•^ \MAXIMUM PHASE MARGIN V. ADJUST r^^RANGE MINIMUM '^>^^ ^ 1 Jl- > ISO 140 ai LU 100 5 lij Q 60 aj z < 20 LU < I a 0.01 0.02 0.04 0.1 0.2 0.4 0.6 1 2 4 6 8 10 FREQUENCY IN KILOCYCLES PER SECOND 20 -20 -60 40 Fig. 7 — DC amplifier gain and phase, production model. 229 228 227 Q d 226 5 225 LU a. en u 2 24 UJ _i ID < 223 222 221 / ^ OBJECTIVE ^^ 100,000 OHMS / ^ -''' /^ ^MEASURED 130,000 TO 170,000 OHMS A r <^''' / '} / OPERATING CONDITIONS 1. SERVO DISABLED 2. TWO REGULATORS IN PARALLEL 3. MAXIMUM AMPLIFIER GAIN 4. FIXED LINE VOLTAGE / --> 40RMAL VOLTAGf WORKING E RANGE 100 200 300 400 500 600 700 800 SERIES TUBE PLATE POTENTIAL IN VOLTS 900 1000 Fig. 8 — Load regulation. TRANSATLANTIC CABLE POWER SYSTEM 155 over 60 degrees. Fig. 7 also shows the characteristics at the extremes of gain control, the range of control being about 8 db. Fig. 8 shows the measured performance of the dc regulators, the servo system being disabled in order to obtain a plot of the performance of the dc amplifier and associated circuits. Twenty-two regulator units were manufactured and measured and the curves of Fig. 8 show the extreme limits observed, the differences between individual regulators being due primarily to differences between electron tubes. The measured range of source impedance, 130,000 to 170,000 ohms, allows margin for regulator tube aging above the 100,000-ohm objective. AC Servomechanism As noted earlier, the servo system shown in Fig. 2 is part of the cur- rent regulating scheme and holds the series tube plate potential within reasonable limits by adjusting the rectifier input voltage. In an emer- gency, a "turndown" feature, operated from several remote points, either manually or automatically, will reduce the autotransformer output to zero in less than two seconds. For simplicity, only the manual turn- down feature is shown in Fig. 2. It operates simply by switching one end of the motor control winding from one corner of the bridge to the other, thus applying half of the input voltage to the control winding. Manual operation of the autotransformer tap is provided to raise the cable current slowly, either initially or after a turndown. In manual operation a dynamic brake, consisting of a short circuit on the motor control winding, prevents the motor from creeping or coasting when the operator releases the hand wheel, as it otherwise would since the fixed phase of the two-phase motor is always energized. The turndown feature takes precedence over the short circuit of the motor control winding, automatically, to energize the motor should the operator inadvertently cause abnormally high cable voltage or current. One essential feature of the servo design is the dead band of the series tube plate voltage in which the servo remains stationary, even though there are small changes in the incoming signal. This band can be varied from 10 to 100 volts under control of a gain-adjust potentiometer across the control winding of the two-phase motor. Without this dead band, the servo would be constantly in operation correcting for small random variations in line voltage or earth potentials. Furthermore, since it is extremely difficult to set the current regulators at the two ends of a cable to exactly the same current, the servo dead band permits some margin of error. Otherwise the servo associated with the current regu- 156 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 lator trying to regulate for a slightly higher cable current, would drive its rectifier voltage to its stop or maximum output, unbalancing the cable voltages. System Stability* A complete analysis of system stability represents an exceedingly formidable, if not impossible, task. It has been established analytically that for a linear network the two dc regulators in parallel and the system as a whole are unconditionally stable. The details of this proof are too long to be presented here but the line of reasoning with respect to the overall system is as follows. The system of Fig. 1 is symmetrical about a vertical plane through the middle of the figure. Under these conditions, the system will be stable if, and only if, the following three simpler sys- tems! are stable: (a) A power supply short-circuited; (b) A power supply feeding an impedance equal to twice that of the half cable short-circuited ; and (c) A power supply feeding an impedance equal to twice that of the half cable open-circuited. The transfer function of the servomechanism was measured over the frequency range of principal interest, 0 to 1 cps, the behavior near zero frequency being determined from the asymptotic slope of the unit step response. J In this frequency range the dc amplifier gain is a real constant, flat gain and negligible delay as previously shown, therefore only the ac servo feedback loop characteristic has to be known to predict the sta- bility of condition (a). The Nyquist loop for this transfer function shows that condition (a) above is satisfied. A similar examination of the Nyquist plot, including the readily computed cable impedance shows that condi- tions (b) and (c) above are satisfied. Thus the linear analysis indicates stable operation for the system of Fig. 1. This result was confirmed by tests of conditions (a), (b), and (c) individually and by the behavior of the system as a whole, both in the laboratory with a simulated power network for the cable and in the final installation. One of the most obscure aspects of the power system behavior is that of equilibrium conditions after one or a series of large earth potential * The analysis briefly summarized here was made by C. A. Desoer. t In this discussion of simpler sj'stems a power supply consists of only the elements shown in Fig. 2. J In the course of these time-domain measurements, it was quite apparent that the ac control loop could be considered as a linear network only in an approximate sense and thus that the analytical results were primarily useful in interpretation of observed behavior of the system. TRANSATLANTIC CABLE POWER SYSTEM 157 disturbances. While the system is stable in the sense that the transient due to a perturbation will disappear in a finite time once the disturbance has been withdrawn, the range of possible equilibrium positions (disre- garding the overvoltage protective feature) is extremely wide — from perhaps 1,300 to 2,500 volts at the cable terminals. The upper limit of 2,500 \-olts is set by the maximum output available from one power plant; this also sets the lower limit of the associate power plant at the far end of the cable. This situation is illustrated diagrammatically in Fig. 9. The behaviors of the servomechanisms at the two ends of a given cable are nearly enough alike that the repeated introduction of simulated earth potential in the laboratory was found not to disturb substantially the equilibrium point. This was true for earth potentials of either polarity up to 1,000 volts and with these potentials introduced at am^ point along the artificial cable. A rate of change of earth potential of 20 ^'olts per second was adopted in these tests with the thought that such values would be realistic. With regard to the long-term stability of the equilibrium condition described above, it is, of course, important that the controls which es- tablish the cable current at the two ends of the same cable be adjusted for very nearly the same value. Unless this is done, the cable voltage at (jue end will gradually increase or decrease and the voltage at the other end will move equally in the opposite direction. This would eventually 3000 UJ O < ^ 2000 - > CD < 1000 221 1-2= _ 224.75 MA 224.75 MA Apt B, ->i r^— 225.25MA c, i; I ^il I |Bi I AREA OF -EQUILIBRIUM C, DiCpDs 225.25 MA 223 225 227 CABLE CURRENT IN MILS 229 1-2 c 8.5 K , AAA 8.5 K J V V V t V V V ° 1000 1 1 + I CD e, >200M UJ < < 2000 > LEAKAGE IMPEDANCE UJ _i CD < MAPPING EQUATIONS (VOLTS & MA) 3000 eg = 17.00036 1, -1.00004 6, >-< ,= 1.00004 1 , -e,/200,000 Fig. 9 — Equilibrium diagram. 158 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 bring in alarms and necessitate manual readjustment. In this connection, the voltmeters which indicate the drop through the series regulating tubes provide a very convenient magnification of any drift in cable cur- rent. The multiplying factor is the effective dc impedance of the regu- lated system, that is, more than 100,000 ohms. Thus 25 volts, which is an appreciable fraction of the nominal 300 volts across the series regu- lating tubes, is equivalent to less than 0.25 ma., which is of the order of 0.1 per cent of normal cable current. As a matter of fact, the behavior of this voltage provides the final criterion for precise adjustment of cable current to assure long-term stability. EQUIPMENT DESIGN Description Fig. 10 shows the complete dc equipment for supplying one polarity of power to one cable. Similar equipment provides the opposite po- larity to the other cable. The tw^o equipments are located facing each other across a common aisle with their conmion control bays directly opposite. Regulator 1 on the right is normally operated in parallel with Regulator 2. Regulator 3 on the left is the spare regulator, normally off. The common bay, between Regulators 1 and 2, includes the cable Fig. 10 — DC regulator and common control bays. TRANSATLANTIC CABLE POWEK SYSTEM 159 termination and power separation filter. This equipment and all the live parts of the circuit, back to the common point to which the switches in the individual regulator bays are connected, is enclosed in a high voltage compartment. The paralleling control switches are mounted in high voltage compart- ments in their respective regulating bays and must remain completely enclosed, as their common cable connections are alive during cable operation. These switches have an interrupting capacity of 1 ampere at 3,000 volts, thus providing a large safety factor over the 0.245 ampere maximum load current. Fig. 11 illustrates some of the special design features built into the equipment to facilitate maintenance. The high voltage compartment shown open at the top is locked whenever the cable is in operation and this protection feature will be described below. Pull-out drawers at the bottom contain metering shunts, a test unit for adjusting voltage and current protection limits, a voltage protection unit, a current protection unit, and an alarm unit. While only one of these compartments is to be pulled out at a time, they are arranged so as not to endanger personnel or to affect service during adjustment when open. Doors are provided on all bays to prevent accidental disturbance of adjustments and to protect against damage to controls. Corona The high voltage ac elements of the complete regulator bays were tested for corona with 4,000 volts ac applied, and furthermore, if corona was observed on increasing the applied rms voltage to 5,000 volts, it was required to extinguish when the voltage was reduced to 3500 volts. The maximum acceptable leakage was 20 microamperes at 4000 volts across the circuit (200 megohms) . A dc corona requirement of 4000 volts was applied to the dc elements of the regulator bays and 5000 volts for the common bay, with a maximum permissible leakage of 5 microamperes. The higher corona requirements on the common bay were intended to eliminate the necessity for turning down the entire system for repair. A high standard of workmanship is required to provide such performance. There can be no sharp projections and no loose strands of wire. Solder must be applied in such a manner as to obtain a rounded smooth joint and high voltage wiring must be dressed away from exposed grounded metal, bus bars, etc., so that the outer braid (other than polyethylene) does not come in contact with metal. 160 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 Fig. U — Common control bay. TRANSATLANTIC CABLE POWER SYSTEM 161 Crosstalk and Outside Interference 111 order to meet the severe crosstalk requirements between receiving and transmitting circuits and to guard against feeding office noise po- tentials into the carrier transmission system, arrangements were made so that office grounds are carefully separated from the outer conductor of the cable and from all circuit elements within the power separation filter. Pickup of external radio-frequency fields by the power separation filters was greatly reduced by completely enclosing in a copper shield the cable terminal and the power separation filter elements nearest to the terminal. The shielding itself and the cans of PSF capacitors and oil-filled coils are connected to the return tape of the cable which is insulated from office ground until it reaches sea water, thus reducing the coupling to the other cable as compared to tying both tapes together at the office or bay frame ground. Protection of Personnel A key locking system is provided to safeguard against any hazard to personnel from high voltages. In the common bay, the high voltage com- partment can be entered only by operating a switch which shorts the cable to ground and releases a key for the compartment doors. In each regulating bay, the key system assures that the bay is disconnected from the cable and hence from the paralleling power supplies. Where access is required to the interior of any compartment, the key system insures that the ac power to the bay also be switched off. The test compartment contains pin jacks, provided for maintenance operations which are always performed with the regulator bay con- nected to a low resistance load. Access to this compartment can be ob- tained with ac power connected to the bay. However, for such access, the key system enforces the operation of the output disconnect switch, which also transfers the bay to a low-resistance load. Moreover, a me- chanical interlock with the autotransformer assures that the test voltages are reduced to safe ^'alues. In addition to its function in protecting personnel, the key system also insures that no more than one regulating bay is disconnected at one time so that continuity of service is protected at all times by two parallel regulators. FACTORY AND SHIP CABLE POWER In addition to the above cable power supplies at the ocean terminals, similar dc cable current regulating equipment was designed for use at 162 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 the cable factory and abroad the cable ship Monarch. Well protected and closely regulated reliable power was considered essential during the cable loading and lajang operations. It was necessary to have power on the cable continuously, except when splices were made, in order to detect a fault immediately, to measure transmission characteristics for equali- zation purposes and finallj" to alle^date the strain on the glassware and tungsten filaments of the repeater tubes during the difficult laying period.^ REFERENCES 1. H. A. Lewis, R. S. Tucker, G. H. Lovell and J. M. Eraser, System Design for the North Atlantic Link. See page 29 of this issue. 2. T. F. Gleichmann, A. H. Lince, AL C. Wooley and F. J. Braga, Repeater Design for the North Atlantic Link. See page 69 of this issue. 3. J. S. Jack, Capt. W. H. Leech and H. A. Lewis, Route Selection and Cable Laying for the Transatlantic Cable System. See page 293 of this issue. Electron Tubes for the Transatlantic Cable System By J. O. McNALLY,* G. H. METSON,t E. A. VEAZIE* and M. F. HOLMESt (Manuscript received October 10, 1956) Electron tubes for use in repeatered underwater telephone cable systems must be capable of operating for many years with a reasonable probability of proper functioning. In the new transatlantic telephone cable system the section of the cable between Nova Scotia and Newfoundland contains re- peaters developed by the British Post Office Research Station at Dollis Hill. These repeaters are built around the type 6P12 tube developed at that re- search station. The repeaters contained tn the section of the cable system be- tween Newfoundland and Scotland are of Bell System design and depend on the 175 HQ tube developed at Bell Telephone Laboratories. In this paper the philosophy of repeater and tube desigji is discussed, and the fundamental reasons for arriving at quite diferent tube designs are pointed out. Some of the tube development problems and the features intro- duced to eliminate potential difficulties are described. Electrical characteris- tics for the two types are presented and life test data are given. Fabrication and selection problems are outlined and reliability prospects are discussed. INTRODUCTION Electron tubes suitable for use in long submarine telephone cables must meet performance requirements that are quite different from those imposed by other communication systems. In the home entertainment field, for example, an average tube life of a few thousand hours is gen- erally satisfactory. In the field of conventional land-based telephone equipment, where the replacement of a tube may require that a mainte- nance man travel several miles, an average life of a few years is considered reasonable. In deep-water telephone cables such as the new transatlantic system, the lifting of a cable to replace a defective repeater may cost several hundred thousand dollars and disrupt service for an extended * Bell Telephone Laboratories, t British Post Office. 163 164 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 period of time. These factors suggest as an objective for submerged re- peaters that the tubes should not be responsible for a system failure for many years, possibly twenty, after the laying of the cable. Such very long life requirements make necessary special design features, care in the selection and processing of materials that are used in the tubes, unusual procedures in fabrication, detailed testing and long aging of the tubes, and the application of unique methods in the final selection of individual tubes for use in the submerged repeaters. As indicated in the foreword and discussed at length in companion papers, the British Post Office developed the section of the cable system between Clarenville, Newfoundland, and Sidney Mines, Nova Scotia. This part of the transatlantic system uses the 6P12 tube which was devel- oped at the General Post (3ffice (G.P.O.) Dollis Hill Research Station. The submerged portion of this system contains 84 tubes in 14 repeaters. Bell Telephone Laboratories developed the part of the system between Clarenville, Newfoundland, and Oban, Scotland. This section requires 102 repeaters, including 30() tubes, of a type known as the 175HQ. Although a common objective in the development of each of the two sections has been to obtain very long life, the tube designs are quite dif- ferent. The Bell System decided on the use of a repeater housing that could be treated as an integral part of the cable to facilitate laying in deep Avater. The housing is little larger than the cable and is sufficiently flexible to be passed over and around the necessary sheaves and drums. In such a housing the space for repeater components is necessarily restricted. This space restriction, combined with the general philosophy that the num- ber of components should be held to an absolute minimum and that each component should be designed to have the simplest possible structural features, has resulted in the choice of a three-stage, three-tube repeater. In this design, each tube carries the entire responsibility for the con- tinuity of service. The Post Office Research Laboratories, prior to the development of the transatlantic cable system, had concentrated their efforts on shorter systems for shallow water. The placing of the repeaters on the bottom did not present the serious problems of deep-sea laying, so more liberal dimensions could be allowed for the repeater circuit. A three-stage ampli- fier was developed which consisted of two strings of three tubes each, parallel connected, with common feedback. The circuit was so designed that almost any kind of tube failure in one side of the amplifier caused very Httle degradation of circuit performance. This philosophy of having ELECTRON TUBES FOR A TRANSATLANTIC TELEPHONE CABLE 165 the continuity of service depend on two essentially independent strings of tubes has been carried over to the repeater design for the Clarenville- Sidney Mines section of the transatlantic cable. In the Post Office system containing 84 tubes in the submerbed re- peaters, five tube failures randomly occurring in the system will result in slightly over fifty per cent probabilitj^ of a system failure; one tube failure in the 306 tubes in the Newfoundland-Scotland section of the system will result in certain system failure. It is not surprising, therefore, to find the tube designed for the Newfoundland-Scotland section of the cable to have extremely liberal spacing between tube elements in order to minimize the hazards of electrical shorts. This results in a lower trans- conductance than is found in the tubes designed for the Nova Scotia- Newfoundland link. Other factors in the design will be recognized as reflecting the different operating hazards involved. Early models of the British Post Office and Bell Laboratories tubes, together with the final tubes used in the cable system, are shown in Fig. 1. mmmm ifc Fig. 1 — The final designs of tubes for the Nova Scotia-Newfoundland section of the cable (right) and for the Newfoundland-Scotland section (left). Earlv models of each type stand behind the final models. 166 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 TUBES FOR THE NEWFOUNDLAND-SCOTLAND CABLE Early Development Considerations In Bell Telephone Laboratories, work on tubes for use in a proposed transatlantic cable was started in 1933. This was preceded by a study of what type of tube would best fit the needs of the various proposed ampli- fier systems and by consideration of what might be expected to give the best life performance. At the time this project was started, reasonably good tube life had been established for the filamentary types used in Bell System repeaters. Some groups of tubes had average lives of 50,000 or 60,000 hours (6 or 7 years) . Equipotential cathode tubes were not then used extensively in the plant, and there was no long life experience with them. However, there appeared to be no basic reason why inherently shorter thermionic life should be expected using the equipotential cathode and there were several advantages in its use. One was the greater freedom in circuit design afforded by the separation of the cathode from the heater. Also there was the possibility of operating the heaters in series and using the voltage drop across the heaters for the other circuit voltages. It was felt, in addition, that the overall mechanical reliability would be greater if the cathode were stiff and rigidly supported. The first equipotential tubes made were triodes. They were designed for use in push-pull amplifiers wherein continuity of service might be re- tained in case of a tube failure. This circuit was abandoned in favor of a three tube, feedback amplifier that was the forerunner of the present repeater. The pentode was favored over the triode for this amplifier for obvious reasons, and in 1936 the triode development was discontinued. Early in the development of the tube three basic assumptions were made. These were, (a) that operation at the lowest practical cathode temperature would result in the longest thermionic life, (b) that operat- ing plate and screen voltages should be kept low, and (c) that the cathode current density should be kept as low as practicable. The first assumption, concerning the cathode temperature, was based on the observation of life tests on other types of tubes. While the data at the time of the decision were not conclusive, there was definite indica- tion that too high a cathode temperature shortened thermionic life. Little was known about life performance in the temperature range below the values conventionally used. The second assumption, concerning low screen and plate voltages, had not been supported by any experimental work available at the time of decision. Sixty volts was originally considered for the output stage; this ELECTRON TUBES FOR A TRANSATLANTIC TELEPHONE CABLE 167 value was later lowered when other operating conditions were changed. Subsequent results showed that in this range the voltage effects on thermionic life were relatively negligible. The third assumption, that low cathode current density fa\'ored longer thermionic life, affected the tube design by suggesting the use of a large coated cathode area. This implied the use of relatively high cathode power. It was decided early in the planning of the repeater that the voltage drop across the three heaters operated in series would be used to supply part or all of the operating plate and screen potentials. For a 60-volt plate and screen supply, the heater voltage could be as high as 20 volts. A quarter of an ampere was considered a reasonable cable cur- rent consistent with voltage limitations at the cable terminals. Thus 5.0 watts were available for each cathode. With this power, a coated area of 2.7 square centimeters was provided. The "\'alue of the cathode current, the cathode area, and the interelectrode spacings define the transcon- ductance. Very liberal interelectrode spacings were provided consistent with reasonable tube performance. The original design called for a spac- ing of 0.040 inch between control grid and cathode. This value was later reduced to 0.024 inch, and a satisfactory design was produced which gave 1,000 micromhos or one milliampere per volt at a cathode current drain of approximately 2.0 milliamperes. The resulting current density of approximately 0.7 milliampere per square centimeter is in sharp con- trast with values such as 50 milliamperes per square centimeter used currently in tubes designed for the more conventional communication uses. Subsequent data, discussed later, indicate that for current densities of a few milliamperes per square centimeter, the exact value is not critical in its effect on thermionic life. Subsequent Production Programs The development of the tube was pursued on an active basis through the years leading up to World War II. During the war development ac- tivity essentially stopped. It was only possible to keep the life tests in operation. After the war the development of the tube was completed and a small production line was set up in Bell Telephone Laboratories under the direct supervision of the tube development engineers to make and select tubes for a cable between Key West, Florida, and Havana, Cuba. This cable turned out to be a "field trial" for the transatlantic cable which was to come later. A total of G submerged repeaters containing 18 tubes were laid and the cable was put in operation in June, 1950. The cable has been in operation since this date without tube failure, and 168 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 Fig. 2 — Parts used in the stem and a finished stem of the 175HQ tube. The separate beading of the leads maj' be noted. periodic observations of repeater performance indicate no statistically significant change in tube performance over the 6 years of operation. Sufficient tubes were made at the same time as the Key West-Havana run to provide the necessary tubes for a future transatlantic cable. These tubes were never used principally because the tubes had been assembled with tin plated leads. Tin plating, subsequent to the laying of the Key West-Havana cable, was found to be capable of growing "whiskers".^ In 1953 another production setup was made, also in Bell Telephone Laboratories, for the fabrication of tubes for the Newfoundland-Scotland section of the transatlantic cable. On the completion of this job fabrica- tion was continued to provide tubes for an Alaskan cable between Port Angeles, Washington, and Ketchikan, Alaska. After a pause of several months another run was made to provide tubes for a cable to be laid between California and the Hawaiian Islands. Mechanical Features The tube, shown on the left in Fig. 1, is supported in the repeater housing by two soft rubber bushings into which the projections of the two ceramic end caps fit. All leads are flexible and made of stranded beryllium copper which has been gold plated before braiding. Both for ELECTRON TUBES FOR A TRANSATLANTIC TELEPHONE CABLE 1G9 convenience in wiring in the circuit and to hold down the control-grid to anode capacitance, the grid lead has been brought through the opposite end of the tube from the other leads. A number of somewhat unusual constructional features appear in the tube. The stem on which the internal structure is supported consists of a molded glass dish into which seven two-piece beaded dumet leads are sealed. The parts used in a stem, and also a finished stem, are shown in Fig. 2. It is usual to embed the weld or "knot" between the dumet and nickel portions of the lead in the glass seal to provide more structural stiffness. This has not been done in this stem because it was believed that a fracture of a lead at the weld could be detected more easily if it were not supported by the seal. It might be questioned why the modern alloys and fiat stem structure have not been used. It is to be remembered that one gas leak along a stem lead would disable the system, and experience built up with the older materials provides greater assurance of satis- factory seals. The structure of the heater and cathode assembly is uniciue, as may be seen in Fig. 3. A heater insulator of aluminvmi oxide is extruded with 7 holes arranged as shown. This insulator is supported by a 0.025 inch molybdenum rod inserted in the center hole. The heater consisting of about 36 inches of 0.003 inch tungsten is wound into a helix having an outside diameter of 0.013 inch. After dip coating by well known tech- niques the heater is threaded through the 6 outer holes in the insulator. A suspension of aluminum oxide is then injected into the holes in the insulator so that on final firing the heater becomes completely embedded. CATHODE SLEEVE, MOLYBDENUM . CATHODE / CORE ROD ^ CERAMIC INSULATOR \ , TUNGSTEN I /HEATER I / I / I i I Fig. 3 — Heater, heater insulator and cathode assembly of the 175HQ tube, 170 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 The cathode sleeve, which is necked down at one end as shown in Fig. 3, is sUpped over the heater assembly and welded to the central molyb- denum rod which becomes the cathode lead. By this means a uniform temperature from end to end of the cathode is obtained. Under normal operating conditions the heater temperature is approximately 1100°C, which is very considerably under the temperature found in other tubes. Connection of the heater to the leads from the stem presented a serious design problem. Crystallization of tungsten during and after welding and mechanical strains developed by thermal expansion frequently are the causes of heater breakage. This problem was successfully overcome by the means illustrated in Fig. 4. Short sections of nickel tubing are slipped over the cleaned ends of the heater coil and matching pieces of nickel wire are inserted as cores. These parts are held together by tack welds at the midpoints of the tubing. The heater stem leads are bent, flattened and formed to receive the ends of the heater, which are then fastened by welds as indicated in the drawing. Fig. 4 — Heater tabbing arrangement of the 175HQ. ELECTRON TUBES FOR A TRANSATLANTIC TELEPHONE CABLE 171 A serious attempt has been made in the design of the tube to hold the number of fastenings that depend entirely on one weld to an absolute minimum. The grids are of conventional form in which the lateral wires are swaged into notches cut in the side rods or support wires. The side rods as well as the lateral wire are molybdenum. This produces grids which are considerably stronger than those using more conventional materials. The upper mica is designed to contact the bulb and the bulb is sized to accurate dimensions to receive and hold the mica firmly. The tube in its mounting will withstand a single 500g one millisecond shock with- out apparent changes in mechanical structure or electrical characteris- tics. It is estimated from preliminary laying tests that accidental or un- usual handling would rarely result in shocks exceeding lOOg. Electrical Characteristics and Life The average operating electrical characteristics for the 175HQ tube are given in Table I, and a family of plate- voltage versus plate-current curves for a typical tube is given in Fig. 5 for a region approximating the operating conditions. The development of a long-life tube offers good opportunities to ob- serve effects which are more likely to be missed where shorter lives are satisfactory. For example, some of the earliest tubes made, after 20,000 hours on the life racks, began to show a metallic deposit on the bulbs. Table I — Average Operating Electrical Characteristics for THE 175HQ Tube Heater Current Heater Voltage Heater Power Control-Grid Bias Screen Voltage Plate Voltage Screen Current Plate Current Transconductance Capacitances (cold, with shield) Input Capacitance Output Capacitance Plate to Control-Grid Capacitance Stages 1 & 2 Stage 3 220 217 milliamperes 18.2 18.4 volts 4.0 4.0 watts -1.3 — 1.4 volts 38 40 volts 32 51 volts 0.3 0.3 milliamperes 1.3 1.4 milliamperes 980 1010 micromhos All Stages 9.2 MMf 15.6 MMf 0.03 ^L^li 172 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 4.5 4.0 ^ 3.5 UJ a. ULl Q. 2 3.0 S2.5 z 2 2.0 OJ a. tr D O 1.5 LU H < 0.5 0 10 20 30 40 50 60 70 80 90 100 110 120 PLATE VOLTAGE Fig. 5 — Typical plate voltage-plate current characteristics for a type 175HQ tube. SCREEN VOLTAGE = 40 VOLTS CONTROL- GRID VOLTAGE = 0 ] / ^ / " -0.5 r -1.0 \r -1.5 h^ ' -2.0 ^ -2.5 -3.0 -3.5 Immediate concern for the lowering of insulation resistance across mica spacers prompted an investigation. The source was traced to the use of plates made from a grade of nickel from which magnesium as a contam- inant was evaporating. A change was made to molybdenum which has been used successfully since that experience. The effect on the thermionic life of operating at different cathode cur- rent densities was of interest. Life tests were started in which the cathode current drain in one group of tubes was approximately 7.5 milliamperes (2.8 ma/cm^) and in another group the average cathode current was 0.6 milliamperes (0.2 ma/cm^). The results presented in Fig. 6 after 120,000 hours, or approximately 14 years, show that at the cathode temperature of approximately 710°C* selected for the test, there is practically no current density effect in this 12 to 1 current range. The circles indicate average values, while the dots and crosses at each test point show the positions of the extreme tubes of the group. Similar life tests set up to show the effect of operating at plate and screen voltages of 60 volts as compared to 40 volts indicate no essential differences in performance after 8 years of operation. * All cathode temperatures referred to in this paper are "true" temperatures, not imcorrected pj^rometer temperatures. ELECTRON TUBES FOR A TRANSATLANTIC TELEPHONE CABLE 173 LU o z LU cr UJ u. 105 100 z LU u LU ^95 < 5 90 Q Z (J 85 ^80 75 70 X CATHODE CURRENT 0.6 MA % '^^ N V 9 1 1 X N [ h- f^*« > ; ) ( )! r^ :;"" T i 1 ft 2 1 4 1 6 1 8 1 10 1 12 1 k 14 1 20,000 40,000 60,000 80,000 100,000 120,000 LIFE IN HOURS AND YEARS Fig. 6 — Results of life tests on eighteen 175HQ tubes operating at two differ- ent current densities. The cathode temperature is one of the most critical operating vari- ables affecting thermionic life. As mentioned above, the early develop- ment objective was a cathode power of 5.0 watts which corresponded to 710°C for the cathode design used at that time. The results of op- erating at this condition are illustrated in Fig. 7. No tubes have been lost from the test where the direct cause has been failure of emission. Several tubes were lost because of mechanical failure resulting from design defects which were subsequently corrected. It will be observed 120 110 100 90 80 70 60 50 40 CATHODE TEMPERATURE = 710''C • "^. • < . * V • < 1 1 1 1 > ( 4 > > 1 < 1 ■ • --^ — -^ * 1 1 , ( ' i < 1 i 1 2 1 4 1 6 1 ( s 10 12 14 1 1 5 18 1 20,000 40,000 60,000 80,000 100,000 120,000 140,000 160,000 LIFE IN HOURS AND YEARS Fig. 7 — Results of life tests on sixteen 175HQ tubes operating at a cathode temperature of 710°C. 174 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 that at the end of 17 years the average transeonductance is 80 per cent of its original value, and the poorest tube has dropped to 69 per cent. There is reason to believe that test set difficulties may very well account for a large part of the variation shown in the first three years. The cathode coatings used in all experimental and final tubes for the Newfoimdland-Scotland link of the transatlantic cable are the con- ventional double carbonate coatings. The cathode base material is an International Nickel "220" nickel. The particular melt used for the transatlantic cable is known as melt 84. A typical analysis for melt 84 nickel cathodes is given in Table II. Table II — Typical Analysis of Inco 220 Nickel Cathode Melt 84 (Analysis made prior to hydrogen firing) Impurity Per Cent Impurity Per cent Aluminum 0.008 <0.004 0.46 <0.005 0.028 0.093 0.046 Manganese Silicon . 0.11 Boron 0.033 Cobalt Chromium Copper Iron Magnesium Titanium Oxygen Sulphur Carbon 0.032 0.0001 0.0016 0.058 The relatively high carbon content (0.058 per cent) of melt 84 cathode nickel is capable of producing excessive reduction of barium in the cathode coating.-- ^ A treatment in wet hydrogen, prior to coating, at 925°C for 15 minutes reduces the carbon in the cathode sleeve to about 0.013 per cent. Melt 84 was as close as was obtainable in composition to melts 60 and 63 previously used for the Key West-Havana tubes. The results of up to five years of life testing were thus available on materials of very similar composition. One common cause of tube deterioration mth life is the result of formation of an interface layer on the surface of the cathode sleeve. It is known that the rate of development of this layer depends in a complex way on the chemical composition of the nickel cathode core material. The effect of such a layer is to introduce a resistance in series with the cathode. This results in negative feedback and reduces the effective transeonductance. Since the effect of a given feedback resistance in this location is proportional to transeonductance, the relatively low value for the 175HQ tube tends to minimize this feedback effect. In addition, the low cathode temperature tends to reduce the rate of formation of inter- face resistance, and the relatively large cathode area tends to further minimize the effects. The final decision to use melt 84 was based on ac- ELECTRON TUBES FOR A TRANSATLANTIC TELEPHONE CABLE 175 celerated aging tests which showed it to be superior to melts 60 and G3 from an interface standpoint. The interface problem will be discussed further in a later section. As the development of the tube proceeded, both the processing of the parts and the cleanliness of the mount assembly were impro\'ed and the cathode emission level increased. Life tests indicated that better therm- ionic life might be obtained by operating at a lower cathode tempera- ture. Accordingly a cathode power of approximately 4.0 watts was adopted, which corresponds to a temperature of 670°C. A life test, now 45,000 hours or about 5 years old, shows the results in Fig. 8 of operating groups of tubes at three different cathode temperatures. This is a well controlled test in that the tubes for the three groups were picked from tubes having common parts and identical fabrication histories. It may be noted that the average of the 725°C lot has lost approximately 5 per cent of the initial transconductance, whereas the 4.0 watt group after about 5 years has lost essentially none of its transconductance. The 3.0 100 LU o z o Q Z o o in z < a. \- LU o z LU cc LJJ LL m cc LL O z LU o cc LU 105 100 95 105 100 95 90 85 80 75 70 <>" 1 CATHODE TEMPERATURE =670° C ( 1 1 1 ) i ( \ s ^ -— ' ' CA' MODE TE^^ PERA TURE = 615' 'C 1 1 1 1 4 1 1 1 ' 2 1 3 1 i \ 5 1 6 1 0 10,000 20,000 30,000 40,000 50,000 LIFE IN HOURS AND YEARS Fig. 8 — Results of operating thirty-six 175HQ tubes divided equally among three different cathode temperature conditions. For each of the curves the cathode core material used was half from melt 60 and half from melt 63. The conditions in cable operation are essentially those represented by the center curve. 176 THE BELL SYSTEM TECHNICAL JOT'RNAL, JANUARY 1957 watt (61o°C) group shows serious instabilities in its performance. In some of the tubes the cathode temperature has not been sufficiently high to provide the required emission levels. The design of the repeaters in the Newfoundland-Scotland section of the cable is such that reasonably satisfactory cable performance would be experienced if the transconductance in each tube dropped to 65 per cent of its original value. The life test performance data presented in Figs. 7 and 8, and other tests not shown, indicate that operation of the 175HQ tubes in the transatlantic cable at approximately 4.0 watts will assure satisfactory thermionic performance for well oxev 20 years. Mention was made that cleanliness in the assembly of the mounts was a factor which affected thermionic activity. Interesting evidence sup- porting this view was obtained during the fabrication of tubes for the Key West-Havana cable. The cjuality control type of chart reproduced in Fig. 9 shows the average change in transconductance between two set values of heater current for the first 5 tubes in each group of approxi- 11.6 11.2 I- z LU O10.8 DC LU Q-10.4 ^10.0 O < 9.6 LU ^ 9.2 LU 8.4 -> <- -1 \'k ^^ /y l\ fi -UPPER CONTROL LIMITS \ t If V V 1 ,R, ,"";"' _I \ 1 If ' ^ \l\ V, V AVEF RAGE V 1 AVEF , rJ m A — LIFE TEST AND MEASURING CONDITIONS: ANODE =90 VOLTS SCREEN = 60 VOLTS ANODE CURRENT = 6MILLI- AMPERES HEATER = 5.5 VOLTS y P / / a / A / k H / \ r V V 1 i i / J v V V 1 1 1 I c 3 1 3 1 5000 10,000 15,000 20,000 LIFE IN HOURS AND YEARS 25,000 30,000 Fig. 10 — Behaviour of a group of 50 tubes deliberately left with a "gas gen- erator" (tube type 6P12). free to recover from transconductance failure when the gas attack has passed. In Fig. 10 is shown the behaviour of a group of 50 tubes which have been deliberately left in possession of a component capable of gen- erating carbon-monoxide over a prolonged period of time. The curve shows the characteristic recovery of a platinum-cored oxide-cathode with the gradual passing of what is thought to be a typical gas attack. One problem that has attracted much attention at Dollis Hill is the actual manner in which a platinum-cored cathode recovers from a gas attack. The mechanism must involve the dissociation of a small fraction of the oxide cathode itself with the retention of barium metal in the oxide lattice and the evolution of oxygen. That such an essential mecha- nism does in fact exist has been proved by the slow accumulation of barium metal in the platinum core. This accumulation takes the form of a dis- tinctive alloy of barium and platinum and only occurs when the cathode 184 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 is passing current. The barium regenerative process seems therefore to be electrolytic in nature and, depending only on current flow and a stock of oxide, would appear to be virtually inexhaustible. These few remarks are perhaps sufficient to give some idea of the lines on which the British research effort has run during the past decade. More detailed descriptions have ah-eady been presented elsewhere.^- s. e, 7 Electrical and Mechanical Characteristics Electrical Characteristics The main electrical characteristics of the 6P12 are shown in Figs. 11 and 12. The heater voltage used for both sets of curves is 5.5 volts, the same value as that used in the British amplifier. Fig. 11 shows the change of transconductance with anode current, with screen voltage as parameter. An anode voltage of 40 volts and a suppressor voltage of zero correspond with the static operating condi- tions in the first two stages of both the Aberdeen-Bergen and the British 7.2 6.8 O > cr 6.4 ai Q. in 111 tr 6.0 LU CL < _l 5.6 ~ 5.2 m o z < U 4.8 3 Q Z o o in z < tr 4.4 4.0 3.6 .-7^ C/ / sc REEN V( DLTAGE = 30/ // ^/ A / / / / 20/ V V // // / w / / ii 1 ANODE = 40 VOLTS SUPPRESSOR = 0 VOLTS HEATER = 5.5 VOLTS // / 1 2 3 4 5 6 7 ANODE CURRENT IN MILLIAMPERES Fig. 11 — Typical transconductance-anocle current characteristics for a type r)ri2 tvihe (No. 457/6). ELECTRON TUBES FOR A TRANSATLANTIC TELEPHONE CABLE 185 22 20 if) 18 UJ a. UJ D. 16 5 < 14 12 z 10 cr a. 3 « LU 8 e z < SCREEN = 60 VOLTS SUPPRESSOR = 10 VOLTS CONTROL -GRID VOLTAGE = = -0.5 ^ ^— / / L ^^ ' — -t.o 1 r 11 v^ — ' -1.5 if r ■ — ' ' -2.0 ^ - — ^ -2.5 20 40 60 80 100 ANODE VOLTAGE 120 140 160 Fig. 12 — Typical anode voltage-anode current characteristics for a type 6P12 tube (No. 457/6). transatlantic telephone (T.A.T.) amplifiers. The screen voltage and anode current of the first two stages of the British T.A.T. amplifier were chosen to be 40 volts and 3 ma respectively. Fig. 12 shows the normal anode voltage-anode current characteristics for conditions corresponding to the output stage of the amplifier (static operating point, anode voltage = 90, screen voltage = 60, anode cur- rent = 6 ma) . A final electrical characteristic worthy of comment is the level of reverse grid current. For all specimens tested at the time of se- lection, after about 4,000 hours life test, the level is very low, about 100 micromicroamperes per milliampere of anode current. Lije Performance The life performance of the 6P12 is still a matter for conjecture. The only concrete evidence available is the behaviour of a group of 92 tubes which w^ere placed on hfe test some three years ago. The change of the average transconductance of this group (with anode current constant at 6 ma) is shown in Fig. 13. It may be clearly appreciated that there is no definite trend over the past year which permits any firm prediction of life expectancy. Examination of other tube characteristics is equally un- productive from the point of view of prediction of failure. 18C) THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 6.8 10,000 15,000 20,000 LIFE IN HOURS AND YEARS 30,000 Fig. 13 — Behaviour of a group of 92 type 6P12 tubes over a period of three years. In the early stages of the test there were eight mechanical failures. The cause in all instances was identified and corrected in subsequent production before the start of the T.A.T. project. Mechanical Characteristics The chief mechanical characteristics of the 6P12 have been mentioned before in that they are, as explained, very similar to those of the 6P10. A photograph of the interior of the tube is shown in Fig. 14. Tube Selection Techniques Not all the tubes, found after production to be potentially suitable for the British T.A.T. amplifier, remained equally suitable after the life test period of about 4,000 hours. A brief account of how the best were se- lected is given below. The fact that every tube had to pass conventional static specification limits needs little emphasis here. This test was, however, supplemented by three additional types of specification. First, every tube was tested in a functional circuit, simulating that stage of the amplifier for which the tube was ultimately intended. Here measurements were made of shot noise (appropriate to first stage usage) and harmonic generation (ap- propriate to the output stage) in addition to the usual measurements of transconductance, anode impedance and working point. ELECTRON TUBES FOR A TRANSATLANTIC TELEPHONE CABLE 187 Second, all tubes were subject to intensive visual scrutiny in which some 80 specific constructional details were checked for possible faulty assembly. Third, the Ufe characteristics of transconductance, total emission and working point were examined over the test period of about 4,000 hours for unsatisfactory trends. Although this type of specification is more difficult to define precisely, its application is probably more rigorous and exacting than any of the previous specifications. Only if a tube passed the conventional test and the three supple- mentary tests was it considered adequate for inclusion in a repeater. Fig. 1-1 — View of interior of a 6P12 type tube. 188 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 CONCLUSION The laying of the present repeatered transatlantic cable represents by far the most ambitious use to date of long life, unattended electron tubes. On this project alone there are 390 tubes operating on the ocean bottom. If to this number are added the ocean bottom tubes from earlier shorter systems, those used in the Alaskan cable completed a few months ago, and those to be used in the California-Hawaiian cable to be laid in 1957, the total number on the ocean bottom will be about one thousand. The capital investment dependent on the satisfactory performance of these tubes is probably about one hundred million dollars — ■ strong evidence of faith in the ability to produce reliable and trustworthy tubes. It is of interest to note that the two groups working on the tubes on opposite sides of the Atlantic had no intimate knowledge of each other's work until after the tube designs had been w^ell established. As a result of subsequent discussions, it has been surprising and gratifjdng to find how similarly the two groups look at the problems of reliability of tubes for submarine cables. The authors would be completely remiss if they did not mention the contributions of others in the work just described. These projects would have been impossible if it were not for the enthusiastic, cooperative and careful efforts of many people working in varied fields. Over the years chemists, physicists, electrical and mechanical engineers, laboratory aides, shop supervisors and operators all have made essential contribu- tions to the projects. It would be impractical and unfair to attempt to single out for mention the work of specific individuals whose contribu- tions are outstanding. There are too many. REFERENCES 1. K. G. Compton, A. Mendizza and S. M. Arnold, Filamentary Growths on Metal Surfaces — "Whiskers," Corrosion, 7, pp. 327-334, Oct. "l951. 2. M. Benjamin, The Influence of Impurities in the Core-Metal on the Thermionic Emission from Oxide-Coated Nickel, Phil. Mag. and Jl. of Science, 20, p. 1, July, 1935. 3. H. E. Kern and R. T. Lynch, Initial Emission and Life of a Planar-Type Diode as Related to the Effective Reducing Agent Content of the Cathode Nickel (abstract only), Phys. Rev., 82, p. 574, May 15. 1951. 4. G. H. Metson, S. Wagener, M. F. Holmes and M. R. Child, The Life of Oxide Cathodes in Modern Receiving Valves, Proceedings I.E.E., 99, Part III, p. 69, March, 1952. 5. G. H. Metson and M. F. Holmes, Deterioration of Valve Performance Due to Growth of Interface Resistance, Post Office Electrical Engineers Journal, 46, p. 193, Jan., 1954. 6. M. R. Child, The Growth and Properties of Cathode Interface Layers in Re- ceiving Valves, Post Office Electrical Engineers Journal, 44, p. 176, Jan., 1952. 7. G. H. Metson, A Study of the Long Term Emission Behaviour of an Oxide Coated Valve, Proceedings I.E.E., 102, Part B, p. 657, Sept., 1955. Cable Design and Manufacture for the Transatlantic Submarine Cable System Bv A. W. LEBERT,* H. B. FISCHER* and M. C. BISKEBORN* (Manuscript received September 19, 1956) The transatlantic cable project required that two repeatered cables be laid in the deep-water crossing between Newfoundland and Scotland, and one across the shallower waters of Cabot Strait. The same structure was adopted for the cables laid in the two locations. This paper discusses the considerations leading to design of the cable and describes the method of manufacture, the means and equipment for control of cable quality, the process and final inspection procedures, the electrical characteristics of the cable, and factors relating to mechanical and electrical reliability of the final product. DESCRIPTION OF CABLE General features of the cable structure adopted for the transatlantic cable project^ are illustrated in Fig. 1. The cable consists of two basic parts: (1) the coaxial, or the electrical transmission path, and (2) the armor or outer protection and strength members. The coaxial is made up of three parts: (1) the central conductor, (2) the insulation, and (3) the outer or return conductor. The central con- ductor is composed of a copper center wire surrounded by three helically applied copper tapes. The insulation is a polyethylene compound which is extruded tightly over the central conductor. The insulated central con- ductor is called the cable core. The outer or return conductor is com- posed of six copper tapes applied helically over the insulation. The protection and strength components shown in Fig. 1 for the type D deep water cable are provided by a teredo tape of thin copper applied over the outer coaxial conductor, a fabric tape binding, a layer of jute rove for armor bedding, the textile covered armor wires and finally, two layers of jute yarn flooded with an asphaltum-tar compound. This cable is characterized by the extra tensile strength of its armor wires and by the extra precautions taken to minimize con-osion of these wires. * Bell Telephone Laboratories. 189 100 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 At the shallow water shore ends, the armor types are characterized by the use of mild steel wires which are increased in diameter in steps as the landing is approached. These types are designated A and B and will be described in greater detail later. The transmission loss of this cable structure at the top operating fre- quency of 164 kc is 1.6 db per nautical mile and is 0.6 db per nautical mile at 20 kc, which is the lower end of the frequency band. The high frequency impedance of the cable is about 54 ohms. BASIS OF DESIGN A coaxial structure was first used for telephone and telegraph service in a submarine installation in 1921, between Key West and Havana, Cuba. Three coaxial cables with continuous magnetic loading and no submerged repeaters were laid. One telephone circuit and two telegraph circuits were provided in each cable for each direction of transmission. In 1950, a pair of submarine coaxial cables,^ which included flexible submerged repeaters, was laid between Key West and Havana, Cuba. Each cable furnished 24 voice circuits. One cable served as the "go" and the other as the "return" for the telephone conversations. The transat- lantic telephone cable design is similar to this cable except that the nominal diameter of the insulation is 0.620" instead of 0.460". An out- standing difference between the transatlantic and Key West-Havana systems is cable length — about 2,000 nautical miles as compared with 125. This difference influenced significantly the permissible electrical and mechanical tolerances applying to the cable structure. The installation of some 1,200 miles of cable with island based re- peaters for a communication and data transmission system for the U. S. Air Force, between Florida and Puerto Rico,^ followed the 1950 sub- marine cable system. The design of this cable is identical with that of the transatlantic cable, except for differences in the permissible dimen- sional tolerances on the components of the electrical transmission path. Data obtained on the electrical performance of the Air Force cable pro- vided the transmission characteristic to which the repeaters for the transatlantic project were designed. The design of this cable installation was the result of many years of cable development effort, which was guided by the successes and failures of the earlier submarine telegraph cables. The 1950 Key West-Havana and the Air Force cables differed from the earlier struc- tures in one important respect, namely, the lay of the major components. A series of fundamental design studies during the 1930's and 1940's and extensive field tests in the Bahamas in 1948 demonstrated that having CABLE DESIGN AND MANUFACTURE 191 the same direction of lay of the major components of a cable was very important in minimizing kinking and knuckling. In addition, other lab- oratory tests pointed the direction for the adoption of new materials and techniques in the manufacture of these cables. These and subsequent improvements in materials and manufacturing techniques were included in the transatlantic cable design. Since the electrical characteristics of a cable have a direct bearing on the overall system design and performance, considerable emphasis was placed on this phase of the design of the transatlantic cable. The size of COAXIAL< PROTECTION AND STRENGTH < COPPER CENTER WIRE 3 COPPER SURROUND TAPES INSULATION POLYETHYLENE COMPOUND 6 COPPER RETURN TAPES COPPER TEREDO TAPE TREATED COTTON TAPE JUTE BEDDING WITH BINDING STRING 24 COTTON COVERED ARMOR WIRES JUTE LAYER OUTER JUTE LAYER Fig. 1 — Structural features of the deep water type of cable. 03 Q c3 C 0) El 0) -2 u c c o CU UJ o c3 +3 a. cc Q. C < o3 <0 -f- 7 e^- O O 1- 'r. < 0) a Ul a -1-3 o tu -1-3 (0 =« LU o T H _x O ei z -t-3 tr T3 a D CVJ U < Q Q UJ '^ til ^ o; HI o _l z Q a X Q. o > o tl (D 1 1- cc a. < a. < ■M a. < -u 3 S .Sf o 3 ' ' 0. 2 M o < oo o T ■^ 1- Q ^ ( ) o Q ^ lil u. ^ H O o o I* + * 192 CABLE DESIGN AND MANUFACTURE 193 central conductor and core used in the Air Force cable resulted in low unit attenuation and low dc resistance. These advantages resulted in the adoption of this size of cable. However, the outside diameter of the core and the diameter of the central conductor of the coaxial do not fulfill the requirements generally described as optimum for minimum attenuation. Mathematical analysis shows that there is a preferred diameter ratio which results in minimum transmission loss. For the 0.620'' core diameter employed in the Air Force cable, the central conductor diameter chosen was smaller than the ideal central conductor required to satisfy the pre- ferred diameter ratio. The diameter chosen retained the central conductor size which the Key West-Havana and Air Force cables proved to be satisfactory from a manufacturing standpoint. The choice was also com- patible with the dc resistance requirement for transmission of power over the cable to each of the repeaters. While production of the cable was proceeding, cable manufactured to the transatlantic specification was tested near Gibraltar in March, 1955. These tests provided a final evaluation of the mechanical and electrical characteristics of this cable before the actual laying of the transatlantic link. DETAILS OF STRUCTURAL DESIGN OF CABLE The structural features of the coaxial and of types A, B and D armor are summarized in Fig. 2. A composite central conductor was chosen to provide a conductive bridge across a possible break in any one of its elements, due to a hidden defect, such as an inclusion of foreign material in the copper. The dimen- sions of the components of the central conductor were preciselj^ con- trolled, and a light draw through a precision die was used to compact and size the assembly. Use of high molecular weight polyethylene (grade 0.3) for core in- sulation is a major departure from the materials used in early submarine telephone and telegraph cables. The development of synthetic polymers such as polyethylene had led to the replacement of gutta percha as cable insulation, since polyethylene possesses better dielectric properties and mechanical characteristics and is lighter in weight. Ordinary low molecular weight polyethylene is subject to environ- mental cracking, especially in the presence of soaps, detergents and cer- tain oils. High molecular weight material is much less subject to crack- ing, and by adding 5 per cent butyl rubber, further improvement in crack resistance is obtained. Six copper tapes applied helically over the core comprised the return 19-i THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 conductor and thus completed the coaxial structure. The dimensions of these tapes were precisely controlled. The helical structure was chosen to impart flexibility to the coaxial. Insulation of some of the early submarine telegraph cables suffered from attack b}^ marine borers such as the teredo, pholads and limnoria. To protect against such attack, a thin metallic tape was placed over the insulation in the early submarine cables. The necessity for such protec- tion for the transatlantic cables, especially in deep water, may be ques- tioned, but the moderate cost of this protection was considered cheap in- surance against trouble. The copper teredo tape was applied directly over the return conductor, as a helical serving Avith overlapped edges to completely seal the coaxial from attack by all but the smallest marine organisms. A cotton tape treated with rubber and asphaltum-tar compound was applied over the teredo tape to impart mechanical stability to the co- axial during manufacture. A small gap between adjacent turns of the helix was specified to permit ready access of water to the return tape structure and to the surface of the core. The use of a gap was based on laboratory tests which showed that transmission loss was dependent to a modest extent on thorough wetting of the exterior of the coaxial. Since transmission loss measurements are made on repeater sections of cable shortly after manufacture to determine whether any length adjustments are required, it was essential that the wetting action be as rapid as possible. The design of the protection and strength components of the cable was modified according to the depth of the water in which the cable was to be laid. To prevent damage to the coaxial by any cutting action of the armor wires during manufacture and laying, a resilient cushion of jute roving was placed between the armor wires and coaxial. For type-D cable, a single layer of jute was used; for types A and B cable, the bed- ding was made up of two layers of jute. To protect this jute from micro- biological attack, a cutching treatment was employed. The traditional Table I Armor Wire Type Number of Wires Diameter in Inches Material Application A B D 12 18 24 0.300 0.165 0.086 .Mild Steel Mild Steel High Strength Steel Up to 350 fath. 350 to 700 fath. Greater than 700 fath. CABLE DESIGN AXD MANUFACTURE 195 cutching process consists of treating the jute with a vegetable compound called catechu or cutch. Armor wires were applied over the bedding jute. The use of heavy or intermediate weight near shore has been established by experience with ocean cable. This type of armor is generally employed where the cable may be exposed to wave action, bottom currents, rocks, icebergs, ship's anchors and fishing trawlers. A lighter weight structure having higher tensile armor wires is needed in deep water. Table I shows the essential differences between the armor types employed in the transatlantic cable and the approximate range of depths in application. In addition to the above armor types, a shore length of 0.6 nautical mile was provided with an insulated lead sheath under Type A armor to facilitate preferred grounding arrangements and to provide signal to noise improvement. Where the tensile strength of the armor wires is most important, as in the type D design, each of the wires was protected against corrosion by a zinc galvanize plus a knitted cotton serving or helically applied tape, the whole assembly being thoroughly saturated with an asphaltum- tar compound. The effectiveness of such protection is clearly apparent Avhen early submarine cables, which used this protection, are recovered and examined. For the heavier armor types, the protection was similar to that of type D, except that the textile serving was replaced by a dip treatment to coat each wire with an asphaltic compound. As the armor wires were applied to each type of cable additional pro- tection was obtained by flooding the cable with a special asphaltum-tar compound and then applying two layers of jute yarn over the wires. The jute yarn was impregnated with an asphaltum-tar compound before ap- plication to the cable and then flooded with another asphaltum-tar compound after application. Formulation of cable flooding materials re- quired the use of compounds having a relatively high coefficient of fric- tion to avoid slippage of the cable on the ship's drum during laying. To assure satisfactory handling characteristics during the laying op- eration, all of the metallic elements of the cable were applied with a left- hand direction of lay and the lengths of lay (except for the teredo tape) were chosen so that approximately the same helical length of material was used per unit length of cable. Since the teredo tape was relatively soft and ductile compared to that of the other metallic components, it was not necessary to equate its helical length to that of the other com- ponents. Width and lay of the teredo tape were selected to give a smooth, tight covering. The choice of direction and length of lay of the jute layers was based 196 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 on experience with cable in factory handling and laying trials. Experi- ence, particularly with the direction of lay, has shown that improper choice of lays for the two outer layers of jute may result in a cable that is difficult to coil satisfactorily in factory and ship storage tanks. The combination of lays selected for the cable components provided good performance in all the handling operations, including the final laying across the Atlantic. MANUFACTURE OF THE CABLE Before considering the manufacture of the cable, it should be under- stood that the repeater gain characteristic was designed to compensate for the loss characteristic of the cable. Therefore, once this loss charac- teristic was established, it was essential that all cable manufactured conform with this characteristic. To obtain the required high degree of conformance, close control had to be kept over all stages of manufacture and over the raw materials. Controls to guide the manufacture of the cable were set up with two broad objectives: 1. To produce a structure capable of meeting stringent transmission requirements. 2. To assure that the manufactured cable could be laid successfully and would not be materially affected by the ocean bottom environment for the expected life of the cable system. Attainment of a final product capable of meeting the stringent trans- mission requirements is described in a later section of this paper. Process and raw material controls in manufacture were provided by an inspection team which checked the quality of the various raw materials and the functioning of the several processes during the manufacturing operations. This type of inspection coverage is somewhat unique with submarine cable. It assures the desired final quality by permitting each error or accident to be investigated and corrected on an individual basis. Cable for the transatlantic crossing was manufactured in America by the Simplex Wire and Cable Company and in England by Submarine Cables, Limited. Differences in machinery and equipment in the plants of the two manufacturers necessitated minor differences in the sequence of the operations and in the processes. The sequence of operations in assembly of the cable was as follows: Step No. Operation 1 Stranding of central conductor 2 Extrusion of insulation 3 Runover examination, repair where necessar}- CABLE DESIGN AND MANUFACTURE 197 4 Panning and testing of core 5 Jointing of core 6 Application of return tapes, teredo tape, fabric tape, jute bedding and binding string 7 Application of armor wire and outer jute layers 8 Storage in tanks, testing 9 Splicing in repeaters, testing The only important difference in the sequence of the manufacturing operations at the two plants was the use of separate operations for steps 6 and 7 at Submarine Cables and the combination of these operations in one machine at Simplex. Other minor differences in process methods related to raw materials. For example, the American supplier purchased polyethylene already compounded with butyl rubber and antioxidant in granule form, ready for use. The British supplier purchased polyethylene, butyl rubber and antioxidant separately, and performed the compounding in the cable factory. STRANDING OF CENTRAL CONDUCTOR The central conductor was stranded on a machine which included a revolving carriage with suitable arbors for the three surround tapes. It was equipped with brakes designed to assure equal pay-off tension among the tapes and with detectors to automatically stop the strander in case of a tape break. Each tape was guided through contoured forming rolls to shape the tape to the center wire. The joints between successive reels of wire and tape used in fabrication of the central conductor were butt brazed. The brazes w^ere staggered to avoid more than one braze in a given cross-section of the conductor. The quality of the brazes in these components was controlled by a qualifica- tion technique described below in the section on core jointing. The strand was drawn through several forming dies to size the finished diameter of the central conductor accurately. No lubrication was used because the removal of the resultant residues, which could contaminate the polyethylene insulation, was difficult. The taper in the central con- ductor diameter due to the die wear w^as controlled by appropriate re- placement of tungsten carbide dies, where used, or by the use of a diamond die where the rate of die wear is less than 1 or 2 micro-inches per mile. The stranding area in both plants was enclosed and pressurized to guard against dirt and dust settling on the central conductor. A high standard of cleanliness was maintained for parts of the machine which touched the conductor or its components. Undue wear of the guide faces 198 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 c a o G '■B a 03 03 o3 bO C u "Sh a; > CO bb CABLE DESIGN AND MANUFACTURE 199 or capstan sheaves was cause for replacement of the sheaves and adjust- ment of the machine. A photograph of the stranding area is shown in Fig. 3. EXTRUSION OF INSULATION To avoid possible contamination of the polyethylene insulating com- pound in the extruder-hopper loading area, a pressurized enclosure pre- vented entry of air-borne dust and dirt, and the containers of poly- ethylene compound were cleaned with a vacuum cleaner before being brought into the hopper area. A fine screen pack placed in the extruder reduced the possibility of contamination in the core. In passing through the extruder, the central conductor was payed-off of a large reel with controlled tension, into the pay-out capstan, through an induction heater, through a vacuum chamber, and thence into the cross-head of the extruder. The induction unit heated the central con- ductor and provided means for controlling the shrinkback of the core insulation and the adhesion of the conductor to the insulation. Shrink- back is a measure of the contained stresses in the insulation. On the output side of the extruder, the core was cooled in a long sec- tionalized trough containing progressively cooler water from the input to the output end. The annealing of the polyethylene in the cooling trough also served to hold the shrinkback of the core to a low value. The extru- sion shop is shown in Fig. 4. An important addition to the extrusion operation consisted of the use of an improved servo system to control the extruder automatically to attain constant capacitance per unit-length of coaxial. The system used is described in a subsequent section. RUNOVER EXAMINATION Following extrusion, the core was subjected to continuous visual and tactual examination in a rereeling operation called "runover". The pur- pose of the runover operation was the detection of inclusions of foreign material in the dielectric and the presence of abnormally large or small core diameters. Core not meeting specification requirements was cut out or repaired. In addition to visual inspection of the cable, examination of short lengths of core was made at regular intervals with a shielded source of light arranged to illuminate the interior of the dielectric material. Provi- sion of this internal illumination facilitated detection of particles of foreign material well beneath the surface of the core. Strip chart records 200 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 o o o bX) > bio CABLE DESIGN AND MANUFACTURE 201 Fig. 5 — Special water tank or pan for tests on immersed cable core. of the unit-length capacitance of the core obtained during extrusion were used as a guide in searching out regions of uncertainty. PANNING AND TESTING After runover, the core was coiled in tanks of water, as shown in Fig. 5. Precautions were taken to remove the air dissolved in the water and thus prevent the formation of bubbles on the surface of the core. The water was also temperature controlled and circulated to maintain uniform temperature throughout the tank. Thermocouples placed at different levels in the tank determined when the temperature was uniform. Measurements of dc conductor resistance, ac capacitance, insulation re- 202 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 sistance, and dielectric strength were then made. These measurements are discussed in detail in a later section of this paper. JOINTING OF CORE LENGTHS The cable core was manufactured in lengths much shorter than a re- peater section, which necessitated connecting the individual core lengths together. Jointing techniques consisted of brazing the central conductor with a vee-notch type of junction and of molding in a short section of the polyethylene insulation. After silver-soldering the vee-joint, a safety wire consisting of four fine gauge tinned copper wires was bridged across the junction in an open helix and soft soldered at the ends. Extreme care was taken to remove any excess rosin and to eliminate any sharp points on the ends of the safety wires. The safety wire is intended to maintain continuity of the electrical path in case the braze should fail. Visual examination of brazes in the actual cable was the only means available for their final inspection. To assure a high degree of quality on these brazes, a system was devised for checking the performance of the operator and the brazing machine initially and at frequent intervals through the use of sample brazes in each of the components, which were tested to destruction. To control the uniformity of brazes, the brazing of the copper wire and tapes was made as automatic as possible by the use of controlled pressure on the components, appropriate sized wafers of silver solder, and an automatically timed heat cycle. The tests on the brazes used to qualify operators and machinery indicated that a high de- gree of braze performance was achieved. Pressure and temperature were carefully controlled during the molding of the insulation over the conductor. Periodic checks similar to those described for brazes were made on operator and molding-machine to maintain a satisfactory level of performance. In addition, each molded joint placed in the actual cable was X-rayed and subjected to a high voltage test while immersed in water. APPLICATION OF RETURN TAPES AND ARMOR WIRES After the core lengths were joined together, they were pulled through the return taping and armoring operations. The machine for applying return tapes was designed specifically for the purpose and was similar in characteristics to the corresponding portion of the strander for the cen- tral conductor. Controlled pay-off tension, automatic breakage detectors, precision guides, and contoured forming rolls to shape the tape, were incorporated in the construction. CABLE DESIGN AND MANUFACTURE 203 The return tape, teredo tape, and fabric tape were applied from taping heads, and the bedding jute and binding string were appHed from serving heads in a tandem operation. Another set of tandem operations inchided the appHcation of armor wires, outer jute layers and the appropriate asphaltum-tar flooding compounds. In the American suppliers plant, both sets of tandem operations were combined into one continuous pro- duction line. In the British plant, these operations were divided into two separate production lines. A view of the armoring machine area is shown in Fig. 6. Following the application of the flooding compounds, whiting is applied either at the take-up capstan on the armoring line or in the storage tanks as the cable is coiled. To avoid core damage, the flow of hot flooding compound w^as stopped when the cable in the armoring line was stopped. One of the major sources of such stoppages was the reloading of the various applicating heads. STORAGE AND TESTING In a continuous haul-off operation, the cable was conveyed from the armoring machine to the tank house for storage. The cable was coiled in spiral layers, called flakes. Each flake started at the outside rim of the tank and worked toward the central cone. Several 37-nautical mile re- peater sections were stored in each tank. Water was circulated through the cable tanks to establish uniform temperature conditions throughout the mass of cable. When thermo- couples located at appropriate points in the tank indicated that the cable temperature was uniform, measurements were made of attenuation, in- ternal impedance irregularities and terminal impedances, dc resistance, dc capacitance, insulation resistance, and dielectric strength. To facilitate these tests without interrupting production, successive repeater section lengths were placed in alternate tanks. By this pro- cedure, a group of four or five sequential repeater section lengths, called an "ocean block", was stored in two tanks. The ends of each repeater section were brought out of the tank to a splicing location. After all tests were completed and the specification requirements met, the repeaters were spliced in. Testing of the ocean block for transmission performance completed the manufacturing operations. RAW MATERIALS Stringent requirements were placed on all raw materials used in the manufacture of the transatlantic cable. Detailed specifications covered 204 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 c3 O 3 a a o n, o 7} CABLE DESIGN AND MANUFACTURE 205 the basic requirements and the methods of controlHng their quahty on a samphng inspection procedure. The requirements for the materials were estabhshed to insure that their use would not jeopardize the life of the cable. Since cable life is critically related to the integrity of the insulation, all materials had to be scrutinized for their tendency to cause environ- mental cracking. These tests were necessarily made on an accelerated basis. Since no correlation exists at present between accelerated tests and long term (20 year) life tests, only conservative design selections can be justified. Close tolerances such as dzO.0002 inch for the diameter of the solid center wire in the central conductor were specified for all copper com- ponents of the coaxial. In addition, these components had to be free from slag or other inclusions, and the wire drawing and rolling of the tape had to be controlled to assure smooth surfaces, edges of prescribed shape, and freedom from filamentary imperfections. Compounds used in drawing and rolling operations were selected to minimize the possibility of con- taminating or causing cracking of the polyethylene. Residual quantities of compound on the wire or tapes were removed prior to annealing, which was controlled to prevent the formation of oxides and to assure clean and bright copper. The dielectric constant range of the polyethylene-butyl compound was limited to 2.25 to 2.29. These limits were determined by the limited ac- curacy of the measuring equipment available at the time. Restrictions covered the allowable amount of contamination since its presence in other than minute quantities might reduce the dielectric strength or de- grade the power factor of the compound. In addition, the melt index (a factor related to molecular weight) of the final insulating compound composed of polytheylene resin, butyl rubber, and antioxidant, was held to 0.15 to 0.50. The melt index of or- dinary polyethylene used for insulation generally, is 2.0 or higher. Choice of the low index assured the maximum resistance to environ- mental cracking. The cutching and fixing processes used in the manufacture of bedding jute were adjusted to limit the alkalinity of the jute because of the ad- verse effect of alkaline materials on polyethylene compound. Oils used in the spinning of the jute were selected to obtain types which were not strong cracking agents for polyethylene, and the quantities used were reduced to the workable minimum. The presence of such impurities as bark and roots was restricted to provide the desired fiber strength. The impregnation of the jute w^as controlled to ensure adequate distribution 206 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 of the coal tar throughout the fibers without having an excess that would make the jute difficult to handle during the armoring process. The size, composition, and processing of the armor wires were also placed under close control. Purity, tensile strength, and twist recjuire- ments were designed to ensure that the wire could be applied to the cable, and welded, and that it could withstand the expected tensions during laying and pickup. Strength considerations made it mandatory that inclusions of slag or piping of the wire be eliminated. Piping is an unusual condition encountered during rolling or drawing which results in a hollow shell of steel which may be filled with slag. CONTROL OF TRANSMISSION CHARACTERISTICS From a broad point of view, the attainment of a final product capable of meeting the stringent transmission requirements was achieved by the following basic steps. 1. Precision control of the dimensions of the copper conductors, in- cluding the diameter of the fabricated central conductor. 2. Automatic control of the insulating process to maintain a constant capacitance, thus compensating for deviations in central conductor diam- eter and dielectric constant of the insulation. 3. Factory process control, by means of a running average of the measured attenuation characteristic of current production, to guide the adjustment of suitable parameters when necessary. As indicated in the sections above on the method of manufacture and the control of raw materials, precautions were taken to obtain a central conductor that had predictable electrical performance, and a controlled taper in overall diameter along its length. The need for such effort is ex- plained by consideration of the factors that determine the attenuation of a coaxial structure. The attenuation, a, of the cable is directly proportional to the ac re- sistance, /?, and inversely proportional to the characteristic impedance, Zo , as a satisfactory approximation. That is, a = -=- db/nm where "a" is a coefficient depending on the units. It is thus clear that control of a may be attained by control of R and Zo . Since the resistance is a function largely of the diameter of the central conductor, and since it is held to close tolerances, the constancy of impedance completes the requirement for attenuation control. CABLE DESIGN AND MANUFACTURE 207 The characteristic impedance of a transmission line is determined by: Zo = b -y/e log -J ohms where e is the dielectric constant of the insulating material, D is the inside diameter of the outer conductor, d is the diameter of the inner conductor, and 6 is a numerical coefficient. If the dielectric constant of the insulating material (polyethylene) does not vary, control of charac- teristic impedance reduces to control of capacitance. This follows from the fact that the capacitance, C, is related to the D/d ratio as follows: D ... ke - = antilog ^ where fc is a numerical coefficient. Precision control of capacitance during the insulating process is achieved by a double-loop linear servo system, as shown in a simplified block diagram, Fig. 7. The two loops consist, respectively, of one capable of introducing relatively fast capacitance corrections of only modest accuracy and of one capable of highly precise capacitance control on a relatively long time basis. The servo system controls the capstan payout SUPPLY REEL ><]extruder TJ- _n COOLING TROUGH PAYOUT CAPSTAN DRIVE MOTOR ^ DIAMETER "SENSING UNIT DIAMETER CONSOLE MOTOR SPEED CONTROL HIGH -PASS FILTER RECORDER ^ SUMMING NETWORK CAPACITANCE MONITOR TAKE- ELECTRODE UP —7 REEL OSCILLATOR '/////////, BRIDGE REFERENCE STANDARD CAPACITOR DETECTOR RECORDER LOW -PASS FILTER Fig. 7 — Simplified block diagram of capacitance monitor servocontrol system. 208 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 speed of the central conductor feeding into the extruder applying the core insulation, as shown in the block diagram. Since the extruder de- livers insulating material at a constant rate, an increase in central con- ductor speed results in a thinner than normal wall of insulation and thus causes an increase in capacitance. The sensing element for the control loop consists of a capacitance monitor. This is a device capable of measuring the unit length coaxial capacitance of the cable core continuously as it moves through the water in the trough. Since the capacitance of a polyethylene insulated core is temperature sensitive, the monitoring electrode must be located at a point in the cooling trough where the temperature of the core is stable and known to a degree commensurate with the overall accuracy objec- tives. The distance from the extruder to the electrode corresponds to about 10 minutes of cooling time; hence, a servo system based on this loop would be necessarily slow, due to the 10-minute delay in detecting a drift in capacitance. Analysis shows that fast capacitance information of only moderate accuracy may be used in combination with the slow loop to speed up the response of the overall system to a satisfactory degree, without sacrifice of precision of the slow loop. The sensing element used for the fast loop consisted of a light-ray diameter gauge, which measures the diameter (changes in diameter are the approximate inverse of the ca- pacitance) of the hot core close to the extruder. The slow and fast data are combined to control the extruder, as shown in the block diagram. The servo constants were chosen to minimize the deviations in unit length capacitance occurring in core lengths corresponding to less than J wave length of the top operating frequency. Stated in other words, the objective for choice of servo loop constants was to assure equality in the capacitance of all I wave sections of core. Echo measurements indicated that a highly satisfactory degree of control was achieved. Overall servo system performance was such that the standard deviation of the ca- pacitance of the core lengths manufactured for the two crossings was ±0.1 per cent. The capacitance monitor electrode and the servo console is illustrated in Fig. 8. ADJUSTMENT OF CONCENTRICITY Means for setup and adjustment of the extrusion process to achieve relatively accurate centering of the conductor in its sheath of insulation was provided by a device called a concentricity gauge. This device op- erates on the principle that two small, plane electrodes on opposite CABLE DESIGN AND MANUFACTURE 209 Fig. 8 — Photograph of capacitance monitor electrode and servo-controller console in laboratory setup. sides of the core will have different direct capacitances to the central conductor, when the conductor is not properly centered. A simplified block diagram of the concentricity gauge is shown in Fig. 9. Data obtained with two sets of electrodes displaced 90° were recorded on a strip chart recorder, with the output of the two sets of electrodes being displaj^ed alternately. A satisfactory degree of centering was moderately easy to maintain. ELECTRICAL MEASUREMENTS To assist in achieving the goal of matching the cable and the repeater characteristics with a minimum of deviations, electrical measiu'ements were made throughout the process and close tolerances were placed on the electrical parameters in each stage of production. Measurements on the repeater section lengths of cable were used as a final check to deter- mine the extent to which all of the controls had been successful. The primary standards used were calibrated by the Bureau of Standards in the United States or the National Physical Laboratories in England. These precision standards were used to calibrate the bridges frequently. The dc resistance of the central conductor was measured under con- stant temperature conditions with a precision type of Wheatstone bridge. The permissible range of resistance was 2.514 and 2.573 ohms 210 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 per nautical mile at 75°F. In practice, the spread of resistance values was well within these limits. The 20-cycle core capacitance was also measured under constant- temperature conditions. For this measurement, the two ends of the central conductor were connected together and the measurements made l)etween the central conductor and ground, which was provided by the water. A capacitance-conductance bridge was used for this purpose. The capacitance limits set initially were from 0.1726 to 0.1740 microfarads per mile at 75°F. Analysis of the core measurements indicates that at each factory the range of capacitance was held more closely than indi- cated, which illustrates the benefits of servo control to the insulating process. The dc insulation resistance of the core was also measured by applying 500 volts for one minute. A minimum insulation resistance requirement of 100,000 megohm-miles at 75°F was established, but any lengths that had less than 500,000 megohm-miles were scrutinized for possible sources of trouble and were subject to rejection. As a general rule, insulation resistances considerably in excess of 500,000 megohm-miles were ob- tained. The core was tested also at a voltage of 90,000 volts dc for a period of one minute. This test was designed to catch any gross faults in the SPRING-LOADED ELECTRODES RECORDER Fig. 9 — SimpUfied block diagram of concentricity gauge for continuous meas- urement of centering of central conductor. CABLE DESIGN AND MANUFACTURE 211 core caused by foreign particles which escaped detection by the other mechanical and electrical tests made on the core. As discussed under the section on jointing, the core lengths were as- sembled and joined together to form a repeater section of cable. In general, an effort was made to produce the core for a repeater section of cable on a particular strander, extruder, and armoring line, and to join the lengths together in the order of manufacture. Practical difficul- ties such as the fact that the outputs of two stranders were required to supply one extruder made it impossible to achieve this objective in all cases. Capacitance deviations from the desired nominal resulted from a variety of causes, such as inaccurate control of the temperature of the water in the core cooling troughs and improper adjustment of the control apparatus. To minimize the reflection which would result from joining together two lengths of core of widely different capacitances, cores were not joined together if their measured ac capacitances differed by more than 0.3 per cent. When such capacitance differences did exist, the core length involved was removed from its normal sequence and placed in a position near the middle of the repeater section. Because the taping and armoring processes were combined in one € CABLE UNDER TEST 3E ISOLATING TRANSFORMER MATCHING TERMINATION SPLITTING PAD \ SERIES MATCHING TERMINATIONS SWITCHED AT POWER FREQ RATE FINE GAIN CONTROL CRO OSCILLATOR CONSTANT VOLTAGE REGULATOR t STANDARD FREQUENCY GENERATOR t 1 ATTENU- ATOR S MATCHING < TERMINATION TUNED DETECTOR CONSTANT VOLTAGE REGULATOR 11 AC SOURCE AC SOURCE Fig. 10 — Simi)lified block diagram of cable attenuation measuring set. 212 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 production line in the American factory, no other electrical measure- ments could be made on the components of the cable until it was com- pletely armored. In the British factory, tests for information purposes only were made on the cable in the coaxial stage. These tests included measurements of attenuation, internal impedance irregularities, and terminal impedances. They served as a means of evaluating the changes in the electrical performance during armoring. The insulation resistance requirement after armoring and storage under water for at least 24 hours was 100,000 megohm-miles. The cable had to withstand 50,000 volts for a period of one minute without failure. ATTENUATION MEASUREMENTS As an aid in achieving the desired uniformity of product, new meas- uring equipment of improved accuracy was provided. A block schematic of this equipment is shown in Fig. 10. The requirements for this equip- ment were that it should be capable of measuring a 37 to 44 mile section of cable with an absolute accuracy of 0.04 db and a precision of 0.01 db in the frequency range from 1 to 250 kc. The attenuation of the cable was measured at 10 kc intervals from 10 kc to 210 kc and measured values were corrected to 37°F, using the changes in attenuation owing to temperature, shown in Fig. 11. By comparing the corrected values with the design characteristic shown in Fig. 12, the deviations were determined. Both the attenuation charac- ic'''°"'' u. y m 1.4 yT r a UJ Q. UJ 1.2 _i 5 y y NAUTICAL b ^ ^^ DECIBELS o y^ / ' 0.4 20 40 60 80 100 120 140 FREQUENCY IN KILOCYCLES PER SECOND 160 180 Fig. 11 • — Change in cable attentuation due to temperature as a function of frequency. CABLE DESIGN AND MANUFACTURE 213 40 60 80 100 120 140 FREQUENCY IN KILOCYCLES PER SECOND 180 Fig. 12 — Design characteristic of cable attentuation as a function of fre- quency for 37°F and atmospheric pressure. teristic and the changes in attenuation owing to temperature were de- rived from factory measurements of attenuation made on the Florida- Puerto Rico cable. By comparing the running average and spread of these deviations with the design requirements, it was possible to assess the performance of the cable and, if required, to make any necessary adjustments in parameters for subsequent sections. In addition, these deviations were used to determine the length adjustment required for each repeater section to keep the sum of the deviations at each frequency in any one ocean block to a minimum. Typical average attenuation deviation characteristics are shown in Fig. 13. TEMPERATURE AND PRESSURE COEFFICIENTS Measurements of primary constants were made on 20-foot lengths of cable and core placed in a temperature and pressure controlled tank. These measurements were used to compute the temperature coefficients of attenuation in order to check the values derived from measurements made on the Florida-Puerto Rico cable section. Additional attenuation measiu'ements were made on several repeater section lengths of cable over a range of temperature from approximately 40° to 70°F, to estab- lish further the magnitude of the changes in attenuation with tempera- 214 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 ,xtO-'* UJ -J 2 < u 1- < Z cr UJ Q. in CO u UJ Q -120 -160 40 60 8C 100 12 FREQUENCY IN KILOCYCLES PER 0 140 SECOND 160 180 Fig. 13 — Deviation of measured cable attentuation from design characteris- tic as a function of frequenc.v. Typical average values for Types A, B, and D for 37°F and atmospheric pressure. tiire. The measurements indicated that the derived temperature co- efficients were accurate to within ±10 percent. Measurements also were made to determine the effect of pressure on the primary constants of the cable. These measurements indicated that capacitance was the only parameter affected by pressure. The capaci- tance increased linearly 0.1 percent for each 500 pounds per square inch of applied pressure. Since the attenuation, a, is inversely proportional to the impedance, it is evident that if C is the only parameter affected by pressure, a will also be affected b}^ pressure to an amount equal to approximately one half the pressure effect on C. The pressure coefficient of oc was therefore established as 0.05 percent per 500 pounds per square inch of pressure. LAVING EFFECT Analysis of the Florida-Puerto Rico cable data indicated that the measured ocean bottom attenuation was less than the attenuation predicted from factory measurements. The differences were large enough to warrant study and indicated that the measurements were in doubt or sea bottom conditions w^re not known accurately or that some un- explained phenomenon was taking place. In March of 1955, approximately 22 miles of cable of the transatlantic design were laid in 300 fathoms of water off the coast of Spain in the Bay of Cadiz, and another equivalent length was laid in 2,300 fathoms off Casablanca. Precise measurements of attenuation were made in both cases, and it w^as established that a difference did in fact exist CABLE DESIGN AND MANUFACTURE 215 UJ ^-0.01 _j < o 3-0.02 < 2 q: LU °- -0.03 (Tl _l UJ CD U LU -0.04 Q -0.05 ~~^ ^^ 300 FATHOMS X V ^- ^ \ 2300 FATHOMS " 20 40 60 80 100 120 140 FREQUENCY IN KILOCYCLES PER SECOND 160 180 Fig. 14 — ■ Laying effect or deviation of measured attenuation from predicted attenuation as a function of frequency, as observed in Gibraltar trials. between measured values of attenuation at the ocean bottom and values predicted from factory measurements. It was further established that the difference in 2,300 fathoms was about twice that in 300 fathoms. The measured differences are shown in Fig. 14. It was established during these trials that the difference increased slightly with time. Measurements made on the cable in 300 fathoms immediately, 18 hours, 48 hours, and 86 hours after laying indicated that measurable changes in attenuation were taking place. However, the change between 48 and 86 hours was so small that it was concluded only very small changes would occur in a moderate interval of time. The tests also indicated that the attenuation of the two lengths of cable decreased somewhat during loading of the cable ship. The total difference between the attenuation at the ocean bottom and the values predicted from factory measurements, taking the temperature and pressure coefficients into account, was designated "laying effect". Various theories, such as the consolidation of the central conductor, consolidation of retvu'n structure, and changes in the dielectric material have been advanced to explain these differences. Each of these has been under study, but at the time of writing this paper, no conclusive ex- planation has been established. The shape of the "laying effect" versus frequency characteristic was such that the adjustment of repeater section lengths in conjunction with several fixed equalizers, which had approximately 4 db loss at 160 kc and 0.6 db loss at 100 kc, would provide a good system characteristic. The matter of equalization is covered in greater detail in the article^ on the overall system. The magnitude of the laying effect observed during the laying of the two transatlantic cables substantiated the trial results. 216 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 PULSE ECHO MEASUREMENTS Process controls, such as the use of a capacitance monitor and the jointing of the core in manufacturing sequence provided the means for controlling the magnitude of reflections due to impedance mis-matches. However, to insure that the final product met these requirements, measurements of terminal impedance and internal irregularities were made using pulse equipment. A block schematic of the circuit of the echo set is shown in Fig. 15. For the submarine cable tests, a 1.5-microsecond raised cosine pulse OSCILLOSCOPE AND AMPLIFIER ATTENUATOR BALANCING NETWORK HYBRID COIL -^3C PULSE GENERATOR REPEATER SECTION OF CABLE UNDER TEST Fig. 15 — Simplified block diagram of pulse echo set for measurement of ter- minal impedance and internal impedance irregularities. was used, and the impedance of the balancing network was calibrated at 165 kc. The 165-kc impedance of the repeater sections was maintained well within a range of 54.8 =b 1 ohm. The internal irregularities at the point of irregularity were maintained at least 50 db below the magnitude of the measuring pulse. The requirement was 45 db. ACKNOWLEDGMENTS The authors wish to acknowledge the many contributions made by the members of the staff of the Simplex Wire and Cable Company, Submarine Cables Limited, the British Post Office, and the Bell Labora- tories groups involved during cable design and manufacture. REFERENCES 1. E. T. Mottram, R. J. Halsej', J. W. Emling, and R. G. Griffith, Transatlantic Telephone Cable System — Planning and Over-All Performance. See page 7 of this issue. 2. J. J. Gilbert, A Submarine Telephone Cable with Submerged Repeaters, B.S.T.J., 30, Jan, 1951. 3. P. T. Haury and L. M. Ilgenfritz, Air Force Submarine Cable System, Bell Lab. Record, Sept., 1956. 4. H. A. Lewis, R. S. Tucker, G. H. Lovell and J. M. Fraser, System Design for the North Atlantic Link. See page 29 of this issue. System Design for the Newfoundland-Nova Scotia Link By R. J. HALSEY* and J. F. BAMPTON* (Manuscript received September 14, 1956) The design and engineering of the section of the transatlantic cable sys- tem between Newfoundland and Nova Scotia were the responsibility of the British Post Office. The tj-ansmission objectives for this link having been agreed in relation to the overall objectives, the paper shows how these were translated into system and equipment design and demonstrates how the objectives were realized. INTRODUCTION Under the terms of the Agreement/ it was the responsibility of the British Post Office to design and engineer the section of the transatlantic cable system between Newfoundland and Nova Scotia. In common with other parts of the system, all specifications were to be agreed between the Post Office and the American Telephone and Telegraph Company, but as both the British and the American types of submerged repeater had been carefully studied and generally approved by the other party prior to the agreement, the basic pattern of the system was clear from the beginning. The service and transmission objectives for the overall connections London-New York and London-Montreal were agreed- in early joint technical discussions in New York and Montreal and the agreed total impairments were divided appropriately between the various sections. In this way, the transmission objectives for the Newfoundland- Nova Scotia link were established. ROUTE The choice of Clarenville as the junction point of the two submarine sections of the transatlantic system was determined primarily in relation * British Post Office. 217 1? p o bX) 218 SYSTEM DESIGN NEWFOUNDLAND-NOVA SCOTIA LINK 219 to the Atlantic crossing and the desire to follow a transatlantic route to the north of existing telegraph cables.^ There were a number of possi- bilities for the route between Clarenville and the east coast of Cape Bre- ton Island, the most easterly point which could be reached reliably by the radio-relay system through the Maritime Provinces of Canada. One possibility, which had been considered earlier, was to cross New- foundland by a radio-relay system and to employ a submarine-cable link across Cabot Strait only. The final decision to build a cable system between Clarenville and Sydney Mines raised a number of problems in respect of the route to be followed, concerned primarily with poten- tial hazards to the cable brought about by: (a) The existence of very extensive trawling grounds on the New- foundland Banks. (b) The location of considerable numbers of telegraph cables in the vicinity. (c) Grounding icebergs. The route finally selected after thorough on-the-spot investiga- tions^' ^' ^ (Fig. 1) is satisfactory in respect of all these hazards, in- volving no cable crossings and being inshore of the main fishing grounds. The straight-line diagram of the route is shown in Fig. 2; the total cable length is 326 nautical miles, of which 54.8 nautical miles are between Clarenville and Terrenceville, Newfoundland, where the cable finally enters the sea. The maximum depth of water involved is about 260 fathoms. QUEENS COVE S. W. ARM TERRENCEVILLE R2 PLACENTIA BAY y R1 h— - -12.31 •-K- 20.02- ADEYTOWN RANDOM /SOUND HILLVIEW t i CLARENVILLE -K 22.52 H SYDNEY MINES R16 RIO E R9 R3 TERREN CEVIL N X X X X f«---1l.68-^»|< -)f -- ^^ ^ - 6.094 --*j«-- -5.707 >j< ^ 4*--2.932 >| Fig. 2 — Straight-line diagram of route. R. Repeater. E. Equalizer. All dis- tances are in nautical mile,s. ♦Repeater spacing R3-R9 and R10-R16, 20.4 n.m. 220 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 CABLE Choice of Design Since 1930, when the Key West-Havana No. 4 cable was constructed,^ it has been usual to extrude the insulation of coaxial submarine cables to a diameter of about 0.62 inch, and most of the cables in the waters around the British Isles are of this size. The experience of the British Post Office with submerged repeaters'^ in its home ^vaters, dating from 1944, when the first repeater was laid between Anglesey and the Isle of Man,* has therefore been mainly with 0.62 inch cables, first with para- gutta as a dielectric and later with polyethjdene. Most of these cables were originally operated without repeaters, and the 60-circuit both-way repeaters which are now installed on the routes were designed to match their characteristics. In planning a new system, the size of cable will be determined by one of the following considerations: (i) Minimum annual charges for the desired number of circuits. (ii) Terminal voltage required to feed the requisite number of re- peaters. (iii) Maximum number of repeaters or minimum repeater spacing which is considered permissible. (iv) Maximum (or minimum) size of cable which can be safely handled by the laying gear in the cable ship. Fig. 3 • — Cross-section of cable across Newfoundland showing make-up. A. Centre conductor, 0.1318-inch in diameter copper. B. Three 0.0145-inch copper surround tapes. C. Polyethylene to 0.620-inch diameter. D. Six 0.016-inch copper return tapes. E. 0.003-inch overlapped copper teredo tape. F. Impregnated cotton tape. G. Five iron screen tapes. H. Impregnated cotton tape overlapped. J. Poly- ethylene sheath to 1.02-inch diameter. K. Inner serving of tanned jute yarn. L. Armour wire 29 x 0.128-inch diameter. M. Outer serving of tarred jute yarn. SYSTEM DESIGN' — XEWFOUXDLAXD-XOVA SCOTIA LIXK 221 When the 36-circuit system between Aberdeen, Scotland, and Bergen, Norway, was planned in 1952, the route length (300 nautical miles) greatly exceeded that of any other submarine telephone sj^stem, and it was decided to use a core diameter of 0.935 inch, first, to keep the number of repeaters as low as seven, and second, because the system was in- tended as a prototype of a possible Atlantic cable. The cable dielectric is polyethylene (Grade 2) with 5 per cent polyisobutylene. For the Clarenville-Sydney Mines link it proved possible to design for minimum annual charges. With increasing experience and confidence in submerged repeaters, it was no longer considered necessary to restrict the number of repeaters as for Aberdeen-Bergen, and the terminal volt- age requirements were reasonable. At the current prices of cable and repeaters in Great Britain the optimum core diameter for 60 both-way circuits is about 0.55 inch, but the increased charge incurred by using 0.62-inch cable is less than 5 per cent (0.62-inch core is optimum for 120 both-way circuits). In order to facilitate manufacture and the provision of spare cable, it was therefore logical to adopt the same design as that proposed for the Atlantic crossing and described elsewhere.^' ^ After investigating various possible types of cable for the overland section in Newfoundland, it was decided to use a design essentially the same as the main cable but with additional screening against external interference.* As far as the outer conductor and its copper binding tape, the construction (Fig. 3) is identical with that of the main cable except that the compounded cotton tape is overlapped. Outside this are five layers of soft-iron tapes each 0.006-inch thick, the innermost being longi- tudinal and the others having alternate right- and left-hand lays at 45° to the axis of the cable. After another layer of compounded cotton tape there is extruded a polyethjdene sheath 0.080 inch thick, and the whole is jute served and wire armoured. As a check on the efficiency of the screening, the maximum sheath-transfer impedance at 20 and 100 kc was specified as 0.005 ohm per 1,000 j^ards. It was thus possible to treat the entire link from Clarenville to Syd- ney Mines as a uniform whole, using the same type of repeater on land as in the sea. A small hut at Terrenceville contains passive networks only. Attenuation Characteristics When the system was designed, precision measurements of cable at- tenuation were not available. The design of the Oban-Clarenville link ^vas based on laboratorv measurements on earlier 0.62-inch cable of a 222 THE BELL SYSTEM TECHNICAL JOURNAL, JAXUARY 1957 similar t3^pe, but the available data applied only to frequencies up to about 180 kc, whereas the Clarenville-Sydney Mines link was to operate at frequencies up to 552 kc; extensive extrapolation was therefore in- volved. As soon as the first production lengths of cable became available in February, 1955, lajang trials were carried out off Gibraltar, and it was found that there were serious changes of attenuation on la3dng, over and above those directly attributable to temperature and pressure effects, and that the assumed characteristics were inaccurate. Although the attenuation in the factor}' tanks had been in reasonable agreement with that of the earlier cable, there were changes on transfer to the ship's tanks and again on lajdng, amounting in all to a reduction of about 1.5 per cent at 180 kc. This would have been comparatively miimportant had the discrepanc}' been of 'cable shape', i.e., the same fraction of the cable attenuation at all frequencies and therefore exactly compensated bj^ a length adjustment of the repeater sections. As this was not so, and as the cable-equalizing networks in the repeaters were settled by this time, it was clear that precise information must be obtained in order that suitable additional equalizers could be provided for insertion in the cable on laying. There are a number of factors which can lead to small changes of attenuation on laying, but most of these tend to increase the losses. The primary reason for the observed changes appears to be contact variations between the various elements of the inner and outer con- ductors, i.e. the wire and three helical tapes forming the centre conduc- tor and the six helical tapes forming the return conductor. These contact resistances tend to change with handling, and as a result of a slight degree of 'bird caging' when coiled, it seems that the attenuation de- creases as the coiling radius increases, and vice versa. Also, the effect of sea pressure is to consolidate the conductors and thereb}^ further reduce the attenuation — an effect which appears to continue on a diminish- ing basis for a long time after laying. To obtain reliable data for the Clarenville-Sydney Klines link, 10 nautical miles of cable with A-type armour was laid at about the mean depth of the system (120 fathoms), off the Isle of Skye. The attenua- tions, coiled and laid, are shown in Fig. 4, due allowance ha^dng been made for temperature and pressure. The ordinates — attenuation versus frequencj^ — are such that the value should be approximately con- stant at high frequencies. In making a final determination of the cutting lengths for the re- peater sections, it was assumed that the factory measurements of at- tenuation would be reduced by 1.42 per cent at 552 kc on laying, that the temperature coefficient of attenuation would be +0.16 per cent SYSTEM DESIGN NEWFOUNDLAND-NOVA SCOTIA LINK 223 ^ 0.0041 o o o .^ LU CL (/) _l LU $ U LU Q z g < D Z LU 0.0040 0.0039 .-' -— (a) 1 1 • ./" 1 1 1 I 1 1 I 1 / / ^ -ibl_. ^ o > 1 I i 1 < (C) > 0— R 1 / 1 / / / / / / K# L> - v^d) ^ \* V /^ \ \ y^ 20 50 100 FREQUENCY 200 300 400 IN KILOCYCLES PER SECOND 500 640 Fig. 4 — Cable attentuation characteristics — Skj-e trials, (a) Characteristic originally assumed. (6) Characteristic measured in factory tank (flooded), (f) Characteristic measured in ship's tank (flooded), (c?) Characteristic measured after laying. per deg C and that the true pressure coefficient of attenuation was negligible at the depths involved. DESCRIPTION OF SYSTEM Circuit Provision and Frequency Allocation It was originally thought that a design similar to that of the Aber- deen-Bergen system would be suitable for the Clarenville-Sydney Mines route in that it Avould provide more circuits (36) than the long section across the Atlantic. This potential excess capacity, which was required for circuits between Newfoundland and the Canadian mainland, dis- appeared when it was found that 36 circuits could, in fact, be provided over the longer link. The Aberdeen -Bergen design was therefore modi- fied to provide a complete supergroup of 60 circuits, the same capacity as the earlier British projects.^ The system thus requires broad-band transmission of 240 kc in each direction. In the earlier British projects the frequency bands transmitted are 24-264 and 312-552 kc, but for the present purpose the lower band is 224 THE BELL SYSTEM TECHNICAL JOUKNAL, JANUARY 1957 . (/) ai m mo l-LU o o < CP o z < z c^ Ci -3 O lij 36 lJ OH- O < f\J Q. O a. tr m Q. So a u O i =i CO O t^oit e>l z|<3 ^ c a; si t o S n ■) c> ^^ rr tn o U) UJ o rr t?z LU 5 z a. (0 UJ ^ = 1 / 5 SYSTEM DESIGN — NEWFOUNDLAND-NOVA SCOTIA LINK 225 dropped by 4 kc to 20-260 kc, so that the loAvest frequency is the same as on the Atlantic cables. This enables common frequency-generating equipment to be used at Clarenville for the two links and minimizes crosstalk problems. The main transmission bands and the allocation of the five 12-circuit groups are shown in Fig. 5, together with the ancillary channels; the facilities pro^dded are discussed later. Submerged Repeaters The submerged repeaters emploj^ed are fully described elsewhere/" and it will suffice to note here that they are rigid units, approximately cylindrical in shape, 9 feet long and 10^ inch maximum diameter. The}' are capable of withstanding the full laying pressure in deep water, al- though this of little importance in the present application. They are arranged for both-way transmission through a common am- plifier which has two forward paths in parallel, with a single feedback path. The two halves of the amplifier are so arranged that practically any component can fail in one, without affecting the other. Power-Feeding Arraiigements The submerged repeaters are energized by constant-current dc sup- plies between the center conductor and ground, the power units at the two ends being in series aiding and the repeater power circuits being in series with the center conductor, i.e., without earth connections, as in Fig. 6. This is the only arrangement by which it is possible to control the supply accurately at every repeater, the insulation resistance of cable and repeaters being sufficiently great that the current in the center conductor is virtually the same at all points. The constant-current fea- ture of the supply ensures that repeaters cannot be overrun in the event of an earth fault on the system. On the Oban-Clarenville link the anode voltage is derived from the drop across the electron tube heaters. This results in the heaters being at a positive potential with respect to the cathodes, a condition which tends to break down the heater-cathode insulation." In the Ameri- can electron tubes this insulation is very robust and the risk is considered to be negligible, but in the current British electron tubes, which have a much higher performance, the arrangement is undesirable. In view of the much smaller number of repeaters it was possible to derive the heater and anode supplies as in Fig. 6 and thus to reverse the sense of the heater-cathode ^•oltage and also to proA'ide an anode voltage of 90, against 55 in the longer link. 226 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 With this arrangement the Unk requires a total supply voltage of about 2,300. The power-feeding equipment^^ at each terminal station is designed to feed a constant current of 316 ma at this voltage, and it is permissible to energize the system from one end only, if necessary. The repeater capacitors — the limiting factors in respect of line voltage — are rated very conservatively at 2,500 volts, so that a single-ended supply of 2,300 volts, with the possibility of superimposed ground-po- tential differences, is near the desirable maximum. The two terminal power units are therefore designed to operate in series and to share the voltage. With access to the cable provided at Terrenceville it is possible to operate the power system on the following bases: (a) No ground at Terrenceville, power from both ends on a master- and-slave basis (to ensure that the constant-current units do not build up an excessive voltage) ; this is the normal arrangement. (6) No ground at Terrenceville, power from one end only. (c) Ground at Terrenceville, with the Clarenville and Sydney Mines SYDNEY MINES FROM CARRIER EQUIPMENT HIGH PASS FILTER LOW PASS FILTER POWER UNIT GROUND PLATES IN SEA 1 X" (a) CLARENVILLE TO CARRIER EQUIPMENT HIGH PASS FILTER LOW PASS FILTER POWER UNIT ANODES I CATHODES PF m^xJi^^^v^^^ 0.5V 6 HEATERS 33V PF 0.5V (b) Fig. 6 — Power-feeding arrangements, (a) General schematic, (b) Repeater power circuit. P.F. — Power filter. SYSTEM DESIGN — NEWFOUNDLAND-NOVA SCOTIA LINK 227 power units energizing the land and sea cables respectively; this ar- rangement has been particularly useful during the installation period. The presence of high voltages on the cable constitutes a potential danger to personnel, hence special precautions are taken in the design of the equipment in which the cable terminates and in which high volt- ages exist or may exist. The ground connections for the power circuits at the two ends are via special ground cables and ground plates located about half a mile from the main cable, and metering arrangements are provided to check that the current does in fact take this path. These measures ensure that the current returning via the cable armour is never sufficient to cause serious corrosion. Arrangement of Terminal Equipment Fig. 7 show the arrangement of the terminal equipment. In accord- ance with an early agreement defining precisely the various sections of the project, the link is considered to terminate at the group distribu- tion frames at Clarenville and Sydney Mines, i.e. at the 60-108 kc inter- connection points. In addition to the cable-terminating and power-feeding equipments (A and B) , the following are provided at the terminals : (a) Submarine-cable terminal equipment (C) consisting of repeaters to amplify the signals transmitted to and received from the cable, equalizers and frequency-translating equipment to convert the line fre- quencies to basic supergroup frequencies (312-552 kc). (6) Group-translating (group-bank) equipment (D) to convert the basic supergroup to five separate basic groups (60-108 kc) and vice versa. (c) Equipment for the location of cable and repeater faults (E and F) . (d) Speaker and printer circuit equipments (G and H) to provide two reduced-bandwidth telephone circuits, two telegraph circuits and one alarm circuit for maintenance purposes. It is clear that such circuits should be substantially independent of the main transmission equip- ment. Two principles were agreed very early in the planning; first, that the engineering of the various links should be integrated as far as possible, and second, that the items of equipment at each station should be pro- vided by the party best in the position to do so. In consequence: (i) Items of standard equipment were provided by the A.T. and T. Co. at Clarenville and Sydney Mines (and by the Post Office at Oban), thus simplifying maintenance and repair problems. OO -nil! inn UJ _l _l > z lU DC < u H en LU LU z > in I ^ o ,^^ u OO iTTTnTTT] c — • C C jr .« (U « c3 S o3 s a. « ^ •■" ^ c/i 0^ d-t^S. ^gg -0 ojn vii- 3 ^feco 111 ^ n 0-9*'- ffl .^cc 0 H ■^ r^ 0 - .- « ^ — ' __^ ^«s fi M„, 2 c-2 S-^ c3 3^2^ 111 * ;- r* n: :^ — < 1- •— ^ u. 0 z LU 5 gc"^ -t^ . ->^ LU ( 1 D- /-s c a ^ ■ ^ u ^ -^^ n' -J CL Q 228 SYSTEM DESIGN — NEWFOUNDLAND -NOVA SCOTIA LINK 229 (ii) Basic power plant and the carrier supplies for supergroup and group translation were provided by the A.T. and T. Co. for both ter- minal equipments at Clarenville. (iii) Terminal equipment special to the Clarenville-Sydney Mines link was provided by the Post Office. In view of the importance of the link, the power-feeding and trans- mission equipment are completely duplicated. The submarine-cable terminal equipment is arranged to transmit the basic supergroup, directly over the cable in the east-to-west direc- tion. In the west-to-east direction the supergroup is translated to the range 20-260 kc, using a 572 kc carrier. DESIGN OF TRANSMISSION SYSTEM Performance Requirements The agreed transmission objects for the Clarenville-Sydney Mines link were as follows : Variation of Transmission Loss. The variation in the transmission loss of each group should have a standard deviation not greater than 0.5 db; this implies that the varia- tion from nominal should not exceed 1.3 db for more than 1 per cent of the time. A ttenuation/ Frequency Characteristics. Only the overall characteristics of the individual circuits were pre- cisely specified, the limits being the C.C.I.F. limits for a 2,500-km cir- cuit and the target one-half of this. With this objective in view, the group characteristics in each link must clearl}^ be as uniform as is practicable. Circuit Noise. The total noise contributed by the link to each channel in the busy hour (i.e., including intermodulation noise) should have an r.m.s. value not exceeding -(-28 dba* (corresponding to —56 dbm) at a point of zero relative level. * This refers to the reading on a Bell System 2B noise meter (FIA weighting network); the noise level (dba) is relative to a 1 kc tone at —85 dbm. In Europe, noise is measured on a C.C.I.F. Psophometer (1951 weighting network), which is calibrated in millivolts across 60(? ohms; this is commonly converted to picowatts (pw). The white noise equivaleTir<^ of the two instruments is given bj' dba = 10 logio pw — 6 = dbm -f- 84; the agreed limit of -{-28 dl)a is therefore equivalent to 2513 pw (1.2.3 mv or —56 dbm). The corresponding C.C.I.F. requirement at 4.0 pw/km would be 2,400 pw, this vidue not to be exceeded for more than 1 per cent of the time. 230 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 Crosstalk. The minimum equal-level crosstalk attenuation should be 61 db for all sources of potentially intelligible crosstalk; this was accepted as a target for both near- and distant-end crosstalk. Although go-to-return crosstalk is not important for telephony (it appears as sidetone) and a limit of 40 db is satisfactory even for voice-frequency telegraphy, it assumes great importance for both-way music transmission ; also, it was desired to be non-restrictive of future usage. Assessment of Requirements The design of the high-frequency path to meet the agreed require- ments involves consideration of: (a) Noise, including fluctuation (resistance and tube) noise and inter- modulation. (6) Wide-band frequency characteristics, including the effects of the directional filters at the terminal and in the repeaters. (c) Variations of (a) and (6) in respect of temperature and aging. The noise requirement is by far the most important factor in the design of the line system. The choice of route and cable having been made, the total loss was known and it was necessary to determine the minimum number of re- peaters to compensate for this loss and to meet the noise requirement with adequate margin for inaccurate estimates of cable attenuation after laying, temperature variations, aging and repairs. An attempt to achieve the necessary gain with too few repeaters would result in exces- sive noise. Design of the amplifiers in the British repeaters is such that, with both forward paths in operation, the overload point is about +24 dbm, and with a loading of 60 channels in each direction, this permits planning levels of about —4 dbm at the amplifier output after allowing reasonable margins for errors and variations. ^^ Previous experience shows that, at such output levels, intermodulation noise can be neg- lected and the full noise allowance allotted to fluctuation noise. The effect of tube noise is to increase the weighted value of resistance noise by about 1 db to —137.5 dbm, or —53.5 dba, at the input to the amplifier in each repeater. At the highest transmitted frequency the equalizers, power filters and directional equipment introduce losses of about 1 db and 4 dh at the SYSTEM DESIGN — NEWFOUNDLAND-XOVA SCOTIA LINK 231 input and output of the amplifier respecti\-ely ; these losses must, effec- tivel}', be added to the loss in the cable. Two other pieces of information are necessary before the repeater system can be planned — the permissible transmitting and receiving levels at the shore stations. The transmitting equipment provided at Clarenville can be operated at channel levels up to +20dbm, and it is logical to allow the same recei\dng level at the shore end as at inter- mediate repeaters. On the above basis it is possible to construct a curve (Fig. 8) relating the total circuit noise to the number of intermediate repeaters, and it is seen that the minimum number is 15, each of which must have an overall gain of 59 db (amplifier gain, 64 db) at 552 kc. The actual provision is 16 repeaters, each having a gain of 60 db at 552 kc, the additional gain being absorbed in fixed and adjustable networks at points along the route, as indicated in the follomng section. Level Diagram The actual level diagram (planning levels are shown in Fig. 9) differs somewhat from that which can be deduced directly from the preceding because of the following considerations: (a) The location of the first repeater from Clarenville (i.e., on land) -100 10 12 14 16 18 20 NUMBER OF REPEATERS Fig. 8 — Variation of circuit noise with number of repeaters. 232 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 was dictated b}- topography and the desire to locate both it and the second repeater in ponds; thus the transmitting level at Clarenville is substantially lower than the permissible maximum. (h) There are equalizing networks at Terrenceville and facilities for their adjustment to compensate for temperature variations. (c) Because of the difference between the actual cable attenuation and that for which the repeaters were planned (see section on Attenuation Characteristics) it was necessary to include an equalizer unit in the sea, midway between Terrenceville and Sydney Mines. Loss equivalent to 9 nautical miles of cable was also introduced at this point to ensure that repeater No. 16 would be sufficiently far from the shore at Sydney Klines. (d) Cable simulators are included in the cable-terminating equipment at Sydney Mines to build out this section to a standard repeater section; the actual cable length was, of course, unknown until the cable was complete. Taking into account the existence of the intermediate networks, the repeater spacing is such that when both land and submarine cable sections are at mean temperature the compensation is as accurate as possible. In general the highest frequency is of greatest importance in this respect. Since the low -frequency' channels experience less attenua- tion than the high-frequency channels, it is permissible to transmit them at a somewhat lower level, thereby increasing the load capacity of the amplifiers which is available to the high-frequenc\' channels. i SYDNEY MINES 1 CLARENVILLE I > _J 0 LU > P -20 < ^*»^ k ^..^20 KC ^~ "S"' ^^ ^~~~~. _) LU cH -40 \ \^ -60 \ '^260KC N \ \ \ ^ REPEATER NO. 16 1 5 10 • 9 3 • 2 SUBMERGED TERRENCEVILLE E QUALIZE R Fig. 9 — System level diagram. SYSTEM DESIGN — NEWFOUNDLAND-NOVA SCOTIA LINK 233 Temperature Effects and their Compensation The effect of temperature changes is hkely to be somewhat complex. The land-and-sea cable sections are expected to behave in different ways in this respect, but data on the manner of variation are not very precise. The submarine cable crosses Cabot Strait, where melting icebergs drift- ing down from Labrador as late as June can be expected to keep the sea- bottom temperature low until well into the summer; temperatures just below 0° C were, in fact, recorded when the cable was laid in May. On land, the cable is buried 3 feet deep in bog and rock, and traverses many ponds; some data on temperatures under similar conditions in other parts of the world were available. For planning purposes it was clear that the assumptions made would have to be somewhat pessimistic, and the assumed ranges of tempera- ture, with the corresponding changes of attenuation at 552 kc, were: Sea section . . . . 2.3 ± 3° C; ±4 db Land section . . . . 7.5 ± 10° C; ±3 db A possible method of circuit adjustment for temperature changes is to increase the gains equally at the sending and receiving terminals as the temperature rises and to reduce them ecjually as it falls. Under such conditions the effect of temperature variations on resistance noise is not \e\y important; the levels at repeaters near the center of the route remain substantially constant, and the increase in noise from the repeaters whose operating levels are reduced is partly compensated by the reduction in noise from those whose levels are increased. The effect of the level changes on repeater loading is, however, more important as it is undesirable that any repeater in the link should overload, and ad- ditional measures which can be readily adopted to avoid serious changes in repeater levels are clearty desirable. The estimated change of attenuation of the land sections is seen to be roughly ecjual to that of the submarine section, so that, from the point of view of temperature changes, Terrenceville is near the electrical center of the link. It was thus both desirable and convenient to provide adjustment at this point: Fig. 10 illustrates the advantage of seasonal changes in equalizer setting at Terrenceville, showing the way the output levels of repeaters are likelj^ to vary along the route. The system of tem- perature compensation adopted therefore involves adjustable networks at both ends of the system and at Terrenceville. All the networks are cable simulators; hence the process of temperature compensation con- sists, effectively^ in adding 'cable' when the temperature falls and re- moving it when the temperature rises. 23-i THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 At Terrenceville, the networks permit adjustments equivalent to ±1 nautical mile of cable (3 db at 552 kc), but at Clarenville and Syd- ney Mines adjustments equivalent to 0.5 db at 552 kc are provided. It should therefore always be possible to maintain the overall loss of the system within ±0.25 db, and the level at any repeater should never change by more than ±2 db. System Pilots The use of pilot tones applied at constant level at the input of a system with indicating or alarm meters at the receiving end is standard on land systems on both sides of the Atlantic, although the philosophies underlying the methods of use differ. On the submarine cables round the British Isles, with or without submerged repeaters, pilot tones are used SYDNEY MINES TERRENCEVILLE CLARENVILLE AT MINIMUM TEMPERATURE Fig. 10 — Deviation from mean of transmission levels with optimum adjust- ments of equalizers at Sj'dney Mines, Terrenceville and Clarenville. ^ W-E at 260 kc. ■ E-W at 552 kc. jVIaximum deviation in the two directions occurs at the above frequencies. SYSTEM DESIGN ^ NEWFOUNDLAND-XOVA SCOTIA LINK 235 to indicate the attenuation of the transmission path; these pilots are normally located just outside the main transmission bands in each direction. In the Clarenville-Sydney Mines system the frequency bands just outside the main transmission bands are occupied by telephone speaker and teleprinter circuits and by monitoring frequencies associated with the repeaters (see Fig. 5) ; this prevents the use of out-of-band pilots. Fortunately, the standard Bell System group equipment is designed to apply 92-kc pilots to each group and to measure the corresponding received level. Although these are essentially group pilots, being applied and measured at points in the 60-108-kc band, it was decided that they could reasonably replace the out-of-band pilots. These pilots are blocked at each end of the system and therefore function as section pilots only. Normal Post Office practice, both on land and submarine systems, is to use recording level meters to provide a continuous and permanent record of the pilot levels. In the present system such recording meters are used on the 92-kc pilots of two groups in each direction of transmission. In addition to the section pilots the system carries the 84.080-kc end-to-end pilots in each of the three transatlantic groups. MAINTENANCE FACILITIES Speaker and Printer Circuits It was part of the planning of the transatlantic system that two low- grade telephone (speaker) and two telegraph (printer) circuits should be provided over the submarine cables, outside the main transmission bands, and that the speaker circuits in particular should be reasonably independent of the main terminal equipment. One speaker circuit is re- quired for local communication between the terminals of each section, the other to form part of an omnibus circuit connecting the principal stations on the route including Montreal. The arrangement for tele- printer communication was that one channel should be an overall all-station omnibus printer, the other being a direct London-New York printer. Independent frequency-translating equipment is provided to connect the speaker and printer bands (each 4 kc) to the line. The carrier fre- quencies required for the speaker are provided by independent oven- controlled crystal oscillators, but for the printer the independent genera- tion of high-stability 572-kc carriers was not considered to be justified and the main station supplies are used. Two half -bandwidth telephone circuits are provided in the 4 kc speaker 236 THE BELL SYSTEM TECHXICAL JOUHXAL, JAXUAUY 1957 bands by the use of standard A.T. and T. band-splitting equipment (EB banks). Signalling and telephone equipment are provided to give the required omnibus facilities on one circuit and local-calling facilities on the other. The arrangement of the speaker and printer equipment at Sydney Mines is shown in Fig. 11. In the telegraph band a third channel transmits an alarm to the re- mote terminal when the 92-kc pilots incoming from that terminal fail simultaneously. Fault Location The speed}^ and accurate location of faults in repeatered cables is of very great importance, owing to the number of circuits involved and the difficulty and cost of repairs. The standard dc methods which have been applied in the past to long telegraph cables are, of course, available. The application of these methods is, however, recognized as being rather more OMNIBUS PRINTER TO NEXT STATION DIRECT PRINTER OMNIBUS SPEAKER 0 - 2 KC y , " M 0-4 KC ,, 308- 312 KC 312-552 KC ,. 264- ♦ > 268 KC DCO V V V V ' — TO ALARM — CIRCUITS 0-4 KC t^ 552- , 556 KC 1^ V 16-20 KC 16-268 KC 308- 556 KC TO "CLARENVILLE Fig. 11 — Arrangement of speaker and printer equipment at Sydney Mines. A. Submarine cable terminal equipment. B. Speaker circuit equipment. C. Emer- gencj'-band bank equipment. D. Omnibus speaker telephone. E. Local speaker telephone. F. Printer circuit ecjuipment. G. Three-channel telegraph equipment. H. Printer. SYSTEM DESIGN — NEWFOUXDLAND-XOVA SCOTIA LINK 237 in the nature of an art than a science and usually requires an intimate knowledge of the behaviour and peculiarities of the particular cable concerned. While the problem appears at first sight to be simple it is complicated by: (a) The presence of ground-potential differences along the cable, some- times amounting to hundreds of volts; these vary with time. (6) Electrolytic e.m.f. generated when the center conductor is exposed to sea water. (c) Absorption effects in the dielectric of the cable. When repeaters are added the position is further complicated by: (d) The lumped resistance of the repeaters, which is current-dependent and exceeds the cable resistance. (e) The lumped capacitance of the repeaters with an absorption char- acteristic which differs from that of the cable. It is a great advantage of both-way transmission over one cable that, by introducing some form of freciuency changer at each repeater, signals outgoing in one direction can be looped back to the sending terminal. There have been a number of developments based on this principle, and in the Clarenville-Sydney Mines link two methods are available for use. Of these, the so-called 'loop-gain' method uses steady tones and depends on selective frequency measurements to discriminate between repeaters ; the second is a pulse method in which repeaters are identified on the basis of loop transmission time. The use of these methods under fault conditions depends on the pos- sibility of keeping the repeaters energized. Work is in progress to de- velop methods of fault location which are of general application and do not depend on the activity of the repeaters, but these are outside the scope of the present paper. Loop-Gain Method. In the loop-gain method, the frequency changer in the repeater takes the form of a frequency doubler and each repeater is identified uniquely by one of a group of frequencies spaced at 120 cycles and located im- mediately above the lower main transmission band in the frequency range 260-264 kc. Since the frequency changing is in an upward sense, the measuring terminal is Sydney Mines, which transmits the lower band. On the Clarenville side of the directional filters in each repeater is connected, via series resistors, a crystal filter accepting the test fre- quenc3^ appropriate to the repeater [see Fig. 12(a)]; this frequency is doubled, filtered and returned to the repeater at the same point at which 238 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 JF / SYDNEY MINES BAND PASS FILTER 2f BAND PASS FILTER j CABLE 1 1 "*"" 1 REPEATER LF HIGH PASS FILTER / / \ 1 LOW PASS FILTER HIGH PASS FILTER 2f BAND PASS FILTER BAND PASS FILTER FREQUENCY DOUBLER CABLE J L J L J L UJ U 2 HI a. UJ u. UJ 16 15 14 13 12 11 10 REPEATER NUMBER (b) LU o z UJ a. lu u. UJ a. Fig. 12 — Fault location — loop-gain method, (a) Block schematic. Fre- quency/is in the band 260-264 kc. (6) Diagram of display. r-| \ SYDNEY -■ "- ' MINES HIGH PASS FILTER LOW PASS FILTER \ A ^ LOW PASS FILTER 1 HIGH PASS FILTER REPEATER Fig. 13 — Fault location: pulse method. A. Pulse generator. B. Display of received pulses. C. Point of intermodulation (output of amplifier). SYSTEM DESIGN NEWFOUNDLAND-NOVA SCOTIA LINK 239 the original frequency is selected. From this point it passes via the high-pass directional filters through the amplifier and back to Sydney Mines, where the level is measured on a transmission measuring set. Information obtained in this way on each repeater can be compared at any time with that obtained when the system was installed and any gain variations localized. The test equipment provided has the additional facility of an automatic sweep of the test frequency at 4 cycles and a display of the returned-signal levels on a cathode-ray tube as in Fig. 12(5). Although the transmitted signals lie outside the band of the W-E supergroup, the received signals, 520-528 kc, lie within the band of the E-W supergroup, and two channels must be removed from traffic to carry out the tests; these channels are in a "local" group. Piihe Method. As applied to the present system, the pulse method utilizes the over- load characteristic of the amplifier to effect the frequency change in the repeater. At Sydney Mines a continuous train of single-frequency pulses is applied in the lower transmission band, such that either the second or third harmonic is returned in the upper band, as in Fig. 13; at Clarenville two-frequency pulses are applied in the upper band such that either a second- or third-order difference product is returned in the lower band. The pulse length is 0.15 millisecond, and the frequencies used are given in Table I. At Sydney Mines the signals can be sent and re- ceived either on the line itself or via the group equipment; in the latter case only one group need be taken out of service. At Clarenville line measurements only are provided for. The primary display is on a cathode-ray tube with a circular time- base, and any one returned pulse can be accurately compared with the reference pulse on a second tube with a linear time-base. The pulse selected for such measurement is automatically blacked out on the pri- mary display. Table I Station Send to line Product /i h Sydney Mines kc 216 144 530 530 kc 380 340 2/i 3/i 2/2 - /l kc/s 432 Clarenville 432 150 150 240 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 Usefulness of the Loop-Gain and Pulse Methods. Both ineth(xls require that all the repeaters between the testmg ter- minal and the fault can he energized. If the fault is in the cable there is a \ery high probability that the center conductor will be exposed to the sea, in which case the power circuit can be maintained on one side of the fault at least, although it may be somewhat noisy. Because the system is short, it is permissible to energize the link full}' from one end onh'. The condition can never arise — ■ as it can in the Oban-Claren\-ille link — that the line current is limited by the maximum permissible terminal voltage. The loop-gain test is concerned with the amplifiers in their linear regime and gives no mdication of the overload point ; for this the pulse test must be used. On the other hand, the pulse test does not permit ac- curate measurement of levels, since the pulse level reaching a particu- lar repeater may be restricted by the o^•erload of an earlier repeater in the chain. The pulse test is particularly useful in providing a check that both sides of each amplifier are in operation and in locating a fault of this type. Each method depends for its operation on non-linearitj' at a point within each repeater and can only identify a fault as lying between two such consecutive points in the link. It is therefore desirable that these points should be as close as possible to the terminals of the repeater in order to ensure that the faulty unit can be identified. In this respect the loop-gain test has the advantage o^•er the pulse test. EXECUTION OF WORK Problems due to the remoteness of the site were overcome without undue difficult}' with the co-operation of the other parties concerned in the project, but the present paper would be incomplete without a brief reference to the cable- and repeater-laying operations in Newfoundland and at sea. The terrain and conditions in Newfoundland were quite unlike those with which the British Post Office normally has to contend, involving trenching and cabling through bog, rock and ponds in country of which no detailed surve}' or maps were available. Maps were constructed from aerial surve}', and alternative routes were explored on foot before a final choice was made. As much use as possible was made of water sections in the sea, river estuarj^ and ponds; some 22 miles were accounted for in this way, leaving about 41 miles to be trenched by machine or blasted. A contractor Avas engaged for this purpose and to lay the cable in the trench, but all jointing was done by the Post Office. The standards of conductor and core jointing were the same as those in the cable factories SYSTEM DESIGN — NEWFOUNDLAND-NOVA SCOTIA LINK 241 and on ship, portable injection-moulding machines and X-ray equip- ment being specially designed for handling over the bog. A single pair cable was also laid in the main cable trench to provide speaker facilities between Clarenville and Terrence\'ille (which has no public telephone), with intermediate positions for use of the lineman. As a measure of pro- tection against lightning strikes, two bare copper wires were buried about 12 inches apart and 6 inches above the cable. Both the construc- tional work in Newfoundland"* and the laying operation at sea^ have been described elsewhere. TEST RESULTS In the interval between the completion of the link in May, 1956, and its incorporation in the transatlantic system, tests were carried out to establish its performance and day-to-day variations; an assessment of the annual variations has, of course, been impossible at this date. Variation of Transmission Loss Close observation of the transmission loss of the 92 kc pilots on Groups 1 and 5 leads to the following tentative conclusions: (a) Over periods of 1 hour the variations are not measurable, i.e., less than =b0.05 db. (6) Over periods of 24 hours there are no systematic changes; ap- parently random changes of about 0.1 db are probably attributable to the measuring equipment. (c) Over a period of eight weeks (July and August, 1956) there was a systematic increase in loss of about 0.3 db. By means of the loop-gain equipment it has been possible to deduce that most of this change has occurred in the land section. The results indicate that the submarine cable link has better day-to- day stability than the best testing equipment which it has been possible to provide. Many more data will clearly be necessary befoi'e the annual variations can be definitely established, but the present indications are that these will be less than those assumed in the design of the link. A ttenuation/ Frequency Characteristics The frequency characteristics of the supergroup in the two directions of transmission are shown in Fig. 14. It will be seen that in no transat- lantic groups does the deviation from mean exceed ±0.35 db. Circuit Noise Table II shows the noise level on Channels 1 and 12 of each of the five groups measured without traffic on the system. 242 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 To assess the magnitude of intermodulation noise, all channels in one direction were loaded simultaneously with white noise and measure- ments taken on each channel in the opposite direction. From the talker volume data assumed in the design of the sj'stem, the expected mean talker power is —11.1 dbm at a point of zero relative level, with an ac- tivity of 25 per cent. For an equivalent system loading, therefore, the level of white noise applied to each chamiel under the above test condi- tions should be —14.1 dbm. Since this loading gave no sensible increase in the circuit noise, the test levels were raised until a reasonable increase in the noise level was obtained. In order to raise the channel noise to the specified maximum of 28 dba it was necessary to raise the channel levels to about — 1 dbm and — 4 dbm in the lower and upper bands re- spectively. These levels, some 13 db and 10 db above the assumed maximum loading of the system, give noise levels at least 26 db and 20 db above normal, and it is seen that adequate margins exist for varia- tions and deterioration of the link. Closely alUed to the problem of intermodulation is the overload characteristic of the sj^stem. Table III shows the measured overload point of the Hnk expressed as an equivalent level at the output of the amplifier in the repeater nearest to the transmitting terminal. It also shows the margm between the channel level at that point and the over- load point of the sj^stem; according to Holbrook and Dixon^' the mini- mum requirement in this respect is 18 db. 1.0 0.5 ffl u UJ O z o < D 2 lU t- I- < -0.5 -1.0 1.0 0.5 0 ■0.5 -1.0 GROUPS 3 f\ (a) /v hv ^~ -x ^ \j W (b) \ r^ V \ v^"^ ^\l \J 312 360 408 456 504 FREQUENCY IN KILOCYCLES PER SECOND 552 Fig. 14 — Attenuation versus frequency characteristics of supergroup, (a) Sydnej^ Mines — Clarenville. (6) Clarenville — Sydney Mines. SYSTEM DESIGN — NEWFOUNDLAND-NOVA SCOTIA LINK 243 Table II Group Channel Noise level Sydney Mines Clarenville dba dba 1 1 25.0 24.5 1 12 24.5 23.2 2 1 24.0 22.5 2 12 23.5 22.0 3 1 24.0 20.5 3 12 25.0 17.5 4 1 24.5 17.5 4 12 24.5 16.5 5 1 24.5 17.5 5 12 27.0 18.0 These results justify the assumption made in the design of the Hnk, that intermodulation noise is neghgible. Crosstalk The crosstalk requirements are met in all respects. CONCLUSIONS The submarine-cable link between Clarenville, Newfoundland, and Sydney Mines, Nova Scotia, was completed in May, 1956, and provides five carrier telephone groups, each capable of carrying twelve high-grade telephone circuits or their equivalent. The transmission objectives have been met in everj^ respect. Three 12-circuit groups are connected to the three groups across the Atlantic between Scotland and Newfoundland; the other two groups are available to provide 24 circuits between Newfoundland and the mainland of Canada. Table III Frequency Equivalent at amplifier in first repeater Channel level Overload Margin kc db db db 552 -2 -1-20 22 312 -4 -f24 28 260 -5 +25 30 20 -5 -1-25 30 244 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 ACKNOWLEDGMENTS It has been the authors' privilege to present an integrated account of the work of many of their colleagues in the Post Office and in industry. Post Office staff have been responsible for designs and for inspection and testing at home and in the field, as well as the laying of the sub- marine-cable system by H.M.T.S. Monarch. In Great Britain, Submarine Cables, Ltd., and the Southern United Telephone Co., Ltd., provided the submarine and overland cables respectively, while Standard Tele- phones and Cables, Ltd., supplied and contributed much to the design of the submerged repeaters and terminal equipment. On site, the as- sistance rendered by the Ordnance Survey of Great Britain, the Ca- nadian Comstock Co., Ltd., who laid the cable across Newfoundland, the Northern Electric Co., Ltd., who carried out the terminal equip- ment installations, and by the other partners in the project, the Ameri- can Telephone and Telegraph Co. Inc., the Canadian Overseas Tele- communication Corporation and the Eastern Telephone and Telegraph Co., has been invaluable. The permission of the Engineer-in-Chief of the Post Office to make use of the information contained in the paper is gratefully acknowledged. 11. BIBLIOGRAPHY 1. Transatlantic Cable Construction and Maintenance Contract, Nov. 27, 1953. 2. E. T. Mottram, R. J. Halisey, J. W. Emling and R. G. Griffith, Transatlantic Telephone Cable System — Planning and Over- All Performance. See page 7 of this issue. 3. M. J. Kelly, Sir Gordon Radlev, G. W. Gilman and R. J. Halsev, A Trans- atlantic Telephone Cable, Proc. I.E.E., 102B, p. 117, Sept., 1954, and Com- munication and Electronics, 17, pp. 124-136, March, 1955. 4. H. E. Robinson and B. Ash, Transatlantic Telephone Cable — The Overland Cable in Newfoundland, Post Office Electrical Engineers' Journal, 49, pp. 1 and 110, 1956. 5. J. S. Jack, Capt. W. H. Leech and H. A. Lewis, Route Selection and Cable Laying for the Transatlantic Cable Svstem. See page 293 of this issue. 6. H. A. Affel, W. S. Gorton and R. W." Chesnut, A New Key West-Havana Carrier Telephone Cable, B.S.T.J., 11, p. 197, 1932. 7. R. J. Halsey and F. C. Wright, Submerged Telephone Repeaters for Shallow Water, Proc. I. E. E., 101, Part L p. 167, Feb., 1954. 8. R. J. Halsey, Modern Submarine Cable Telephonv and Use of Submerged Repeaters', Jl. L E. E., 91, Part III, p. 218, 1944. 9. A. W. Lebert, H. B. Fischer and M. C. Biskeborn, Cable Design and Manu- facture for the Transatlantic Submarine Cable Sj'stem. See page 189 of this issue. 10. R. A. Brockbank, D. C. Walker and V. G. Welsby, Repeater Design for the Newfoinidland-Nova Scotia Link. See page 245 of this issue. 11. G. H. Metson, E. F. Rickard and F. M. Hewlett, Some Experiments on the Breakdown of Heater-Cathode Insulation in Oxide-Coated Receiving Valves, Proc. I. E. E., 102B, p. 678, Sept., 1955. 12. J. F. P. Thomas and R. Kelly, Power-Feed System for the Newfoundland- Nova Scotia Link. See page 277 of this issue. 13. B. D. Holbrook and J. T. Dixon, Load Rating Theorv for Multi-Channel Amplifiers, B.S.T.J., 18, p. 624, 1939. Repeater Design for the Newfoundland-Nova Scotia Link By R. A. BROCKBANK,* D. C. WALKER* and V. G. WELSBY* (Manuscript received September 15, 1956) The Newfoundland-Nova Scotia cable required the provision of 16 sub- merged repeaters each transmitting 60 circuits in the bands 20-260 kcfrom Newfoundland to Nova Scotia and 312-552 kc in the opposite direction. The paper deals with the design and production of these repeaters. Each repeater has a gain of 60 db at 552 kc, and the amplifier consists of two for- ward amplifying paths with a common feedback network. Reliability is of paramount importance, and production was carried out in an air-condi- tioned building with meticulous attention to cleanliness and to very rigid manufacturing and testing specifications. The electrical unit is contained in a rigid pressure housing 9 feet long and 10 inches in diameter with the sea cables connected to an armor clamp and a cable gland at each end. A submerged equalizer was provided near the middle of the sea crossing. INTRODUCTION The British Post Office has engineered many shallow-water submerged- repeater systems/ and there has been a progressive improvement in de- sign techniques and in the reliability of components which has been re- flected in a growing confidence in the ability to provide long-distance systems having an economic life. The seven-repeater scheme from Scot- land to Norway laid in 1954 introduced for the first time repeaters which would withstand the deepest ocean pressure together with an electrical circuit which embodied improved safety and fault-localizing devices. Also, since a repeater is only as reliable as its weakest component, much greater attention and control was directed at this stage to the design, manufacture and inspection of all components, both electrical and me- chanical. This repeater design was, in fact, envisaged as a prototype for a future transatlantic project. * British Post Office. 245 246 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 In the finalized plans^ for the Newfoundland-Nova Scotia cable it was required to carry 60 circuits, so that some redesign of the 36-circuit 'prototype' repeater became essential. It was accepted, however, as a guiding principle throughout the redesign that there should be no de- parture from previous practice without serious consideration and ade- quate justification. It was obviously not an occasion to experiment with new ideas. Post Office and Bell Telephone Laboratories experiences were pooled for the project, and the whole technical resources of both organizations were freely available at all times for consultative purposes. Detailed manufacturing and testing specifications were exchanged and approved, and each party was free to inspect the other's production methods. This mutual interchange was undoubtedly highly beneficial, and in the British case it resulted in a still more rigorous control of manufacturing and in- spection methods. PLANNING General Preliminary design calculations indicated that it should be possible to increase the circuit-carrying capacity of the Anglo-Norwegian proto- type repeater from 36 to 60 circuits, and tests on a model confirmed that, with band frequencies of 20-264 and 312-552 kc, a 60.0 db gam at 552 kc could be realized with satisfactory margins against noise, dis- tortion and overload. This gain fixed the repeater spacing at about 20.0 nautical miles so that on the selected route two repeaters would be re- quired on the land section between Clarenville and Terrenceville and 14 in the Terrenceville-Sydney Mines sea section. It was noted that the land repeaters might have to work with an ambient temperature 12°C higher than in the sea repeaters. Each repeater would need to be energized with a direct current of 316 ma at 124 volts so that the total route voltage would be about 2,300 volts. This voltage would be quite acceptable to the repeaters, but for normal operation it was proposed^ to feed from both terminals simul- taneously, thereby halving the maximum voltage to ground.^ The precise localization of any faulty or aging repeater would be of paramount importance. It was decided to retain the two supervisory methods which on the prototype had worked satisfactorily in this re- spect. These consisted of a pulse-distortion equipment requiring no addi- tional components in the repeater and a loop-gain monitoring set in- volving a special unit in the repeater and the allocation of a 4-kc band (260-264 kc) for its operation. REPEATER DESIGN — NEWFOUNDLAND-NOVA SCOTIA LINKS 2-17 Manufacture and testing of the electrical units was again to be carried out by a contractor in a temperature- and humidity-controlled produc- tion building, and in order to enable manufacture to start as early as possible, arrangements were made for the contractor to co-operate with the Post Office at an early design stage so that engineering could follow fast on the heels of the design. The outer housing and method of braz- ing-in the bulkheads had all proved entirely satisfactory on the proto- type, and therefore these operations could proceed according to previous production. The Post Office assumed responsibility for the production and testing of the glands, since no contractor had experience of this work. Forward planning in early 1954 scheduled the first electrical unit to be completed in June, 1955, with units following at 5-day intervals. This target was, in fact, delayed until August, 1955, but all 16 working re- peaters were available fully tested before the commencement of the alying operation in May, 1956. Distortion Monitoring Equipment The pulsed-carried supervisory method as used on previous systems^ is employed primarily for measuring the distortion on repeaters. Under normal operating conditions the distortion level may be only just notice- able above the noise, but should appreciable distortion occur, e.g., failure of one amplifying path in a repeater, it could be readily located, since the pulse amplitude from the faulty repeater, would increase by about 12 db for second-harmonic distortion and about 18 db for third-order distortion. Loop-Gain Monitoring Equipment For the loop-gain monitoring equipment' the repeaters have to be designed to incorporate a second-harmonic generator operating at a frequency unique to each repeater at 120-cycle spacing in the 260- 264-kc band. The second harmonics return to Sydney Mines in the 520- 528-kc band, and these two channels must be taken out of service during the measurement. Levels and Equalization Controlling Factors. In practice, deviations from an ideal system wherein all repeaters match the cable and operate at all times at the same levels require the repeaters to be designed with specific margins against overload and intermodulation to meet an agreed maximum noise figure for the system 248 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 under all working conditions.'^ Factors involved in assessing these mar- gins and in planning the equalization and level diagram for the s^^stem are as follows: (a) Temperature. — The final assumed sea-bottom temperature was 2.3°C, with a maximum annual variation of ±3°C. The maximum change in attenuation might therefore be ±4 db at 552 kc. The land section change would be ±3 db at 552 kc due to a possible ±10°C change on a mean of 7.5°C. The effect of these seasonal changes would be reduced by the provision of manually adjusted equalization at Clarenville, Terrenceville and Sydney Mines. The repeaters show a small change in gain (less than 0.05 db) during the warming-up period after energization, but the effect of ambient- temperature change is negligible. (6) Repeater spacing. — The repeater-section cable lengths were to be cut in the cable factory such that the expected attenuation at 552 kc when laid at the presumed mean annual temperature of the location should be 60.0 db. An anticipated decrease in attenuation of 1.42 per cent at 552 kr was assumed when laid. The assumed mean annual tem- perature of sections of the route varied between 1.7 and 4.0°C. Tempera- ture corrections employed an attenuation coefficient at 552 kc of -f-O.lG per cent per degree centigrade. It was expected that the total error at 552 kc after laying seven repeaters would not exceed 1.5 db, and this could be largely corrected as explained in (c) . (c) Cable Characteristics. — The cable equalization built into the re- peater was based on a cable attenuation characteristic which was later discovered to be appreciably different from the laid characteristic. Cut- ting the cable as described in (b) overcomes this difficulty at 552 kc, where the signal/noise ratio is at a minimum. The new shape of the characteristic, however, indicated that at about 100 kc the error would reach 7 db on the complete route. To reduce this deviation it was de- cided to introduce a submerged equalizer in the middle of the sea section to correct for half this error and to insert in each of the four-wire paths of the transmit and receive equipments equalization for one-quarter of this error. There is an appreciable signal/noise margin in hand at this frequency, so that the system would not be degraded below noise speci- fication b}^ these equalizer networks. It was also decided that the splice at the equalizer which would con- nect the halves of the link together should not be completed until after the laying operation had commenced. An excess length of cable was pro- vided on the equalizer tail, and this could be cut at a position indicated by measurements taken during the laying of the first half-section so that REPEATER DESIGN — NEWFOUNDLAND-NOVA SCOTIA LINKS 249 the equalization at the 552-kc point could be largely corrected for laying and temperature-coefficient errors. It is not, in practice, easy to separate these two factors. (d) Repeater characteristic. — The repeater was designed to equalize the original cable-attenuation characteristic to ±0.2 db, as this was possible with a reasonable number of components. This ^-ariation ap- peared as a roll in the gain/frequency characteristic, which was expected to be systematic and would therefore lead to a ±3 db roll in the overall response. It was proposed that equalization for this should be provided at the receive terminal. Manufacturing tolerances were expected to be small and random. (e) Repeater interaction. — At the lower frecjuencies where the loss of a repeater section is comparatively small, a roll in the overall frequency response will arise due to changes in the interaction loss between re- peaters. The design aimed at providing a loop loss greater than 50 db which would reduce rolls to less than ±0.03 db per repeater section and therefore to about 0.5 db at 20 kc with systematic addition on the whole route. Planning of Levels From a critical examination of all these variables it was concluded that the repeater should be designed to have an overload margin of 4 db above the nominal mean annual temperature condition. It was also desirable for the system to be able to operate within its noise allowance if one path of a twin amplifier failed. Tests on a model amplifier gave overload values of +24 dbm and +19 dbm for two- and one-path operation, respectively, so that with a single-tone overload requirement of 18 dbm"* at a zero-level point, the maximum channel level at the amplifier output would be —3 dbr for a single amplifying path. Thermal-noise considerations (i.e. resistance plus tube noise) fixed the minimum channel level at the repeater input at — 69 dbr in order to meet the allowable S3^stem noise limit of +28 dba at a zero-level point. At 552 kc the amplifier gain is 65 db, so that the minimum level at the amplifier output is —4 dbr. A system slope of ±4 db due to temperature variations, corrected by similar networks at the transmit and receive terminal, would, however, degrade the noise by 0.5 db. Intermodulation noise was estimated^ on an average busy -hour basis, and it was concluded that the increase in noise at 552 kc from this source was negligible — less than 1 db, even with several repeaters in which the amplifier had failed on one path. At lower frequencies the contribution from inter- modulation noise is greater, and at 20 kc it exceeds resistance noise. 250 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 However, at 20 kc the total noise is some 8 db below the specification limit, and therefore again several amplifiers could fail on one path be- fore the noise exceeded the specification limit. Actually it was discovered that the predominant source of third-order intermodulation on the re- peater was in the nickel-iron/ceramic seals on high-voltage capacitors and followed a square law with input levels. From a more detailed examination of the factors briefly mentioned above it was decided that the initial line-up should be based on a nominal flat —3.5 dbr point at the amplifier output and the final working levels decided upon as the results of tests on the completed link. With equal loading on the grid of the output tube at all frequencies the worst signal/noise ratio exists at 552 kc; some pre-emphasis of the transmit signal should therefore prove to be beneficial. In fact, after completing the tests on the link it was decided to improve the margin on noise by raising the level at 552 kc by 2 db, thus giving a sloping level response at the amplifier output in the high-frequency band. To main- tain the same total power loading, the low-frequency band levels were decreased bj^ 1 db, still retaining a flat response. Laying It was proposed to use laying methods with continuous testing similar to those employed successfully on the Anglo-Norwegian project. The complete link with a temporary splice at the equalizer would be assem- bled and tested on board H.M.T.S. Monarch and laying would proceed from Terrenceville to Sydney Mines in the high-frequency direction of transmission. A detailed description of the actual laying operation is given elsewhere.^ After completion of tests on the submarine section the land section to Clarenville would be connected with appropriate equaliza- tion at Terrenceville. DESIGN OF ELECTRICAL UNIT OF SUBMERGED REPEATER General The equipment is contained in a hermetically sealed brass cylinder (filled with dry nitrogen) 7| inches in diameter and 50 inches long, which is bolted at one end to one of the bulkheads of the housing. A flexible coaxial cable emerges through an 0-ring seal at each end, and these are ultimately jointed to the cable glands. The various imits forming the complete electrical unit are mounted within a framework of Perspex (polymethylmethacrylate) bars w^hich forms the main insulation of the REPEATER DESIGN — NEWFOUNDLAND-NOVA SCOTIA LINKS 251 / J- Fig. 1 — Internal unit. repeater, and these units may operate at 3 kv do to the grounded brass cylinder. Fig. 1 shows the construction. A schematic of the electrical circuit is given in Fig. 2. The direct cur- rent for energizing the repeater is separated from the carrier transmission signals by the A- and B-end power separating filters, and passes through the amplifier tube heaters and a chain of resistors developing 90-volt high- voltage supply for the amplifier. The carrier-frequency signals pass through the same amplifier \-ia directional filters. Equalization is pro- vided in the amplifier feedback circuit (about 20 db) and in the equal- izers and the bridge networks which combine the directional filters. The main purpose of the bridges, however, is to reduce the severe harmonic requirement on the directional filters due to having high- and low-level signals present at the repeater terminals. The whole carrier circuit is designed on a nominal impedance of 55 ohms. Attached to the B-end of the repeater is the loop-gain supervisory unit and also, via a high-volt- age fuse, a moisture-detector unit used primarily during the high-pres- sure test to confirm that the housing is free from leaks. The latter com- prises a series-resonant circuit at about 1.3 mc, in which the inductance is varied by the gas pressure on an aneroid capsule mounted in the space between the electrical unit and the housing. The presence of moisture in this cavity increases the gas pressure owing to the release of hydrogen by the reaction of water vapor with metallic calcium held in a special container. At a later stage the fuse is blown to disconnect this circuit. The circuit design of the repeater introduces multiple shunt paths r^ QcnS ZcOh , <<-i mQLy_ D V > a. o Oct ZLU LU -I Dm OD > UJO Lt q:q IIJ LL n 01 AND ASS LTER mo-o; 1 c3 C<1 bi) 252 REPEATER DESIGN — NEWFOUNDLAND-NOVA SCOTIA LINKS 253 across the amplifier, and care has to be taken to ensure that there is adequate attenuation in each path. In general, the design is such that the combination will give a loop loss of at least 40 db in the working band (to reduce rolls in the gain characteristic) and 20 db at all frequencies (as a guard against instability), even when one repeater terminal is open- or short-circuited to simulate a faulty cable. Unit Details Power Filter. The power filters are, in effect, a series pair of high- and low-pass filters (see Fig. 2). The shunt capacitors may have to withstand 3 kv, and clearances on the input cable and some wiring have to be adequate for this voltage. The inductors have to carry the line current of 316 ma dc, and the intermodulation must be extremely low (see section on in- ductors below). Directional Filter. The directional filters are a conventional Zobel high-pass and low-pass filter pair with a susceptance-annulling network. Silvered-mica capacitors and carbonyl-iron dust-cored inductors are used. The bridges combining the 'go' and 'return' filters reduce the distortion due to the ferromagnetic material to an acceptable level. Bridge and Equalizer. A simple non-resonant bridge is used at the B-end of the repeater, but the A-end bridge is a resonant type and provides a substantial degree of equalization (see Fig. 2). The equalizers are of conventional form. Trimming capacitors (se- lected on test) were provided for critical capacitances in order to utilize standard tolerances on all capacitors. A pad of 0.2 db and 0.4 db is pro- vided on each equalizer unit so that the repeater low-frequency or high- frequency path can be independently trimmed to give the best match to the target response for the repeater. The components in the above circuit were small air-cored inductors, silvered-mica capacitors, and wire-wound resistors, except for a few high- resistance ones, which were of the carbon-rod type. Included in this unit are coaxial chokes whose purpose is to separate parts of the circuit to avoid the effect of multiple grounding. They are merely inductors wound with coaxial wire on 2-mil permalloy C tape ring cores. 25-1: THE BELL SYSTEM TECHNICAL JOURXAL, JANUARY 1957 Supervisory Unit. The supervisory unit comprises a frequency-selection crystal filter of about 100-cycle bandwidth in the range 260-264 kc fed from the low-fre- quency output end of the repeater via a series resistor. This filter feeds a full-wave germanium point-contact crystal-rectifier bridge which acts as a frequency doubler. The second harmonic in the band 520-528 kc is filtered out by a coil-capacitor band-pass filter, and fed back through a resistor to the same point in the repeater. The two series resistors mini- mize the bridging loss of the unit on the repeater and ensure that a faulty supervisory component has negligible effect on the normal working of the repeater. DC Path. The dc path includes a resistor providing the 90-volt supply and the heater chain of six electron tubes (see Fig. 2). The voltage drop across the heater chain is not utilized for the ampUfier high-voltage supply, as the heaters would then be at a positive potential with respect to the cathodes, thereby increasing the risk of breakdown of heater-cathode insulation. There w^ould also be a complication in maintaining the con- stant heater current, particularly should the high-voltage supply current fail in one path of the amplifier. The normal amplifier high- voltage supply current is 32 ma. It is essential to maintain a dc path through the repeater even under fault conditions in order that fault-location methods can be apphed. Special care has therefore been taken to provide parallel paths capable of withstanding the full line current. For example, the high-voltage re- sistor actually consists of a parallel-series combination of ten resistors, and the whole assembly is supported on Sintox (a sintered alumina) blocks which maintain a good insulation at 3 kv dc, even at high tem- peratures. Electron tube operation for consistent long life indicates the necessity to maintain a specific constant cathode temperature, and to achieve this, electron tubes are grouped according to heater characteristics into six heater-current groups between 259 and 274 ma and stabilized to ±1 per cent. The appropriate heater-shunt resistor is applied so that the tube operates correctly with 316-ma line current, but for convenience the shunt is taken across each set of three tubes, all in one heater group, forming one amplifier path. Rl is fixed (300 ohms) and R2 is selected to suit the tubes. Rl is the resistance winding of a special short-circuiting fuse; when energized by the full line current should a heater become REPEATER DESIGN — NEWFOUNDLAND-NOVA SCOTIA LINKS 255 open-circuited, it causes a permanent direct short-circuit across the heater chain. The Hne voltage will be temporarily increased by about 95 volts while the fuse operates (1 min) and will then drop to 12 volts below normal. Amplifier. The amplifier circuit is shown in Fig. 3. It consists of two 3-stage amplifiers connected in parallel between common input and output trans- formers with a single feedback network. This circuit arrangement al- lows one amplifier path to fail without appreciably affecting the gain of the complete amplifier (less than 0.1 db for all faults except those on the grid of VI and the anode of V3, but the overload point is reduced by about 5 db and distortion at a given output level is increased (about 12 db for second harmonics). Care has been taken to ensure that the open- or short-circuiting of a component in one amplifier path will not affect the performance, life or stability of the remaining path, and this involves the duplication of certain components. Mixed feedback is employed to produce the required output imped- ance ; the current feedback is obtained from the resistor feeding the high- voltage suppl}^ to the output transformer, and the voltage feedback is developed across a two-turn winding on the output transformer, which also serves as a screen. The output of the feedback network is fed in series with the input signal to the grid of VI. The gain response of the amplifier is chiefly controlled by the series-arm components in the feedback net- work, which resonate at 600 kc. The input transformer is built out as a filter and steps up in imped- ance from 55 ohms to 17,000 ohms. Protective impedances minimize the effect of a short-circuit on the grid of one of the first-stage tubes. The anode load of the first stage resonates at 600 kc, and is roughly the in- verse of the feedback network so as to give constant feedback loop gain over the working frequency band. The output tube has about 5.5 db of feedback from its cathode resistor, and the pair of output tubes feed the output transformer, which steps do^vn from 5,000 to 55 ohms. Specially designed long-life tubes are used.'^ The first two stages are operated at about 40 volts on the screens and anodes; each anode cur- rent is 3 ma, giving a mutual conductance of 5.1 ma/v. The output stage is operated at 60 volts on the screen, -|-15 volts on the suppressor grid to sharpen the knee of the Va/h characteristic, and nearlj^ the full high- voltage suppl}^ of 90 volts on the anode ; the anode current is 6 ma, giving a mutual conductance of 6.6 ma/v. The tube dynamic impedance is ap- proximately 300,000 ohms. To obtain an anode current nearest to the + X I I I I I -A^^ iM^Jj-vWiiLr' ■ cc H UJ — < ^\/Ar ■^WV oz UJOJ Zo "-^ _ a:z5< OQ-O <^ ti^F INPUT EQN /^ (A END) ^ / 100 200 300 400 500 FREQUENCY IN KILOCYCLES PER SECOND Fig. 13 — Repeater gains and losses. 600 was monitored on recorders in both directions. Owing to the insertion and withdrawal of repeaters in the power circuit from time to time, the repeaters were subjected to several power-switching operations and temperature cycles. Stability of electrical characteristics, particularly gain, between the pre-housing tests and the completion of the 'confidence trial' some four months later was regarded as an important criterion of the reliability of a repeater. Unfortunately test conditions and differences ])etween, and i LU u LU a z _i z UJ 2 < Q Z D LL 5 3 ai CO _j lij > LU O z o tr < 95 90 85 80 75 70 65 60 55 50 45 40 35 30 ^5 20 V_ TWO- PATH- - AMPLIFIER >\ \ / / \ ^^ ^"^ "^ ^ s. THIRD^^N. '^>^, HARMONIC ^ \ SECOND"^ ^HARMONIC \ \ ^-^. •--> ^^ N > ^ \ \ \ p-.. \ \ \ ■■\ N \ 1 \ ONE -PATH -- AMPLIFIER ^\ \ \ i \ \ 1 \ 1 W u 1 6 8 10 12 14 16 1 FUNDAMENTAL OUTPUT LEVEL 1 8 20 22 24 26 N DBM Fig. 14 — Amplifier distortion. tri _l UJ m u LU Q Z z < Q. o o _l 40 30 20 10 -10 -20 / \ /J./i GAIN / \ /i/3 PHASE TWO-PATH AMPLIFIER-^ ' / A TWO OR ONE-PATH ONE-PATH AMPLIFIER-/ y \\ AMPLIFIER / ■ > // f \ V- ^•— 1 / / /" A 1 ' ,^' .^'■' N \ /, / r \ \ ■^ /-, y V \ 300 200 100 1/1 m LU a. O LU Q z < LU ID -100 I CL o -200 q 10" ^ 10 2 ^ ,o2 2 5 ,o3 2 FREQUENCY IN KILOCYCLES PER SECOND 10^ 10= Fig. 15 — Amplifier nfi characteristic. 271 272 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 Stability of, the testing eciuipinents reduced the uccurac.y originally ex- pected, but even so, changes of over 0.1 db were regarded as significant. Connection of Repeaters to Cable On board the cable ship the cable ends were prepared by making tapered molded joints to 0.310-inch tail cable, sliding the domed ends of the repeater up the cable and forming the armor wires round the ar- mor clamps. The tapered joint included a castellated ferrule on the center conductor, which, operating on the principle of the main gland, acts as a barrier against the possible passage of water down the center conductor into the repeater. The final assembly operation consists of jointing the tail cables, bolting the armor clamps to the repeater housing and screwing on the domed ends. Fig. 12 shows a completed repeater connected to a cable. 90 80 / / / i \ / t 55 OHM /^ \ N TERMINATIONS ~ "*^7 \ \ \ \ / 70 /I \ / / / 1 \ \ , / / SHORT-CIRCUIT . ' 1 1 \ / BOTH TERMINALS , ^N 1 \ vy Li \ 60 \ 1 ■•*> 1 \ 1 n / 1 N 1 > / . l/l / 1 ^' ^y 1 \ iil / / 1 / 50 / "^ ^-j \ . IM«^ [/ f\ V h I'l*! / '^****.,^,^^^^^ 1 I .' ' ' I / ^X \ /' 1 ■ > ■ < u 1 40 \i.' \ 1 i 1 III 1 t — ^ 1 v^ X P ifiii^ 1 1 '^ III 1' NORMAL 1 v_/ III y ■ ill '' 1 It TARGET MARGIN' > / 30 \ ! l/y \l '^< 11 1 20 1 1 1 vl 1 1 1 ■~" " -y-' TARGET MARGIN - — ^ ~ ■ ~ ^ FOR CABLE FAULT CONDITION 10 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0.6 0.8 1 4 6 8 10 20 40 60 100 200 FREQUENCY IN KILOCYCLES PER SECOND 400 600 1000 Fig. 16 — Repeater loop loss measured at amplifier input. REPEATER DESIGN — NEWFOUNDLAND-NOVA SCOTIA LINKS 273 m u LU Q z z < o < h- O cr < > 0.4 0.3 0.2 O.I -0.2 -0.3 -0.4 ORIGINAL BRITISH POST OFFICE MODEL REPEATER 50 100 )50 200 250 300 350 400 450 500 550 600 FREQUENCY IN KILOCYCLES PER SECOND Fig. 17 — Repeater-gain response. PERFORMANCE The gains and losses of various sections of the repeater are shown in Fig. 13. Figs. 14 and 15 show, respectively, the harmonic distortion and the stabilit}^ characteristics of the amphfier with one and two paths operating. The total shunt loss across the amplifier is shown in Fig. 16 as a margin above the amplifier gain. The curves show the result with 55-ohm terminations on the repeater and with a short-circuit on each terminal. Fig. 17 shows the production spread in gain of the 16 repeaters for the system as a deviation from the target value. The highest standard deviation (at 260 kc) was only 0.11 db. In all respects the production repeaters proved to be very consistent and satisfactory in their per- formance and differed httle from the original laboratory-built model. Typical electrical characteristics of a repeater and the submerged equalizer are showTi in Appendices 1 and 2 respectivel3\ The characteristics of the completed link are described elsewhere,^ but it is of interest to note that the overall tests showed that the link behaved as predicted and met the noise requirement and the design margins. ACKNOWLEDGMENTS It will be appreciated that the design and manufacture of these re- peaters has been an undertaking of teams rather than of individuals. The authors are very grateful to Standard Telephones and Cables, Ltd., 274 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 and Submarine Cables, Ltd., for their unsparing efforts to ensure the very highest standards in the engineering, production and testing of these repeaters. Numerous firms have also co-operated in specialized fields, and the authors are very appreciative of their help. The authors also wish to acknowledge the enthusiastic assistance of their many colleagues in the Research Branch of the Post Office in the design and in the supervisory inspection during manufacture. Finally a grateful acknowledgment is made to the Engineer-in-Chief of the British Post Office for permission to publish the paper. Appendices 1 performance of typical submerged repeater (a) Insulation resistance 8000 megohms (cold) . (b) DC resistance at 20°C. Current, ma DC resistance, ohms 5 343.0 20 343.2 50 344.2 100 347.9 (c) Voltage drop at 316 ma 124 volts (d) Carrier gain (55 ohms) without moisture detector. Frequency, kc Gain, db Frequency, kc Gain db 20 11.54 308 44.52 30 13.82 312 44.87 50 17.47 320 45.56 100 25.06 330 46.29 150 30.86 350 47.75 200 35.81 400 51.19 230 38.40 450 54.20 260 40.96 500 57.31 264 41.13 552 60.01 268 40.83 (e) Noise level. A terminal (312-552 kc) -59.8 dbm B terminal (20-260 kc) -70.3 dbm (/) Harmonic level. 170 kc fundamental level at B terminal +10 dbm 340 kc second harmonic level at A terminal — 60 dbm 510 kc third harmonic level at A terminal —58 dbm REPEATER DESIGN NEWFOUNDLAXD-XOVA SCOTIA LINKS •zio (g) Supervisory — 260.800 kc (nominal). Fundamental level at B terminal, dbm -12 -2 +8 Second harmonic level at A terminal, dbm -26 -13.8 -3.6 (h) Moisture detector. Resonant f requeue}^ with 30-f t cable tail (i) Impedance. Return loss against 55 ohms 1,237 kc A-terminal B-terminal Frequency, kc return loss, db return loss, db 20 17 8 50 17 13 100 16 15 200 16 4 260 16 4 312 13 21 350 14 14 500 18 16 552 16 25 2 PERFOR^L'\.NCE OF SUBMERGED EQUALIZER (a) Insulation resistance 8,000 megohms (h) DC resistance at 20°C 9.2 ohms (c) Voltage drop at 316 ma 3.0 "\'olts (d) Carrier loss (55 ohms) — without moisture detector. Frequency, kc Loss, db Frequency, kc Loss, db 20 4.28 260 15.90 30 4.23 312 18.26 50 4.87 350 19.96 100 7.47 400 21.75 150 10.35 450 23.16 200 13.04 500 24.55 230 14.52 552 25.97 (e) ^loisture detector. Resonant frequenc}^ with 5-ft cable tail 1,387 kc (/) Impedance Return loss against 55 ohms A-terminal B-terminal Frequency, kc return loss, db return loss, db 20 35 31 50 19 19 100 25 25 260 34 27 552 30 23 276 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 REFERENCES 1. R. J. Halsev and F. C. Wright, Submerged Tilvbene Repeaters for Shallow Water, Proc. I.E.E., 101, Part I, p. 167, Feb., 1954. A. H. Roche and F. (). Rop, The Xetherlands-Demark Submerged Repeater System, Proc. I.E.E., 101, Part I. p. ISO, Feb., 1954. D. C. Walker and J. F. P. Thomas, The British Post Office Standard Submerged Repeater System for Shallow Water Cables (with special mention of the England-Netherlands System), Proc. I.E.E., 101, Part I, p. 190, Feb., 1954. 2. M. J. Kellv. Sir Gordon Radlev, G. W. Gilman and R. J. Halsev, A Trans- atlantic Telephone Cable, Proc. I.E.E.. 102B, p. 117, Sept., 1954, and Com- munication and Electronics, 17, pp. 124-136, March, 1955. 3. J. F. P. Thomas and R. Kelly, Power-Feed Sj-stem for the Xewfoundland- Xovia Scotia Link. See page 277 of this issue. 4. B. D. Holbrook and J. T. Dixon, Load Rating Theorv for Multi-Channel Am- plifiers, B.S.T.J., 18, p. 624, 1939. 5. R. A. Broakbank and C. A. A. Wass, Xon-Linear Distortion in Transmission Systems, Jl.I.E.E., 92, Part III, p. 45, 1945. 6. J. S. Jack, Capt. W. H. Leech and H. A. Lewis, Route Selection and Cable Lay- ing for the Transatlantic Cable System. See page 293 of this issue. 7. J. O. McXally, G. H. Metson, E. A.'Veazie and ^L F. Holmes, ElectronTubes for the Transatlantic Cable System. See page 163 of this issue. 8. S. X. Arnold, Metal Whiskers — A Factor in Design, Proc. 1954 Elec. Comp. Symp., pp. 38-14, May, 1954, and Bell System Monograph 2338. 9. R. J. Halsey and J. F. Bampton, System Design for the Xewfoundland-Nova Scotia Link. See page 217 of this issue. I Power-Feed System for the Newfoundland-Nova Scotia Link By J. F. P. THOMAS* and R. KELLYf (Manuscript received September 22, 1956) Design engineers now have available the results of many years of operat- ing experience with submerged-repeater systems supplied from electronic, electromagnetic and rotary -machine power equipments. To meet the very high standards of reliability required for the transatlfintic telephone system, a scheme has been evolved that is a combination of new developments and the best features of previous methods. Electronic-electromagnetic equipment forms the basis of an automatic no-break system requiring very little routine maintenance. INTRODUCTION The operating power for the submerged repeaters of the Clarenville- Sydney Mines Hnk is derived from a constant current suppHed over the central conductor from power equipments located at the two terminal stations. In order to protect the electron tubes in the repeaters the cur- rent must be closely maintained at the design value, irrespective of changes in the mains supply voltage or ground potential differences be- tween the two ends of the link. Automatic tripping equipment must be provided to disconnect the cable supply should the current deviate be- yond safe limits, but otherwise there must be a minimum of interrup- tions due to power-equipment and primary -source failures. Earlier British Post Office schemes have been powered by electron- ically controlled units feeding from one end only.t Manual change-over to standby units has been provided at the end feeding power and at the distant end — a method which has satisfactorily met the economic requirements of short schemes. * British Post Office, f Standard Telephones and Cable Ltd. X Walker, D. C, and Thomas, J. F. P., The British Post Office Standard Sub- merged-Repeater System for Shallow-Water Cables (with special reference to the England-Netherlands System), Proc. I.E.E., 101, Part I, p. 190, Feb., 1954. 277 278 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 For the Clarenville-Sydney Mines link a new and more reliable de- sign of equipment has been developed. An automatic no-break system provides an uninterrupted supply to repeaters unless equipments at both ends of the link simultaneously fail to deliver power. The main improvement in the reliability of the equipment is the re- placement of all high-power electron tubes by electromagnetic compo- nents. The automatic no-break system takes advantage of the fact that the rating of the repeater isolating capacitors has been chosen to permit single-end feeding. Normally the link is fed from both ends, but in the event of one equipment failing to deliver power the link is powered from the other end without interruption to the cable suppl^^ If the failure is due to a power-equipment fault, double-end feeding can rapidly be re- established by manual switching to the standby. During an ac-supply failure, single-end feeding must be maintained until the supply is re- stored. In view of the very reliable no-break ac supply provided at both stations, the possibility of a simultaneous ac supply failure at both ends of the link is extremeh' remote. The power equipments at each end of the link must be capable of suppl^dng the whole of the power to the cable should one end fail, which requires that each should be capable of operating as a constant-current generator. If two constant-current generators are connected in series, unless precautions are taken, an unstable combination will result and the unit suppl3'ing the higher current will driA-e the other unit 'off load.' Manual adjustment could be provided to equalize the currents fed from the two ends, but a different solution has been developed in which one of the units is a constant-current master and controls the line current, while the other unit is a slave whose voltage/current characteristic in the normal operating range is such that its current is always equal to that of the master unit. If the slave unit fails, the master will take over the suppl}^; if the master unit fails, the slave unit will take over the suppl}' and automatically assume the role of a master unit. The first unit sAvitched on to an unenergized link operates as a master generator and the other unit, on being switched on, automatically operates as a slave. Other than ensuring that the link is safe for energizing, there is no need for any cooperation between the two ends when putting the equip- ment into service. DETAILS OF METHOD EMPLOYED The Master-Slave System of Operations The output-current/output-voltage characteristics for the equipments are shown in Fig. 1, and are the same for both regular and alternate POWER-FEED SYSTEM — NEWFOUNDLAND-NOVA SCOTIA LINK 279 328 en 324 ^322 LU I 320 < =! 316 Z .3 12 LU a. 308 D O D 304 CL 300 296 POTENTIAL BALANCE 1 1 ^ ADJUSTMENT RANGE (b) 1 c \ N, D 'V \J E (a) ^ lA F (C) S s. \ \, >fB H FULL SYSTEM VOLTAGE 1 0.5 1.0 1.5 2.0 OUTPUT IN KILOVOLTS 2.5 3.0 Fig. 1 — Output-current versus output-voltage characteristics, (a) Master. (6) Slave, (c) Master versus master shut-down. equipments at both ends of the link. Any equipment can operate with any of the characteristics (a), (h) or (c). Normally the choice between characteristics (a) and (b) is made auto- matically by the equipment. If the output voltage does not reach 80 per cent of the full link voltage (approximately 2 kv) , the unit will have the slave characteristic (6) (DCAB). If the output voltage reaches or exceeds 2 kv, the unit automatically switches to the master characteristic (a) (EAF) . Once having switched to the master characteristic the equip- ment does not automatically change back to the slave characteristic even if the output voltage falls below 2 kv. When the link is energized, the first equipment switched to line will come on as a slave unit ; its output voltage will then pass 2 kv and it will automatically be switched to the master characteristics and the complete link will be energized from one end. The second unit switched to line will come on as a slave unit, and having a higher output current, will drive down the output voltage of the master unit at the other end until the current of the slave unit has become equal to that of the master (DCA in Fig. 1). The output voltage of this equipment will not exceed 2 kv and it will not switch to master. The cross-over point of the two characteristics. A, will determine the potential fed from each end, and this can be adjusted as indicated by the dotted lines near C. In an emergency, an equipment can be taken out of service by switch- ing off the ac supply, and the links will then be powered from the dis- 280 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 tant end only. Should the master end be switched off, the distant slave unit will switch to master characteristic as soon as its output voltage exceeds 2 kv. This abrupt disconnection of one equipment causes un- necessary voltage surges on the cable, and when an equipment is re- moved for normal maintenance purposes the following procedure is adopted. The slave equipment is switched to the master characteristic (an external key is provided for changing from master to slave or vice versa, but see the limitation described in the next paragraph). This leaves two master equipments feeding the cable, but any redistribution of voltage is slow since the currents are approximately equal. An external control (master/master shut-down), is then operated on the equipment to be taken out of service, changing its characteristic to that shown in Fig. 1(c). The output voltage of this unit will then be slowly reduced, and when it is zero the equipment can be switched off without causing surges on the cable. The current deviations occurring over the slave characteristic (c) (from 4-2 per cent to —3 per cent) are the maximum permitted by the tube design engineers for the tubes in the submerged repeaters, and are permitted only for short periods. The circuit associated with the manual switching of the equipment to the slave characteristic is there- fore made inoperative if the output voltage exceeds 2 kv, since in this range the slave characteristic is the extension of the line CAB on curve (6) and the current is outside the permitted range. The slave characteris- CABLE TERMINATING EQUIPMENT I REG POWER'" EQUIPMENT ALT SYDNEY MINES 14 REPEATERS GROUND PLATE REPEATERS CABLE TERMINATING EQUIPMENT I \ ALT _x_,. "■GROWER EQUIPMENT CLARENVILLE Fig. 2 — Current paths on Clarenville-Sydney Mines link. POWER-FEED SYSTEM — NEWFOUNDLAND-NOVA SCOTIA LINK 281 tic over the range CAB is controlled by a voltage-sensitive circuit con- nected near the output of the equipment, and the stability of the charac- teristic against input \'oltage and component aging is the same as for the master characteristic. Changes in the distribution of the system potential due to supply variations and component aging are therefore small. Overall Current and Voltage Distribution Facilities have been provided at the j unction of the land and sea cables (Terrenceville) to connect a power ground to the center conductor of the cable. Normally this ground will be disconnected, but during installation it enables the land and sea sections to be energized separately and may subsequently be of assistance in the localization of cable faults near Terrenceville. The full line in Fig. 2 shows the current path with normal double-end feeding, while the broken lines show the current paths when a ground is connected at Terrenceville. The full line (d) in Fig. 3 shows the voltage distribution along the link 2500 SYDNEY MINES TERRENCEVILLE CLARENVILLE Fig. 3 — Potential distribution on Clarenville-Sydney Mines link, (a) Single- end feeding from Sydney Mines, (b) Single-end feeding from Clarenville. (c) Ground at Terrenceville; double-end feeding, (d) Normal operation; double- end feeding. 282 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 / f I/) / (\jO < > 1 1 1 1 1 1 lN3VNdinD3 aaMOd 3iVNa31"lV 01 SNOIiOSNNOD "lV0llN3ai "X '43 c3 o tc 4 POWER-FEED SYSTEM — NEWFOUNDLAND-NOVA SCOTIA LINK 283 with normal double-end feeding, the broken lines (a) and (6) show the distribution with single-end feeding from Sydney Mines and Claren- ville respectively and the broken line (c) shows the distribution when a power ground is connected at Terrenceville. DETAILS OF EQUIPMENTS Connection of the Equipment to the Cable Each station is provided with two power equipments and one cable- terminating equipment interconnected as shown in Fig. 4. When the live side of the output of the regular equipment is connected to the cable via SWD and the link LKl, the alternate equipment output is connected to its own dummy load (equi^'alent of RVl) and vice versa. The grounded sides of the regular and alternate equipments are made common and then connected via a removable link, LK2, to the sea ground. A safety resistor R2 connects the sea ground to the station ground to restrict the rise in potential to 100 ^•olts if the sea ground becomes disconnected. During maintenance on the sea-ground circuit the link LK2 can connect the power equipment ground to the station ground. If, for maintenance purposes, it is necessary to feed from the distant end onl}^, the link LKl can connect the cable to the power-equipment ground and disconnect the live side of both power equipments from the line. Safety Inter-locks Safety interlock circuits are installed to protect the maintenance staff if the equipments are used incorrectly and are not the normal methods employed for controlling the power supplies. With double-end feeding, dangerous ^'oltages are generated at both ends of the system, and when access is gained to any point in the equipments personnel must be pro- tected from the local and distant power sources. To minimize interruptions to traffic, the units of the cable-terminat- ing equipment have been grouped under three headings (see Fig. 4), namely (a) Transmission equipment (Si) isolated from the dc cable supply: this includes cable simulators and monitoring facilities not associated with the power supplies. (b) E(fuipment associated with the dc supply that can be made safe without interrupting traffic. (c) Equipment that can be made safe only by intei-rupting traffic. zo uj Lu tr Zcri- DO '" 'wr cwr 1 I — ^Mfij ^ nwi (A) (MO > a H I (N d 296 ROUTE SELECTION AND CABLE LAYING 297 nautical miles would have resulted in a reduction in the number of voice channels which could be derived from the facility. On Fig. 2 are shown a number of the routes to which consideration was given in the early planning stages. The distances shown are actual cable lengths and include an allowance for the slack necessary to assure conformance of the cable to the profile of the ocean bottom. Route 1, from Eire to Newfoundland, at 1,770 miles, is the shortest route and in point of fact was provisionally suggested in 1930 for a new cable. But the difficulty of onward transmission of traffic to London made this route unattractive. Route 2, from Newfoundland to Scotland, compared favorably in length with Route 1, but its adoption was dependent upon location of a suitable landing site in Scotland. Route 3, from Newfoundland to Cornwall, England, approximated 2,000 miles laid length and would have been very attractive had not so many existing cables terminated in southern Ireland or the southwest corner of Cornwall, which would lead to a great amount of congestion and consequent hazards to the telephone cables. Route 4, from New York to Cornwall, was too long to be considered as its length amounted to some 3,200 miles. Routes 5, 6, 7 and 8 were indirect via the Azores. They were attractive, as only relatively short lengths were involved and suitable sites for intermediate cable stations could have been found on one of the several islands in the Azores. But difficulties attendant upon landing rights, and staffing problems in foreign territory could be foreseen. Clearance for Repairs Repair of a faulty cable or repeater necessitates grappling, and in deep water this is likely to be a difficult operation. To avoid imperiling other cables while grappling for the telephone cables and, con^'ersely, to provide assurance against accidental damage to the telephone cables from the grappling operations of others, it was considered essential that the route selected provide adequate clearance from existing cables. Suitable clearance is considered to be 15 to 20 miles in the ocean, with less permissible in the shallower waters of the continental shelves. Trawler and Anchor Damage Possibilities It is probable that fishing trawlers cause more interruption of sub- marine cables than any other outside agency. Cables laid across good fishing grounds are always liable to damage from fouling by the otter 298 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 boards of the trawlers. Final splices, either initial or as a result of repair operations, are especially vulnerable to damage because of the difhculty in avoiding slack bights at such points. It was desired, therefore, to avoid fishing grounds if at all possible. If cables are laid in or near harbors frequented by merchant shipping, damage must be expected from vessels anchoring off shore in depths of less than 30 fathoms and proposed routes should, therefore, avoid such areas. Cable Terminal Siting Location of the cable terminal stations must be considered from the standpoints of suitability of shore line for bringing the cables out of the water and also from the standpoint of amenities for the staff. This latter factor is most important in keeping a permanent w^ell-trained staff. For example, owing to staff difficulties, it w-as necessary to move a terminal station of one company from the west side of Conception Bay in New- foundland to a site within easy reach of St. Johns. A further factor in proper siting of the cable terminals is consideration for onward routing of the circuits carried by the cables. And finally in view of the importance, generally, of submarine cable facilities, it is considered desirable to avoid cable terminal locations in or near a potential military target area and, if at all possible, consider- ation should be given to underground or protective construction for the terminal stations. Preliminary Selection The routes for the telephone cables were considered in the light of the foregoing and after preliminary discussion it was agreed that the two new cables should lie north of all existing cables, should avoid ships' anchorages and should lie on the best bottom which could be picked, clear of all known trawling areas. In 1930, A.T. & T. Co., in conjunction with the British Post Office, gave serious consideration to the laying of a single coaxial telephone cable between Newfoundland and Frenchport, Ireland (Route 1, Fig. 2). A tentative route was plotted and the cable ship Dominia steamed over this taking a series of soundings. These soundings indicated that good bottom w^as to be found about 20 miles north of the Hearts Con- tent — Valencia cable of 1873. This cable was the most northerly of the telegraph cables spanning the Atlantic. Study of its life history ROUTE SELECTION AXD CABLE LAYIXG 299 indicated that faults clear of the continental shelf were few and far be- tween throughout its long life. The latest British Admiralty charts and bathymetric charts of the U. S. Hydrographic Office for the North Atlantic Ocean were scrutinized and from these and a study of all other relevant data, two routes were plotted which appeared to fulfill the necessary requirements so far as possible. However, it was agreed that if possible the selected routes should be surveyed so that minor adjustments could be made if desirable. Landing Sites East End — It was now necessary to find suitable landing sites having regard for the decision that the telephone cables should be routed north of all other existing cables. On the British side it was necessary to look north of Ireland. The North Channel, the northern entrance to the Irish Sea, divides northern Ireland from Scotland and had this channel been suitable, the telephone cables might have been run through it to a terminal station on the southwest coast of Scotland in the vicinity of Cairn R\'an. How- ever, the tidal streams through the channel are strong, at least 4 to 5 knots at spring tides; the bottom is rocky and uneven, with overfalls, and any cable laid through it would have a very short life indeed. It was therefore necessary to search farther north. The west coast of Scotland presents a practically continuous series of deep indentations and bald, rocky cliffs and headlands. The chain of the Hebrides Islands stretches almost uninterruptedly parallel with and at short distances from the coast. It was obviously most desirable to land the cable on the Scottish mainland, and close to rail and road communication if at all possible. From previous cable maintenance experience it was known that Firth of Lome which separates the island of Mull from the mainland was a quiet channel, little used by shipping or frequented bj^ trawlers and with tidal streams which were not strong. Earlier passages of Post Office cable ships through the Firth had yielded a series of echo sounding surveys which indicated that except for a distance of about 5 or 6 miles in the vicinity of the Isles of the Sea, the bottom was fairly regular. Several small bays on the mainland side of the Firth just south of Oban appeared from seaward to be very suitable landing sites and this was confirmed by a survey party, which selected a small bay localh' named Port Lathaich for the cable landing and site of the station. The fore .shore was mainly firm sand with outcroppings of rock which could be avoided easily when landing the cables. The seaward approach 300 ROUTE SELECTION AND CABLE LAYING 301 was clear of danger and there was ample room to land two cables with a separation on the shore of some 30 yards. Port Lathaich is only about 3 miles by road from Oban. Additional land cables would be necessary, however, to carry traffic to the main trunk network. From a strategic point of view, although Oban might only just be considered a target area, the cable landing was sufficiently remote to be relatively safe, especially if the cable terminal station was sited in the rocky hillside. To ascertain whether any serious chafing or corrosion would result if cables were laid over the une\-en bottom in the Firth, some 8 miles of coaxial cable with E type armoring were laid over the area and recovered after 2 years. There was no evidence of any chafing or corrosion. It was therefore decided that the telephone cables should be routed through the Firth of Lome to the cable terminal station site at Port Lathaich. West End — The choice of a suitable cable landing in Newfoundland was more difficult to make, in view of the rugged and sparsely populated nature of the countr3\ From Fig. 3 it will be seen that the existing tele- graph cables spanning the Atlantic land either just north of St. Johns, in Conception Bay, or in Trinity Bay. North of Cape Bonavista the coast becomes more broken, and the sea approach is not good. Accord- ingly, there was no good alternative to routing both telephone cables into Trinity Bay, close to and northwest of the telegraph cable landing at Hearts Content on the southern shore of the bay. A survey party made an extensive examination of all likely places on the western side of the bay from Cape Bonavista in the north to Bull Arm at the southern end where, incidentalh^ the first successful telegraph cable was landed. Careful consideration of all of the places visited led to the agreement that Clarenville was the best site for a landing and for a cable terminal station. Clarenville is at the head of the Northwest Arm of Random Sound. It is a junction on the main railway, and a good road to St. Johns will pass through the town in traversing its course from St. Johns to Port aux Bascjues. Clarenville has a growing population of some 1,600 inhabi- tants, with stores and repair facilities of various sorts. Good cable land- ing sites are available just out of town and the approach from the sea up the Northwest Arm presents no navigational difficulties. Such few small vessels as ply to Clarenville during the summer months are not likel}' to interfere with the cables. Final Route Agreement Having agreed Clarenville, Newfoundland, and Oban (Port Lathaich), Scotland, for shore terminations, it was possible to complete the routes (/, UJ (/) luj X- cc tr DC UJ '^' < XOQ. a 3 i-f\j Lu 2 a tr < Lu O J3 O a m O o z < a. UJ Z Q tr Z h- UJ NJ liJ liJ I h- u < -1 ^ s: - LU < u u < Q. 30 o <^ UJ O-l IJ 1- CC UJ m CD I/) >^ A ? O UJ i 302 ROUTE SELECTION AND CABLE LAYING 303 for the two cables as shown in Figs. 3 and 4. The final routes are clear of existing cables and avoid crossing known trawling areas and anchorages. The cable stations are well sited with regard to staff amenities, accessi- tnlity and strategic requirements. Soundings taken during the laying of the two cables showed a very even bottom except in the Firth of Lome and one or two places in Trinity Bay. The general profile of the route is shown on Fig. 5. It is considered that these routes have been selected with care and meet all of the requirements of a well planned cable project. Time alone will tell how well the objectives have been met. Cable Laying Earhj Methods In 1865 when the legendary Great Eastern was pressed into service to lay the first successful transoceanic telegraph cable she was fitted out with certain special cable handling gear. The need for such gear had been amply demonstrated by events which transpired during two earlier and unsuccessful attempts by H.M.S. Agamemnon and U.S.S. Niagara. For her assignment, Great Eastern was fitted with three large tanks into which her cargo of cable could be coiled. She was also provided with a large drum about which the cable could be wrapped in the course of its passage from the tanks to the sea. This drum was connected to an adjustable braking mechanism which provided the drag necessary to assure that the cable pay-out rate was correct with relation to the speed of the vessel. In addition, a dynamometer Avas provided so that the stress in the cable would be known at all times. A large sheave fitted to the stern of the ship provided the point of departure of the cable in its journey to the sea bottom. On Friday, July 13, 1866, Great Eastern steamed away from Valencia, Ireland, and 14 daj's later, on July 27, she arrived off Trinity Bay, Newfoundland, and completed the landing of the western shore end. H.M.T.S. Monarch Earl}' in the planning for the transatlantic project it was realized that in no small measure the success of the venture would depend on avail- abilitj' of a vessel suitable for laying the cables. It was fortunate that one of the partners to the enterprise was also the o\Mier and operator of the largest cable ship in all the world, and one well suited to the task at hand. 304 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 The twin-screw cable ship Monarch, Fig, 6, was built for H.M. Post Master General by Messrs. Swan, Hunter and Wigham Richardson, Ltd., at their Neptune Works, Walker-on-Tyne. She was completed in 1946. This ship is of the shelter deck type having principal dimensions as follows: Length overall 482 feet 9 inches Breadth moulded 55 feet 6 inches Depth moulded to shelter deck 40 feet 0 inches Gross tonnage 8,056 The ship has an overhanging bow which carries three cable sheaves, a cruiser stern with the after paying out cable sheave offset on the port quarter, a semi-balanced rudder having extra large surface, and a cel- lular double bottom extending from the collision to the aft peak bulk- heads. Both main and shelter decks are steel and extend her complete length. The cable is carried in four welded steel cable tanks fixed to the tank top plating. These are arranged along the ship's center line in a fore and aft direction forward of the main propelling machinery space. They are each 41 feet in diameter and have the following cubic capacities: Coiling Space Gross Cubic Feet No. 1 Tank 33,730 31,820 30,865 30,230 40,170 No, 2 Tank 38,460 No. 3 Tank No. 4 Tank 37,375 36,300 The opening in the shelter deck above each tank is a circular hatch 8 feet in diameter. A water tight cone of steel plates is built in the center of each tank to insure against fouling of the cable during payout. Further control 1854 1750 1500 1250 NAUTICAL MILES 1000 750 500 250 2500 Fig. 5 — Profile of ocean depths between Clarenville and Oban. ROUTE SELECTION AND CABLE LAYING 305 s o ^ ^ ^ 30G THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 Fig. 7 — Interior of cable tank showing central core, crinoline and flake of cable. of the cable is provided by a crinoline, Fig. 7, which is a circular spider of steel tubing normally suspended from 1 foot to 3 feet above the top layer of cable in the tank. The crinoline tends to prevent flj'ing bights of cable and also provides a safety platform, in case of trouble, for the men who work in the cable tanks. Each crinoline ma}^ be raised and lowered by an electric motor drive. The maximum cable carrying capacity is approximately 5,000 long tons, or almost 2,000 miles of the deep sea type of cable used on this project if no repeaters were involved. ROUTE SELECTION AND CABLE LAYING 307 Monarch is driven by two steam engines. The maximum propeller revolutions are estimated at 110 per minute, giving a ship's speed of about 14 knots. Two cable engines are fitted forward, both capable of being used for picking up or paying out. These are driven by electric motors having a maximum rating of 160 hp, which will permit picking up at a rate of 0.9 nautical miles per hour with a stress of 20 tons, or at 3.5 knots with a stress of 5.3 tons. The drive system is constant current, so designed that a uniform torque may be held at the drum for any setting of the speed control. When paying out, these motors operate as generators to provide electrical braking, and auxiliary mechanical brakes are also provided. A single cable engine is fitted aft and this is the main paying out gear. In addition to the electrical brake, the aft engine is provided with a multiple drum externally contracting band brake, manually adjustable and water cooled, and with a further auxiliary fan brake. The fan shaft is driven in such a manner that when cable is being paid out at approxi- mately 8f knots the fan will revolve at 1,000 rpm and absorb 120 bhp. Adjustments in this are effected by varying the amount of opening in the fan shroud so that as little as 27 bhp may be absorbed. Dynamometers, both fore and aft, provide for measurement of the cable tension. Taut wire gear is furnished on the starboard quarter to provide an effective means for calculating the amount of slack paid out. With this gear, steel piano wire, anchored to the bottom, is paid out at constant tension and provides a rough measure of distance steamed over the ground. A test room with trunks to each cable tank is provided on the shelter deck and fitted with instruments for measuring and locating faults. Modifications for Flexible Repeaters In the normal cable-paying-out process, the cable is drawn from the tank, carried along fairleads to the holdback gear (a mechanism for ap- plying slight tension to the cable so that it will snub tightly around the drum), and then wrapped around the drum of the cable engine from two to four turns depending upon the weight of the cable and the depth of the water. At the drum, a fleeting knife is fitted which pushes over the turns already present to make way for the oncoming turn. From the drum the cable passes through the dynamometer and thence to the overboarding sheave. The Bell System repeaters, manufactured by the Western Electric 308 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 Company, were designed with the objective of making them act as much Hke cable as possible.^ Despite this, their presence introduced a loading and laying problem as their ability to bend without injury is limited to about 3^ ft radius, and their structure is such that unnecessary bending may involve a hazard to their water tightness. As the majority of the sheaves and drimis of the conventional laying gear are considerably smaller than 7 ft diameter, a number of modifications were required in Monarch's equipment to satisfy the repeaters. For the most part, the new gear was designed by the Telegraph Construction and Maintenance Co., Ltd., to broad requirements sup- plied by the A.T.&T. Co. The modifications included providing the port bow sheave with a flat tread to bring its diameter to 6' 10", and replac- ing both forward dynamometers and the aft dynamometer by a new design employing a 7-foot wheel in a pivoted "A" frame bearing on Elliott pressure type load cells. Port and starboard forward drums were replaced with the maximum diameter drums possible without a major change in the complete gear. This diameter proved to be 6'10" on the tread. The after paying out drum was replaced with one having a 7'0" diameter. The forward port and aft cable drums were equipped with Fig. 8 — General view of modified after cable gear (one of 2 hold back sheaves, drum with fleeting knife and ironing board, and, at extreme right, dynamometer sheave). ROUTE SELECTION AND CABLE LAYING 309 Fig. 9 — Cable payout over the stem. ironing boards. (An ironing board is a curved shoe placed adjacent to the cable drum and spring loaded so that it will force the repeater to conform to the curvature of the drum as it goes on.) The forward port and starboard draw-off gear sheaves were replaced with larger ones 7'0'' in diameter which were made traversable. The aft hold-back gear, of the double sheave type, was also replaced with units having 7'0" sheaves. Fig. 8 shows a general view of the modified after cable gear, and the 7-ft stern sheave may be seen in Fig. 9. A line schematic of the gear will be found on Fig. 10. Roller type fairleads shaped into arcs of minimum 3^' radius were fitted at each cable tank hatch, with smaller roller guides at convenient points to assure fair lead of the cable from the tanks to the cable ma- chinery. Electric hoisting gear was provided for the crinoline in each tank as it was necessary to raise the crinoline whenever a repeater left the tank. o _2 so >• o uio: < q: }£.< ID< O UJ Q UJ O "J -lO -) o I 310 ROUTE SELECTIOX AND CABLE LAYING 311 The test room was greatly enlarged and fitted with the special gear necessary for powering and measuring the system during laying. Loading Considerations When the ship is loaded, the cable is coiled carefully in the tanks, layer upon layer — each layer being called a "flake". The coihng is started from the outside of the tank and progresses clockwise toward the center so that the armor is untwisted one revolution for each com- plete turn in the tank. When paid out in the reverse order, this twist is restored. Handling of the repeaters during loading presents a problem because of the need to restrict their bending. After some experimental work was carried out, splints were de^'ised to provide the needed rigidity. These consisted of two angle irons each 12 ft long and equipped at the ends with cold rolled steel rods ranging in length from 1| ft to 6 ft. By this device it was possible to maintain rigidity over the main central portion of the repeater, including the junction of the core tube with the end nosing, and provide limited flexibility along the outer ends of the core tubes which are less sensitive to bending. The splints were re- moved once the repeater reached the tank. Repeaters are always stowed at the outside of the flake where they need be subjected to only a minimum of bending. They are protected with wood dunnage, which must be removed before the repeater is paid out. With these modifications all repeaters and equalizers were laid successfully from either forward or aft gear at a cable speed of around three knots. Testing and Equalization Purpose — Once a submarine cable system has been installed, it is accessible only at the ends for adjustment to improve performance, save at great difficulty and large cost. As some irregularities cannot be corrected from the ends, it behooves the designers to discover and ac- count for such irregularities and to correct them before the cable is finally on the ocean bed. The laying period offers the last opportunity for accomplishing this, and indeed all too frequently, also the first. This fact, coupled with the broadband design of the link and with the presence in the system of active elements (the repeaters), necessitated a very comprehensive program of tests and measurements during laying. 312 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 The program had three specific purposes; (1) to detect immediately any fault which might develop during laying; (2) to perinit the design and execution of corrective system adjustments while en route so that transmission performance of the completed link would fall within speci- fied objectives; and (3) to gather data on system characteristics at intermediate points for eventual use in fault location or in aging studies. The need for parts (1) and (3) of the program is more or less self evident, but part (2) merits some further discussion. In an ideal submarine cable system in an average environment, the attenuation of the cable from one repeater to the next would be offset exactly across the frequency band by the gain of the following repeater. Such a result is never achieved in practice, as the temperature and pres- sure environments (which affect cable attenuation) cannot be known precisely in advance, and the cable structure itself cannot be manufac- tured for mile after mile without variation in transmission characteristic. Additionally, the mechanics of the laying process induce minor changes in the physical structure of the cable which reflect in attenuation changes. If such deviations from desired characteristic produced only differ- ences from the specified system gain objective, compensation could be readily applied at the ends of the submarine link. Unfortunatel}^, this is onlj^ partl}^ the case. Their more important effect is the resulting misalignment of operating levels of individual repeaters from design objective. Misalignment magnitudes must be watched carefully, for at best misalignment narrows the system latitude for seasonal temperature changes and for aging, and at worst it can result in intolerable sj^stem noise. If a repeater is preceded by too much cable the signal to noise ratio at the repeater input will be less than desired because of thermal noise. In the opposite case of too little cable, the signal level will be too high and the resulting overloading in the repeater will also affect the signal-noise adversely. Once present on the signal, the noise cannot be removed, and so the cure for excessive misalignment must be applied before the misalignment has developed. Adjustments at intermediate points along the route must therefore be contemplated. Testing Program — The program which was evolved to meet the three objectives outlined was meticulously reviewed and practiced before the start of laying, and various forms were prepared for entering data and plotting and evaluating results. This was essential to avoid wasting effort or missing \'aluable data. The wisdom of this was fully apparent to all involved after experience with the close time schedules and the mental tensions which developed during the actual laying. ROUTE SELECTION AND CABLE LAYING 313 Staffing for testing was provided by crews of 2 or 3 trained engineers located at the transmitting cable station and on shipboard. Those on the ship served 4| hour watches at 9 hour intervals, which permitted a reasonable amount of rest and avoided continuous "dog watch" duty by any one crew. Close contact between shipboard and cable station crews was essen- tial, and was achieved by means of cable and radio order circuits (or "speakers"). Communication from shore to ship when the cable was powered made use of the standard cable order wire circuit at the cable station to apply a signal in the frequency band 16-20 kc. The signal was demodulated and amplified aboard ship by a special stripped version of this same gear. The radio order circuits employed special land anten- nas and equipment, and for the most part the ship's standard single sideband telephone set, although other equipment at medium frequency was sometimes used for short distances. Radio telegraph with hand keying was available for back-up when conditions were too poor for the radiophone sets. Plans called for powering the cable at all times except when splices were being made. This was necessary for the measurement program, of course, but also provided additional assurance of safe laying of repeaters, as the glassware and tungsten heaters of the vacuum tubes are more re- sistant to damage when hot. Power for the first half of each crossing was provided from the cable station. Beyond this point, the required voltage would have become excessive and so the shipboard supply was inserted into the series power loop and its voltage adjusted in proportion to the amount of second half cable actually in the loop. Monitoring against the possibility of faults was accomplished by measurement of a pilot tone at 160 kc, transmitted over the cable at all times except when data were being taken or power was turned down. Audibly alarmed limits were set on the measurement to indicate any significant deviation in transmission. In actuality, all unanticipated re- ceived alarms were found to have resulted from frequency or voltage shifts in the primary shipboard supply for the measuring equipment. During the design of the system,- consideration of the misalignment problem had indicated the desirability of splitting the cable for each crossing into a number of sections, called ocean blocks. These contained either 4 or 5 repeaters, and were 150 to 200 miles in length. In loading the ship, the two ends of each ocean block were left accessible for con- nection to the test room and for splicing operations. Measurements made in the spring of 1955 off Gibraltar had indicated an unexpected change in attenuation called "laying effect",^ which re- quired some last minute adjustment of the repeater section lengths. 314 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 With incorporation of these changes, it was known that the factory lengths of cable between repeaters were adequate to keep misalignment within an ocean block within reasonable limits. The system could then be equalized between ocean blocks so that the signal level at the first repeater of a new block would be approximately correct, and the total system noise thus would fall within limits. This equalization was accomplished in two ways. Excess cable of the order of | to 3 miles in length was provided at the top end* of each ocean block. Based on measurements, this could be cut longer or shorter than the nominal spacing of repeaters, so that the repeater gains and cable losses would be matched at some frequency in the band. Residual devia- tions in other parts of the band could then be mopped up if necessary by inserting a simple equalizer, housed in a container similar to those used for the repeaters. Ten such equalization points were provided in each cable. In practice, sending levels were adjusted at the cable station to give test tones at the grids of the output tubes of the repeaters which if the system equalization were perfect, would be flat across the frequenc}^ band, and at the proper level. These tones were measured on shipboard at the end of the ocean block being paid out. The results were plotted against mileage, with one sheet for each frequency being measured. Because of the "laying effect" and of temperature and pressure changes on the cable as it progressed to the bottom, these plots displayed a slope. The value of loss (or gain) to be ascertained for each frequency was that which would exist when the entire ocean block was on the bottom. To obtain this, it was necessary to extrapolate the cur^'es to the mileage point representing the end of the block in question. The extrapola- tion was required to avoid stopping the ship at the end of the block, and so had to anticipate the time needed for turning over and cutting the cable end at the proper point, and making one or two splices (depending on whether or not an equalizer was inserted at the point in question). Having read the extrapolated values from the curves, these were com- pared with objectives for that block junction, and the deviations plot- ted. Transparent overlays, showing the net effect of each of several types of equalizer combined with varying amounts of cable around the nom- inal spacing, greatly facilitated the final decision as to cutting point and equalizer choice. This implementation of the system undersea equalization represented a very large part of the effort required of the testing crews during laying. Additional data gathered for fault location, aging studies and other * First end out of the cable tank. ROUTE SELECTION AND CABLE LAYING 315 purposes included precise determination of repeater crystal frequencies on the bottom, gain frequency runs to show up any fine grained structure which might exist in the band, and values of line current and driving voltages. Copper resistance and capacitance measurements proved to be of dubious value; in the first case because of the temperature/resistance characteristic of the vacuum tube heaters; in the case of capacitance, probably because of polarization effects in the castor oil capacitors used in the repeaters. Shipboard Test Equipment — A new test room had been equipped for making the above measurements with transmitting and receiving trans- mission measuring sets^ including the crystal test panels. These sets were provided in duplicate to forestall difficulty should one set develop trouble during the laying. The transmitting consoles were recjuired only for use in calibrating the receiving sets, and for some measurements which were made on individual ocean blocks in the ship's tanks. Additional gear in the test room included a cable current power sup- ply,-* and a "Lookator" which is a pulse echo type of fault locator useful from a point in the cable to the adjacent repeater on either side. Laying Sequence H.M.T.S. Monarch is the largest cable ship afloat, \\ith capacity for about 2,000 miles of the Type D deep sea cable in her tanks. However, because of the inherent limitation on their bending radius, the presence of flexible repeaters in the cable puts a restriction on the height to which the coil can be permitted to rise in the tanks. For repeatered Type D cable, therefore. Monarch's capacity is cut back to about 1,600 nauti- cal miles. Types A and B cable, used in shallower waters, are considerably larger and heavier than Type D and consequently, less of these can be car- ried. The ideal laying program would have involved one continuous pas- sage across the North Atlantic from cable station to cable station. How- ever, this would have required carrying over 1,900 miles of cable in- cluding about 300 miles of Type A and something less than 50 miles of Type B. Such an amount of cable would greatly exceed the ship's capacity. Each cable was, therefore, laid in 3 sections. The No. 1 cable (southern- most), which transmits from west to east, was laid in the following se- quence: Clarenville to just beyond the mouth of Trinity Bay, a distance of 200 miles; thence about 1,250 miles to Rockall Bank (a submerged 316 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 plateau) ; and finally the remaining 500 miles from Rockall Bank to Oban. The No. 2 cable followed the opposite sequence, starting at Oban and proceeding in 3 sections of 500 miles, 1,250 miles, and 200 miles to the terminal at Clarenville. Shore ends, about f mile long at Clarenville and 2 miles at Oban, were prepared and put in place in advance of the time when they would be needed. At each intermediate point, the cable was "buoyed off" with a mushroom anchor, connecting lines, and a surface buoy of size appropriate for the water depth. The mileages indicated are actual cable lengths. They exceed the geographical distances between the points involved because of the slack allowance which experience has shown to be necessary to assure reason- able conformance of the cable with the contour of the ocean bed. Nor- mally, about 5 per cent slack is considered desirable in deep water, with the allowance decreasing in steps to zero in shallow water. All available information indicated that the most favorable weather conditions in the North Atlantic could be anticipated in the period ^lay through August. Prior to May, ice could be expected along the western sections of the route and after August, hurricanes were likely, and later the winter storms. The laying of the No. 1 cable was started June 28, 1955, and com- pleted September 26. The actual laying period took in but 24 days in this interval, the remainder of the time being spent in transit and in re- loading. The No. 2 cable was started June 4, 1956, and completed August 14. About 16 of laying days were involved. The routine aboard ship during laying consisted in passing out cable at the rate of 6 to 7 knots for a repeater section length of a little over 37 nautical miles, then slowing down to about 3 knots as the repeater passed through the cable machinery and overboard, then back to speed again. During all of this period the testing crews, both on shipboard and at the transmitting cable station, were busy measuring, recording data and planning the equalization trimming. At a point shortly after the passage of the next-to-last repeater in an ocean block, special meas- ures were required for the equalization program. From that point until the joints associated with the connection to the following ocean block had been completed, the speed was reduced to 5 knots. The need for this arose from the following considerations. Stopping of the ship in deep water introduces serious possibility of formation of kinks in the cable, and is to be avoided at all costs. To per- mit continuous laying, it was necessary to determine the amount of cable needed for equalization, measure out this cable, and complete the splices before reaching the end of the block being laid. ROUTE SELECTION AND CABLE LAYING 317 The addition of an equalizer at the end of the block requires two joints and armor splices. Preparing the cable ends, brazing together the center conductor and associated tapes, injection molding the polyethylene around the center conductor, replacing and overlaying the armor wires and binding the splice consumes 6 to 7 hours for a single splice, and 8 to 9 hours for two splices when overlapping of operations is practical. An allowance of 3 hours is considered necessary for remolding in event of a defective joint (disclosed by X-ray inspection). The time allowance required to complete the splicing of ocean blocks is therefore 9 to 12 hours. About 1^ hours are needed to carry out the extrapolation, make the equalization decision and turn over cable to the cutting point. Dur- ing the interval between the cable cut and the completion of the joint, the ship's speed was maintained at 5 knots so as to minimize the distance over which extrapolation of equalization data had to be extended. Even so, the final extrapolation covered the last 60 to 75 miles of each ocean block. During the jointing intervals, system power was turned down to avoid any hazard to the members of the jointing crew. It was restored as soon as the moldings had been X-rayed and the outer or return tapes had been brazed. These activities were so timed that in almost every case the system was powered as each repeater went overboard. CLARENVILLE-SYDNEY MINES LINK Route Selection Clarenville having been selected as the site of the cable terminal sta- tion on the west end of the ocean crossing, it was necessary to consider how the system was to be extended to Nova Scotia for connection with the North American continental network. A number of alternatives were possible as described below: Alternative 1 contemplated radio relay across Newfoundland to Port aux Basques, and thence across the Cabot Strait. However, a survey revealed that maintenance access to suitable sites would be most diffi- cult, particularly in winter, and primary power was not obtainable. Alternative 2 involved a poor submarine route around the Avalon Peninsula to possibly Halifax, Nova Scotia. The length of the sea cable would be about 600 nautical miles. It would be necessary to cross many working telegraph cables, (Fig. 3). Trawler damage could be expected as the cable would need to traverse known trawling areas, and during the winter months any repairs would be costly and prolonged. Also it was 318 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 not desired to lay another cable out of Trinity Bay as the route might be wanted for a second transoceanic cable at some time in the future. Alternative 3 involved a submarine cable from Clarenville out through the North West Arm to Rantem at the head of Trinity Bay, a short land cable across the isthmus, and thence either a submarine cable direct to Sydney, Nova Scotia, or a land crossing of the Burin Peninsula at Garnish and thence by submarine cable to Sydney. This route involved three open sea sections with one or two land sections. There was rather limited space for a cable in Placentia Baj" and the bottom was uneven and rocky. Existing cables laid around the Burin Peninsula have had interruptions which indicated an unsuitable bottom and fishing trawlers had been seen in the vicinity recently. Alternative 4 also involved a cable overland, from Clarenville to Terrenceville at the head of Fortune Bay, there to join a direct sub- marine cable to Sydney Mines. Three short underwater sections would be involved in the Clarenville-Terrenceville link, but these could be in shallow water out of harm's way. The main submarine route from Ter- renceville to Sydney Mines would be clear of other cables and would avoid trawling areas and anchorages, a not inconsiderable achievement in view of the congestion of submarine cables and the fishing activity around the southeast corner of Newfoundland. Further, a good landing site in Nova Scotia was available on property near Sydney Mines owned by Eastern Telephone and Telegraph Company. After due consideration. Alternative 4 was chosen as being the most satisfactory from all aspects and the final route is shown on Figure 3. This route is considered to be most likely to have a good life history. While it would have been possible to have one continuous land cable between Clarenville and Terrenceville, the three short underwater sec- tions saved a considerable amount of trenching without adding undue hazard to the system. Clarenville-Terrenceville Route It having been decided to route the Post Office single cable system overland from Clarenville to Terrenceville a number of other matters required decision. The first was the type of cable to be employed for this section. Several alternatives were considered, bearing in mind factors such as the type of terrain, access, aA'ailability of primary power, possi- ble future expansion of capacity and, of course, interference from static and radio frequency pick-up. The advantages of using standard solid dielectric coaxial ocean cable with submarine-type repeaters were judged EOUTE SELECTION AND CABLE LAYING 319 to outweigh all other considerations and left only one problem, namely, shielding from interference. Up to this time shore ends of submarine cables used by the Post Office were shielded for about a quarter of a mile from shore by a lead sheath insulated from the return tapes of the coaxial by a polyethylene barrier. Experience indicated that such shielding might not be adequate over a long distance on land. The question was resolved by the addition of iron shielding tapes and a plastic jacket to standard submarine cable. The structure is described elsewhere.^ Through the use of this robust, wire armored cable and two steel housed submarine repeaters, no limitations from the noise pickup angle were placed on the detailed route selection for the overland section. The first thought was to try to proceed directly across country from Claren- ville to Pipers Hole River, saving at least 10 miles over a route which followed the road, and on which advantage might be taken of quite long water stretches into which the cable could be dropped. Black River Pond, for instance, is 4| miles long. This proposal was abandoned after surveys, because of the very rocky nature of the country and difficulty of access both for construction and any subsequent maintenance, and it was decided to follow the general course of the roads. It was possible to avoid trenching in the rocky, precipitous cliff coun- try from Clarenville to Adeytown by laying about 6 miles of cable in the water of Northwest Arm. Similar considerations dictated the choice of two miles of cable in the sea across Southwest Arm. Thence the route followed the road, at a distance ranging from 250 yards to more than a mile, as far as Placentia Bay, taking advantage of the larger ponds where possible to avoid trenching. Reaching the 800 foot high ground beyond the Pipers Hole River from the north of Black River proved quite difficult. Here the road is carved out of the foot of the cliffs as far as Swift Current and the country behind is solid rock. Plans exist for a hydro-electric project involving dams in Pipers Hole River just north of the road crossing and it is naturally not desirable to bury a cable in such a locality. The river estuary itself pass- ing by Swift Current presents only a narrow 6 foot deep navigable chan- nel at low water but it was decided that this could be used for some 6 miles by employing a barge and a shallow draft tug for the laying. A suitable route out of the basin up through wooded gorges to the top took about a week of very hard going to locate. Thereafter all was plain sailing taking advantage of ponds such as Long Pond (4 miles) and Sock Pond (3 miles) until the route arrived within G miles of Ter- renceville. 320 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 Here it was reluctantly decided to bury the cable in a deep trench on the inner side of the road, as the other side falls sharply to the sea. The desire to avoid roads was due to their instability and the methods used for construction and repair. This road is dirt only, with no foundations, and in this particular section has been known to slide away into the river bed below\ The final length of cable laid was just short of 55 nautical miles. Cabot Strait Laying Coaxial submarine cables in which rigid repeaters are inserted cannot be laid with the existing cable laying machinery except by stopping the ship, removing the turns of cable from the drum and then passing the repeater by the drum and restoring the turns. Special equipment is also needed for launching the repeater over the bow sheaves. Ship Modifications The following equipment was installed on Monarch for the laying of cables carrying rigid repeaters. A gantry over the bow baulks, consisting of a 22 foot steel beam pro- jecting 6 feet beyond the sheaves, was installed for handling repeaters at the bow. This gantry was fitted with an electrically operated traveling hoist for lifting the repeaters over the bow sheaves and lowering them into the sea. A standby hand operated lifting block and traveller were provided to guard against failure of the power point. A rubber-tired steerable steel dolly (or trolley) was developed from the chassis of a small car to transport the repeaters from the cable tank hatches to the bow sheaves. These repeaters weigh about 1200 pounds' Storage racks were built up from steel sections provided with shaped, rubber lined wood blocks and were fitted at each cable tank hatch on the shelter deck. Each rack held 4 repeaters in double tiers. A hand operated lift was furnished for moving the repeaters from the storage racks to the dolly. A special quick release grip was furnished for use when lifting the repeaters by the electric hoist on the bow gantry. Deflection plates were also fitted on the fore deck around dynamometers and hatches to avoid their fouling the dolly. Launching Rigid Repeaters The rigid repeaters were stowed in their racks in the order of their laying. The bights of the cable attached to the ends of the repeaters ROUTE SELECTION AND CABLE LAYING 321 were brought up the sides of the cable tanks, secured along the arms of the crinoline and up the sides of the hatch coamings to the deck, clear of the running length of cable and from where the repeater could be drawn forward along the deck on the dolly. When the time came for a repeater to be laid, speed was reduced and the ship finally stopped head to wind. A 6x3 compound rope from the starboard cable drum was secured to the cable just abaft the bow baulks. Sufficient cable was then paid out until the tension was taken up by this rope. The turns of the running cable were then removed from the port cable drum and the resulting slack cable worked overboard by paying out the starboard drum rope which was holding the tension. When the excess cable had been cleared from the deck, the repeater on its dolly was carefullj^ hauled along the fore deck to the traveling hoist of the o\'erhead gantr3^ Cable was then drawn from the tank so that the turns could be re-formed on deck and replaced on the port cable drum. The repeater was lifted from the trolley and traversed outboard as soon as it was high enough to clear the bow baulks. It was then lowered to the water's edge and when the tension had again been taken by the cable, the quick release grip was slipped and the starboard diTim rope cut. Paying out was then resumed. Laying Program ^ On February 1, 1956, Monarch, having returned to Ocean Works, Erith, after refitting, commenced loading the various sections of cable to be used for the Terrenceville-Sydney Mines route. The sections were all carefull}^ tested and measured in the Works before loading. The cable ends were clearly marked and dogged together by a length of rope which was not removed until the repeater had been jointed into its connecting sections of cable. Loading of the cable and splicing in of repeaters was finished by April 10 and the system tested and checked. Monarch sailed for Sydney Mines on April 18 and arrived there April 30. The cable station is situated about 1^ miles inland from the shore, with a small lake intervening. A length of Type B, insulated outer conductor, lead covered cable had previously been laid from the station across the lake to a narrow strip of land which separates it from the sea. The joint to the main cable was to be made on this strip. Two medium sized shore based motor boats were used to tow the end of the double armored section of cable from Monarch to the shore. During this journey the cable was supported by empty oil drums at close intervals. When the motor boats had reached 322 THE BELT. SYSTEM TECHNICAL JOURNAL, JANUARY 1957 shoal water the end of the cable was secured to a landing line and two tractors took over the hauling. When enough cable was on shore to make the joint and the splice, the barrels were cut away and Monarch weighed anchor and paid out this section of double armored cable on the agreed route and buoyed off the end. She then steamed over the proposed track to Terrenceville, taking soundings and sea bottom temperatures as required, and an- chored off Terrenceville on May 3. Preparations for landing the end were at once put in hand and the ship's motor launches towed the end of the cable towards the cable land- ing, the cable again being supported by empty oil drums. This end was jointed and spliced to a piece of cable which had been laid previously from the Terrenceville cable hut to a sand spit which juts across the head of Fortune Bay, about a mile away. Upon completion of the splice, overall tests were made from the ship to the Terrenceville cable hut, and all being well, paying out toward the buoj^ed end off Sydney Mines was begun on May 4. The first repeater went over about two hours after the start of lajdng and the others followed at approximately 4f hour intervals. On May 7 the cable buoy on the Sydney Mines end was recovered and the end hove inward. After tests in both directions, the final joint and splice were made. This operation was completed on ]May 9, and on receipt of a signal that all was well. Monarch proceeded into harbor at Sydney to land testing equipment, a spare equalizer and other equipment. Equalization and Testiyig The cable had been loaded into the ship in repeater section lengths, so cut that when laid at estimated mean annual sea temperature, the ex- pected attenuation would be 60.0 db at 552 kc. A correction for the change in attenuation of the cable when coiled in the factorj' tanks and when laid in about 100 fathoms had been determined from tests on two 10-mile lengths of cable, laid off the Island of Skye. The correction amounted to a decrease in attenuation when laid of 1.42 per cent. This was essentially an empirical result, and as the mechanism of the change was not fully understood, a possible further inaccuracj'' of equalization might arise. Sea bottom temperatures along the route were obtained from informa- tion supplied by the Fisheries Research Board of Canada, })ut unfor- tunately, this information was rather meager ^nd varied considerably with locahty. ROUTE SELECTION AND CABLE LAYING 323 Since the cable equalization built into the repeater differed appreciably from the final determination on laid cable, it was found necessary at a comparatively late stage to introduce an undersea equalizer into the center of the sea section. This was intended to eliminate a flat peak of loss of 3.5 db, expected at about 100 kc. So that the last repeater should not he too near the beach at Sydney Mines, a network simulating 9 miles of cable was also inserted in the undersea equalizer. The repeaters were spliced into the cable lengths on board Monarch and tests were made at every stage of the buildup of the system. The eciualizer was permanently jointed to the first half section of 7 repeaters and left with an excess length of tail which could be cut as desired during the laying operation to further improve the equalization. The first and second halves of the system were temporarily connected through power separation filters so that the whole system could be energized just prior to laying. The test routine carried out included attenuation measurement at 5 frequencies in each direction of transmission, noise, pulse and loop-gain, supervisory measurements, dc and insulation resistance and capacitance. Monarch test room contained, therefore, two sets of terminal equipments similar to those installed at Clarenville and at Sj^dney Mines. It was decided to energize the system continuously during the laying except for the few hours when power had to be removed to make the equalizer splice. This enabled a continuous order (speaker) circuit to be operated over the cable and minimized the number of energizing and warm-up periods. The only disadvantage, considered to be slight, was the necessary omission of insulation resistance and capacitance measure- ment during laying, except in the course of the equalizer splicing operation. The plan was to lay from Terrenceville in the direction of the high- frequency band and to test the system to Monarch during the laying from this shore station. The overland section between Clarenville and Terrenceville, which contained two repeaters, was connected on with appropriate equalization after the submarine section had been satisfac- torily completed and tested. At Terrenceville, after the cable end had been taken ashore and the beach joint completed, the system was energized from Monarch with a dc power ground at Terrenceville for the necessary 4 hour minimum warming up period. The first set of routine measurements of the laying operation was then carried out. Thereafter, a complete set of measure- ments on the Terrenceville half of the system was made after every 10 miles of cable laid. An occasional check set of measurements was also made on the Sydney Mines half of the system in the tanks. 324 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 The primary object of these tests was to determine what length of cable should be inserted between the equalizer and the 8th undersea repeater to obtain the optimum system. In practice this resulted in arranging for a length of cable such that the output level of the 8th repeater at 522 kc should be equal to that at the output of the first re- peater at the assumed mean annual temperature of 35.1°F. The estimated length of cable required for this purpose was plotted after each measurement. It became evident soon after laying the 5th repeater (94.6 nautical miles of cable laid) that the linear relation ob- tained could be extrapolated with adequate accuracy to safely specify a length of 6.06 nautical miles of cable between the equalizer and the adjacent repeater. This decision on length was taken, and after removing power the equalizer was accordingly jointed in, the operation being completed before it was necessary to pay out the splice. During this period capaci- tance and conductor and insulation resistances were checked on each half. During the laying of the second half, measurements were made as for the first half. On arrival at the buoyed shore end a final complete set of measurements was made and these suitably corrected for the shore end length, transmitted to Sydney Mines so that the first measurements from Sydney Mines to Clarenville could be checked with those obtained on the ship. SIDELIGHTS Weather Weather is the big question mark in cable laying and repair activities. With few exceptions the transatlantic project was blessed with remark- ably good weather. The exceptions were, however, noteworthy. Heavy snow squalls were encountered off Terrenceville during the operation in that \'icinity. At Rockall Bank on the first laj' one hea\'y storm came up as the last repeater in the 1,200-mile section was going over, and made this launching and the subseciuent buojdng of the end very difficult operations. Both were accomplished successfully as a result of the superb seamanship of Monarches commander, Captain J. P. F. Betson, and his officers and crew. A second, and worse storm was encountered upon the return to Rockall. This was a manifestation of hurricane lone, with wind velocities above 100 mph and very high seas. The ship had given up searching for the buoy (later reported drifting more than 500 miles awaj- off the Faeroe Islands) and was grappling for the cable, when the storm hit. Fortun- ROUTE SELECTION AND CABLE LAYING 325 ately, the cable had not yet been found, so the ship could head into the wind and ride it out. She was driven many miles off course in the process, and the seas will be long and vividly remembered by all present. In- cidentally, the cable was picked up shortly after the storm had mod- erated. Generally speaking, the effect of the weather on the engineering super- numeraries on board was not severe, although Monarch's stock of dram- amine was somewhat depleted by the end of the project. Miscellaneous Events At the start of the first transatlantic lay, several icebergs were en- countered. One, a small one at the mouth of Random Sound, lay in the planned path of the cable and caused an involuntary, though minor, revision of the route. The others, beyond the mouth of Trinity Bay, were larger but also farther away. Whales and grampuses got to be common sights, although much film was expended at first by the uninitiated. An occasional bird rested on the ship far from land, obviously ex- hausted from its long and presumably unintended journey. Progress Bulletins Daily progress bulletins were radioed to headquarters of all partners during the laying. In addition, because a telephone cable system differs considerably from submarine telegraph cables, the officers and crew were briefed by the engineering personnel as to the repeater structure, the need for equalization and the general objectives of the venture. This proved to be a very profitable move indeed, for the cooperation of all hands was everything that could be wished. As a follow up, daily performance bulletins were posted in strategic parts of the ship so that everyone no matter what his duties, could know just how the evolving system was performing with respect to objectives. Cable Order Circuit One way conversation from shore to ship over the cable was possible all the time the repeaters were energized. This was a source of very great satisfaction to the shipboard test crew, as it was concrete evidence that the cable was working, and working well. When power was turned down, the recourse to radio telephone provided a comparison which generally left no doubt as to the future value of the cable. 326 THE BELL SYSTEM TECHXICAL JOURNAL, JANUARY 1957 ACKNOWLEDGEMENTS When the final spHce was shpped into the water of Clarenville Harbor, on August 14, 1956, there was completed a venture quite unique in the annals of submarine cable laying. And in the lajnng perhaps more than in am^ other phase of the transatlantic project did the successful con- clusion provide evidence of the friendly and harmonious relationships between the different organizations and nationalities involved, and of the close coordination of their efforts. REFERENCES 1. T. F. Gleichmann, A. H. Lince, M. C. Wooley and F. J. Braga, Repeater Design for the North Atlantic Link. See page 69 of this issue. 2. H. A. Lewis, R. S. Tucker, G. H. Lovell and J. M. Fraser, System Design for the North Atlantic Link. See page 29 of this issue. 3. A. W. Lebert, H. B. Fischer and INI. C. Biskeborn, Cable Design and Manu- facture for the Transatlantic Submarine Cable System. See page 189 of this issue. 4. G. W. ]\Ieszaros and H. H. Spencer, Power Feed Equipment for the North Atlantic Link. See page 139 of this issue. 5. R. J. Halsey and J. F. Bampton, System Design for the Newfoundland-Nova Scotia Link. See page 217 of this issue. I I i Bell System Technical Papers Not Published in This Journal Baldwin, M. W., Jr.,^ and Nielsen, G., Jr.^ Subjective Sharpness of Simulated Color Television Pictures, J. Am. Optical See, 46, pp. 681-685, Sept. 1956. Barbieri, F,,^ and Durand, J.' Method for Cutting Cylindrical Crystals, Rev. Sci. Instr., Shop Note, 27, pp. 871-872, Oct., 1956. Bemski, G.^ Quenched-In Recombination Centers in Silicon, Phys Rev., 103, pp. 567-569, Aug. 1, 1956. Bommel, H. E., see Mason, W. P. Brady, G. W., see Mays, J. M. Brown, W, L., see Montgomery, H. C. Cutler, C. C} Instability in Hollow and Strip Beams, J. Appl. Phys., Letter to the Editor, 27, pp. 1028-1029, Sept., 1956. Dacey, G. C., see Thomas, D. E. Dail, H. W., Jr., see Gait, J. K. Dehn, J. W.,1 and Hersey, R. E.i Recent New Features for the No. 5 Crossbar Switching System, Commun. and Electronics, 26, pp. 457-466, Sept., 1956. Durand, J., see Barbieri, F. Farrar, H. K., see Maxwell, J. L. • Bell Telephone Laboratories, Inc. 327 328 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 Fay, C. E.i Ferrite -Tuned Resonant Cavities, Proc. I.R.E., 44, pp. 1446-1449, Oct., 1950. Feher, G.^ Observation of Nuclear Magnetic Resonances Via the Electron Spin Resonance Line, Phys. Rev., Letter to the Editor, 103, pp. 834-835, Aug. 1, 1956. Ferrell, E. B.i A Terminal For Data Transmission Over Telephone Circuits, Proc. Western Joint Computer Conf., pp. 31-33, Feb. 7-9, 1956. Galt, J. K.,1 Yager, W. A.,' and Bail, H. W., Jr.^ Cyclotron Resonance Effects in Graphite, Phys. Rev., Letter to the Editor, 103, pp. 1586-1587, Sept. 1, 1956. Garrett, C. G. B.^ The Physics of Semiconductor Surfaces, Nature, 178, p. 396, Aug. 25, 1956. Goldey, J. M., see Moll, J. L. Goldstein, H. L.,^ and Lowell, R. J.' Magnetic Amplifier Controlled Regulated Rectifiers, Proc. Special Tech. Conf. on Magnetic Amplifiers, pp. 145-147, Juh', 1956. Guldner, W. G.^ AppHcation of Vacuum Techniques to Analytical Chemistry, Vacuum Symp. Trans., pp. 1-6, 1955. Harrower, G. A.i Energy Spectra of Secondary Electrons from Mo and W for Low Primary Energies, Phys. Rev., 104, pp. 52-56, Oct., 1956. Hersey, R. E., see Dehn, J. W. HiTTiNGER, W. C, see Warner, R. M., Jr. HoLONYAK, N., see Moll, J. L. ^ Bell Telephone Laboratories, Inc. i TECHNICAL PAPERS 329 HOSFORD, J. A.'' The Development of Automatic Manufacturing Facilities for Reed Switches, Comniun. and Electronics, 26, pp. 496-500, Sept., 1956. HOVGAARD, O. M.l Capability of Sealed Contact Relays, Commun. and Electronics, 26, pp. 466-468, Sept., 1956. Ireland, G.^ Management Development in the Communications Field, Elec. Engg., 75, pp. 881-884, Oct. 1956 Jaccarino, v., see Shulman, R. G. Jaycox, E. K.,1 and Prescott, B. E.^ Spectrochemical Analysis of Thermionic Cathode Nickel Alloys by Graphite-to-Metal Arcing Technique, Anal. Chem., 28, pp. 1544-1547, Oct., 1956. Jones, H. L.'' A Blend of Operations Research and Quality Control in Balancing Loads on Telephone Equipment, Proc. Am. Soc. for Quality Control, June, 1956. KlSLIUK, P.i The Dipole Moment of NF3 , J. Chem. Phys., Letter to the Editor, 25, p. 779, Oct., 1956. Knapp, H. M.i Design Features of Bell System Wire Spring Relays, Commun. and Electronics, 26, pp. 482-486, Sept., 1956. KucK, R. G.s Microwave Facilities with Built-in Reliability, Commun. and Elec- tronics, 26, pp. 438-441, Sept., 1956. Kunzler, J. E.' Liquid Nitrogen Vacuum Trap Containing a Constant Cold Zone. Rev. Sci. Instr., Shop Note, 27, p. 879, Oct., 1956. 1 Bell Telephone Laboratories, Inc. ^ Western Electric Company. ^ Pacific Telephone and Telegraph Company, San Francisco, Calif. * Illinois Bell Telephone Company, Chicago, 111. 330 the bell system technical journal, january 1957 Lewis, H. W.^ Ballistocardiographic Instrumentation, Rev. Sci. Instr., 27, pp. 835- 837, Oct., 1956. Lowell, R. J., see Goldstein, H. L, Luke, C. L.^ Determination of Traces of Gallium and Indium in Germanium and Germanium Dioxide, Anal. Chem., 28, pp. 1340-1342, Aug., 1956. Lu^E, C. L.i Rapid Photometric Determination of Magnetism in Electronic Nickel, Anal. Chem., 28, pp. 1443-1445, Sept., 1956. Mason, W. ?.,• and Bommel, H. E.i Ultrasonic Attenuation at Low Temperatures for Metals in the Nor- mal and Superconducting States, J. Aeons. Soc. Am., 28, pp. 930-944, Sept., 1956. Maxwell, J. L.^ and Farrar, H. K.^ Automatic Dispatch System for Half-Duplex Teletypewriter Lines, Commun. and Electronics, 26, pp. 441-445, Sept., 1956. Mays, J. M.,i and Brady, G. W.^ Nuclear Magnetic Resonance Absorption by H^O on TiOj , J. Chem. Phys., 25, p. 583, Sept., 1956. McLean, D. X.' j Tantalum Capacitors Use Solid Electrolyte, Electronics, 29, pp. 176- 177, Oct., 1956. Meszar, J.i The Full Stature of the Crossbar Tandem Switching System, Com- mun. and Electronics, 26, pp. 486-496, Sept., 1956. Moll, J. L.,' Tanenbau.m, M.,^ Goldey, J. M.,' and Holonyak, X.' P-N-P-N Transistor Switches, Proc. I.R.E., 44, pp. 1174-1182, Sept., 1956. ' Bell Telephone Laboratories, Inc. '" Pacific Telephone and Telegraph Company, San Francisco, Calif. V 1 J TECHNICAL PAPERS 331 Montgomery, H. C./ and Brown, W. L.^ Field -Induced Conductivity Changes in Germanium, Phys. Rev., 103, pp. 865-870, Aug. 15, 1956. Moore, E. F.' Artificial Living Plants, Sci. Am., 195, pp. 118-126, Oct., 1956. Moore, E. F.,' and Shannon, C. E.^ Reliable Circuits Using Less Reliable Relays, J. Franklin Institute, 262, pp. 191-208, Sept., 1956, pp. 281-298, Oct., 1956. MosHMAN, J., see Tien, P. K. Nelson, L. S.^ Sapphire Lamp for Short Wavelength Photochemistry, J. Am. Optica] Soc, 46, pp. 768-769, Sept., 1956. Nelson, L. S.,^ and Ramsay, D. A.^ Absorption Spectra of Free Radicals Produced by Flash Discharges, J. Chem. Phys., Letter to the Editor, 25, pp. 372-373, Aug., 1956. Nelson, L. S.,^ and Ramsay, D. A.^ Flash Photolysis Experiments with a Sapphire Flash Lamp, J. Chem. Phys., Letter to the Editor, 25, p. 372, Aug., 1956. Nielsen, G., Jr., see Baldwin, M. W., Jr. Ohm, E. a.' A Broad-Band Microwave Circulator, Trans. I.R.E., PGMTT, MTT-4, pp. 210-217, Oct., 1956. Owens, C. D. a Survey of the Properties and Applications of Ferrites Below Micro- wave Frequencies, Proc. LR.E., 44, pp. 1234-1248, Oct., 1956. Owens, C. D.' Modem Magnetic Ferrites and Their Engineering Applications, Trans. I.R.E., PGCP, CP-3, pp. 54-62, Sept., 1956. ' Bell Telephone Laboratories, Inc. * National Research Council, Ottawa, Canada. 332 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 Phelps, J. W.^ Protection Problems in Telephone Distribution Systems, Telephony, 151, pp. 20-22, 47-48, Sept. 1, 195G. Prescott, B. E., see Jaycox, E. K. Powell, W.^ So You've Invested in Modem Plant — Now What?, Telephony, 151, pp. 27-28, 48-50, Sept., 195G. Ramsay, D. A., see Nelson, L. S. Reiss, H.^ Refined Theory of Ion Pairing. I — Equilibrium Aspects. II — Irre- versible Aspects, J. Chem. Phys., 25, pp. 400-413, Sept., 1956. Remeika, J. P.^ Growth of Single Crystal Rare Earth Orthoferrites and Related Com- pounds, Am. Chem. See. J., 78, pp. 4259-4260, Sept. 5, 1956. Richards, A. P., see Snoke, L. R. Robertson, S. D.^ Recent Advances in Finline Circuits, Trans. I.R.E., PGAITT, MTT-4, pp. 263-267, Oct., 1956. Schmidt, W. C.^ Problems in Miniaturization, Proc. Design Engg. Conf., pp. 40-54 May 14-17, 1956. Seidel, H.^ Anomalous Propagation in Ferrite-Loaded Waveguide, Proc. I.R.E,, 44, pp. 1410-1414, Oct., 1956. Shannon, C. E., see Moore, E. F. " Shulman, R. G.,1 and Jaccarino, V.^ Effects of Superexchange on the Nuclear Magnetic Resonance of MnF. , Phys. Rev., Letter to the Editor, 103, pp. 1126-1127, Aug. 15, 1956. I 1 Bell Telephone Laboratories, Inc. ^ New York Telephone Company, New York City. TECHNICAL PAPERS 333 Shulman, R. G./ and Wyluda, B. J.^ Nuclear Magnetic Resonance of Si-^ in n- and p-Type Silicon, Phys. Rev., Letter to the Editor, 103, pp. 1127-1129, Aug. 15, 1956. Slepian, D.i A Note on Two Binary Signaling Alphabets, Trans. I.R.E., PGIT, IT-2, pp. 84-86, June, 1956. Snoke, L. R.,^ and Richards, A. P.^ Marine Borer Attack on Lead Cable Sheath, Sci., Letter to the Editor, 124, p. 443, Sept. 7, 1956. Sproul, p. T.i A Video Visual Measuring Set with Sync Pulses, Commun. and Elec- tronics, 26, pp. 427-432, Sept., 1956. SUHL, H.i The Nonlinear Behavior of Ferrites at High Microwave Signal Levels, Proc. LR.E., 44, pp. 1270-1284, Oct., 1956. Tanenbaum, M., see Moll, J. L. Tien, P. K.,^ and Moshman, J.' Monte Carlo Calculation of Noise Near the Potential Minimum of a High-Frequency Diode, J. Appl. Phys., 27, pp. 1067-1078, Sept., 1956. Thomas, D. E.,i and Dacey, G. C.^ Application Aspects of the Germanium Diffused Base Transistor, Trans. LR.E., PGCT, CT-3, pp. 22-25, Mar., 1956. Uhlir, A., Jr.i Two-Terminal p-n Junction Devices for Frequency Conversion and Computation, Proc. LR.E., 44, pp. 1183-1191, Sept., 1956. Van Titert, L. G.^ Dielectric Properties of and Conductivity in Ferrites, Proc. LR.E., 44, pp. 1294-1303, Oct., 1956. ' Bell Telephone Laboratories, Inc. * Wm. F. Clapp Laboratories, Inc., Duxbury, Mass. 334 the bell system technical journal, january 1957 Van Uitert, L. G.^ Nickel Copper Ferrites for Microwave Applications, J. Appl. Phys., 27, pp. 723-727, July, 1956. Warner, R. M., Jr.,i and Hittinger, W. C.^ A Developmental Intrinsic -Barrier Transistor, Trans. I.R.E., PGED, ED-3, pp. 157-160, July, 1956. Weinreich, G.^ The Transit Time Transistor, J. Appl. Phys., 27, pp. 102,5-1027, Sept., 1956. Weiss, M. T.i Improved Rectangular Waveguide Resonance Isolators, Trans. I.R.E., PGMTT, Mtt-4, pp. 240-244, Oct., 1956. W^OLFF, P. A.^ Theory of Plasma Resonance, Ph3's. Rev., 103, pp. 845-850, Aug. 15, 1956. Wyluda, B. J., see Shulman, R. G. Yager, W. A., see Gait, J. K. ^ Bell Telephone Laboratories, Inc. I Recent Monographs of Bell System Technical Papers Not Published in This Journal Baldwin, M. W., Jr., and Xielsen, G., Jr. Subjective Sharpness of Simulated Color Television Pictures, Mono- graph 2617. Boyd, R. C, Eberhart, E. K., Hallenbeck, F. J., Perkins, E. H., Smith, D. H., and Howard, J. D., Jr. Type-Pl Carrier System - Objectives and Circuit and Equipment Description, INIonograph 2644. Crawford, A. B., and Hogg, D. C. Measurement of Atmospheric Attenuation at Millimeter Wave- lengths, ]\Ionograph 2646. Cutler, C. C. The Nature of Power Saturation in Traveling Wave Tubes, Mono- graph 2647. Eberhart, E. K., see Boyd, R. C. Felder, H. H., Pascarella, A. J., Shoffstall, H. F., and Little, E. N. IntertoU Trunks — Automatic Testing and Maintenance Techniques, [Monograph 2652. Forster, J. H., and Miller, L. E. Effect of Surface Treatments on Point-Contact Transistor Charac- teristics, Monograph 2650. GoHN, G. R. Fatigue and Its Relation to Mechanical — Metallurgical Properties of Metals, Monograph 2598 * Copies of these monographs may be obtained on request to the Publication Department, Bell Telephone Laboratories, Inc., 463 West Street, New York 14, N. Y. The numbers of the monographs should be given in all requests. 335 336 THE BELL SYSTEM TECHNICAL JOURXAL, JANUARY 1957 Hallenbeck, F. J., see Boyd, R. C. Hogg, D. C, see Crawford, A. B. Howard, J. D., Jr., see Boyd, R. C. Kelly, J. L., Jr. A New Interpretation of Information Rate, Monograph 2649. King, A. P., and Marcatili, E. A. Transmission Loss Due to Resonance of Converted Modes, Mono- graph 2656. LiNviLL, J. G., and Schimpf, L. G. The Design of Tetrode Transistor Amplifiers, ^Monograph 2657. Little, E. N., see Felder, H. H. Marcatili, E. A., see King, A. P. Miller, L. E., see Forster, J. H. Nielsen, G., Jr., see Bald\\-in, M. W., Jr. Pascarella, a. J., see Felder, H. H. Perkins, E. H., see Boyd, R. C. Schimpf, L. G., see Linvill, J. G. Seidel, H., see Weisbaum, S. Shoffstall, H. F., see Felder, H. H. Smith, D. H., see Boyd, R. C. Tien, P. K. A Large Signal Theory of Traveling -Wave AmpHfiers, Monograph 2610. Turner, D. R. Anode Behavior of Germanium in Aqueous Solutions, Monograph 2570. I i monooraphs 337 Van Haste, W. Statistical Techniques and Electron Tubes for Use in a Transmission System, ^lonograph 2041. Van Roosbroeck, W. Theory of the Photomagnetoelectric Effect in Semiconductors, Monograph 2607. Weisbaum, S., and Seidel, H. The Field Displacement Isolator, Monograph 2661 . Contributors to This Issue J. F. Bampton, B.Sc. in Engineering 1941; British Post Office Engineering Department 1936. ]\Ir. Bampton progressed by competitive examinations to a professional grade in 1942, and in 1944 he was loaned for two years to the government of India to assist with the rapid expan- sion of carrier telephone and telegraph systems. Since then he has been associated with most of the submerged repeater transmission systems around the British Isles, taking charge of a group in the Transmission and Main Lines Branch of the Engineering Department in 1950. From 1953 to 1956 he was concerned entirely with the transatlantic sub- marine telephone cable system. Associate Member of The Institution of Electrical Engineers. M. C. BiSKEBORN, B.S. in E.E., S. Dak. School of Mines, 1930; Bell Telephone Laboratories, 1930-42. Western Electric Company, 1942-44; Bell Telephone Laboratories, 1944-. His early work at the Laboratories was concerned with the development of multi-pair carrier and coaxial cables. During World War II, he assisted in the development of one of the first automatic radars, of microwave resonant cavities and of micro- wave coaxial for the Bureau of Ships. Later, Mr. Biskeborn worked on the development of apparatus for high-frequency electrical measure- ments on cable. He holds several patents and has written several tech- nical papers including an A.I.E.E. prize paper. At present, he heads a subdepartment on Cable Development. As a part of these responsibili- ties he was concerned with the design of the transatlantic telephone cable and was responsible for the specifications for it. He is an Associate Member of the A.I.E.E. F. J. Braga, B.E.E., Univ. of Minnesota, 1930; Illinois Bell Telephone Company, 1930-33; Bell Telephone Laboratories, 1934-. IVIr. Braga has engaged in development of transmission networks for carrier systems. During AVorld War II he worked on gun computers and networks and circuits for radar applications. He is currently engaged in the develop- ment of networks for undersea systems. He is a member of I.R.E. 338 CONTRIBUTOKS TO THIS ISSUE 339 R. A. Brockbaxk, B.Sc. in Engineering, London University 1922, Ph.D. London University 1934. Dr. Brockbank joined the Research Branch of the British Post Office in 1933 after 10 years in industry, in- cluding dielectric research on the original transatlantic cable proposed in 1928. He designed the repeater equipment for the first coaxial cable system in England, 1938. During the war, he was engaged in coaxial developments and on high power negative feedback wideband trans- mitters. Following the war, he was associated with television trans- mission over coaxial systems and with submerged repeater development. In 1949 he specialized in this latter work, and since 1953 has been in charge of research and development of submerged repeater sj^stems. J. W. Emlixg, B.S. in E.E., L'niv. of Pennsj'lvania, 1925; Develop- ment and Research Department of American Telephone and Telegraph Co., 1925-34; Bell Telephone Laboratories, 1934-. While at A. T. et T. Mr. Emling was particularly concerned with transmission stand- ards and with developing a sj'stem of effective transmission rating. He continued this work at Bell Laboratories. In World War II he was con- cerned with studies in the field of underwater acoustics. Subsequently he has been concerned with systems engineering studies in the fields of engineering economy, voice frequency transmission, rural carrier, radio and television. One of his recent responsibilities covered the early trans- mission and planning studies of the transatlantic telephone cable sys- tem. He is currently Director of Transmission Engineering with re- sponsibilit}' for the systems engineering aspects of exchange and long distance transmission, carrier transmission over wire, telephone stations and some forms of digital transmission. He is a member of the Acoustical Society of America, A.I.E.E., Eta Kappa Nu and Tau Beta Pi. H. B. Fischer, B.S. in E.E., Univ. of Wisconsin, 1924; AVestern Electric Company, 1924-25; Bell Telephone Laboratories, 1925-. Mr. Fischer first worked on broadcast receivers, but after the develop- ment of aircraft communication apparatus was started he engaged in the design of aviation receivers. This was followed by work on various types of aviation communication equipment, mobile radio equipment for Bell Sj'stem use and radio receiving equipment for aircraft instru- ment landing sj'stems. During the war he worked on various types of electronic equipment for the Armed Forces. Later he worked on over- seas radio telephone equipment, video transmission and testing ecjuip- ment, and submarine communications .'systems. ^lore recently he has worked on the transatlantic telephone cable project in connection with the manufacture of cable in England. 340 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 John M. Fraser, B.E.E., Polytechnic Institute of Brooklyn, 1945; Bell Telephone Laboratories, 1934-. Prior to World War II, Mr. Fraser was concerned with the evaluation of subjective factors affecting the transmission performance of telephone systems. This included the de- sign of equipment for simulating transmission systems in the laboratory. During the war he was chiefly concerned with the design and evaluation of communication sj^stems for the military. Later he was engaged in transmission work on long distance carrier systems. On the trans- atlantic telephone cable he was mainly concerned with the System Engineering aspects of the cable system. He is a member of Sigma Xi, Tau Beta Pi and Eta Kappa Nu. T. F. Gleichmann, B.E., Johns Hopkins Univ., 1929; Bell Telephone Laboratories, 1929-. Until 1942 Mr. Gleichmann was engaged in the design and development of open wire and cable carrier systems. During the period of World War II he worked on the design and development of radio telephone pulse communication systems for military and Bell System applications. He then engaged in development work in connec- tion with coaxial cable carrier systems. He was in charge of the group responsible for the circuit and mechanical design of the repeater unit for the transatlantic submarine telephone cable. He is a member of Tau Beta Pi. R. G. Griffith, graduate I.E.E., London 1924. Studied general engineering in Royal Naval Air Service and Communication Engineering in London. INIr. Griffith left England in 1924 to join Ail-American Cables Inc. (now American Radio and Cable Corporation) becoming Project Engineer in 1925, supervising ac telegraph transmission superimposed tests (then termed "wired wireless") on dc duplex telegraph cable be- tween Balboa Canal zone and Fishermans Point, Cuba. He developed and supervised the introduction of the synchronous fork cable signal regenerator, which established the through cable circuits between New York and Buenos Aires via the west coast cables of South America. In 1929 Mr. Griffith was appointed Assistant Chief Engineer of Creed and Company, and in 1932 w^as placed in charge of development. In 1935 he joined Cable and Wireless Limited. From 1943 to 1946 he was loaned to the foreign office communication center in charge of special machine cipher development. He became Chief Engineer of Cable and Wireless London Communications center in 1946, and in May 1954 joined the Canadian Overseas Telecommunication Corporation as Chief Engineer. Mr. Griffith holds some 60 patents relating to telecommunications. CONTRIBUTORS TO THIS ISSUE 341 R. J. Halsey, B.Sc. in Engineering, London University, City and Guilds College, 1926; Diploma of the Imperial College, 1926. Mr. Halsey entered the Engineering Research Branch of the British Post Office in 1927 where he was engaged on line transmission problems in- cluding, from 1938, the design of submerged repeaters and systems. In 1947 he became Head of the Line Transmission Division, and in 1952, Assistant Engineer-in-Chief concerned with all submarine cable matters; in this capacity, his primary concern has been the transatlantic sub- marine telephone cable. Associate of the City and Guilds of London Institute and Member of the Institution of Electrical Engineers. William W. Heffner, B.S. in Industrial Engineering, Pennsylvania State University 1929; Western Electric Company, Kearny, New Jersey, 1929-1932; Consulting work on industrial engineering in the Management Field 1932-1936; Western Electric Company 1936-. Mr. Heffner 's initial work at Western was concerned with jacks, keys, and mica capacitors. In 1942, he became a Department Chief in charge of manual telephone apparatus. In 1947 he was made an Assistant Superintendent in engineering for manual apparatus. His assignments continued through 1952 in engineering for several manufacturing engi- neering functions, including factory engineering, manufacture of manual apparatus and equipment, metal finishing, material handling, and packing. Between 1952 and 1954 he was Assistant Superintendent in charge of the Relay Assembly Shops at Kearny, New Jersey. In 1954 he was placed in charge of operating, production control, plant opera- tions, and maintenance at Hillside, New Jersey, where the flexible repeaters for the transatlantic submarine telephone cable were manu- factured. More recently, he was placed in charge of the Fairlawn, New Jersey, shop of Western Electric, where telephone apparatus and switch- ng equipment are being built. Mr. Heffner is a member of Sigma Tau. M. F. Holmes, B.Sc. in Physics 1937; British Post Office 1938-. Mr. Holmes transferred to the Engineering Department in 1942 and since 1944 has been concerned primarily with thermionics. He is now engaged in the study of factors leading to changes of tube characteristics. John S. Jack, Mountain States Telephone and Telegraph Company 1919-1930; American Telephone and Telegraph Company, Long Lines Department, 1930-. IMr. Jack was engaged in various Plant assignments in Colorado and Wyoming between 1919 and 1930. In 1930, he became Division Outside Plant Engineer for Long Lines in Denver; in 1938 he 342 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 transferred to Chicago as Division Plant Engineer, and three years later, moved to Omaha, Nebraska as District Plant Superintendent. He was transferred to the Personnel Department in New York in 1945 as General Supervisor of Wages and Working Practices. In 1949 he returned to the Plant Department as General Construction Supervisor, and in 1951 became Engineer of Outside Plant. In 1953 he was appointed Assistant General Manager — Special Projects; in this capacity he helped direct construction of the transatlantic submarine telephone cable. Mr. Jack is a licensed professional engineer in Nebraska. M. J. Kelly, B.S., Missouri School of Mines and Metallurgy, 1914; M.S., Univ. of Kentucky, 1915; Ph.D., Univ. of Chicago, 1918; honorary degrees — D.Eng., Univ. of Missouri, 1936; D.Sc. Univ. of Kentucky, 1946; LL.D., Univ. of Pennsylvania, 1954; D.Eng., New York Univ., 1955; D.Eng., Polytechnic Institute of Brooklyn, 1955. Western Electric Company, 1918-25. Bell Telephone Laboratories, 1925-. Dr. Kelly became Director of Vacuum Tube Development in 1928; Development Director of Transmission Instruments and Electronics, 1934; Director of Research, 1936; Executive Vice President, 1944; President, 1951. He was awarded the Presidential Certificate of Merit in recognition of his contributions in World War II and now serves on several advisory boards in the Department of Defense and the Department of Com- merce. Dr. Kelly is a Fellow of the American Physical Society, the Acoustical Society of America, I.R.E., and A.I.E.E. He is a Foreign Member of the Swedish Royal Academy of Sciences and a member of the National Academy of Sciences, the American Philosophical Society, Sigma Xi, Tau Beta Pi and Eta Kappa Nu. He is a Life Member of the M.I.T. Corporation and a Trustee of Stevens Institute of Tech- nology. His honors include the Air Force Association Trophy in 1953; the Industrial Research Institute Medal in 1954; and the Christophei Columbus International Communication Prize in 1955. R. Kelly, Associate of Royal College of Science, Ireland 1925; B.Sc. University College, Dublin 1937. After four years experience on power work for the Dublin United Tramways, he joined the power section of Standard Telephones and Cables in 1925. Following ten years of labo- ratory and field experience on carrier telephone and VF telegraph equipment, he took charge in 1936 of power development for trans- mission equipments. Harold A. Lamb joined the Western Electric Company Installation Department in 1920, where he became engaged in installation and I \ CONTRIBUTORS TO THIS ISSUE 343 installation engineering of telephone equipment. In 1923, he entered the Engineer of Manufacture Organization at Hawthorne, where he be- came concerned with relays, panel, step-by-step, and crossbar machine switching apparatus. During this time, he attended the Lewis Institute of Technology. In 1936 he was appointed a Department Chief on step- by-step apparatus. During World War II, Mr. Lamb transferred to the Passaic, New Jersey, Shops as Assistant Superintendent in the Western Electric Radio Division. Here he was engaged in engineering the manu- facture of submarine radar and radar bomb sights. Returning to the Western Electric, Kearny, New Jersey, Works in 1947, he was concerned principally with central office apparatus, including the card translator, and in 1953 was placed in charge of the Hillside, New Jersey, Engineer- ing and Inspection Organizations for building the flexible repeaters for the transatlantic submarine telephone cable. He is at present Resident Head of the Hillside Shops on flexible repeater manufacture. Andrew W. Lebert, B.S. in E.E., New York Univ., 1932; Cornell- DubiHer Corporation, 1932-1936; Bell Telephone Laboratories, 1936-. For the first five years at the Laboratories, Mr. Lebert worked on trans- mission engineering on open wire and cable carrier systems. He then was concerned with fault location problems. During World War II, he turned to mihtary communications on cable and open wire, and, following this period, he spent eight years on coaxial cable systems development. Since 1952 he has been connected with transatlantic telephone cable development. He is a member of I.R.E., Tau Beta Pi and Psi Upsilon. Capt. W. H. Leech entered the British Post Office in 1920 as Third Officer of H.M.T.S. Alert and was later promoted to the old H.M.T.S. Monarch of which ship he became Chief Officer. Both of these ships were subsequently lost by enemy action in World War II. After a year ashore as Assistant Submarine Superintendent in 1938-39 he took command of H.M.T.S. Aeriel and, in 1940, of H.M.T.S. Iris. In 1944 his ship was engaged in laying cables to the Normandy Beach head, an operation for which he was awarded the Distinguished Service Cross. In 1946 he be- came Submarine Superintendent, in immediate charge of the Post Office cable fleet and as such, directed the operations of H.INI.T.S. Monarch during the lajdng of the transatlantic cables. He is an Officer of the Order of the British Empire (O.B.E.). Herbert A. Lewis, E.E., Cornell Univ., 1926; Bell Telephone Labo- ratories, 1926-. Before World War II Mr. Lewis worked on the design 344 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 of equipment for manual and dial central offices, PBX's and broad-band carrier installations. During the war, he was concerned with the mechani- cal design of radar systems for the military. He was later responsible for transmission and equipment development for various carrier tele- phone systems. As project engineer for the Laboratories phases of the transatlantic telephone cable he was responsible for its transmission and equipment development. He is now Director of Outside Plant Develop- ment and is responsible for the devising and developing of new and improved methods, materials and equipment for that part of the tele- phone network which connects one central office with another and which ties the telephone customer's equipment into the central office. He is a senior member of I.R.E. Arthur H. Lince, B.S. in E.E., Univ. of Michigan, 1925; Bell Tele- phone Laboratories, 1925-. Until 1941 Mr. Lince worked on the engineer- ing and design of dial central office equipment. During World War K he was concerned with engineering and design of radar for the armed forces. He then became involved with the development of microwave antennas, towers, waveguides and related items for microwave radio relay systems and testing equipment. He was engaged in the building of repeaters for the Havana-Key West submarine cable. Beginning in 1953, he has been in charge of the group responsible for the design of water- tight enclosures for the repeaters used on the transatlantic telephone cable. G. H. LovELL, B.S. in E.E., Texas A & M College, 1927; M.S. in E.E., Polytechnic Institute of Brooklyn, 1943; N.Y. Edison Co., 1927- 28; Bell Telephone Laboratories, 1929-. From 1929 until 1948 Mr. Lovell was concerned with the development of crystal filters for carrier systems. He then worked on the development of networks for use in broad -band amplifiers. For the transatlantic telephone cable project he worked on the amplifier networks and the equalization of the undersea system. J. O. McNally, B.S. in E.E., Univ. of New Brunswick, Canada, 1924; Western Electric Company, 1924-25; Bell Telephone Laboratories, 1925-. Mr. McNally has speciahzed in research and development on electron tubes for Bell System communication and military uses. This included work on voice and carrier repeater tubes, electron tubes for the first commercial transatlantic radio system, and for the talking movie industry. During World War II, he had development responsibility for CONTRIBUTORS TO THIS ISSUE 345 many of the klystrons used in radar equipment. Later he again be- came concerned with the development of long-hfe tubes for submarine telephone cables. He has been awarded several patents on electron tube construction and operation. He is a FeUow of the I.R.E. and a member of the American Physical Society. George W. Meszaros, B.E.E. 1939, College of the City of New York; Bell Telephone Laboratories, 1926-. INIr. ]\leszaros started his Bell System career in the Systems Drafting Department. After spending a short time in several engineering groups of the System Department, he transferred to the Power Development Department in 1941. Here he has specialized in electronically controlled power equipment. Currently he is in charge of a group designing transistorized power supphes for the electronic switch- ing system and for several mihtary projects. G. H. Metson, B.Sc. in Engineermg, University of London 1931; M.Sc. in 1938 and Ph.D. in AppHed Science and Technology, Queens Universitj% Belfast 1941. Dr. Metson is in charge of the Thermionics Group at the Post Office Research Station and is particularly concerned with oxide coated cathodes and problems of tube life. He was responsible for the tubes used in the British submerged repeaters. Member of the Royal Institution and an Associate Member of The Institution of Electrical Engineers. Elliott T. Mottram, B.S. Columbia University 1927, M.E. 1928; Western Electric Company 1922-25; Bell Telephone Laboratories, 1928-. Mr. Mottram's first assignments were in the development of disc re- cording and reproducing machines and equipment. Later he was con- cerned with sound on film recording and reproducing equipment, and with tape recording. From 1939 to 1950, he was engaged in development of airborne radio and radar equipment, electronic computer and bomb sights, and airborne homing missiles. As Dh*ector of Transmission Systems Development since 1950, he has been concerned with the de- velopment of transmission systems and equipment for military purposes, transmission test equipment, and television and wire transmission systems. In this capacity, he was responsible for technical liaison with the British Post Office on submarine cable matters and was in charge of Laboratories' activities in this field. He is a member of the A.S.M.E. and I.R.E. Sir Gordon Radley, B.Sc. in Engineering, University of Lon- don 1919; Ph.D. L'niversity of London 1934. Sir Gordon's under- 346 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 graduate studies were interrupted by military service in World War 1. Engineering Research Branch of the British Post Office 1920, where he was engaged initially on materials problems and later on interference, corrosion, and long distance signaling. He became Head of Research in 1939, and in 1949 was made Deputy Engineer-in-Chief. In 1951 he became Engineer-in-Chief, and in this position, was one of the principal architects of the transatlantic submarine telephone cable system. In 1954 he was made Deputy Director General, and in 1955 Director General — the permanent Head of the British Post Office. He became a Conmiander of the Order of the British Emphe (CBE) in 1946 and was honored with a knighthood in 1954. In 1956, he became a Knight Com- mander of the Bath (KCB) and is President of The Institution of Electrical Engineers for the year 1956-57. H. H. Spencer, B.S. in :\I.E., Univ. of New Hampshire, 1923; Bell Telephone Laboratories, 1923-. He has been engaged primarily in the development of power supplies for broadband carrier, long distance and repeater equipment, including automatic plants for unattended opera- tion on J, K, and L carrier systems and TD-2 microwave radio relay systems. Mr. Spencer is an Associate ^Member of the American Institute of Electrical Engineers. J. F. P. Thomas, B.Sc. London University 1942; British Post Office Research Branch, 1937-. In his early years, J\Ir. Thomas was engaged on investigations into contact phenomena and dust core magnetic ma- terials. In 1948, he was transferred to the Submerged Repeater Group, where his main work has been the design and construction of power feeding equipment and pulse monitoring equipment used for fault loca- tion in submerged repeater sj'-stems. Associate Member of The Institu- tion of Electrical Engineers. Rexford S. Tucker, A.B., Harvard College, 1918; S.B., Harvard Engineering School, 1922; American Telephone and Telegraph Com- pany, 1923-34; Bell Telephone Laboratories, 1934-. Mr. Tucker's early work was on noise and crosstalk prevention. During World War II he was engaged in classified military projects and served as co-editor of a War Department technical manual. Electrical Communications Systeins Engineering. After the war he worked on mobile radio systems engineering and then the transatlantic telephone cable. He is an Associate Member of A.I.E.E., Senior Member of I.R.E., Charter Member of Acoustical Society of America, member of Sub-Committee No. 1 of CONTRIBUTORS TO THIS ISSUE 347 American Standards Association Sectional Committee C63, Harvard Engineering Society, and Phi Beta Kappa. Edmund A. Veazie, B.A. in Physics, Univ. of Oregon, 1927; Bell Telephone Laboratories, 1927-. His early assignments included the design of multi-grid tubes for use in aircraft radio receivers, police transmitters, and carrier telephone systems. During World War H he concentrated on tubes for radar and other military applications, in- cluding proximity fuses and gun directors. Since then he has been engaged principally in the design, fabrication control, testing, and selec- tion of tubes for use in submarine telephone cable systems. He holds several patents on electron tubes and associated circuits. He is a Senior Member of I.R.E. and a member of Phi Beta Kappa. D. C. Walker, B.Sc. in Engineering and Diploma of the Imperial College from the City and Guilds College, University of London, 1937; British Post Office Research Branch 1938. Mr. Walker's early work Avas on interference and protection problems and during the war on special investigations for the services. Later engaged on development and equip- ment for carrier telephone systems, and since 1946 has specialized on submerged repeater systems. He is in charge of the group concerned with the design of the internal electrical unit of the rigid transatlantic tele- phone cable repeaters and the special terminal equipment. Associate Member of The Institution of Electrical Engineers. V. G. Welsby, B.Sc. London University 1934; Ph.D. London Univer- sity 194G; Research Branch of the British Post Office, 1936. Dr. Welsby was at first a member of a group dealing with the design of multichannel carrier apparatus. Since 1947 he has been engaged in submerged repeater development, and during the last few years, has been in charge of the group concerned with the mechanical design of repeater housings and glands, and with the laying of rigid repeater systems. His Ph.D. degree was awarded for his work on dust-cored inductors. He is the author of a text book on inductor theory and design. Associate Member of The Institution of Electrical Engineers. M. C. WooLEY, B.S. in E.E., Ohio Northern Univ., 1929; Bell Tele- phone Laboratories, 1929-. Mr. Wooley was engaged in the development and design of inductors until 1935. Capacitor development then occupied his attention until 1949, concluding with the development and produc- 348 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 tioii of capacitors for the Key West-Havana submarine cable repeaters. He then became concerned with fundamental development, primarily on materials and processes used in capacitors, including those for the transatlantic submarine telephone cable. He is currently supervising a group engaged in development and design of capacitors and resistors for submarine cable repeater applications for other systems. He is a member of Xu Theta Kappa. HE BELL SYSTEM nicai lournal \^^y AM VOTED TO THE SCIENTIFIC ^W^ AND ENGINEERING PECTS OF ELECTRICAL COMMUNICATION LUME XXXVI MARCH 1957 ^«*i^'5> NUMBER 2 f { A New Carrier System for Rural Service APK «5 136/ B. C. BOYD, J. D. HOWARD, AND L. PEDERSEN 349 An Experimental Dual Polarization Antenna Feed for Three Radio Relay Bands R. w. dawson 391 The Character of Waveguide Modes in Gyromagnetic Media H. SEIDEL 409 Measurement of Dielectric and Magnetic Properties of Ferro- magnetic Materials at Microwave Frequencies WILHELM VON AULOCK AND JOHN H. ROWEN 427 Sensitivity Considerations in Microwave Paramagnetic Resonance Absorption Techniques g. feher 449 The Determination of Pressure Coefficients of Capacitance for Certain Geometries d. w. mccall 485 Reading Rates and the Information Rate of a Human Channel J. R. PIERCE AND J. E. KARLIN 497 Binary Block Coding s. p. lloyd 517 Selecting the Best One of Several Binomial Populations AflLTON SOBEL AND MARILYN J. HUYETT 537 Bell System Technical Papers Not Published in This Journal 577 Recent Bell System Monographs 583 Contributors to This Issue 588 COPYRIGHT 1957 AMERICAN TELEPHONE AND TELEGRAPH COMPANY THE BELL SYSTEM TECHNICAL JOURNAL ADVISORY BOARD A. B. GOETZE, President, Western Electric Company M. J. KELLY, President, BeU Telephone Laboratories B. J. McNEELT, Executive Vice President, American Telephone and Telegraph Company EDITORIAL COMMITTEE B. MCMILLAN, Chairman S. E. BRILLHAHT B. I. GBBBN A. J. BUSCH B. K. HONAMAN 1 L. B.COOE H. B. HUNTLEY A. C. DICKIE80N F. B. LACK B. L. DIETZOLD J. B. PIERCE K.E.GOULD Q. N. THAYER EDITORIAL STAFF J. D. TEBO, Editor B. L. SHEPHERD, Production Editor T. N. POPE, Circulaiion Manager THE BELL SYSTEM TECHNICAL JOURNAL is published six times a year by the American Telephone and Telegraph Company, 195 Broadway, New York 7, N. Y. F. R. Kappel, President; S. Whitney Landon, Secretary; John J. Scan- Ion, Treasurer. Subscriptions are accepted at $5.00 per year. Single copies $1.25 each. Foreign postage is 65 cents per year or 11 cents per copy- Printed in U. S. A. i THE BELL SYSTEM TECHNICAL JOURNAL VOLUME XXXVI MARCH 1957 number 2 Copyright 1957, American Telephone and Telegraph Company A New Carrier System for Rural Service By R. C BOYD, J. D. HOWARD, JR, and L. PEDERSEN (Manuscript received July 19, 1956) A study of the problem of providing telephone service to rural customers indicated the need for a flexible carrier system that could be used economically on new and existing rural cable and open wire lines. The desire for low cost required new approaches to almost every phase of the carrier system design for rural service, which has been designated Type PI . Use of transistors led to sweeping changes in the detailed circuitry and also created demand for other new components. Mounting and intercon- necting the circuit components by means of printed wiring boards empha- sized the necessity for close coordination between design and manufacturing objectives. The low power-drain requirements of t^'ansistor circuitry were supplied economically by the use of similar solid state devices, a new storage battery, and efficient packaging. A fast, accurate and simple method has been evolved for applying the PI carrier system to rural lines with a minimum of line treatment or rearrange- ment. Plug-in equipment, readily accessible test points, and a carrier test set provide the ease of maintenance needed in the use of telephone equipment at remote locations. Use of the PI carrier system will extend the application of electronic equipment outside of the telephone central office and provide a carrier system ivhose performance will be consistent with requirements for high quality communication service at low cost. 349 350 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 1. INTRODUCTION Although carrier has been used successfully to provide trunks in the Bell System for more than 35 years, it has not been economically feasible, up to the present time, to apply carrier telephone techniques extensively to the rural telephone plant. The technical and economic problems as- sociated with providing telephone service to customers in rural areas has long been one of the most difficult problems facing the telephone indus- try. The widely scattered locations of customers in rural areas have led to a large number of rural telephone routes with only a few customer lines per route. This has precluded the use of large cables on any one route, which would be economically attractive in urban areas. The ex- tensive use of carrier has not been feasible because the distances from the rural customers to the Central Ofhce are in the 5- to 20-mile range in which carrier has not been generally economical in the past. The two lines of attack which were taken on this problem were to reduce the cost of telephone plant through less expensive small cables and open-wire plant,^ and to provide an economically attractive carrier system designed to meet the particular needs of rural telephone service. This paper discusses the broad objectives for a rural customer carrier system, the major parameters of the Pi system which was developed to meet those objectives, and its circuit, equipment, and power arrange- ments. It also covers the engineering and maintenance methods to be used by the Bell System Operating Companies to install and operate the system. 2 2. BROAD OBJECTIVES FOR PI CARRIER SYSTEM The broad objectives for the Type PI carrier system resulted from the stringent economic limits imposed on the system to enable it to prove in over conventional rural plant of the latest and most economical de- sign, from the requirements of rural telephone transmission and signaling, and from Bell System experience gained with earlier carrier systems for customer and trunk use. The low cost objective for this system also im- plied the need to achieve an appropriate balance among an economic first cost of equipment, low in-place cost due to simplified engineering and installation practices, and accompanying low annual costs due in part to simplified system maintenance. To achieve an economic carrier system for rural telephone use, the dc power requirements of the terminals and repeaters had to be kept low. ' Lester Hochgraf and R. G. Watling, Telephone Lines for Rural Subscriber Service, A.I.E.E. Communication and Electronics, No. 18, p. 171, Ma}', 1955. 2 These aspects of the PI system are covered in more detail in four papers on "The PI Carrier System." A.I.E.E. Communication and Electronics, No. 24, pp. 188, 191, 195, 205, May, 1956. THE TYPE PI CARRIER SYSTEM 351 This was especially important since previous Bell System experience indicated that where commercial power is used to supply the system, some form of reserve must be provided, and where commercial power is not available, the use of primary batteries places a premium on mini- mizing the power i-equired. From these considerations two additional major objectives were de- rived : low manufacturing costs for the components and assembled equip- ment, and the use of transistors to minimize power supply drains. In addition, flexibility was needed in the proposed carrier system because of the difficulty of accurately forecasting the demand for rural service. These objectives have been met in the design of the Type Pi rural customer telephone system. It is a fully-transistorized system con- sisting of independent two-way carrier channels applicable in increments of one to four at a time in the frequency band above the regular voice frequency circuit. Each channel uses a terminal at the central office and at a remote point with intermediate repeaters as necessary. Between terminals, the system is equivalent to a rural voice frequency line with no changes required in the central office or rural customer equipment. Be- yond the outlying terminal, distribution is by voice frequency wire on a single or multiparty basis. The system can be applied to existing and new lines utilizing combinations of fine gauge exchange cable and copper or steel open- wire. Systems can be used on each of several pairs on a given pole line, the number depending on the line characteristics. 3. MAJOR PARAMETERS OF PI CARRIER SYSTEM This section summarizes the important features incorporated in the PI carrier system and the reasons governing their choice. The system has a number of features in common with Bell System toll carrier sys- tems, but it also differs in several important aspects because of specific rural requirements. One aspect is the signaling, which requires different arrangements at the two ends of the circuit because of the widely' differ- ent signals carried in the two directions. Another is that the remote ter- minals of the individual channels are usually distributed along the line rather than grouped at a common location. 3.1 Transmission Plan It is difficult to divorce the considerations leading to the choice of carrier frequency range from those affecting the choice of modulation in the carrier system. Studies of growth on rural lines indicated that a system giving three or four channels (customer circuits) on one pair of wires, in addition to the physical circuit, should be sufficient if systems could be applied to each of several pairs on a given open-wire line. 352 THE BELL SYSTEM TECHNICAL JOUKXAL, MARCH 1957 The blocking out of the frequency range was controlled by a number of factors. Cost considerations required that the carrier frequencies be kept above the voice frequency range. If carrier extended into the voice range, the voice frequency circuit would be lost on a carrier pair. One of the carrier channels applied to that pair would have to be used to re- place it. Thus, the addition of four carrier channels to a pair would yield a net gain of only three channels. This in turn would increase the net cost per gained channel. Filter costs determined how close to the voice frequency band the carrier frequency range could be placed and in con- junction with the number of channels required how closely the channels could be placed to each other. Crosstalk considerations restricted the carrier frequency range to below about 100 kc in order to reduce the cost of line treatment and rearrange- ment of pairs on existing rural lines. By using this frequency range it appeared possible to apply more than one carrier system to crossarms on an open-wire route. The rapid rise in attenuation with frequency of steel wire used on rural lines dictated that the range of frequencies be kept low. As a result of these two sets of considerations, development work on the PI carrier system was concentrated in the 8- to 100-kc range. Amplitude modulation of the carrier frequencies was chosen over other forms of modulation because of the simpler terminal circuitry and equipment and because of the saving in bandwidth. Use of ampli- tude modulation and the use of compandors, discussed in a later section, were felt to compensate for possible transmission advantages that could STACKABLE NORMAL GROUPED STAGGERED GROUPED 1 1 1 2 1 t 2 1 3 ,CH ANNEL NUMBERS-^ ♦ 1 1 1 1 r^^ 3 4 4 T r t t ) t 3N t 2N 3N 4N T' T T 1N 2N 4N 1 IN j 1 2S t 1 IS 3S CUT IS 1 1 2S 3S J I L APART FREQUENCY I _l I l_ J I L P=PILOT FREQUENCY FOR REPEATER REGULATION J I 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 FREQUENCY IN KILOCYCLES PER SECOND ARROWS SHOW USUAL DIRECTION OF TRANSMISSION f TOWARD CENTRAL OFFICE I FROM CENTRAL OFFICE Pig. 1 — Type PI Carrier Frequeucy Plan. THE TYPE PI CARRIER SYSTEM 353 be obtained by using angular modulation (frequency or phase) with a large modulation coefficient. Cost was again a major factor in the choice between double sideband and single sideband amplitude modulation. Past experience with other carrier systems has indicated that filters are a major part of the cost of a system and, when frequency space is available, double sideband filters are, in general, less expensive than those for single sideband. In addition, the cost of a single sideband system would be increased because of the problem of obtaining the necessary carrier supply at the terminal. The frequency plan developed for the PI carrier system is shown in Fig. 1. The unusually wide carrier spacing of 12 kc was adopted in order to minimize filter costs. Since the remote terminals are generally distribu- ted along the line, it was not practical to use double modulation to ac- complish filtering in the most efficient frequency range. Instead, filtering was done at line frequencies. Every effort was made to achieve channel filter designs with maximum efficiency of element utilization. Advantage was taken of the more leisurely rising characteristics of the double side- band filters permitted by the wide frequency spacing. The stackable frequency arrangement Avas provided for non-repeatered operation, because when the lowest two carrier frequencies are used to provide a channel, it can be used over substantially longer distances than channels using higher frequencies. The grouped arrangements were pro- vided for repeatered systems to reduce the cost and number of the re- peater filters and amplifers needed to separate the two directions of transmission. The staggered grouped arrangement can be used with the normal grouped arrangement on a pole line having poor crosstalk coup- ling in order to increase the effective coupling loss between carrier channels on different pairs. The grouped and stackable arrangements cannot be used on the same pole line, because certain frequencies would be used for both directions of transmission. This would produce large differences between transmitted and received carrier power at terminals and repeaters which would lead to intolerable crosstalk. A number of terminal arrangements were studied in order to implement the above frequency plan. The arrangement for a remote terminal shown in Fig. 2 was chosen as the simplest terminal meeting all of the system requirements. It is very similar to the channel terminal arrangement used in the Type Nl carrier system, another double sideband amplitude modulation sj^stem used for long distance trunks of the Bell System. The several shaded portions in the figure show the breakdown of the terminal functions into individual sub-units, which are the basis for the equipment arrangements discussed in Section 5 of this paper. A number of the other important features that make up the terminal arrangement are discussed in the following sections. a 3d o c c O IJ LU < -I ^ OqLUz^ > UJ 2 (J) U 354 THE TYPE PI CARRIER SYSTEM 355 3.2 Use of Transistors Transistors were chosen for use in the PI system because they are low voltage, low power devices as compared to electron tubes suitable for transmission circuitry. Also, transistors are expected to be lower in cost and inherently longer life devices than electron tubes, thus contributing to reduced initial and operating costs. The dc power requirements for the PI system, using transistors, may be compared to those for a channel terminal in the Type Nl system as an indication of the dc power saving that has been achieved with the Pi system. A transistorized PI terminal requires about 1.2 watts while it is in operation compared to 40 watts required for an Nl terminal, INPUT OUTPUT ' ■ BATTERY Fig. -3. — PI transistor transmitting amplifier circuit. which represents a substantial power reduction achieved by the use of transistors. Because part of the PI terminal is turned off during idle periods, the average power required over a day is about 0.9 watt. During the development of the PI terminals it was found that a single design of a transistor amplifier could be used in se^'eral different places. These included the compressor and expandor amplifiers, the transmitting amplifier and the input portion of the receiving amplifier. The circuit for that amplifier is shown in Fig. 3. The amplifier uses Western Electric NPN grown junction type tran- sistors coded 4B for the voice frequency amplifiers and 4C transistors for the carrier amplifiers. The first transistor is connected as a common col- lector and the second as a common emitter. By using them in this man- ner it is possible to employ the same type of transistor in both stages. Feedback is obtained by using hybrid coils at both the input and output 356 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 19o7 of the circuit in much the same manner as for electron tube circuits. One significant difference is that in this transistor circuit only the second transistor introduces a 180-degree phase shift. This permits both input and output coils to return to a common ground as in a three-tube electron- tube circuit and thereby avoids the circuit complications of a two-tube circuit where one of the coils must float off ground. A simple resistance interstage is used and battery filtering completes the circuit. 3.3 Low Voltage Protection Use of transistors gave rise to the need for supplementary protection from voltage surges on the line below those for which conventional carbon blocks afford protection. This additional protection was obtained by using the reverse voltage breakdown characteristics of newly developed silicon-aluminum junction diodes as shown in Fig. 4. Protection is pro- vided in the 50- to 1,000-volt range by the diodes and above a nominal value of 750 volts by the carbon blocks. During the normally short period of operation the small diodes carry a current of up to 10 amperes. 3.4 System Levels and Carrier Line Loss The carrier frequency output power of the transistorized transmitting amplifier in the terminals was set at -|-6 dbm. This level was limited primarily by the power handling capabilities of the transistors used. Be- cause of the loss of the secondary protection circuitry, band filters, and the line transformer, this became +4 dbm at the carrier line terminals. This is equal to the highest carrier power transmitted by the Type Nl carrier system. With 50 per cent modulation of the carrier, the effective sideband level at the transmitting line terminals is only 2 db below that transmitted by the Type 0 carrier system, the most recent carrier system used for open-wire long distance trunks of the Bell System. TO CARRIER EQUIPMENT CURRENT-LIMITING RESISTOR V\A — SECONDARY PROTECTION DIODES \ TO CARRIER LINE CARRIER LINE TRANSFORMER Fig. 4 — Secondary protection circuit in carrier portion of PI carrier terminal. THE TYPE PI CARRIER SYSTEM 357 The +4 dbm output level coupled with noise and crosstalk considera- tions indicated that 30-db bare carrier line loss between terminals would be possible. A survey of existing and planned Bell System rural telephone lines indicated that substantial amounts of entrance cable and open wire would be encountered in potential carrier layouts. Calculations of carrier frequency loss of those facilities showed that 30-db loss would not be sufficient to care for all of the necessar}^ rural applications, which con- firmed the need for carrier repeaters. 3.5 Compandors Compandors were incorporated in the PI system because their several advantages more than offset their added cost. The crosstalk and noise advantage provided by their use reduced the need for expensive line treatment to reduce crosstalk. In addition, the compandor noise advan- tage permitted lower received carrier levels to be used, thus increasing the permissible carrier line loss. Compandors also eased the requirements on terminal and repeater filters, thus reducing filter cost. The compandor in the PI sj^stem is a simplified version of the syllabic compandor used in Type Nl and 0 carrier systems, but its performance is comparable to those units. The new problem of matching the com- pressor and expander characteristics in PI terminals operating in differ- ent ambient temperatures has been simplified by the use of silicon-alumi- num junction diodes in the compandor variolossers and control circuits. 3.6 Channel Regulation Channel regulation was necessary to provide satisfactory transmission performance and keep maintenance adjustments to a minimum. The regulation was designed to compensate for daily and seasonal carrier circuit net loss variations caused by changes in line attenuation with temperature. It would be desirable to have the terminal regulation range equal to 30 db, the maximum line loss that can be spanned between the terminals, to ease engineering layout considerations. However, cost con- siderations led to a 15-db range, with span pads used where required by system layout to adjust the received carrier power to the center of the range of the regulator. The regulation in the receiving amplifier is of the backward-acting type. A reference control signal, derived from the receiving amplifier output, is used to vary the loss of the balanced diode variolosser at the amplifier input. The regulator "stiffness" of 1.6-db change in channel voice frequency output for 15-db variation in carrier input is obtained 358 THE TYPE PI CARRIER SYSTEM 359 by the combination of the rectified control signal voltage exceeding the reference voltage of a silicon-aluminum junction diode and by the ex- pansion characteristic of the variolosser. The variolosser uses a specially coded set of the silicon diodes which are matched for both ac and dc characteristics. Modulation products introduced by the variolosser have been kept below those produced in the associated receiving demodulator. 3.7 Signaling The need to transmit customer signaling information over a carrier channel required the development of means of passing dialing and super- vision signals toward the central office. It also required passing ringing information to the remote terminal for the types of multiparty ringing generally used in the Bell System, including four-party selective service, eight-party semi-selective service and divided code ringing. These requirements were met in such a way that the carrier system can be inserted into a normal voice frequency circuit and function with- out requiring any change in the existing signaling equipment in the central office or in the customer's telephone. The central office ter- minal is activated by 20-cycle ringing signals which are reproduced at the remote terminal. The remote terminal is activated by switchhook signals and dial pulses which are reproduced at the central office termi- nals. Thus, the two directions of signaling require completely different circuits. A block schematic of the arrangement used is shown in Fig. 5. 3.7.1 Ringing The customer signaling originating in Bell System central offices con- sists of 20 cycles superimposed on plus or minus battery and applied between either tip or ring and ground. These signals control the trans- mission over the PI carrier system of three in-band frequency tones, the proper combination of two of them serving to select the party to be rung from the far end. The third tone (2,500 cycles), modulated at a 20-cycle rate, carries the information as to whether 20-cycle ringing is present or absent. In-band frequencies were chosen to encode ringing information for transmission over the carrier channel because of the substantially lower cost of in-band filters as compared to those required for out-of-band transmission. The three signaling tones are generated by three transistor tone oscil- lators incorporated in a PI central office terminal. One set of three oscil- lators can be arranged to supply four central office channel terminals. The transmission of the tones is controlled by three diode-operated 3G0 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 2^ UJ 13 (/) Z < ^ o _1 < /: 1 10 20 30 40 50 60 70 FREQUENCY IN KILOCYCLES PER SECOND 80 90 100 Fig. 8 — PI repeater gain-frequency characteristic. proper value for the nonregulated repeater and to adjust the power of the received carriers to the center of the regulator range for a regulated repeater. The output span pads are used where it is necessary to adjust the repeater output power in order to equalize levels between a PI sys- tem and other PI systems or other types of carrier systems operating on the same open wire line. These pads provide attenuation in 2 db steps up to 30 db. The repeater amplifiers were designed to have a wide enough frequency band to cover both high and low groups of frequencies, so that each re- peater contains two identical amplifiers. Each amplifier has three transis- tors with each stage connected as a common emitter. Western Electric Company PNP 7B and 6B transistors are used in the first and last stages, respectively, and a NPN type 4C transistor is used in the second stage. Local feedback is required around each transistor to reduce the gain spread and phase variations among units. Overall feedback is obtained around the three transistors with hybrid coils at input and output. The repeater equalizer characteristic represents a compromise for several types of transmission facilities generally encountered in the rural plant. The equalizer design also covers both the high and low freciuency groups so that identical equalizers are used for both the high group and low group sides of the repeater. A preUminary characteristic for the overall repeater gain is shown in Fig. 8 plotted against the design objective. There is a significant depar- ture in shape only at the cut-apart frequencies. This will be corrected sufficiently to permit as many as four repeaters to be used in tandem. As the design objective is a compromise of the loss of several types of lines that may be encountered in the use of this system, the departures 364 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 _i LU CD O LU Q 2 < 90 80 70 60 50 40 30 20 10 r^ r- ■S3s. NO FEEDBACK A r^' ^. i « -^/w \ \ I ™ 1 FEEDBACK 1 "^ K \ \ X % 1 2 4 6 8 10 20 40 60 100 200 400 600 1000 FREQUENCY IN KILOCYCLES PER SECOND Fig. 9 — PI Repeater amplifier gain-frequencj' characteristic. in system performance may vary considerably from that shown. The repeater ampUfier gain frequency characteristic, plotted in Fig. 9, shows a non-regenerative peak gain of the three-stage transistor amplifier of 80 db and a feedback gain characteristic of 50 db. This provides 20 db or more of feedback over the transmitted band to produce the necessary operating stability with temperature and power supply variations, and a working value of modulation svippression. 3.9 Repeater Regulation Repeater regulation will be furnished as an option where variations in line loss exceed the terminal regulating range. It will usually be neces- sary on sj-^stems employing more than one repeater in order to control noise performance. Repeater regulation in the direction of transmission from central office to remote terminal is controlled by the total carrier power of the channels working on one system. In the opposite direction, the repeaters will regulate on a low level carrier frequenc}'' pilot because the channel carriers are not always present in that direction of transmis- sion due to their signaling function. The pilot frecpencies are showTi in Fig. 1. The repeater regulator, shown in schematic form in Fig. 10, functions in much the same manner as the terminal regulator. The principal dif- ferences between the two regulators arise from the requirement that interchannel modulation must be appreciably less than 1 per cent in the repeater. To limit the contribution of the repeater regulator to a small value, the variolosser operates into a lower impedance and at a higher control current than used in the channel regulator. THE TYPE PI CARRIER SYSTEM 365 The input section to the control amphfier is either a flat bridging pad for the case where all carriers are always present on the line or a pilot pick-off filter and its associated single transistor amplifier where carriers are turned on and off for supervision. The latter extra amplifier is neces- sary because the pilot power is 20 db below the power in each normal carrier. The regulator stiffness provided by the repeater regulator results in a variation of 1 db in output carrier power for a 10-db variation in re- ceived total carrier or pilot power. 4. COMPONENTS Development of the passive components of the PI carrier system, including the various filters and other networks, were influenced by three major considerations. The manufacturing cost had to be as low as possible consistent with the traditional standards of Bell System service life. The components had to lend themselves to maximum utilization of the printed wiring techniques to be used as the basic equipment method. And lastly, advantage wherever possible was to be taken of the fact that transistors are low" power devices. 4.1 Filters Component-wise, filters are the most important single assembly de- termining the first cost of a carrier system employing frequency division multiplexing and frequency separation for obtaining equivalent four-wire FROM TRANSMITTER VARIOLOSSER REPEATER AMPLIFIER TO TRANSMITTER REFERENCE BIAS AND DC DIFFERENTIAL AMPLIFIER LEVEL ■ADJUSTMENT CONTROL AMPLIFIER RECTIFIER PILOT PICK-OFF FILTER AND TRANSISTOR AMPLIFIER OR PAD Fig. 10 — PI Repeater regulator block schematic. 366 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 Fig. 11 — Miniaturized inductor for PI carrier. operation on the line. Past experience has shown that one-quarter or more of the first cost is often chargeable to the various filter. The decision to employ double sideband modulation was largely based on the knowl- edge that when frequency space is available the double sideband channel filters are generallj' the least expensive. With this decision made, every effort was directed toward the achieve- ment of channel filter designs of maximum efficiency in element utiliza- tion. Inexpensive wide-limit capacitors were used, and the desired per- formance achieved through the use of an adjustable ferrite inductor expressly developed for the PI system. The filters are rapidly adjusted in the manufacturing process using visual display testing circuits. 4.2 Inductors The inductor which makes this possible is shown in Fig. 11. It is de- signed for printed wiring use and provides a wide range of inductance while maintaining excellent "Q" performance in the carrier and voice range. This is accomphshed in a single basic design by so selecting the winding for particular nominal inductances that the air-gap adjustment remains at or near its most efficient setting. Inductors of this tj^pe were THE TYPE PI CARRIER SYSTEM 367 used not only in all the channel, demodulator, and signaling filters in the terminal and in the directional filters at the repeater, but also in the channel oscillators and other parts of the circuitry where an inexpensive, adjustable element offered manufacturing or service advantages. 4.3 Capacitors Most of the wide-limit capacitors used in the filters are of the com- mercially available molded mica type. Where the capacitance values would require large and expensive mica units both in filters and other parts of the circuit, newly available foil-Mylar capacitors were used. These take the form of very small pigtail units in a range of physical sizes similar to those of the solid tantalum capacitors described below. The Mylar capacitors have low working voltages in these miniature sizes and can Fig. 12 — Prototype solid tantalum capacitors for PI carrier. 368 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 be employed because of the low voltage protection provided for the tran- sistorized circuits. Both cost and space savings an; realized in these ca- pacitors since no cans or potting are rerjuired due to the stability of the Mylar dielectric under moisture exposure. Another new type of capacitor has foinid widesprc^ad use in the PI system. This is a solid tantalum electrolytic capacitor used in place of the usual paste or liquid electrolytic capacitor. The solid electrolyte is manganese dioxide deposited upon the capacitor surfaces. The anode is made from tantalum metal and upon its surfaces is deposited the tanta- lum oxide which forms the dielectric. The cathode is an enveloping metal completing the capacitor structure. This new design of capacitor is now available in values up to 100 microfarads in a very small volume. It is expected to be less expensive than other electrolytic capacitors while at the same time providing a rugged structure which is relatively inert elec- trochemically and which has better stability in operation and storage. Fig. 12 shows prototype models of typical solid tantalum units. 4.4 Transformers Transformer needs in the PI system are met by two miniature struc- tures wliich were made possible by the use of low power transistor cir- cuits. The carrier frequency units employ a manganese zinc ferrite core, a spool winding and wire terminals which permit assembly on printed Fig. 13 — Carrier and voice frequency transformers for PI carrier. THE TYPE PI CARRIER SYSTEM 369 S Fig. 14 — Example of PI carrier line network. wiring boards. They are potted with an asphalt compound in a cyhndri- cal ahiminum can. The voice frequency transformers are wound on lam- inated core structures of permalloy. The units are potted in an epoxy resin in rectangular aluminum cans. The terminal plate carrying the wire terminals for mounting is a cast unit of a styrene polyester. Both types of transformer are shown in Fig. 13. 4.5 Ldne Networks and Filters Also deserving mention is a new series of line networks and filters (which do not form part of either the terminal or repeater equip- ment) with specific functions described in Section 7. All of the networks have been designed with the same tj^pe mounting arrangement sho'RTi in Fig. 14 with two sizes used depending on the number of components housed. The networks are cast in a styrene poh^ester. High voltage pro- tection is self-contained and sturdy terminals are provided for bridle wire connection. By means of side slots in the casting the network is mounted on a wedge-shaped holder which is fastened to the crossarm or pole. A flexible rubber cover is snapped over the face of the network to protect against weather effects. 5. EQUIPMENT ARRANGEMENTS The emphasis placed on economy in this development project made it necessary to consider a number of different approaches before deciding on the physical arrangement pro^'ided for both central office and pole mounted equipment. At both locations the terminals for each channel 370 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 Fig. 15 — Front and back of typical printed wiring board. were treated on an independent basis, thus providing maximum flexibil- ity in application. While the use of transistors made it possible to take advantage of miniaturized components, the major emphasis in design has not been on miniaturization; instead it has been to achieve low manu- facturing costs, simplicity of engineering and installation, and a mini- mum of maintenance effort. The recent trend toward automation in THE TYPE PI CARRIER SYSTEM 371 manufacture of electronic equipment has also influenced the design to a great extent. 5.1 Printed Wiring Boards To best meet these objectives, use has been made of plug-in units which have proved successful in other carrier systems, such as the Nl and 0. The assembly technique used here, however, is an entirely new approach for carrier equipment in that the plug-in unit consists of a printed wiring board on which all components are mounted. Printed wiring, which is a comparatively new engineering technique, was selected because of its applicability to automatic assembly, including mass soldering of con- nections. In addition, the use of printed wiring greatly simplifies testing and inspection and assures a more uniform product. The two sides of a typical printed wiring board are shown in Fig. 15. 5.2 Interconnection of Boards The interconnection of the various plug-in units or printed wiring boards, required to make up a complete PI terminal or repeater, is ac- complished by means of a wire connector specifically developed for this project. Basically, the connector consists of a number of accu- rately spaced bare wires running parallel to each other and imbedded in cross member strips of insulating plastic material. At fixed intervals the wires are exposed, and this is where contact is made to terminal con- nectors mounted on the printed wiring boards. These terminal connec- tors, shown in Fig. 16, are made of spring tempered phosphor bronze Fig. 16. — Closeup of terminal connectors. 372 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 and consist of bifurcated cantilever springs, providing a total of four contacts for each connection. As can be seen in Fig. 17, the wire connector is actually a molded phe- nolic box into which are inserted all of the printed wiring boards that make up a complete terminal or repeater. The terminal connectors on the boards thus engage the wires that are imbedded in the back of the connector. To insure contact reliability, a finish of precious metal is pro- vided on both the wires of the connector and the terminal connectors on the board. Additional flexibility in the interconnection of the boards is Fig. 17 — Prototype model of connector box unequipped showing grid wires. Fig. 18 — Typical terminal netw( mounted in a prototype connector b( THE TYPE PI CARRIER SYSTEM 373 obtained by cutting the wires at various points by simply drilling holes in the phenol structure supporting the wire. 5.3 Terminal and Repeater Mounting A complete terminal ready for installation at a remote location is shown in Fig. 18. The top position in the connector is shown vacant. This is where the connections to line and power supply are made by means of another plug-in printed wiring board with attached flexible wiring for the external connections. Fig. 19 — PI carrier remote terminal in pole mounted cabinet. 374 THE BELL SYSTEM TECHNTCAL JOURNAL, MARCH 1057 The equipment described here is equally adaptable to central office mounting and pole mounting at remote locations. At the remote loca- tions, however, it is necessary to provide the equipment with an outer housing which gives protection from all kinds of weather and even from moisture condensation. The opened housing is shown in Fig. 19. Fig. 20 shows a typical remote mounting of the housing on the left. In previous electron tube carrier systems the amount of heat generated by the equip- ment itself was sufficient to pre\'ent moisture condensation. In the case Fig. 20 — Example of remote mounting of PI terminal and ac power supply. THE TYPE PI CARRIER SYSTEM 375 of the PI carrier, however, the heat dissipation during the idle period is less than 1 watt for the entire terminal. To prevent condensation, the housing or apparatus case is sealed by means of a neoprene gasket. To further reduce the moisture content of the trapped air, the use of a desic- cant is specified. The apparatus case is made of die-cast aluminum with the outside walls finished in white enamel to keep heat absorption to a minimum. The system was designed to operate between temperature extremes of — 40°F and +140°F. This limitation might necessitate the additional installation of sun shields in a few cases where extreme temper- atures prevail. The terminal equipment at the central office makes use of the same type of printed wiring boards plugged into a connector as used at the remote location. In the central office, however, the outer housing is dis- pensed with and the connector is mounted on mounting brackets on standard relay racks. The relay rack layouts can be arranged in a number of ways to suit the particular installation, since no shop wired bays are used. A tj^pical 11'6" relay rack layout will provide for 10 ter- minals. No line jacks or alarm features are provided and fusing may be obtained from existing fuse boards in the office. The equipment also lends itself to wall mounting in locations where relay rack space is not available. 5.4 Testing and Maintenance Features One great advantage of the equipment design used in the PI carrier system is the ease with which an entire terminal or repeater can be trans- ported to, and installed at, a remote location. In case of trouble, the entire equipment unit, be it a terminal or a repeater, can be readily re- placed. It is not expected that the maintenance man will attempt to replace an individual printed board at a remote location; however, this procedure is perfectly feasible in a central office. To facilitate the loca- tion of trouble in a unit, the various boards are provided with test points located at the outer end of the boards so as to be easily accessible to the maintenance man. Certain precautions will have to be taken at central repair centers in replacing defective individual components in order not to damage the printed wiring. Too much heat applied by a large soldering iron will de- stroy the adhesive bond between the copper conductor and the phenolic board, but repair can be made under certain controlled conditions. A limited amount of wiring modifications can also be made to the printed wiring by inserting strap wires in place of components. 376 THE BELL SYSTEM TECHNICAL JOURNAL, ^L\KCH l!)o7 6. POWER SUPPLIES The design of a carrier system with low power drain made possible the development of a low-cost, reliable dc power supply for the carrier equip- ment. Because the central office carrier terminal was designed to utilize standard central office voltages (24 or 48 volts), onl}' the power supply for the remote equipment will be described here. Early exploratory studies showed that conventional power supply- designs would miss the first and annual cost objective by an uncomforta- ble margin. A number of unconventional approaches were studied: (a) Storage batteries charged over the carrier line. (b) Storage batteries placed in service with full charge and removed to a central point for recharging. (c) Solar power plants. (d) Wind power plants. (e) Thermoelectric power plants. (f) Dry cells. In all of the above cases the power plant was either too costty, too large, or technicalh- unfeasible, and none could prove in ovev the con- ventional conversion of ac to dc where commercial power is available. This was true despite need for a storage batterj- to operate the s^-stem during ac power failure intervals and to provide peak ringing power. 6.1 AC Rectifiier-Storage Battery Plant The basic elements of the power plant circuit, as shown in Fig. 21, are the con\-ersion section represented by the step-down transformer Tl and VOLTAGE CONTROL f ft ■ -- AC STEPDOWN TRANSFORMER TRl ■■^:'^^ 16V -22V 10 CELL STORAGE BATTERY Fig. 21 — Schematic of ac rectifier-battery power supply THE TYPE PI CARRIER SYSTEM 377 the semiconductor rectifier bridge CRl, the voltage control circuit rep- resented by that part of Fig. 21 enclosed in dashed lines, and the energy- storage circuit represented by the battery. Rectification is obtained with germanium rectifiers that are very effi- cient, have long life with negligible aging, and are very compact phys- ically. The output of this rectifier is not constant, because the output voltage will vary with the ac input voltage and the dc load current drawn by the carrier terminal. Thus a i-egulating circuit must be provided. The regulating network senses the voltage across the battery and compares this voltage to a reference obtained from a silicon junction diode biased in the reverse dirction.^ Any error in the output voltage is converted to a current signal in the first amplifier stage and amplified by the second stage transistor Q2. The amplified error current is then used to control the impedance of transistor Ql which acts as a current shunt around the battery. The fundamentals of the operation of this regulating system are shown in Fig. 22. If the load voltage is too high, the network adjusts the re- sistance of transistor Ql so that some of the rectifier output current is shunted around the load. The load voltage will then return very quickly to the regulated value. Because the rectifier circuit must not be over- loaded by a discharged battery, some form of current limiting must be provided; this is automatically taken care of by resistor Rl. The rectifier is capable of supplying indefinitely the current that would be drawn to charge a battery after a very long power failure. The storage battery is shown in Fig. 23 near the bottom of the power plant housing. It is a new design with a hfgh specific gravity sulphuric ^ D. H. Smith, Silicon Allo}^ Junction Diode as a Reference Standard, A.I.E.E., Communication and Electronics, No. 16, pp. 645-651, Jan. 1955. Eo UjEr£^ < o > \ N X \ N N \ N 22 VOLTS ""X^ 1 XS 175 MA CURRENT • Ll. (b) Fig. 22 — Simplified schematic and regulation characteristic of ac power supply 378 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 '^p^ Fig. 23 — PI carrier ac power plant in cabinet for pole mounting. acid electrolyte for good low temperature operation and lead calcium alloy electrodes for long life. The battery has 10 cells housed in two jars of five cells each. It is operated at about 23.5 volts and weighs about ten pounds. It provides about six days' reserve for a remote terminal or about two days for a remote repeater. The battery should not freeze at temperatures as low as 40°F, but the storage capacity may be reduced 90 per cent at this extreme. The battery is mounted on steps so that the electrolyte level can be seen through the transparent plastic batterj^ jars. Fig. 23 also shows the compact packaging of the entire power supply within the same type of aluminum housing as used for the carrier termi- nal. A tj^pical pole mounted installation is shown in Fig. 20. Fig. 24 is a THE TYPE PI CARRIER SYSTEM 379 close-up of the bottom of the rectifier chassis which shows the regulating network mounted on a printed wiring board. 6.2 Air Cell Primary Battery Plant Because ac will not be readily available at all remote locations, an alternate power supply has been de^•eloped and this is shown in Fig. 25. PI aoj volts Fig. 2-i — Close-up of Ijottom of rectifier chassis. 380 THE BELL SYSTEM TECHXICAL JOURNAL, MARCH 1957 The alternative supply uses oxj-gen-depolarized primary cells having an alkaline electroMe, and has been used for many \'ears in railway signaling circuits and in the telephone plant. Sixteen batter}- cells are connected in series to provide enough power for three years of operation of a remote terminal or about one year for a remote repeater. The battery is discarded when fulh- discharged and is then replaced by a new battery. 7. APPLICATIOX OF PI CARRIER TO RURAL TELEPHONE LINES The Pi carrier system is to be applied to normal exchange loop plant facilities engineered in accordance with the present Resistance Design Fig. 25 — Primary battery power plant. THE TYPE PI CARRIER SYSTEM 381 Methods used generallj^ throughout the Bell System.* These facilities consist of mixed gauges of high capacitance cable extended at their outer ends by 109-mil steel, 104 mil-copper or copper steel open wire. In engineering the carrier line design or carrier layout, the Plant Engi- neer will determine the carrier line laj^out necessary to meet the over-all requirements for a suitable carrier transmission path on the available physical facilities. To do so he need only be familiar with the general capabilities of the carrier system, its basic "building blocks," and the limitations that must be considered in applying the system to the physi- cal line. The capabilities of the carrier system have been described in earlier sections. From those descriptions it can be seen that the basic "building blocks" for a PI carrier system are: 1. Central office channel terminals 2. Remote channel terminals 3. Repeaters 4. Ac or dc remote terminal and repeater power supplies 5. Carrier line networks and filters A carrier application of these "building blocks" is shown in schematic form in Fig. 26. The low-pass filters or carrier blocking networks shown are placed at the junctions of the carrier line and side leads of customer drops served by ph}' sical or derived voice frequency circuits on the base carrier facil- ity. These filters are required to reduce the bridging loss of the side leads at carrier frequencies and to keep carrier frequencies out of the customer drops to prevent annoyance to the customers. High-pass filters are pro- vided to make the carrier line continuous at carrier frequencies, but divide it into isolated sections for voice frequency distribution. In addition to these blocks, an autotransformer may be required at the junction of the open wire and cable. The autotransformer, either alone or in conjunction with a junction line filter, is required to eliminate reflection losses and reduce crosstalk at carrier frequencies due to im- pedance mismatch between the cable and open wire. The junction line filter is required to allow the carrier and physical voice frequency circuit to be used on different pairs in the cable and on the same open-wire pair beyond the cable-open-wire junction. This is necessary where the physi- cal circuit is so long that load coils are required on the voice frequency cable pair and non-loaded cable pairs are required for carrier. A pair of junction line filters may also be used to provide a voice frequency by-pass around a repeater. As illustrated in Fig. 26, this may be necessary *L. B. Bogan and K. D. Young, Simplified Transmission Engineering in E.\- change Cable Plant Design, A.I.E.E. Communication and Electronics, No. 15 page 498, Nov. 1954. 382 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 Is :3 bC THE TYPE PI CARRIER SYSTEM 383 to serve customers beyond that point from physical voice frequency circuit. A carrier Hue termination network is also provided to terminate the end of the carrier line at all frequencies and thus prevent reflections from interfering with the transmission at remote carrier terminals spaced along the line. This network and all of the other line networks are available in the pole or crossarm mounted arrangement shown in Figure 14 and de- scribed in Section 4.5. Fig. 26 also gives examples of two types of subscriber distribution beyond the remote carrier terminals. One, wire distribution, is indicated by the voice frequency extensions of Channels 1 and 4 and the other, filter distribution, is shown for Channels 2 and 3. Filter distribution permits the carrier line to be used simultaneously for carrier transmission and voice frequency distribution of the derived voice frec^uency circuit, thus saving the pair of wires required if wire distribution were used. 7.1 Layout Procedure and Ground Rules PI carrier channel laj^outs for a given rural line will be based on the forecast of commercial requirements for that route. The Plant Engineer must determine the number and arrangements of channels which can be applied within the system limits to meet that forecast. The locations of remote terminals are then chosen based on customer locations, channel freciuency arrangements, and the availability of commercial ac power. With the terminal locations fixed, the line losses are determined at ap- propriate frequencies and repeaters are specified as necessary along with any line networks and filters required for the layout. The characteristics and limitations of the Pi system lead to certain simplified ground rules which may be used in laying out the carrier chan- nels. Some of these rules are summarized in Fig. 27. The stackable fre- quency arrangement is used for non-repeatered operation, and the design of the carrier channels permits the bare line loss of each individual chan- nel to be 30 db at the top frequency between the central office terminal and the remote terminal. Another limit shown in the figure is that the dc loop resistance of the voice frequency extension beyond the remote terminal can not exceed 390 ohms (5 miles of 109-steel wire) . The 390-ohm limit is determined by the talking battery supply requirements of the 500-type customer telephone sets when the battery is supplied from the remote PI terminal power supply. The PI carrier system has been designed to operate with the 500-type telephone set. The improved dialing, ringing and transmission features of that set wall help to insure satisfactory performance of the 384 THK BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 over-all carrier derived circuit. In keeping with the system objectives, the over-all transmission of a carrier channel and its voice frequency extension, using the 500-type telephone set, will be as good or better than that obtained on long rural lines using phj^sical plant laid out by the Resistance Design Method mentioned earlier. As shown in Fig. 27, the normal and staggered grouped frequency arrangements used for repeater operation allow 30-db bare line attenua- tion at the top freciuency (96 kc) between the central office terminal and the first repeater or between repeaters, and about 30 db between the last repeater and each remote channel terminal at the top frequency used for that channel. Directional filter characteristics limit the repeater sys- tem can use a maximum of four repeaters for a total line loss of about 150 db at 96 kc. However, noise and crosstalk requirements will permit no more than two of the four repeaters to be used in the open-wire line, with the last cable repeater at least one mile back in the cable from the cable- open-wire junction, as show^n in Fig. 27. Spacings must be limited to somewhat less than 30 db on certain line facilities such as B rural wire to insure proper terminal regulation.^ CENTRAL OFFICE CARRIER TERMINAL CABLE AND OPEN WIRE 30DB AT MAX. FREQ. OF THE INDIVIDUAL CHANNEL CABLE OR OPEN WIRE REMOTE CARRIER TERMINAL 390 OHMS VF EXTENSION TO MOST REMOTE CUSTOMER (a) STACKABLE FREQUENCY ARRANGEMENT: NON-REPEATED CENTRAL OFFICE CARRIER TERMINAL CABLE 1 MILE- A I 30 DB AT 96 KC : OPEN WIRE REMOTE CARRIER TERMINAL A i I 30 DB AT 96 KC (NOTE 1) NOTE t CHECK MAXIMUM LOSS AT 30KC AND IF LESS THAN GAIN IN REMOTE TERMINAL TO CENTRAL OFFICE DIRECTION, PLACE INPUT PAD EQUAL TO DIFFERENCE AT INPUT OF REPEATER. / 30 DB 390 AT MAX. FREQ. OHMS OF THE INDIVIDUAL CHANNEL (NOTE 2) NOTE 2 CHECK MINIMUM LOSS AT MINIMUM FRE- QUENCY OF EACH CHANNEL FOR THE LAST REPEATER TO REMOTE TERMINAL SECTION AND IF THIS IS LESS THAN THE REPEATER GAIN AT THAT FREQUENCY, PLACE PAD IN OUTPUT OF TERMINAL TO BUILD SECTION OUT TO REPEATER GAIN VALUE. (b) GROUPED FREQUENCY ARRANGEMENTS: REPEATED Fig. 27 — PI carrier application ground rules. ^ C. C. Lawson, Rural Distribution Wire, Bell Lab. Record, pp. 167-170, May, 1954. THE TYPE PI CARRIER SYSTEM 385 In addition to bare line loss, the ground rules make allowance for ap- proximately 3 db of miscellaneous losses in any normal channel layout, including bridging losses of carrier blocking networks and other terminals on the carrier line, insertion losses of high-pass filters, and losses in the autotransformer and junction line filters used at the cable-open-wire junction. Since these losses do not all add directly, it is simpler to use an average loss factor to co\'er most conditions rather than make compu- tations to determine a definite loss for each set of conditions that might exist. Thus for channels using a stackable frequency arrangement, a maximum of about 33 db loss, including the bare line loss and miscel- laneous losses, may be expected between the points where the terminals connect to the line. A further loss is experienced because the remote terminals are bridged onto the carrier line. As a result the carrier power transmitted toward the central office terminal is only +0.5 dbm due to a bridging loss of about 3.5 db at that point. Therefore, in the remote-to-central office direction, the minimum power will be —32.5 dbm (0.5 dbm — 33 dbm) at the line terminals of the central office terminal. The minimum carrier power in the central office to remote direction will be —29 dbm (+4 dbm — 33 dbm) at the bridging point of the remote terminal. 7.2 Terrninal and Repeater Location In laying out the carrier line design, it is ffi"st necessary to determine the possible locations for the remote terminals based on distances to the customers to be served and the a\'ailability of conmiercial ac power, since this is the most economical power source. (When commercial ac power can not readily be made available, the primary air cell batteries can be used.) Having determined the ideal location of the terminals from a physical standpoint, the makeup of the physical circuits back to the central office must be determined and computations made of the carrier frecjuency attenuation of the facilities. These loss computations are used to determine the number of repeaters required, if any, and their locations, once again modified by availability of commercial power. The Plant Engineer must also check for the necessity of input and output pads at the terminals and repeaters. The need for loss computations led to the development of length-loss charts so that a carrier line design could be made in a manner ^•ery similar to the loop cable design using the Resistance Design JNIethods as men- tioned earlier.* Fig. 28 shows one of the 96-kc length-loss charts used to lay out repeater spacings and Channel 4 over-all circuit design. Fig. 29 shows the 48-kc length-loss charts as an example of the charts that are provided at each carrier frequency other than 96 kc for terminal-to- 386 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 2 $ O < 10 10 I (0 UJ ca < 3 3 o < 15 LU z _J _1 < Z _1 i'j a Q z UJ UJ < < < z UJ I cr n UJ cr < Ul cr z z Ul z _l < Z) N cu rr cc -1 n Q m -> < 3 5 'I LU 1- LU Q LU tr cc < 5? H z 5 ' cr O u a _i T u. o o 1- UJ < (J < co < CC o z sigaioaa ni 9son 3Nn aavg THE TYPE PI CARRIER SYSTEM 387 LU ..liJ to in 3 ' z5 _i u. UJo QC O < (*1 m + < 5 D o ZliJ z ? - < Zlu i< z 2in< trtr ja UJUJ<3 '-f? > ' <<£ cc UCL _J O u. z 5 o I en < _i < cc CC CD * o tr D DO 1 1 1 ■ ' 1 ' I ! 1 ! . 1 1 1 . ; . 1 , r i 1 1 ill' ! II;' [■ ■ '111!, V ' . 1 ! . ■ ( 1 1 ?V "A '"^'-'^-'-~'- ->^V\- J? : ^ i^s^K^ '^'' '^ < i^ X s ^A ^ >i^ N^vX V xVu ^"^ \\^^ — rr-\- r-r- ""^'i "Os.. ^5i\ in to \- O 3 -J O > UJ < < z o-i UJ _i ZUJ ^ <-( UJ Z Z lO < f) cc < ^^LUU ■7 a q:_iq. UJuj I x IT H u. o O O u < ■7 7 1- LU Ml Q- >- i/) o 1 1 , 1 i ' ' -n^- t" T ® o 1 — -t^TTTT ] , , i -rt+F-? "^ Zl 1 1 1 1 _-_ (- X X 1 ■ \ ft- -TT ■ - lO Z x5: ^i" + 'H — lO -1 tr ■^. — \ *H — - IJI _l 3 _--- cc i:--- -3r :; ; :- - - --0 S m V;-; - \^ rr. . _■;": :.■ - in !i! tr TpS^ ^-- ■ _- ,n 5 _ ^ < i_^-j-J - - — ■ ^' u o . — - ^^\ — 'V : '^ < -^ — \ — ^T J_ — „ .-- - ^ o ^ __^ — ^1^^ ^ O 1- rr:: V- xr;: ~^~~;~" ;^_ - o <~1 ^ \ \: : ::r: : : . ^ o — ^: ;-?V ~ : \ A .n iM^: t l\- \ - ■■" " tvi ^^ A Sl r J O 0^+^: S V V ■ t\l -rrr: ^;;- N, V.\: "" O ":.:. N^^ ^ S W f\j -^^>* \ \\V Q ^ ^ Ov\ _ :„ ■ ^^ -^^ OOOA ^^^ Si f~\ bC '30 ii; (\J o in o OJ — — o ro in (\j o in o cy — — o in o in o (\j — — 91391930 Nl S90~l 3Nn 3bVa 388 THE BELL SYSTEM TECHNICAL JOURXAL, MARCH 1957 terminal section layouts of all channels using the stackable frequency arrangement or repeater-to-terminal section layouts for channels using grouped normal or staggered frequency arrangements. 7.3 Pad Selection The Plant Engineer is given general ground rules for determining the values of input and output pads used in the terminals and repeaters. Charts are provided for use in determining the input and output pads, and they are so arranged that the engineer can take values directly from the length-loss charts and enter them into the appropriate slots to cal- culate the proper pad values. 7.4 Crosstalk Limitations The Plant Engineer must be given information showing how many carrier channels can be applied to each circuit of open wire, cable or B- rural wire on a rural route. Crosstalk studies and tests have indicated that the stackable frequency arrangement or the grouped frequency arrangements used singly or in combination can be used on cable or B rural wire with a full system complement of channels applied to each pair. However, in the case of open wire, the frequency arrangement and number of channels which can be applied is very dependent on the type of transposition system used. The Rl design is the most commonh^ used transposition design on rural lines of the Bell System, and Fig. 30 gives CHANNEL NOS, (a) stackable: (b) GROUPED: POLE PAIR NONE N,2N,3N,4N IN,2N,3N,4N (a) stackable: (b) grouped: FREQUENCY ARRANGEMENT: N - NORMAL GROUPED S = STAGGERED GROUPED Fig. 30 — Number of PI carrier channels on an Rl transposed line. THE TYPE PI CARRIER SYSTEM 389 the carrier assignments for the various frequency arrangements on a one and two-crossarm route using the Rl transposition design. Use of a transposition system giving better carrier frequency crosstalk perform- ance than the Rl design is expected to permit the apphcation of a number of additional channels over those shown in Fig. 2. It will be noted that the grouped arrangement provides four channels less on a two-crossarm basis than the stackable arrangement. From a transmission standpoint, equal numbers of channels would be possible by assigning one or two channels to a pair, but these arrangements will usually be uneconomical for grouped systems because of the high cost per channel of repeaters. 7.5 Line Networks The location of the line networks and filters, which are a permanent part of the carrier layout, will be designated by the Plant Engineer, and the location and type of the remaining networks, which will vary with changes in subscriber service, will be selected by the plant forces. The low-pass filters or carrier blocking networks used on the carrier lines are simple resonant circuits designed to match given ranges of capacitance that will be presented by the drop wire or open-wire side leads. Since this capacitance varies considerably with various lengths of facility, a method will be provided by which the total capacitance of the drop can be determined and the proper network chosen. The other line networks are applied to the line as necessary to achieve their particular functions. 8. INSTALLATION AND MAINTENANCE A portable field test set has been developed which will simplify the installation and maintenance of the PI carrier sj^stem. The new set, known as the 7F test set, will provide the carrier and audio frequen- cies and a means of measuring them required to align and troubleshoot units of the system. The set, which is battery operated, contains a carrier oscillator to supply test frequencies from 10 to 100 kc, an audio fre- quency oscillator having six selected frequencies in the range of 250 to 2,500 cycles, a modulator to modulate the carrier frequency signal with the audio signal, a demodulator for calibrating the modulated signals, and a wide-band amplifier-detector for making level and transmission measurements. The model of the set shown hi Fig 31 included a pre- cision dial for signaling testing which was subsequently found mmeces- sary and eliminated. An ac operated set providing the same desired fa- cilities is now under development. 390 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 The carrier channel installation and lineup procedure is set up on the basis of using the test set and a generally available \'olt-ohmmeter to make a series of measurements in a specified order. This will permit potentiometers to be adjusted as necessary until the specified meter readings are obtained at built-in test points. Lineup of the terminals and repeaters done first in the central office to insure proper operation and then at the in-plant locations to check system performance. Maintenance will be handled on a complete terminal replacement basis and will consist of making a series of checks with the test set to determine whether the terminal is functioning satisfactorily. If it is not and it cannot be adjusted to restore satisfactory operation, a replace- ment terminal will be used to restore service. All repairs and isolation of trouble within the terminal unit or on the individual boards will be han- dled at a centralized testing or repair point so as to require a minimum of personnel with electronic experience. The test set has been designed to handle all tests for a PI carrier system, when used with the volt-ohm- meter, and when used bj^ trained personnel will permit trouble to be isolated to a given printed wiring board in the Pi carrier equipment. 9. ACKNOWLEDGMENTS The authors wish to thank all their colleagues for their important and necessary contributions to this paper. Particular appreciation should be expressed to E. H. Perkins for his contribution to the first half of the paper and to D. H. Smith for Section 6 on power supplies. Fig. 31 — PI carrier 7F test set. An Experimental Dual Polarization Antenna Feed for Three Radio Relay Bands By R. W. DAWSON (Manuscript received April 26, 1956) The fundamental problems associated with coupled-wave transducers which operate over a 3-to-l frequency hand have been explored and usable solutions found. The experimental models described are directed toward the broad objectives of feeding the horn-rcficctor antenna with two polarizations of waves in the 4-, 6- and 11-kmc radio relay bands. INTRODUCTION There are at least two communications problems which require fre- quency selective filters that operate in waveguides over an approxi- mately 3-to-l frequency interval: (1) channel-separation filters for a circular-electric waveguide system in which it is desirable to use the medium from perhaps 35 to 75 kmc,^ and (2) band-separation networks needed for the horn reflector antenna that permits simultaneous trans- mission or reception in the 4, 6 and 11 kmc bands with both polariza- tions.--^ The research reported in this paper was directed at deter- mining the capabilities of coupled-wave transducers for solving such problems. Experimental work was directed toward the second problem (above) because it is more immediate. Fig. 1 , which is a schematic representation of the feed array, comprised of three sets of directional couplers, shows that the -l-kmc bands are mB j:^ ^1 - IMI ii_ I IE n — n H I _ .n — n N o D E J TT h K Fig. 1 — -Schematic of dual-polurizatioii feed for three microwave bands. 391 4 392 THE BELL SYSTEM TECHXIf'AL JOUKXAL, MARCH 1957 separated one at a time at the antenna end of the arraj'. The 6-kmc bands are separated next and the 11-kmc bands are added or removed at the far end of the array. GENERAL OBJECTIVES Neghgiblc loss of power should result when coupling TEio° waves to TEu° waves for the six bands concerned.* The 6- and 11-kmc waves of both polarizations must pass through the round guide of the 4-kmc transducers without significant attenuation. Waves in the 11-kmc band must also pass through the circular guide of the 6-kmc transducers without appreciable loss. A good impedance match is desired at all ports. No cross coupling is desired between the orthogonally polarized waves in the round guide. FUXDAMEXTAL PROBLEMS EXCOUXTERED The frequency-selectivit}^ required to separate various bands in the same polarization can be achieved in a coupled-wave device bj^ either varying the coupling coefficient and/or var\'ing the phase constant, as illustrated by the expression for the amplitude of the selected wave:^ E\ = , :„ ==^,,Ax/\^[^-^^^\\cx (1) 7rTfiiy--it^-(-)'l Avhere c = coupling coefficient X = length of coupling array jS = phase constant In the present designs some of the frequency selectivity is in the coupling holes. The greater part of the selecti^'ity is in the design of the phase constants; the\' are made equal in the band to be selected (|(3i — /3o = 0) and ver}^ unequal (' 2c > in the frequency bands to be passed. The size of the coupling hole must be controlled to avoid coupling hole resonance in any of the three bands that may be present. This problem is especially bothersome in the 4 kmc coupler where signals are present * As used in this article, superscripts O and D refer to round and rectang- ular waveguides, respectively. AN EXPERIMENTAL DUAL POLARIZATION ANTENNA FEED 393 in all three bands. To keep the coupler length within a reasonable size, the individual hole dimensions must be on the order of Xo/4 (at 4 kmc), which will permit coupling hole resonance within the 3-to-l frequency l)and. A further consideration is the selection of the hole shape to avoid perturbing the TEii° wave that is orthogonal to the strongly coupled TEii^ wave. Spacing of the coupling holes nuist not be \g/2 to avoid: (1) large re- flections in the driven waveguide, and (2) large backward-travelling waves in the adjacent coupled waveguide. This requirement is easily met in the 11-kmc coupler where only one band is present; however, the presence of signals in two or three bands makes the non Xg/2 spacing more difficult in the 6- and 4-kmc couplers. Another phenomena of importance exists in coupled waveguides operat- ing over an extended frequency range. A coupling aperture in the side wall (see Fig. 1) may interact with a high-order mode at the latter's cutoff frequency, resulting in a significant perturbation of the desired coupling. For example, at the frequency where TEoi^ passes through cut off, the coupling between TEu^ and TEio° will be perturbed if the coup- ling hole is of sufficient size. Small coupling holes do not allow this pertur- bation to manifest itself. Coupling holes in a realistic design do become large enough to allow this effect to appear. Since dominant mode guides in the 4- and 6-kmc bands can support other modes in the higher fre- quency bands, considerable caution must be exercised in selecting the round guide sizes on this account alone. (The size of the round guide is determined also by the phase velocity in the rectangular guide). SELECTION OF COUPLING APERTURES A series of holes in either the narrow or broad side of the rectangular guide can, in principle, be used to achieve complete power transfer from TEio° waves to TEn° waves. The specific consequences of coupling through holes located along the center line of the broad side will be considered first. (Off center holes are not of interest because they couple TEio'"' waves to both polarizations of TEii° waves in a frequency-sensitive way.) The transverse magnetic field H^ and the electric field Ep of the TEii° waves can couple to TEio° waves. When two fields couple, the back- ward wave in the undriven guide can be greater than the forward wave in the same guide. To avoid this possibility, transverse slots can be used to prevent electric field coupling. The coupling of a transverse slot in- creases as the frequency is increased which suggests that 11 kmc signals be introduced at the position nearest to the antenna because the largest tolerable apertures for an 11-kmc coupler would not perturb 6- or 4-kmc 394 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 waves. Unfortunately, coupling to slots in this orientation is small, re- ([uiring several hinidred for complete power transfer. Such a large num- ber would make the coupler too long. Coupling through holes in the center of the narrow wall of the rec- tangular waveguide as shown in Fig. 2 allows only the longitudinal mag- netic field Hz to couple when the electric field of the TEii° wave is parallel to the hole containing wall. No coupling exists between the TEio° waves and the TEu^ wave having an electric field perpendicular to the plane of the hole. The use of longitudinal slots where practicable minimizes perturbation of this wave. Since the desired TEio° — TEu coupling decreases by 15 db from the 4 kmc to the 11 kmc bands (for 1.872 X 0.872" and 2.2" diam. guide), the layout of Fig. 1 suggests itself since some coupling discrimination is present for the higher frecjuency waves that pass through the lower frequency couplers. DESIGN OF ll-KMC COUPLER The objective of this design is to transfer all of the power from a dominant mode rectangular guide into one polarization of the TEii° forward traveling wave in an adjacent circular guide. Fundamental coupled-wave theory"* shows that phase velocities must be matched in the two guides to achieve complete power transfer. A standard rectangular guide size is selected and the round guide size that has the same phase constant is calculated for the center of the 1,000-mc wide band. An approximate total length is selected for the series of coupling holes that permits the holes to be spaced approxi- mately X3/4 apart. The hole spacing is not critical although the non- directional properties of \g/2 spacing must be avoided. The required magnitude of multiple discrete couplings is shown in equation (40) of Reference 4 to be: a (2) where n is the number of coupling holes and a is the amplitude of the wave transferred at a single coupling hole for unit incident amplitude. Equation (3) expresses the power coupled from TEii° waves to TEio° waves through a circular hole in a common wall of zero thickness where P2 is the power propagating away from the coupling point in either direction in the undriven guide, and Pi is in the driven guide. This deriva- tion is based on the work of H. A. Bethe^ and some unpublished notes of S. P. Morgan. AN EXPERIMENTAL DUAL POLARIZATION ANTENNA FEED 395 p. 0.6805XoV6 -. - ..«y > - (ly /: - (3-^y <3) The quantities a and b are the large and small dimensions of the rec- tangular waveguide and R is the round guide radius. The wavelength in air is designated by Xn , and the radius of the coupling hole by r. A cor- rection for the finite thickness of the wall is made by. considering the circular coupling hole to be a mund wa\'eguide beyond cutoff. The ad- ditional loss is where t is the wall thickness. Total coupling loss per hole is defined by 20 1ogioa = 10 log :^' - A (5) The number of coupling holes n is found from the approximate coupling length and hole spacing. Equation (2) is used to find a and then the hole radius r is calculated from (3). Wa^'eguide dimensions must be corrected to allow for the perturba- tion of the phase constants due to the coupling holes. The perturbed phase constant* for the round guide is d where d is the hole spacing and p is the coupling between a pair of round guides ^o 0.1056r%2 p - R' [l ( '« Yl L \3.413i?/ J (7) The perturbed phase constant for the rectangular guide is D _ ^D ,__ VP° /3p^ = /3" + -^ (8) P = 9a%' [' - m (9) This correction is due to S. A. Schelkunoff as noted on page 708 in Reference 4. 396 THE BELL SYSTEM TECHXICAL JOURNAL, MARCH 1957 0.454"R n =28 EQUIVALENT UNIFORM HOLES T=0.022"' °-^^° Fig. 2 — 11-kmc coupler sketch. _) UJ m o UJ o to in o _J rr UJ u. z < 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 - ■ 1 — IN • \ - OUT ^ ] : o \ \ ^ Ir. V -'/.-.- " T-I_l 1 e r*i-ii A a t -T A-ri r\Ki \ \ COUPLES \ 1 ^ \ \ i 1 \ \cALCULATED \ \ MEASURED^ \ \ \ \, V ► s >^ L, 1 1 ■ sc — ~ ^ 9.0 9.4 9.8 10.2 10.6 11.0 11.4 H.8 FREQUENCY IN KILOMEGACYLES PER SECOND 12.2 Fig. 3 — 11-kmc coupler transfer loss. AN EXPERIMENTAL DUAL POLARIZATION ANTENNA FEED 397 The perturbed phase constants are made etiual through a suitable choice of R and a, this choice being somewhat influenced by the coupUng- hole radius r. Three coupling a{)ertures of successively reduced size are used at the ends of the array of identical holes to produce four reflections having the relative amplitudes of 1, 2.7, 2.7, 1. The modified binomial distribution was chosen because impedance matching can be secured over a broader 20 1 & LU u Q 16 12 1 0 Z o I- tr LU CO z > ^s-^ K / /o N \ rf / N V J / V ^ ) / ■^ / IN Zo OUT ^^ y \ ] (0 CI ; ^ s- VWv c^ THIS F C 'OLAF OUPL (IZATION ES 1 1 1 1 6 4 9.2 9.6 10 10.4 10.8 n.2 11.6 FREQUENCY IN KILOMEGACYCLES PER SECOND 12 Fig. 4 — 11-kmc coupler insertion loss. band (with minor degradation of the center-frequency match) when compared to a standard binomial distribution. Amplitude reflections* from the start of the coupling array are Ar = 47rrf (10) where Q is the reflection from a single coupling hole. Fig. 2 is a sketch of the coupler with, the final design dimensions. Fig. 3 shows the measured and theoretical transfer loss of an 11 kmc coupler. Fig. 4 indicates the measured insertion loss for the same coupler. DESIGN OF 6-KMC COUPLER The 6-kmc coupler as shown in Fig. 5 utilizes a partially dielectric- filled rectangular guide coupled to the circular guide. The use of dielectric loading makes it possible for the phase velocities to be equal in the two guides in the center of the 500-mc wide 6-kmc band, and unequal in * Information given to S. E. Miller by S. A. Schelkunoff in an informal com- munication. 598 THE BELL SYSTEM TECHNICAL JOURXAL, MARCH 1957 0.060" I n = 30 EQUIVALENT UNIFORM HOLES FOR ONE ROW HOLE SIZE =0.030" X 0.627" SPACING — 0.660" 10.622" 0.211" Fig. 5 — 6-kmc coupler sketch. 1.0 _i UJ 5 0.8 o ID o ? 0.6 o cr UJ u. z < i- 0.4 0.2 5.6 5.8 IN OUT ^^ (D=3 1 1 LU ) /^ ^ y \ \ v,^ TR/ ^NSF ER L OSS ^ X^' V 6.0 6.2 6.4 6.6 6.8 FREQUENCY IN K ILOMEGACYL ES 7.0 7.2 Fig. 6 — Transfer loss of 6-kmc coupler. AN EXPERIMENTAL DUAL POLARIZATION ANTENNA FEED 399 the 11-kmc band; thereby low transfer loss is obtained in the 6-kmc band and a high transfer loss in the 11-kmc band. Measurements have shown that when the cut-off frequencies of higher modes occur in the band of interest an uncontrolled increase of coupling may result. Special precau- tions are recjuired in selecting the round guide size to avoid this condi- tion. The design process is shown in Appendix I. Figs. 6 and 7 show the transfer and insertion losses in the G-kmc; band. 16 UJ m o UJ o 14 - 12 tn O z o I- cr UJ If) z 10 ROUND GUIDE INSERTION LOSS / -^ ^ ^ ^ / N V IN OUT ■— — 1 1 5.6 5.8 6.0 6.8 Fig. 7 6.2 6.4 6.6 FREQUENCY IN KILOMEGACYLES - Insertion loss of 6-kmc coupler. 7.0 7.2 SLOT SI ZE= 0.740" X 0.0786" SPACING= 0.780" POST DIA = 0.300" GUIDE SIZE= 1.724" X 0.872" COUPLING ARRAY CONSISTS OF 38 FULL SIZE SLOTS 8. 6 REDUCED SIZE SLOTS Fig. 8 — 4-kmc coupler sketch. 400 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 56 48 _] UJ 5 40 u UJ Q z 32 o -" 24 q: LU ll_ 10 z 16 < tr (4) L , (6) t 00 / ft V A ft , '1/ V II hi 1 IN 1 .{II 1 1 1 I / mouT v 3.4 3.8 4.2 4.6 5.6 6.4 7.2 8. C 8.8 9.6 10.4 11.2 FREQUENCY IN Kl LOMEGACYCLES PER SECOND 12.0 12.8 Fig. 9 — Transfer loss of 4-kmc coupler in 4-, 6- and 11-kmc bands. in _i - b U LU Q ? ^ in i.,-,j_^. 1 ■ HP' IP " -v. 1 1 1 i ^^^^^_ '-^^^£3^^ """""" B ii 1 ^ ?; - ^ ... N ■ wm ■ ^^M^H \ r^ "" -SH^ ■ 1 1 1 ■ 1 In 1 ■ "^T^^^ ■ Fig. 14 — Mandrel and rectangular guide. 404 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 :3 AN EXPERIMENTAL DUAL POLARIZATION ANTENNA FEED 405 kmc band is due to an appreciable coupling of TEii° waves to TEso^ waves in the 4 kmc couplers in the vicinity of the TEso^ cutoff. The TEso^ cutoff might be moved above the 11 -kmc band by using ridged rectangu- lar guide. SUMMARY A combination of three pairs of coupled-wa\'e transducers has suc- cessfully permitted six distinct bands to be fed from individual TEio'"' rectangular waveguides into the two orthogonal polarizations of TEn^ waves in a multi-mode round waveguide. The resulting structure en- abled low transfer loss values to be obtained simultaneously over two 500-mc wide bands and one band 1000-mc wide distributed over a 3-to-l frequency interval. ACKNOWLEDGMENT A substantial portion of this work was carried out as a joint project with H. E. Heskett and S. E. Miller. Appendix I DESIGN OF 6-KMC COUPLER A rectangular guide size is chosen and a reasonable value selected for the phase constant such as /3° = I.Stt/Xo . The resulting round guide size must prevent modes from cutting-off within the 6-kmc band and preferably the cut-off frequencj^ should be above the 6-kmc band. The thickness of the dielectric (polystyrene) strip is determined^ from (11), (12), and (13) where Ki and K2 are transverse wave numbers of the air- filled and of the dielectric sections of the guide. Cot K^ = -~ cot IU{a - d) (13) In the above equations Er is the relative dielectric constant and d is the slab thickness. After soh-ing for d the equations are resolved for Ki and Ki values at the 6-kmc band edges and also at the lower end of the 11-kmc band. Resulting rectangular-guide phase constants should cause a very 400 THE RELL SYSTEM TECHXTCAL JOURXAL, MARCH ] 9o7 low and a high vahie of tran.sfcr loss as indicated b\' (14) which repre- sents the forward traveling coupled wave amplitude where ex is the total coupling strength/ ^-,^/(..^.o.,/-'"[/^^^i^^^1" (14) At midband ex = tt 2 and experience has shown .r = 10 Xn ; therefore c = 7r/20Xo at midband. The coupling hole radius is found from (3). Because longitudinal slots are used instead of round holes the equivalent hole radius r is found from fr^ = P(^, where P is the magnetic polariza- bility' and ( is the length of the chosen slot. To avoid slot resonance in either band, the length was chosen to be approximately Xci/4 in the 6-kmc band and fX,) in the 11-kmc band. The power expression of (3) must be corrected by the wall thickness effect (4) and also multiplied by the factor F due to the presence of the dielectric .slab' (15). 7ri3n\a[Ki{di - \ sui 20i) + A^K.id. - \ sin 2^2)] B. = KM - d) e. = M A = (^pYs^^ XKo/ cos 60 Theoretical coupling lo.ss per hole is defined by 20 logio a = 10 log ^- - (A + 10 logio F) , (16) i 1 An additional correction which reduces the coupling loss is due to the long length of the slot. Although the slot resonates near 9 kmc, an in- crease of 3 db in a single slot coupling results at 6 kmc. This effect was found experimentall}' from a sample test line with several slots. To avoid excessive length two rows of coupling slots were employed. The}' were staggered to impro^'e the continuity of coupling from discrete points. An approximate design is on hand at this point. The final dimensions for the guides and coupling holes are found after the perturbations of the phase constants are considered by the same process as noted in the dis- cussion of the 11-kmc design. Impedance matching for the dielectric strip and the coupling slot array was patterned after the technique shown for the coupling hole array in the 11 kmc design. AN EXPERIMENTAL DUAL POLARIZATION ANTENNA FEED 407 Appendix II DESIGN OF 4-KMC COUPLER A round guide size is selected so that no modes are cut-off in the three bands. CoupUng power varies with wavelength as shown in (17) for TEio to TEii° coupling. Y = (17) 3.413/? )■] To maintain the minimum variation across the band, the following re- quirements must be met which were deduced from the coupled wave theory and (17). sin (cx)i = sin (cx)2 (18) (cx)i _ ^0 (^ ~ i /i / Xo \' (19) V \saisr) (cx)i + (c.r)2 = T (20) The equations are solved for sin ex (the minimum band edge transfer loss) which for a diameter of 2.10" is 0.5 db. A value of 30 db is chosen for a, (2), as the first approximation. Because the band edge transfer loss is 0.5 db due to frequency variation of coupling, an additional loss of only 0.2 db is allowed for the phase constant difference (/3l° — /8°). It is now necessary to make jS*^ = ^l° , where /3l° is the phase constant of the loaded rectangular guide. Equation (21) gives a theoretical periodic loading formula where L is the spacing between loading elements.^ cos 0L°L = A cos (i8°L + *) lAHU Assume initially that L = -k/^^ . The required susceptance 6o of the ca- pacitive rods can be found experimentally from a loaded test line by varying 6o until the first rejection band covers the 6 kmc band. An iterated process is used to find L because it is dependent on j8° which is the parameter being sought. Measurements indicated that (21) does not predict |8° very accurately and for that reason an experimental adjust- ment of (/3l° - /3°) is desirable. The guide dimensions are now known; however, they must be cor- rected for the perturbations of the phase velocities as outlined in the 11- 408 THE BELL !^YSTEM TErilXirAL JOURNAL, MARCH 1957 knic coupler design. A single row of longitudinal coupling slots which are not resonant in the 6- or 11-kmc bands is used. The radius of a round hole ecjuivalent to the slot is obtained as in Appendix I, In' setting ir' = Pf. Impedance matching of the coupling array and of the loading elements is accomplished by tapering the amplitude of the end elements as indi- cated b}' a discrimination function of the coupled wave theory. For a 5 element series 1 —th —n^ —ui — 1 ^ 'lin, + 1) + n. ■<" 47rZ , SttZX , (22) 1 cos — h cos ^,^ 1 + n-i where Z is the spacing between elements. The discrimination D is set equal to infinit}^ which permits the de- nominator to be set equal to zero and solved simultaneously for ?h and Ho by using both band edge wave-lengths. Round hole sizes are readily obtained .since the coupling coefficient is directly proportional to the cube of the hole radius from which the necessary equivalent longitudinal slot can be calculated. Susceptance values of the capacitive posts are found from the absolute value of the reflection coefficient which equals ho REFERENCES 1. S. E. Miller, Waveguide as a Communication Medium, B.S.T.J., Nov., 1954. 2. A. T. Corbin and A. S. May, Broadband Horn Reflector Antenna. Bell Labora- tories Record. 33, p. 401, Nov.. 1955. 3. A. P. King, Dominant Wave Transmi.ssion Characteristics of a Multimode Round Waveguide, Proc. I.R.E., 40, Aug., 1952. 4. S. E. ^liller, Coupled Wave Theory and Waveguide Applications, B. S.T.J. , Mav, 1954. (See page 681.) 5. H. A. Bethe, Physical Review, 66, p. 63, 1944. Also Report 43-22, Lumped Constants for Small Irises, Mar. 24, 1943; Report 43-26, Formal Theory of Wave Guides of Arbitrary Cross Section, Mar. 16, 1943; and Report 43-27, Theory of Side Windows in Wave Guides, Apr. 4, 1943; from M.I.T. Radia- tion Lab. 6. X. Marcuvitz, Waveguide Handbook, p. 408, McGraw HiU. 7. H. Seidel, private communication re: Slab Width Determination and Effects on Coupling Parameters in Partial Dielectric Loading. 8. S. B. Cohn, Determination of Aperture Parameters by Electrolytic Tank Meas- urements, Proc. I.R.E., Nov., 1951. 9. J. C. Slater, Microwave Electronics, p. 183, Van Xostrand. The Character of Waveguide Modes in Gyromagnetic Media By H. SEIDEL (Manuscript received August 31, 1956) A magnetized gyromagnetic medium is birefringent. The effect of bire- fringence is studied in rectangidar and circular waveguides with special attention paid to propagation characteristics in guides of arbitrarily small cross-section. Propagating , small-size structures are found in certain ranges of magnetization for both types of guide. I. INTRODUCTION A gyromagnetic medium, isotropic in the absence of a magnetizing field, becomes axially symmetric with respect to that field when mag- netized. A tensor susceptibility^ is thus produced which reflects the resulting anisotropy. Two essentially different types of rays appear in the medium in much the same manner in which the ordinary and extra- ordinary optical rays form in a calcite crystal. These rays may combine to produce results in a ferrite loaded waveguide quite alien in character to those of a conventional isotropic guide. Since the ferrite is, to first order, characteristic of general gyromagnetic media we shall discuss all gyromagnetic phenomena in terms of ferrites alone. One very startling phenomenon observed in ferrite loaded waveguides is the occurrence of propagation in a waveguide of arbitrarily small transverse dimensions.- We shall show that this type of wave guide behavior is a consequence of the particular form of the birefringent character of the medium. In order to understand the nature of the ferrite loaded case let us first consider the conventional isotropic small wave guide. Fig. 1 shows, schematically, the field distribution encountered in a small rectangular waveguide operating in a (1,1) mode. The .r axis is shown along the wide transverse dimension and z is along the narrow height dimension. The y axis is chosen to coincide with the guide axis. The field solutions of such a wa^•eguide may be obtained as a super- 409 410 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 Z VARIATION *>X X VARIATION Fig. 1 — Rectangular waveguide mode in isotropic medium for cutotT guide. position of plane waves of dependence c"'*'^. If we represent k cartesian frame, the wave equation is satisfied for the condition ni a h' = ki + hi + k; = cc'ns where n and f are the permeabiUt}' and permittivity respectively of the medium. Satisfaction of wall boundary condition requires that k^ and /;, be real and that each be of the order of the reciprocal of the transverse guide dimensions. Small transverse dimensions thus cause ky~ to be negative, driving the waveguide into a cutoff condition. We shall now find that birefringence permits another class of modes in the small size ferrite loaded waveguide. Letting the magnetic axis be in the z direction, it will be shown in the text that corresponding to any mode of the guide ky and k, are unique. Birefringence generally requires that two different magnitudes of k occur simultaneously, causing two different values of A-^ to appear. In particular, let us postulate that both these values of A-;^ are imaginary. Given two exponentials, it is possible now to satisfy the requirements of electric field nulls at either side wall, as shown in Fig. 2. At the other side wall we shall show that the ex- ponentials decay so fast as to effectively cause the field to vanish there. Since A-^i, o are now negative ciuantities, there is no contradiction in pre- suming that ky maj'' now be positive, thus permitting propagation in an arbitrarily small size waveguide. The effect of birefringence may then be that of transforming a class of longitudinal!}' cutoff modes into another class that propagates longitu- dinally but cuts off transversely. The condition of this occurrence will be shown to be that for which the diagonal term of the Polder tensor, ^t, is positive and is less in magnitude than the magnitude of the off" diagonal term k. In the case of a small rectangular guide, propagation occurs anomalously for negative values of n, as well but in a manner not as WAVEGUIDE MODES IN GYROMAGNETIC MEDIA 411 substantially dependent on the birefringent character of the medium for large width to height aspect ratios of the waveguide. We shall find, further, that propagation occurs with entirely real values of kx and k^ . It will be shown that the proper wave equation for one of the two birefringent rays is satisfied in the small waveguide limit by the rela- tionship A-/ + kV + A-Z/m = 0. In the region of ^ > 0, and /.-, real, we confirm somewhat more rigorously the recjuirement stated earlier that either kx or ky be imaginaiy. However, kx and ky may both be real over a range of negative values of /x, permitting boundary conditions to be satisfied, approximately, in waveguides having aspect ratios of the type discussed earlier, by just one class of rays in the small size wa^'eguide. Propagation in small size circular guide employing the essential charac- ter of birefringence, occurs o^'er the entire range of | ^ | < | k |. This range is di^'ided into that of m > 0 and that of /x < 0. Transmission occurs in one sense of circular polarization in each of these regions and for both senses for n < 0. Thompson has suggested that propagation in a small circular wa\'eguide might be attributed to the negative permea- bility of one preferred polarization; it appears, however, that propaga- tion is possible over a considerably wider range of conditions and for somewhat different reasons. In the case shown in Fig. 2, higher propagating modes occur in a rectangular waveguide when one half or more sinusoids of field varia- tion occurs in the z direction. These simply produce the result of stronger RESULTANT^ X VARIATION Fig. 2 — Mode in ferrite filled rectangular guide. 412 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 transverse cutoff. Therefore, by demonstrating the existence of the lowest order mode we show that an infinite number of these anomalous modes may propagate simultaneously. These modes are, however, bound A'ery tightly as svu'face waves to the side walls of the guide because of their strong transverse cutoff. The medium is therefore used in a verj'' inefficient manner and high loss results, the loss increasing with mode number. The higher propagating rectangular wa^'eguide modes have an ana- logue in the higher propagating modes in a ferrite filled circular wave- guide. This analogue occurs in terms of the integral number of peripheral \'ariations. "We find, similarly, an infinite number of such propagating modes each one corresponding to a given polarization sense and having a given number of peripheral variations. The reservations on practical transmission still hold in the same manner as in the rectangular case. In the course of preparing this publication it was brought to the author's attention that ^Mikaelj'an employed an anah^sis similar, in part, to that developed here. It is felt, in the present analj^sis, that the physical results are made more readily evident by a consideration of the limiting case of small guides, with large ratios of width to height in the case of rectangular wa^•eguides. The choice of such large ratios is made to simplify analyses invohdng imaginary values of Avi and /.■;r2 , wherein the wave is considered to be bound to one wall of the guide and reflec- tions from the opposite wall are of negligible amplitudes. II. ANALYSIS OF TRANSVERSELY MAGNETIZED FERRITE IN RECTANGULAR GUIDE The character of the ferrite medium is introduced through the Polder permeability tensor : r = I -k M 0 I (1) 0 0 1, The quantities m and k relate to the self and inducti^'e permeabilities transverse to the z axis. The relative permeability' along the z axis is given as unit3\ These permeabilities may be expressed as follows in gaussian units.^ , = 1 + «^ (2a) COO" — CO" , = i![^ (2b) coo" — CO" WAVEGUIDE MODES IN GYROMAGNETIC MEDIA 413 T = 2.80 Mc/sec/oersted coo = 7-^0 Hq = Internal dc magnetic field 4-7ril/s = Saturation magnetization Maxwell's equations are given as: Curl H = io^eE (3a) CurlE = -ic^(jioT-H (3b) Assuming a plane wave of dependence £»(»'-*'■'*>, and appropriately combining (3a) and (3b), we have, [kk - k'l + o:'£iJLoT]-H = 0 (4) The operator in square brackets is a dyadic which may be repre- sented in matrix form. The quantity / is the idemf actor, having a unit diagonal representation. If we are to require that a non-trivial field H exist, the determinant of the operator in (4) must vanish. Since all rays traveling perpendicularly to the magnetizing axis are equivalent the medium is degenerate in the transverse plane, and some simplification is achieved in causing k to lie in the yz plane and letting k^ = 0. Some further simplification is achieved in normalizing the Polder tensor such that fig 0\ ^ ^ -ig f 0 T W£)UO (5) 0 0 h The following secular equation is then formed. -/v-+/ ig 0 -ig 0 h/yKz ICyK yi^z -A-/ -f h = 0 (6) Introducing the substitution p = k^~/k , and recognizing that Ky Kz m we have upon expanding (C), pW - g')h + /'/(f - Jh - g')] + V[{h - f)h' - k'if ^ fh - g')] + kjf = 0. (7) 414 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 We note, in general, two solutions in j) corresponding to each value of A'j , indicating birefringence of the medium. In particular A-^ must be non-vanishing for birefringence to occur or, stated alternatively, rf field gradients must exist parallel to the applied magnetic field to obtain birefringence. The characteristic vector solutions of (4) may be expressed for each solution of (7) ; they are the magnetic fields, 1 H = H. 9 \ P ^ V ) (h - h' ( 1 -P P . — Hkyy+kzz) (8) and the corresponding E fields. 0)£ h J- P h - kj" 1 - P P -1 —iikyy+h^z) (9) The sign indeterminacy above is defined Avith respect to the ratio ky/ks , the upper sign being given by the positive value of this ratio. We shall analyze the rectangular waveguide by first seeking parallel plane solutions and then utilizing these solutions to form those of the rectangular guide. We choose as parallel planes those perpendicular to the applied magnetic field, or z direction and having a separation b. Because of the absolute uniformit}^ of this type of structure, the field configurations as a function of the coordinates transverse to the magnetic field, X and y, may change only by a uniform phase factor. Again, the choice of transverse axes is made such that these phase variations occur only along y. From (7) we would find that a specification of ky leads to a quadratic equation in p, ^\■ith an appropriate consequent multiplicity in k,~. Let us define as a partial wave any standing wave in the z direction corre- AVAVEGUIDE MODES IX GYROMAGXETIC MEDIA 415 sponding to some linear combination of the positive and negative values of kz for one of the values of kz-. Examination of (9) reveals that the ratio of Ey to E^ , the field components tangent to the bounding walls, to be independent of the sign of kz . Hence, each partial wave has an individual value of this ratio irrespective of its standing wave distri- bution in the z direction. It is thus impossible, in general, to provide a mutual cancellation of two or more partial waves at the electric walls by combinations of such partial waves, with the consequence that each partial wave must individually satisfy the boundary reciuirement. We find, then, that each partial wave takes on the familiar condition kz = mir/h. The parallel plane wa\'es now will be appropriately oriented and superposed to satisfy the side wall boundary conditions in the rectangular guide. Since, as shown in Fig. 2, mutual cancellation is required on the side walls of the rectangular guide, the rate of vertical variation must be identical for all the component parallel plane waves; thus 7n is a constant of the waveguide mode and k, is uniquely specified. Two essential characteristics thus define a rectangular waveguide mode in a transversely magnetized, ferrite filled, medium. 1. The modes are ordered by integral values of m in the relationship /.% = 7mr/b. 2. The propagation constant ky is uniquely specified. Standing waves ma}' now be formed in the z direction satisfying electric boundaiy conditions at the parallel planes. Each partial wave of the electric field may then be expressed as follows corresponding to its appropriate value of p: E = viir biCE H. I . 1 (mir\ \ . niTT I sm VlTZ — i(mx/6) (1— p/p) iy (10) Let us now specialize our analysis to the small guide case. The require- ment of birefringence to produce small guide propagation demands that A-2 be non-\-anishing and that 7n take on an integral value of unity or greater. "We have, from (7), the two limiting values of p corresponding 416 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 to a small value of b, Vi = f M P'2 = k f -h M - 1 f - h Kz - 1 P — fh — g- co-fiuE yi 2 - /X - k2 (11a) (lib) Discarding the z dependence in equation (10) and dropping a constant multiplier, the two characteristic electric field solutions become: .(1) fl- K i Um-' J (,mTlb)n iy (12) E''' ^ '0' (mrlb)y (13) Equations (12) and (13) are parallel plane solutions obtained for some arbitrary direction, y, transverse to the magnetic field. This direc- tion need not be intrinsically real; mathematically, it simply satisfies Maxwell's equations. We may transform to a desired waveguide frame of reference by rotations ^i and ^2 , corresponding to pi and p-2 , about the z axis, where these rotations may possibly be made through complex angles. We then have for the electric fields in the new space: ^(1) 1 - M COS (fl + i sin ^1 1 - M sin 2+-''sirn?2) (15) The new 7 axis of the transformeil coordinates is now considered the longitudinal axis of the waveguide. The partial wave fields of (14) and (15) may be joined to form a single I WAVEGUIDE MODES IN GYROMACxNETIC MEDIA 417 mode by equating the propagation constant. Therefore, cos ^2 = M ' COS^l (16) where cos v?2 is imaginary for propagation. Propagation may therefore occur for n > 0 and cos 0 both of the birefringent rays have transverse decay. Since the magnitudes of fcj, , are large in small size guide (see Introduction) boundary conditions need be satisfied for practical purposes at only a single wall. We are then left with the sim- plification of only two equations in two unknowns. Setting X = 0 in (14) and (15) and taking equation (16) into account, we ha^•e the boundary conditions — sin v^i + i cos (pi I + BlijT' cos ^i] = 0 (17) ^[m~^] + 5 = 0 (18) With the result that cot^Pi = -1^ = (pL] (19) Choosing ky positi\e real, A^i is positive imaginaiy for k positive and negative imaginary for k negative. The rf field therefore hugs the right wall for K > 0 and the left for k < 0, or, alternatively, switches sides in the change from a forward to backward direction of propagation. Equation (19) may be written equivalently as 2 cos' 0, is ob- tained for 1 ju ! < I K |. Let us now analj^ze, the possibility of small guide propagation for M < 0. We find, from (16), that cos 9?i is real for this case. Two cases arise; the first for which | cos ^i | < 1 and the second for the reverse situation. Let us first consider the case of | cos ^i | < 1. From (14), ^^i is real whereas from (15) l\^ is imaginary. Let us associate wave amplitudes 418 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 with X dependences as follows: Be'"'" r\„»*x2(x— a) where a is the guide width. Let us assume that kx^ is a sufficiently large imaginary quantity of such sign that This assumption will be seen to be consistent with the solution. [(26b) for small size guide.] Setting up the boundary conditions for Ey and Ez at x = 0, we have from (14), (15), and (16), (A - B) (^ -) sin 0 case, propagation may possibly not occur for a range of lower order integral values of m. As n becomes increasingly large in magnitude, m must likewise take on increasingly higher values for transmission to occur. The case of cos \ k\ and /x < 0. If the Polder tensor components given in (2a) and (2b) are plotted (see Fig. 5). We find that this last set of inecjualities form an impossible combination. Summarizing we find that a rectangular waveguide of any dimension (and, in particular a guide of arbitrarily small dimensions), filled with a lossless transversely magnetized ferrite medium, will support an infinite number of freely propagating modes at any frecjuency for which | m | < \ k\. The character of these modes differs considerably in the two regions of M < 0 and /x > 0 and somewhat different viewpoints of propagation must be taken. We shall find similar results relating to the longitudinally magnetized ferrite filled circular waveguide in the following section. III. ANALYSIS OF LONGITUDINALLY MAGNETIZED FERRITE IN CIRCULAR GUIDE We now proceed to a second structural geometry in which an anoma- lous behavior occurs attributable to the birefringence of the medium. 420 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 This is the circular guide which has been the subject of considerable analysis by Suhl and Walker. It is instructive, however, to repeat the analysis of this case, in the small guide limit, showing more pointedly its behavior from the viewpoint of combinations of the two types of waves in the medium. The character of transmission in undersized circular waveguide is very similar to that of the undersized rectangular case. We may demon- strate the physical significance of this statement by the following argu- ment. The excitation in a rectangular waveguide, for | /x | < \ k\ and M > 0, is essentially that of a surface wave bound very tightly to a single wall. Considering this wall alone, which may now be extended to arbitrary dimensions but Avith k^ kept large, it may be wrapped upon itself either about the magnetic field as an axis or containing the mag- netic field peripherally. In either event, the wrapped guide must start and terminate at the same phase, requiring a multiplicity of 2ir around the circumference, and the wave must thus continue to have a large kg value. Considering the large value of k^ and the state of excitation of the ferrite, the small circular guide may propagate. Analysis will demonstrate that propagation also takes place in the region ^Lt < 0. The quantity k^^ is real and k^^ imaginary, see (26), leading to a case essentially similar to that of the rectangular waveguide. The analogy is appropriate to the case of h/a of finite value for which the rectangular guide requires the appearance of both refractions. We now proceed to obtain the field solutions for the circular guide. Referring to (9) for the plane wave solution of the electric field, let us define to within a constant multiplier. Ey' £ —i{kyy+kzz) (27) Eg where, for the case of large kg (9, 12, 13) ^(x) ^ l^2± E''' = 0 'X (1) _ p(2) U — -C'2 (1) _ • -i 7?(2) E^'^ = E'^' = -1 Er = iiT' EY' = i I fcj^ _ . _J ky^ _ ^ Kz Kg We shall consider here, of the two possible wrapped-wall structures, that case in w^hich the magnetic field is applied axially as shown in Fig. 3. Referring to Fig. 4, the cylindrical drical electric wave satisfying Max- WAVEGUIDE MODES IN GYROMAGNETIC MEDIA 421 GROUND PLANE— > FERRITE SLAB TRANSVERSE FIELD DISTRIBUTION Fig. 3 — Axially magnetized filled circular guide formed by wrapping wall. DIRECTION OF SINGLE RAY Fig. 4 — Transformation to polar coordinate frame. 422 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 I well's equations and the boundary conditions for this structure is ob- tained by integrating plane waves of the form of (27) traveling at all possible angles \l/, the integration being subject to a weighting factor G(\l/) to obtain the most general field. The coordinates (r, cp) refer to the physical system and the coordinate \{/ identifies a plane wave traveling along a particular // axis. We have thus in an (/-, (p, z) coordinate frame: 2t Jo GirP) Recognizing that cos i" sin f 0 — sin ^ cos I 0 0 0 1 diA = ^r y = r sin f G{^) = G{^ - ) (29) i where En is that partial expansion of the total field E, corresponding to the number of angular variation «, and p = kyr. There are two values of p corresponding to the two A-alues of A^ , and each leads to a partial wave. Let .4 and B be the respective partial wave amplitude; satisfying the boundary conditions on E^ and E^ , we have from (29) : 1 ./,/(pi) nA Pi Jnipi) - Jnip-d = 0 Afx V„(pj) + BJ^ip.^ = 0 (30a) (30b) where pi and p-y are defined for r = A', the radius of the cylinder Recog- I WAVEGUIDE MODES IN GYROMAGNETIC MEDIA 423 nizing that pi = m~'P2 , we have from (30) ^ J/(pi) + n -^-^ = 0 * (31) K Pi where pi = ikzyT^R. Equation (21) may be modified by a recurrence relationship to become tj^^^P^JpM (32) For /x > 0 the quantity pi is a pure imaginary for large real values of A-j . Since the n order Bessel function is monotonic in imaginary argu- ments and possesses the multiplier (i)", the right-hand side is negative for n positive. For n > 0, propagation occurs for \k\ > \n\ sgn K = — sgn fji Inspection of (31) reveals that a reversal of the sign of n is equivalent to reversing the sign of k. This conforms to the physical situation in which reversal of the sense of circular polarization is equivalent to the reversal of magnetic field. Thus for n < 0 and n > 0, \ k\ > \ n\ Sgn K = sgn /Lt We find, from the above arguments, that just one sense of circular polarization propagates in an undersized circular guide for n > 0 and for a given direction of the magnetic field. It will be demonstrated shortly that propagation occurs f or ju < 0, but with an entirely different struc- ture of modes. The right-hand side of (32) is monotonic as a function of p for ^t > 0, leading to only one solution for each value of n. This will not be the case for n < 0. It is of interest first, however, to observe the limiting approach to M = 0 in the region of ^ > 0. The right-hand side of (32) is finite for finite imaginary values of pi , so that the only solution as /x approaches zero is that for which the magnitude of pi becomes infinitely great. The Bessel function is asymptotically expansible as a cosine divided by a square root of its argument. Thus Jn(pi) = - a/- (f'('" + f^"+^>^'^^''» + ^-i(Pl+12n+l](./4))) (33) 2 V Pi * Equation (31) maj' likewise be obtained from the small radius limit in (34) of Reference 2. 424 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 Considering pi to be positive imaginaiy, as pi -^ rx , (32) becomes K M tpi n (34) Substituting for pi , we have riK (35) Thus, as fj. approaches zero from \'akies greater than zero, the propaga- tion constant tends to become singular. Physically, however, n does not vanish but approaches a small imaginary value caused by ferrite losses. The propagation constant k^ becomes complex and takes on a large imaginary component, signifying large guide attenuation. Since these losses occur in the limited neighborhood of m = 0, we may construe this waveguide behavior as corresponding to a system resonance. In the region m < 0, pi becomes real while p2 remains imaginary. The right-hand side of (32) is now composed of onh^ real arguments. Since the zeros of diiferent order Bessel functions alternate, the right side of (32) contains a succession of poles and zeros, leading to an infinite number of branches with each containing a solution pi to the equation. Thus there are an infinite number of propagating modes corresponding to each value Fig. 5 — Frequenc}' characteristics of Polder tensor components WAVEGUIDE MODES IN GYROMAGNETIC MEDIA 425 of n, in marked contrast to the case of ^ > 0. The solutions remain identi- cal, as before, if both k and /; are simultaneously reversed in sign, but differ if only one of the two quantities is nnersed. Since n = 0 is a branch point, the limiting condition as m approaches zero for \'alues ju < 0 differs from that for the re^■erse case. Efjuation (32) is now satisfied in the limit of small m by the real zeros of ./„(pi). Since these roots are finite, A% , ecjual to —{ — nYpi/R, tends towards zero for all modes. Since the formulae developed in this paper always presume large wa\'e numbers, we may infer a ^•anishing \'alue of A'j to simply represent a value which is small relative to the reciprocal of the wave- guide radius. In any event. A,, is no longer singular at m = 0, and there is no resonance in the approach from negati^'e values of m- In sum, the features of the circular guide strongly resemble those of the rectangular guide in the region of pi > 0. This was to be anticipated by the "wrapped wall" construction where the wa^'e is tightly bound to the wall. The wrapped equivalences do not hold in the region ^ < 0 since, with harmonic transverse dependence, the waA-e is no longer bound to the wall. This lack of equivalence is manifested in the matter of ordering modes. For a rectangular waveguide of finite aspect ratio, we find from (25) that there are but a finite number of modes corresponding to each \-alue of m for ju < 0. The circular guide differs in pro\'iding an infinite number of modes corresponding to each A'alue of n. Further, whereas the circular guide covers the entire range of | m | < | « |, (25) in- dicates that the various modes of the rectangular guide covers a more restricted range determined by the guide aspect ratio. IV. CONCLUSIONS The waveguide beha\ior analyzed in this paper has been experi- mentally observed^ and good correlation has been obtained. From the viewpoint expressed of forming a guide cross-section by wrapping a wall to which a surface wave is bound, we may anticipate that the unusual behavior observed in the two types of guides examined is probably characteristic of manj^ other structures. It is not clear, at this time, if the complete set of modes of either the rectangular or circular guides have been exhausted. We already observe that an infinite number of modes propagate simultaneously so that scattering problems become considerably more complex than in the usual cases. It is felt by the author that the field of waveguide analysis calls for new methods and techniques of modal synthesis when ferrite loaded structures are considered. 426 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 ACKNOWLEDGMENT I feel particularly indebted to R. C. Fletcher and H. Boyet for their many valnable comments and suggestions. REFERENCES 1. D. Polder, Phil. Mag., 40, p. 99, Jan., 1949. 2. H. Suhl and L. R. Walker, B.S.T.J., 33, 3, May, 1954. See Fig. 9g, p. 615, and Table I, p. 642. 3. G. H. B. Thompson, Nature, 175, p. 1135, June 25, 1955. 4. A. L. Mikaelyan. Dokladv, A. N. USSR, 98, 6, pp. 941-944, 1954. 5. H. Seidel, Proc. I.R.E., 44, p. 1410, Oct., 1956. i Measurement of Dielectric and Magnetic Properties of Ferromagnetic Materials at Microwave Frequencies By WILHELM VON AULOCK and JOHN H. ROWEN (Manuscript received August 15, 1956) Some experimental techniques are discussed which permit measurement of the magnetic and dielectric properties of ferrite materials in the micro- wave region by observing the perturbation in a cylindrical cavity due to insertion of a stnall ferrite sample. A comparison of the properties of thin disc samples with those of small spheres shows that discs yield more accurate results in the region below ferromagnetic resonance whereas spheres are pre- ferable for the study of ferrite properties near resonance. A short description of instrumentation for cavity measurements at 9,200 mc is given and experi- mental results of disc measurements are reported for a low-loss BTL ferrite and several disc diameters. A cornparison of experimental results with Polder's theory indicates that the loss of poly crystalline ferrites below reson- ance is considerably lower than that predicted from an evaluation of the width of the resonance absorption line. 1. INTRODUCTION The dielectric and magnetic properties of semi-conducting ferromag- netic materials such as ferrites have been the subject of intense study in recent years. Analytical expressions for the components /z and k of the permeability tensor of a loss-free single-crystal ferrite were derived by Polder. 1 These expressions were later modified to include a loss factor a.~- 2 Yager and others'* measured the resonance absorption of single crystals of nickel ferrite and found very good agreement with theoiy provided the loss factor a was determined from the width of the meas- ured resonance absorption line. However, when Artman and Tannen- wald^ measured the real and imaginary parts of m and k for polycrj'stal- line ferrites they found that agreement with theory was somewhat less than perfect if a was also determined from the measured line width. Discrepancies were observed for both real and imaginary parts of /i + 427 428 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 K in the region below resonance because the effects of polycrystalUne structure and anisotropy forces were neglected in Polder's and Hogan's^ analysis. Furthermore, it was assumed in the derivation of the perme- tihility tensor that the ferrite is saturated with a biasing dc magnetic field which is large compared to Ihe microwave magnetic field. There exists a great need for experimental data for all those conditions where some of the above assumptions do not hold. In particular, the region of biasing magnetization between zero and ferromagnetic reso- nance is of interest because it is the operating region for many ferrite devices such as phase shifters, modulators, and field displacement iso- lators. Techniques for the measurement of ferrite parameters below resonance were investigated and it was found that the measurement of the perturbation of a degenerate cylindrical cavity by a thin ferrite disc yielded accurate results, whereas observation of the cavity perturbation caused by a small sphere produced less accurate data. It is the purpose of this paper to describe and discuss the thin disc method and to compare it with other techniques described in the litera- ture.^' ^ After defining the ferrite parameters as constants in Maxwell's equations it is shown how these parameters can be obtained from various measuring techniques. Instrumentation for the thin disc tech- nique is described and a few remarks are made pertaining to experi- mental difficulties. Finally, some measurements of low-loss ferrites are reported and compared with values predicted bj^ Polder's relations. 2. DESCRIPTION OF FERRITE PARAMETERS It is customary^ to define the electric and magnetic polarization vec- tors P and M in terms of the field vectors E (electric field intensity), T) (electric displacement), l} (magnetic field intensity), and B (mag- netic induction). In the M.K.S. system we have: P =D - £oE M = B/fio - S €o = 8.854 X 10"^^ farad/meter, permittivity of free space Mo = 4x X 10~^ henry/meter, permeability of free space Then, the intrinsic parameters of a ferrite medium are defined as those quantities which relate P and M to the electric and magnetic fields in the medium respectively. P = fox J ill = Tn^ Whereas the electric susceptibility Xe is a scalar quantity in ferrites the MEASUREMEXT OF DIELECTRIC AHD MAGNETIC PROPERTIES 429 magnetic susceptibility Xm is known to have tensor properties. Assum- ing that the static magnetic field Hr is in the ^-direction we have Xm — Xm -JK u JK Xm 0 0 0 0 (1) If we restrict ourselves to sinusoidal time variation of the RF fields we may describe electric and magnetic losses in the ferrite bj' regarding Xe , Xm , and K as complex quantities: Xe Xe Xm ^^ X" JXe ■ jXr. ^ = k' - Jk" Thus, it is seen that the RF properties of a ferrite medium regardless of geometry are completely described by six "intrinsic" parameters, Xe', Xe" , Xm , Xm" , K , SLiid k" . The diclectric constant e and permeability TT of the material are obtained from £ = Xe + 1 "m = x^ + 1 where 1 is the unit matriix. It is the objective of the measurement to obtain each of the above parameters as a function of one or more variables of interest such as frerjuency, saturation magnetization, static magnetic field, temperature, applied power and others. Aleasurements may be made on single ferrite crystals — ■ mostly for research purposes — or on polycrystalline ma- terial for many purposes in connection with the development of ferrite materials and devices. These measurements are generally compared to the behavior of Xm and k as predicted by Polder's equations. One ob- tains from the equation of motion of magnetization^ Xm = M — 1 = CO' (0 \y\M. ym,^ - 0,2 Using Suhl and Walker's notation this may be WTitten as _ po- Xm ~ft "7 (T^ — I V - 1 430 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 where p — \y \ M,/co normalized saturation magnetization a- = I 7 I H,/cc normalized static magnetic field in the ferrite I 7 I = 2.8 mc per oersted, gyromagnetic ratio CO = operating frefjueney It appears that some cavity techniques measure the eigenvalues of (1), Xm + K and Xm — K, directly, which are seen to be Xm±K= -^ (2) Suhl and Walker show that a loss term may be introduced by replacing 0- by (7 + 7a:(sgn p) in (2).* Separating real and imaginary parts we get > , r _ p{a ± 1) . . ^" ■ ~ (cr ± ly + a' ^^ „ , apisgn p) , For the determination of a from measurements it is convenient to define a loss tangent Xm" ± k" ^ a(sgn p) ^ dz K (T ± 1 5± = 7—. T = T-T— <^^) Typical curves for Xm ± k and 8^ assuming p = 0.5 and a = 5 X 10^' are shown on Figure l.f For the purpose of describing and comparing experimental results, it may be convenient to distinguish among various regions of H^ as indicated on the graph because a difTerent measurement technique may be required for accurate measurements in each region. 3. METHODS FOR MEASURING MAGNETIC PROPERTIES Three measurement methods have been reported in the literature all of which employ the detuning and change in 1/Q of a resonant cavity by a small ferrite sample. Ya,n Trier used very thin long cylindrical samples in a coaxial cavity. Artman and Tannenwald" emploj^ed small spheres, and we used thin discs^ both placed close to the endwall of a cylindrical degenerate cavity excited by a TEm mode (Figs. 2 and 3). Recently, Berk and Lengvel suggested the use of a cylindrical post at the center * By definition sgn p = +1 for p > 0 and sgn p = — 1 for p < 0. t Since it is customary to use Xm + k for the designation of the resonance line this notation has been used here. Consequentl}', p and a shovild be assumed nega- tive. MEASUREMENT OF DIELECTRIC AND MAGNETIC PROPERTIES 431 +1 -4 A \ / Xm-A-' ^^ — "s x;„+/r' ^ ^ > \ ,\j 12 10 8 + Q Z 6 + 2 «-- UNSATURATED < BELOW RESONANCE >|<- RESONANCE ->t«--ABOVE RESONANCE — > . p =1 r\M^/u> = o.b a = 0.05 i \ I 1 ' 1 Xm*«- m-L , \ / — -^ 1 \m ~ A" Jj v\. n -X^ ^^— -= 0.10 —7 0.05 O Z I 0.2 0.4 0.6 0.8 1.0 1.2 NORMALIZED STATIC MAGNETIC FIELD, (7 = 14 1.6 1.8 Fig. 1 — Theoretical values of Xm ± k and loss tangent 5± versus normalized static field a. of a degenerate rectangular cavity.* In principle, all these methods per- mit the determination of the six parameters Xe', x/j x™', Xm , «', and k" . However, in practical applications there are significant differences, e.g., * As this paper was being written another variation of the thin cylinder tech- nique using the TMuo mode in a circular cavity was reported by Spencer and LeCraw at the I.R.E. Convention, New York, Mar. 21, 1956. 432 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 between the use of a spherical sample and a thin disc, such as the per- turbing effect on the cavity field, the accuracy of small loss measure- ment, the occurrence of resonance at a static field where the intrinsic parameters are not at resonance, and the possibility of making accurate measurements of the electric susceptibility. Therefore, the sphere method and the disc method will be reviewed briefly and an attempt will be made to compare their capabilities. It is hoped that this comparison will also be helpful for the evaluation of other measuring techniques not covered in this paper. 3.1 The Small Sphere Method In order to appreciate the significance of the quantities measured with the small sphere method it is expedient to define an effective suscep- tibility tensor Xms by relating the magnetization vector* to the applied ^-L=Xg/2— I H. Fig. 2 — Degenerate TEui cylindrical cavity with ferrite sphere. [-- L=Xg/2--| H, Fig. 3 — Degenerate TEm cj'lindrical cavity with ferrite disc. * R. A. Waldron (Institute of Electrical Engineers, Convention Oct. 29 to — ♦ Nov. 2, on Ferrites, London, 1956) related the magnetic induction vector B in a MEASUREMENT OF DIELECTRIC AND MAGNETIC PROPERTIES 433 field //° and observing that the RF components of M and IT (denoted by lower case letters) are related in a cylindrical coordinate system by 7 0 • 7 0 nir = Xms'lr " JkJ10 me = jKjir + -Kmshe Placing the small ferrite sphere close to the endwall of the cavity (Fig. 2) and observing the splitting of the resonance into two frequencies co± (related to the positive and negative circularly polarized modes) and the two changes in 1/Q of the cavity after application of a static magnetic field in the axial direction leads to two measurable quantities Acoj. = ojd — coj. frequency shift A(l/Q)^ = l/Q± — l/Qo change in internal Q of the cavity where coo and Qo are resonance freciuency and Q of the empty cavity. It can be shown that real and imaginary part of Xms and Ks can be ob- tained fromf ^^'^^ = 0.6982 )i ■ ii (x./ ± ./) (7) COo 7)2 L Xo do 3 3 A(l/Q)± = 0.6982 ^ • ^ (xms" ± Ks") (8) The quantities do , D, and L are the sphere diameter, cavity diameter and length respectively, Xo is the wavelength in free space associated with COo . In order to obtain the intrinsic parameters Xm and k from (7) and (8) one may use the relationships'" Il° =^ H + M/S (9) 3(xm ± k) . . Xms db /Cs = -— (10) Xm ± K + 3 \ * *-♦ - 4-» sphere to the applied field by writing — B = MsH^ where jus may be designated the Mo external relative permeabilitj^ tensor. It can be readily shown that Waldron'sre- suits are in agreement with ours if one notes that (2/3)xms = ms — 1- We found that the use of the effective susceptibility tensor Xms is much to be preferred over Us because it simplifies notation and interpretation of experimental results in terms of the intrinsic quantities X"> and k. t Equations (7) and (8) are identical to Artman and Tannenwald's^ expressions, if 47r2Z)V(13.56 + irWyi^) is substituted for Xo^. 434 THE BELL SYSTEM TECHNICAL JOURXAL, MARCH 1957 Equation (10) luijs a pole at %,„ ± k = —3 which simply indicates the resonance condition for a sphere as derived by Kittel.^° This can be verified from (2) : Xn.±K = -^ (11) cr rb 1 Xote that p and o- are either both positive or both negative, hence, only one of the two ciuantities (xm + a) or (xm — k) goes through resonance at I 0- I = 1. A similar situation exists for Xms ± Ks expressed in terms of (11) ^""^ "^ "' ^ V+W±T) ^^^^ One of the two quantities (xms ± Ks) goes through resonance at U l« = 1 - I P 1/3 (13) Observing that the field in the sphere is given bj^ (9) this may be written as = H. + MJZ = H,' (14) ItI (Kittel's resonance frequencj^ of a ferrite sphere) It is easily seen that this resonance of the spherical sample makes the evaluation of Xm and k from (10) rather unattractive because one would expect inaccurate results for Xm and k in the vicinity of the sphere reso- nance as . Furthermore, for all numerical computations (10) must be separated into real and imaginary parts / , ' _ Q (Xm' ± k' + 3)(xm' ± li') + iXm" + k") /, -^ """" ^'' -'^ (x.' ±k' + 3y + ixr." ± K'y ^^^^ ■V " -I- '" / ' _. / ' Q Xm ^t li (I r\ Xma ± Ks —if , , / , qN" r / 'ii~^ vy) ^^^! yXm ± K + 3j- + \Xm ± K )- In general higher order terms of Xm" and k" ma}' be neglected, but in the vicinity of sphere resonance these terms predominate as the term Xm ± k' + 3 vanishes. It can be seen from the preceding discussion that the determination of Xm', Xm", «', and k" from Xms and k^ has its difficulties. Fortunately, there is an easier way to the interpretation of Xms and Ks in terms of the intrinsic parameters Xm and k. "We use (9) to define a new quantity ® u > o wv X ■fr ■fr Q z o u in tr CL I ■^ (-Q. ttZ u — > ^ ^s(V oz UJ LiJ tri- '5 I- li- ^)<^ VA o I- > _) X n. ■I ^ u o q: ►r . rt o o a z ui cj o o '^ u O X z i^ ^UJ O o (3 cc o <=!Q. IJUI- O "5 D _lOO ■^ tr Ul h- Z 3 O o 111 n n • O 01 u -i^ -J (U -I c O I cc o _) o in tr ■O- Hi' 1 MEASUREMENT OF DIELECTRIC AND MAGNETIC PROPERTIES 439 5. INSTRUMENTATION Our measurement technique has been influenced by a number of prac- tical considerations including the need for determining accurately and quickly a figure of merit for a large number of different ferrite materials. In particular, a variety of low loss materials has become available in experimental quantities requiring a precise technique for measuring small loss factors below resonance as a guide for further ferrite develop- ment. Therefore we were faced with the problem to develop an instru- mentation capable of measuring these small loss factors but simple enough to be operated without detailed knowledge of microwave tech- niques. Fortunately the use of thin discs permits us to introduce a fairly large volume of ferrite into the cavity without violating the basic as- sumption of a small perturbation. As a consequence frequency shifts of the order of 10 mc are obtained at static magnetic fields just sufficient to saturate the material. Thus the quantities Xm' and k' may be measured without difficulty in the regions below and above resonance. The thickness of the disc should be chosen to attain an aspect ratio (diameter/thickness) of 50 or larger. Discs of 0.005 to 0.007-inch thick- ness were employed in actual measurements at 9200 mc. For a typical measurement of a 0.005-inch disc at 9200 mc, a change of 1/Q of about 2 per cent corresponds to a loss term Xm" -f- /' = 2 X 10"*. Measure- ment of Q with a reproducibility of 1 per cent has been accomplished initially by careful work, and it has been our objective to maintain this accuracy in routine measurements by semiskilled operators. This re- quired the use of rather elaborate circuitry for the precise measurement of the changes in l/Q of the cavity. Although most of these techniques have been used before in the field of microwave spectroscopy we hope that the description of this instrumentation will be of interest. Fig. 5 shows a block diagram of the circuit. A klystron Type V58 (Varian Associates) is swept through a frequency band of about 80 mc at X-band. The resulting signal with a center frequency of 9,200 mc is used to excite a TEm mode cylindrical cavity. Incident and reflected signals are separated by means of directional couplers and displayed on an oscilloscope. Both signals can be aligned with the aid of a shorting gate and a precision attenuator in front of the cavity. The reflected signal shows clearly the cavity resonance which splits into two if a ferrite disc is placed against the endwall of the cavity and magnetized along the cavity axis. One of the major problems of the measurement is the accurate deter- mination of these new cavity resonance frequencies and of the line width of the displayed resonance curves between half-power points. In the 440 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 solution of this problem, more than ordinary emphasis was placed on ease of operation and elimination of ambiguities in the frequency de- termination. The resulting instrumentation uses as a stable reference frequency a crystal-controlled oscillator and a frequency multiplier which yields three reference frequencies; 55.8, 223.3 and 4,020 me. These are mixed in a crj^stal harmonic generator and mixer leading to a line spec- trum of numerous reference frequencies with a constant spacing of 55.8 mc. The same crystal mixer produces a beat frequency signal between the incident signal from the kl3\stron and each of these reference fre- quencies. A communication receiver with modified IF stage permits selection of a frequency marker out of these beat frecjuency signals. This marker appears as a blank spot on the traces of incident and reflected signal, and can be moved to any desired point bj^ simply changing the frequency setting of the receiver. Since the receiver dial cannot be read with great accuracy on the high frequency ranges, a frequency counter connected with the local oscillator of the receiver permits a reading of the oscillator frequency to an accuracy of 1 kcps. Noting that the local oscillator is 0.455 mc removed from the difference signal, one obtains the frequency of the difference signal with more than sufficient accuracy. 6. Results of Measurements Transmission- and reflection-type cylindrical cavities have been em- ployed for measurements with linearly and circularly polarized excitation in the 6,000- and 9,000-mc frequency bands. Circular polarization is pre- ferable in the region below saturation where frequency shifts are small. It is not necessary to choose ferrite discs of relatively small diameter for the purpose of staying within the region of circular polarization close to the cavity axis. The derivation of Xm ± k is not restricted to circularly polarized fields, and the result takes into account that the field becomes more and more elliptically polarized as one approaches the edge of the cavity. This can be seen l)y rewriting (19) and (20) as follows: X"/ ± k' = ^^^^^^^ [Acoi (/?! + R,) - Aco^ (i?i - 7?2)] xn," ± k" = ^^^ [A(l/Q)±(/?i + R-^ - Ml/QURr - i?2)] (26) where F = t\o-/{2U). The factor (/?i — 7? 2), which is zero for circular polarization, corrects the values for x». ± k if the disc extends into the region of elliptical MEASUREMENT OF DIELECTRIC AND MAGNETIC PROPERTIES 441 polarization. For relatively small discs {Ri = R2), one obtains Xm' ± k' = „„ Aa)± 2^ oioFRi (27) xJ' ± k" = ^A(l/Q)± A large number of measurements was made with a half-wave, reflec- tion-type cavity and linearly polarized excitation. Some typical results Avill be discussed below to demonstrate the applicability of the disc technique. The frequency shift measurements and x»/ ± 1^' for a ferrite material of 1,300 oersted saturation magnetization are shown on Fig. 6. The ferrite disc has a thickness of 0.0063 inch and completely covers the endwall of the ca^'ity. If the field in the cavity were circularly polarized throughout, then the freciuency shift would vary as x»/ ± «'• However, elliptical polarization causes a deviation of the measured curves for Aco_t from Xm ± k'. Agreement between theoretical and experimental values of Xm' ± k' is good in the regions below and above resonance. Measurements in the resonance region are not possible with a disc of this size because frequency shift and change in Q are so large that the assumption of a small perturbation is violated. In order to establish further that measurements of Xm' ± n' are independent of disc diameter three discs of the same material (saturation magnetization 1300 oersted) with diameters of 0.249, 0.400, and 1.050 inches were measured in the aboA'e-mentioned cavity. Plots of x»/ and k' (Fig. 7) indicate good agree- ment for k' and some scattering of values for Xm'- This can be explained by noting that the resonance frequency of the empty cavity enters into the computation of Xm', but cancels out for k (equation 19). Conse- quently, a very small change in the length of the cavity, as might be ex- pected from opening and reassembling the device, will produce a notice- able error in the low-field region. A change in cavity length of 10~^ inch will produce a freciuency shift of 1 mc at an operating frequencj^ of 10,000 mc and introduce an error of the order of 0.02 into the measure- ment of Xm'- This error may be minimized by using a relatively large disc. Discs Avith a diameter of 0.4 inch yielded good measurements of the imaginary quantities Xm" ± k" in the low-field region. A typical result for a low-loss ferrite (Fig. 8) show\s the measured quantities A{l/Q)^ and the corresponding Xm" ± k" as a function of the applied magnetic field. (The internal field in the ferrite is obtained by subtracting the magnetization from the applied field). It is noted that only A{l/Q)_ can be obserA-ed in the resonance region, whereas A(l /Q)+ becomes too 442 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 60 40 CO 20 ui _l o >- o < o uJ 0 2 +1 < -20 -40 \ Au; + HICKNESS =0.00617 INCHES i;o=92IO MC (EGION WHERE /lEASUREMENTS \RE IMPRACTICAL ra-f v. .'' ~-^. """^ •■ \ ^^ Au;_ — ^^ AaJ+* \ 1.6 1.2 0.8 0.4 +1 -0.4 ■0.d -1.2 A THEORETICAL VALUES MEASURED VALUES ^m-A ; ■ ^ -^T^- ^ . x'-a:' — __. - ^^^^ \ « V « I I 1000 2000 3000 4000 5000 6000 7000 H .APPLIED FIELD IN OERSTEDS Fig. 6 — Evaluation of x'm ± k' from measurements of frequency shift Aa>± and comparison with Polder's theory. Low-loss BTL ferrite, saturation magnetization 1300 oersted. MEASUREMENT OF DIELECTRIC AND MAGNETIC PROPERTIES 443 1000 2000 3000 4000 5000 6000 H, APPLIED FIELD IN OERSTEDS 7000 Fig. 7 — Measurement of x-™' ^nd k' versus applied static field for three differ- ent discs, cut from the same ferrite block. large to be measured. Knowledge of A(l/Q)_ is not sufficient to determine Xm" — k" in the resonance region because here the correction term A(l/Q)+(/?i — i?2) (cf. ecjuation 26) becomes comparable to the term A(l/Q)-(/?i + R'l) and is needed to compensate for the anomalous peak of the A(l/Q)_ curve. The loss parameters Xm" ± k" assume values of the order of 10~- below and above resonance. The estimated error of the measurement is 3 X 10~'. 444 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 O z < X o 0.03 0.02 5C +1 0.01 ,,,,, .J,,,....... ,.,... .x1:.:.:.:.:.:.:.>:.:M.:. \ 1 \ i 1 ,:-; ^ <,-a:" 1 1 1 1 - 1 \ ■ \ \^'r^^fc" ' y' X ^ ^^^_ <^^ ^y -J— .... -4 ^ — - •••••.. ^ 1000 2000 3000 4000 5000 h",applied field in oersteds 6000 7000 Fig. 8 — Evaluation of xm" ± k" from measurements of A(l/Q)± for low-loss BTL ferrite, saturation magnetization 1300 oersted. Whereas it is possible to obtain good agreement between measured and theoretical curves of Xm' ± k from Polder's relations (3), such an agreement cannot be obtained for Xm" ± k" from a comparison with (4). This discrepancy is assumed to be caused by the fact that Polder's theory was developed for single ferrite crystals and did not take into account the random orientation of crystal axes in polycrystalline ma- terials, such as the ferrites used in these measurements. It is reasonable to expect a broadening of the resonance line and a departure from the Lorentzian shape in polycrystalline ferrites; hence, the expression for the absorption line (4) no longer holds. Measurement of the electric susceptibility of ferrites did not present any major difficulties, provided some care was used in the suspension of the discs at the cavit}' center. Summing up these results it may be said that the disc method has 3'ielded satisfactory measurements of the intrinsic parameters of poly- crystalline ferrites below and above resonance as well as in the un- MEASUREMENT OF DIELECTRIC AND MAGNETIC PROPERTIES 445 saturated region. ^Measurements of single crystals and of resonance curves with this method have not yet been made. It is anticipated that in both cases smaller and thinner discs would be needed than have been available so far. However, it can be hoped that these difficulties will be overcome in the near future and that the disc method will be useful also for the study of ferromagnetic resonance phenomena. Appendix perturbation of a degenerate cylindrical cavity due to a thin DISC The general perturbation equation for a lossless cavity can be derived from energy considerations or directly from Maxwell's equations. We obtain for the shift of resonance frequency due to a small perturbation: ^ / w-^* dv + - P-E'^^ dv u) , TT^ w c^o ,,, r -^ -. . . W'^' Jvi coo resonance frequency of the empty cavit}^ coi resonance frequency of the cavity after insertion of the perturbing sample h^ magnetic field intensity vector in the empty cavity E electric field intensity vector in the empty cavity vi volume of sample V2 volume of cavity * indicates the conjugate value The denominator in (Al) indicates the total energy TF^'^ stored in the empty cavity at resonance, whereas the numerator is equal to the addi- tional magnetic energy TF^^^^ and electric energy We^^ stored in the perturbing sample. Equation (Al) is valid if the frequency shift is small. Aoj _ oji — 0)0 coo 1 COo « 1 (A2) and if the field in the cavity remains essential!}' unchanged after insertion of the sample. In order to apply (Al) to the determination of the tensor components Xm and k we should attempt to satisfy three conditions: the electric field should vanish at the sample, the magnetic field should be normal to the static magnetic field, and the relationship between RF 446 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 magnetization m and RF magnetic field hP in the cavity should be sim- ple. All three conditions can be satisfied if a thin ferrite disc is placed against the endwall of the cavity (Fig. 3). Noting that the tangential component of the magnetic field intensity is continuous at the plane face of the disc we have: 7 0 • 7 0 nir = Xmhr — JMe me = jKhr + Xmhe Inserting (A3) into (Al) we find the additional magnetic energy stored in the disc Wj'^ =^ [ [x.Xhr%'* + /l«%°*) +JK{hr%'* - /l,0/l,0*)] dv (A4) Z Jvi In order to evaluate (A4) we use the fact that the TEm-mode can be expressed as the sum of two circularly polarized modes rotating in opposite directions Thus, we have hri.2 = B — Ji{kcr)e^^' cos ^z rCr. (A5) he J = ±jB y^ J,{Kr)e'^^' cos ^z (A6) hzi,2 = BJiikcrje"^^^ sin ^z B ./i ^ = = (i3o' - h r) kc = Pi'/a /3o = 27r/Xo L Xo a Xa = 2L Pi' = 1.841 Eri.2 = zhB^ MKr)e'^'' sin ^z Eei.2 = jB ^" J,'(kcr)e^'' sin ^z kc amplitude factor Bessel function of the first kind propagation constant in the ^-direction propagation constant in the r-direction propagation constant in free space length of cavity wavelength in free space radius of cavity wavelength in the cavity first zero of the derivative of Ji (A7) MEASUREMENT OF DIELECTRIC AND MAGNETIC PROPERTIES 447 Integration of the electric or magnetic field over the volume of the cavity yields the stored energy in the empty cavity at resonance for one of the two circularly polarized modes W''' = 0.2387 ^° • f^' B'a'L (A8) 4 kc^ The magnetic energy Wj'^ in the disc is found by integrating (A4) over the volume of the disc and assuming that the field is constant over the thickness t of the disc. We obtain: Wj" = 0.2387 "^ f- BVtixmR, ± kU.} (A9) The two functions Ri and Rt depend on the ratio of disc radius to cavity radius R, = 4.1893 ^ ^{J,{Kn)Y + [l- -^}j (J,(/c,ro))'] (AlO) Rt = 2.4720 (Ji(/Ccro))' (All) It is interesting to note that these two functions are approximately equal (Fig. 4) if the disc radius is less than half the cavity radius. In this region the field in the cavity is essentially circularly polarized, whereas elliptical polarization exists near the wall of the cavity. Inserting (A8) and (A9) into (Al) we find the desired relationship between the two frequency shifts associated with positive and negative circular polarization and the tensor components Xm and k. 2, ojo 2 L^ Equations (Al) and (A12) hold for complex Xm and k if a complex frequency shift is introduced as follows: c?(y = CO — ojo + j{cx — ao) (A13) The attenuation constant a may be defined in terms of the internal Q of the cavity, a = §co/Q and the internal Q is defined as ^ _ w (energy stored in circuit) average power loss Thus, the imaginary part of the frequency shift may be expressed as the difference between (l/Q) of the perturbed cavity at the new reso- nance frequency w and (1/Qo) referring to the empty cavity at wo . A(l/Q) = ^ - ^ = 2 ^^LZL^ (A14) We note that the imaginary part of the right hand side of (Al) does indeed represent the power dissipation in the perturbing sample over the stored energy times co. Hence, taking the imaginary part of (A12) 448 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 we have a relationship between the change in (l/Q) and the loss terms Xm" and k" A(l/Q)± = ^ ^ (xJ'i^i ± k"R2) (A151 Clearly, (A 15) holds only if the initial Q of the empty cavity is very high and the change in Q is quite small. The electric susceptibility of the ferrite disc can be obtained in a similar way, provided we place the disc at the cavity center where the electric field has a maximum. Then, the additional electric energy stored in the disc is found to be We'-' = 0.2387 ^ Moxe p B'ahR^ (A16) It should be noted that there is an important difference between loca- tion of a thin disc at the endwalls and at the center of a C3'lindrical cavity. Whereas the electric field at the endwall may be neglected en- tirely, the magnetic field at the cavity center has a component parallel to the cavity axis. The effect of this component bn the stored energ}' in the disc may be minimized by magnetizing the disc beyond saturation in the ^-direction. With the assumption that the effects of the magnetic RF field may be neglected we obtain relationships for the electric susceptibility and electric loss factor: 2(AC./C0o) - jMl/Q) = iXe' - jXe") ~{ /?! (Al7) Since Xe is a scalar quantity there is no splitting of the cavity resonance^ j ACKNOWLEDGMENT We would like to thank L. G. ^"an Uitert who supplied the ferrite ma- terials, Barbara De Hoff who did all of the numerical computation and Edward Kankowski who made most of the measurements shown herein. REFERENCES 1. D. Polder, Phil. Mag., 40, p. 99, 1949. 2. C. L. Hogan, Rev. Mod. Phys., 25, p. 253, 1953. 3. H. Suhl and L. R. Walker, B.S.T.J., 33, p. 579, 1954. 4. W. A. Yager, J. K. Gait, F. R. Merritt, and E. A. Wood, Phys. Rev., 80, p. 744, 1950. 5. J. O. Artman and P. E. Tannenwald, J. Appl. Phvs. 26, p. 1124, 1955. 6. A. D. Berk and B. A. Lengvel, Proc. I.R.E., 43, p. 15S7, 1955. 7. A. A. Th. M. Van Trier, Appl. Sci. Res., 3, p. 305, 1953. 8. J. Stratton, Electromagnetic Theorj-, Chapter 1, McGraw-Hill Book Co., New York, 1941. 9. J. H. Rowen and W. von Aulock, Phvs. Rev., 96. p. 1151, 1954. 10. C. Kittel, Phys. Rev., 73, p. 155, 1948. Sensitivity Considerations in Microwave Paramagnetic Resonance Absorption Techniques By G. FEHER (Manuscript received February 9, 1956) This paper discusses some factors which limit the sensitivity of microwave paramagnetic resonance equipments. Several specific systeins are analyzed and the results verified by measuring the signal-to-noise ratio with known amounts of a free radical. The two most promising systetns, especially at low powers, employ either superheterodyne detection or barretter homodyne de- tection. A detailed description of a swperhetrodyne spectrometer is given. Table of Coxtents Page I. Introduction 450 II. General Background 450 III. Q Changes Associated with the Absorption 450 IV. Coupling to Resonant Cavities for Maximum Output 451 A. Reflection Cavitj^ 452 1. Detector Output Proportional to Input Power 453 2. Detector Output Proportional to Input Voltage 454 B. Transmission Cavity 455 1. Detector Output Proportional to Input Power 455 2. Detector Output Proportional to Input Voltage 456 V. Minimum Detectable Signal Under Ideal Conditions 457 VI. Signal-to-Noise in Practical Sj'stems 459 A. General Considerations 459 1. Why Field Modulation? 459 2. Choice of Microwave Frequency 460 3. Optimum Amount of Sample to be Used 461 a. Losses Proportional to E- 461 b. Losses Proportional to Hi^ 462 B. Noise Due to Frequency Instabilities 462 C. Noise Due to Cavity Vibrations 465 D. Klystron Noise 465 E. Signal-to-noise Ratio for Specific Systems ,. 466 1 . Barretter Detection 467 a. Straight Detection 469 b. Balanced Mixer Detection 470 2. Crystal Detection 472 a. Simple Straight Detection 473 b. Straight Detection with Optimum Microwave Bucking 473 c. The Superheterodyne Scheme 475 F. Experimental Determination of Sensitivity Limits 477 1. Preparation of Samples 477 2. Comparison of Experimental Result with Theory 478 449 450 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 Page VII. A Note on the Effective Bandwidth 480 VIII. Saturation Effects 482 IX. Acknowledgement 483 I. INTRODUCTION Within the past few years the field of paramagnetic resonance ab- sorption has become an important tool in physical and chemical re- search. In manj^ ways its usefulness is limited by the sensitivity of the experimental set up. A typical example is the study of semiconductors in which case one would like to investigate as small a number of impuri- ties as possible. It is the purpose of this paper to analyze the sensitivity limits of several experimental set ups under different operating condi- tions. This was done in the hope that an understanding of these limita- tions would put one in a better position to design a high sensitivity electron spin resonance equipment. In the last section the performance of the different experimental arrangements is tested. The agreement obtained with the predicted performance proves the essential validitj' of the analysis. This paper is primarily for experimental phj'sicists con- fronted with the problem of setting up a high sensitivity spectrometer. II. GENERAL BACKGROUND We will not consider here the detailed theory of the resonance phe- nomenon but consider this part of the problem only from a phenomeno- logical point of view. When a paramagnetic sample is placed into an RF field of amplitude Hi of a frecjuency w at right angles to which there is a dc magnetic field Ho , magnetic dipole transitions will be induced in the neighborhood of the resonance condition /ico = gmo (1) where g is the spectroscopic splitting factor, h is Planck's constant and /3 is the Bohr magneton. As a result of these transitions power will be absorbed from the microwave field Hi . This power absorption is asso- ciated with the imaginary part of the RF susceptibility x" ■ The trans- mitted (or reflected) Hi will also experience a phase shift which is associated with the real part of the RF susceptibility x'- The sensitivity of the setup is then determined by how small a power absorption (or phase shift) one is able to detect when going through a resonance III. Q CHANGES ASSOCIATED WITH THE ABSORPTION The average power absorbed per unit \olume of a paramagnetic sample is P = ^o^HiY (2) MICROWAVE PARAMAGNETIC RESONANCE ABSORPTION 451 For low enough powers x" is not a function of Hi (and even for very high powers never drops off faster than \/Hi), so that for a large power ab- sorption one would like a large RF magnetic field. This suggests a re- sonant cavity which indeed is used in all experimental setups. The Q of a cavity into which a paramagnetic sample is placed is given by 'dV. 1 f H' Q ^ Energy Stored ^ Sr Jy^ ^ ,^. Average Power Dissipated IT 2 // Pi -f - CO / Hix dV, z Jv, where Pi = power dissipated in the cavity in the absence of any para- magnetic losses, Vs is the sample volume and Yc the cavity volume. Assuming that the paramagnetic losses are small in comparison with Pi we get f H;YdVs \ Hi' dVc / (4) /. AQ = QoAiirx V where Qo is the cavity Q in the absence of paramagnetic losses and 17 is the filling factor and depends on the field distribution in the cavity and the sample. For example, in a rectangular cavity excited in the TEioi mode T7 A (5) where d is the length of the cavity and a the width along which the E field varies. In the above example it was assumed that the sample is small in comparison to a wavelength and is placed in the max. Hi field. IV. COUPLING TO RESONANT CAVITIES FOR MAXIMUM OUTPUT Having established the Q changes associated with the resonance absorption, we will next determine the proper coupling to the resonant cavity in order that the Q changes result in a maximum change in trans- mitted or reflected power (or \-oltage). The derivation will be based on the assumption that we have a fixed amount of power available from our source and that the Q change is not a function of the RF power (no saturation effects). 452 THE BELL SYSTExM TECHNICAL JOURNAL, MARCH 1957 A. Reflection Cavity Fig. 1 shows a magic (liybrid) T which serves to observe the reflected power from the cavity. Arm 3 has a shde screw tuner which serves to balance out some of the power coming from arm 2. This does not affect the present analj^sis and will be considered later in connection with detector noise. It should be mentioned, however, that a certain ampU- tude or phase unbalance has to be left. This insures that the signal in arm 4 will be a function of either x' oi' x"-^ In the case that the magic T is completely balanced out the signal in arm 4 will be a function of both x' and x" and the experimental results become difficult to analyze. Fig. 2 shows the equivalent circuit for a reflection cavity.^ The \/2 in the source voltage arises from the fact that half the power is lost in arm 3. From this equivalent circuit we can define the following relations: Unloaded Q = Qo = — (Losses due to cavity alone) r External Q = Qx = Loaded Q = Ql = coL (Losses arising from power Ron^ leaking out of the cavity) coL (Losses due to both cavity Rou^ + r and leakage out) (6) (7) (8) MAGIC _ SLIDE T^r- SCREW TUNER SIGNAL SOURCE AP, ^>^ DETECTOR — CAVITY C Fig. 1 — A simple arrangement to observe the reflected power from cavity C. Ron^ r C ■^TT nm^ — 2 i:n L L Fig. 2 — Equivalent circuit for a reflection cavity. MICROWAVE PARAMAGNETIC RESONANCE ABSORPTION 453 We define the coupling coefficient /3 = Qx/Qa such that: Critically coupled cavity j8 = — ^ = -^— = 1 (9) Overcoupled cavity ^ > 1 VSWR = /3 = ^ (10) Undercoupled cavity ^ < 1 VSWR = 1 = -^, (11) We will see that the coupling coefficient for maximum output depends on the characteristics of the detecting element. Two cases will be treated: the power (square law) detector and the voltage (linear) detector. 1. Detector Output Proportional to Incident Power Power into the cavity at resonance r Vn V ^' \\/2) (Ron^ + ry Max. power available from source (in arm 1) (VnY „ „ 2Ronr Pc = P 0 " 4/?on2 " {R,n^ + rf The change in reflected power APr equals the change in the power inside the cavity APc (since the incident power stays the same). AP. = ^ Ar = 2Pon^Po ,g"^' ~ ' Ar (12) dr {Ran + ry We want to optimize APc with respect to the coupling parameter n^ (or Rm^), i.e., .-. ^ = 2 ± V3 r the positive sign being associated with the overcoupled, the negative with the undercoupled case. The experimentally measured quantity is the voltage stanchng wave ratio VSWR = 2 + \/3 = 3.74 correspond- ing to a reflection coefficient of 0.58. Putting this value into (12) we get for the maximum signal ^ = ± 0.193 - = =F 0.193 ^ = T (0.193)(47r)x"7?Qo (14) Po r Qo 454 THK BELL SYSTEM TEf'HXirAL JOURXAL, MARCH 1957 the last step being obtained with tlie aid of (4). Equation (12) is plotted in Fig. 4. From the symmetry of the graph it is obvious that for a given ^'8AVR, the signal will be the same for the overcoupled and undercoupled case. However, as we will see later from the standpoint of noise the 2 cases are not necessarily identical. 2. Detector Output Proportional to Input Voltage Let r be the reflection coefficient, then T'refl from the cavity is 2^'s^v Khefl - ^2 ^ " V2 VvswrTT/ " V2 1 - + ij \SWR With the aid of (10) and (11) this gives for the undercoupled case: _ JL( "^r \ and the overcoupled case ^ ^^^ " V2 V Tim' + r) We are interested only in the change of output voltage which is: A7rk.. = ^^ Ar = ± V2 FAr ^-^4^ (15) dr [Ron- + r)2 The two signs corresponding to the undercoupled or overcoupled case, respectively. In order to find the optimum coupling d(AV) d{Ron') = Ron - r = 0 rW_ ^ ^ r Putting this value into (15) we get the max. value ^Z552 = ± ^' ^_: = T ^ ^» = T 5^ 4.x",<3. (16) V 4 ;• 4i Qo 4 (15) is again plotted in Fig. 4. From this graph we see that for maximum sensitivity we want to work near match. However, one should not work so close to match that the absorption signal will carry the cavity through the matching condition while .sweeping through a resonance fine. This would result (due to the sign reversal of the signal at match) in a dis- torted line. Incidentally, the sign of the signal may be conveniently used MICROWAVE PARAMAGNETIC RESONANCE ABSORPTION 455 (a) Rl.= Ro DETECTOR (b) Fig. 3 — Equivalent circuit for a transmission cavity. to determine whether the cavity is overcoupled or undercoupled. This information may be necessary in Qo determinations.^- B. Transtnission Cavity Fig. 3 shows the equivalent circuit for a transmission cavity, the generator and the detector being matched to the waveguide, i.e., Rg = Rl = Ro Analogous to the reflection cavity we define again two coupling coeffi- cients ^1 = RoUi /32 = R(>ni r r the relation between the unloaded and loaded Q being Qo = Ql(1 + iSi + /32) 1. Detector Output Proportional to Input Power (18) (19) Power into load Pl = Tr2 "* ''t-> V Hi iii'Ro (i?or?i2 + r + Roni^y (Vn,y Max. power generator can deliver Po = dr 2V\i niRo {Ro7h' + r + RoUi') 4(ni2/?o) A/- (19) 456 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 In the case of the transmission cavity we have two coupling coefficients whose optimum value we have to determine. d(ni'Ro) d(:n,^Ro) (20) .*. ?ii 7?o = 712 Ro = r which means that the input and output coupling should be identical. Relation 20 looks superficially like a matching condition. However, it should be noted that the input impedance to the cavity contains besides the cavit}^ impedance the load impedance. Hence, the "\"SWR is Rou^ + r Ron^ which represents an undercoupled case. One never can overcouple a transmission cavit}^ with equal input and output couplings. Putting condition (20) into (19) we get: APl 8 Ar 8 AQo / 8 " Po 27 /• 27 Qo V27, 2. Detector Output ProportioJial to In-put Voltage The voltage across the load 47rx"r?Qo (21) ^» ^j. _ Vnin-iRo V L — Roni" + r + i^o^h' Again for max. sensitivity both couplings should be the same AVr AV, V dr ' [('• + 2Ro7hy'y] Ar ^^^ A .7? .,2 _ r din^Ro) ^ "^''' 2 1 Ar 1 AQo 1 _, 8 r 8 Qo 8 ''^ "iQ (22) (23) (24) Fig. 4 is a plot of (12), (15), (19), and (22). It should be noted that the sensitivities of the reflection cavity are normalized to the input of the magic T (in Fig. 1) and not to the input of the cavity as in the trans- mission cases. This results in a 3-db decrease in output and causes the power sensitivity of the transmission cavity to look relatively higher. However this is somewhat arbitrary since a balanced transmission type scheme would also require a magic T with an accompanying reduction in usable power. MICROWAVE PARAMAGNETIC RESONANCE ABSORPTION 457 All the previous sensitivity expressions are proportional to x"- For an unsaturated condition it may be replaced by x whenever the output is sensitive to phase changes in the cavity. It should be noted that we maximized the output from the detector. This will result in a maximum signal to noise ratio if the noise is a constant independent of the microwave power. This, however, is in general not the case and in the next section we will in\'estigate the signal to noise ratio taking into account its dependence on the RF power. v. MINIMUM DETECTABLE SIGNAL UNDER IDEAL CONDITIONS The minimum signal is ultimately determined by the random thermal agitation. Due to this cause the power fluctuates by an amount kT^v, where k is Boltzmann's constant, T the absolute temperature and Aj/ the bandwidth. The minimum detectable microwave power will be then of the order of kTAv. This is the problem one faces when designing sensi- tive microwave receivers. However, our problem is of a different nature. We want to detect a small change in the power level of a relatively large UNDERCOUPLED x(4 77r77Qo) OVER COUPLE D 0.3 \ N^ 0.2 1 Po (R.c.) '^^^ 0.1 1 0 0.1 0.2 0.3 0 /I AV (T.C.) /I > ^^^ ^ '^y / \ h } ^0 N \ 8 6 4 212 4 6 8 VOLTAGE STANDING WAVE RATIO Fig. 4 — Output versus V.S.W.R. for reflection and transmission cavity. 458 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 microwave signal. This change in power level will ha^•e to be consider- ably larger than kTAv before it can be detected.' The physical reason for this is that the fluctuating fields a.s.sociated with the noise power com- bine with the microwave fields to produce power fluctuations much larger than kTAv. It is more straightforward to compare noise voltages rather than powers, especiallj'' since the power changes are not neces- sarily a constant of the system. In Fig. 1 for instance, the power change in arm 4 is no whereas the power change in arm 2 (for the same voltage change) is APo = Rn It also shows that one wants to maximize the change in output voltage as was done in Section TV. The open terminal R^IS noise voltage of a system with an internal impedance Ro is given b\' Frms = V-iR^kTAv If we terminate this system with a noiseless resistor Ro , the voltage across it will be \/RokTAv. However, the terminating resistor is also at temperature T, so that the total RMS voltage across it will be V2 VRokTAv. Comparing this RMS noise voltage with the signal ^•oltage obtained in (16), we get for the reflection cavitj-* AT" = V V^wx'-nQo = V2 VRokTAv (25) As an example let us consider the following typical value for a 3-cm setup. Qo = 5 X 10^ Ap = 0.1 cps, Po = 10~' Watts = If 4 ^ 4F, '^ Fe /dV- ~ 10 cm' • For this case (Xmin")(T^.) = ~2 X 10"" * In most cases the behaviour of the transmission and reflection cavity is similar, so that they will not be treated separately. MICROWAVE PARAMAGNETIC RESONANCE ABSORPTION 459 This corresponds for an unsaturated Lorentz line^ to a static suscepti- bility xn = \/Zx"{^^/^), where ^w is the hne width between inflection points. For the free radical diphenyl picryl hydrazyl having a 2 oersted line width this expression at i-oom temperature gives for the min. number of spins 10'". A plot of the minimum RF susceptibility and minimum number of electrons versus microwave power is shown in Fig. 5. VI. SIGNAL-TO-NOISE IN PRACTICAL SYSTEMS .4 . General Considerations 1 . Why Field Modulation? From a design point of view it is instructive to consider the mini- mum fractional voltage change corresponding to the above Xmin"T's of 2 X 10"'*. This turns out to be, see (16), V 2 X 10 -10 From this figure one may safely conclude that it is not feasible to use an}^ system in which the microwave carrier level reflected from the cavitj^ has to be kept constant to this accuracy. Such systems would include straight detection, the dc being bucked out and amplified or systems employing amplitude modulation of the carrier. (Although ICROWAVE POWER FROM KLYSTRON, Pq [w] Fig. 5 — Minimum RF susceptibility aiid number of electrons which should be observable under thermal noise limitations. The conditions for the minimum number of spins correspond closeh" to those under which the experimental set-ups were tested. 460 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 the latter sj'stem maj' be improved b}' microwave bucking, it still re- mains very much inferior to the field modulation system to be described presently.) A system commonly used in which the requirements on the constancy' of the microwave level is less stringent, makes use of a small external magnetic field modulation of angular frequency w.u super- imposed on the sloAvly ^-arying dc magnetic field. Thus in the absence of a resonance line the output is zero except for some small Fourier com- ponents of the random fluctuations at the frequency aj.v . If the ampli- tude of the field modulation A//_m is small in comparison to the line width \H this method will sweep out the derivative of the line, i.e., the signal will not be proportional to x" as previously assumed but to dx" /dH (AH m). In order to preserve the line shape one should sweep onlj' over a fraction of the line ^^idth. The sensitivity will thereby be reduced by roughly the same fraction. It should be noted, however, that even if one overmodulates the line (in order to increase the sensitivity) the resonance condition (i.e., place of zero signal, corresponding to new slope in the absorption) will not shift for a S3nnmetrical line and the correct gr- value may be obtained. Also from the knowledge of the ampli- tude of the modulating field the increase in line width may be corrected for. For those reasons we will not be concerned with the reduction in sen- sitivity due to this field modulation scheme. 2. Choice of Frequency Referring to (26) mm- and the minimum total number of electrons N', iV.,„ = x.r, cc (Z-A (^) -^ (27) Assuming that we are dealing with the same type of cavity mode at different frequencies, the same power, and that the line width Aw is constant, we have ^c °^ -^ , Qo °^ -^ CO"* 0}' .-. iN^znin « -1 (28) w"- Equation 28 shows that in order to see the smallest number of spins we want to go to as high as frequency as possible. The upper limit is given by the availabilit}" of components in the millimeter region, by the difficulty of handling them and by the maximum available power. The most commonly used setups operate at a wavelength of 1 cm and 3 cm. MICROWAVE PARAMAGNETIC RESONANCE ABSORPTION 461 The latter was used in the experimental part of this paper. From (28) we see that with a 1 cm setup the number of observable electrons should be approximately 40 times less than with a 8-cm setup. However, in most practical cases one is not limited by the amount of a\-ailable sample, since one usually can increase the sample size at longer wavelengths. Therefore a better criterion is the minimum number of electrons per unit volume Keeping now the filling factor Vc/Vs constant we see that the sensi- tivity of a 3 cm setup as defined in (29) is only -y/s worse than of a 1 cm setup. In addition the power outputs of .3-cm klystrons are usually sufficiently higher than those of 1-cm klystron to overcome even the -\/3 advantage. If RF saturation comes in, the power argument is not valid, but one has to consider the RF magnetic field Hi inside the cavity which for a given power and Qo is prop, to co. Thus at the higher fre- quencies (1 cm) saturation effects become more pronounced reducing again the advantage of a 1-cm over a 3-cm setup. In deciding the choice of the frequency in special cases (e.g., when Aco is a function of the mag- netic field, or the sample is larger than a skin depth) (29) should be used. There are, of course, considerations, other than those of max. sensi- tivity, which have to be taken into account. For example one would always like to satisfy the condition Aco/co < -^^ the Kb noise figure of the amphfier can be reduced to nearly unity. We^\-ill as- sume in the following analysis that this has been done. The noise temperature of the barretter Ib was thought to be approxi- mately 2 since it is merely a platinum wire operating at an ele\'ated temperature. To our surprise the measured value turned out to vary for different units between -i and 40. f The noise figure was measured on about 20 different units obtained from 4 different manufacturers (P.R.D.; F.X.R. Xarda, Sperry). The reason for this noise is not en- tirely clear at present. A possible explanation is the non -uniform heat- ing of the wire which could set up air currents. They in turn can cool the wire in a random fashion giving rise to an additional noise com- ponent. An improvement of the noise figure was noted upon evacuating the barretter. The noise figure of a unit which was initially 10, dropped to the expected value of 2 after evacuation. However, it should be pointed out that this cannot be taken as a definite proof for the "air current theorj^" since the characteristics of the barretter changed markedly after evacuation. The sensitivit\' of the evacuated barretter went up from oV.'mW to 200n 'mW which necessitated a reduction of the dc current from 8 to 1.5 niA. Also the response time went up by a factor of 20, so that the effectiveness of any noise mechanism with a 1// spec- trum would be greatly reduced. This approach however looks definiteh- promising in trying to design more sensitive and less noisy barretters. In the present work commercial unevacuated barretters were used, their noise temperature being taken as 4 in the following anah^sis. Under * We are indebted to R. G. Shidman for bringing this tube to our attention. t One unit which exhibited an extreme!}' large noise figure of 1,000 was elim- inated entirely. The solder point of the platinum wire was apparentl}' defective. MICROWAVE PARAMAGNETIC RESONANCE ABSORPTION 469 those assumptions (36) becomes: 1 // Xmin — /kTA QorjT \ Po 4 + NkG' G , (43) a. Straight detection A block diagram of the microwave part of a simple barretter system is shown in Fig. 6. The attenuator serves the purpose of preventing power saturation of the sample or burn out of the bolometer at high powers. By means of the slide screw tuner and magic T arrangement one makes the system sensitive to either the real or imaginary part of the suscepti- bility. The characteristics of a typical barretter (like the Sperry No. 821) are: R = 250 Q; k = 4.5 U/niW; Pmax = 32 mW. We take the worst generator noise figure reported, i.e., Nk = 5,000 Prf (see Section VID). The ratio of the minimum susceptibility xmin-obs that can be de- tected with this system to the minimum theoretical value if one were limited by thermal noise only becomes with the aid of (41) and (43) n Xmin-obs // Xmin-th ^4 + NkG^ . G , 1 -f 5 X WPuFk'- r rfl RF^ dc R'{1 - h'k) fc^ LRPL. (44) RF-I do PHI - Uk) ATTENUATOR STABILIZED KLYSTRON ISOLATOR SLIDE :^^SCREW TUNER MAGIC -- T 't. Pa DETECTOR CAVITY — Ho + AH SINO^t Fig. 6 — Essential microwave parts of a simple barretter or crystal set-up. 470 THE BELL SYSTEM TECHXICAL JOURNAL, MARCH 1957 10 10 10 m I o H z z s5 ^5 X X. iO 1 0 5 2 \ ^ \ ) \ V SIMPLE BARRETTER 2 ? \ (SEE FIG. 7} \ p 5 \ k 2 -r r \ V ■ \ 5 j- ^-BALANCED MIXER ^' (SEE FIG.9) 1 L 2 10"'' iO"6 iO-S 10"'* <0"^ 10-2 )0-< MICROWAVE POWER FROM KLYSTRON, Pq [w] Fig. 7 — The ratio of the minimum detectable susceptibility to the minimum theoretical value versus microwave power for 2 different barretter schemes. Full lines correspond to the predicted sensitivity and dots indicate experimental values. Equation (44) is plotted in Fig. 7. From this plot we see that the system is extremely poor at low powers (which is due to the low conversion gain of barretters) and also starts getting worse at high powers (due to the signal generator noise). The latter point is not of great importance since one can alwaj^s buck down the microwave power by means of the slide screw tuner to the desired level. By using the evacuated barretter as mentioned earlier, the curve in Fig. 7 would be shifted to the left corresponding to the increased conversion gain. b. Balanced mixer detection An improved barretter scheme is shown in Fig. 8. It eliminates the poor conversion gain at low powers by employing a balanced mixer into which a large amount of microwave power P2 can be fed from the same signal generator. Since the barretter noise should not be power MICROWAVE PARAMAGNETIC RESONANCE ABSORPTION 471 dependent (unlike in crystals) this procedure improves the conversion gain without increasing the noise. Since a balanced mixer is used the noise from the signal generator is also cancelled. A necessary precaution in this set-up is to include extra isolation between the second magic T and the mixer in order to prevent any microwave power from leaking through the balanced mixer into the cavity. For this arrangement (44) becomes: Xmin-obs Xmin-th V2|/| (45) The factor of \/2 arises from the fact that we had to split the power Po in the first magic T . vSince in this scheme we are at liberty to vary the input power to the barretter we want to maximize G with respect to Fi . For a fixed total power to the barretter given by its burn-out ratings (i.e., Fi + Pdc = constant) (41) is a maximum for Ft ^^ Pdc ^^ p ^]^- Taking again the data for the No. 821 barretter we get for Gmax 0.5 and for Xmin-obs // Xmin-th 1-^^ 4 (46) Since the value of Fi can be held constant irrespective of the power in the cavity, this ratio will be a constant (see Fig. 7). It should be pointed out that in this S3'stem a wrong phasing of arm Fi will result not only in a reduction of the signal, but also in an ad- niLxtui-e of x' and x"- Therefore after changing the power by means of a STABILIZED KLYSTRON PHASE ATTENUATOR SHIFTER BALANCED MIXER / Pn ISOLATOR T-l SLIDE SCREW TUNER / /^ T-2 r^ rt ISOLATOR X ,' BARRETTERS -^ ._---CAVITY Hn+AH SIN CoX Fig. 8 — Barretter system with balanced mixer. 472 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 variable flap* attenuator (which also introduces a phase shift) or after changing the slide screw tuner the system has to be rephased again. This makes saturation measurements less convenient than in the superhetero- dyne sj'stem to be discussed in the next section. The obvious advantage of the homodyne detection scheme is that it requires only one micro- wave oscillator. 2. Crystal detection A simple set-up is shown in Fig. 6. Although its microwave components are identical to the ones used in the barretter scheme, the analysis of this set-up is more comphcated. The reason is that not only do cr3'stal characteristics vary greatly from unit to unit but they cannot be de- scribed by one simple relation over the entire range of incident micro- wave power. One can roughlj^ divide their characteristics into a square law region where the rectified current / is proportional to Pa (holds for Po < 10" Watts) and the Hnear region where / is proportional to y/Wo . (holds for Po > 10~ Watts). The output noise of a crj^stal can be represented in general by the relation.''' ' P.v = n^ + 1 kTA, t (47) where/ is the frequency' around which the bandwith Av is centered. This relation reduces for the square law region to : p^ = (^lll + 1 j hTAb (48) and for the linear region to jPrf Pn = ( -^ + 1 ) kTAv (49) The average values of /3 we determined experimentally are: /3 ~ 5 X 10" Watt"- sec"^ and 7 c^ lO" Watt~^ sec"^ The conversion gain G of the crj^stal can be represented by G = 5Prf (50) in the square law^ region and by G = constant = C (51) * The phase shift associated with the Hewlett-Packard X-382-A attenuator is quite small. t Values of a for if -band crystals are quoted in References 6 and 7. Thej' differ however from each other bj^ appro.ximatelj^ 3 orders of magnitude. MICROWAVE PARAMAGNETIC RESONANCE ABSORPTION 473 in the linear region. Values of S and C for the 1N23C were found to be S c^ 500 Watt"' and C ~ 0.3. a. Simple straight detection If one does not make use of the bucking possibilities of the magic T (i.e., eliminate the slide screw turner in Fig. 6) one has the simplest possible set-up sensitive to x" • Under those conditions the microwave power reaching the crystal will be identical to the reflected power from the cavity. Equation (36) becomes: Xmin-obs _ (GNk + Fx^ip 4~ ^ ~ 1 Xmin-th With the aid of (48), (49), (50), and (51), this relation reduces for the 1N23C in the square law region to: ;;•■- (^■^^v.^r.HP+.-ij (52) " /i 1 r V, ir»9] Xmin-obs /I + 5 X lOPo X" /^on - -I (o3) Xmin-th 50Po and for the linear region to: '^^^^i^ = (3 X lO^Po)' (54) Xmin-th A plot of (53) and (54) is shown in Fig. 9. As before the assumption was made that Prf/A ^^0.1 (see barretter case). The noise figure of the amplifier Famp was taken as unity which again can be closely ap- proached by means of a step-up transformer. The field modulation frequency was assumed to be 1,000 c.p.sec, although (47) shows that from a point of view of noise one would like to go to as high a frequency as possible. However practical consideration such as power require- ments for getting a given modulation field, pick-up problems, skin depth losses in the cavity wall usually set an upper limit. The modula- tion frequency may be also dictated at times by the relaxation times of the investigated sample. h. Straight detection with optimum microwave bucking From Fig. 9, we see that the straight crystal detection scheme suffers at low powers because of the poor conversion gain of the crystal and at high powers because of excess crj^stal noise. This situation can be greatly improved by adding some microwave power to the crystal when the reflected power from the cavity is low (to be referred to as positive bucking) or subtracting some of the power in the other case (negative bucking) . In this section we will find the improvement over the unbucked system and the amount of bucking required to effect it. 474 THE BELL SYSTEM TECHXICAL JOURXAL, MARCH 1957 10- o o t z 5 10' z 10 : / / \ simple straight t\ detection / i+9DB > - ; / ■^ITH OPTIMUM RF BUCKING -f-9 DBc ) ^v t ^ l^ ■ y 1-20. 08 h-Z2 DB PUCKING 1 VODB ODBQ/ ^Q \ i-lODB [bucking]-- /-38 DB "1 -[bucking/ - A 6 i A T - ^ ^ SUPER- " ^HETERODYNE DETECTION ' 10 -7 10' 10' 10" 10' 10 -2 10" microwave POWER FROM KLYSTRON, Pq [w] Fig. 9 — The ratio of the minimum observable susceptibility to the minimum theoretical value versus microwave power for different crystal detection schemes. Full lines correspond to the predicted sensitivitj' and dots indicate experimental values. We define the bucking parameter B by the relation Px = BP RF (55) Where Prf is the microwave power at the crystal before and Px after the bucking is applied. We further assume that after the bucking is ap- plied the crystals will operate in the square low region. Combining (49), (50), and (52) and neglecting the term GXk which is small in compari- son to the other term we get for the bucking scheme: 1 1 Xmin-obs Xmin-th AMP + f (56) SBPrp In order to find the optimum bucking parameter, we set dB\ Xmin-obs 77 Xmin-th ^ = 0 which results in B = MP J (57) MICKOWAVE PARAMAGNETIC RESONANCE ABSORPTION 475 Putting in the numerical values for the 1N23C as quoted previously we get that B = lA X 10~^ /Prf . Equation (56) becomes with the opti- mum bucking parameter Xmin-obs 77 Xmin-th 2F AMP (58) For the case under discussion this ratio turns out to be c^50 independent of Po . Fig. 9 shows a plot of (58) . The values in parenthesis indicate the degree of bucking necessary to accomplish this ratio as determined from (57). It should be noted that the negative bucking can be easily accom- plished by means of the slide screw tuner in the magic T arm (see Fig. 6) whereas for large positive buckings a scheme like in Fig. 8 has to be used. (Some positive bucking can of course be also accomplished by means of the slide screw tuner) . c. The siiperheterodyne scheme The RF bucking system just described bears a certain resemblance to the balanced mixer barretter scheme. In both cases additional micro- wave power was added to the detector in order to increase the con- version gain. However in the crystal scheme this resulted in an increase in noise power whereas this should not be the case with barretters. The question arises whether a decent conversion gain in crystals has to be always accompanied by a large noise power. An inspection of (49) shows that around frequencies of tens of megacycles* or higher the noise output of the crystal becomes negligible. As pointed out earlier such high magnetic field modulation frequencies are not feasible. How- ever in a superheterodyne system the crystal outputs will be at an intermediate frequency of 30 or 60 mc. This will make the flicker noise components negligible even at high powers where the conversion gain is good. The conventional way to obtain the intermediate frequency is to beat the reflected signal from the cavity with a local oscillator (see Fig. 10) which is removed from the signal generator by the I.F. fre- quency. In order to eliminate the noise from the local oscillator a bal- anced mixer should be employed. The ratio /xMiN^sN ^^^^^^^^^ ^hen from equ. 52 f^i^-ti-IliY (59) Vxmin-th / \ ^ / The expression in the brackets is called in radar work'^ the overall * It was shown by G. R. NicolP that this equation holds up to this frequency range. 476 THE BELL SYSTEM TECHXICAL JOURNAL, MARCH 1957 noise figure of the receiver F. We found that a noise figure of about 11-14 db is easily attainable with commercial I.F. amplifiers and balanced mixer. This would give us a ratio of // Xmix-obs ^ - -77 — ^ Xmin-th which is plotted together with the other crystal schemes in Fig. 9. Al- though this system does necessitate 2 stable microwave sources, it is not difficult to operate once the}" are set-up. This was not considered as a major disadvantage at least not at X-band. The phasing problem dis- cussed in connection with the mixer barretter scheme of comparable sensitivity is eliminated. An additional small advantage is the rugged- ness of crj^stals in comparison to barretters and the availabihty of good commercial balanced cr\'stal mixers. There are other double frequency schemes which do not need 2 separate microwave signal generators. The other frec[uenc3' may be obtained b}' amplitude or phase modulating one signal generator b}" an IF frecjuency. The side bands which are pro- duced m this way are displaced by just the IF frequency and may be utilized instead of the second signal generator. Schemes of this sort look particularly promising for frequencies well above X-band in which case it might prove difficult to maintain the difference frequency of two separate microwave generators within the band width of the IF. F. Experimental Determination of Sensitivity Limits 1 . Preparation of samples In order to get an experimental check on the previous analysis, samples with a known number of spins had to be prepared. Two sets of samples were made. One consisted of .single CuSOi -51120 crystals of varying sizes hermetically sealed between 2 sheets of pol3'eth3dene. The other set con.sisted of different amounts of diphenyl picryl hydrazj-l* which were similarly sealed up. D.P.H. samples having less than lO'' spins were prepared by dissolving known amounts of the free radical in benzene and putting a drop of this solution on the poh-eth\dene. After the benzene had evaporated, it was sealed up with another sheet of poh^ethylene. The ^-values of CUSO4 -51120 and D.P.H. differ enough so that both samples can be eonvenientl}' run simultaneousl3\ This was done in order to check the self consistency of the two sets of samples. The measured integrated susceptibility of all the D.P.H. samples We are indebted to A. X. Holden for supplying us with this material. MICROWAVE PARAMAGNETIC RESONANCE ABSORPTION 477 with more than 10^ spins agreed within a few percent with the calcu- lated value. The calculated value being based on the known amount of D.P.H. and the measured value being referred to the known amount of CUSO4 -51120. D.P.H. samples with less than lO'^ spins had all a smaller number of effective spins than calculated. The discrepancy was more pronounced the smaller the sample. There Avas also evidence that the smaller D.P.H. samples deteriorated with time. As a typical example we quote a sample which started out as 10 " effective spins and was reduced after 4 wrecks to 4 X 10 effective spins and another one which initially had 10^^ spins, deteriorated in the same time interval to 10^^ spins. Since only the smaller samples were noticeably affected, this deterioration seems to be associated with a surface reaction. It was also observed that the line width between inflection points of the D.P.H. samples with less than 10 spins increased from 1.8 oersteds to 2.7 oersteds. This broadening probably arises from a reduction in the ex- change narrowing mechanism due to the spreading out of the sample. S. Comparison of experimental results with theory In checking the sensitivity of the equipment D.P.H. samples were used and the signal to noise was estimated from the recorded output. The experimental points thus obtained are shown in Fig. 7 and Fig. 9. We believe that the results are significant to within a factor of 2, the main error arising from the estimate of the RMS noise. The band width of the lock-in detector was Av = 0.03 sec~\ Qo = 4,000, and the field modulation used was 3 oersteds p.t.p., 100 c.p.sec. for the barretter schemes and 1,000 c.p.sec. for the crystal schemes. This large modula- tion field somewhat distorts the line, but, as mentioned earlier was done in order to get the full signal. The D.P.H. samples were calibrated against CuS04-5H20 before each run. Even so it was not felt safe to use samples which had less than 10^^ spins. Referring to Fig. 8 we see that for the straight barretter detector the experimental points agree fairly well with the predicted value, l)ut in the balanced mixer scheme fall short by about a factor of 4. A possible ex- planation of this discrepancy is that the barretters were not completely matched in which case the noise from the local oscillator would not be compensated for. Fig. 9 shows the experimental points for the crystal schemes. For powers between 10~ W and 10"^ W the system used fell between the simple straight detection scheme and the one utilizing optimum RF bucking. The reason is that it was very easj^ to obtain a certain amount of positive bucking (+9 db) by merely adjusting one arm of the magic T. 478 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 MICROWAVE PARAMAGNETIC RESONANCE ABSORPTION 479 It would however have been a great deal more difficult to obtain the entire bucking of +22 db at 10"^ W since a set-up like in Fig. 8 would have to be used. Thus for the sake of simplicity the extra factor in signal to noise of 2 or 3 was abandoned. The amount of negative bucking at the higher powers will be limited by the stability of the bridge. A prac- tical limit of (40-50) db was characteristic of our set-up. We see from Fig. 9 that the agreement between the experimentally determined sensi- tivity and the theoretically predicted sensitivity is satisfactory. The experimental results on the superheterodj'ne scheme agrees again verj^ well with the predicted values up to a power level of 10"^ W. (This corresponds to less than 10'^ spins in D.P.H.) Above this level Ti (see fig. 10) has to be balanced to better than 40 db to keep the IF carrier amplitude within the required value. Instabilities in the bridge due to mechanical vibrations and thermal drifts start to contribute to the noise. Thus at high power levels the superhet scheme starts to loose some of its advantages unless special precautions are being taken to eliminate the above mentioned noise factors. A great deal in this direc- tion could probably be accomplished by shock-mounting the micro- wave components and better temperature stabilit}^ for slow drifts. Since we were mainly interested in powers below 1 mW, our efforts were limited to controlling the temperature of the room to ±1°C. Since the superhet scheme was found to be the most sensitive one, it might be w'orthwhile to discuss it in more detail. A block diagram of the set up is shown in Fig. 10. The signal generator feeds into the magic T, where its power is split between arm 2 and 3. Arm 2 has the reflection cavity with the sample, the reflected voltage being bucked out with the aid of arm 3. For this purpose arm 3 has a phase shifter and attenuator, an arrangement which was found to be more satisfactory than a shde screw tuner as far as stability and ease of operation goes. The desired signal appears then in arm 4. It is fed into a balanced mixer which receives the local oscil- lator power from the stabilized klystron II. The output of the balanced mixer is then fed through the IF amplifier, detector, audio ampHfier and lock-in detector. The circuits of each of those components is fairlj^ standard and will not be dwelled upon further. The microwave power is measured in arm 2 of the magic T. The power reflected from the cavity is also monitored in arm 2. This is of great help in finding the cavity when klystron I is sw^ept in frequency by means of a sawtooth voltage on its reflector. Since the klj'stron mode itself might have some dips in it, (which might be mistaken for the cavity), it proved helpful to display on the scope the klj'^stron mode simultaneously with the reflected power •iSO THE BELL SYSTEM TECHNICAL JOURNAL, AL^RCH 1957 from the cavity. This also provides a convenient way to measure the Qo of the cavity. " The frequency is measured roughly b}^ means of a cavity frequency meter and more precisely by means of a transfer oscillator and high speed counter. The magnetic field is measured by means of a nuclear magnetic resonance set-up, its frequency being measured on the same counter as the microwave frequency. The nuclear resonance signal is recorded on the same trace as the electron resonance signal. Thus if the magnetic field is homogeneous enough, the nuclear sample will see the same field as the electronic sample and g-values can be conveniently determined to the accuracy of the nuclear moment (this also assumes that the signal is large enough, so that no additional error is introduced in determining the exact location of the resonance.) The field modula- tion coils are mounted on the pole faces and are energized by a oO-watt power amplifier. A field of 50 oersteds p.t.p. is available at 1,000 cps and a slightly higher field at 100 cps. The magnet is a Verian 12" modified so that it can rotate around an axis perpendicular to Ho . This was done mainly in order to make anistropy measurements more convenient. This enables one to make quick saturation measurements in isotropic materials without having to change the incident RF power. This is accomplished by rotating the magnetic field and measuring the signal strength versus angle. Since onlj'- the RF field perpendicular to the do field causes transitions, the signal in an unsaturated isotropic sample should go as cos^ d; where 9 is the angle between Hi and Ho . From the deviation from tliis dependence, the saturation parameter can be found. This could also be done by rotating the cavity, but at microwaves is not as easy as rotating the field. VII. A NOTE ON THE EFFECTIVE BANDWIDTH There seems to be some confusion as to how narrow one should make an audio amplifier preceding a phase sensitive detector (lock-in) or why the band width of the IF amplifier doesn't enter in a superhet scheme. Those and similar questions have to do with the effective band width of the system Ap which appears in (26). Since similar questions have been rigorouslj^ analyzed by other authors,^^' ^^ the present discussion will try to stress some of the phj^sical ideas underlying the different detection schemes. We consider first the simple scheme illustrated in Fig. 11. It consists of an amplifier with band width Aj^i centered around vi followed by a phase sensitive detector with a reference voltage at Vi . The output of the phase sensitive detector has an RC filter of band width Ai'2 . One can see that in such a system the only noise components centered around MICROWAVE PARAMAGNETIC RESONANCE ABSORPTION 481 vi (this being also the reference frequenc}') in a band width Avo will con- tribute to the output noise. This is because the beat between 2 noise components like Vn and Vm (see Fig. 11) is too far removed from vi to produce an output voltage. (This statement implies the condition that Ai'i < vi otherwise the beat between 2j'i and vi could come through.) Thus in this system the band width of the amplifier is immaterial as long as the noise voltages are not so large as to saturate it. A more serious situation may arise in the absence of a reference volt- age. In this case the noise components within the band width Aj^i can beat with each other and produce a noise output which would increase with the band width. This could become especially detrimental in a superheterodyne scheme in which the IF band width can be a million times larger than the output band width. It can be shown, however, that if the carrier voltage Vc at the output of the IF is large enough the IF bandwidth AFip does not enter into the noise consideration^^ the cri- terion essentially is that TV > G'2kTZAF IF (60) where G is the IF amplifier gain, and Z the input impedance. Condition (60) means that we want the noise which beats with the carrier to be greater than the beat between 2 noise terms. Since the former is propor- tional to the carrier, its predominance can be easily ascertained experi- mentally by increasing the IF carrier and noting whether the noise output increases proportionally. If it does, (60) is fulfilled. V, AMPLIFIER TUNED to;', Ay, V2 PHASE SENSITIVE V3 RC FILTER V4 DETECTOR LOCK -IN 1 REFE RENCE VOLTA GE AT ^1 ' (a) (b) y,-y-* Fig. 11 — Effective band width of a phase sensitive detector Sveit = Aj-.. Note that the band width of tlie amplifier does not enter as long as ^vi < vi . 482 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 In order to see what maximum gain G (60) imposes on a typical sys- tem we assume AFjf = 5 X 10^ c.p.sec. Z = 10'l2; Vc ^ IV. Under those conditions we get from (60) that G has to be smaller than approxi- mately 10^ If on the other hand G is very small the signal level at the audio amplifier input is so low that the flicker noise of the detector can still come in. A good practical figure for the IF amplifier gain is around 60 db. VIII. SATURATION EFFECTS In all the previous considerations RF power saturation effects were neglected, i.e., we have assumed that the power absorbed is proportional to Hi, where Hi is the RF magnetic field. When this assumption is no longer satisfied, the question of sensitivity has to be re-examined for different degrees of saturation. However it is difficult from an experi- mental point of view to change the conditions of the experiment for each degree of saturation and therefore an elaborate analysis of this case does not seem to be warranted. However it might be of interest to see the effect on the in phase component of the signal at complete or nearly complete saturation The change in output voltage for a reflection cavity is (15) and from (4) The RF magnetic field in the cavity is given by H^ = CQod - r')P,„ (71) where C is a constant dependent on the geometr}^ of the cavity the re- flection coefficient. Assuming a simple homogeneous saturation be- haviour we substitute for x" the saturated value of Xs //(I) xJ' = ^ = ^^^^- - - (72) ^' 1 + -Yi'Hi^TiT, 1 + yi'TiT,CQ,{l - r^)P,-„ ^ ' where X"" is the unsaturated value of the susceptibility and Pin the power from the microwave source. At* V r 1 -j- yi-liloQoii- — T')Fin and the output voltage AV. MICROWAVE PARAMAGNETIC RESONANCE ABSORPTION 483 For a high degree of saturation 7'TiT2CQo(l - r-)P,„ » 1 and substituting for Ron r r = 2 - 1 Ron + 1 we get : Pinyi'TiT2C ^ ^ The above relation shows that under saturated conditions the Q of the cavity does not enter and one might as well not use one or use a very much overcoupled cavity. This is one of the reasons why in microwave gas spectroscopy,* where lines are easier saturated a cavity is not used. (The more important reason is that in most cases one sweeps the fre- quency of the source, so that a cavity is difficult to use.) Equation (75) also shows that the signal and also signal to noise goes down with increasing RF power. The above argument does not hold for the out-of-phase (dispersion) signal, in particular it breaks down com- pletely for signals observed under fast adiabatic passage conditions.^ For the latter case one wants as high an RF field as possible. IX. ACKNOWLEDGEMENT I profited greatly from discussions with various members of the resonance group at the University of California in particular with Profs. A. F. Kip, and A. M. Portis and at Bell Telephone Laboratories with Drs. R. C. Fletcher and S. Geschwind. I would like especially to thank E. Gere for his expert help in the construction of the equipment and to Prof. C. P. Slichter and Dr. R. H. Silsbee for helpful criticism of the manuscript. REFERENCES 1. See for example F. Bloch, Phys. Rev., 70, p. 460, 1946. N. Bloembergen, E. M. Purcell, R. V. Pound, Phys. Rev., 73, p. 679, 1948. * In microwave gas spectroscopy the fractional power loss per unit length a is used. Its relation to the susceptibility is a = 8, 2x"/^a where Xc? is the guide wavelength. 484 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 2. Montgomery, Technique of jMicrowave Measurements, Had. Lab. Series. Xo. 11. 3. C. H. Townes and S. Geschwind, J.A.P., 19, p. 795, Aug.. 1948. 4. Hamilton, Knipp and Kupper. Klystrons and Microwave Triodes. McGraw Hill. 1948, Rad. Lab. Series Xo.'G, p. 475. 5. Torrev. H. C. and Whitmer, C. A., Crystal Rectifiers, Rad. Lab. Series, Vol. 15, McGraw Hill, 1947. 6. M. W. P. Strandberg. H. R. Johnson, J. R. Eshbach, R.S.I., 25, pp. 776-792, Aug., 1954. _ 7. Townes and Schawlow, Microwave Spectroscopy, McGraw Hill, 1955. 8. Miller, P. H., Xoise Spectrum of Crystal Rectifiers, Proc. LR.E., 35, p. 252. 1947. 9. G. R. Xicoll, X'oise in Silicon Microwave Diodes, Proc. I.E.E., 101, pp. 317-29, Sept., 1954. 10. See for example K. Holbach, Helv. Phvsica Acta, 27, p. 259, 1954; A. ^L Portis, Phys. Rev., 100, p. 1219, 1955. 11. Pound, R. v.. Microwave Mixers, M.I.T. Radiation Lab. Series 16, McGraw Hill. 12. E. D. Reed, Proceedings of the X'ational Electronics Conference, 7, p 162, 1951. 13. S. O. Rice, B.S.T.J., 23, pp. 282-332; B.S.T.J., 24, pp. 46-156, 1945. 14. A. van der Ziel, Xoise, Prentice Hall, Inc., 1954. The Determination of Pressure Coefficients of Capacitance for Certain Geometries By D. W. McCALL (Manuscript received Februarj^ 15, 1955) Expressions are derived for the pressure coefficients of capacitance of parallel plate capacitors subjected to one-dimensional and hydrostatic pressures and of cylindrical capacitors subjected to radial compression. The derivations apply to systems in which the dielectrics are isotropic, elastic solids. I. INTRODUCTION The electrical capacitance between two conductors separated by a dielectric is a quantity which can be calculated with ease only in certain geometrical arrangements of high symmetry. Even the classic example of parallel plates presents major difficulties as one may only perform the calculation exactly for the case of plates of infinite area or vanishing separation. The approximation becomes poor when (area) '/(separation) becomes small and the theoretical treatment of edge effects is sufficiently difficult that it has not been solved though the solution would greatly facilitate dielectric constant measurement. When pressure enters into the situation as a variable the difficulties are enhanced as one must be able to describe the geometry effects as well as the change in dielectric constant. The engineers responsible for designing submarine cables are con- fronted with the necessity of knowing the manner in which capacitance depends upon pressure as may be illustrated in the following way, A submarine telephone cable is composed of a central copper conductor surrounded by a sheath of dielectric material. Due to the extreme length repeaters must be placed at intervals, the separation being deter- mined by the attenuation of the cable. The attenuation, a, of a coaxial telephone cable may be written a = {G/2)(L/Cf + (R/2)(C/Lf where G is the conductance of the dielectric per unit length, C the 485 48G THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 capacitance, L the inductance, and R the conductor resistance per unit length. The second term contributes about 99% of the attenuation. Considering only this term we deduce {\/ot){da/dP) ^ (l/R)(dR/dP) + (l/2C){dC/dP) - (l/2L)(dL/dP) Accurate knowledge of the coefficient (l/C)(dC/dP) is thus essential in designing very long cables which are to be exposed to high pressures. In evaluating dielectric materials for use in cables it is often desirable to make measurements on sheet specimens rather than cable. It thus be- comes necessary to be able to translate sheet data into cable data. It is the purpose of this paper to analyze the problem of calculating pres- sure coefficients of capacitance for certain simple geometries and to consider the methods of measurement which have been used. It will be shown that results of theory and experiment are in as good agreement as can be expected but more accurate measurements of electric and elastic properties are needed. The equations which will be derived are also necessary if one wishes to determine the dependence of dielectric constant on pressure using any of the geometries described herein. The problems treated in this paper are particularly simple and amen- able to mathematical treatment but many problems encountered in sub- marine cable design are at present subject to solution only by empirical means. Fundamental investigations of the effects of pressure on dielectric materials are needed. II. THEORETICAL TREATMENT In the following treatment we consider that the dielectric substance is an elastic solid which obeys Hooke's law. We denote the relative per- mittivity or dielectric constant by e, the permittivity of free space by £o ,* the principal stresses and strains by th and en , the density by p, the compressibility by k, and Poisson's ratio by a. 1 d£ A. Calculation of ^ •^ £ dP One of the quantities which will be needed in the evaluation of i^ac . 1 a£^ CdP ^^ E dP As £ is not dependent on the geometric configuration it can be calculated €0 = 8.86 X 10-12 farads/meter. PRESSURE COEFFICIENTS OF CAPACITANCE 487 in general and the result applied to each of the special cases to follow. A relation between dielectric constant and density is required and usually, when dealing with non-polar dielectrics, one assumes that the Clausius-Mosotti relation gives the proper dependence. That is = (constant) p (1) £-^ 2 This formula may be differentiated to give i ^ = (g - l)(g + 2) 1 ap_ . . £ dP 3e p dP ^ ^ In the theory presented herein, (1) will be used though it is at best an approximation. Corrections to the Clausius-Mosotti formula which have been given do not seem applicable to polymer dielectrics and in- troduce parameters which must be fitted. B. The effect of a One- Dimensional Pressure Acting on a Disc Consider a one-dimensional pressure, —P, acting along the axis of a circular disc of dielectric material with electrodes affixed to opposite faces. Assume the disc is constrained such that no lateral displacement can occur. Let t be the thickness and A the area of the disc. The capacitance of such a capacitor is given by the equation C — £€q — so the desired pressure coefficient is CdP ~ E dP T dP ^ ^ where use has been made of the condition that the area is constant (i.e., no lateral displacement). Hooke's law states k ^^i = ;T71 ?rT [txx — (^{Tyy + Tz^] (4) ^yy 3(1 k 2a) 3(1 k 2-^ ■^. ^ ..^ ^ ^"""^T^^^^ s (C) READER C i ^^^ c r-^ ^. ^ r; , ^--^ ^ 2 3 4 SYLLABLES PER WORD Fig. 3 — Effect of word length and familiarity. READIXG RATES 503 o z o o LU 10 a. a. in a n. o 5 4.5 4.0 3.5 3.0 2.5 3.5 3.0 2.5 2.0 A rr^ ^ K A r^ \ J IJ k^ n u^ M r V \ Y y \l r V "t^ READER A V 1 i »v A Jr >^ H M ^ V W L/ V A M '^ "Dreader b r 0-3 3.0 1 1 reader c n ——C^^ V ^'^ ^ S^ / N^ H rv rv ^n.^ ^n. n M 2.5 2.0 cr \ 1/^6- -0--X J r '>y T V 0 2 4. 6 8 10 12 14 16 18 20 22 24 26 28 SUCCESSIVE READINGS OF NONSENSE WORD LISTS Fig. 4 — Confirmaton- demonstration of the effect of familiarity upon reading rate. with word order have been removed and the bits/word depend only on the frequency of occurrence of words in prose, which is known. Thus, Shannon^ gives a figure of 11.82 bits/ word which apphes to scrambled prose, provided the prose has the same word frecjuencies as that from which the statistics were derived. The information rates for words from a 5,000-word dictionary (Experiment 1) for the preferred lists, and for scrambled prose are given in Table II. The information rate for scrambled prose is less reliable than the others, because we are not sure that the word frequencies used by Shannon apply to the prose used by us, but we used the tjT^e of material cited by the reference he quotes. It is clear that the information rate for scrambled prose is high as compared with most other lists. Table II shows the gain which may be made h\ fitting the task to the human being — in this case, by choosing a suitable word list. We may note that the gain appears greater in the case of reader A than in the case of reader B. This need not be experimental error. One would sup- pose that there are optimal lists for individuals. Indeed, if we compare Figs. 3(a) and 3(b) we see that for reader A the word rate for mono- syllables drops by a factor 0.72 in going from the first thousand to the tenth thousand, while for reader B the drop is onlj^ a factor 0.88. This .504 THE BELL SYSTEM TEfHXirAL JOURXAL, MARCH 1957 7 6 5 >- U z LU 4 D O LU DC 3 U- 2 1 A ENGINEERS n RESEARCH ASSISTANTS O SECRETARIES X WAITRESSES • PORTERS \ 1 A A 1.5 2.0 2.5 3.0 WORDS PER SECOND 3.5 4.0 17 23 28 34 BITS PER SECOND 40 45 Fig. 5 — Distribution of reading rates for preferred vocabulary. indicates that the optmial list would be somewhat different for reader A than for reader B. ]\Iore extensive data would, however, be required to confirm this hj^pothesis. Experiments not described here in detail showed that reading rates for digrams (successive pairs of words related as in English text) are intermediate between those for prose and discrete words. Experiment 5: Effect of Multiple Channels Licklider^ has found that when the reader attempts simultaneous} j' to perform a tracking operation while he is reading, his reading rate re- mains almost unimpaired, and the tracking information is added to that of reading alone. This two-channel transmission gave him his highest rate of transmission. We obtained the reverse finding. Reading the preferred list gave us our highest transmission rate. Simultaneous Table I Information Rate (bits/sec) A B C Preferred list 42 24 48 39 23 47 34 Prose (5 bits/word) Prose (10 bits/word) 19 39 READING RATES 505 Table II Information Rate (bits/sec) A B C 5,000-word dictionary Preferred list 33 42 43 33 39 39 26 34 Scrambled prose 32 reading and tracking gave a lower total transmission rate. However, Licklider and we agree on the magnitude of this maximum — between 40 and 45 bits/sec for facile test subjects. Measurements on combined reading and tracking rates were made in Experiment 5 using words from the preferred lists. Whereas Licklider's readers made a dot within a box next to the word read, our readers placed a dot as close as possible to a vertical line next to the word read (e.g. dog |-)- The computation of transmission rate is shown in Ap- pendix II. The reading-while-tracking rates were 2.4, 2.0 and 1.4 words/ sec. The computed information rates are given in Table III. It may be seen that the reading rate during tracking dropped so much that the two channels together give a total information rate less than those for reading the preferred list alone. Licklider's reading lists were words chosen randomly from a dictionar}^ and are presumably not chosen optimally for maximum information rate — his information rates for reading alone were 30-35 bits/sec, as compared with the 32-43 bits/sec found here for the scrambled prose and preferred lists. However, if we assume that our reading-while-tracking rate, which is much slower than the reading rate for scrambled prose or for the preferred lists, is limited largely by tracking, we might have obtained a slightly higher informa- tion rate in reading-while-tracking by using a larger list of words. This is suggested by the fact that Licklider's and our experiments obtain about the same reading- while-tracking speeds. Table III Information Rate (bits/sec) A B c Reading (while tracking) Tracking (while reading) Reading and Tracking (Rates for same word list from Experi- ment 3 — reading only) 26.6 10.7 37.3 (42) 22.1 11.0 33.1 (39) 15.4 11.7 27.1 (34) 506 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 Experiment 6: Effect of Phij. biological Utterance Limitations One of our best indications that the maximum reading rate of a subject is determined by mental rather than by physical limitations is that discrete word lists were read no faster silently than aloud. This may appear contrary to very high silent reading rates widely fjuoted. This can be explained by the fact that in reading much prose we do not and need not recognize every word in order to get the sense. Presumably, if an author made every word say something, his prose could not be read with understanding at such high rates. We can also show in another way that the mere uttering of the N\'ords does not determine the reading speeds observed. A memorized prose phrase ("This is the time for all good men to come to the aid of their country") was repeated several times at rates of 7.5, 9.1 and 8.4 words/ sec for the three readers. Fig. 6 compares word rates for repeating a phrase with the word rates previously discussed. The radically faster rate for repeating a phrase is not the only feature to be observed in this figure; the three readers are not in the same order of speed as is preserved through the reading experiments. This would suggest that it is word recognition rather than speaking speed which accounts for differences among the reading rates of different people. 10 7 O §6 LU Q. O 4 IT o 5 ^ REPETITIVE PHRASE PROSE SCRAMBLED PROSE "PREFERRED" LIST READING _WHILE _ TRACMNG READER ABC ABC ABC ABC ABC Fig. 6 — Effect of physiological utterance limitations. READING RATES 507 DISCUSSION' AND SUPPLEMENTARY EXPERIMENTS Conclusions from Principal Experiments The conclusions which can be reached with reasonable assurance from these experiments are rather narrow. They might be stated: 1. Information is best transmitted through a human channel by means of well-chosen acts (reading well chosen words in this case) in- ^•olving many bits per act, that is, much choice per act. Cutting down drastically the bits per act does not substantially increase the speed at which the individual act is accomplished. 2. The lower bound of information transmission through the human channel of rapid readers seems to be about 43 bits/sec. This estimate is a little higher than that found bj'- Licklider,- and may be close to a limiting rate. 3. This limiting rate can be achieved by the simple act of reading either randomized lists from suitably selected words or scrambled prose. -i. Both familiarity and length of words are important in determining reading speed. The relative effect of these two variables on reading speed is rather complex. Be\'ond these narrow conclusions, there is much understanding yet to be achieved in the general field of the speed of human mental and physical responses and operations. Thus, it seems worth while to men- tion other experiments which were done in the course of the present investigation and experiments carried out by other workers, and to speculate somewhat concerning the whole of this experimental work. Multiple Tasks The reading- while-tracking experiments touch on an important prob- lem. We have all heard of wireless operators who can receive and sub- sequently type out a message while carrying on a conversation or playing chess. There is nothing in this feat to indicate an information rate greater than that we have found. Actually, the rate of receiving prose by Inter- national Morse Code by ear is around 0.58 word/sec;^ this is slow com- pared with the rates we have considered. Our experiments with tracking followed experiments in which words in the lists were randomly printed in red or black, and in which the subject spoke red words in a louder tone of voice than black words, or pressed one key for red words and another for black words. In these cases, the added information, one bit per word, was so small as to make no clearly discernible difference in information rate for the large vo- 508 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 cabularies. The speed for reading loud and soft was less than for reading- while-keying. This may imply something about the relative efficiency of human beings performing two tasks by using two sets of muscles as against using one set in two different ways. It is common experience that we can walk about and carry out other simple tasks while talking or thinking. It is possible though not obvious that some sort of automatic, almost purely reflexive response — ■ as, moving the left hand when the right hand is touched — could with practice be carried out cjuite independentlj^ of a task such as reading. The information rate for such responses would be small, the experimental error would make it difficult to settle the question, and the interpretation of such an experiment would not be entirel}^ clear. The Patterns Which Govern Reading Time Early in the experiments the question was raised whether readers may not read letter b}^ letter or syllable by syllable. Several findings bear on this. Fig. 3 shows clearly that the reading time for a two-syllable word is much less than twice the reading time for a one-syllable word. One of us knows a negligible amount of German. German syllables are, however, reasonably familiar. It was found that in reading German aloud he had the same reading rate in syllables per second as a man whose native language was German had in words per second. The two readers had substantial!}'' the same reading speed in English. Presumably in reading German one man recognized syllables and the other recog- nized words. This also reinforces the conclusion that reading rate is not limited by the time taken to utter words. Some experiments were done using lists of common Chinese characters and lists of the corresponding English words. Average word rates over three lists for two readers Avho could read both languages are given in Table IV. The slightly lower rate for English is plausibly explained by the fact that Chinese was the reader's native language. All words were Table IV Words/sec Chinese VV'ords English Words E F 2.7 3.3 2.3 3.2 READING RATES 509 35 30 CO 25 o oc o $ o cc UJ CL in a z o u UJ in 20 10 READER D .xi _^ r < —< ■^^ J y y k ^ 0 12 3 4 SYLLABLES PER WORD Fig. 7 — Patterns governing reading time. necessarily monosyllables in Chinese and happened to be monosylla- bles in English. In one case a word is made up of a sequence of letters, each standing for a sound, and in the other it is made up of a number of strokes which are meaningless individually, yet in each case a word is taken as a unit or pattern reciuiring nearly the same time for reading. We found that the rate for reading arable numerals is substantially the same as for reading familiar words. Each numeral is an individual pattern to be recognized. • In a fii'st effort to find the effect of syllable length on reading rate, a subject read se^'eral lists made up respectively' from vocabularies of l(i single-syllable, 16 two-syllable, 16 three-syllable, and 16 four-syllable words. None of the words was very unfamiliar to start with, and all were presumably very familiar after the subject had read several randomized lists composed of the same words. The outcome of the experiment is shown in Fig. 7. For comparison, the points associated with the lower straight line are time for 60 words for repeating, as rapidly as possible, a one-, a two-, a three- and a four- syllable word. The points on the upper curve are reading time for 60 words for the randomized lists of the familiar one-, two-, three- and four- syllable words. In dealing with such groups of highly and uniformly familiar words, it appears that, roughly, a certain time is required to recognize the word regardless of length, and this time governs the reading rate up to the 510 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 Table V Words/sec Scrambled Prose Scrambled Paragraph Prose A B C 3.7 3.3 2.7 4.0 3.7 2.9 4.8 4.7 3.9 point at which the reader is uttering words continuous! j^ as fast as he can. This is consistent with a strong subjective feehng that what hmits the rate is the difficult}' of "recognizing" the word as one looks at it, and that once the word is recognized one can utter it while recognizing the next word. It would of course be wrong to conclude from this experiment that multisyllable words are in general recognized as quickly as single syllable words, for it would be possible to recognize one among a known group of 16 multisyllable words without looking at the whole word. Indeed, Fig. 3 indicates a substantial difference of reading rate between one- and two-syllable words of like freciuency of occurrence. This was not ob- served in reading the specialh' familiar lists of one- and two-syllable words. Why is prose read faster than scrambled prose? It might be that some short phrases are recognized as individual patterns. However, there is another factor at work. A scrambled paragraph of prose is read slower than the same paragraph in its natural word order but faster than scrambled prose from a book or a long strefch of prose, as can be seen from Table V. It should be noted that reading speed differs for different prose, and that when comparisons among prose, scrambled paragraphs and scram- bled prose are made, similar material should be used. The fact that a scrambled paragraph is read faster than scrambled prose might be explained by saying that we expect, we are more readj^ to recognize, words which are repetitions of earlier words or words which are closely related in sense to earlier words than we are unrelated words. Thus, the greater reading speed for prose than for scrambled prose seems to be due only in part if at all to the recognition of phrases rather than words as individual patterns. Rate of Mental Processes The rate at which information passes through a human channel in reading experiments is indisputable. Quastler^ has attempted to go READING RATES 511 beyond this and estimate information processing rates in the brain from the performance of hghtning calculators, by dividing the performance of the calculation into a sequence of tasks ecjuivalent to consulting memorized multiplication tables and performing additions. It is hard to interpret such a study clearly, for it is quite possible that there are many sorts of mental acts which take different times to perform, just as multi- plication and addition take different times in an electronic computer. A tentative experiment we performed indicated something of the sort. Randomized lists were made up from \'ocabularies (a) of names of common animals and vegetables in equal numbers, and (b) of common men's and women's names in equal numbers. In reading these, a subject w^as asked, not to read the word aloud, but merely to press one key with his right and another key with his left hand; in (a) left-animal, right- vegetable; in (b) left-man, right-woman. The same subject later read the lists aloud. Pressing keys took 40 per cent longer than reading aloud. (The additional time is not related to the keying operation itself; for a 2 word list, for example, keying speed is much faster than reading speed.) Presumably an additional mental operation was involved, but it was not one for which the time was equal to that for reading. This experiment was not pursued further, partly because no clear conclusion could be drawn from it. Had it been pursued and randomized lists of the same words used repeatedly, the rate might have gone up. Conceivably, cow and horse could become for a subject merely different ways of spelling left, and lettuce and carrot variant spellings of right. In this case we would end with a two-word reading experiment. Reading Rate as a Psychometric Datum It is interesting to speculate on the possible relationship of reading rate to general intelligence or some other aptitude. Certainly, Fig. 5 indicates some such relationship. We might also ask in connection with Fig. 3, does a rate which falls less rapidly with frequency of occurrence indicate a larger vocabulary, and can we measure vocabulary by reading speed tests? Certainly, measuring the speed of reading aloud is very simple, and such tests might have some psychometric utility. The Channel Capacity Required for Satisfactory Communication In conclusion, we cannot help but wonder that the highest information rate noted — 43 bits/second — is so much lower than the channel capacity* of a telephone or a television circuit (around 50 thousand * This is the limiting channel capacity given by (2.1) of Appendix II. The prac- tical rate at which binary digits can be sent over a telephone circuit with simple equipment is less than 1(X)0 bits/second. 512 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 bits/second for telephone and 50 million bits/second for TV). This would not be surprising if the limitation we observe had been one of the speeds at which words can be uttered, but it appears rather to be a mental one, one of recognizing what is before the eyes. To the authors, it seems reasonable that this mental limitation may apply to a human being's ability to absorb information, that is, to the information rate needed to present a satisfactorj- sensory input to a human being. If it does, then why do we need so much channel capacity to convey to him an acceptable sound or picture? This can be explained in part bj^ the inefficienc}^ of our present com- munication methods. Despite its present imperfections, the vocoder makes it clear that clearly understandable speech can be transmitted using far less channel capacity than that required in ordinary telephony.^ However, it is quite likely that even with the most efficient of en- coding means we will have to use far more than 43 bits/second for a picture transmission channel. While only a portion of the image of the transmitted picture falls on the fovea at any instant, we can cast our eyes on any portion of the received picture. If the pick-up camera de\dce and the received picture followed eye movements, a much less detailed picture would serve. Even with our eyes fixed, we can concentrate our attention on a particular part of our field of vision, and this is something that the pick-up camera cannot track. There may be similar effects in our apprehension of sounds. In the light of present knowledge it is impossible to estimate the minimum channel capacity required to transmit sound and pictures in a satisfactory manner. It will take work far beyond the measurement of reading rates to enable us to make such an estimate. ACKNOWLEDGMENTS The writers are indebted to D. L. Letham, w^ho carried out some work preliminary to that reported here, to J. L. Kelly for helpful comments, to D. Slepian for help in putting the appendices in a mathematically more acceptable form, to Miss Renee Hipkins who carried out most of the experiments, and to three indefatigable readers, ^Irs. Mary Lutz, S. E. Michaels and A. P. Winnicky. Appendix I ON OBTAINING GOOD VOCABULARIES The experiments in the body of the paper indicate that the choice of a good vocabulary is important in attaining a high information rate in reading lists of words. READING RATES 513 In these experiments the randomized hsts may be regarded as an in- formation source consisting of a sequence of code elements or sjmibols (words) in which there is no correlation between successive symbols. If in making up the lists the sth word of the vocabulary is used with a normalized probability ps , the entropy in H in bits per word, and hence the amount of information per word, is H = -J2ps log2 Ps bits (1.1) s If all words appear with an equal probabilitj^ 1/?/? where m is the number of words in the vocabulary, as in the case of experiments 1-3, ps is 1/m for each of the ni words and in this special case H = log2 m (1.2) In the case of scrambled prose, for instance, the probabilities are different for different words. This will be true also if in making up word lists we choose words randomly from a box containing different numbers of different words. Let ts be the time taken to read the sth w^ord of the ^'ocabulary. Let us assume that ts is the same for the sth word no matter what context that word appears in in the randomized list. If this is so, the average reading time per word, t, will be t = Z Psts (1.3) s the word rate will be 1/t, and the information rate R will be IT Z P» l0g2 Ps i 2^ Psts s Suppose we have available a vocabulary of words and know the reading time ts for each word. The problem is to choose ps in terms of ts as to maximize R. This is easily done; however the result can also be obtained as a special case of the problem treated in Appendix 4 of "The Alathematical Theory of Communication."^ In Shannon's ^ii'\ the sub- scripts i, j refer to passing from state i to state j. In our case there is only one state, and ^{/'^ should be identified with ts for all i and j. Similarly, we identify pi/"^ with ps . C is the maximum rate, so log2 W = C. Shannon's equation PiJ =^.^^ ' 514 THE BELL SYSTEM TECHXICAL JOURNAL, MARCH 1957 becomes Vs = 2-^'' (1.5) since there is only one B. Shannon's determinantal equation 1 E IF^'--^'' - S,, I = 0 s becomes S2~'''^ = 1 (1.6) In (1.5) and (1.6) we have a means of evaluating -ps in order to attain the maximum inlormation rate R. The data we actually have concerning words is that for some class s of words, say, the monosyllables in the 8,000-9,000 words in order of familiarity, the reading time has some value ts , presumed to be the same for all words in the class, and that there are Ns words in this class. In this case we must assign to each word in the sth class the same prob- ability Ps given b}^ Ps = 2-^'^ (1.7) and we must have J^NsPs = i:-V^2-^'' = 1 (1.8) s s Using the same amount of data given in Fig. 3, for the 20,000 most common words, but for a different reader, estimates were made of Ns and ts for all the classes consisting of words of each number of syllables in each range of occurrence of 1 ,000 words. Then the optimum values of Ps for word.s in each class and the maximum rate R were computed. Using (1.4), rates were also computed for choosing words with equal probability from among the first w thousand words and from among the first ?n thousand monosyllables, as functions of m. These rates had Table VI Nature Maximum Rate Maximum for equi-probability monosyllables (from first 8,000 words) Maximum for equi-probabilitj- among words of all lengths (first 5,000 words) Computed Rate, bits/sec 33.5 32.4 30.2 READING RATES 515 maxima for vocabularies of optimal sizes. Table Yl compares the various rates computed. As it is much easier to make up lists from the 2,500 monosyllables among the first 8,000 words with equal probabilities than it is to make up lists from among all words with a different probability for each class, and as the information rates computed were close together, the former alternative was chosen. The use of scrambled prose provided an easy way to make up good lists. Appendix II TRACKING EXPERIMENT A well-known formula for channel capacity R in bits/sec is* R = B logo. (^1 + 0 (2.1) This gives the limiting rate at which information can be transmitted over a channel with a bandwidth 5 by a signal of power P^ , in the pres- ence of a gaussian noise of power P„ , with an error rate smaller than any assignable number. In most cases, the actual rate is much smaller than this limiting rate. In general, the rate is the entrop}- of the received signal minus the entrop}" of the noise. In the particular case of a gaussian signal source as well as a gaussian noise, each represented by 2B samples a second, the calculation based on entropies gives exactly (2.1). Let us then apply (2.1) to the tracking experiment. Suppose that a large number A" of samples do have a gaussian dis- tribution of mean square amplitude x^. Suppose that we make an error dn in reproducing the nth sample, that these errors are gaussian, and that the mean square error is d'^ ^ = ^r S ^ We see from (2.1) that ideall}" we can use these reproduced samples to transmit M bits of information where M =tl log, (^1 + ^ j (2.2) In the reading and tracking experiments, randomized words from the 2,500 commonest monosj'llables were arranged with equal vertical 516 THE BELL SYSTEM TErilNir'AL JOT-IJXAL, AIARril 1057 spacings but with \'arious horizoiilal positions. 'I'o the right of each word was a short vertical line. The distances x„ of these lines from the vertical centerline of the paper were obtained from a list of random numbers with a gaussian distribution such that for the list x- = 1 inch. Of course, X- for each list would depart from this value. As the words were read, the reader used a pencil to make a dot as near as possible to the correspond- ing vertical line. For each sheet, the departures (!„ from the vertical lines in inches were measured and (P was computed. The number of bits M for pointing for that sheet were then taken as M = f log, (^1 + V^ (2.3) REFERENCES 1. E. E. David, Naturalness and Distortion in Speech Processing Devices, Jour. Acoustical Soc. Am., July, 1956. 2. J. C. R. Licklider, K. N. Stevens, J. R. M. Haj'es, Studies in Speech, Hearing and Communication, Technical Report, Acoustics Laboratory, MIT, Sept. 30, 1954. 3. H. Quastler et al, Human Performance in Information Transmission, Report No. R-62, Control Systems Laboratory, University of Illinois, March, 1955. 4. C. E. Shannon and W. Weaver, The Mathematical Theorj^ of Communication, University of Illinois Press, 1949. 5. G. Dewey, Relative Frequency of English Speech Sounds, Harvard University Press, '1923. 6. E. L. Thorndike, A Teacher's Word Book of the Twenty Thousand Words Found Most Frequentlj^, Teachers College, Columbia University, 1932. 7. C. E. Shannon, Prediction and Entropy of Printed English, B.S.T.J., 30, pp. 50-64, Jan., 1951. 8. E. B. Newman and C. J. Gerstman, A New Method for Analyzing Printed English, J. Exp. Psychol., 44, pp. 114-125, 1952. 9. Keith Hennej-, Radio Engineers Handbook, 3rd Ed., p. 568, McGraw-Hill, 1941. Binary Block Coding By S. P. LLOYD (Manuscrii)t received March 16, 1956) From the work of Shannon one knows that it is possible to signal over an error-making binary channel with arbitrarily small 'probability of error in the delivered information. The effects of errors produced in the channel are to be eliminated, according to Shannon, by using an error correcting code. Shannon's proof that such codes exist does not provide a practical scheme for constructing them, however, and the explicit construction and study of such codes is of considerable interest. Particularly simple codes in concept are the ones called here close packed strictly e-error-correcting {the terminology is explained later). It is shown that for such a code to exist, not only 7nust a condition due to Hamming be satisfied, but also another condition. The main result may be put as follows: a close-packed strictly e-error-correcting code on n, n > e, places cannot exist unless e of the coefficient vanish in (1 + xy(l — x)"~^~^ when this is expanded as a polynomial in x. I. IXTRODUCTIOX In this paper we investigate a certain problem in combinatorial analysis which arises in the theory of error correcting coding. A develop- ment of coding theory is to be found in the papers of Hamming^ and Shannon^; this section is intended primarily as a presentation of the terminology used in subsequent sections. We take (0, 1) as the range of binary variables. B}^ an n-word we mean a sequence of n symbols, each of which is 0 or L We call the individual symbols of an 7?-word the letters of the 7?-word. We denote by -B„ the set consisting of all the 2" possible distinct ??-words. The set 5„ may be mapped onto the vertices of an n-dimensional cube, in the usual way, by regarding an n-word as an ?i-dimensional Cartesian coordinate ex- pression. The distance d(u, v) between w-words u and v is defined to be the number of places in which the letters of u and r differ; on the ?z-cube, this is seen to be the smallest number of edges in paths along edges be- tween the vertices corresponding to u and v. The weight of an 7?-word u 517 518 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 is the number of I's in the sequence u; it is the distance between u and the »-word 00- • -0, all of whose letters are 0.* A binary block code of size K on n places is a class of K nonempty dis- joint subsets of Bn where in each of the K sets a single ?i-word is chosen as the code word of the set.f Each such set is the detection region of the code word it contains, and we shall say that any ?i-word which falls in a detection region belongs to the code word of the detection region. The set consisting of those /«-words which do not lie in any detection region we call limbo.t A close packed code is one for which limbo is an empt}' set; i.e., a code in which the detection regions constitute a partition (disjoint covering) of £„ . A sphere of radius r centered at 7i-word u is the set [v:d(u, v) ^ r] of n-words v which differ from u in r or fewer places. A binary block code is e-error-correcting if each detection region includes the sphere of radius e centered at the code word of the detection region. We say that a binary block code is strictly e-error-correcting if each detection region is exactly the sphere of radius e centered at the code word of the detection region. This paper is devoted to the consideration of close packed strictly e-error-correcting binary block codes. We shall refer to such a code as an e-code, for bre\dt3'. Hamming observes that a necessary condition for the existence of an e-code on n places is that 1 + n + I n(n - l) + . . . + (^^ (1) be a divisor of 2". In this paper we derive an additional necessary condi- tion. Our condition includes as a special case a condition of Golay for the existence of e-codes of group type, and applies to all e-codes, whether or not they are eciuivalent to group codes. § * If Bn is regarded as a subset of the real linear vector space consisting of all sequences a = (ai , 02 , • • • , an) of n real numbers, then the "weight" of an n-word is simply the A norm (defined as || a ||i = ^J" I "" 1^' ^^'^ ^"-'^ "distance" is the metric derived from this norm. t The term "block code", due to P. Elias. serves to distinguish the codes of fixed length considered here from the codes of unbounded delay introduced by Elias, Reference 3. J In a communications S3-stem- using such a code, the transmitter sends onh- code words. If, due to errors in handling binary symbols, the receiver delivers itself of an n-word other than a code word then: (a) if the «-word lies in a detec- tion region, one assumes that the code word of the detection region was intended; (b) if the n-word lies in limbo, one makes a note to the effect that errors have occurred in handling the word but that one is not attempting to guess what they were. § The terms "group alphal)et" (Slepian^), "systematic code" (Hammingi), "symbol code" (Golay^), "check symbol code" (Elias'), "paritj- check code", are roughly synonymous. More precisely, a group code is a parity check code in which all of the parit}' check forms are homogeneous ("even"), so that 00 ■ • • 0 is one of the code words; see Reference 5. BINARY BLOCK CODING 519 II. DISTRIBUTION OF CODE WORDS Suppose an c-code on n places is given. Let us inquire as to the dis- tribution of weights of code words. We denote by v^ the number of code words of weight s, 0 ^ s ^ r?, and by G{x) = Z Psx' (2) the generating function for these numbers, with x a complex but other- wise free variable. We show in this section that G(x) satisfies a certain inhomogeneous linear differential equation of order e. If there exists an e-code on n places then this differential equation will have G(x) as a polynomial solution; the necessary condition for the existence of an e-code on n places given in Section 4 is essentially a restatement of this fact.* First, however, we must derive the differential ecjuation and obtain its solutions. If Wa is a code word of the given e-code (1 ^ a ^ K), define the set oi j -neighbors of Wa as the set of n-words which lie at distance exactly 7 from iVa ; designate this set by Sj(Wa). (So(Wa) is the set whose only element is Wa itself.) Our derivation is based on the observation that, in an e-code on ?i places, U U Sjiw„) = Bn t (3) a=l i=0 is a partition of 5„ . For, the detection regions: e U SiiWa), I Sa^ K 3=0 are disjoint, and in each such sum representing a detection region the summands are disjoint (the distance function being single valued). Furthermore, each n-word of S„ lies in some detection region (close packed property) and hence appears in one of the sets Sj{Wa) for some a and for some j satisfying 0 ^ j ^ e. The set U Sj(iv„) a = l * The author is not yet able to demonstrate the converse. That is, suppose one obtains a polj-nomial sohitionGfi) of (11), below, satisfying; appropriate boundary conditions, and from it some coefficients p^ , 0 ^ s ^ n. It does not follou- from the methods of this article that there is actually some e-code on n places for which these vs represent the number of code words of weight s. t U = set union. 520 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 consists of the 7i- words which are ^-neighbors of some (not specified) code word ; let us refer to these 7i-words simply as j-neighbors. Denote by ifj,, the number of ^'-neighbors which are of weight s (with vo.s = j^s , as above). Applying (3) to the n-words of weight s, we see that Ps + P1.S + • • • + Pe,s = r\ 0 ^ s ^ n (4) is the total number of n-words of weight s. If we multiply (4) by x' and sum on s, we ha^'e G(x) + G,(x) + • • • + Ge(x) = (1 + xy (5) where n GA^) = 2 yj.^^' (6) s=0 is the generating function (with respect to s) for the numbers Vj,s . We now express Gj(x), 0 ^ j ^ e, in terms of G{x). Suppose code word w is of weight s; that is, w consists of s ones and n — s zeros in some order. A j-neighbor of iv is obtained by choosing J places out of n and changing the letters of w in these places, O's to I's and I's to O's. If, in this procedure, q of the I's of iv are changed to O's, so that j — q of the O's are changed to I's, then the resulting ^-neighbor of iv is of weight s — q -{- (j — q). Xow, there are ( 1 ways of choosing q places among (11 — s \ . _ 1 ways of choosing j — q places among the n — s where the letters of ic are 0. Thus, of the ( . j different j-neighbors of w, the number ( j • _ ) ^^^ ^^ weight s + J — 2q. We may regard each of these as con- tributing l-.r^'^"'"^' to the generating function Gj(x) of (6) (provided 0 ^ j ^ e, so that there is no overlap) ; hence, summing over all j-neigh- bors of a code word and then over all code words, Gj(x) =±v.t (')h " ') x^^--'^ Q^j^e* (7) s=0 9=0 V?/ V "~ f// From the easily verified polynomial identitj' j=o Q=o \Q/\J ~ Q f] - S)^«+/-27 * The limits (0, x) on the q summation are merely for convenience; the bi- nomial coefficients vanish outside the proper range, under the usual convention. BIXAKY BLOCK CODIXG 521 (w, s integers, 0 ^ s ^ n) it follows that f. fs\{n - s\ ^.+i_2, _ 1 f {x + yYil + xyy-' . k \q)\j -q) ~ 2^- h W' ^ where contour C is, say, a small circle around the origin, taken posi- tively. Thus _ 1 f a+xyr (x + y\ (8) = LjGix) where the operator Lj is thus defined. Change of integration variable gives T .rM - (1 - •^')""'' f G{z) dz (9) 2Tri JcA^ - xzy-''+^{z - xy+^ (1 - xY''' d' G(z) ^0 \j - vl dz' (1 — xzy-'+^ (1 - xYd^Gix) pi dxP (with Cx a small circle enclosing x but not x~^, x" 7^ 1). Thus Lj may be regarded as a Hnear differential operator of order y, (Lo = 1). Using this result, (5) may be given the form (1 + xT = [Lo + Li + • • • + UG{x) = 1 [ ql^l (1 + xyTGi^^A dy (10) 2x1 Jc 1 — y \1 + xy/ = MG{x) this last expression as a definition of operator M. Written as a differential equation, (10) is ^ (1 - .V -g /n - A ^, d^^ ^ p! ^o\ r / dxP It is straightforward that the only singularities of this equation are regular singularities^ at .r = ±1, =c. III. THE DIFFERENTIAL EQUATION In this section we discuss (11) without reference to the fact that G{x) is supposed to be a generating function. That is to say, with n and e 522 THE BELL SYSTEM TECHNK'AL JOURNAL, MARCH 1957 fixed but arbitrary non-negative integers, we denote by G(x) = f: UsX (12) s=0 any solution of (11) regular in the unit circle. It proves convenient to introduce certain functions /„, {(a;) defined by /„.,(.r) = (1 + x^d - xy-' A (13) s=0 where the coefficients 0 s! when f is not an integer, and e , Ve~i , • • • , yo are those of (31). This condition is discussed a little further in Appendix A. BINAEY BLOCK CODING 529 using the differential operator form for Ly, (9). On the other hand, the function iPy{n, n) 2x1 Jt (^ - n)ipe(n - 1, ^) L \x) = V ' 7 , + (Pe(w - l,n) s even 1 + w \\s / \\s '.-=r^{(:)+"(-^)'"-(r(::;i)} ^-^ Case V: e = 2, ?i = 90 The double error correcting codes for n = 2, 5 are covered by Cases II, III, respectively. The discovery that 1 + 90 + K90)(89) = 2'- is due to Golay. We have 2^2(n - 1, ^) = (2^ - n + 1)^' - (n - 1) with roots i[w - I ±{n - 1)-] Since these roots are not integers when n = 90, there can be no 2-code for n = 90.* H. S. Shapiro has shown (in unpublished work) that the Hamming condition for e = 2 is satisfied only in the cases n = 2, 5, 90, so that the only nontrivial 2-codes are those equivalent to the majoritj^ rule code on 5 places. Case VI: e = 3, n = 23 Golay finds: 1 + 23 + K23)(22) + (23)(22)(21)/6 = 2" and gi\'es explicitly a 3-code on 23 places of group type. We have ^■M - 1, .^) = (2^ - n + l)[(2s^ - n + 1)"' - (3/^ - 5)] and when n = 23 we verify that the roots are the integers 7, 11, 15. Computations by the author show that for n < 10 the Hamming con- dition for e = 3 holds only when n = 3, 7, 23. * This settles a question raised by Golay, who shows that there is no code of group type in this case, but not that there is no code at all. BINARY BLOCK CODING 533 For e = 4 we have 2M(n - 1, ^) = [(2^ - n -\- 1)" - (3n - 7)]' - ((3/?" - 80w + 40) For n = 4, 9 this reduces to the forms given under Cases II, III. Pre- liminary calculations by the author shows that any other solutions of the Hamming condition for e = 4 must be such that n > 10^°, so that the question of the existence of 4-codes (other than the majority rule code) is somewhat academic. Computations of Mrs. G. Rowe of the Mathematical Research De- partment show that Cases I-VI cover all cases of the Hamming condition being satisfied in the range 0 ^ e ^ n, 1 ^ /^ ^ 150 Appendix A From (13) we have \l-{-xJ (1+.t)''^o E '-«=5(:)(:::)C^:;J (^^) The coefficients Kp,s(7i, t; i) vanish unless s ^ ^ + p; if n and p — t are non-negative integers then the coefficients Kp,s(n, r; t) are positive integers provided t — p -\- t :^ s and vanish otherwise. In particular, (setting r = 1, t = e), 2''('' ~ ^)^M - 1,^) = Z {-iy'-%.s p[t+i] (t < k) (2) then we shall certainl}^ be content with the selection of any one of the associated t populations as the best one. As an index of the true difference (or distance) between the best and second best populations we introduce the symbol d - P[i] - Pm (3) 540 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 It is assumed that if the difference d between the best and second best populations is small enough, then the error involved in wrongly select- ing the second best process as the best one is an error of little or no con- sequence. The experimenter is therefore asked to specify two quantities which will determine the number n of observations he is required to take from each process. Specification: He specifies the smallest value d* (0 < cZ* ^ 1) of rf for which it would be economically desirable to make the correct selection. He also specifies (4) a probability P* (0 ^ P* < 1) of making a correct selection that he would like to guarantee whenever the true difference d ^ d*. Letting Pes = Pes (?>[!] , • • • , Vw) denote the probability of a correct selection we can now rewrite the specification that the experimenter wants to satisfy in the simple form Pes ^ P* for d ^ d* (5) [The word "specification" will be used below to denote the specified pair of constants (d*, P*) as well as the condition (5); it will be clear from the text which is meant.] Since the final selection is to be made on the basis of the observed frequency of success, the essential problem is to find the number n of observations required per process to satisfy the specification (5). The possibility that d may be less than d* is not being overlooked. The region d < d* is being regarded as a zone of indifference in the sense that ii d < d*, then we do not care which process is selected as best so long as its p- value is within d* of the highest p- value pn] . For values of P* S i/k no tables are needed since a probability of 1/k can be at- tained by chance alone. Some comments on the above approach and on a possible modifica- tion have been placed in Appendix I in order to preserve the conti- nuity of the paper. CONFIDENCE STATEMENT After the experiment is completed and the selection of a best process is made, the experimenter can make a confidence statement with confi- dence level P*. Let ps denote the true p-"\'alue of the selected population and let pa denote the maximum true /}-\'alue over all unselected popula- SELECTING THE BEST OXE OF SEVERAL BIXOML\L POPULATIONS 541 tions. Then the confidence statement, consisting of two sets of inequah- ties P[i] - d* ^ ps ^ p \ 11] ^PV2] S Pu ^ Pvi\ + d*^ or 0 ^ p[i] — ps ^ d* 0 S Pu - 7^12, ^ ci*^ has confidence level P*. It should be noted that the above confidence statement is not a statement about the value of any p but is a statement about the correctness of the selection made. LEAST FAVORABLE CONFIGURATION The main idea used in the construction of the tables was that of a least favorable configuration. Before defining this concept we shall define the set of configurations Pm - d = p[2\ = Pm = • • • = pik] (6) obtained by letting d in (6) varj^ o\'er the closed interval {d*, 1) as the Less- Favorable set of configurations. It is intuitively clear and will be rigorously shown in Appendix II that if our procedure satisfies the specification for any true configuration (6) with d = d and p[i] = p^, then it will also satisfy the specification when pli] - / ^ Pm ^ Pi?] ^ • • • ^ P[k] (7) Of course, we shall be interested particularly in the case in which d equals the specified value d*. If d = d* is fixed in (6), then (6) specifies the differences between the p- values, but the '"location" of the set is still not specified. We shall use p[i] to locate the set of p-values. The proba- bility Pes of a correct selection for configurations like (6) with d — d* depends not only on d*, n and k but also on the location pm of the largest p- value (except for the special case h = 2 and n = 1). [In the corresponding problem for selecting the largest population mean of k independent Normal distributions with unit variance," this probability Pes depends only on the differences and, hence, only on (/ in the configura- tion correspondhig to (6)]. When (6) holds with any fixed value of c?, the probability Pes (for any fixed n) may be regarded as a function of p[ii where d ^ p[\] ^ 1). This function is continuous and bounded over a closed interval and therefore assumes its minimum value at some point p[i] {d) = p[i\ {d;n) in the closed interval {d,\). Fig. 1(b) gives the value of p\i] (d) as a function of d for A- = 3 and for 7i = 1, 2, 4, 10 and x . For any particular value 542 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 of n and for d = d* we .shall be particular!}^ interested in the value p(^] = P[i] (d*;n) since this (as shown in Appendix II) gives the smallest probability Pes of a correct selection for all the configurations included in the statement of the experimenter's specification. This particular con- figuration (6) with d = d* and p^] = pl^ (which depends on n) is called the Least-Favorable Configuration. Although the least fa\-orable configuration depends on n, it has been empirically found that for n ^ 10 (and in some cases for n ^ 4) the least favorable configuration is approximately given by p[i] = I (1 + d*) in which the two values, p[i] and p^2] = Pm — d* are symmetric about §, This symmetric configuration clearly does not depend on n. Fig. 1(b) shows that as n —^ y^ the least favorable configuration approaches this symmetric configuration (i.e., the straight line marked n = x) q^(ite rapidly for any value of d. In Appendix III it is proved that the sym- metric configuration is least favorable as n -^ x. Fig. 1(a) shows for k = 3,n = 10, and any vsdue of d the error in Pes which arises as a result of using the symmetric configuration instead of the true least favorable configuration. 0.0002 a. o (T 0.0001 a. LU 0 1.0 0.9 or O.J cr o 0.7 0.6 0.5 (a) '^ -^ n = i (b) ^ ^ ^ ^ -^ ^^ ^ ^ V 2_ ^<^ ^ EXACT FORMI. ^ ,,, 13d +12 JLA FOR n=2 ^^:^^^ -'V25d2 +24d = 00 ■^I'J 18 0.1 0.2 0.3 0.4 0.5 0.6 d (or d*) 0.7 0.8 0.9 1.0 Fig. 1 — (a) Error in P cs as a result of using the sj-mmetric configuration in- stead of the least favorable configuration for k = 3, n = 10, and any common true difference d. (b) Least favorable value pd] (d) of pd) as a function of the common true difference d = p[i] — pn] , i ^ 2, for A- = 3 and selected values of n. (for d = d*, Pdi (d) = pui) SELECTING THE BEST ONE OF SEVERAL BINOMIAL POPULATIONS 543 CONSTRUCTION OF THE TABLES Consider any fixed value of d*. For each of a set of increasing values of n the minimum probability Pes of a correct selection for d ^ d* (i.e., the probabiUty for the least favorable configuration) was computed. These calculations were then inverted to find the smallest n for which the Pes is greater than or equal to the specified value P*. Tables I through IV give the smallest value of n for k — 2, 3, 4, and 10, for d* = 0.05 (0.05) 0.50, and for selected values of P*. Graphs corresponding to these tables are given in Figs. 2 through 5. For small values of n (say, ?t < 10) it was necessary to approximate P[i] by calculating the Pes exactly for several values of p[i] and proceed- ing in the direction of the minimum probability Pes- For the special case n = 2 and A; = 3 an explicit formula for p[i] is given on Fig. 1. For large values of n (say, n > 10) the Pes was calculated by assum- ing the symmetric configuration. Here it was necessary to make use of the normal approximation to the binomial. Fortunately the appropriate table needed in this normal approximation is already published." The proof that this table is appropriate is given in Appendix III. The result- ing value of 71 is given by n^^,(l-d*')^^, (8) where the constant B, depending on P* and k, is equal to jC and C is the entry in the appropriate column of Table I of R. E. Bechhofer's paper. A short table of B values. Table V (see page 550), is included in this paper to make it self-contained. The middle expression in (8) will be referred to as the normal ap- proximation and the right hand expression in (8) will be referred to as the "straight line" approximation. In many cases it has been empiri- cally found that these two expressions give close lower and upper bounds to the true value. Thus by noting the curves drawn in Figs. 4 and 6 for k = 4, P* ^ 0.75 it appears that for all values of d* the true Pes is between the normal approximation and the straight line approximation. Assuming this to be so, it follows that for k = 4, P* '^ 0.75 the required value of n satisfies the inequalities [A (1 - .-)] S n S [,4J (9) where [x] denotes the smallest integer greater than or equal to the en- closed quantity x. This result (9) is empirical and not based on any mathematically proven inequalities. It is used here only to estimate the 544 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 Table I — Number of Units Required per Process to Guarantee A Probability of P* of Selecting the Best of A: Binomial Proc- esses WHEN THE True Difference p[i] — p[o^ is .\t Least d*. (k = 2) The three values in each group are: (1) Normal approximation, (2) Straight line approximation, and (3) Smallest integer required. d* P* 0.50 0.60 0.75 0.80 0.85 0.90 0.95 0.99 0.05 0 0 0 12.81 12.84 14 90.77 90.99 92 141.30 141.66 142 214.29 214.83 215 327.66 328.48 329 539.77 541 . 12 541 1079.70 1082.41 1082 0.10 0 0 0 3.18 3.21 4 22.52 22.75- 23 35.06 35.41 36 53.17 53.71 54 81.30 82.12 83 133.93 135.28 135 267.90 270.60 270 0.15 0 0 0 1.39 1.43 2 9.88 10.11 11 15.39 15.74 16 23.33 23.87 24 35.68 36.50- 37 58.78 60.12 60 117.57 120.27 120 0.20 0 0 0 0.77 0.80 1 5.46 5.69 6 8.50- 8.85+ 9 12.89 13.43 14 19.71 20.53 21 32.47 33.82 34 64.94 67.65+ 67 0.25 0 0 0 0.48 0.51 1 3.41 3.64 4 5.31 5.67 6 8.06 8.59 9 12.32 13.14 14 20.29 21.64 22 40.59 43.30 42 0.30 0 0 0 0.32 0.36 1 2.30 2.53 3 3.58 3.93 4 5.43 5.97 6 8.30 9.12 9 13.68 15.03 15 27.36 30.07 29 0.35 0 0 0 0.23 0.26 1 1.63 1.86 2 2.54 2.89 3 3.85- 4.38 5 5.88 6.70 7 9.69 11.04 11 19.38 22.09 21 0.40 0 0 0 0.17 0.20 1 1.19 1.42 2 1.86 2.21 3 2.82 3.36 4 4.31 5.13 5 7.10 8.46 9 14.21 16.91 16 0.45 0 0 0 0.13 0.16 1 0.90 1.12 2 1.39 1.75- 2 2.11 2.65+ 3 3.23 4.06 4 5.33 6.68 7 10.65+ 13.36 13 0.50 0 0 0 0.10 0.13 1 0.68 0.91 1 1.06 1.42 2 1.61 2.15- 3 2.46 3.28 4 4.06 5.41 5 8.12 10.82 10 SELECTING THE BEST ONE OF SEVERAL BINOMIAL POPULATIONS 545 Table II — Number of Units Required per Process to Guaran- tee A Probability of P* of Selecting the Best of k Binomial Processes when the True Difference p[i] — p[2] is at Least (/*. (/c = 3) The three values in each group are: (1) Normal approximation, (2) Straight line approximation, and (3) Smallest integer required. d* P* 0.50 0.60 0.75 0.80 0.85 0.90 0.95 0.99 0.05 30.89 30.97 31 78.16 78.36 79 205.06 205.58 206 272.36 273.04 273 363.06 363.97 364 496.14 497.38 498 732.63 734.46 735 1305.21 1308.49 1308 0.10 7.66 7.74 8 19.39 19.59 20 50.88 51.39 52 67.58 68.26 69 90.08 90.99 91 123.10 124.34 125 181.78 183.62 184 323.85+ 327.12 327 0.15 3.36 3.44 4 8.51 8.71 9 22.33 22.84 23 29.66 30.34 31 39.53 40.44 41 54.02 55.26 55 79.77 81.61 82 142.12 145.39 145 0.20 1.86 1.94 3 4.70 4.90 5 12.33 12.85- 13 16.38 17.07 17 21.84 22.75- 23 29.84 31.09 31 44.07 45.90 46 78.51 81.78 81 0.25 1.16 1.24 2 2.94 3.13 4 7.71 8.22 9 10.24 10.92 11 13.65- 14.56 15 18.65+ 19.90 20 27.54 29.38 29 49.07 52.34 52 0.30 0.78 0.86 2 1.98 2.18 3 5.20 5.71 6 6.90 7.58 8 9.20 10.11 10 12.57 13.82 14 18.57 20.40 20 33.08 36.35- 35 0.35 0.55+ 0.63 2 1.40 1.60 2 3.68 4.20 5 4.89 5.57 6 6.52 7.43 8 8.91 10.15 10 13.15+ 14.99 15 23.43 26.70 26 0.40 0.41 0.48 1 1.03 1.22 2 2.70 3.21 4 3.58 4.27 5 4.78 5.69 6 6.53 7.77 8 9.64 11.48 11 17.17 20.45- 20 0.45 0.30 0.38 1 0.77 0.97 2 2.02 2.54 3 2.69 3.37 4 3.58 4.49 5 4.90 6.14 6 7.23 9.07 9 12.88 16.15+ 15 0.50 0.23 0.31 1 0.59 0.78 2 1.54 2.06 3 2.05- 2.73 3 2.73 3.64 4 3.73 4.97 5 5.51 7.34 7 9.81 13.08 12 546 THE BELL SYSTEM TECHNICAL JOT*RX.\L, MARCH 1957 Table III — Number of Units Required per Process to Guar- antee A Probability of P* of selecting the Best of /,■ Binomial Processes when the True Difference 7>[i] — p[2] is at Least d*. (fc = 4) The three values in each group are : (1) Normal approximation, (2) Straight line approximation, and (3) Smallest integer required. d* P* 0.50 0.60 0.75 0.80 0.85 0.90 0.95 0.99 0.05 69.85- 70.02 71 132.65+ 132.99 134 282.27 282.98 283 357.52 358.42 359 456.82 457.96 458 599.53 601.03 601 848.30 850.42 850 1438.12 1441.72 1442 0.10 17.33 17.51 18 32.91 33.25- 34 70.04 70.74 71 88.71 89.61 90 113.35- 114.49 114 148.76 150.26 150 210.48 212.61 212 356.83 360.43 360 0.15 7.61 7.78 8 14.44 14.78 15 30.74 31.44 32 38.93 39.82 40 49.74 50.88 51 65.29 66.78 67 92.37 94.49 94 156.61 160.19 160 0.20 4.20 4.38 5 7.98 8.31 9 16.98 17.69 18 21.51 22.40 23 27.48 28.62 29 36.06 37.56 38 51.03 53.15+ 53 86.50+ 90.12 89 0.25 2.63 2.80 3 4.99 5.32 6 10.61 11.32 12 13.44 14.34 14 17.17 18.32 18 22.54 24.04 24 31.89 34.02 34 54.06 57.67 57 0.30 1.77 1.95- 3 3.36 3.69 4 7.15+ 7.86 8 9.06 9.96 10 11.58 12.72 13 15.19 16.70 17 21.50- 23.62 23 36.44 40.05- 39 0.35 1.25+ 1.43 2 2.38 2.71 3 5.07 5.77 6 6.42 7.31 7 8.20 9.35- 9 10.76 12.27 12 15.23 17.36 17 25.82 29.42 28 0.40 0.92 1.09 2 1.75- 2.08 3 3.71 4.42 5 4.70 5.60 6 6.01 7.16 7 7.89 9.. 39 9 11.16 13.29 13 18.92 22.53 21 0.45 0.69 0.86 2 1.31 1.64 2 2.79 3.49 4 3.53 4.42 5 4.51 5.65+ 6 5.92 7.42 7 8.37 10.51 10 14.19 17.80 17 0.50 0.53 0.70 2 1.00 1.33 2 2.12 2.83 3 2.69 3.58 4 3.43 4.58 5 4.51 6.01 6 6.38 8.50+ 8 10.81 14.42 13 SELECTIXG THE BEST OXE OF SEVERAL BIXOMIAL POPULATIONS 547 Table IV — Number of Units Required per Process to Guaran- tee A Probability of P* of Selecting the Best of k Binomial Processes when the True Difference p[i] — pi2] is at Le.\st d*. (k = 10) The three values in each group are: (1) Normal approximation, (2) Straight line approximation, and (3) Smallest integer required. d' P* 0.50 0.60 0.75 0.80 0.85 0.90 0.95 0.99 0.05 216.96 217.50+ 218 312.51 313.29 314 511.15+ 512.43 513 604.04 605.55+ 606 722.50- 724.31 725 887.54 889.77 890 1165.49 1168.41 1169 1798.01 1802.51 1803 0.10 53.83 54.38 55 77.54 78.32 79 126.83 128.11 128 149.87 151.39 151 179.27 181.08 181 220.22 222.44 222 289.18 292.10 291 446.12 450.63 449 0.15 23.62 24.17 25 34.03 34.81 35 55.66 56.94 57 65.77 67.28 67 78.67 80.48 80 96.64 98.86 98 126.90 129.82 129 195.77 200.28 198 0.20 13.05+ 13.59 14 18.80 19.58 20 30.75- 32.03 32 36.33 37.85- 38 43.46 45.27 45 53.39 55.61 55 70.10 73.03 72 108.15 112.66 111 0.25 8.16 8.70 9 11.75- 12.53 13 19.22 20.50- 20 22.71 24.22 24 27.16 28.97 29 33.37 35.59 35 43.82 46.74 46 67.59 72.10 70 0.30 5.50- 6.04 7 7.92 8.70 9 12.95+ 14.23 14 15.31 16.82 17 18.31 20.12 20 22.49 24.72 24 29.53 32.46 32 45.56 50.07 48 0.35 3.90 4.44 5 5.61 6.39 7 9.18 10.46 11 10.84 12.36 13 12.97 14.78 15 15.93 18.16 18 20.92 23.85- 23 32.28 36.79 35 0.40 2.85+ 3.40 4 4.11 4.90 5 6.73 8.01 8 7.95- 9.46 10 9.51 11.32 11 11.68 13.90 13 15.34 18.26 17 23.66 28.16 26 0.45 2.14 2.69 3 3.08 3.87 4 5.05- 6.33 6 5.96 7.48 8 7.13 8.94 9 8.76 10.98 11 11.50+ 14.42 14 17.75 — 22.25+ 20 0.50 1.63 2.18 3 2.35- 3.13 4 3.84 5.12 5 4.54 6.06 6 5.43 7.24 7 6.67 8.90 9 8.76 11.68 11 13.52 18.03 16 1.00 0.80 0.60 O.bO 0.40 0.30 0.20 0.10 0.08 0.06 0.05 0.04 0.03 0.02 0.01 ^^^ *"^ --- ^^o^^ "^^O^"^ ^ *S^^ ^^^^w '******«»w '"***^ ►^r* *\ "^^v. ^^^^^['v^^^ -v ^ ^ ^ .^^^ \ nS^ 9 V. \ •s ^"^^ ^ ^^ \ ^ 1 V "vJ \ ^V,^^ V ^ ■ "v, s^^ ^ ""^O-ff \ s ■v \ "^^ ;^ X ^ ^ ^ ^ \ V ^ 5 6 8 10 20 30 40 50 60 80 100 n 200 300 400 Fig. 2. — Number of units /; required per process to guarantee a probability of P* of selecting the better of two binomial processes when the true difference d is at least d*. t.oo 0.80 0.60 0.50 0.40 0.30 0.20 0.10 0.08 0.06 0.05 0.04 0.03 0.02 0.01 ^^^^^^^j~^^ ^^^ ^^-~N^' ""-o-,,.^^! ^^^^ ^^^O*'^ "-^ ^ \.^^ ^\^ o<;\^ ^ ^ '"^^^ ^^^ \ ^ Sv ^^$^ r^ \ \ \ ^ "V \ \ \ \ ^ \ ^ ^ ^^^ % ^^^^^ ^ - \ ^•-Sn -^ - ^<^ ^ \ Si •^ C:^C^<^^^ \ ^ ^\ ^^^ ^ ^ ^ ^ ^X V \ \ \ "-^^^ ^ 1 1 1 1 ^ ^ 4 5 6 8 10 20 30 40 50 60 80 100 n 200 300 400 Fig. 3. — Number of units n required per process to guarantee a probability of P* of selecting the best of three binomial processes when the true difference d is at least d*. 548 1.00 0.80 0.60 0.50 0.40 0.30 0.20 0.10 0.08 0.06 0.05 0.04 0.03 0.02 0.01 ^^r- -..^ ;"^ ^ 1 -^ ^ x_ 5 ■v. \r ■^ ^ \/\, ^ ^\ \ V >^;^^" ^ ^*i 9- \ \ V ^ \ ^ :::^ ^ ^ 8 \ ^ V \ v ^ g ^ V ^ ^ c^"^^\ \ K \ ■s SS> ^^[^ V - ^ v^ 'v >s ^^ ^^ "^ V, \!^ ^ V k. ^^^ ^^ ^ ^ \ V^ 1 1 1 4 5 6 8 10 20 30 40 50 60 80 100 n 200 300 400 Fig. 4 — Number of units n required per process to guarantee a probability of P* of selecting the best of four bionimal processes when the true difference d is at least d*. 1.00 0.80 0.60 0.50 0.40 0.30 0.20 0.10 0.08 0.06 0.05 0.04 0.03 0.02 0.01 ^^^ --^^_l "^^ ^^^^^ xi ^^ §^ ""--^^ ^ 1 ^ "^ •^^ \ ^ \ ^ > ^^^ ::vCi ^-^ 4.. ■^ \ '^ \^^ ^^\ ^ ^ ^ ^ 59 0 ^ 1 fe :^^ - *"s ^ k .^<::>^^ s - \ ^ ■0^ ^ "^^ v ^^ "^^ "^ 1 1 1 1 5 6 8 10 20 n 30 40 50 60 80 100 200 300 400 Fig. 5 — Number of units n required per process to guarantee a probabilitj"" of P* of selecting the best of ten binomial processes when the true difference d is at least d*. 549 550 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 1.00 0.80 0.60 0.50 0.40 0.30 0.20 0.10 0.08 0.60 0.50 0.04 0.03 0.02 0.0 1 — - — — — L ro' "^ \ ^^^, ^^^^^ •J^/1- ^ > T***" ^^^ r>^.^ ^0^. ^'°^v^^=:^,V T^^'^^^J^.^a,. ^^ -'vo; -<=S!^ ^ ^ ^ %v ^^^ ^1 ^. ^ "V X A^ ^ ^ ^ ^ -~v ^ V. ^^ v,^ - "^ ^ ^Q>_ - \ ^ V ^0 - "^ ^^^ ^ 1 1 1 1 5 6 8 10 20 30 40 50 60 80 100 n 200 300 400 Fig. 6 — • Bounds for the number of units 7i required per process to guarantee a probability of P* of selecting the best of four binomial processes when the true difference d is at least d*. Table V — Values of B = |C^ to be Used with the Normal Approximation (8) where C is Obtained from Table I OF R. E. Bechhofer's Papers Prob. of Correct Selection * = 2 * = 3 * = 4 k = 10 0.99 2.7060 3.2712 3.6043 4.5063 0.95 1.3528 1.8362 2.1261 2.9210 0.90 0.8212 1.2434 1.5026 2.2244 0.85 0.5371 0.9099 1.1449 1.7965+ 0.80 0.3541 0.6826 0.8961 1.5139 0.75 0.2275- 0.5139 0.7074 1.2811 0.70 0.1375- 0.3832 0.5575- 1.0892 0.65 0.0742 0.2792 0.4347 0.9256 0.60 0.0321 0.1959 0.3325- 0.7832 0.55 0.0079 0.1294 0.2468 0.6569 0.50 0.0000 0.0774 0.1751 0.5438 SELECTING THE BEST ONE OF SEVERAL BINOMIAL POPULATIONS 551 order of magnitude of the error in our large sample calculations. For ex- ample, if k = 4, f/* = 0.05 and P* = 0.90, then from Table Y we find that B = 1.5026 and the two expressions in (8) yield 599.54 and 601.04. Hence, it would follow from (9) that n is 600 or 601 or 602. Based on an investigation of the behavior of these two approximations in the case of smaller P* or larger d* values, it is estimated that the true value of n is 601. Even if the correct value is 600 or 602 the error would be less than | of 1 per cent. Fig. 6 illustrates these bounds on the Pes for ^ = 4, P* = 0.50, 0.75 and 0.99. For P* ^ 0.60 the straight line approxima- tion is a closer lower bound than the normal approximation. It is estimated that all integer entries in Tables I through IV have an error of at most 1 per cent and, in particular, that all entries under 100 are exact. OTHER VALUES OF k In addition to the tables and graphs for k = 2, 3, 4 and 10 there are also graphs (Figs. 7 through 14) on which interpolation can be carried out for k = 5 through 9 and on which extrapolation can be carried out for /.• = 11 through 100. By plotting n versus log k (or 7i versus A" on semi-log paper) and drawing a straight (dashed) line through the values of n for A' = 4 and k = 10 we obtain results which are remarkably good approximations for k > 10. The solid curve in these figures connects the true values obtained for k = 2, 3, 4 and 10. For large values of k the theoretical justification for a straight line approximation is gi^•en in Appendix V. In order to check the accuracy of our procedure of drawing the straight line through the values of 7i computed for A- = 4 and A- = 10, we have chosen two points at A; = 101 for an independent computation of the probability of a correct selection. For P* = 0.90, d* = 0.10 and A- = 101 the dashed line in Fig. 12 gives n as approximateh" 400. To check this we computed the normal approxi- mation to the probability Pes of a correct selection for the least favor- able configuration in the form Pes ^ r F''\x + h)f{x) dx = -]r r F''\xV2 + /i)e~"' dx (10) where 2d* V^ Vl - d*~ (= 4.02015 in this example) (11) fix) is the normal density and Fix) is its c.d.f. This was computed by a method suggested by Salzer, Zucker and Capuano^ and the result was 552 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 700 600 500 400 300 200 100 APPROXIMATION X ^ y y x" y / ^^* o,-l°. y y - —•''*'' .1 .. _[a20. K).25 1 3 4 5 6 8 10 k 20 30 40 50 60 80 100 Fig. 7 — Number of units n required per process to guarantee a probabilit}- of P* = 0.50 of selecting the best of k binomial processes when the true difference P[il ~ Pl2i is at least d*. 700 600 500 400 300 200 100 ^ /- T- / / APPROXIMATION / / * ^ • / y / / / / / / / ,.,. 0;^0, " ** ." 1^-''' z. / , , = -----"' *"a25"' — — 1 1 4 5 6 10 k 20 30 40 50 60 80 100 Fig. 8 — Number of units n required per process to guarantee a probabilitj- of P* = 0.60 of selecting the best of k binomial processes when the true difference Pdl "~ Pl2i is at least d*. SELECTING THE BEST OXE OF SEVERAL BINOMIAL POPULATIONS 553 700 60O 500 400 300 200 100 4''' APPROXIMATION J / / / / / f J A f 0,1°- ^■0^ ^^ ^^' ^-«* // f/ ^^t^*^ 0.\5 / / / / / --■ » ^ ^ ^ * , 1 1 1 1 1 3 4 5 6 8 10 k 20 30 40 50 60 80 100 Fig. 9 — Number of units n required per process to guarantee a probability of P* = 0.75 of selecting the best of k binomial processes when the true difference P 111 ~ V [2) is at least d*. /uu — / 1 600 500 400 300 200 100 r— APPROXIMATION / / / / // // // f ^-^^ ,-' ^-"•* ^» * ■■ *^ / / / / /'/ ^ ^ ^ ■" _^ —. — — 1 ^__J___ 0-2.^ ■"0.20 — 1~ rri-j-ivi-- 0 /■''=^^^--- r=== '. 1 1 i , 1 0.25 1 5 6 8 10 k 20 30 40 50 60 80 100 Fig. 10 — Number of units n required per process to guarantee a probabilit}^ of P* = 0.80 of selecting the best of k binomial processes when the true difference Pin ~ P[2i is at least d*. 554 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 1400 1200 1000 800 600 400 200 EXACT APPROXIMATION y y y^ /" p^ y^ y y y ."' y y y y y y y/ f — —• * ^^- .2.--- .— • "* ■— - -— ^ y y ^^ ^ C=^ m == — — r 0.20f_4-; "0.25r ! 1 1 3 4 5 6 8 10 k 20 30 40 50 60 80 100 Fig. 11. — Number of units n required per process to guarantee a probability of P* = 0.85 of selecting the best of k binomial processes when the true differ- ence p[i] — p[2i is at least d*. 1400 1200 1000 800 600 400 200 y' * y y — -y y * APPROXIMATION r.'^' j;-' y y y > y y y y y y ,'/ / y' y y^ ■/ ____^--- o_^o. — — ^^ — 1 1 1 J 0,.15 _0.20 'o'a" ^-L-. ^, 1 0 K^^ig^----^^- 3 4 8 10 k 20 30 40 50 60 80 100 Fig. 12 — Number of units n required per process to guarantee a probability of P* = 0.90 of selecting the best of A; binomial processes when the true difference Pfi) ~ V\i\ is at least d*. SELECTING THE BEST OXE OF SEVERAL BINOMLIL POPULATIONS 555 1400 1200 1000 800 600 400 200 y y y y 1 APPROXIMATION ,^ f y y / / / / ^ y y y y y y / ^^* _^— --- • y - o-iP . ^^ ■-'"' ^ ^^ ** L-J- _0jb ""^•JQ ^5725 ' — in — — ^ J ' lilt 1 [ 4 5 6 8 to k 20 30 40 50 60 80 100 Fig. 13 — Number of units n required per process to guarantee a probability of P* = 0.95 of selecting the best of k binomial processes when the true difference V\\\ ~ P[2i is at least d* . 1400 1200 1000 800 600 400 200 ^^ / EXACT APPROXIMATION J y y y y / y ^^^'^ •-• "^ 0^^--- -'^' ^,^ — • ■^ 0.1_5 P- — ... *— — < \ _0.£0 1 1.1,1, 1 1 4 5 6 8 10 20 30 40 50 60 80 100 Fig. 14 — Number of units n required per process to guarantee a probability of P* = 0.99 of selecting the best of k binomial processes when the true difference Pdl ~ ?)[2i is at least d*. 556 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 >J^ Pes = 0.9168 as compared to the value 0.90 in Fig. 12. The expression (10) is derived in Appendix III. Another check was made at P* = 0.99, d* = 0.20 and k = 101. The value of 71 from Fig. 14 is 162. The value of the Pes computed from (10) using Salzer, Zucker and Capuano^ is 0.9925+. Further calculation using (10) yielded the more accurate results 378 and 154 instead of 400 and 162, respectively, in the above illustrations. The error in both cases is less than 6 per cent; for smaller values of k the percentage error Avill, of course, be much less. For interpolation the results are estimated to be within 1 per cent of the correct value. For example we estimate from Fig. 11 that the re- quired value of n for k = 5, P* = 0.85 and d* = 0.05 is 523. This value was computed by the normal approximation and found to be 522. TIED POPULATIONS In computing the tables and graphs it was assumed that if two or more populations are tied for first place then one of these is selected by a chance device which assigns equal probability to each of them. The experi- menter may want to select one of these contenders for first place by economic or other considerations. In most practical problems we may assume that such a selection is at random as far as the probability of a correct selection is concerned. Hence, it appears reasonable to use the tables in this paper without any corrections even when the rule for tied populations is altered in the manner described above. It is interesting to note that in the yield problem the experimenter may settle the question of ties for first place by taking more observa- tions mitil the tie is broken. However, in the life-testing problem he may not settle ties by letting the test run beyond time T since the best process for time T is not necessarily the best for a time greater than T. In some applications when there are two or more populations tied for first place, the experimenter may prefer to recommend all these con- tenders for first place rather than select one of them by a chance device. In this case we shall agree to call the selection a correct one if the recom- mended set contains the best population (or, when /;[i] = 'p[2] , if the recommended set contains at least one of the best populations). Exact tables for the procedure so altered have not been computed. However, if the value of ?i is large and this rule for tied populations is used, then the experimenter may reduce the tabled Aalues by an amount ecjual to the largest integer contained in l/d*. For example, using the abo^•e rule for tied populations for the case k = 2, P* = 0.99, d* = 0.30, the tabled value 29 can be reduced by 3 giving the result 26. SELECTING THE BEST OXE OF SEVERAL BINOMLA.L POPULATIONS 00/ ALTERNATIVE SPECIFICATION If the experimenter has some a priori knowledge about the processes, then he will prefer to specify the following three quantities in order to determine the number n of observations he is required to take from each process. Specification: He specifies pm and p[2] (0 ^ p[2] ^ ^ 1) in the neighborhood of his estimate of the 4: P[l] probabihties associated with his processes. He also speci- fies a probability P* (0 ^ P* < 1) that he would hke to guarantee of making a correct selection whenever the true p[i] ^ p[i] and the truep[2] < * (12) Table VI — Number of Units Required per Process to Guaran- tee A Probability of P* of selecting the Better of Two Bi- nomial Processes when the True p[i] ^ p* ] and the True P[2] ^ p*2] . (Alternative Specification, k = 2) p* P*[i] = 0.75 p'li] = 0.95 pU = 0.90 P*li] = 0.85 p\i] = 0.95 p\^] = 0.60 p],^ = 0.80 pU = 0.80 ^*2) = 0.80 p\.^ = 0.90 0.50 1 1 1 1 1 0.60 2 2 3 9 6 0.75 10 6 13 53 27 0.80 14 8 19 83 40 0.85 21 11 28 124 60 0.90 32 16 42 189 91 0.95 53 25 68 312 149 0.99 106 49 135 623 298 Table VII — Number of Units Required per Process to Guar- antee a Probability of P* of Selecting the Best of Four Bi- nomial Processes when the True p^ ^ pfu and the True P[2] ^ p*2] . (Alternative Specification, k = 4) p* P[i] = 0-75 Pli] = 0.95 P*li] = 0.90 PU] = 0.85 p\i] = 0.95 /.[*jj = 0.60 PU] = 0.80 />*,) = 0.80 /.*,, = 0.80 pU = 0.90 0.50 7 4 10 42 21 0.60 14 8 18 79 39 0.75 28 14 37 168 80 0.80 35 18 46 211 101 0.85 45 22 59 268 128 0.90 59 28 77 350 171 0.95 83 39 107 493 239 0.99 139 65 182 831 399 558 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 Again we can rewrite the specification that the experimenter wants to satisfy in the simple form (13) Pea ^ P* for pii] ^ p*] and p^] S pfaj Tables VI and VII give the number of observations required per proc- ess for several selected triplets of specified constants (p*] , pfi] , P*) wtien k = 2 and ^- = 4. These results are also given in graphical form in Figs. 15 and 16. 180 170 160 150 140 130 120 1 10 100 I 90 80 70 60 50 40 30 20 10 IT ' ■ / : / / 1 / 11 / / Pm = 0.85/ 1 // / i // P[1] = 0.8o/ / kj 1 / i / r\ // I / / ^ -^ <^ /° )^ ^ y:^ ^W ^ 0.5 0.6 0.7 o.a 0.9 1.0 Fig. 15 — Number of units required per process to guarantee a probability of P* of selecting the better of two binomial processes when the true p [ij ^ p*i] and the true pn] ^ pi^] • SELECTING THE BEST ONE OF SEVERAL BINOMIAL POPULATIONS 559 For example, on the basis of past experience the experimenter may estimate that the probabilities associated Avith his k = 4 processes are all in the neighborhood of 0.60. This constitutes his a priori knowledge. He may then decide that he would like to make a correct selection with probability P* = 0.85 when the best process has a yield of at least 75 per cent and all the others have a yield of at most 60 per cent. Enter- ing column 1 of Table VII we find that n = 45 observations per process are required. It is much more difficult to furnish tables for the alternative specifica- 170 160 1 / / / 150 y \ / / / 140 130 / / / 1 / 1 / / 120 no / / P* =0.85/ 1 \ rr 100 11^ / I / 90 Pf2j = 0.80/ 0 95/ / / 80 1 / y 1 / J / 70 0.90/ / / / 1 / 0.90/ / 60 / / / , / / f / / / / 50 / / / /0.75 / / / 0.80 / > / / 40 / / / / / / / / 0.95y 30 / y y y/o.i^O y y y y >^ ^y^ ^ 20 10 n / ^y ^^ \^ _^ ^ ^^ ^^^ r-'o.f 30 — r^ ' 0 5 0 6 0 7 0 a 0 9 1. Fig. 16 — Number of units required per process to guarantee a probability of P* of selecting the best of four binomial pi-ocesses when the true pm ^ p*i| and the true p(2i ^ p[2) . 560 THE BELL SYSTEM TECHNICAL JOURNAL, ^L\ltCH 1957 tion since there is an extra parameter to vary and the appropriate tables for the normal approximation are not available. In the computation of these probabilities the least favorable con- figuration P[i] = P*i] and p*2] = p[2] = piz] = Pik] (14) was used. It follows from Appendix II that if the probability of a correct selection is at least P* when (14) holds, then it will also be at least P* when Pm ^ pfi] and p*2] ^ pi2] ^ Pm ^ • • • ^ p [k] (15) For small values of n, exact calculations were carried out. A typical exact calculation is shown in Appendix IV. The approximations used for large ?i are given in Appendix III. I.OO 0.90 0.80 0.70 0.60 P2* 0.50 O40 0.30 O20 0.10 A K / / V, A / / y / / ^ / / / / / / / / AeJ/ / A {. / / / / / 0 / Y <' / / / / / i V y y /< ^ ^M^ 0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Fig. 17 — Illustration of the varying zones of indifference and the least favor- able configuration for ^• = 4 and P* = 0.85. (For n ^ 5 the longest vertical segment occurs at the point An where the abcissa and the ordinate are svmmetrical about 0.5) SELECTING THE BEST ONE OF SEVERAL BINOML\L POPULATIONS 561 COMPARISON OF THE T\\^0 SPECIFICATIONS It should be pointed out that for a given Z; the same value of n would satisfy the specification for different specified triplets For example with k = 4, P* = 0.85 and n fixed we could vary p*] in the alternative specification and compute for each p[i] the correspond- ing largest value of p*2] such that the specification (P*, p*j , p*o]) is satisfied. This is shown in Fig. 17 for n = 5, 10, 20 and 60. The vertical distance in Fig. 17 between the appropriate curve and the 45° line (n = 3c) is the length of the indifference zone (p[i] , P[2]). The indif- ference zone widens in the center and narrows at both ends. In fact we find just as in the original specification that for n greater than (say) 4 the indifference zone is widest when p* ] and p* ] are symmetrical about 0.5. It is clear that the two specifications would coincide if we took d* in the original specification and set p*] = § (1 + d*), p[2] = | (1 — d*) 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 ^ — ^==3 '■ ^^ ^^ n=ioc 4 zfe ^"^ "t:^ / 5o/ ///^ / X / / 2S/ / / / y^ /// / / / / / /// / y^ / / ////° ^ /f/7 5/ 1 //// / ^ / V 1 0.5 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 d Fig. 18 — Probability of a correct selection as a function of tlie true difference '^ — V\\\ ~ P[3] under the least favorable configuration for k = 2 and selected values of n. 562 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 in the alternative specification. We shall be interested in comparing the alternative specification (P*, p*] , p*]) "with the original specification with the same P* and with d* set equal to p*] — pf2] • It is clear that the value of n required for the original specification will always be larger. The original specification is simpler and is preferable to the alternative specification when little or nothing is known about the processes on test, but the price that has to be paid for ignorance is an increase in the 0.95 y^ y"^^^^^^^^^^^ / i / /■ /" y^ .^' n = ioo/ 1 / 1 y / / X 0.90 / 1 / / ^ / y 1 / / // ' X / y 0.85 / '°' ' // / / /^ 1 / / / / / / 25/ / / / / < 0.80 1 /p/ / / / Iff / / ^ / 0.75 0.70 I , '//«/ / If 'Ma y^ ^ 0.65 0.60 0.55 0.50 0.45 0.40 ft, W/ A / '/ /// / / / ///// O.Jj jv 0.30 0 0.05 0.10 0.15 0.20 0.26 0.30 0.35 0.40 0.45 Q50 d Fig. 19 — Probability of a correct selection as a function of the true difference ^ — Pdl ~" P(2i under the least favorable configuration for ^• = 3 and selected values of n. SELECTING THE BEST ONE OF SEVERAL BINOMIAL POPULATIONS 563 required number of observations. In the example of the preceding sec- tion the value of n required for the alternative specification is 45 as compared to 51 observations per process required to satisfy the original specification with the same P* and with d* = p*i) — 'p*2]. Here the saving is only moderate. The saving will be much larger if pfij and 1. 00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.25 n = ioo^ / ^;^7;:^=^;:>?:^=^ so/ / ^ V- 1 /20/ // / / / / ' //, 7 ,0. / / r //// / / / / // / / / // 11 / / / // f f / //// / / //// f / V h / r 11 1 1 V '/ / 0 0.05 0.10 0.15 0.20 025 030 0.35 Q40 0.45 0.50 d Fig. 20 — Probability of a correct selection as a function of the true difference f^ = P[i) — p[2] under the least favorable configuration for A: = 4 and selected values of n. 564 THE BELL SYSTEM TECHNICAL JOUKXAL, MARCH 1957 p*2) are further from 0.5 and d* is small. For example, for fc = 4, P* = 0.95, p[i] = 0.95 and p[2] = 0.90 the value of n required for the alter- native specification is 239 as compared to 850 observations per process required to satisfy the original specification with the same P* and with d* = 0.05. The alternative specification is justified on the basis of a priori or previous information about the approximate values of the p's. REVERSING THE TABLES The experimenter may wish to use the tables of this paper in reverse. For example, if n is fixed and d* is specified by the experimenter, then by using the appropriate table he can find the probability of a correct selection that is guaranteed for d ^ d*; i.e., a greatest lower bound to the probability of a correct selection for d ^ d*. This process of re- versing the given ^^alues and the values to be computed can most easih' be carried out on graphs. For example, the above problem of finding the guaranteed probability of a correct selection given d* and n is most easily carried out on Figs. 18, 19, and 20. Appendix I MODIFICATION OF THE ORIGINAL SPECIFICATION The same value of n will, of course, satisfy the specification for dif- ferent pairs of specified values (d*, P*). From a purely mathematical point of view it is not necessary that d* should be the smallest difference for which the experimenter desires to make a correct selection. For ex- ample, if k = 3 the experimenter could specify any one of the four pairs (0.10, 0.60), (0.25, 0.90), (0.30, 0.95) or (0.40, 0.99) and obtain the same result, namel}^ n = 20. The experimenter may prefer to specify the curve or set of points corresponding to a fixed n. Several such curves are given in Figs. 18, 19, and 20 for k = 2, 3, and 4, respectively. The experi- menter would decide in advance on some property of the curve that he considers desirable and from the appropriate figure he could find the curve with the smallest n-value that satisfies the desired property. The main point of the above paragraph is to point out that the original specification in the body of the paper is one particular way, but not the only way, of stating a specification that will determine a value of n. The only criterion for a good way to state the specification is that the experimenter should be able to bring his best judgment (or best guesses) to bear on the quantities that have to be specified in advance. SELECTING THE BEST ONE OF SEVERAL BINOMIAL POPULATIONS 565 Appendix II MONOTONICITY PROPERTIES We shall prove that for any fixed d (0 ^ d ^ 1) the probability Pes of a correct selection is smaller for the configuration: P[l] - d = P[2] = P[3] = ■■■ = pik] (Al) than for any configuration given by P[i] - d ^ p[2] ^ p[s] ^ • • • ^ Pik] (A2) where pn] is considered fixed and the p^] (i ^ 2) are variables. In other words, for fixed p[i] the probability Pes is a strictly increasing function of each of the differences Pm - P[i] ii ^ 2) We shall need the following lemma. Lemma 1: For any pair of integers x, n (0 ^ x ^ n) and any 6 {0 S d ^ 1), not depending on p, the function Hix; p, d) = i; crpxi - pY-' + ec:p'{i - py-^ (as) is a decreasing function of p over the unit interval (0 ^ p ^ 1). More- over, it is strictly decreasing unless (x = 0 and 6 = 0) or (x = ?i a7id e = i). Proof: Differentiating (A3) with respect to p gives after telescoping terms {6 - l)xCxV(l - p)""" - d(n - .r)C.V(l - p)"~"~' (A4) which is negative for 0 < p < 1 unless (x = 0 and 6 = 0) or (x = n and 6 = 1). Since ^ is continuous in p at p = 0 and p = 1 the lemma follows. Let X(i) denote the chance number of successes that arises from the binomial process associated with Pii] (*■ = 1, 2, • • • , n) the value of the integer n is assumed to be fixed throughout this discus- sion and it will usually not be listed as an argument. The probability Pes of a correct selection for any configuration with p^j > p[2] is given by the expression on the top of the next page. 566 THE BELL SYSTEM TECHNICAL JOURNAL, \L\.RCH 1957 k Pes = P{X(o < Xa) for t ^ 2} + i J^ P{Z(„) = Zo) and X(o < Xd) for i ^ 2, i ^ a} + " • (A5) + T-P{X(1) = X(2) = ••• = X{k)} It will be necessary to write the Pes for any configuration with p[i] > p[2] in another form which is more useful for the purpose at hand. Corre- sponding to an}' binomial chance variable A' (which takes on integer values from 0 to n) we define a "Continuous Binomial" chance variable Y by letting Y be uniformly distributed in the interval (j — 2) i + 2) with the same total probabiHty in this interval as the ordinary binomial assigns to the integer j, namelj'' C/V(i -py~' (i = o, 1, ..-,71) We will now show that the probability Pc^ of a correct selection is unal- tered if we replace each of the k discrete binomials b}' its corresponding continuous binomial. Let F(o denote the continuous binomial (CB) chance variable associated with p[i] and let ya) denote any value it can take on. Let X(,) denote the nearest integer to F(o and let i\i) denote the nearest integer to y^i) {i = 1, 2, • • • , A;). Then X(,-) is a discrete bi- nomial (DB) with the same parameters (/)[,] , n). Let g{x, p) = CxV(l - pr-' (X- = 0, 1, . • ., n) Then the density g(y, p) of the continuous binomial (disregarding the half-integers) is given by g{y, p) = g(x, p) where x is the nearest integer to y. For two continuous binomials (i.e., k = 2) the probability Pes of a correct selection for any configuration with p[i] > p[2] is given bj' /n+l/2 P{Yi2) < 2/(1)1^(^(1) ;P[i])dya) (A6) 1/2 " /-5;(l) + l/2 = J2 / P{y{2) < y(i)]g(ya) -yPii]) dya) (A7) a;(l)=0 Jx(i)-l/2 (A8) Within any interval (x^) — h, •'C(i) + h) ^'6 have P{Y,2) < yo)} = P{X(2) < Xa)} -f P{Z(2) = a-a)}P{F(2) < ya) 1 X(2) = .T(i)} = P{X(2) < Xa)} + h P{X<2) = Xa)} (A9) which depends only on Xa) . Hence from (A7) SELECTING THE BEST ONE OF SEVERAL BIXOML^L POPULATIONS 567 PcsiCB) (AlO) 2(1)=0 = P{X(2) < Xd)} + iP{X(2) = Za)} (All) = PcsiDB) (A12) The above is easily generalized to hold for any k > 2. The details of this generalization are omitted. For general k this equality holds not only for the important special case pn] > p[2] but also for the more general case (2) for any t < k. Since the latter result is not needed here, the proof is omitted. If we let G(y;p) denote the c.d.f. of the continuous binomial then lemma 1 can be restated in the following form. Lemma 2: For any integer n and any y, the function G{y;p) is a non- increasing function of p. In particular, for — | < y < n -\- ^ it is a strictly decreasing fuyiction of p. Proof: For any y, set x = x(y) and d = d(y) equal to the integer part and the fractional part of (y -\- h), respectively. Then for any y we have the identity in p G(y;p) = H(x;p, d) (0 ^ p ^ 1) (A13) For any ^o such that — | < //o < w + | we have 0 ^ x{yo) ^ n and 0 ^ diijo) S 1- The inverse function y{x,d) = x -\- 6 — | is a single- valued function of the pair {x,d); the two particular pairs (0,0) and (w,l) correspond to the unique values y = —^ and y = n -\- ^, re- spectively. Hence the pair [x{yo), ^(^o)] must be different from these two particular pairs above since it corresponds only to yo which is in the interior of the interval ( — Ij ^ + h)- Lemma 2 then follows from lemma 1 and the fact that G(y;p) is identically zero in /; fei- y ^ —h and identi- callj^ one in /) for ?/ ^ n + |. The probabilitj^ Pes of a correct selection for k discrete or k continuous binomials for any configuration with p[i] > pi2] can now be A\Titten as /«+l/2 r k -j n P{Yu^ < 2/(1)} g(ya) ; Pm) dy^) (A14) 1/2 Lt=2 J /7!+l/2 r k n G{y;p[;]) g(:y;p[i]) dy. (A15) 1/2 L»=2 Clearly if any one or more of the p[,] (i ^ 2) decreases, holding p^] fixed, then it follows from lemma 2 that the right member of (A 15) is 568 THE BELL SYSTEM TECHNICAL JOURNAL, >L\.RCH 1957 strictly increasing, i.e., for fixed p^j the Pes is a strictly increasing func- tion of each of the differences pm — p[i] (i ^ 2) as was to be shown. It follows from the above result that in searching for a least favorable configuration among all those in which the experimenter wants his specification satisfied w^e may restrict our attention to those of the form (Al). Moreover, we may set d in (Al) equal to d* since, for d > d* and fixed p[i] , the difference d — d* may be added to each p[i] {i ^ 2) and the probability of a correct selection is increased. Then (A 15) reduces to /n+l/2 G'-\y;Pw - d*)g(r,Pii,) dy (A16) -1/2 It was shown in the section on the least favorable configuration that there is a value p[i\ of p{\] which when substituted in (A16) gives the minimum value Pes oi Pes • We can now prove the following result in which p[i] is not fixed. For any specified pair p*2] ^ p*i] the probability Pes of a correct selection is smaller for the configuration P[i] = P*i] ; P*2] = Pm = Pm = •■' = p[k] (A17) than for any configuration given by P[i] ^ pti] ; pfo] ^ Pm ^ P[3] ^ ••• ^ Pik] (A18) This is shown by considering two separate steps. The first step is to increase p[i] holding all the other p's fixed at p[2] . For any arbitrary set of values of pn] with pn] > pi2] the probability of a correct selection can be written as Pes =J: f"^''\ n G{y,p,,,)'] [1 - G(y,pn,)]g(y,pu^) dy (A19) ;=2 J-ll2 L»=2. if^i J by adding the probabihties that Y(i) > yu) > niin { F(2) , • • • , Yu-d , Yu+d , " , Y^k) } for For j = 2,3,---,k Pm > Pm = Pm = • ■ • = Pm = ph this reduces to Pes = (k _ 1) r^ " [1 - G(y;p,^,)]G'-'(y;pt2d9(y,ph) dy (A20) J-1I2 SELECTING THE BEST ONE OF SEVERAL BINOMIAL POPULATIONS 569 This resuK can also be obtained by starting with (A16) with P[2] = • • • = Pl^.] = p[ij - Cl* = p* ] and integrating by parts. It is clear from (A20) that for fixed p[i] (i ^ 2) the Pes is an increasing function of p[i] and is indeed strictly increasing for p[i] in the unit interval. The second step is to hold pn] fixed and to decrease the values of P[i] {i ^ 2). This increases the probability of a correct selection by our previous result above. This proves the monotonicity property for the alternative specification. Appendix III LARGE SAMPLE THEORY ■ — ORIGINAL SPECIFICATION For p[i] > p[2] the probability of a correct selection satisfies the in- equalities P{Xa, > X,i){i = 2, 3, ••• ,1-)} < Pes < P{Xa) ^ X,i,{i = 2,3, ••• ,/c)} (A21) unless p[i] — 1 and p[2] = 0 in which case equality signs hold since the three quantities above are all unity. Letting ^[i] = 1 — p[\] , we can write the left member of (A21) as P {Zi > . ^*^ = (t = 1, 2, ...,/. - 1)\ vpmgm + (pm - rf*)(?[i] + d*) J (A22) where 7 = X(i) - Z(.-+i) - nd* (■ ^ -i r, I — ^\ (A23) For the configuration (Al) with d — d* the chance variables Z,- tend to normal chance variables iV(0,l) with zero mean and unit variance as n — > X . We have purposely omitted any continuity correction in (A22) in order to get a better approximation for the smaller values of Ji. To derive the least favorable configuration for large n we can restrict our attention to those configurations given by (Al) with d = d*. The quantity pfi] , which minimizes (A22), is obtained by maximizing the expression in (A22) Q(p) = p(l -p)^(p- f/*)(l -p + d*) (A24) = -2p' + 2(1 + d*)p - d*(l -\- d*) (A25) 570 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 The derivative of Q{p) vanishes at IHn = HI + ^/*); q[l^ =- HI - d*) (A26) Avhich gives the symmetric configuration. Clearly this value of p gives to Qiv) its maximum value, ^1 — d*^). This proves that the symmetri- cal configuration is least favorable in the limit as n -^ oc . Under the configuration (Al) with d = (/* and n -^ co the distribution of the chance variables Zi {% = \, 2, ■ ■ ■ , k — \) approaches a joint multivariate normal distribution with zero means, unit variances and correlations given by piZ.Z,) = , , ^''''^''' — y^ a ^ j) (A27) ?>[i]9[i] + {Vm - d*){qii] + d*) which do not depend on n. For the symmetric configuration this reduces to the simple form p{ZiZj) = i a y^j). (A28) This is precisely the case which arises in [1] and consequently the tables in [1] can be used for our problem when (the answer) w is large. The con- stants C = C(P*, k) tabulated in [1] solve the equation P Izi >-:^{i = l,2,---,k-l)\ = P* (A29) for standard normal chance variables Zi satisfying (A28). If we equate C/s/2 and the corresponding member of (A22), then we obtain for the symmetric configuration X.^ d*Vn V2 — /i " (A30) or solving for n and letting B = jC this yields the large sample normal approximation n^-^Jl-d*') (A31) Since d* is usually small when n is large and since the solution in (A31) is usually somewhat smaller than the true value, then it is of interest to examine the simpler approximation n ^ ^^ (A32) which is greater than the result in (A31). This is called the straight line approximation since it plots as a straight line on log-log paper as shown SELECTING THE BEST ONE OF SEVERAL BINOMIAL POPULATIONS 571 in Figs. 2 through 5. As d* —* 0 both the normal approximation and the true value are asymptotically equivalent to the straight line approxima- tion. The normal approximation to the probability of a correct selection can also be written in another form similar to (A16) which is actually more useful for numerical calculations. The left member of (A21) can be written as < ^^^1 Vp[i]g[ii + (P[i] - P[i]) VnX] p ,j^^ ^ ^^^ Vp[i]q[i] iJ where TTr -X"(t) — np[i] / KnA\ Wi = / it = 1, 2, • • • , k) (A34) and Wi is the same function of X(i) as Wi is of X(i) . The outside summa- tion in (A33) is over the values taken on by wi as x^d runs from 0 to n. As n ^ [ii - P[i]) Vn i:[pc- Vpami] f{w)dw (A35) where J{t) is the standard normal density and F{t) is the standard normal c.d.f. For the symmetric configuration, which is least favorable for large n, (A3o) reduces to Pes ^ r F'-' (w + -f ^^ \ fiw) dw (A36) ^-^ \ Vi - d*y A straightforward integration by parts gives the alternative form 2d* V~n ^ ''—00 L 1 - F[iv - Vi - rf*v- F' -{w)f(w)dw (A37) which corresponds to (A20). A simple method for computing such integrals based on Hermite poly- nomials is described by Salzer, Zucker, and Capuano. LARGE SAMPLE THEORY — ALTERNATIVE SPECIFICATION The expression corresponding to (A22) for the alternative specification IS pL, > -/Pm-Pr2])vg (^• = 1, 2, . . . , k - 1)) (A38) ^ vpfi]?*!] + Pr.]q[2] i 572 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 which is ah-eady -written for the least favorable configuration. The tables^ are not immediately applicable since the correlations piZ^Zi) = , J'*'^'^ , a ^ j) (A39) are not, in general, equal to ^. In the cases treated in Tables VI and VII, p*2] ^ 0.5 and hence p^gii] < P[2]?[2] so that the correlations (A39) are all less than |. It was found that linear interpolation on the required value of n between the results for p = 0 and p = ^ gives moderately good results when n is large. The result for p = J is given by n - X ^P^fl^^ + ^:-y'^ (A40) with \ = 2B where B is given in Table V. The result for p = 0 is given by (A40) \vith X = Xo^ where Xo is the solution of the equation P{Z > -Xo} = P*"^'-'^ (A41) which can easily be found from univariate normal probability tables. An explicit expression for the result of this linear interpolation is \ ^ Pu]g[ii(4i?-Xo-) +Pt2ig[2]Xo (^^^ ^* ^ ^ Q _) (^^^2) P ^ CS / * * s iP[l] - P[2]) The expressions for the probability of a correct selection for the al- ternative specification corresponding to (A36) and (A37) are cs T)^ n^ r F''~' {aw + h)fiw) dw (A43) = a(A; - 1) 1°° Tl - ^('^^^) F'-\w)f(w) dw (A44) „ = /^ > 0 a,.d „ ^ ^"'-'-/"f^" a 0 (A45) ^ PmQvi] Vp[2]9[2] These expressions can also be e\'aluated by the method described by Salzer, Zucker and Capuano. where SELECTING THE BEST ONE OF SEVERAL BINOMIAL POPULATIONS 573 Appendix IV TYPICAL EXACT CALCULATION A. Original Specification The exact expression (A5) for the probabiUty of a correct selection for any configuration simphfies if the configuration is least favorable. For any pair of integers (j,n) we define b,, = P{Xa) = j\ = CyVpfiO'Cgm)""' (0 ^ J ^ n) (A46) b^j = P{X,,y = j] = CrivU - d*yigii} + d*r^' {O^j^ n) (A47) B,j = P{X(2) ^ j} (A48) Then the exact probability Pes of a correct selection for the least favorable configuration can be written as Pes = j: hj Z -%^. bh B^ (A49) 3=0 1=0 L -\- I where B2,-i is defined to be zero. Here, for each value of X(i) , the letter i denotes the number of processes that tie with X(i) for first place and for any given value of i the conditional probability of a correct selection is 1/(1 + i). Taking k = 4 as a typical case, we can write (A49) more explicitly as n Q n n Pes = Z^ bijB^j-i + ^ Z^ bijbijBij-i + 2^ bijb2jB2j-i (A^O) 1 " + 1 S K^lj 4 j=o If n ^ 10 then we may use the symmetric configuration, i.e., we may set Pui = 2 (1 + d*), in computing from (A49) or (A50). B. Alternative Specification The probability P^s of a correct selection for the alternative specifi- cation is the same as in (A49) and (A50) except that we now define bii = P{X(,) = j} = C/'(pti,y(qti,r~\i = 1, 2) (A51) B2J = P{Zc2) ^ j] (A52) A typical exact calculation for A; = 4, using (A50), (A51) and (A52) with Pm = P[i] = 0.75 574 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 and Pl2] Vm = Vw = V{2\ is given in Table AI. Exact values for the individual and cumulative binomial probabilities were obtained from References 4, 5 and 6. Table AI — Calculation of the Pes Vm = P*i] = 0 7^ >; P[2] = Piz] = P[4i = Pm = 0.60; fc = 4 j *..,• b2J B!.,-l b\.i H. 5L,_, bLm 0 0.00000 0.00010 0.00000 0.00000 1 0.00003 0.00157 0.00010 0.00000 0.00000 0.00000 0.00000 2 0.00039 0.01062 0.00168 0.00011 0.00000 0.00000 0.00000 3 0.00309 0.04247 0.01229 0.00180 0.00008 0.00015 0.00000 4 0.01622 0.11148 0.05476 0.01243 0.00139 0.00300 0.00016 5 0.05840 0.20066 0.16624 0.04026 0.00808 0.02764 0.00459 6 0.14600 0.25082 0.36690 0.06291 0.01578 0.13462 0.04939 7 0.25028 0.21499 0.61772 0.04622 0.00994 0.38158 0.23571 8 0.28157 0.12093 0.83271 0.01462 0.00177 0.69341 0.57741 9 0.18771 0.04031 0.95364 0.00162 0.00007 0.90943 0.86727 10 0.05631 0.00605 0.99395 0.00004 0.00000 0.98794 0.98196 Check totals. . . . 1.00000 1.00000 10 3 = 1 0 10 1 3 = 1 10 2 ^IJ" ^2,; Bl 3=1 ;_i = 0.44715 y_i = 0.08493 ,_i = 0.01464 1 1" 4 ,=0 h\,, = 0.00145 Pes To tal = 0.54817 = Appendix V In this appendix it will be shown that for large values of k the value of n required to meet any fixed specification (d*, P*) is approximately equal to some constant multiple of (In A). Let n = n(k) denote the unique positive decimal solution of the equa- tion [" F'~\iv + h \/n)f{w) dw = P' (A53) SELECTING THE BEST OXE OF SEVERAL BIXOML\L POPULATIONS 575 where f(iv) and F(w) are defined above, P* and b are known constants with 1/k < P* < 1 and b > 0 and the argument k is a positive integer. Let £ be a (small) fixed number such that 0 < e < Min (P*, 1 — P*). Then c < P* — l/k for sufficiently large A;. Let A = A{e) be defined by f /(ly) Jit; = 1 - £ (A54) so that 0 < f F''~\iD + ?> aA)/(mO rfw ^ £ (A55) •'|to|>.l for any integer k ^ 1, any n > Q and any 6 > 0. Let n' and n" be the unique positive decimal solutions, respectively, of the equations 1 F'"'(w + b \/n')I{w) dw = P* - £ (A56) f F'"\w + ^ \//^)/(«^) dw = P* (A57) where P*, b and ^- are the same as in (A53). It follows from (A55), (A56) and (A57) that for any integer k ^ 1 n' ^11 S n" (Ao8) From (A54) and (A57) we have f F^'-'iw + by/^')fAw) dw = -^ (Ao9) where f.iiw) is the density of the normal distribution, truncated at A and —A. The right hand member of (A59) is positive and less than unity since £ < 1 — P*. Hence there exists a Wa with \wa \ ^ A such that ( F'-'iw + b^^')fAw) dw = F'~\wa + bV^') (A60) J— A Since Wa is bounded and 7i" is large for large k we can use the well-known approximation L V^iriwA + b\/n") J _ , (A61) ^ ^^ f_ 0^1) exp [-(wa-{- bVn"f/2\ '2^iwA + bVn") i where only the leading term is considered. Hence from (A59), (AGO) 576 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 and (A61) - Inln i— -M + In (/.• - 1) V ^* / (A(J2) = h(wA + bV^'f + In (uu + hVn^) Since Wa is bounded and In \/n" = o{n") it follows that for large k n" ^ (2/6') In (/,• - 1) ^ r' in /.• (A63) where (7 is a proportionality factor. Starting with (A54) and (A56) the same argument gives the same result as (A63) for n' . Hence, bj^ (A58), the same result must hold for yi. ACKNOWLEDGMENT The authors wish to thank R. B. Murphy, J. W. Tukey, E. L. Kaplan, S. S. Gupta, E. Bleicher, S. Alonro, all of Bell Telephone Laboratories, and Prof. R. E. Bechhofer of Cornell University for helpful suggestions and constructive criticism in connection with this paper. REFERENCES 1. Bechhofer, R. E., and Sobel, M., On a Class of Sequential Multiple Decision Procedures for Ranking Parameters of Koopman-Darmois Populations with Special Reference to ]\Ieans of Normal Populations, in preparation. 2. Bechhofer, R. E., A Single-Sample Multiple Decision Procedure for Ranking Means of Normal Populations with Known Variances, Ann. Math. Stat., 25, pp. 16-39, 1954. 3. H. E. Salzer, R. Zucker, and R. Capuano, Table of the Zeros and Weight Fac- tors of the First Twentv Hermite Polynomials, Journal of Research of the N.B.S.,48, pp. 111-116,' 1952. 4. National Bureau of Standards, Tables of the Binomial Probabilitj- Distribu- tion, App. Math. Series 6, 1950. 5. Ordnance Corps, Tables of the Cumulative Binomial Probabilities, ORDP 20-1, 1952. 6. Harvard Computation Laboratory, Tables of the Cumulative Binomial Prob- ability Distribution, Harvard University Press, Cambridge, 1955. Bell System Technical Papers Not Published in This Journal Allison, H. W., see Moore, G. E. Anderson, P. W., and Talman, J. D.^ Pressure Broadening of Spectral Lines at General Pressures, Conf. Proc. Breadth of Spectral Lines, pp. 29-61, Oct., 1956. Arnold, S. M.^ The Growth and Properties of Metal Whiskers, Tech. Proc. Am. Electroplaters Soc, pp. 26-31, 1956. Bala, V. B., see Geller, S. Bashkow, T. R.i Effect of Nonlinear Collector Capacitance on Collector Current Rise Time, Trans. LR.E. PGED, ED-3, pp. 167-172, Oct., 1956. Beach, A. L., see Thurmond, C. D. BiRDSALL, H. A.,1 and Gilkensen, P. B.^ The Application of Electrical Instruments for Measuring Moisture Contents of Textiles, Am. Dyestuff Reporter, Proc. Am. Assoc. Tex. Chem. and Colorists, 45, pp. 935-945, Dec. 17, 1956. Committee report of which Messrs. Birdsall and Gilkensen were members. Bridgers, H. E.,^ and Kolb, E. D.' The Distribution Coefficient of Boron in Germanium, J. Chem. Phys., 25, pp. 648-650, Oct., 1956. 1 Bell Telephone Laboratories, Inc. ' Western Electric Company. 677 578 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 Buck, T. M.,' and McKim, F. 8.1 Depth of Surface Damage Due to Abrasion on Germanium, J. Elec- trochoni. Sue, 103, pp. 51)3 5!)7, Nov., l!)5(j. COMPTON, K. (i.' Potential Criteria for the Cathodic Protection of Lead Cable Sheath, Corrosion, 12, pp. 37-44, Nov., 1956. David, E. E., Jr.,i and McDonald, H. S.^ Note on Pitch-Synchronous Processing of Speech, J. Aeons. Soc. Am., 28, pp. 1261-1266, Nov., 1956. Dickinson, D. J.,'* Pollak, H. 0.,' and Wannier, G. H.^ On a Class of Polynomials Orthogonal Over a Denumerable Set, Pacific J. Alath., 6, pp. 239-247, 1956. Felker, J. H.^ Complexity With Reliability, I.R.E. Stndent Quarterly, 3, pp. 7-11, Dec, 1956. Geller, S.^ A Set of Effective Coordination Number (12) Radii for the ^-Wolfram Structure Elements, Acta Crys., 9, pp. 885-899, Nov. 10, 1956. Geller, S.,^ and Bala, V. B.^ Crystallographic Studies of Perovskite-like Compoimds. II — Rare Earth Aluminates, Acta Crys., 9, pp. 1019-1025, Dec. 10, 1956. GULDNER, W. G.^ The Application of Vacuum Techniques to Analytical Chemistry, Vakuum-Technik, pp. 159-166, Oct., 1956. GULDNER, W. G.^ Tentative Method for Analysis of Carbon in Nickel, A.S.T.INI., Chem. Anal. Electronic Nickel (E107-56T), pp. 20-25, Sept. 1956. 1 Bell Telephone Laboratories, Inc. ^ Pennsylvania State University, University Park. TECHNICAL PAPERS 579 GULDNER, W. G.' Tentative Method of Test for Oxygen, Hydrogen and Nitrogen in Nickel, A.S.T.M., Chem. Anal. Electronic Nickel (E107-56T), pp. 26-33, Sept., 195(5. GuLDNER, W. G., see Thurmond, C. D. Hagstrum, H. D.' Auger Ejection of Electrons from Molybdenum by Noble Gas Ions, Phys. Rev., 104, pp. 672-683, Nov. 1, 1956. Auger Ejection of Electrons from Tungsten by Noble Gas Ions, Phys. Rev., 104, pp. 317-318, Oct. 15, 1956. Metastable Ions of the Noble Gases, Phys. Rev., 104, pp. 309-316, Oct. 15, 1956. Haring, H. E., see Taylor, R. L. Klemm, G. H.i Automatic Projection Switching for TD-2 Radio System, Commun. and Electronics, 27, pp. 520-527, Nov., 1956. KoLB, E. D., see Bridgers, H. E. Kompfner, R.i Some Recollections of the Early History of the Traveling Wave Tube, 1956 Yearbook Phys. Soc. London, pp. 30-33, 1956. Krusemeyer, H. J.,^ and Pursley, M. V.^ Donor Concentration Changes in Oxide Coated Cathodes Due to Changes in Electric Field. J. Appl. Phys., 27, pp. 1537-1545, Dec, 1956. Lewis, H. W.i Surface Energies in Superconductors, Phys. Rev., 104, pp. 942-947, Nov. 15, 1956. LovELL, L. Clarice, see Vogel, F. L., Jr. 1 Bell Telephone Laboratories, Inc. 580 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 Mallina, R. F.i Solderless Wrapped Connections, Trans. I.R.E., PGT-1, pp. 12-22, Sept., 1956. Matthl\s, B. T.,' Miller, C. E.,' and Remeik^a, J. P.' Ferroelectricity of Glycine Sulfate, Phvs. Rev., 104, pp. 849-850, Nov. 1, 1956. ISIason, W. p.' Internal Friction and Fatigue in Metals at Large Strain Amplitudes, J. Aeons. See. Am., 28, pp. 1207-1218, Nov., 1956. Physical Acoustics and the Properties of Solids, J. Acous. See. Am., 28, pp. 1197-1206, Nov., 1956. Matreyek, W., see Winslow, F. H. McDonald, H. S., see David, E. E., Jr. :McKim, F. S., see Buck, T. :\I. McSkimin, H. J.i Wave Propagation and the Measurement of the Elastic Properties of Liquids and Solids, J. Acous. Soc. Am., 28, pp. 1228-1232, Nov., 1956. Miller, C. E., see Matthias, B. T. Miller, R. C.,' and Savage, A.^ Diffusion of Aluminum in Single Crystal Silicon, .J. Appl. Phys., 27, pp. 1430-1432, Dec, 1956. MoxFORTE, F. R., see Van Uitert, L. G. Moore, G. E.,^ and Allison, H. W.^ Emission of Oxide Cathodes Supported on a Ceramic, J. Appl. Phys., 27, pp. 1316-1321, Nov., 1956. Oswald, A. A.^ Early History of Single Sideband Transmission, Proc. T.R.E., 44, pp. 1676-1679, Dec, 1956. ^ Bell Telephone Laboratories, Inc. TECHNICAL PAPERS 581 Pierce, J. R.,' and Walker, L. R.' Growing Electric Space-Charge Waves, Phys, Rev., 104, pp. 30G-307, Oct. 15, 1956. Pollak, H. 0., see Dickinson, D. .J. Pursley, M. v., see Krusemeyer, H. J. Remeika, J. P., see Matthias, B. T. Rice, J. W.=* Manufacture of Wire Spring Relays for Communication Switching Systems, Commun. and Electronics, 27, pp. 513-518, Nov., 1956. Rose, D. J.^ The Townsend Ionization Coefficient for Hydrogen and Deuterium, Phys. Rev., 104, pp. 273-277, Oct. 15, 1956. Savage, A., see Miller, R. C. Struthers, J. D.^ Solubility and Diffusity of Gold, Iron, and Copper in Silicon, J. Appl. Phys., Letter to the Editor, 27, p. 1560, Dec, 1956. SuHL, H., see Walker, L. R. 0 Swanekamp, F. W., see Van Uitert, L. G. Taylor, R. L.,^ and Haring, H. E.^ Metal-Semiconductor Capacitor, J. Electrochem. Soc, 103, pp. 611- 613, Nov., 1956. Talman, J. D., see Anderson, P. W. Thurmond, C. D.,^ Guldner, W. G.,^ and Beach, A. L.^ Thurmond, C. D.,^ Guldner, W. G.,' and Beach, A. L.^ Hydrogen and Oxygen in Single -Crystal Germanium as Determined by Vacuum Fusion Gas Analysis, .7. Electrochem. Soc, 103, pp. 603- 605, Nov., 1956. 1 Bell Telephone Laboratories, Inc. 582 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 ToRREY, Mary N.^ Quality Control in Electronics, Proc. I.R.E., 44, pp. 1521-1530, Nov., 1956. Trumbore, F. a.' Solid Solubilities and Electrical Properties of Tin in Germanium Single Crystals, J. Electrochem. Soc, 103, pp. 597-600, Nov., 1956. Van Uitert, L. G.,^ Swaxekamp, F. W.,^ and AIoxforte, F. R.' Method for Forming Large Ferrite Parts for Microwave Applications, J. Appl. Phys., Letter to the Editor, 27, pp. 1385-1386, Nov., 1956. VoGEL, F. L., Jr.,^ and Lovell, L. Clarice^ Dislocation Etch Pits in SiUcon Crystals, J. Appl. Phys., 27, pp. 1413- 1415, Dec, 1956. Walker, L. R., see Pierce, J. R. Walker, L. R.,^ and Suhl, H.' Propagation in Circular Waveguides Filled With Gyromagnetic Ma- terial, Trans. I.R.E., AP-4, pp. 492-494, July, 1956. Wannier, G. H., see Dickinson, D. J. Weinreich, G.^ Acoustodjntiamic Effects in Semiconductors, Phys. Rev., 104, pp. 321- 324, Oct. 15, 1956. Wertheim, G. K.^ Carrier Lifetime in Indium Antimonide, Phys. Hew, 104, pp. 662-664, Nov. 1, 1956. Winslow, F. H.,^ and Matreyek, W.^ Pyrolysis of Cross-Linked Styrene Polymers, J. Poly. Sci., 22, pp. 315-324, Nov., 1956. ^ Bell Telephone Laboratories, Inc. Recent Monographs of Bell System Technical Papers Not Published in This Journal* Anderson, 0. L. Effect of Pressure on Glass Structure, Monograph 2666. Bemski, G. Quenched-In Recombination Centers in Silicon, Monograph 2681. Bridgers, H. E. p-n Junctions in Semiconductors by Variation of Crystal Growth Parameters, Monograph 2668. Brown, W. L., see Montgomery, H. C. Campbell, Mary E., see Luke, C. L. Carlitz, L., and Riordan, J. The Number of Labeled Two-Terminal Series-Parallel Networks, Monograph 2667. Chase, F. H. Power Regulation by Semiconductors, Monograph 2685. David, E. E., Jr. Naturalness and Distortion in Speech-Processing Devices, Mono- graph 2687. Dodge, H. F., and Torrey, Miss M. N. A Check Inspection and Demerit Rating Plan, IMonograph 2669. * Copies of these monographs may be obtained on request to the Publication Department, Bell Telephone Laboratories, Inc., 463 West Street, New York 14, Y. Y. The numbers of the monographs should be given in all requests. 583 584 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 Eder, M. J., see Veloric, H. S. Fisher, J. R., and Potter, J. F. Apparent Density for Evaluating the Physical Structure of Steatite, Monograph 2688. Fuller, C. S., see Reiss, H. Geller, S., and Gilleo, M. A. Gadolinium Orthof errite : Crystal Structure and Magnetic Proper- ties, Monograph 2670. Gilleo, M. A., see Geller, S. GoHN, G. R. Hardness Conversion Table for Copper-Beryllium Alloy Strip, j\Iono- graph 2665. Harrower, G. a. Dependence of Electron Reflection on Contamination of Reflecting Surface, Monograph 2689. Harrower, G. A. Energy Spectra of Secondary Electrons from Mo and W for Low Primary Energies, Monograph 2690. Hovgaard, 0. M. Capability of Sealed Contact Relays, Monograph 2697. Knapp, H. M. Design Features of Bell System Wire Spring Relays, Monograph 2693. Lewis, H. W. Two-Fluid Model of an "Energy-Gap" Superconductor, Monograph 2671. MONOGRAPHS 585 Luke, C. L., and Campbell, Mary E. Photometric Determination of Germanium and Tin With Phenyl- fluorone, Monograph 2608. Manley, J. M., and Rowe, H. E. Some General Properties of Nonlinear Elements. I — General Energy Relations, Monograph 2672. McLean, D. A., and Power, F. S. Tantalum Solid Electrolytic Capacitors, Monograph 2673. McMahon, W. Dielectrics by Solidifying Certain Organic Compounds in Electric or Magnetic Fields, Monograph 2694. Montgomery, H. C, and Brown, W. L. Field-Induced Conductivity Changes in Germanium, Monograph 2695. Moore, E. F., and Shannon, C. E. Reliable Circuits Using Less Reliable Relays, Monograph 2696. Pietruszkiewicz, a. J., see Reiss, H. Potter, J. F., see Fisher, J. R. Power, F. S., see McLean, D. A. Prince, M. B., see Veloric, H. S. Reiss, H. Refined Theory of Ion Pairing, ]\Ionograph 2698. Reiss, H., Fuller, C. S., and Pietruszkiewicz, A. J. Solubility of Lithium in Doped and Undoped Silicon, Monograph 2702. 586 THE BELL SYSTEM TECHNICAL JOURNAL, MA.RCH 1957 RiESS, H. Theory of Ionization of Hydrogen and Lithium in Silicon and Ger- manium, Monograph 2700. Remeika, J. P. Growth of Single Crystal Rare -Earth Orthoferrites and Related Com- pounds, Monograph 2699, Richards, A. P., see Snoke, L. R. RiORDAN, J., see Carlitz, L. Rowe, H. E., see Manley, J. M. Shannon, C. E., see Moore, E. F. Shulman, R. G., and Wyluda, B. J. Trapping Center Properties of Germanium, Monograph 2674. Snoke, L. R., and Richards, A. P. Marine Borer Attack on Lead Cable Sheath, Monograph 2675. ToRREY, Miss M. N., see Dodge, H. F. Uhlir, a., Jr. Two -Terminal p-n Junction Devices for Frequency Conversion and Computation, Monograph 2704. Van Uitert, L. G. Nickel Copper Ferrites for Microwave Applications, Monograph 2676. Veloric, H. S., Prince, M. B., and Eder, M. J. Avalanche Breakdown Voltage in Silicon Diffused p-n Junctions, Monograph 2705. monographs 587 Weinreich, G. Transit Time Transistor, Monograph 2706. Wernick, J. H. Diffusivities in Liquid Metals by Temperature -Gradient Zone Melt- ing, Monograph 2677. Wolff, P. A. Theory of Plasma Resonance, jNIonograph 2707. Wyluda, B. J., see Shuhnan, R. G. Contributors to This Issue Richard C. Boyd, B.S., Northwestern University, 1946; B.S.E.E., University of Michigan, 1947; M.S.E.E., University of Michigan, 1948; Bell Telephone Laboratories, 1948-. After completion of the Labora- tories Communication Development Training program in 1950, Mr. Boyd was concerned with transmission engineering and systems studies. He was a supervisor during the exploratory trial of experimental PI carrier in 1953 and 1954. He is now responsible for transmission engineer- ing of PI carrier for rural subscriber use, and for adaptation of P and Nl carrier to exchange trunk use. He is a member of Tau Beta Pi and Phi Kappa Phi. Robert W. Dawson, Newark College of Engineering; Rutgers Uni- versity; Bell Telephone Laboratories, 1941-. All of ]\Ir. Dawson's work has been with the Radio Research Department. Together with A. C. Beck, he was concerned with conductivity measurements at microwave frequencies, and they were co-authors of an article on this subject. INlr. Dawson, a member of the Institute of Radio Engineers, worked on the Manhattan Project at Los Alamos while serving in the Army from 1942 to 1946. George Feher, B.S, in Engineering Physics, University of Cali- fornia, 1950; M.S.E.E., University of California, 1952; Ph.D. in Physics, University of California, 1954; Bell Telephone Laboratories, 1954-. Dr. Feher has been a member of the Semiconductor Research Department since joining the Laboratories. He has been engaged particularly in studies of electron spin resonance absorption, and is the author of several articles on this subject. He is a member of the American Physical So- ciety, the Institute of Radio Engineers, and Sigma Xi. John D. Howard, B.E.E., University of Louisville, 1947; Southern Bell Telephone Company, 1947-. After a year and a half in the Plant Department at Southern Bell, Mr. Howard joined the Engineering De- partment and remained there until late 1952. At that time he was called to the 0. & E. Department of the A. T. & T. Co. where he was con- cerned with exchange transmission. After completing this assignment he 588 CONTRIBUTORS TO THIS ISSUE 589 returned to Southern Bell where he is now Exchange Transmission Engineer. Mr. Howard is a member of the A.I.E.E. Marilyn J. Huyett, A.B., Susquehanna University, 1954; Bell Tele- phone Laboratories, 1954-. Since joining the Laboratories, Miss Huyett has been concerned with statistical research for the reliability group at Allentown, where she has had a great deal of experience with IBM com- puting machines. She is a member of the American Statistical Associa- tion. While in college, she received the Stine Mathematical Prize, an award for proficiency in mathematics. John E. Karlix, B.A., University of Cape Town, 1938; M.A., Uni- versity of Cape Town, 1939; Ph.D., University of Chicago, 1942; Bell Telephone Laboratories, 1945-. Dr. Karlin was engaged in psycho- acoustic research from 1945 to 1947. From 1947 until the present he has been concerned with user preference research, and since 1952 he has been in charge of the group doing this research. During the war years, 1942-1945, Dr. Karlin was at Harvard University, engaged in conmiuni- cations research on military projects. He is a member of the LR.E., the Acoustical Society of America, the American Psychological Association and Sigma Xi. ^to^ Stuart P. Lloyd, S.B., 1943, University of Chicago; M.S., 1949 and Ph.D., 1951, University of Illinois. Bell Telephone Laboratories, 1952-. Engaged in work relating to probability theory and information theory. Member, Institute for Advanced Study, Princeton, 1951-52. Member of American Mathematical Society, Institute of Mathematical Statistics, American Physical Society, A.A.A.S., Phi Kappa Phi, Sigma Xi and Phi Beta Kappa. D. W. jMcCall, B.S., University of Wichita, 1950; M.S., 1951 and Ph.D., 1953, University of Illinois; Bell Telephone Laboratories, 1953-. Dr. McCall is engaged in fundamental studies of the properties of di- electrics. He is a member of the American Chemical Society, the Ameri- can Physical Society, Sigma Xi, and Phi Lambda Upsilon. LuDwiG Pedersen, Christiania Technical School (Norway), 1919; Western Electric International Co. (Oslo), 1919-20; Western Electric Co., 1920-25; Western Electric Co., Field Engineering Force, 1944-45; Bell Telephone Laboratories, 1925-. He has been concerned with circuit design for machine switching systems, development of telegraph equip- 590 THE BELL SYSTEM TECHNICAL JOUHXAL, MARCH 1957 meiit, design of transmission equipment for the armed forces, and toll transmission systems. He served as a technical observer with the U. S. Armj^ in the European theater. He is now Systems Development En- gineer at the IMerrimack Vallej' Laboratory with responsibility for voice frequenc}'^, broadband carrier, short haul carrier and rural carrier sys- tems. ]\Iember of the A.I.E.E. John R. Pierce, B.S., 1933, M.S., 1934 and Ph.D., 1936, California Institute of Technology; Bell Telephone Laboratories, 1936-. Director of Research in Electrical Communications at Bell Telephone Labora- tories. He has specialized in the development of electron tubes, micro- w^ave research, electronic devices for military applications, and com- munications circuits. Dr. Pierce has been granted 55 patents and is the author of three books. For his research leading to the development of the beam traveling wave tube, he was awarded the 1947 INIorris Lieb- mann jMemorial Prize of the L R. E. He was voted the "Outstanding Young Electrical Engineer of 1942" by Eta Kappa Nu. Member of National Academy of Sciences, British Interplanetary Society, A.I.E.E., Sigma Xi, Tau Beta Pi and Eta Kappa Xu. Fellow of American Physical Society and I.R.E. John H. Rowen, B.E.E., 1948 and M.Sc, 1951, Ohio State Univer- sity. Mr. Rowen worked at the Antenna Laboratory of the Ohio State University Research Foundation in Columbus, 0. from 1948 to 1951. He joined Bell Telephone Laboratories in 1951, shortly after being awarded his master's degree. Since then J\Ir. Rowen has specialized in the applied physics of solids, and the development of microwave ferrite devices. He is a member of the Solid State Device Development Depart- ment at the Murra}' Hill Laboratory. Mr. Rowen is a member of the Institute of Radio Engineers and of Eta Kappa Nu. Harold Seidel, B.E.E., 1943, College of the City of New York; :\I.E.E., 1947 and D.E.E., 1954, Polytechnic Institute of Brooklyn; Microwave Research Institute of Polytechnic Institute of Brooklyn, 1947; Arma Corp., 1947-48; Federal Telecommunications Laboratories, 1948-53; Bell Telephone Laboratories, 1953-. He has been concerned with general electromagnetic problems, especially regarding wave-guide applications, and with analj'sis of microwave ferrite devices. Member of Sigma Xi and I.R.E. Milton Sobel, B. S., 1940, College of the City of New York; M.A., 1946 and Ph.D., 1951, Columbia I^niversity; U. S. Census Bureau, stat- CONTRIBUTERS TO THIS ISSUE 591 I istician, 1940-41 ; U. S. Army War College, statistician, 1942-44; Colum- bia University, department of mathematics, 1946-50; Wayne University, assistant professor of mathematics, 1950-52; Columbia University, visit- ing lecturer, 1952; Cornell University, fundamental research in mathe- matical statistics, 1952-54; Bell Telephone Laboratories, 1954-. He has been engaged in fundamental research on life testing and reliability problems with special application to transistors. Consultant on many Bell Laboratories projects. Member of Institute of Mathematical Sta- tistics, American Statistical Association and Sigma Xi. WiLHELM VON AuLOCK, Dipl. Ing., Technische Hochschule, Berlin, 1937; Dr. Ing., Technische Hochschule Stuttgart, 1953; Dr. von Aulock worked in Berlin from 1938 to 1942 for the A. E.G., Kabelwerk; in Gotenhafen (Gdynia) for the Torpedoversuchsanstalt from 1942 to 1945; and for the United States Navy Bureau of Ships in Washington from 1947 to 1953, where he was involved in work on torpedo counter- measures and studies of electromagnetic induction fields in sea water. He joined Bell Telephone Laboratories in 1954. Since then he has been principally engaged in analytical and experimental studies of phase shift and loss characteristics of ferrite-loaded waveguides, and the ap- plication of these properties. He is an associate member of the Institute of Radio Engineers. HE BELL SYSTEM Jechnical fournal VOTED TO THE SC I E N T IFIC^W>^ AND ENGINEERING PECTS OF ELECTRICAL COMMUNICATION LUME XXXVI MAY 1957 NUMBER 3 Radio Propagation Fundamentals kenneth bullington 593 A Reflection Theory for Propagation Beyond the Horizon H. T. FRnS, A. B. CBAWFORD, D. C. HOGG 627 Interchannel Interference Due to Klystron Pulling H. E. CURTIS AND S. O. RICE 645 Instantaneous Companding of Quantized Signals BERNARD SMITH 653 An Electrically Operated Hydraulic Control Valve J. W. SCHAEFER 711 Strength Requirements for Round Conduit g. f. weissmajtn 737 Cold Cathode Gas Tubes for Telephone Switching Systems M. A. TOWNSEND 755 Activation of Electrical Contacts by Organic Vapors L. H. GERMER and J. L. SMITH 769 Bell System Technical Papers Not Published in This Journal 813 Recent Bell System Monographs ' *V>v' ^^^ Contributors to This Issue \\\' rf iqc7 ^^^ COPYRIGHT 1957 AMERICAN TELEPHONE AND TELEGRAPH COMPANY THE BELL SYSTEM TECHNICAL JOURNAL ADVISORY BOARD A. B. GOETZE, President, Western Electric Company M. J. KELLT, President, Bell Telephone Laboratories E. J. ua^ EEiiY , Executive Vice President, American Telephone and Telegraph Company EDITORIAL COMMITTEE B. MCMILLAN, Chairman S. E. BRILLHART A. J. BUSCH L. R. COOK A. C. DICKIESON R. L. DIETZOLD K. E. GOULD E. I. GREEN B. K. HONAMAN H. R. HUNTLEY F. R. LACK J. R. PIERCE G. N. THAYER EDITORIAL STAFF w. D. BULLOCH, EdUor R. L. snEPnEHV, Production Editor T. N. POPE, Circulation Manager THE BELL SYSTEM TECHNICAL JOURNAL is published six times a year by the American Telephone and Telegraph Company, 195 Broadway, New York 7, N. Y. F. R. Kappel, President; S. Whitney Landon, Secretary; John J. Scan- Ion, Treasurer. Subscriptions are accepted at $5.00 per year. Single copies $1.25 each. Foreign postage is 65 cents per year or 11 cents per copy. Printed in U. S. A. THE BELL SYSTEM TECHNICAL JOURNAL VOLUME XXXVI MAY 1957 number 3 Copyright 1957, American Telephone and Telegraph Company Radio Propagation Fundamentals* By KENNETH BULLINGTON (Manuscript received June 21, 1956) The engineering of radio systems requires an estimate of the power loss between the transmitter and the receiver. Such estimates are affected by many factors, including reflections, fading, refraction in the at7nosphere, and diffraction over the earth's surface. In this paper, radio transmission theory and experiment in all frequency bands of current interest are summarized. Ground wave and sky wave trans- mission are included, and both line of sight and beyond horizon transmission are considered. The principal emphasis is placed on quantitative charts that are useful for engineering purposes. 1. INTRODUCTION The power radiated from a transmitting antenna is ordinarily spread over a relatively large area. As a result the power available at most re- ceiving antennas is only a small fraction of the radiated power. This ratio of radiated power to received power is called the radio transmission loss and its magnitude in some cases may be as large as 10^^ to 10"" (150 to 200 decibels). The transmission loss between the transmitting and receiving anten- nas determines whether the received signal will be useful. Each radio * This paper has lieen prepared for use in a proposed "Antenna Handl^ook" to be published by McGraw-Hill. 593 594 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 system has a maximum allowable transmission loss which, if exceeded, results in either poor quality or poor reliability. Reasonably accurat( predictions of transmission loss can be made on paths that approximate the ideals of either free space or plane earth. On many paths of intere.-;t . however, the path geometry or atmospheric conditions differ so much from the basic assumptions that absolute accuracy cannot be expected; ne^'ertheless, worthwhile results can be obtained by using two or more different methods of analysis to "box in" the answer. The basic concept in estimating radio transmission loss is the loss expected in free space; that is, in a region free of all objects that might absorb or reflect radio energ3^ This concept is essentially the inverse square law in optics applied to radio transmission. For a one wave- length separation between nondirective (isotropic) antennas, the free space loss is 22 db and it increases by 6 db each time the distance is doubled. The free space transmission ratio at a distance d is given by: T. = (srf) »* <"" where : Pr = received powder! }■ measured in same units Pt = radiated power j X = wavelength in same units as d gi (or gr) = power gain of transmitting (or receiving) antenna The power gain of an ideal isotropic antenna that radiates power uni- formly in all directions is unity by definition. A small doublet whose over-all physical length is short compared with one-half wavelength has a gain oi g = 1.5 (1.76 decibels) and a one-half wave dipole has a gain of 2.15 decibels in the direction of maximum radiation. A nomogram for the free space transmission loss between isotropic antennas is given in Fig. 1. When antenna dimensions are large compared with the wavelength, a more convenient form of the free space ratio is^ — ^ = ^^ (lb) Pt (\dy- where Ai,r = effective area of transmitting or receiving antennas. Another form of expressing free space transmission is the concept of RADIO PROPAGATION FUNDAMENTALS 595 the free space field intensity Eo which is given by: d (2) where d is in meters and Pt in watts. The use of the field intensity concept is frequently more convenient than the transmission loss concept at freciuencies below about 30 mc, 130 O.t — -120 0.2 0.3 — 0.5 0.7 01 111 _J 5 Z 10 < z z LU I- z < z LU LU 5 I- UJ CD LU u z < I- ■110 Q LU I- < < cr 5 LU z o cc o LL o Q. -100 2- III 5 5 - 10 — 20 — 30 — 50- 100 — 200- 300- 500 • - 90 < X O a. LL a LU ■80 tu tr- LU Q. a z o o LU cr UJ D- in UJ _J o > u < 13 UJ 2 - 30,000 20,000 - 10,000 - 7000 - 5000 3000 ■2000 - 1000 - 700 - 500 - 300 - 200 70 60 _l O > o cc u UJ z o UJ > o < "--hL'OO - 70. - 50 30 H 20 160 — 150 < z z UJ (- z < (J D. o cc I- o 10 z UJ — 140 a — ^ r 10 ■130 120 110 ,-100 50 5 u LU Q ■40 -90 - 80 h Fig. 1 — Free space transmission. 596 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 where external noise is generally controlling and where antenna dimen- sions and heights are comparable to or less than a wavelength. The free space field intensity is independent of frecjuency and its magnitude for one kilowatt radiated from a half -wave dipole is shown on the left hand scale on Fig. 1. The concept of free space transmission assumes that the atmosphere is perfectly uniform and nonabsorbing and that the earth is either infinitely far away or its reflection cbeflacient is negligible. In practice, the modify- ing effects of the earth, the atmosphere and the ionosphere need to be considered. Both theoretical and experimental values for these effects are described in the following sections. II. TRANSMISSION WITHIN LINE OF SIGHT The presence of the ground modifies the generation and the propaga- tion of radio waves so that the received power or field intensity is or- dinarily less than would be expected in free space.^ The effect of plane earth on the propagation of radio waves is given by Induction Field and Secondary Direct Reflected "Surface Effects of the Wave Wave Wave" Ground E_ .^'^ \ /^ D^ ^-1 J^ 1 + Re'^ + (1 - R)Ae'^ + • • • (3) where R = reflection coefficient of the ground A = "surface wave" attenuation factor 4Thih-2 A \d hi,2 = antenna heights measured in same units as the wavelength and distance The parameters R and A vary with both polarization and the electrical constants of the ground. In addition, the term "surface wave" has led to considerable confusion since it has been used in the literature to stand for entirely different concepts. These factors are discussed more completely in Section IV. However, the important point to note in this section is that considerable simplification is possible in most practical cases, and that the variations with polarization and ground constants RADIO PROPAGATION FUNDAMENTALS 597 and the confusion about the surface wave can often be neglected. For near grazing paths, R is approximately equal to —1 and the factor A can be neglected as long as both antennas are elevated more than a wavelength above the ground (or more than 5-10 wavelengths above sea water) . Under these conditions the effect of the earth is independent of polarization and ground constants and (3) reduces to ^Pf =2sin^ = 2sin^^ (4) 2 \d where Po is the received power expected in free space. The above expression is the sum of the direct and ground reflected rays and shows the lobe structure of the signal as it oscillates around the free space value. In most radio applications (except air to ground) the principal interest is in the lower part of the first lobe; that is, where A/2 < 7r/4. In this case, sin A/2 == A/2 and the transmission loss over plane earth is given by: (5) It Avill be noted that this relation is independent of frequency and it is shown in decibels in Fig. 2 for isotropic antennas. Fig. 2 is not vaUd when the indicated transmission loss is less than the free space loss shown in Fig. 1, because this means that A is too large for this approximation. Although the transmission loss shown in (5) and in Fig. 2 has been derived from optical concepts that are not strictly valid for antenna heights less than a few wavelengths, approximate results can be obtained for lower heights by using hi (or h-i) as the larger of either the actual antenna height or the minimum effective antenna height shown in Fig. 3. The concept of minimum effective antenna height is discussed further in Section IV. The error that can result from the use of this artifice does not exceed ±3 db and occurs where the actual antenna height is ap- proximately equal to the minimum effective antenna height. The sine function in (4) shows that the received field intensity oscil- lates around the free space value as the antenna heights are increased. The first maximum occurs when the difference between the direct and ground reflected waves is a half wavelength. The signal maxima have a magnitude 1 + | i? | and the signal minima have a magnitude of 1 — \R\. Frequently the amount of clearance (or obstruction) is described in terms of Fresnel zones. All points from which a wave could be reflected 598 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 with a path difference of one-half \va\'elength form the Isoundary of the first Fresnel zone; similarly, the boundary of the n*^ Fresnel zone con- sists of all points from which the path difference is n/2 wavelengths. The n*'"' Fresnel zone clearance //„ at any distance di is given by: H^ n\di{d — di) d (6) Although the reflection coefficient is very nearly equal to —1 for — 6 — 10 — 20 -50- — 100 -200 -600 — 1000 -2000 — 5000 — 10,000 JL *h k- d--- ->l -10 -20 -50 -100 _ \ •200 -500 -1000 -2000 ■5000 -10,000 •0.1 -0.2 0.5 2 5 20 50., ' — 100 200 — 500 ^1000 CO LU -J z LU O z < 10 in < z z 111 I- z < o a. o cc t- o < \,. y-'' y \ y ^'\ GOOD SOIL V 1- ^ 40 U- Z / V f=30 s ^ V "^<7-= 0.02 MHOS \PER METER \ SEA WATER \ f=80 \, \. 1 \ ff-=4MH0S o \, N. \PER METER -C 20 10 8 6 \ \ \ \ s. \ V N \ \ ^ \ -\ \ \ \ \^ horizontal\ \ ^ V 4 S POLARIZATION ^ \ \ s \ X,^'^ \ \ \ X POOR SOIL \ \ \ s. ,/' \] -e-A M \ 1 \ . 1 10 20 40 60 100 200 400 600 FREQUENCY IN MEGACYCLES PER SECOND 1000 Fig. 3 — Minimum effective antenna height. grazing angles over smooth surfaces, its magnitude ma,y be less than unity when the terrain is rough. The classical Rayleigh criterion of roughness indicates that specular reflection occurs when the phase devia- tions are less than about ±(7r/2) and that the reflection coefficient will be substantially less than unity when the phase deviations are greater t han ± (7r/2) . In most cases this theoretical boundary between specular and diffuse reflection occurs when the variations in terrain exceed | to j of the first Fresnel zone clearance. Experimental results with microwave transmission have shown that most practical paths are "rough" and ordinarily have a reflection coefficient in the range of 0.2-0.4. In addi- tion, experience has shown that the reflection coefficient is a statistical problem and cannot be predicted accurately from the path profile.^ 600 THE BELL SYSTEM TECHNICAL JOURNAL, MAY ]957 Fading Phenomena Variations in signal level with time are caused by changing atmos- pheric conditions. The severity of the fading usually increases as either the frecj^uency or path length increases. Fading cannot be predicted ac- curately but it is important to distinguish between two general types: (1) inverse bending and (2) multipath effects. The latter includes the fading caused by interference between direct and ground reflected waves as well as interference betw^een two or more separate paths in the atmos- phere. Ordinarily, fading is a temporary diversion of energy to some other than the desired location; fading caused by absorption of energy is discussed in a later paragraph. The path of a radio wave is not a straight line except for the ideal case of a uniform atmosphere. The transmission path may be bent up or down depending on atmospheric conditions. This bending may either increase or decrease the effective path clearance and inverse bending may have the effect of transforming a line of sight path into an obstructed one. This type of fading may last for several hours. The frequency of its occurrence and its depth can be reduced by increasing the path clear- ance, particularly in the middle of the path. I 100 5 10 15 20 25 30 35 40 SIGNAL LEVEL IN DECIBELS BELOW MEDIAN VALUE Fig. 4 — Typical fadii g characteristics in the worst month on 30 to 40 mile line-of -sight paths with 50 to 100 foot clearance. RADIO PROPAGATION FUNDAMENTALS 601 Severe fading may occur over water or on other smooth paths because the phase difference between the direct and reflected rays varies with atmospheric conditions. The result is that the two rays sometimes add and sometimes tend to cancel. This type of fading can be minimized, if the terrain permits, by locating one end of the circuit high while the other end is very low. In this way the point of reflection is placed near the low antenna and the phase difference between direct and reflected rays is kept relatively steady. Most of the fading that occurs on "rough" paths with adequate clear- ance is the result of interference between two or more rays traveling slightly different routes in the atmosphere. This multipath type of fad- ing is relatively independent of path clearance and its extreme condition approaches the Rayleigh distribution. In the Rayleigh distribution, the probability that the instantaneous value of the field is greater than the value R is exp [ — {R/Ro}], where Ro is the rms value. Representative values of fading on a path with adequate clearance are shown on Fig. 4. After the multipath fading has reached the Rayleigh distribution, a further increase in either distance or frec^uency increases the number of fades of a given depth but decreases the duration so that the product is the constant indicated by the Rayleigh distribution. Miscellaneous Effects The remainder of this Section describes some miscellaneous effects of line of sight transmission that may be important at frequencies above about 1,000 mc. These effects include variation in angles of arrival, maximum useful antenna gain, useful bandwidth, the use of frequency or space diversity, and atmospheric absorption. On line of sight paths with adec^uate clearance some components of the signal may arrive with variations in angle of arrival of as much as ^° to 1° in the vertical plane, but the variations in the horizontal plane are less than 0.1°.*' ^ Consequently, if antennas with beamwidths less than about 0.5° are used, there may occasionalh^ be some loss in received signal because most of the incoming energy arrives outside the antenna beamwidth. Signal variations due to this effect are usually small com- pared with the multipath fading. Multipath fading is selective fading and it limits both the maximum useful bandwidth and the frequency separation needed for adequate frequency diversity. For 40-db antennas on a 30-mile path the fading on frequencies separated b}'' 100-200 mc is essentially uncorrelated re- gardless of the absolute freciuency. With less directive antennas, uncor- related fading can occur at frequencies separated by less than 100 mc.^' ^ ()02 THE BELL SYSTEM TECHNICAL JOIKXAL, iMAV 1!J57 Larger antennas (more narrow beamwidths) will decrease the fast multi- path fading and widen the frecjuency separation between uncorrelated fading but at the risk of increasing the long term fading associated with the ^'ariations in the angle of arrival. Optimum space diversity, when ground reflections are controlling, requires that the separation between antennas be sufficient to place one antenna on a field intensity maximum while the other is in a field in- tensity minimum. In practice, the best spacing is usually not known be- cause the principal fading is caused by multipath variations in the atmosphere. However, adequate diversity can usually be achie^'ed with a vertical separation of 100-200 wa\'elengths. At frec^uencies above 5,000-10,000 mc, the presence of rain, snow, or fog introduces an absorption in the atmosphere which depends on the amount of moisture and on the frequency. During a rain of cloud burst proportions the attenuation at 10,000 mc may reach 5 db per mile and at 25,000 mc it may be in excess of 25 db per mile.^ In addition to the effect of rainfall some selective absorption may result from the oxygen and water vapor in the atmosphere. The first absorption peak due to water vapor occurs at about 24,000 mc and the first absorption peak for oxygen occurs at about 60,000 mc. III. TROPOSPHERIC TRANSMISSION BEYOND LINE OF SIGHT A basic characteristic of electromagnetic waves is that the energy is propagated in a direction perpendicular to the surface of uniform phase. Radio waves travel in a straight line only as long as the phase front is plane and is infinite in extent. Energy can be transmitted beyond the horizon by three principal methods: reflection, refraction and diff"raction. Reflection and refrac- tion are associated with either sudden or gradual changes in the direc- tion of the phase front, while diffraction is an edge effect that occurs because the phase surface is not infinite. When the resulting phase front at the receiving antenna is irregular in either amplitude or position, the distinctions between reflection, refraction, and diffraction tend to break down. In this case the energy is said to l)e scattered. Scattering is fre- quently pictured as a result of irregular reflections although irregular refraction plus diffraction may be equally important. The following paragraphs describe first the theories of refraction and of diffraction over a smooth sphere and a knife edge. This is followed by empirical data derived from experimental results on the transmission to points far beyond the horizon, on the eftects of hills and trees, and on fading phenomena. RADIO PROPAGATION FUNDAMENTALS 603 Refraction The dielectric constant of the atmosphere normally decreases grad- ually with increasing altitude. The result is that the velocity of trans- mission increases with the height above the ground and, on the average, the radio energy is bent or refracted toward the earth. As long as the change in dielectric constant is linear with height, the net effect of re- fraction is the same as if the radio waves continued to travel in a straight line but over an earth whose modified radius is: a ka = — 1 , « ^ (7) "^ 2 dh where a = true radius of earth — = rate of change of dielectric constant with height CLil Under certain atmospheric conditions the dielectric constant may in- crease (0 < /v < 1) over a reasonable height, thereby causing the radio waves in this region to bend away from the earth. This is the cause of the inverse bending type of fading mentioned in the preceding section. It is sometimes called substandard refraction. Since the earth's radius is about 2.1 X 10^ feet, a decrease in dielectric constant of only 2.4 X 10"^ per foot of height results in a value of A- = ^, which is commonly assumed to be a good average value. ^ When the dielectric constant de- creases about four times as rapidly (or by about 10~^ per foot of height), the value of A- = oo . Under such a condition, as far as radio propagation is concerned, the earth can then be considered flat, since any ray that «ta,rts parallel to the earth will remain parallel. When the dielectric constant decreases more rapidly than 10~'^ per foot of height, radio waves that are radiated parallel to, or at an angle above the earth's surface, may be bent downward sufficiently to be re- flected from the earth. After reflection the ray is again bent toward the earth, and the path of a typical ray is similar to the path of a bouncing tennis ball. The radio energy appears to be trapped in a duct or wave- guide between the earth and the maximum height of the radio path. This phenomenon is variously known as trapping, duct transmission, anoma- lous propagation, or guided propagation.'"- " It will be noted that in this case the path of a typical guided wave is similar in form to the path of sky waves, which are lower-frequency waves trapped between the 604 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 earth and the ionosphere. However, there is httle or no similarity be- tween the virtual heights, the critical frequencies, or the causes of re- fraction in the two cases. Duct transmission is important because it can cause long distance interference with another station operating on the same frequency; however, it does not occur often enough nor can its occurrence be pre- dicted with enough accuracy to make it useful for radio services requir- ing high reliability. Diffraction Over a Smooth Spherical Earth and Ridges Radio waves are also transmitted around the earth by the phenomenon of diffraction. Diffraction is a fundamental property of wave motion, and in optics it is the correction to apply to geometrical optics (ray theory) to obtain the more accurate wave optics. In other words, all shadows are somewhat "fuzzy" on the edges and the transition from "light" to "dark" areas is gradual, rather than infinitely sharp. Our common experience is that light travels in straight lines and that shad- ows are sharp, but this is only because the diffraction effects for these very short wavelengths are too small to be noticed without the aid of special laboratory equipment. The order of magnitude of the diffraction at radio frequencies may be obtained by recalling that a 1 ,000-mc radio wave has about the same wavelength as a 1,000-cycle sound wave in air, so that these two types of waves may be expected to bend around absorbing obstacles with approximately equal facility. The effect of diffraction around the earth's curvature is to make possi- ble transmission beyond the line-of -sight. The magnitude of the loss caused by the obstruction increases as either the distance or the fre- quency is increased and it depends to some extent on the antenna height. ^^ The loss resulting from the curvature of the earth is indicated by Fig. 5 as long as neither antenna is higher than the limiting value shown at the top of the chart. This loss is in addition to the transmission loss over plane earth obtained from Fig. 2. When either antenna is as much as twice as high as the limiting value shown on Fig. 5, this method of correcting for the curvature of the earth indicates a loss that is too great by about 2 db, with the error increasing as the antenna height increases. An alternate method of determining the effect of the earth's curvature is given by Fig. 6. The latter method is approximately correct for any antenna height, but it is theoretically limited in distance to points at or beyond the line-of-sight, assuming that the curved earth is the only obstruction. Fig. 6 gives the loss rela- tive to free-space transmission (and hence is used with Fig. 1) as a func- RADIO PROPAGATION FUNDAMENTALS 605 tion of three distances: di is the distance to the horizon from the lower antenna, c?2 is the distance to the horizon from the higher antenna, and ds is the distance beyond the hne-of-sight. In other woi'ds, the total dis- tance between antennas, d = di -\- d-i -\- d-i . The distance to the horizon over smooth earth is given by: c?i,2 = ■\/2kahi, 2 (8) where /ii.s is the appropriate antenna height and ka is the effective earth's radius. The preceding discussion assumes that the earth is a perfectly smooth sphere and the results are critically dependent on a smooth surface and a uniform atmosphere. The modification in these results caused by the UJ cc SCALE A LIMITING ANTENNA HEIGHT IN FEET 500 300 200 100 50 30 20 10 _L J_ _L i- _L I "I I I I I I r 20 50 100 200 500 1000 2000 5000 10,000 FREQUENCY IN MEGACYCLES PER SECOND 10,000 -r '0,000 oOcr •Jqo Q- UJ- < < y ujq:< -Jtr zo< ~ D-_l ^ ,o u-ia z ** , LJU-J Oct z UJliJO o I 5000- 3000- 2000- 1000- 500- 200- 100- 70- 50- 20- 10- ■5000 -3000 -2000 • 1000 -500 -200 -100 -70 -50 -30 -20 Qtr zm u< iu$ '^< a. Ill Lu to (/5UJ UJ> _IO oo <5 o< lUtM 5E ?^ o. Z -J UJ< DU C(i= ujq: 5- 10- (fl 20- LLI UJ Z 50- S 100- 200- 300 II q: UL I I- H < LU 3 UJ (T to 3 (0 og >- m o UJ z to o Ji to < ■ (O oz JO 2- 3- 5- 10- 15- 20- UJ m u UJ a 30- 40- 40- (O Q < a. y^to 0.5- 1 ■ y y.-'Uj'^ (0 .UJx t- tr u < ui UJ tuj U. I- Oo I- < 10 — 20- 50- I V- < UJ U- o I- < > or D U >- m to 3 < U to (O o _J UJ u UJ Q 30- 20^ 15- 10- 5 — 4 — 2- FiG. 5 — Diffraction less around a perfect sphere. 006 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 presence of hilLs, trees, and bnildings is difficult or impossible to compute, but the order of magnitude of these effects may be obtained from a con- sideration of the other extreme case, which is propagation over a per- fectly absorbing knife edge. The diffraction of plane waves over a knife edge or screen causes a shadow loss whose magnitude is shown on Fig. 7. The height of the ob- struction H is measured from the line joining the two antennas to the top of the ridge. It will be noted that the shadow loss approaches (> db X/ 500' d, ceo ,2 I02 10-=- 10- 10' -10- Qtr ZLU CLQC UZ -° s< Z_l -o Oh Lua CCUJ LL> -0.5 (o -0-7 5_^ ^4/3 <^ to I 2 5< (/) ^a ii_i- Oo —20 gi- < CE II ■50 ^ -2 ■3 -5 -7 -10 -10"' -2 -3 1 — 2 — 3 — 10 r__ LU~10- sx) 20- cc . \ N o ^ 30V 50 — 100 — 200- 300- — 2 -5 LU U Z < 1- Q — 26 30- — 24 28 — — 22 — 20 26 — -18 24 — -16 — 14 22 — -12 — 10 -10 -20 ■30 — 50 — 100 Q LU 20 19- - 8 o CO 10 < tn f) o _i LU 'CD 8.3 - 19- ■200 ■300 20 - — 2 -1 — 1 -2 -3 C\J "O — 4 UJ u z < — 5 1- c/l Q I 1- — 7 5 Q — UJ 1- < U — 10 0 10 if) — 12 < to CO 0 — 15 -I -I UJ m — 20 u UJ 0 II f\j _l -30 N N -40 — 50 Fig. 6 — Dif't'iactiou loss relative to free space transmission at all locations beyond line-of-sight over a smooth sphere. RADIO PROPAGATION FUNDAMENTALS 007 as H approaches 0 (grazing incidence), and that it increases with in- creasing positive vahies of H. When the direct ray clears the obstruction, // is negative, and the shadow loss approaches 0 db in an oscillatory manner as the clearance is increased. In other words, a substantial clear- ance is required over line-of-sight paths in order to obtain "free-space" transmission. The knife edge diffraction calculation is substantially independent of polarization as long as the distance from the edge is more than a few wavelengths. cl,^d, ANT 2 \ -50 -30 -20 \ l-io \ h5\l 5000- 2000- 1000- ^ 500- til LU u- 200 • -3 -2 * 100- 50- 20- 10- - 10,000 - 5000 3000 -2000 -1000 - 500 *-^^ -0.5 -0.3 -0.2 -0.1 1- III - 300 -200 z \100 \ I - 50 \ 30 \ -20 ^ 10 |- 5 3 - 2 - 1 ■^ note: when accuracy greater than ± 1.5 db is required, values on the d, scale should be: 30- 60- 150- 300- 600 1500H 3000 7 6 000- 1 5,000 - .36,000- O z o u LU a. UJ Q. CO LU _l u e) LU 2 U. o LU _l < > 111 > I- < UJ I/) 0- UJ z^ iH / g-0.8 0 - •10 I 1-12 7\A -16 -18 -20 O a. 2b en _i LU m ■30 \l, a z ■35 ^ O -40 -45 - 50 d2 Fig. 7 — Knife-edge diffraction loss relative to free space. 608 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 LU O < a. in 2 o a. u. ffl O UJ o 2.5 FIRST FRESNEL ZONE Fig. 8 — Transmission loss versus clearance. At grazing incidence, the expected loss over a ridge is 6 db (Fig. 7) while over a smooth spherical earth Fig. 6 indicates a loss of about 20 db. More accurate results in the vicinity of the horizon can be obtained by expressing radio transmission in terms of path clearance measured in Fresnel zones as shown in Fig. 8. In this representation the plane earth theory and the ridge diffraction can be represented by single lines; but the smooth sphere theory requires a family of curves with a param- eter M that depends primarily on antenna heights and frequency. The big difference in the losses predicted by diffraction around a perfect sphere and by diffraction over a knife edge indicates that diffraction losses depend critically on the assumed type of profile. A suitable solu- tion for the intermediate problem of diffraction over a rough earth has not yet been obtained. Experimental Data Far Beyond the Horizon Most of the experimental data at points far beyond the horizon fall in between the theoretical curves for diffraction over a smooth sphere RADIO PROPAGATION FUNDAMENTALS 609 and for diffraction over a knife edge obstruction. Various theories have been advanced to explain these effects but none has been reduced to a simple form for every day use.^^ The explanation most commonly ac- cepted is that energy is reflected or scattered from turbulent air masses in the volume of air that is enclosed by the intersection of the beamwidths of the transmitting and receiving antennas.'^ The variation in the long term median signals with distance has been derived from experimental results and is shown in Fig. 9 for two frequencies.^^ The ordinate is in db below the signal that would have been expected at the same distance in free space with the same power and the same antennas. The strongest signals are obtained by pointing the antennas at the horizon along the great circle route. The values shown on Fig. 9 are essentially annual averages taken from a large num- ber of paths, and substantial variations are to be expected with terrain, climate, and season as well as from day to day fading. Antenna sites with sufficient clearance so that the horizon is several miles away will, on the average, provide a higher median signal (less loss) than shown on Fig. 9. Conversely, sites for which the antenna must be pointed upward to clear the horizon will ordinarily result in ap- preciably more loss than shown on Fig. 9. In many cases the effects of path length and angles to the horizon can be combined by plotting the experimental results as a function of the angle between the lines drawn tangent to the horizon from the transmitting and receiving sites. ^^ 20 u < CL If) UJ UJ 40 5 o _i HI CD HI m u HI a 60 80 100 120 MEDIAN VALUE ON PARTICULAR PATHS MAY Qci e ^. N OR MORE FROM THESE LINES V, \ V s s ^c "V; ^ "S ^ \ •v. N V 40 50 60 80 100 200 300 400 600 800 1000 DISTANCE IN MILES Fig. 9 — Beyond-horizon transmission — median signal level versus distance. ()10 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 When the path profile consists of a single sharp obstruction that can be seen iVoni both terminals, the signal level may approach the value predicted by the knife edge diffraction theoiy.'^ While several interest- ing and unusual cases have been recorded, the knife edge or "obstacle gain" theory is not applicable to the typical but only to the exceptional paths. As in the case of line-of-sight transmission the fading of radio signals beyond the horizon can be divided into fast fading and slow fading. The fast fading is caused by multipath transmission in the atmosphere, and for a given size antenna, the rate of fading increases as either the fre- quency or the distance is increased. This type of fading is much faster than the maximum fast fading observed on line of sight paths, but the two are similar in principle. The magnitude of the fades is described by the Rayleigh distribution. Slow fading means variations in average signal level over a period of hours or days and it is greater on beyond horizon paths than on line-of- sight paths. This type of fading is almost independent of frequency and seems to be associated with changes in the average refraction of the atmosphere. At distances of 150 to 200 miles the variations in hourly median value around the annual median seem to follow a normal proba- bility law in db with a standard deviation of about 8 db. Typical fading distributions are shown on Fig. 10. The median signal levels are higher in warm humid climates than in cold dry climates and seasonal variations of as much as ±10 db or more from the annual median have been observed.'* Since the scattered signals arrive with considerable phase irregularities in the plane of the recei\'ing antenna, narrow-beamed (high gain) anten- nas do not yield power outputs proportional to their theoretical area gains. This effect has sometimes been called loss in antenna gain, but it is a propagation effect and not an antenna effect. On 150 to 200 miles this loss in received power may amount to one or two db for a 40 db gain antenna, and perhaps six to eight db for a 50 db antenna. These extra losses vary with time but the variations seem to be uncorrelated with the actual signal le\'el. The bandwidth that can be used on a single radio carrier is frequently limited by the selective fading caused by multipath or echo effects. Echoes are not troublesome as long as the echo time delays are very short compared with one cycle of the highest baseband frequency. The probability of long delayed echoes can be reduced (and the rate of fast fading can be decreased) by the use of narrow beam antennas both within and beyond the horizon.'^' -<' Useful bandwidths of several mega- RADIO PROPAGATION FUNDAMENTALS Gil cycles appear to be feasible with the antennas that are needed to pro- vide adeciuate signal-to-noise margins. Successful tests of television and of multichannel telephone transmission have been reported on a 188- mile path at 0,000 mc.'' The effects of fast fading can be reduced substantially by the use of either frequency or space diversity. The freciuency or space separation reciuired for diversity varies with time and with the degree of correlation that can be tolerated. A horizontal (or vertical) separation of about 100 wavelengths is ordinarily adequate for space diversity on 100- to 200- mile paths. The corresponding figure for the required frequency separa- tion for adequate diversity seems likely to be more than 20 mc. 99.9 99.8 99.5 99 < ^» (/) If) U 95 (/) CD < Z < I 90 80 70 60 50 40 30 20 10 5 2 1 0.5 0.2 0.1 0.05 IT) in LU _l < z o m LU 2 u. O LU o < Z LU u CE LU Q- m w FAST FADING (RAYLEIGH DISTRIBU / TION) ^ oSsy //Ay ~~^' f / / / T 1 // Iff Iff Iff / J / / M SLOW FADING gj (EMPIRICAL DISTRIBUTION k f OF HOURLY MEDIANS) / / M / / / z^" ' W /i^ f / -40 -30 -20 -10 0 10 20 30 DECIBELS RELATIVE TO MONTHLY MEDIAN VALUE 40 Fig. 10 — Typical fading characteristics at points far beyond tlie horizon. 612 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 Effects of Nearby Hills — Particularly on Short Paths The experimental results on the effects of hills indicate that the shadow losses increase with the frecjuency and with the roughness of the terrain.^^ An empirical summary of the available data is shown on Fig. 11. The roughness of the terrain is represented bj^ the height H shown on the profile at the top of the chart. This height is the difference in elevation between the bottom of the valley and the elevation necessary to obtain line of sight from the transmitting antenna. The right hand scale in Fig. 11 indicates the additional loss above that expected over plane earth. Both the median loss and the difference between the median and the 10 per cent values are shown. For example, with variations in terrain of 500 feet, the estimated median shadow loss at 450 mc is about 20 db and the TO TRANSMITTING ANTENNA zf-io o -20 1000 — CC liJ Q. -30 700- _ -500 200- z o z -700"'^^^ 150- I LU D a LU cr -1000 -2000 100- u. 70 — 50 — ■X- REFERRED TO PLANE EARTH VAL UES 7 — -3 * ^-al zm UJo olu ^? ocn I luO LU Q o< XI LUcn in-, o< -ID IS QO o q: u 2 40 i 20 < in _i 111 U 0 -20 -40 ^ S X :^ ^ ^ ^?=^ s s V \ k \ \ S sT^^ V ^ ^ s \ \ \ \ k ^^^^ tN. 1 ^0.2WC < \ s^ \ \ S ^\^^^ s^^ 5X> -','0.4 "S. •v s \ ^ N s. ^\^ SV sWV -' ,0.6 >^ \ \ V \, \, > . \ \ S^ i\ -'1.0 ^ \ \ s ,\ \ \ \ \ \ v^ li iK \. \ ^ s. s. V 15\ \ ^ kW V s, \, \, \ 30\ \ \ \\ kS\ \ V X \ 60\ ' \ \ \ \\ k \ ^ S. 15(X \ \ \ \ \ k\ \ \303X \ \ \ V , \ \ * k\^ 600\ \ ' V \ \ \ \ > , \ \n — MC N V^ H \ ^ \ -^ \ -\ \ ^ 1 1 1 1 1 1 A 1 ^ \ V rt L 1 \ \ \ \ 1 0.6 1.0 4 6 8 10 20 40 60 80100 200 400 600 1000 DISTANCE IN MILES Fig. 13 — Field intensity for vertical polarization over sea water for 1-kw radiated power from a grounded whip antenna. 616 RADIO PROPAGATION FUNDAMENTALS 617 elude the effect of diffraction and average refraction around a smooth spherical earth as discussed in Section III, but do not include the iono- spheric effects described in the next Section. The increase in signal ob- tained by raising either antenna height is shown in Fig. 14 for poor soil and Fig. 15 for sea water. 50 45 40 ui 35 m m O 30 LU a -r 25 ? 20 < O H 15 I O ^ 10 -5 ^.^.^^ ^ ^ ^ '^ ^^-^ -^ ^^ ^^ -^ ^^ ^^,.^^-^600 MC ^ ^ ^ --^ ^^^ ^ 300 ^ ^ ^ ^ ^^' ^^.^-^^ .^ ^ ^ ^•^"^"^ ^^0 t^^ ^ ^ ^^"^ ^ - ^ ^^ ^60 > ^ ^ ^^ ^ ^ ^ ^.--^ 30 ^^ -^ ^^^ ^ 15 ^,.---^ ^ . — ^^ - -- 6 M( - 6 7 8 9 10 20 30 40 50 60 70 80 100 ANTENNA HEIGHT IN FEET 200 Fig. 14 — Antenna height gain factor for vertical polarization over poor soil. 40r 35 ^ 30 LU ffl O 25 LU Q Z 20 15 ^,0 ^ <^ ^ ..^^^ ^^-''^O ,^ ^ ^ ^ -^"'"'^ ^^ ^ ^ ^ ^ ^^ ^^ 300 , ^ ^ "^ ^ ..^ 150 ^^ :=>. " ■^^^^ ——J 60 MC 1 6 7 8 9 10 20 30 40 50 60 70 80 100 ANTENNA HEIGHT IN FEET 200 Fig. 15 — Antenna height gain factor for vertical polarization over sea water. 018 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 V. IONOSPHERIC TRANSMISSION 111 addition to the troposphoric or ground wave transmission discussed in the preceding sections, useful radio energy at frequencies below about 25 to 100 mc may be returned to the earth by reflection from the iono- sphere, which consists of several ionized layers located 50 to 200 miles above the earth. The relatively high density of ions and free electrons in this region provides an effective index of refraction of less than one, and the resulting transmission path is similar to that in the well known optical phenomenon of total internal reflection. The mechanism is generally spoken of as reflection from certain virtual heights.^^ Polarization is not maintained in ionospheric transmission and the choice depends on the antenna design that is most efficient at the desired elevation angles. Regular lonosphei'ic Transmission The ionosphere consists of three or more distinct layers. This does not mean that the space between layers is free of ionization but rather that the curve of ion density versus height has several distinct peaks. The E, F\, and F2 layers are present during the daj'^time but the Fi and Fo combine to form a single layer at night. A lower laj^er called the D layer is also present during the day, but its principal effect is to absorb rather than reflect. Information about the nature of the inosphere has been obtained by transmitting pulsed radio signals directly overhead and bj- record- ing the signal intensity and the time delay of the echoes returned from these layers. At night all frequencies below the critical frequency jc are returned to earth with an average signal intensity that is about 3 to 6 db below the free space signal that would be expected for the round trip distance. At frequencies higher than the critical frequency the signal intensity is very weak or undetectable. Tj^pical values of the critical freciuency for Washington, D. C, are shown in Fig. 16. During the da\'time, the critical frequency is increased 2 to 3 times over the corresponding nighttime value. This apparent increase in the useful frequency range for ionospheric transmission is largely offset by the heavy daytime absorption which reaches a maximum in the 1 to 2- mc range. This absorption is caused by interaction between the free elec- trons and the earth's magnetic field. The absence of appi-eciable absorp- tion at night indicates that most of the free electrons disappear when the sun goes down. Charged particles traveling in a magnetic field have a resonant or gyromagnctic frequency, and for electrons in the earth's magnetic field, of about 0.5 gauss, this resonance occurs at about 1.4 RADIO PROPAGATION FUNDAMENTALS 619 15.0 a z o u 10. u >- u < z - 4 >- o m < o UJ o 40 30 20 to Z 0 _l LU > -10 \ - LA ir Ml RGE CI TY 3ISE TYPICAL SET ^ NOISE / / \ \ ATMOSPHERIC STATIC V. . / y x "-> \ / r / / \ tn S \ /^ / \ / ^ A COSMIC NOISE i^ ^^ THERMAL NOISE (166 DB BELOW 1 WATT) y ' \ ,^ ^/ ' ,''■ y 10 10' 10- 10" FREQUENCY IN MEGACYCLES PER SECOND Fig. 19 — Typical average noise level in u 6-kc band. RADIO PROPAGATION FUNDAMENTALS 625 for latitudes of 40° while in the Arctic region the noise may be 15 to 25 db lower. The corresponding values for other bandwidths can be obtained by adding 10 db for each 10-fold increase in bandwidth. More complete estimates of atmospheric noise on a world wide basis are given in the National Bureau of Standards Bulletin 462.^9 These noise data are based on measurements with a time constant of 100 to 200 millisec- onds. Noise peaks, as measured on a cathode ray tube, may be consid- erably higher. The man made noise shown on Fig. 19 is caused primarily by opera- tion of electric switches, ignition noise, etc., and may be a controlling factor at frequencies below 200 to 400 mc. Since radio transmission in this frequency range is primarily tropospheric (ground wave), man made noise can be relatively unimportant beyond 10 to 20 miles from the source. In rural areas, the controlling factor can be either set noise or cosmic noise. Cosmic and solar noise is a thermal type interference of extra-terres- tial origin. ^^ Its practical importance as a limitation on communication circuits seems to be in the 20- to 80-mc range. Cosmic noise has been found at much higher frequencies but its magnitude is not significantly above set noise. On the other hand, noise from the sun increases as the frequency increases and may become the controlling noise source when high gain antennas are used. The rapidly expanding science of radio astronomy is investigating the variations in both time and frequency of these extra-terrestial sources of radio energy. References 1. H. T. Friis, A Note on a Simple Transmission Formula Proc. I.R.E., 34, pp. 254-256, May, 1946. 2. K. Bullington, Radio Propagation at Frequencies Above 30 IMegacjcles, Proc. I.R.E., 35, pp. 1122-1136; Oct., 1947. 3. K. Bullington, Reflection Coefficients of Irregular Terrain, Proc. I.R.E., 42, pp. 1258-1262; Aug., 1954. 4. W. M. Sharpless, Measurements of the Angle of Arrival of Microwaves, Proc. I.R.E., 34, pp. 837-845, Nov., 1946. 5. A. B. Crawford and W. M. Sharpless, Further Observations of the Angle of Arrival of Microwaves, Proc. I.R.E., 34, pp. 845-848, Nov., 1946. 6. A. B. Crawford and W. C. Jakes, Selective Fading of Microwaves, B.S.T.J., 31, pp. 68-90; January, 1952. 7. R. L. Kavlor, A Statistical Studv of Selective Fading of Super High Frequency Radio Signals, B.S.T.J., 32, pp. 1187-1202, Sept., 1953. 8. H. E. Bussev, Alicrowave Attenuation Statistics Estimated from Rainfall and WaterVapor Statistics, Proc. I.R.E., 38, pp. 781-785, July, 1950. 9. J. C. Schelleng, C. R. Burrows, E. B. Ferrell, Ultra-Short Wave Propagation, B.S.T.J., 12, pp. 125-161, April, 19.33. 10. MIT Radiation Laboratory Series, L. N. Ridenour, Editor-in-Chief, Volume 13, Propagation of Short Radio Waves, D. E. Kerr, Editor, 1951, jNIcGraw- Hill. 626 THE «ELL SYSTEM TECHNICAL JOUKNAL, MAY 1957 11. Summary Technical Report of the Committee on Propagation, National De- fense Research Committee. Volume 1, Historical and Technical survey. Volume 2, Wave Propagation Kxperiments. Volume 3, Propagation of Radio Waves. Stephen S. Attwood, editor, Washington, D.C., 1946. 12. C. W. Burrows and M. C. Grav, The Effect of the Earth's Curvature on Ground Wave Propagation, Proc. I.R.E., 29, pp. 16-24, Jan., 1941. 13. K. Bullington Characteristics of Bevoiid-Horizon Radio Transmission, Proc. I.R.E., 43, J). 1175; Oct., 1955. 14. W. E. Cordon, Radio Scattering in The Troposphere, Proc. I.R.E., 43, p. 23, Jan., 1955. 15. K. Bullington, Radio Transmission Beyond the Horizon in the 40- to 4,000 MC Band, Proc. I.R.E., 41, pp. 132-1.35, Jan., 1953. 16. K. A. Norton, P. L. Rice and L. E. Vogler, The Use of Angular Distance in Estimating Transmission Loss and Fading Range for Propagation Through a Tur])ulent Atmosphere Over Irregular Terrain, Proc. I.R.E., 43, pp. 1488- 1526, Oct., 1955. 17. F. H. Dickson, J. J. Egli, J. W. Herbstreit, and G. S. Wickizer, Large Reduc- tions of VHF Transmission Loss and Fading by Presence of Mountain Ob- stacle in Beyond Line-Of-Sight Paths, Proc. I.R.E., 41, pp. 967-9, Aug., 1953. 18. K. Bullington, W. J. Inkster and A. L. Durkee, Results of Propagation Tests at 505 MC and 4090 MC on Beyond-Horizon Paths, Proc. I.R.E., 43, pp. 1306-1316, Oct., 1955. 19. Same as 13. 20. H. G. Booker and J. T. deBettencourt, Theorj^ of Radio Transmission by Tropospheric Scattering Using Very Narrow Beams, Proc. I.R.E., 43, pp. 281-290, March, 1955. 21. W. H. Tidd, Demonstration of Bandwidth Capabilities of Bevond-Horizon Tropospheric Radio Propagation, Proc. I.R.E., 43, pp. 1297-1299, October, 1955. 22. K. Bullington, Radio Propagation Variations at VHF and UHF, Proc. I.R.E., 38, pp. 27-32, Jan., 1950. 23. W. R. Young, Comparison of Mobile Radio Transmission at 150, 450, 900 and 3700 MC, B.S.T.J., 31, pp. 1068-1085, Nov., 1952. 24. K. A. Norton, The Physical Reality of Space and Surface Waves in the Radia- tion Field of RadioAntennas, Proc. I.R.E., 25, i)p. 1192-1202, Sept., 19.37. 25. Same as 2. 26. C. R. Burrows, Radio Propagation Over Plane Earth-Field Strength Curves, B.S.T.J., 16, pp. 45-75, Jan., 19.37. 27. K. A. Norton, The Propagation of Radio Waves Over the Surface of the Earth and in the Upper Atmosphere, Part II, Proc. I.R.E., 25, pp. 1203-1236, Sept., 1937. 28. Same as 26. 29. National Bureau of Standards Circular 462, Ionospheric Radio Propagation, Superintendent of Documents, U.S. Govt. Printing Office, Washington 25, D.C. 30. National Bureau of Standards, CRPL Series D, Basic Radio Propagation Predictions, issued monthly by LT.S. Govt. Printing Office. 31. National Bureau of Standards Circular 465, Instructions for Use of "Basic Radio Propagation Predictions, Superintendent of Documents, U.S. Govt. Printing Office, Washington, D.C. 32. E. W. Allen, Very-High Frequency and Ultra-High Frequency Signal Ranges as Limited by Noise and Co-channel Interference, Proc. I.R.E., 35, pp. 128-136, Feb.; 1947. 33. D. K. Bailey, R. Bateman and R. C. Kirby, Radio Transmission at VHF by Scattering and Other Processes in the Lower Ionosphere, Proc. I.R.E., 43, pp. 1181-1230, Oct., 1955. 34. J. W. Herbstreit, Advances in Electronics, 1, Academic Press, Inc., ]>p. 347- 380, 1948. A Reflection Theory for Propagation Beyond the Horizon* By H. T. FRIIS, A. B. CRAWFORD and D. C. HOGG (Manuscript received January 9, 1957) Propagation of short radio waves beyond the horizon is discussed in terms of reflection from layers in the atmosphere formed by relatively sharp gra- dients of refractive index. The atmosphere is assumed to contain many such layers of limited dimensions with random position and orientation. On this basis, the dependence of the propagation on path length, antenna size and ivavclength is obtained. INTRODUCTION It was pointed out several years ago^ that power propagated beyond the radio horizon at very short wavelengths greatly exceeds the power calculated for diffraction around the earth. This beyond-the-horizon propagation has stimulated numerous experimental and theoretical in- vestigations.- Booker and Gordon,^ 'S'illars and Weisskopf^ and others have developed theories based on scattering of the radio waves by tur- bulent regions in the troposphere. This paper proposes a theory in which uncorrelated reflections from layers in the troposphere are assumed re- sponsible for the power propagated beyond the horizon. In developing this theory, some arbitrary assumptions of necessity have been made concerning the reflecting laj^ers since, at the present time, our detailed knowledge of the atmosphere is insufficient. However, calculations based on the theory are found to be in good agreement with reported measurements of beyond-the-horizon propagation. Measurement of the dielectric constant of the atmosphere^ has shown that relatively sharp variations in the gradients of refractive index exist in both the horizontal and vertical planes. Although the geometrical structure of the boundaries formed by the gradients is not well knoATO, one may postulate an atmosphere of many layers of limited extent and * This material was presented at tlie I.R.E. Canadian Convention, Toronto, Canada, October 3, 1956. 627 G28 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 arbitrary aspect.* The number and size of the reflecting layers, as well as the magnitude of the discontinuities in the gradient of dielectric con- stant which form them, influence the received power. The reflecting properties of the layers are discussed first. Next, an ex- pression for the received power is obtained by summing the contributions of many layers in the volume common to the ideaUzed patterns chosen to represent the transmitting and receiving antenna beams. f This ex- pression is then used to calculate the effect on received power of changes in such parameters as the orientation of the antennas, wavelength, dis- tance, and antenna size. The MKS system of units is used throughout. REFLECTING ' SURFACE Fig. 1 — Reflection bj' a layer. EFFECT OF LAYER SIZE Propagation from a transmitting antenna of effective area At to a recei\-ing antenna of effective area Ar by means of a reflecting layer is illustrated in Fig. 1. The ray from transmitter to receiver grazes the layer at angle A. The reflection from the layer depends on the ampli- tude reflection coefficient, q, which is a function of the grazing angle, and on the dimensions of the layer relative to the dimension of a Fresnel zone. I Three cases, depending on the layer dimensions, will be considered. * After this paper was submitted for publication, a report was received giving some measurements of sharp variations in dielectric constant gradient and esti- mates of the horizontal dimensions of layers in the troposphere. J. R. Bauer, The Suggested Role of Stratified Elevated Layers in Transhorizon Short -Wave Radio Propagation, Technical Report No. 124, Lincoln Laboratory, ^LI.T., Sept., 1956. t Under some conditions, layers outside the volume common to the antenna beams maj' contribute appreciablj^ to the received power. Phenomena such as multiple reflections and trapping mechanisms are not considered in this study. J The power received bj- reflection from the layer in Fig. 1 can be calculated approximateh" bj- assuming it to be the same as the power that would be received by diffraction through an aperture in an absorbing screen, the dimensions of the aperture being the same as the dimensions of the layer projected normally to the directions of propagation. The field at the receiver is calculated from the distri- bution of Huj'gens sources in the aperture. The received power, e.xpressed in REFLECTION THEORY — PROPAGATION BEYOND THE HORIZON 629 Case 1. Large Layers If the layer were a plane, perfectly reflecting surface of unlimited ex- tent, the power at the terminals of antenna ^4^ would be the same as the power received under line-of-sight conditions, p _ p AtAr If the layer has an amplitude reflection coefficient, q, the received power is. ^> p _ p AtAr 2 This relation applies when the layer dimensions are large in terms of the wavelength and are large compared with the Fresnel zone dimensions; that is, b > \/2aX/A and c > \/2aX. Case 2. Small Layers When the dimensions of the layer are small compared with the Fres- nel zone, but large compared with the wavelength, the received power is given by the "radar" formula, 2 2 D T> AtAr 2/j • \2 : This relation applies when h < -y/'IaX/A and c < \/2aX. terms of Fresnel integrals, is Pr = -Pr^VV [C"^") + SHu)][CHv) + SHv)] where u = — ;= and v = \a V Xa When u and v are very hirge, we have, approximatelj^ C(m) = S{xi) = C{v) = S{v) = \ and the expression for Pr reduces to that given for Case 1 above, except for the factor q^. When both u and v are very small, we have approximately, C(ii) = u C{v) = V S{u) = o Sin) = 0 and the expression for Pr reduces to that given for Case 2. When u is large and v is small the expression for Pr given in Case 3 results. 630 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 Case 3. Layers of Intermediate Size If the layer dimensions, are such that c is large but 6A is small, com- pared with the Fresnel zone dimension, the recei^•ed power is given by ^^ = ^^ 2XW *^' " In the atmosphere, c and b are likely to be about equal, on the average, and we have for this case, \/2aX < h < ■\/2aX/A. All three of these cases may be present at various times, since the structure of the atmosphere changes from day to day. However, for the purpose of the present study. Case 3 is considered most prevalent and is assumed in all the calculations to follow\ Many of the numerous layers that are assumed to contribute to the received power are not necessarily horizontally disposed, they may be oriented in any direction. Therefore, reflection in the direction of the receiver can take place from layers located both on and off the great circle path. If there are N contributing layers per unit ^'olume in the region V common to the radiation patterns of the transmitting and re- ceiving antennas, then for Case 3, « _ ArAnNb 2\'a' f A'q'dV (1) Jv In this relation it has been assumed that the layer size and the number of layers per unit volume remain sensibly constant throughout the com- mon volume. The integration process reciuires expressions for the reflection coefii- cient q and the grazing angle A of the layers in the common volume. These quantities are derived in the following sections. REFLECTION COEFFICIENT OF A LAY'ER The reflection coefficient of a plane boundary (Fig. 2) separating two media whose dielectric constants, relative to free space, differ by an increment de is given by Fresnel's laws of reflection. For both polariza- tions, the plane wave reflection coefficient of the boundary is q = de/^A- 1 Fig. 2 — Reflection at a l)()undary between two homogeneous media. REFLECTION THEORY — PROPAGATION BEYOND THE HORIZON 631 provided 1 » A" » (If. This reflection coefficient for an incremental change in dielectric constant can be used to calculate the reflection from discontinuities in the gradient of the dielectric constant of the atmos- phere such as those shown for a sti-atified medium at .// = 0 and /y = h in Fig. o(b). Such variations of dielectric constant are assumed to be representatix'e of discontinuities in gradient as they exist in the physical atmosphere. The variations form the reflecting layers. The method of calculating the reflection coefficient of such a stratified medium is due to S. A. Schelkunofl" and is illustrated schematically in Fig. 3 in which the medium has been subdi\'ided into incremental steps. Consider the reflected wave from a typical incremental layer, dy, situated a distance ij above the lower boundary of the la^^er, 0. From Fig. 3(a) it is clear that the phase of this wave is -iiTij/X sin A relative to that of a wave reflected from the lower boundary. The incremental reflection co- efficient is c?f/4A^ = —K dy/4:A', where K is the change in gradient of the dielectric constant at the boundaries of the layer. The field reflected by layer dy is therefore, dEn = -Ei K _, j{iiryl\) sin A 4A2 dy One now obtains the complete reflected field by summing the reflec- tions from all increments within the layer of thickness h. E.. f dEr = jE, K\ [1 e -j(iirhl\) sin Ai JO 16xA- sin A This relation shows that the layer is equi\'alent to two boundaries at *-e Fig. .3 — Plane-wave reflection at an incremental layer di/ within a stratified medium extending from y = 0 to y = h. G32 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 7/ = 0 and // = h, each with refloftion cooffiriont If the abrupt change in slope, the soUd Une in Fig. 3(b), is replaced by a gradual change as indicated by the dotted lines, (2) still holds pro- vided d < X/4A. For more gradual changes, d = 7iX/4A where n > 1 , the reflection coeflScient is . irn _ KX ^"^T IGttA^ Trn ~2 and q varies with n between 5 = 0 and ^ ~ IGttA'^ ' Trn Smoothing of the boundaries reduces the value of q. It will be assumed in all the calculations to follow that reflection from layers in the troposphere is described by (2). VARIATION OF STRENGTH OF LAYERS WITH HEIGHT The formula for the reflection coefficient includes the factor K, which represents the change in the gradient of the dielectric constant at the boundaries of the layer. A dielectric constant profile constructed of many randomly positioned gradients is shown schematically in Fig. 4. The variations are showTi as departures from the standard linear gradient. Measurements indicate that the fluctuations of the dielectric constant normalh^ decrease with height above ground. The changes in the dielec- tric constant gradients associated with these fluctuations probablj^ vary in a similar manner so that K is some inverse function of the height above the earth. However, to simplify the computation of received power, to be described later, we have adopted the cylindrical coordinate system shown in Fig. 5, and it is convenient, then, to let K be a function of p, the distance from the chord joining the transmitter and receiver to the point in question. We assume, therefore, that P where Ki is the change in gradient at point .4 in Fig. 5 which, for a typi- REFLECTION THEORY — PROPAGATION BEYOND THE HORIZON 633 >^ AVERAGE e FOR \ ^'"TROPOSPHERE Fig. 4 — Schematic illustration of variation of the dielectric constant in the troposphere. *-z Fig. 5 — Coordinate system for a beyond-the-horizon circuit. cal path length of 200 miles, is about 1,600 meters (1 mile) above the earth or, since p = 2H, 3,200 meters from the z axis. Equation 3 is used in all the calculations to follow. THE GRAZING ANGLE A The grazing angle A at the slightly tilted layer sho^^^l in Fig. 6 is given by tan 2A 2ap a^ — z^ — p2 ()34 THK HKLI. SYSTEM TECHNICAL JOlTliXAL, MAY lO")? Throughuut the volume coiiiiuoii to the aiiteniui patterns, A « 1, p « a and z < a/2. Then a (4) It is evident that A is constant and equal to p/a when the point (p, z) is located on a cylinder with axis TR and radius p. It is this feature that *-z Fig. 6 — Grazing angle A at a layer. I Fig. 7 — Idealized antenna patterns used in this study. 6pz dV, = 2(y-a)/3/9,dA dV, = 2 a Pz '^--\- e+J^^^^^^ Fig. 8 — Integration over the common volume. REFLECTION THEORY — PROPAGATION BEYOND THE HORIZON 635 suggested the unusual idealized antenna patterns shown in Fig. 7, which are described in the next section. CALCULATION OF THE RECEIVED POWER Substituting (2), (3) and (4) in (1), one obtains for the received power, P« = PrMaAuAA'' f p'' dV (5) where M ^ 2000b'Ki^N (6) To integrate over the volume common to actual antenna patterns would be difficult. We have, as mentioned before, replaced the actual patterns with the idealized patterns shown in perspective in Fig. 7 and in plane projection in Fig. 8. The patterns (Fig. 7) are bounded by side planes of the large wedge and by surfaces of cones with axis TR. The com- mon volume is indicated by broken lines and is well defined. Since the grazing angle A is constant for the incremental cylindrical volumes dVi and dVo shown in Fig. 8, it is easy to integrate over the common volume V and we obtain (7) 1+^-^^. -^1^^ ^1 (8) (■ * ? The function f(a/d) is plotted in Fig. 9. The gain of the idealized antennas is G^ = 87r/Q;jS(o! + 26) and the ef- fective area is 2X^ ^ ^ a^{a + 2d) ^^^ The area of a cross section of the antenna pattern is bounded by two straight sides, ra, and two curved sides rd^ and r{d + a)|3. The aspect ratio is defined as the ratio of the sum of the lengths of the curved sides to the sum of the lengths of the straight sides. It is equal to one when Substituting (10) in (9) gives the effective area of the idealized antenna 636 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 f{oc/e) 0.7 ■ 0.6 0.5 0.4 y^ / -f / 0.3 0.2 1 ^ / 0.1 / / 0 J 0.5 1.0 1.5 2.0 2.5 a/d 3.0 3.5 4.0 4.5 5.0 \ Fig. 9 — The function / (a/O). with aspect ratio one, A = a'- (11) Substituting (7), (10) and (11) in (5) gives for identical transmitting and receiving antennas with aspect ratio one, Pu = P: M>^_1_ 1 ^+e -Al (12) For actual antennas, a may be taken to be the half-power beam-width. In the following sections, (12) will be used to derive some of the gen- eral properties of propagation beyond the horizon. * K. Bullington has suggested that a useful form for equation (12) is Pr = e \d a where the first term in brackets represents the power that would be received in free space, the second term involves the characteristics of the troposphere, an(l <)\er the same path, the antenna gains being identical for the two systems, then, on the average, one would expect the received power relative to the free space value at 400 mcs to be 10 db higher than that at 4,000 mcs because of the charac- teristics of the troposphere. Case 11. Equal antenna apertures for the two wavelengths. For this case, ai/ao = X1/X2 and (14) reduces to Rl P (18) Experimental data for this case was obtained on the 150 nautical mile test circuit between St. Anthony and Gander in Newfoundland.^ The antennas for both wavelengths were paraboloids 8.5 meters in diameter. Simultaneous transmission tests at Xi = 0.074 m and X2 = 0.6 m were conducted for a full year. For this circuit, 0 = 0.94° (4/3 earth radius) a, = 66 ^^ = 0.575° 8.0 0.6 aa = t)D — — 8.5 66 ^ = 4.65° Using these values in (18), we get for the ratio of received powers, Pri/Pr2 = 1.01 For antennas of equal aperture in free space, Pri/Pr2 = (X2/X1)' = 65.5 Therefore, Pr\/Pr2 (Beyond Horizon) ^ J_ ^ - 18 1 db Pri^Pr2 (Free Space) 65 The Summarj'^ of Results, Sections 1 and 2 on page 1316 of Reference 8, gives — 17 db for this ratio. The agreement between calculated and meas- ured values is very good. REFLECTION THEORY — PROPAGATION BEYOND THE HORIZON 639 RECEIVED POWER VERSUS DISTANCE If antenna size and wavelength are specified, (12) gives for two dis- tances, ai and aa , Pri I Cl-iX 60 \0l (19) For a-i = 2ai , (19) gives for different values of a/di oc/di = 0.5 1 2 4 Pri/ Pin = 270 (24 db) 197 (23 db) 138 (21.5 db) 104 (20 db) Fig. 1 in Biillington's paper,^ which gives the median signal level in decibels below the free space value as a function of distance, shows an 18 db increase in attenuation when the distance is doubled. This cor- responds to a ratio of received powers of 18 + 6 = 24 db. The examples in the table abo\'e give an average increase in attenuation of 22 db. RECEIVED POWER VERSUS ANTENNA SIZE Equation 14 can be used to calculate the effect on received power of changing simultaneously the size (and, hence, the beamwidths) of the antennas used for transmitting and receiving, the wavelength and dis- tance remaining fixed. n, /«A"-_^ '\e) (20) Pr2 \OLl/ 9 I ^ r /«2\ " ^ d '' \d ) where P^i and P^o are the received powers corresponding to the antenna l)eamwidths ai and a^ respectively. As an example, let a2 be constant and eciual to 4° and let d be 1°, corresponding to a 200-mile circuit. The table below gives the ratio Pri/Pr2 as ai is varied. ai 4° 2° 1° 0.5° 0.25° Pri/Pr2 (db) 0 10 18.5 25.7 31.4 Change in db 10 8.5 7.2 5.7 Since a is inversely proportional to the antenna dimensions, the table shows that continued doubling of the antenna dimensions results in less and less increase in output power. The increase varies from 10 to 5.7 db 640 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 in the table. This is a characteristic feature of beyond-the-horizon prop- agation. In free space, doubling the antenna dimensions would result in a r2-db increase in output power. Large antennas and high power transmitters are costly, and a proper balance between their costs requires careful studies which are outside the scope of this paper. In general, it is not believed worth while from power considerations to increase the antenna size much beyond the di- mensions that correspond to a pattern angle, a, equal to angle d. Another factor to be considered, however, is the effect of antenna size on delay distortion in bej'ond-the-horizon circuits. From simple path length considerations, one concludes that the delay distortion decreases when the beamwidths of the antennas are made smaller. Therefore, delay distortion requirements may dictate antenna sizes that are not justified by power considerations alone. SEASONAL DEPENDENCE Both the effective earth radius. Re , and the magnitude of the discon- tinuities in gradient, Ki , are related to the season of the year. During the summer when the water vapor content of the air is high, the effective radius and the discontinuities in gradient are larger than in winter. Sub- stituting a/Re for 6 and assigning summer and winter values for Re and Ki , (12) may be used to calculate the ratio of the power received in summer and in winter. Pr (Summer) P« (Winter) (21) For example, if we assume Kis = 2Kiw and Res =1.2 Rew , then Prs/ Prw = 11-9 (10.75 db). A seasonal variation has been observed.^ ^ DEPENDENCE OF RECEIVED POWER ON ANTENNA ORIENTATION The variation of received power with orientation of the antennas at the terminals of a be\'ond-the-horizon circuit differs considerably from that observed under line-of-sight conditions. Consider, for example. Fig. 10 which shows the beams of the transmitting and receiving antennas elevated simultaneously. The variation of received power can be calcu- lated from (13). As an example, consider the 188-mile circuit between REFLECTION THEORY — PROPAGATION BEYOND THE HORIZON 641 Crawford Hill, N. J., and Round Hill, Mass., for which experimental data is published.' For this circuit a = 0.05° (3 db points) and di = 1° (4/3 earth radius). The tal)le below gives the calculated variation of re- ceived power as angle d-i is varied. 6; = 1° 1.1° 1.2° 1.4° 1.0° 1.8° 2° 2.2° 10 logio {Prx/Pri) = 0 2.3 4.5 8.5 12 15 17.9 20.5 The received power versus elevation angle, 7 = 02 — ^i , is plotted in Fig. 10. The calculated and experimental curves are in good agreement. If the beams of the antennas are steered simultaneously in the hori- zontal plane. Fig. 11, the calculation of the variation of received power is if) _i LU u UJ Q LU o Q. Q LU > LU U w a. LU > -8 -10 -12 -14 > -16 -18 -20 -22 0 c \ \ \ "-^ \ > \ N N \ \ \ \ \ \ EXPERIMENTAL \ \ REFLECTION " THEORY n\ \ k. ^ k< ^. ^-N X^ ) ^. » -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 VERTICAL ANGLE, /, IN DEGREES Fig. 10 — Relation between received power and vertical angle y. 642 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 comparatively simple. In horizontal steering, the intersection of the axes of the antemia beams moves along line AB in the figure labelled "Cross section at 0." If the intersection of the beams mo\ed along the circle A-C, the recei\'ed power would not change. The decrease in power caused by moving the beams from position ^4 to B is given by (13). The calcu- HORIZONTAL PLANE .4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 AZIMUTH ANGLE, <7, IN DEGREES Fig. 11 — Relation between received power and azimuth angle 5. REFLECTION THEORY — PROPAGATION BEYOND THE HORIZON 643 lations are identical with the calculations for elevation steering; the ele- vation angle 62 is related to the azimuth angle 5 and the beamwidth angle a by A calculated curve of received power versus azimuth angle is shown in Fig. 1 1 for the Crawford Hill-Round Hill circuit together with the re- ported experimental data. The agreement is considered good. THE VALUE OF FACTOR M IN EQUATION (12) An average value for the factor M can be obtained from propagation data. Using equation (12), the ratio of received powers corresponding to free space and beyond-horizon transmission is D n- ^ 0.750' f 2 + f) Pr (tree space) _ \ 6 J , . Pr (beyond-horizon) MKaj © This ratio was found experimentally to be 5 X lO*' (67 db) for the circuit between St. Anthony and Gander in Newfoundland. For this circuit, a = 0.081, 6 = 0.0164, X = 0.6. Substituting these values in (22) we obtain, ilf = 3 X 10"'* (23) Substituting this value for M in (12) leads to the following equation for a beyond-horizon tropospheric circuit. p^ = P^X 10-'" -' a" 1 1 fey e'n~ -il a \ft 2 + d (24) Equations (6) and (23) give b'K'N = 1.5 X 10"'' (25) Although values of the layer dimension, b, the change in gradient, Ki , and the number of layers per unit volume, N, are not known, it is interest- ing to calculate A^ from (25) assuming reasonable values for b and A'l . Assuming A'l = 4 X 10"*", which is half the value of K', the average gradient of the dielectric constant in the troposphere, and b = 1,000 (1 km) we find A^ = 10"^ or 10 layers per cubic kilometer. 644 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 CONCLUDING REMARKS The interpretation of propagation beyond the horizon in terms of re- flection from layers of limited size formed by variations in the gradient of the dielectric constant of the atmosphere leads to relatively simple results which are in good agreement with reported experimental data. The received power depends on the wavelength, the distance, and the size of the antennas used for the circuit and on the strength and size of the reflecting layers. As mentioned earlier, the structure of the atmosphere may change markedly from time to time so that large, small and intermediate size layers play their parts at different times. Furthermore, the effective size of a given layer may be different for widely separated wavelengths, de- pending on the roughness of the layer in terms of the wa^■elength. All that can be expected of a study such as the present one is that it serve as a guide for estimating the roles of the various parameters involved in beyond-the-horizon propagation. REFERENCES 1. K. BuUington, Radio Propagation Variations at VHF and UHF, Proc. I.R.E., 38, p. 27, Jan., 1950. 2. Proc. I.R.E., Oct., 1955. 3. H. G. Booker and W. E. Gordon, A Theory of Radio Scattering in the Tropo- sphere, Proc. I.R.E., 38, p. 401, April, 1950. 4. F. Villars and V. F. Weis.skopf , Scattering of EM Waves by Turbulent Atmos- pheric Fluctuations, Phys. Rev., 94, p. 232, April, 1954. 5. C. M. Grain, Survey of Airborne Refractometer ^leasurements, Proc. I.R.E., 43, p. 1405, Oct., 1955. H. E. Bussej^ and G. Birnbaum, ^leasurement of Variation in Atmospheric Refractive Index with an Airborne Microwave Refractometer, N.B.S. Jour. Res., 51, pp. 171-178, Oct., 1953. 6. H. T. Friis, A Note on a Simple Transmission Formula, Proc. I.R.E., 34, pp. 254-56, May, 1946. 7. S. A. Schelkunoff, Applied Mathematics for luigineers and Scientists, D. Van Nostrand Co., Inc., p. 212., 1948, and Remarks Concerning Wave Propagation in Stratified Media, Communication on Pure and Applied Mathematics, 4, pp. 117-128, June, 1951. See also, H. Bremmer, The W.K.B. Appro.xima- tion as the First Term of a Geometric-Optical Series, Communication on Pure and Applied Mathematics, 4, pp. 10^115, June, 1951. 8. K. BuUington, W. J. Inkster and A. L. Durkee, Results of Propagation Tests at 505 mc and 4,090 mc on Bejond-Horizon Paths, Proc. I.R.E., 43, pp. 1306-1316, Oct., 1955. 9. K. BuUington, Characteristics of Bej'ond-the-Horizon Radio Transmission, Proc. I.R.E., 43, pp. 1175-1180, Oct., 1955. 10. J. H. Chisholm, P. A. Portmann, J. T. deBettencourt and J. F. Roche, Inves- tigations of Angular Scattering and Multipath Properties of Tropospheric Propagation of Short Radio Waves Bej'ond the Horizon, Proc. I.R.E., 43, pp. 1317-1335. Oct., 1955. Interchannel Interference Due to Klystron Pulling By H. E. CURTIS and S. O. RICE (Manuscript received August 26, 1956) A source of interchannel interference in certain multichannel FM systems is the so-called ^'frequency pulling effect.^' This effect, which occurs in systems using a klystron oscillator, is produced hy an impedance mis- match between the antenna and the transmission line feeding it. In this paper expressions are developed for the magyiilude of the interference when the speech load is simidated hy random noise. INTRODUCTION In a recent paper^ the problem of interchannel interference produced by echoes in an FM system was treated. The mathematical development in that paper can be used to calculate the distortion that arises when a Klystron oscillator is connected to an antenna through a transmission line of appreciable length. In the system we study, the composite signal wave (the "baseband signal") from a group of carrier telephone channels in frequency division multiplex is applied to the repeller of a Klystron and thereby modulates the frequency of the Klystron output wave. If the antenna does not match the transmission line perfectly, the output frequency is altered slightly by an amount proportional to the mismatch. This effect, known as "pulling," results in intermodulation between the individual telephone channels. In this study, the composite signal will be simulated by a random noise signal of appropriate bandwidth and power. It is assumed that some particular message channel is idle; i.e., there is no noise energy in the corresponding frequency band (which is relatively narrow in comparison with the bandwidth of the composite signal). If the system were perfect, no power would be received in this idle channel at the output of the FM detector. In the following work, the intermodulation noise falling into this channel because of the "pull- ing effect" will be computed. This leads to "Lewin's integral," so called, which is tabulated herein. 645 646 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 PULLING EFFECT In a perfect FM system the carrier wave can be written E,{t) = A sin [pt + <^(0] (1) where .4 is a constant and the signal is ^S(0 = dxp/dt = (p'(t), measured in radians/second. As mentioned in the Introduction, we assume that when the FM oscillator is connected directly to a transmission line with a slightly mismatched antenna at the far end, its frequency is changed. The reactive component of the input impedance of the line "pulls" the frequency of the oscillator to its new value. When the antenna is perfectly matched, there is no change in oscillator frequency. If the characteristic impedance of the line is Zr and the impedance of the antenna is Zr , the impedance Z looking into the line is y ^ J ^R + ^K ^-^"h P Zk + Zr tanh P _ 7 I + pe — Zjr 1 - pc--^ where p is the reflection coefficient Zr + Zk and P is the propagation constant of the line. If the loss of the line is negligible and the reflection coefficient is small, the input impedance is approximately Z = Zk[\ + 2p(cos o:T - i sin aT)] ohms where w is the oscillator frequency in radians per second and T is twice the delay of the line. It will be observed that the magnitude of the reactive component of Z oscillates as the phase angle coT increases. The dependence of the frequency of an oscillator upon the load reac- tance has been expressed by earlier workers as a "pulling figure." This figure is customarily defined as the difference between the maximum and minimum frequencies observed when the load reactance is varied over one cycle of its oscillation (the variation being accomplished, say, by increasing T). The load is taken to be such that it causes a voltage stand- ing wave ratio of 1.5. This corresponds to a reflection coefficient of 0.20 and 14 db return loss. In our work, we assume that the change in frequency is flirectly pro- INTEKCHANNEL INTERFERENCE DUE TO KLYSTRON PULLING (347 portional to the reactive component of the input impedance. More pre- cisely, we assume that the ideal transmitter freciuency of p + ^'(0 I'adi- ans/sec is changed by the pulUng effect to p + ip'ii) + 2wr sin [T{p + ip'{t))] radians/sec (2) where r is given by r = 2.5 I p I X (Pulling Figure in cycles/sec) POWER SPECTRUM OF INTERCHANNEL INTERFERENCE The distortion produced by the pulling effect is given by the third term in (2). This distortion will be denoted b}^ ^'(0- d'{t) = 27rr sin [pT + T^'(t)] (3) Our problem is to compute the power spectrum of d'((). In particular, we are interested in the case where the signal (p'{f) represents the compos- ite signal wave from a group of carrier telephone channels in frequency division multiplex. All of the channels except one are assumed to be busy. Although the power spectrum of (p'{t) is zero for frequencies in the idle channel, the same is not true for the power spectrum of d'(t). In fact, the interchannel interference (as observed in the idle channel) is given by that portion of the power spectrum of d'{t) which lies within the idle channel. We shall denote the corresponding interchannel interference power in the idle channel by wdf) df where the idle channel is assumed to be of infinitesimal width and to extend from frequency / — df/2 to / -f df/2. The function wdf) will now be computed by using the procedure developed in Reference 1. The first step is to assume the signal ip'(f) to be a random noise current. In order to avoid writing tp' a great many times we shall set (p'(t) = S(t), where now S{t) stands for the signal. Then the autocorrelation function for the distortion d'{t) is Re'(r) = avg [d'(t)9'{t + r)] = (27rr)- avg [sin (Tp + T(o.) = ^' r^V^l - cos2pr)] (6) This follows from (4) since Rs (^) = 0. The auto-correlation function of the distortion, excluding the dc component, is then R,,_r. = ^ [e~''Rs'''][(e'''Rs'''- I) - {e'''^^'^' - 1) cos 2pr] (7) The mterchannel interference spectrum is Wc{j) = 4 /" Rcir) cos 27rfr dr (8) where, by analogy with equation (1.22) of Reference 1, E^{r) = ^' [e-''Rs'''][(e''-'^''> - T'Rs{t) - 1) ^ (9) _ ^^-r'^sir) ^ j.2^^(^) -1 ) cos 2pT] As mentioned before, the function wdf) is of interest because P, = Waif) df (10) is the average interference power appearing at the receiver in an idle channel of width df centered on frequency' /. RATIO OF IXTERCHAXXEL IXTERFEREX'CE TO SIGXAL POWER The average signal power appearing in a bus\' channel of width df centered on the frequency / is Ps = Wsif) df (11) and hence the ratio of the interchannel interference power to the signal INTERCHANNEL INTERFERENCE DUE TO KLYSTRON PULLING 649 power IS P/ _ Weif) Ps (12) We now obtain an expression for this ratio on the assumption that the random noise signal S{t) (which is used to simulate the multichannel signal) has the power spectrum >0 , 0 < / < /6 ws(f) = (13) [o, / > /. where Po is a constant. S(t) is measured in radians/sec and Poft is meas- ured in (radians/sec) . Pofb is given by PoU = Sm = avg [ 0 e-''J(b,a) b e* 0=0 0.25 0.50 0.75 1.00 1.25 0.0 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.25 1.284 0.082 0.072 0.062 0.052 0.042 0.031 0.5 1.649 0.272 0.241 0.209 0.176 0.142 0.107 1.0 2.718 0.761 0.685 0.602 0.511 0.414 0.314 2.0 7.389 1.560 1.440 1.291 1.117 0.919 0.713 3.0 20.08 1.913 1.801 1.645 1.448 1.215 0.968 4.0 54.60 1.974 1.888 1.751 1.566 1.341 1.098 5.0 148.4 1.905 1.844 1.731 1.571 1.372 1.153 6.0 403.4 1.794 1.751 1.660 1.525 1.356 1.166 7.0 1097. 1.680 1.649 1.575 1.463 1.320 1.157 8.0 2981. 1.576 1.552 1.492 1.398 1.277 1.138 Table II — Values of I{b, a) for h < 0 lib .a) b a = 0 0.25 0.50 0.75 1.0 1.25 0.0 0.000 0.000 0.000 0.000 0.000 0.000 -0.25 0.092 0.080 0.068 0.057 0.045 0.034 -0.5 0.349 0.300 0.254 0.210 0.167 0.125 -1.0 1.25 1.06 0.885 0.723 0.576 0.432 -2.0 4.16 3.41 2.76 2.20 1.76 1.34 -3.0 8.03 6.37 4.97 3.88 3.14 2.46 -4.0 12.6 9.66 7.23 5.49 4.55 3.74 -5.0 17.8 13.2 9.40 6.89 5.93 5.19 -6.0 23.6 16.8 11.4 8.00 7.25 6.85 -7.0 30.0 20.7 13.1 8.71 8.48 8.78 -8.0 37.2 24.8 14.5 8.93 9.59 11.0 dimensions of (radians/sec)Vcps. The signal in the same dimensions is Po or {'IwaY/fb. Therefore the ratio of the interchannel interference power to the signal power is: P/ Ps e~'\l{h, a) - I{ - h, a) cos 2pT] (17) The quantity e~ I{b, a) for 6 > 0 is tabulated in Table I. The quantity I{h, a) for 6 < 0 is given in Table II. These tables, which are also given in Reference 1 , are repeated here for the convenience of the reader. When the rms frequency deviation a is so small that h = (2x0-7')" is small compared to unity, the approximation leads to P.S lib, a) ^ ?>V(2 - a)/4 (27rV(7 T')- (2 - a)(l - ros2pT)/2 (18) INTERCHANNEL INTERFERENCE DUE TO KLYSTRON PULLING 651 When 0- and T are such that 6 » 1 , the approximation I{h, a) ^ {2 as a function of aT G52 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 -4 -6 _i LU U LU -16 Q Q -20 -24 -28 -32 (TJ = 0.45 ^ 0.11 ^ 0.08 ^X ^^^_ ,/ \, ^- ,.-" / / \ \ / V y -20 20 40 60 60 100 120 140 ECHO PHASE, pT, IN DEGREES 160 180 200 Fig. 2 — Plot of D2 as a function of echo phase when f = fb The term A depends only on the rms deviation a, the round-trip echo delay T of the hne, the ratio a = f/fb , and the echo phase pT. The term D2 is plotted in Fig. 1 as a function of aT for two channels, one at the top and the other at the bottom of the signal band. Since the carrier frequency may be expected to be very high, the carrier phase 2pT will be a very large number of radians even with ver}^ short wave guide runs. Hence the curves on Fig. 1 are plotted for the average value of cos 2pT which is zero. The curves on Fig. 2 show how D2 depends on pT and the parameter (tT. In this case the channel is taken at the top of the signal band. When pT is an odd multiple of 90 degrees, it turns out that we have even order modulation products onlj'-; and when pT is a multiple of 180 degrees, odd order products only. The curves show that the distortion becomes less dependent on the echo phase as the quantity aT increases. REFERENCE 1. W. R. Bennett, H. E. Curtis and S. O. Rice, Interchannel Interference in FM and PM Systems, B.S.T.J., 34, pp. 601-636, May, 1955. Instantaneous Companding of Quantized Signals By BERNARD SMITH (Manuscript received October 8, 1956) Instantaneous companding may be used to improve the quantized approx- imation of a signal by producing effectively nonuniform quantization. A revision, extension, and reinterpretation of the analysis of Panter and Dite permits the calculation of the quantizing error power as a function of the degree of companding, the number of quantizing steps, the signal volume, the size of the ^'equivalent dc component" in the signal input to the com- pressor, and the statistical distribution of amplitudes in the signal. It ap- pears, from Bennett's spectral analysis, that the total quantizing error power so calculated may properly be studied without attention to the detailed com- position of the error spectrum, provided the signal is complex (such as speech or noise) and is sampled at the minimum information-theoretic rate. These calculations lead to the formulation of an effective process for choos- ing the proper combination of the number of digits per code group and com- panding characteristic for quantized speech communication systems. An illustrative application is made to the planning of a hypothetical PCM sys- tem, employing a common channel compandor on a time division multiplex basis. This reveals that the calculated companding improvement, for the weakest signals to be encountered in such a system, is equivalent to the addi- tion of about 4 to 6 digits per code group, i.e., to an increase in the number of uniform quantizing steps by a factor between 2^ = 16 and 2^ = 64- Comparison with the results of related theoretical and experimental studies is also provided. TABLE OF CONTENTS (Passages marked with an asterisk contain mathematical details which may be omitted in a first reading without loss of continuity.) Page I. Introduction 655 A. Fundamental Properties of Pulse Modulation 655 1 . Unquantized Signals 655 2. Quantized Signals (PCM) 655 B. Quantizing Impairment in PCM Systems 656 653 Go4 THE BELL SYSTEM TECHXIfAL JOX'RXAL, MAY 1957 C. Physical Implications of Nonuniform Quantization 657 1. Quantizing Error as a Function of Step Size 657 2. Properties of the Mean Square Excited Step Size 658 D. Nonuniform Quantization Through Uniform Quantization of a Com- pressed Signal 659 E. The Mechanism of Companding Improvement in Various Communica- tion Systems 661 1. Syllabic Companding of Continuous Signals 661 2. Instantaneous Companding of Unquantized Pulse Signals 662 3. Instantaneous Companding of Quantized Signals 662 F. Applicability of the Present Analj'sis 663 1. Signal Spectrum 663 2. Sampling Kate 663 3. Number of Quantizing Steps 664 4. Subjective Effects Beyond the Scope of the Present Analysis. . . . 664 II. Evaluation of the Mean Square Quantization Error { 1, are potential compression characteristics. The symmetrical nega- tive portion [v{e) = —v{—e)] is not shown. The production of a tapered array of input steps (Ae)i by uniform quantization of the output into steps of (equal) size Az^, is also represented. INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 661 curves, the central problem of choosing the proper distribution of step sizes will be discussed in terms of the choice of the appropriate com- pression characteristic; the reduction of quantizing error, corresponding to nonuniform quantization without change in the total number of steps, will be termed companding improvement. E. The Mechanism of Companding Improvement in Various Communica- tion Systems 1. Syllabic Companding of Continuous Signals^^- -"^ Originally, the compandor consisted of a compressor and comple- mentary expander operating at a syllabic rather than instantaneous rate in frequency division systems, since instantaneous companding was found to imply an undesirable increase in bandwidth in such systems. ^^ In spite of the existence of syllabic power variations, a useful under- standing of such compandor action ma}^ be inferred from the considera- tion of the long-time average power. Thus, in its simplest form, the com- pressor might provide amplification varjdng from a constant value within the range of volumes corresponding to weak speech to little or no ampli- fication for comparatively strong signals prior to transmission. Although it is an amplifying device, the compressor takes its name from the con- traction of the transmitted volume range which results from' selective amplification of the weakest signals. Since the distortion of the signal by the compressor may virtually be confined to a change in loudness, the compressor output may be expected to be intelligible. In interpreting a compression characteristic, syllabic application per- mits the identification of the ordinate and abscissa with -y/^ and -y/^, rather than v and e as shown in Fig. 2. This substitution of rms for in- stantaneous signals not only confines the significance of the compression characteristic to the first quadrant but also removes the need for com- pandor response to input signals below some small, nonzero, threshold value. If we designate the mean square noise voltage in the transmission medium bj^ i»„-, the amplification of weak signals prior to exposure to this noise provides an increase in the transmitted signal to noise ratio from (e2/y„2) to (y^/y^^), i.e., by a factor of (v^/e^). This increase in signal- to-noise ratio may be read directly from the graph of the compression characteristic, and is unaffected by the identical treatment accorded signal and noise at the expandor. Furthermore, noise received during the silent intervals, between speech bursts, is attenuated by the ex- pandor. G62 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 Under these circumstances it is appropriate to resolve companding improvement into the separate contributions of an increased signal to noise ratio for weak speech by the compressor, and a quieting of the circuit in the absence of speech by the expandor. The introduction of an independent source of noise in the channel between the compressor and expandor is the key to such behavior. 2. Instantaneous Companding of Unquantized Pulse Signals Time division systems, emplojdng unquantized pulse modulation (e.g., PAM) are admirably suited to the application of instantaneous companding to the individual pulse samples. Since each pulse is ampli- fied to a degree which varies with its input amplitude, the compressor output is a sampled version of a distorted signal. As in the S3dlabic case, the location of the noise source in the channel between the compressor and expandor permits an improvement of the received signal-to-noise ratio for weak signals. Furthermore, the ex- pandor again assumes the separate and distinct task of suppressing channel noise in the absence of speech. Unfortunately, quantitative expression of the companding improve- ment is not as simple as in the syllabic case. The response to instan- taneous amplitudes much lower than the rms threshold signal (including zero) becomes important and the improvement factor may not (except in the special case of a linear compression characteristic) simply be read from a graph relating instantaneous values of v and e. Instead, one must employ the probability density of the signal in order properl}^ to account for the distinctive treatment accorded individual pvilse amplitudes in a complex signal. 3. Instantaneous Companding of Quantized Signals Although the same physical devices which serve as an instantaneous compressor and expandor in a PAM system may also be used in a PC^NI system, the functional description of companding improvement is differ- ent in the two applications. Whereas the compandor is used to combat channel noise in a PAM sj^stem, encoded transmission permits a PCM sj^stem to assign this task to the devices which transmit and regenerate code pulses. Thus, assuming that error-free encoded transmission is realized, the quantized signal may be regarded as completely impervious to noise in the transmission medium. Quantization is required to permit such transmission. The sole purpose of the PCM compandor is to reduce the (juantizing impairment of the signal by comerting uniform to effec- tivel}' nonuniform cjuantization. INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 663 AlthousH the oxpandor continues to collaborate; witii the coinpi'essor in inipio\iiig the (|uality of weak signals, it is now neithei' necessary nor possible for it to perform the separate function of (luieting the circuit in the absence of speech. Indeed, apart from instrumentational diffi- culties which might arise, it is conceptually sound to transfer the PCM expander to the transmitting terminal, with expansion taking place subsequent to quantization but prior to encoding and transmission. Another interesting peculiarity of the PCM expandor is the restriction of its operation, b}^ quantization, to a finite number of discrete operating points on the continuous characteristic. The use of companding to reduce the quantizing error which owes its very existence to, and is therefore a function of, the signal, is thus sig- nificantly different from the use of companding to reduce the effects of an independent source of noise in the transmission medium. F. AppUcability of the Present Analysis Before we proceed to a detailed analj^sis, it is important to emphasize certain restrictive conditions required for the meaningful application of the results to be derived. 1 . Signal Spectrum A signal with a sufficiently complex spectrum, such as speech, is re- quired to justify consideration of the total quantizing error power with- out regard to the detailed composition of the error spectrum. Although it is known that quantization of simple signals (e.g., sinusoids) results in discrete harmonics and modulation products deserving of indi\'idual attention,*' ^ Bennett has shown that the error spectrum for complex signals is sufficiently noise-like to justify analysis on a total power ba- sis.2' 12 2. Sampling Rate The consistent comparison of signal power with the total quantizing error power, rather than with the fraction of the latter quantity appro- priate to the signal band, might at first appear to impose serious limita- tions on the present analysis. Furthermore, the role of sampling has not been discussed explicitly. It is therefore important to note that the justi- fication for this treatment, in the situation of actual interest, has also been given by Bennett.' We need o\\\y add the standard hypothesis'"^ that the sampling rate chosen for a practical sj-stem would equal the 664 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 miiiiimim acceptable rate (slightly in excess of twice the top signal fre- quency^) in order to inv^oke Bennett's results, which tell us that, for this sampling rate, the cjuantizing error power' in the signal band and the total quantizing error power are identical.- Thus, sampling at the mini- mum rate is assumed throughout. 3. Number of Quantizing Steps As already remarked, the present results are based on the assumption that A'' is not small, inasmuch as we assume a probability density which, although varying from step to step, remains effectively constant within each quantizing step; indeed the step sizes will be treated as differential quantities. Experimental evidence^' "^ ■ ^° (as well as the analysis to follow) argues against the consideration of fewer than five digits (i.e., 2^ = 32 quantizing steps) for high quality transmission of speech. Numerical estimates indi- cate that the present approximation should be reasonable for five or more digits per code group. These estimates are confirmed by the con- sistency of actual measurements of cjuantizing error power with calcula- tions based on the same approximation (see Fig. 8 of reference 2 for 5, 6, and 7 digit data obtained with an input signal consisting of thermal noise instead of speech) . Further indication of the adequacy of this approximation is provided by the knowledge that Sheppard's corrections (see Section II-B) appear adeciuate even when (Ae) is not very small, for a probability density which (as is the case for speech'^) approaches zero together with its de- rivatives at both ends of the (voltage) range under consideration .^^ Therefore, we are not presently concerned with the limitations imposed by this approximation. 4. Subjective Effects Beyond the Scope of the Present Analysis We shall have occasion to study graphs depicting the signal to quan- tizing error power ratio as a function of signal power. Although these curves, and the ecjuations they represent, wall always be of interest for the case where even the weakest signal greatly exceeds the corresponding error power, there exists the possibility of rash extrapolation to the region where this inequality is reversed. Unfortunately, such extra- polation may have little or no meaning. * This is particularly clear when one considers that signals incapable of exciting at least the first quan- tizing step, in the absence of companding, will be absolutely incapable * This is implicit in the deduction of Equation (6). INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 665 of transmission. Under these circumstances, companding may actually res wscz7ate a signal; the mathematical description of resuscitation (as anything short of infinite improvement) is clearl}^ beyond the scope of the present analysis. At the other extreme, it is probable that there exists a limit of error power suppression beyond which listeners will fail to recognize an}^ fur- ther improvement. Our anal3^sis will not be useful in describing this region of subjective saturation. Furthermore, it is possible that the sub- jective improvement afforded a listener by adding to the number of quantizing steps, or companding, may depend on the initial and final states, even before subjective saturation is reached. For example, it is entirely possible that the change from 5 to 6 digits per code group may provide a degree of improvement which appears different to the listener from that corresponding to the increase from 6 to 7 digits, although the present mathematical treatment does not recognize such a distinction. II. EVALUATION OF MEAN SQUARE QUANTIZATION ERROR (a) A.* Generalization of the Analysis of Panter and Dite The mean square error voltage, a-> , associated with the quantization of voltages assigned to the / voltage interval, ey , is adopted as the sig- nificant measure of the error introduced by cjuantization. If e> is to repre- sent any voltage, e, in the range 0, - [. - i^'] . . . [. + <^; = Rj (1) then aj = I \e - ejfPie) de (2) where (e — Cj) is the voltage error imparted to the sample amplitude by quantization and P{e) is the probability density of the signal. The loca- tion of ej at the center of the voltage range assigned to this level mini- mizes Gj since we shall assume an effectively constant value of P{e) within the confines of a single step. If the value of P(e) is approximated by the constant value P{ej) appropriate to Cj in (2), it follows that aj = (Ae)/P(e,)/12 (3) * This passage contains mathematical details which may be omitted, in a first reading, without loss of continuity. ()()() THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 The total mean square voltage error, cr, is equal to the sum of the mean | square quantizing errors introduced at each level, so that, c^ = Z^. = i¥E^(ei)(Ae)/ (4a) i } = AE (Ae)/[P(e,)(A<.),l (4b) 4 which may be rewritten as 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 ■ ■! ] '::^^^^^ i/ i^^f'Z^ ^:<^ <', • / / / J k^/ Y / "y^ / ^ / y /// / y y /// / / '4 S^ // /J- r / /-"^ S'^ // Y \ 1 /^' '/A 0 0.1 0.2 0.3 0.4 0.5 0.6 0 (e/v) .7 0.8 0.9 1.0 Fig. 3 — Typical logarithmic compression characteristics determined by equation (8a). The symmetrical negative portions, corresponding to equation (8b), are not shown. INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS C69 10" > > 10" 10" - 1 .^-^ ^ y - r5^^ / - ^^^^^ ^ / <^ / - ^ / ^ ^ "^ ^ tf^ J y — Mg.Px / y y ^ / / ~ v / / / - y r / / y} y - / / / / .f^ / / J / / rP f / / / / r / / / - / / - / r / / A \ 1 1 1 1 1 1 1 1 1 1 10" ^ %0-2 (e/v) 10" 6 8 Fig. 4 — Logarithmic replot of compression curves shown in Fig. 3, to indicate detailed behavior for weak samples. The characteristic employed in the experi- ments of Meacham and Peterson" (M & P) is also shown. Similarity between this characteristic and the ^ = 100 curve testifies to the probable realizability of these logarithmic characteristics. from consideration of the ratio of step size to corresponding pulse ampli- tude, (A^/f'), since this quantity is a measin-e of the maximum fractional quantizing error imposed on individual samples. Hence the relation, (e/Ae) = [iV/2 log (1 + m)](1 + F/zxe)"' [which follows from (12a)] has been plotted, for /n = 10, 100, and 1000, in Fig. 5. These curves reflect the fact that the sample to step size ratio reduces to the asymptotic forms: {e/^e) -> Ar/2 log (1 + /x) = const for (e/F) » m~^ and (e/Ae) -> [iV/2 log (1 + \j)\{ixe/Y) for (e/7) « m"' 670 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 100 80 60 40 20 10 8 6 O^ 4 o o 1.0 0.8 0.6 0.4 0.2 0.1 - y - ^ - / =;o - ;^ 100_ I ^^ *'*•*' > P" ^ -/ T 1000 ^^ — -^^ ^ ^ / ^"^ .r^,^^ ' y / r / y / - • / / - / / / y A / / o^ - / 'K / 1 - A 4 7 1 y , .0 V f / 1 1 1 1 1 1 1 1 1 1 1 1 \ Iff 1-3 6 8 la -2 2 4 (e/v) 6 8 10" 6 8 Fig. 5 — Pulse sample to step size ratios, as a function of relative sample amplitude, for various degrees of logarithmic companding (i.e.. values of p). The factor (2AY) in the ordinate permits the curves to be drawn without reference to the total number of quantizing steps (.V) ; the factor (100) is included to permit the ordinates directly to convey the proper order of magnitude for (e/Ae), since pres- ent interest will be found to center about values of .V for which 100(2/iV) ~ 1. As noted in the text, the ordinates, which constitute an index of the precision of quantization, approach constancv for (e/F) » yT'^, and vary linearly with abscissa for (e/]') « p-'. The essentially logarithmic behavior (e/Ae = const) for large pulse amplitudes is intuitively desirable since it implies an approach to the equitable reproduction of the entire distribution of amplitudes in a spec- ified signal. Although existing experimental evidence indicates that the small amplitudes are not only most numerous,^* but also most .significant for the intelligihilitif^''^ of speech at constant volume, the absence of comparable e\-idence on the properties of naturalness makes it plausible to consider only tho.se compression characteristics \vhi('h give promi.se of providing the .same, acceptabh' small, upper limit on the fractional quan- tizing error for pulse samples of all sizes. INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 671 For sufficiently small input pulses, (f/Ae) becomes i)roportional to e, as a result of the linearity of the logaritlnnic function in (8) for small arguments. In view of our professed preference for logarithmic behavior, with (e/Ae) = const., it is important to emphasize that the transition to linearity is not peculiar to (8), but is rather an example of the linearity to be expected of any suitably behaved (i.e., continuous, single-valued, with {dv/de)e=o > 1) odd compression function, v(e), capable of power series expansion, in the vicinity of the origin. In (8) this transition to linearity takes place where (e/V) is comparable to /x~ • The extension of the region where (e/Ae) ~ const, to lower and lower pulse amplitudes requires an increase in n, and a concomitant reduction of the (e/Ae) ratio for strong pulses. Further evidence of the significance of the parameter ju may be deduced by evaluating the ratio of the largest to the smallest step size from the asj^mptotic expressions for (e/Ae). Thus we find (Ae)e=v n for jiz » 1 (Ae)e=o which is a special form of the more general relation (Ae)e=v (dv/de)e=o , -, (Ae)e=o (dv/de)e=v which follows from our standard approximation of (de/dv) ^ (Av/Ae) with Av = const. B. Comparison with Other Compandors An upper bound for companding improvement, which permits the ciuantitative evaluation of the penalty incurred (if any) through the restriction to logarithmic companding, is established in the Appendix. Comparison of the results to be derived from (8) with this upper bound will reveal that nonlogarithmic characteristics, which provide somewhat more companding improvement at certain ^'oluraes, are apt to prove too specialized for the common application to a broad volume range envi- sioned herein. The ^t-characteristics do not suffer from this deficiency since the equitable treatment of large samples, which we have hitherto associated with an ''intuitive naturalness conjecture," will be seen to tend to equalize the treatment of all signal volumes. Finally, it will develop that (8), when applied to (0), has the added merit of calculational simplicity. 1 672 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 IV.* THE CALCULATION OF QUANTIZING ERROR A. Lo(iarithmic Commanding in the Absence of ^'DC Bias" As previously noted, we consider the effect of uniformly quantizing a compressed signal. If we designate the uniform output voltage step size by (Av), then (A.) = ?^ (10) since the full voltage range between — V and +F, of extent 2V, is to be divided into A^ equal steps. For a number of levels, N, which is suffi- ciently large to justify the substitution of the differentials df andc?e for the step sizes Av and Ae, differentiation of (8a) yields (Av) V where k = 1/log (1 + n). ^[rrwrj^-^ Combining (10) with (11) and the counterpart of the latter in the domain of (8b), we find and Ae = a{V + Me) for 0 ^ e ^ V (12a) e = a(V - ne) for - F ^ e ^ 0 (12b) a = 2 log (1 + n)/txN (13) where Substitution of (12) into (6) yields a = (a7l2)[F' + mV + 2mF I"^ ] (14) where the c^uantity | e | is introduced by the difference in sign in (12a) and (12b). For ordinary compandor applications, we may write = 2 f eP{e) de (15) •'0 since the symmetry of the input signal provides that P{ — e) = P{e) and 6 = 0. * This passage contains mathematical details which may be omitted, in a first reading, without loss of continuity. INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 673 It is convenient to define the quantization error voltage ratio, ^ _ RMS Error Voltage _ . ,-5.1 . . RMS Input Signal Voltage " ^''^^'^ ' which takes the form D = log (1 + m)[1 + {C/nf + 2AC/4/y/^N (17) when we define the quantities _ T— , ,- _ Average Absolute Input Signal Voltage , . ^-|e|/Ve2 RMS Input Signal Voltage ^ ^ and Compressor Overload Voltage RMS Input Signal Voltage „ ,^ , /= compressor uverioaa voiiage /.„>, C = V/Ve' = T^^/ra T..„„. q;„,..i Ar^u.^^ ^1^^ The simple linear proportionality of Ae to (F ± ixe) results from the properties of the logarithmic function in differentiation. Other, seemingly more simple compression equations, when differentiated, yield much more complicated and unwieldy expressions for Ae. The value of this simplicity is evident in the absence, from (14), of moments of e higher than the second. If we set A = 0, (17) reduces to one deduced by Panter and Dite"; their analysis erroneously associated A with e = 0 rather than with Ye~\, as a result of their tacit assumption that (12a) and (12b) are identi- cal. They also imposed the restriction of considering only that class of input signals having peak values coincident with the compandor over- load voltage, by defining V as the peak value of the signal in specifying C. The definition of C in terms of the independent properties of both signal (e') and compandor (V) is then converted into one based solely on the properties of the signal. This interpretation leads to conclusions quite different from those to be presented here. B. Logarithmic Companding in the Presence of "DC Bias" It has heretofore been assumed that the input signal is symmetrically disposed about the zero voltage level since it may be expected that e = 0 for speech. Although this is a standard assumption, subsequent discus- sion will disclose that it is probable, in actual practice, for the average value of the input signal to be introduced at a point other than the ori- gin of the compression characteristic. In terms of Fig. 1, the signal is 674 THE BELL SYSTEM TECHNICAL JOITRNAL, MAY 1957 present eel to the arrtiy <»f ([iiaiitizinji; steps with its (iui(;scent \tilue dis- placed by an amount c^ horn the center of the voltage interval (—V to +n. Such an effect, regardless of its oi'igin, may formally be described by considering the composite input voltage E = e + e„ (20) where e is the previously considered symmetrical speech signal and Co is the superimposed constant voltage. Substitution of E for e in (8) and (12) yields aE - (a/12)[V' + ^l'E' + 2^iV \E\] (21) where the subscript E is introduced to distinguish this result from (14). Note that the value [e]E=o = —eo now separates the domain of applica- bility of (8a) and (12a) from that of (8b) and (12b), so that (15) is re- placed by yWl = [ \-E)P{e) de + ( EP{e) de (22) J—V •'— eo which reduces to n^ = |7[ + 2eo f " P{c) de - 2 r eP{e) de (23) Since e = 0, and eo = const., we also find ^2 = ^ -f eo (24) C. Application to Speech as Represented by a Negative Exponential Dis- tribution of Atnplitudes It is necessary to assume an explicit function for P(e) in (15) and (23) before applying the general results which have thus far been deduced. We shall assume, as a simple but adec^uate first approximation, that the distribution of amplitudes in speech at constant volume^ may be repre- sented by Pie) = Gexp i-Xe) for e ^ 0 (25) where P(-e) = P(e), G = X/2, and X" = 2/7\ The values of G and X INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 675 follow from the standard relations r Pie) de = J— 00 1 and r e'P{e) de = ? When applied to (15) and (18), with the upper limit in (15) replaced by oc with negligible error, (25) implies that .4 = in /VP = 1/a/2 = 0.707 (26) Hence, (17) will be replaced, for nvmierical calculations, by the relation VSND = log (1 + m)[1 + (C/m)' + \/2C/nf (27) The corresponding substitution of (25) into (23) yields, for the case of eo F^O, lE~\ = eo-\- (?/2)' exp {-V2C/B) (28) where we have introduced the "bias parameter," B = V/eo (29) When (28) is combined with (13), (21), and (24), we find, after some algebraic manipulation, that VsNDe = log (1 + m) •[1 + (C/n)\l + m/5)' + (\/2C/m) exp (- V2C/5)]' where De' = (o-g/e-). It is to be noted that De has been defined in terms of the ratio of as to e^ rather than E-, so that ^ 2 _ Mean Square Error Voltage . ^ Mean Square Speech Voltage _ Average Error Power ('iM.\ Average Speech Power Examination of (30) reveals that it has the re(iuired property of re- ducing to (27) for ^0 = 0, i.e., for 5 -^ oo. Furthermore (27) and (30) indicate that De ^ D so that the addition of a dc component increases the quantizing error power when companding is used. The existence of 676 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 such an impairment maj^ easily be understood in terms of the physical interpretation of (6), as discussed in connection with Fig. 1. Equations (27) and (30) also reveal that the penalty inflicted by a finite Co is largely determined by the ratio {tx/B). If (m/-S) « 1, the pres- ence of eo will be unimportant. At the other extreme, if {ii/B) ^ 1, (1 + n/Bf -^ {y,/Bf and ^/lNDE -> log (1 + m) (32) •[1 + {C/Bf + (V2C/m) exp {-V2C/B)Y which proves to be relatively insensitive to changes in ^u for the values of ju, C and B considered herein. In this case B largely usurps the algebraic role previously assigned to ju in (27). D. Uniform Quantization: pt = 0 The mean sciuare cjuantization voltage error in the absence of com- panding, corresponding to direct, uniform quantization of the input sig- nal, follows immediately from (7) and (10) since Aw = Ae under these conditions. Thus cro = (Ay)7l2 = V^ZN' whence Do = { / / ^^ / / / / / - 6 l/ ,oy T- - V P ^ V / r / - ViNDo^C-., .''^ / / / - / / / / / > / y / / ^/y / y y i& r- — /^= inno \/ y y Lrf< ^ ^ ■•^^ ■"" / i ^ ^ "^ r-»' T i _ 100 L- >^^ / / \ 1 1 1 t 1 1 1 1 1 1 4 6 8 10 4 6 8 c = v//e2 10' 4 6 8 10-^ Fig. 6 — Variation of the rms error to signal voltage ratio (D) with relative signal strength, C = V/w e^, as given by equation (27) for various degrees of logarithmic companding. INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 679 quantity is a constant determined by the statistical properties of the class of signals being studied. With the present choice of an exponential distribution of amplitudes to represent speech, [see (25)], we have seen that .4 takes on the value l/'\/2 = 0.707. It develops that A is not very sensitive to the choice of P(e), as may be judged by the values \/2/ir = 0.798, and \/3/2 = 0.866 which would replace 0.707 if (25) were replaced by Gaussian and rec- tangular distributions, respectively. The value .4 = 1/ V'2 will be used in all numerical calculations; changes in the value of A to describe other classes of signals (e.g., the aforementioned Gaussian or rectangular dis- tributions) will change the plotted results by no more than a fraction of a decibel. 5. Degree of Compression (/x) From the foregoing it is clear that the essence of the compandor's behavior is embodied in the one remaining variable which appears in (8) and (17): the compression parameter ix. The significance of ^ has already received preliminary attention in connection with Figs. 3 to 5. Fig. 6, where comparison of behavior at constant A^ is facilitated by the choice of y/zND as ordinate, exhibits the behavior of the ratio Z) as a function of C at constant ju. It will be observed that the curves in Fig. 6 do not extend below their common tangent which is labeled -v/sA^/^m-min- The significance of this lower bound may be discussed in terms of Fig. 7 and the hypothetical ensemble of compandors to which we now direct our attention. B. Optimum Compandor Ensemble Consider the artificial situation in which our communication system includes an ensemble of instantaneous compandors, the members of which correspond to different values of /x in (8). Since companding im- provement varies with signal strength, we permit ourselves the luxury of measuring the volume (i.e., C) of the input signal in order to assign the optimum degree of companding compatible with (8), to each indi- vidual signal. The compandor assigned to a signal is characterized by that particular value of the compression parameter, ^ = iXc , which is required to minimize D for a particular \'alue of C. This critical compression param- eter may be calculated from the reriuirement that [dD/dlJL]A.C=const = 0 (35) 680 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 which yields SC^ + ficAiS - l)C Mc- = 0 (36)^ where *S = [(1 + /x,.) log (1 + M':)/m<-] — 1, when appHed t(3 (17). The graph of (36) in Fig. 7 may be used to determine numerical values of Mc without repeated recourse to the equation. The curve labeled \/3A^Z)^_min iu Fig. 6 was determined by substi- tuting values of Hc , obtained from Fig. 7, into (27). Each curve in Fig. 6 A-c 8 6 4 - - " ■ — / / / 2 A-l/Vl / / 10^ / - / r c - / 4 " / / / 2 in? / ^ / o - / £ - / ^ - / / 2 10 - / 1 1 / / i 1 1 1 1 1 1 1 I 10 c=v// 10' 6 8 10^ Fig. 7 — Critical compression parameters, /xc , required to minimize the quan- tizing error power as a function of relative signal strength, as determined by equation (36). Each point on the curve defines a compandor in the optimum com- pandor ensemble. It must be understood that such an ensemble provides the best performance consistent with equation (8) rather than the absolute minimum quan- tizing error discussed in the Appendix. * A similar equation, with A = 0 corresponding to the previously noted errone- ous identification of A with e rather than | e \, has been deduced by Panter and Dite.^ Their definition of C as a "crest factor" changes the significance of what we have called D^i-min and does not lead to the ensemble interpretation of nc ■ INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 681 ^- z lU > o ct a. J z Q Z < a. 5 J 30 28 26 24 22 20 18 16 14 1 2 10 SIGNAL POWER IN DECIBELS BELOW FULL LOAD SINUSOID 5 10 15 20 25 30 35 40 45 50 1 1 1 1 1 1 / 1 />[/ = 1000 - ENSEMBLE UPPER LIMIT A 100^ ^Z' >; ^ ■ — "so A = l/V2 ^i? ^ x- ^ /* 7 ^ 20 y / / / , 5 — /^ Jl 'i /i > ^ 7i y / '///^ s / 1 1 1 1 1 1 1 1 1 6 8 10 20 40 60 100 C 200 400 600 1000 Fig. 8 — Companding improvement (in db), as calculated from equation (37), for various values of ix. The saturated improvement for weak signals (relativel}' constant ordinate for large C values) is identical with the asj'mptotic behavior for weak signals which is predicted by Fig. 9. is tangent to this lower bound at the single value of C which corresponds to /X = /ic • In conventional systems, a single common channel compandor, char- acterized by a single value of ju, is substituted for the optimum ensemble. Although Z)^_MiN is then attainable at only one value of C, it is instruc- tive to compare each value of D with the corresponding value of Z)^_min. Indeed, consideration of the optimum ensemble has, in one sense, reduced the problem of choosing an appropriate /x for a given application to the choice of that particular value of C at which eciuality of D and /);i_min is desired. In Fig. 6, the line representing performance in the absence of compand- ing corresponds to (33) for Do . Do and D^_min are seen to be similar for strong signals (low values of C). Furthermore, it is important to note that Do does not constitute an upper bound for D; thus the companding 082 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 < z o If) in < ^ ir- £^ 5 LU > o Q. Z O I- < o o 45 40 35 30 26 20 15 10 5 0 >^ 6 ^^ 3 y^ - 3 —f^- .^ -2 .^^""^ :; 1 I I I I I I I I I I I I I I I I I I I I . I I 0 o Q UJ m So. D D ZO -5 z'=> -O ^^ u z 4 6 8 10 20 40 60 100 200 400 600 !000 < > D O UJ I Fig. 9 — Saturated companding improvement for weakest signals as a function of the degree of logarithmic compression {jx) . Given a value of yu, the corresponding ordinate represents the reduction of quantizing error power (in db) for signals so weak that their peaks satisfy the relation (e/F) o tr Q. o z Q Z < Q. o o 28 26 24 22 20 18 16 14 12 10 SIGNAL POWER 5 1CT 15 IN DECIBELS BELOW FULL LOAD SINUSOID 20 25 30 35 40 45 50 T 'J" r 1 ... 1 1 1 1 / / / 1 1 / / / B=M^ -^ ENSEMBLE UPPER LIMIT B = 00 > / / ^^ 200 ^ "^^ 100 J ^ J ^ -^■^ 50 ^__ / '^ k"^ / J r // • • Y ,/ i / / 1 / 1 1 1 1 1 1 1 1 1 1 6 8 10 20 40 60 100 C 200 400 600 100C Fig. 10 — Modification of companding improvement, for /n = 100, resulting from the shift of the (luiescent value of the signal by an amount fn from the center of the quantized voltage range (see Fig. 1). The relative size of the "dc component" is given i>y the jiarameter B = V |e^^ as defined in equation (211). The algebraic usurpa- tion of the role of /x by B, for B « tx, results in the striking similarity of the weak signal behavior of the curves for 5 = 50 and 100 in Figs. 10 to 13. 684 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 weakest signals, regardless of the shape of the characteristic in the non- linear region. Equation (8) implies {vie) e^O (AVAe)e^o = M/log (1 + m) so that for each ^'alue of ju, the constant companding improvement for the weakest signals is 20 logio [M/log (1 + m)] db which is plotted in Fig. 9. Fig. 8 supplements Fig. 9 in revealing the ac- tual volumes required for the realization of this weak signal saturation, as well as the detailed behavior for stronger signals. D. Companding Improvement for en 7^ 0 Since we will usually regard a nonzero \'alue of Cq as an undesirable I 30 28 26 SIGNAL POWER IN DECIBELS BELOW FULL LOAD SINUSOID 5 10 15 20 25 30 35 40 45 50 24 22 20 18 2 16 > O Q. 2 14 12 (J) z Q Z o 10 ' I 1 1 I I / 1 y^~oQ >L/ = 200 ^ '/ / ^.^^ 100 / :/ / ^ ^ ,^ — ■"■ 50 /! X ENSEM BLE UPPER B = oo LIMIT-^ v)/ / // / nr ^ J/ ' // / / X r / / f 1 1 / 1 1 1 1 1 1 1 1 1 1 6 8 10 20 40 60 C 100 200 400 600 1000 Fig. 11 — The effect of a "dc component" on companding improvement for M = 200. For further detail.s, see the caption of Fig. 10. INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 685 perturbation, we wish to study the modification of companding improve- ment produced by the introduction of a finite value oi B = V/eo , i.e., .substitution of (30) for (27), when A'', V, C, A, and fx, remain unchanged. In Figs. 10 to 13 we have replotted the companding improvement curves shown in Fig. 8 for ^ = 100, 200, 500, and 1,000, respectively. These curves correspond to -B = oo . The difference between these curves and those for finite values of B in Figs. 10 to 13 is the impairment (in db) inflicted by the presence of eo . This impairment may be appreciable for weak signals (large C). As already noted in connection with (32) the im- pairment is not severe for (n/B) <3C 1. Furthermore, the appropriation of the algebraic role of n by B, when B « ju, which was previously noted in (32), manifests itself in the striking similarity of the weak signal be- havior of all the curves for B = 50 and 100 in Figs. 10 to 13. 30 28 26 24 in ^22 u ai Q 20 z K- 18 Z LU 2 16 UJ CL - 12 O Z a 10 z ^ 8 o o 6 4 2 0 SIGNAL 5 10 =OWER IN DECIBELS BELOW 15 20 25 30 FULL 35 LOAD SINUSOID 40 45 50 1 1 1 1 1 '/ 1 / 3 = oo M = 500 / / / 100 ^_ / f ^--^ ''/ /^ t ^ . 50 // \/ ^ ENSEN/ BLE UPPEF B = c» LIMIT - >// / / V / // 7 • • // • / / 1 1 1 1 1 1 1 1 1 1 1 8 10 20 40 60 100 c 200 400 600 1000 Fig. 12 — The effect of a "do component" on companding improvement for M = 500. For further details, see the caption of Fig. 10. 68G THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 5 UJ > O cc Q. Z Q Z < CL O U 30 28 26 24 22 20 18 16 SIGNAL POWER IN DECIBELS BELOW FULL LOAD SINUSOID 5 10 15 20 25 30 35 40 45 50 I 2 10 8 6 4 1 ' 1 ' 1 1 / 1 /J, = \000 i2 ENSEMBLE UPPER LIMIT (/"=>"c);-. , B=oo y^ ^B = oo / WO,,^' 4 / V / /^ , / / f / i ' / y / 52—— / y ^ ^ / f / / / /. , / / • 4 • / / ' 1 1 / 1 1 1 1 1 1 1 1 1 1 4 6 10 20 40 60 C 100 200 400 600 1000 Fig. 13 — The effect of a "dc component" on companding improvement for /i = 1,000. For further details, see the caption of Fig. 10. / VI. APPLICATION OF RESULTS TO A HYPOTHETICAL PCM SYSTEM Consider the application of these results to the planning of a typical, albeit hypothetical, communication system. A. Speech Volumes Suppose it is desired to transmit signals covering a 40 db power range, with the strongest and weakest speech volumes each separated by 20 db from the average anticipated signal power at the compressor input.* The strongest signal power is then used to determine the value of the compandor overload voltage, V. In this case a value of V corresponding to a full load sine wave 10 db above the loudest signal, [see (34)], appears adequate.* Although this choice may at first appear arbitrary. * These values are sufficiently (iluse to those cited as representative by Feld- man and Bennett, in connection with Fig. 2 of Reference 11, to be considered quite realistic. INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 687 the value of 10 db is probably no more than a few db removed from the value which would be chosen in any efficient application of PCM to quality telephon3^ It results from the need to balance the requirement of a value of T' sufficiently high to avoid intolerable clipping of the peaks of the loudest signals against the obvious ad\'antage of reducing the quantizing step size by minimizing the voltage range to be ciuantized. We have neglected clipping in our calculations since it was assumed that the significant peaks of the loudest signals should not exceed T^ for qual- ity telephony. Existing information on clipped speech" " and one digit PCM^" indicates that the clipping impairment we seek to avoid is largely one of loss of naturalness rather than reduction in intelligibility. The choice of a maximum volume 10 db below a sinusoid of amplitude T" implies that speech peaks 13 db, [see (34)], above the maximum rms signal voltage are being ignored, which appears reasonable in the light of available experimental evidence. ' It follows from these assumptions that the average and weakest signals are respectively 30 db and 50 db below full sinusoidal modula- tion. B. Choice of Compression Characteristic 1 . Ideal Behavior for Speech If we adopt the aim of achieving the smallest over-all departure from the ensemble limit of improvement, it seems reasonable to choose that compandor in the optimum ensemble which corresponds to average speech (C = 45). This requirement, in conjunction with Fig. 7, estab- lishes a lower bound of about 150 for /n. The significance of this choice may be clarified by reference to Fig. 14, which depicts departures from the optimum ensemble limit of improvement, resulting from restriction to a single value of m for all volumes. The corresponding upper bound will be determined by the alternative of furnishing optimum improvement to the weakest signals (C = 450) in spite of the concomitant impairment of loud speech. Reference to Fig. 7 then dictates a choice of ^ in the vicinity of 2,500. From Fig. 6 it is clear that this value implies that D is essentially constant and in- dependent of C throughout the range of interest. Appreciably larger values of n would actually lead to the undesirable extreme oi D > ^M-Mix for all signals under consideration. We therefore conclude that attention may profitably be confined to the interval 150 ^ m ,^ 2,500, the magnitude of which is adequately conveyed by the simple expression 100 ^ M ;^ 1,000 (38) 688 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 I- 2 UJ UJ > O a. a. 12 11 10 10 K^ LU — 7LU 6 cct LU _) 4 cr D t- LU Q II SIGNAL POWER IN DECIBELS BELOW FULL LOAD SINUSOID 15 20 25 30 35 40 45 50 ! ! I I — 1 1 1 r I 1 i 1 1 1 > 1 . / \ / J f \ \ / / \ \ / / 7 / f X \ s\^ / f / f / t \ \ \ -> h> v^ r / V / f / 1 1 s b^ ^ >< ^ kl \ 1 4 8 10 20 40 60 C 100 200 400 600 1000 Fig. 14 — Improvement selectivity, i.e., departures from the ensemble upper limit of improvement due to the use of a single value of ^ rather than the ensemble of Me values. The minima at 5^ = 0 locate the signals (C) for which /i andjuc coincide. All curves correspond to the case where the "dc component", eo , is zero. Lest it appear that this range is so broad as to offer very httle practical guidance, it should be noted that (38) defines a rather narrow range of characteristics in Figs. 3 and 4. The assumption that this range may be realized in practice appears reasonable in \'iew of the similarity to the characteristic actually used by Meacham and Peterson, which is shown in Fig. 4. 2. Practical Limitations on Companding Improvement (a) Mismatch Between Zero Levels of Signal and Compandor. Although the present discussion has hitherto been confined to ideal compandor action, it lends itself quite naturally to the analysis of a significant departure from ideal behavior which may be expected to result from the use of an instantaneous compandor on a common channel basis in time division multiplex systems. It will probably l)e impractical to balance the channel gating circuits (required to provide sequential connection of individual channels to a INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 689 single compressor)^' ^ sufficiently to guarantee exact coincidence of the average input signal (e = 0) in each channel and the center of the — V to -\-V voltage range {e = 0) presented by the compressor. Thus the input, e, would appear to the compressor in the form E = e -{- Cq . The consequences of the appearance of the undesirable constant term, eo , may be inferred from study of Figs. 10 to 13 and (80). We shall assume that, owing to the present state of gating technology, B = V/co may reasonably be expected to assume values in the range 100 < 5 ^ 1,000. For companding corresponding to 100 ;S m^ 1,000, Figs. 10 to 13 indicate that, if B can be confined to the vicinity of 1,000, the departure from the ideal behavior corresponding to B = qo will be virtually negli- gible. However, should it prove necessary to work with B = 100, it is clear from Figs. 10 to 13 that the companding improvement for weak signals would be relatively independent of ju in the inter\'al 100 ;S M ^ 1,000 (with a saturation value of about 20.5-22.5 db).* In this event, compres- sion to a degree greater than that represented by fj. = 100 would provide less improvement for strong and average speech without the compensa- tion of significantly greater improvement for weak signals. Reduction of M below 100 would not be fruitful since the sensitivity of companding improvement to changes in n is restored for values satisfying the condi- tion of (fi/B) = (m/100) < 1. The significance of the values eo '^ F/1,000 and TVlOO n^ay perhaps better be appreciated in terms of a comparison of eo with the weakest signals under consideration. Since (B/C) = \/^/eo , a signal to dc bias power ratio may be calculated, in db, from the expression 20 logio {B/C). For the weakest signals under consideration (C '~ 400), the values B = 1,000 and 100 correspond respectively to (v^/<'o) = 2.5 and 0.25, or to signal to dc bias power ratios of +8 db and —12 db. Thus, for the hypothetical system now under study, the value of Co becomes significant (roughly) when it exceeds the weakest rms signal. Actually eo would be expected to vary with time for a given channel and to vary from channel to channel at any instant. On the assumption that I eo I = F/lOO (i.e., B = 100) will constitute the upper bound of such variations, the companding impro^'ement corresponding to a particular value of n must now be specified in terms of the region between the B = 'x> and B = 100 curves in Figs. 10 to 13, i-ather than by refer- ence to a single value of B and its corresponding cuixc. Since the lower * This corre.spoiid8 to tlie beliavior of D^ for (fi/B) » 1 which was noted in the discussion of (30). In this connection, see the discussion of Fig. 19. 690 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 bounds oi' all these regions (see Figs. 10 to 13) are approximately (loinci- dent (for 100 ^ m /^ 1,000), the advantage of increasing /x substantially beyond 100 will depend largely on the expectation of encountering values of Co -^ (TV1,000) with .sufficient frequency in the various channels served by the common compressor. These arguments may of course be applied, with suitable modifications depending on the range of C, n, and B values requiring attention, to any effect capable of formal description in terms of an effective dc bias super- imposed on the signal input to the compressor. (b) Backgrotmd Noise Level. It does not seem reasonable to strive for an increase of the signal to quantizing error power ratio substantially beyond that value which is subjectively equivalent to the anticipated ratio of signal to background noise from other sources. Since the quantizing error power depends on the number of digits per code group, the comparison of ciuantizing error power and noise power is reserved for subsequent discussion of the reciuired number of quantizing steps. It will be noted that the comparison must remain somewhat speculative in the absence of a determination of the subjective equivalence of quantizing error power and noise. C. Choice of the Number of Digits Per Code Group 1 . Ideal Behavior for Speech As previously remarked, the number of quantizing steps will deter- mine the ratio of signal to quantizing error power to which the com- panding improvement is to be added. Since the quantizing error power is inversely proportional to N' = 2 ", this power will be reduced by 6 db for each additional digit. Comparison of this (5 db per digit improve- ment with the roughly 24 to 35 db improvement corresponding to weak signals in Fig. 8 (for 100 ^ m ^ 1,000) reveals that, for such sig7ials, companding is equivalent to the addition of four to six digits per cede group, i.e., to an increase in the mimber of quantizing steps by a factor between 2* = 16 and 2^ = 61^. This equivalence is portrayed in Fig. 9. Our failure to realize a companding improvement of about -43 db as predicted for \x. = 1,000 in Fig. 9 may be traced to the fact that the weakest signals now under consideration are not sufficiently weak to be confined to the linear region (e/V) « ijT^) of the /x = 1,000 characteristic. This is re- flected in the unsaturated improvement exhibited in Fig. S for the weakest signals when /x = 1 ,000. Although it is clearly preferable to suppress (luantizing error power by companding rather than by inci'easing the number of ([uantizing INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 691 36 .^ ^ \ \ — ~^ ENSEMBLE UPPER LIMIT \ \ \ <. ^-L^ n = 6 \ ^ \ ■^^^ - \ \ ^^ \ \ \ \ *v \ \ n=5 \ \ N, \ V \ ^ ■^N. \ N \ \ \ \ •v N \ \ //=200 B = oo \ '\ \, \ ^ NO companding\ (yu. = o);n = 7 \ \ \ V ^ i s \ \ \ N 1 1 1 I 1 1 \ 1 ^ 1 1 s 1 I 8 10 20 40 60 100 200 400 600 1000 C Fig. 16 — Signal to quantizing error power ratios (in db) as a function of rela- tive signal power for companding corresponding to /i = 200. Sj-mbols have the same significance as in Fig. 15. B = « throughout. which have been established for conventional noise and distortion. If these were available, graphs such as those in Figs. 15 to 18 could be used to select the proper number of digits to be used ^^ith various de- grees of compression. In the absence of such information Ave shall com- plete this illustrative study b}^ adopting a signal to ciuantizing error power ratio of at least 20 db as a tentative standard of adequate per- formance at all volumes.* Figs. 15 and 16 show that seven digits (i.e., 2' = 128 tapered quantiz- ing steps) and n = 150 will meet this objective. Furthermore Figs. 17 and 18 indicate that six digits (2 = 64 tapered steps) would suffice provided (38) is replaced by the more stringent limitation. 500 ) may be applied. On the other hand, behavior for B = 100 may be judged from the plot of signal to quantizing error power ratio versus signal power for ju = 100 and 1,000 (with seven digits) shown in Fig. 19. Since this ratio now fails to exceed about 16 db for the weakest signals of interest, we conclude that an increase to eight digits (2 = 256 tapered steps), with a concomitant 6 db improvement for all signals, is required to meet our 20 db objective. These curves also illustrate the previously noted meager improvement for weak speech which accompanies the increase from f^ = 100 to 1,000 when B = 100. Actually, an optimum solution is attained for an intermediate value of ^l, but the advantage is too small to be of interest (see Figs. 10 to 13). o UJ a 36 34 32 SIGNAL POWER 5 10 15 IN DECIBELS BELOW FULL LOAD SINUSOID 20 25 30 35 40 45 50 1 N 1 1 \ ^v '-«., ENSEMBLE UPPER LIMIT ' 1 1 \ \ \ ^ -. yU.= 500 A=1/V2- B = oo \ ^-^, -T*"' i^ 30 28 26 n=7 N \ ^ """-•^ ^'"~-- \ 1 \ S, """■■ — \ \ , \ \, 24 22 20 n=6 \ \ \ \ ^"^"^ •^ N \ \ NO CO vIPANDING j n — 7 \ s. ^ \ \, 18 16 14 12 10 8 n=5 -\ 1 \ \ \ ^^ S \ V s. \ N \ \, \ \ s \ 1 1 1 1 1 1 \ 1 W 1 1 1 1 10 20 40 60 100 200 400 600 1000 C Fig. 17 — Signal to quantizing error power ratios (in db) as a function of rela- tive signal power for companding corresponding to n = 500. Symbols have the same significance as in Fig. 15. B = oo throughout. 694 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 The recognition that use of B = 100 rather than a value approaching 1,000 may imply a change from six to eight digits per code group (e.g., for ju = 1,000), representing an increase of 33 per cent in the required bandwidth in the transmission medium as well as a significant increase in the complexity of the multiplex terminal eciuipment, provides the proper perspective for competent appraisal of the cost of improving gate circuitry to the point where B would approach 1,000. These con- siderations might be of crucial importance in the planning of actual PCM systems. Finally these results also show that caution is required in attempting to determine an adequate nimiber of digits and/or degree of compression from listening tests employing preliminary experimental equipment. If the conditions of the test do not duplicate exactly the expected behavior of the channel gates to be used in the final system, the transition from the laboratory to practice might lead to an embarrassing disappearance 40 38 36 34 32 SIGNAL POWER IN DECIBELS BELOW FULL LOAD SINUSOID 5 10 15 20 2S 30 35 40 45 50 cr 30 ? O Q. CH o a. a: LU IS z N 22 28 26 24 Z < a < z (J in 20 18 16 14 12 1 \ 1 — 1 1 1 ■I - 1 ' 1 \ yti:=1000 B = oo N \ ^v. 'x. ENSEM 3LE UPPER LIMIT — // -'\- n— 7 \ \ 1 n = 7 \ 1 *«^. ""-^ »■«., \ — '.^yf "^^1^^ \ ^ S^ "■- n = 6 \ \ \ S \ N \ \ ~ -—^ NO COMPANDING i, f //, — 01 • n — 7 ^ S^ n = 5 \ \ N \ •V=^ \ \ -- \ \ "^ ^. 1 1 1 1 1 \ 1 1 1 1 1 N 1 4 6 8 10 20 40 60 100 C 200 400 600 1000 Fig. 18 — Signal to quantizing error power ratios (in db) as a function of rela- tive signal power for companding corresponding to /x = 1,000. Symbols have the same significance as in Fig. 15. B = co throughout. INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 695 34 32 30 SIGNAL POWER IN DECI 5 10 15 20 BELS BELOW FULL LOAD SINUSOID 25 30 35 40 45 50 O 28 ? O a. a. O cr a: UJ O z isl t- z < D O 26 24 22 20 18 16 14 < Z 10 1 ■T 1 1 1 1 1 1 /Z = 100 "- ■ ■"" 1000 N, ■•■^, -^ \ '■V N s ^ n = 7 A=1/V2 B = 100 \ \ \ \\ \ \ Rn \ \ ^ \ i 1 1 1 1 1 1 1 1 1 > 1 V 6 8 10 >0 40 60 C 100 200 400 600 1000 Fig. 19 — Signal to quantizing error power ratios (in db) as a function of rela- tive signal power for companding corresponding to ju = 100 and 1,000 when n = 7 digits per code group and a dc component corresponding to B = 100 is present in the signal. The influence of the dc component may be judged by comparing these curves with those shown in Figs. 15 and 18 for n = 7. Corresponding results for dif- ferent values of n may be derived bj- the addition or subtraction of appropriate multiples of 6 db from each ordinate. of virtually all the anticipated companding improvement for weak signals. (6) Background Noise Level. We have already noted the probable futility of increasing the signal to cjuantizing error power ratio consider- ably beyond that value which is subjectively equivalent to the antici- pated ratio of signal to background noise from other sources. If the subjective relation between quantizing error power and noise power were known, the curves in Figs. 15 to 19 could be redra^Mi for meaningful comparison with ratios of signal to backgroimd noise. In the absence of such information, we shall assume as a first approxima- tion, that noise and quantizing error power are directl}^ comparable.* Suppose that we set an upper limit on the background noise by con- * The similarity between noise and ciuantizing error power has often been noted. For example, one may consult references 2, 6 and 12 as well as Appendix I on "Noise in PCM Circuits" in Reference 11. The assumption of direct com- parabilit}' is also to be found in Reference 4. 696 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 40 38 36 34 32 30 28 26 24 22 20 18 16 14 SIGNAL POWER IN DECIBELS BELOW FULL LOAD SINUSOID 5 10 15 20 25 30 35 40 45 50 < CC LU 5 o Q. tr O tr tr < z // = 100 200 n = 7 0=6 B=oo A=l/Y2 — V SIGNAL TO MAXIMUM '\ NOISE POWER RATIO Fig. 20 — Curves illustrating the comparison of signal to quantizing error power ratios with the ratio of signal to background noise. The line representing the signal to maximum noise ratios corresponds to the hypothetical case where the maximum background noise is determined bj- the requirement that the signal to noise ratio be 20 db for a signal 50 db below full sinusoidal modulation. sidering a value providing a signal to noise ratio of 20 db for the weakest signals in our hypothetical system. A signal to maximum noise power curve may then be dra^Mi as a function of signal power for this constant value of noise power. Such a graph has been combined, in Fig. 20, with curves such as those which have previously appeared in Figs. 15 to 19. These curves have been terminated at their intersections with the line representing the signal to maximum noise power ratio since we are assuming that little benefit will be derived from a signal to quantizing error power ratio in excess of the signal to ma.ximum noise power ratio. From Fig. 20 it is apparent that the previous conclusions that six and seven digits are worthy of consideration are unaffected by the stipu- lation that the signal to cjuantizing error power ratio should not greatly exceed the signal to maximum noise power ratio. Similarly, the con- clusions based on Fig. 19 (for B = 100) remain unchanged since the curves therein fall below the maximum noise curve of Fig. 20 for all values of the abscissa. INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 697 D. Possibility of Using Automatic Volume Regulation The realization that the quantizing impairment experienced by weak signals in the absence of compression stems from their inability to excite a sufficient number of the quantizing steps which must be pro^aded to accommodate loud signals, leads directly to the suggestion that auto- matic volume regulation be used to permit all signals to be "loud," i.e., to excite the entire aggregation of quantizing steps. In its simplest form, this would be accomplished by automatic amplification of the long time average speech power in each channel to provide a constant volume input to the common channel ecjuipment. Study of the present results indicates that if all signals were of con- stant volume, about 10 to 15 db below full sinusoidal modulation (to provide an adequate peak-clipping margin), satisfactory operation, corresponding to signal to c^uantizing error power ratios in excess of 20 db, might be achie\'ed without companding by using as few as five or six digits per code group. In evaluating this alternative, the advantages of reduction of bandwidth, decreased complexity of c^uantizing and coding equipment, and elimination of the common channel compandor, must be balanced against the disadvantage of providing separate volume regulators in each channel. to"- E. Comparison with Previous Experimental Results The literature contains seemingly contradictory statements about whether fi\'e, ' six, or seven ' ' digits per code group are required for satisfactory performance in speech listening tests. Evaluation of these conclusions is frecjuently hampered by the lack of specification of either the degree of companding employed or the range of speech volumes requiring transmission. Different conclusions may therefore be consist- ent, inasmuch as the systems may differ significantly in the required \olume range, degree of companding, size of the "effective dc component" in the signal, and even in the subjective standards used to judge per- formance. Fortunately, the description of an experimental toll quality system by Meacham and Peterson is sufficiently detailed to permit some com- parison. The range of volumes they considered suggests that direct comparison with our hypothetical system is fairly reasonable. Their empirical choice of seven digits, with a compression characteristic vir- tuall}" indistinguishable from that corresponding to fj. = 100 (see Fig. 4) is in excellent agreement with the present conclusions. Furthermore, the conclusion that five or six digits, without compand- 098 THE BELL SYSTEM TECHNICAL JOUKXAL, MAY 1957 iiig, might he employed in coiijunetioii with volume regulation is com- pletely consistent with Goodall's experimental results.^" VII. CONCLUSIONS An effective process for choosing the proper combination of the num- ber of digits per code group and companding characteristic for quantized speech communication sj^stems has been formulated. Under typical con- ditions, the calculated companding improvement for the iveakest signals proves to be equivalent to the addition of about 4 to 0 digits per code group, i.e., to an increase in the number of quantizing steps by a factor between 2 =16 and 2^ = 64. Although a precise application of the results requires a more detailed knowledge of the subjective nature of the quantizing impairment of speech than is presently available, the assumption of reasonably typical S3^stem requirements yields conclusions in good agreement with existing exnerimental evidence. ACKNOW^LEDGMENTS Frequent references in the text attest to the indebtedness of the author to the writings of Bennett and Panter and Dite. It is also a pleasure to acknowledge stimulating conversations on certain aspects of the problem with J. L. Glaser, D. F. Hoth, B. McAIillan, and S. 0. Rice. Appendix THE minimization OF QUANTIZING ERROR POWER In spite of the demonstrated utilit\^ of the ^-characteristics, one can- not avoid speculating about the possibility of achieving substantially more companding improvement by using a characteristic which differs from (8). We shall therefore outline a study of the actual minimiza- tion of quantizing error power without regard to the relative treatment of various amplitudes in the signal. The results will confirm that a signifi- cant reduction of the quantizing error power beyond that attainable with logarithmic companding is self-defeating — for it not only imposes the risk of diminished naturalness, but also implies a compandor too "vol- ume-selective" for the applications envisioned herein. 1. The Variational Problem and Its Formal Solution Equation (6) may l)e (expressed in the form ^ -%^[ (dv/de)-'P(e) de (A-1) INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 699 where P(e) has been assumed to be an even function. The function, v(e), which will minimize (^4-1), subject to the usual l)oundary condi- tions at e = 0 and c = V, may be obtained by solving the Euler differ- ential e(iuation of the vaiiational problem. For (^4-1), this takes the form (dv/de) = KP"^ (A-2) where the constant K is given by K = V / f P'" de (A-3) Hence the minimum quantizing error is given by f P"'de /sN' (A-4) = o'min — ^ 2. Representation of Speech by an Exponential Distribution of Amplitudes We shall assume, as in (25), that the distribution of amplitudes in speech at constant volume may be represented by P(e) = G exp (-Xe) for e ^ 0 (A-5) where P{-e) = P(e), G = X/2, and X' = 2/?. With this choice of P(e), the solution of (A-2) f is (v/V) = l-exp[(-V2C/3)(./F)] 1 - exp(-V2C/3) Thus, for any given relative volume (i.e., for each value of C = V /{e^f'^), (A-6) specifies the compression characteristic required to minimize the quantizing error power. We are therefore led to study the properties of the family of charac- teristics of the form iv/V) = 1 - exp(-me/F) ^^^, 0 ^ c ^ V (A -7) 1 — exp ( — m) * An alternate derivation of (A-2) and (A-4), has been given by Panter and Dite,' who also acknowledge a prior and dif'fereni deduction by P. R. Aigrain. Upon reading a preliniinary version of the present manuscript, B. McMillan called my attention toS. P. Lloyd's related, l)ut luipublished work, which proved to con- tain still another derivation. I am grateful to Dr. Lloj'd for access to this material. t In the vocabulary of analytical dj'namics, the direct integrability of the Euler equation may be ascribed to the existence of an "ignorable" or "cyclic" coordinated^ 700 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 w m O O o o K O o m h-( « CM o O 3 e en a W '^ A-^ o a s? O +J u O bC 0) a a. 2 S -If §r2 C S » < X c W ^ ° « .a S.2 'T' bC c^ S '-I m CO + bC O O tc > OJ to += &3:2 S a. + bC O 1^ a. + b£ O a. + 1— ( + a. ^ ■^ ^s. '« <1 a o a t-i a" hC a 'S Q VI VI o o a" " • i-H — CO Si CO o3 Q 03 'm fl oS 03 O -t^ 0) > fl o 03 n S to c 03 to 01 O k' -|j a o 11 a (4 o N bfl (h ffi U-i o o o n CO .2 '■♦J o 03 CO 03 (-. to INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 701 O o O O > Oh a" 5 CIS i M.sf O fl »3 -1 tc m 3 (D S; > eo l(N X as ,1^ > o ^ CO ^ '« O i-H S 1 a. 1 1 'a! + II CI CO bC 1 3. 'o > o + 6i\ a. 1-H 1 IB > + d + ,-— «s T— 4 O) ■7— A 1 bC O "^ 1 1 bJD O II i 1 o bC o O II a. n"« + w ^ ''i U \ o :2 ir^ + a. > rH CO c^ + > 1-H ^ cc -^ '^ h M bO <1> r^ !- O C W OJ— c o p:5 bC-- CO a; O O ;-< txi .s .2 S 0) o o tH o bC A 702 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 with v{ — e) = —v{e) as usual. The "m-characteristics" specified by (A-7) are to be compared with the "^-characteristics" specified by (8). From the derivation of (A-6) it is known that optimum companding will be produced when m is given by the critical value, rric = \/2C/3 This is the analogue of (36) defining jXc for the ju-ensemble. (A-8) 3. Properties of the ''m- Ensemble^' We shall now interpret the properties of the /n-ensemble of compan- dors, for which the ensemble improvement limit (m = nic) actually 1.0 0.9 0.7 0.6 > > 0.5 0.4 0.3 0.2 0.1 0 '^^/^ ^ X ^ / 7 / '^o > ^ ^ / / y / A 1 > / A / v ^ / / ^ / 1 / / / 1/ / / / ^ \ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 (e/vj Fig. 21 — Typical m-ensemble compression characteristics determined by equation (A-7). Note the strong emphasis on weak signal amplitudes. These curves may be compared with those for the ^u-ensemble in Fig. 3. INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 703 minimizes the total (luantizing error power, when the probability density is specified by (A-5). Table I summarizes the important properties which may be derived by replacing (8) by (A-7) in the pre\'ious detailed analysis of the /x-ensemble. (a) Compression Characteristics Compression characteristics, corresponding to various values of m are displayed in Figs. 21 and 22 for direct comparison with the curves in Figs. 8 and 4. The ^/? -characteristics assign very little weight to the larger signal amplitudes in view of the infrequent occurrence of the latter. 10" > 10" 10" - ^^ ?»--■ "Z^ '"^ / - ^ \^ y ^ y/^ / - y ^y y y y ^ / - < 1 ^ ^/ [/ / y / / / / / / / / / / - / , / / /^ / ~ / ' / / / .o: V / / / \ A f/ > y / / / J. / / / • - / • / • -/ / / • 1 1 1 1 1 1 1 _L 1 1 1 1 10" 4 6 8 10" 4 6 8 e/v 10" 4 6 8 Fig. 22 — Logarithmic replot of compression curves of the type shown in Fig. 21 to indicate detailed behavior for weak samples. These may be compared with the M-ensemble curves in Fig. 4. 704 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 (6) Sample to Step Size Ratio Fig. 23, where the sample to step size rutio (e/Ae) is plotted in the same manner as in Fig. 5, reveals the relative fiuantizing accuracy accorded various pulse amplitudes. 100 80 60 40 20 10 8 6 I, — ^1 — -1^ o 9 2 1.0 0.8 0.6 0.4 0.2 0.1 10' - —7 - / - 100 M"' 1 1 exp(-1) = 36.8N/ / - ^ ^ -^ VI ^ ■:^ ^ X ^ \ \ /^ ^^ / ^ / / / \ \ r y r A • / \ - / / ^ \ , / / } ^ - / / X \ - / 5 / / / \ \ / / b ^P \ \ 1 I / f {o' \ \ > / 4 \ \ -/ 4 \ \ / / / \ ' \ f 1 1 1 1 1 1 1 1 1 1 1-3 * °10-2 4 6 8 (e/v) 10" I 4 6 6 Fig. 23 — Pulse sample to step size ratios as a function of relative sample \ amplitude, for various compandors in the //i-ensemble. The maxima exhibited by these curves occur at ejV = m~^; M = 1 — exp(— m). Compare with Fig. 5. INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 705 (c) Saturated Improvement of Weak Signals For signal.s whose largest samples are confined to the region (e/V) « m^ , compression is linear, with a saturation improvement noted in Table I and plotted in Fig. 24 for comparison with Fig. 9. in < z (- CO OJ < CD Q S' „l ir E o ^1^ LL X z LU 1 ?l ^1 UJ > o a. a. z o \- < cr D t- < 1/1 o 6 o _i o 55 50 / / / 9 / 45 |/ 8 / 40 / 7 / 35 30 25 /^ 6 / / 5 / / y 4 20 / ^z' 15 > / / 3 ^/ y / 2 10 5 y^ ^ y 1 ■"^ 0 I 1 , 1 1 1 1 1 1 1 1 0 (J o a. LU m zo -l4 < LLI tr o z 6 8 10 20 40 60 100 200 400 600 1000 m Fig. 24 — Saturated companding improvement for the weakest signals as a function of the degree of "m-type" compression. Given a value of m, the corre- sponding ordinate represents the reduction of quantizing error power (in db) which results from companding of signals so weak that signal peaks satisfy the relation (e/F) O a: a. 1 14 U z Q Z < a. O u SIGNAL POWER IN DECIBELS BELOW FULL LOAD SINUSOID 5 10 15 ■ 20 25 30 35 40 45 50 16 12 10 1 1 1 ' 1 1 / ' 1 _ MAXIMUM IMPROVEMENT m-pKjcpKyiQt p ijpppo 1 1M|T*L --- m = 35 (m = mc=Y2C/3) i y / ^ ^ " 20 y^ k / // ^- — • — " 10 // // / / / / / / / / / / / / / 1 • / oj o o o ,.-' / 1 1 EJ 1 I 1 1 1 1 8 10 20 40 60 100 200 400 600 C 1000 Fig. 25 — Companding improvement curves for representative members of the m-ensemble. These curves are to be compared with those for the ^-ensemble in Fig 8. Note the important difference between the two ensembles for strong sig- nals (small values of C) . INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 707 (c) Signal to Quantizing Error Power Ratios The curves in Fig. 26 are drawn for the representative case oi N = 2^ = 128 quantizing steps (7 digit PCM). The corresponding ensemble limit is constant, as might be expected from (A-4), except for strong signals where the effects of peak clipping become noticeable. In the region where this ensemble limit is constant, departures from the improvement limit resulting from the use of a single value of m for all volumes may be read directly from the ordinates shown at the right in Fig. 26. In comparing these departures from maximum improvement with the analogous ^-ensemble curves in Fig. 14, it must always be recalled that, in view of its role in the solution of the variational problem, the m-ensemble limit represents the actual minimum quantizing error power consistent with the probability density specified by (A-5). SIGNAL POWER IN DECIBELS BELOW FULL LOAD SINOSOID 5 10 15 20 25 30 35 40 45 50 JO <5 36 OI 8 34 lij ^^32 Z Q 30 !< « i V ^ ^ "^^ ^« .,---, "^ r ^ ^ (m = nnc=V2"c/3T 0 r^ ^ / \ \ V ~ 2 5 -1 i A. / \ > \^ t, ~ 4 t- Z OI 4 \ \ 1 ( \ \ \ — 6 5 OI > o^\ f ^y \ \ . H' ~ 8 §9 |A( 10 -o LU -1 CC 12 CD o 5 u- \ \ ^ - ' / \ / \ f \ \ V \ \ \ - / \ 1 \ \ V N ko V \ - 14 ^^3 \ y \ V \ \ > k 16 ' U \ \ k^ \ \ V CC 7 DIGITS B = 00 \ \ X \ V \ \ 20 ^ LU CC 22 D t- (r \ \ \ \ 1 \ V > \ ~ 24 ^ LU Q 1 I 1 1 1 k \ \, 1 1 \ 26 , ■> , i ( 5 f 3 1 0 2 0 4 c 0 6 0 K )0 2( 30 4( DO 6( 30 10 00 Fig. 26 — Signal to quantizing error power ratios as a function of relative signal power for 7 digits and various ^/-compandors. The curves may he compared with those for 7 digits in Figs. 15 to 18. The auxiliary ordinates at the right of the pres- ent figure ai)ply for C >, 10, where the ///-ensemble limit is effectively constant; departures from this limit, resulting from the use of a single value of vi for all volumes, may be read directly from this scale, for comijarison with Fig. 14. The latter comparison illustrates the narrow volume limitation of the members of the '/i-ensemble. 708 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 (/) Illustrative Application Consider the possibility of choosing a member of the m-ensemble for application to the hypothetical PCM system already discussed in con- nection with the /i-ensemble. It will be recalled (see Figs. 15-18) that we were able to choose degrees of logarithmic compression which would yield signal to quantizing error power ratios in excess of about 20 db for all volumes (4.5 S C ^ 450) by using as few as six or seven (depending on the choice of /x) digits per code group. In contrast, Fig. 26 reveals that no value of m will meet this requirement since the curves fall so rapidly on either side of the sharp maxima. In short, the members of the m-ensemble are each too specialized for successful application to such a broad volume range. Further detailed comparison between the numerical results for the two ensembles seems inappropriate, since it is not at all clear that the inequitable treatment of the various samples in a given signal by mem- bers of the m-ensemble (see Fig. 23) permits an adequate description of signal quality solely in terms of quantizing error power. Under these cir- cumstances, subjective effects beyond the scope of the present analysis might assume a dominant role. REFERENCES 1. H. S. Black, Modulation Theory, Van Nostrand, N. Y., 1953. 2. W. R. Bennett, Spectra of Quantized Signals, B. S.T.J. , 27, pp. 446-472, July, 1948. 3. Oliver, Pierce and Shannon, The Philosophy of PCM, Proc. I.R.E., 36, pp. 1324-1331, Nov., 1948. 4. Clavier, Panter and Dite, Signal-to-Noise-Ratio Improvement in a PCM System, Proc. I.R.E., 37, pp. 355-359, April, 1949. 5. P. F. Panter and W. Dite, Quantization Distortion in Pulse-Count Modulation with Nonuniform Spacing of Levels, Proc. I.R.E., 39, pp. 44-48, Jan., 1951. 6. L. A. Meacham and E. Peterson, An Experimental Multichannel Pulse Code Modulation System of Toll Quality, B.S.T.J., 27, pp. 1-43, Jan., 1948. 7. H. S. Black and J. O. Edson, Pulse Code Modulation, Trans. A.I.E.E., 66, pp. 895-899, 1947. 8. Clavier, Panter and Grieg, Distortion in a Pulse Count Modulation Sj'^stem. Elec. Eng., 66, pp. 1110-1122, 1947. 9. J. P. Schouten and H. W. F. Van' T. Groenewout, Analysis of Distortion in Pulse Code Modulation Systems, Applied Scientific Research, 2B, pp. 277- 290, 1952. 10. W. M. Goodall, Telephony by Pulse Code Modulation, B.S.T.J., 26, pp. 395- 409, July, 1947. 11. C. B. Feldman and W. R. Bennett, Bandwidth and Transmission Performance, B.S.T.J., 28, pp. 490-595, July, 1949. 12. W. R. Bennett, Sources and Properties of Electrical Noise, Elec. Eng., 73, pp. 1001-1008, Nov., 1954. 13. C. Villars, Etude sur la Modulation par Impulsions Codies, Bulletin Tech- nique PTT, pp. 449-472, 1954. 14. J. Boisvieux, Le Multiplex a 16 Voies h Modulation Codde de la C.F.T.H., L'Onde Electrique, 34, pp. 363-371, Apr., 1954. INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 709 15. E. Kettel, Der Storabstand bei der Nachrichteniibertragung durch Codemodu- lation, Archiv der Elektrischen tjbertragung, 3, pp. 161-164, Jan., 1949. 16. H. Holzwarth, Pulsecodemodulation und ihre Verzerrungen bei logarith- mischer Amplitudenquantelung, Archiv der Elektrischen Ubertragung, 3, pp. 277-285, Jan., 1949. 17. Herreng, Blonde and Dureau, Systeme de Transmission Telephonique Multi- plex a Modulation par Impulsions Codecs, Cables & Transmission, 9, pp. 144-160, April, 1955. 18. W. B. Davenport, Jr., An Experimental Study of Speech-Wave Probability Distributions, J. Acous. Soc. Amer., 24, pp. 390-399, July, 1952. 19. S. B. Wright, Amplitude Range Control, B.S.T.J., 17, pp. 520-538, Oct., 1938. 20. Carter, Dickieson and Mitchell, Application of Compandors to Telephone Circuits, Trans. A.I.E.E., 65, pp. 1079-1086, Dec, 1946. 21. J. C. R. Licklider and I. Pollack, Effects of Differentiation, Integration and Infinite Peak Clipping upon the Intelligibility of Speech, J. Acous. Soc. Amer., 20, pp. 42-51, Jan., 1948. 22. D. W. Martin, Uniform Speech-Peak Clipping in a Uniform Signal to Noise Spectrum Ratio, J. Acous. Soc. Amer., 22, pp. 614-621, Sept., 1950. 23. J. C. R. Licklider, The Intelligibility of Amplitude-Dichotomized, Time- Quantized Speech Waves, J. Acous. Soc. Amer., 22, pp. 820-823, Nov., 1950. 24. H. Cramer, Mathematical Methods of Statistics, Princeton Univ. Press, Princeton, N. J., 1946, see pp. 359-363. 25. T. C. Fry, Probability and its Engineering Uses, Van Nostrand, N. Y., 1928, see pp. 310-312. 26. A. C. Aitken, Statistical Mathematics, Interscience Pub. Inc., N. Y., 3d Ed., 1944, see pp. 44-47. 27. W. F. Sheppard, On the Calculation of the Most Probable Values of Frequency- Constants for Data Arranged According to Equidistant Divisions of a Scale, Proc. London Math. Soc, 29, pp. 353-380, 1898. 28. R. Courant and D. Hilbert, Methods of Mathematical Phj^sics, Vol. 1, Inter- science Pub. Inc., N. Y., English Ed., 1953, see Chapt. IV, especially pp. 184-187, and p. 206. 29. E. T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, Cambridge Univ. Press, 4th Ed., 1937, see p. 54. W. D. Bulloch Appointed Editor of B.S.TJ. W. D. Bulloch, formerly Editor of the Bell Laboratories Record, has been appointed Editor of the Bell System Technical Journal. Mr. Bulloch received a bachelor's degree from Dartmouth College and a Master of Science degree in Physics from the University of North Carolina. He taught physics, mathematics and astronomy in the latter institution for several years before joining the staff of Bell Telephone Laboratories. An Electrically Operated Hydraulic Control Valve By J. W. SCHAEFER (Manuscript received August 3, 1956) The electrohijdraulic transducer used in the servos that drive the control surfaces of the NIKE missile is described and its operating characteristics are discussed. Special attention is directed to the secondary dynamic forces that exist in a high-gain device of this type and to the resulting tendency to oscillate. The application of the valve to a servo system is discussed briefly. IXTRODUCTIOX Early in the study of the NIKE guided missile project, it became apparent that the requirements for the fin actuators could not be ful- filled by the servo-mechanisms available at that time (1945). All exist- ing types failed to meet the combined rec^uirements of small size, light weight, high torque, and rapid response. Further investigation showed that the development of a hydraulic servo employing an electrohy- draulic transducer appeared to provide a promising solution. A control system of this type, therefore, has been developed for the NIKE missile. The design of the transducer, or control valve, was one of the principal problems in the development of the missile control systems and is the subject of this article. The specific design of the valve that will be dis- cussed here is knoAvn as "Model J-7", and represents the state of the development in 1950. Valves of this type, with varying degrees of modifi- cation, are used in missiles of several other projects. APPLICATION Fig. 1 is a simplified schematic of the roll positioning system in the NIKE missile. It is the simplest of the three applications of the valve in the missile, but will serve to illustrate the situation in which the valve operates. The purpose of the roll servo is to keep the missile in a predict- able roll orientation. 711 712 AX ELECTRICALLY OPERATED HYDRAULIC CONTROL VALVE 713 The roll system's reference is an "Amount Gyro," which is a free-free gyro oriented on the ground prior to missile launch. The brush of a four- tap potentiometer (Item 2 in Fig. 1) is corniected to the outer gimbal and provides a dc signal whose sign and magnitude indicate the roll position with respect to the stable e(iuilii)rium point. This signal is the principal input to the servo amplifier that drives the valve. A roll-position error exists in the situation illustrated in Fig. 1. The valve is driven in the direction to cause the oil flow to rotate the ailerons, which in turn will roll the missile toward the null position. As the missile rolls, the winding of the roll-amount potentiometer rotates with it. The brush stays fixed in space with the gyro gimbal. The aerodynamic coupling between the aileron position and the mis- sile's roll position is a complex and variable term in the feedback loop of the servo. The nature of the aerodynamic coupling is such that an other\\ase simple servo problem becomes considerably more compli- cated. During a normal flight the aerodynamic stiffness, and hence the gain in the feedback loop, varies over a 50:1 range. A first order correc- tion for this change is accomplished by a variable gain local loop around the valve, cylinder and amplifier. A potentiometer (Item 3 in Fig. 1) is geared to the fin in such a way that a dc signal is produced, which is proportional to fin position. The gain of this local loop is varied by supplying the potentiometer with voltages that are directly propor- tional to the measured aerodynamic stiffness. In this way the amount of the deflection of the aileron is made inversely proportional to the aerodynamic stiffness. This effect results in an approximately constant torcjue about the roll axis of the missile for a given signal. The local loop around the fin position also reduces the effect of any non-linear charac- teristics of the valve. A third input to the servo amplifier is provided by a potentiometer that is driven by a spring-restrained gyroscope mounted so that the sensitive axis is aligned with the missile's roll axis. The dc signal pro- duced is proportional to the roll rate. This signal provides some anticipa- tion to the roll position loop. It performs the function of a tachometer in a conventional servo. It also insures that the roll rate is limited to a value that can be handled by the position loop. If very high roll rates were allowed to exist, the roll amount gyro would produce a signal changing in sign at such a rate that the ailerons would be unable to keep up or reduce the rate. The roll servo insures that the missile's orientation is aligned with the free-free gyro. This enables the yaw and pitch servos to steer about their assigned axes in a consistent manner. The two steering servos are i^ ^-^>->^ CO o CQ CD O > c3 > b£ ^&^r u 714 i AN ELECTRICALLY OPEKATED HYDRAULIC CONTROL VALVE 715 identical to each other and somewhat similar to the roll system described above. Each of the three systems employs identical valves. GENERAL DESCRIPTION Basically, the J-7 valve is a conventional four-way type. Fig. 2 illus- trates the porting arrangement. The parts in sections A, B and C are inserts that are shrunk-fit into the valve body. The plunger accurately fits the holes in the inserts, so that oil cannot flow between the plunger and inserts except where the diameter of the plunger is reduced. The annular space around the outside of the center insert is connected to the high pressure oil supply. The radial passages in this insert (part A) carry the oil to its internal cusps. With the plunger centrally located its center land completely covers the port formed by the cusps and no oil flows. With the plunger moved to the right the oil is carried to the cylinder and back to the exhaust in the manner illustrated by the small sketch in the upper right corner. If the motion of the plunger is to the left, a similar performance occurs but the piston and fin are driven in the opposite direction. To illustrate the construction of the inserts, detail sketches are also shown at the top of Fig. 2. The inserts and the plunger are made of hardened steel. Fig. 3 show- their location in the complete valve. The thickness of the inserts, hence the longitudinal location of the ports, is held to an extremely close tolerance by lapping their parallel faces. Their outside diameter is ac- curately ground so that a tight seal will occur between the various pas- sages when they are shrunk fit into the internal bore of the body. After assembly, the internal bore formed by the holes in the various inserts is lapped to a straight and accurate cylindrical shape. This process is con- trolled to provide a diametral clearance of 0.0002 inch on an inter- changeable basis. The plunger must slide freely in the bore in spite of the small clearances involved. The longitudinal location of the lands on the plunger must be controlled to a high degree for reasons that will become apparent. Those parts shown in Fig. 2 are not sectioned in Fig. 3. The valve proper is clamped between two manifolds (O and P) ; these are moved apart in the picture to better illustrate the internal construction. The brazed laminated manifolds provide the mounting means for the valve and also serve to connect the multiple outlets of the valve body to stand- ard hydraulic fittings for external connections. The manifolds are designed to adapt the valve to a specific application. In this Avay, different plumljing arrangements can be utilized without changes in the valve proper. The manifold, O, has fittings to connect to the cylinder, 716 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 I O i I i AN ELECTRICALLY OPERATED HYDRAULIC CONTROL VALVE 717 Fig. 4 — J-7 solenoid valve with manifolds. and the lower manifold, P, serves to connect the pressure and exhaust lines to ports in the structure to which the valve is mounted. The joints between the passages in the manifolds and those in the body are sealed by rubber "O" rings that are inserted in the recesses about the holes on the inner faces of the manifolds. These recesses can be seen in Fig. 3, but the "O" rings are not illustrated. Similarly, "O" rings are used to seal the joints between the manifold, P, and the flat surface to which it mounts. A pole piece, F, is screwed to each end of the plunger by means of the threads visible in Fig. 2. These parts move as an assembly and form S3^ - > .» ^ ^^'^i Fig. 5 — Exploded view of J-7 solenoid valve. •18 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 Fig. 6 — J-7 solenoid valve. the armature of the valve. The push rod, G, attached to the armature, is connected to an S shaped spring, H, which tends to keep the movable assembly centered, or the valve closed. When a current passes through the coil, J, magnetic flux passes through the fixed pole piece, K, through the coil housing, L, then across the small annular air gap, M, to the moving pole piece, F, and across the air gap between the pole faces near the center of the coil. Flux in the latter gap causes a force on the armature which tends to pull it and the valve o ^i Fig. 7 — Hydraulic parts of the J-7 valve. AN ELECTRICALLY OPERATED HYDRAULIC CONTROL VALVE 719 plunger toward that coil. If an equal current is flowing in the other coil the forces are balanced and the valve remains centered and closed. If the currents in the two coils are not equal, the valve plunger is moved until the differential magnetic force is balanced by the force in the spring. In this manner the amount of oil flow can be regulated by vary- ing the difference of the currents in the two coils. The coil housing is attached to the valve body by means of a non- magnetic stainless steel adapter, N. The adapter isolates the steel plunger and inserts from the magnetic flux. Because of the close fit between these parts the presence of flux would cause sticking. A push rod attached to the armature drives an aluminum piston, R, in a cylin- der, Q. The small radial clearance between these parts is filled with a viscous fluid so that a damping force is produced that is proportional to armature velocity. Fig. 4 shows the complete assembly with manifolds attached, while Fig. 5 gives an exploded view of the valve proper with all details in their correct relative positions. Other views of the valve parts are shown in Figs. 6 and 7. Fig. 8 is a view looking into the bore of the hy- draulic assembly. This is the hole that is normally occupied by the plunger. The ports formed by the internal shapes of the inserts are clearly visible. CHARACTERISTICS OP THE ACTUATING MECHANISM The J-7 valve is designed to be driven by a push-pull dc amplifier. When the amplifier has no input signal, the output current in each side is 10 ma. When a signal is applied, the current in one side is increased and that in the other is decreased; at maximum signal, the current in one coil reaches 19 ma and zero in the other. The dissipation in each coil for (luiescent current is about 0.4 watt, and the full signal power is 1.5 watts. The requirements that the frequency response must extend to dc and that the control power consumption be held to a minimum suggest the use of a dc push-pull output stage. The cjuiescent dc plate current is used as the magnetizing current for the solenoids instead of providing the field by a permanent magnet or separate coil. In spite of the small output current available from the amplifier, relatively large forces and a high resonant frequency are realized. This is accomplished by an effi- (!ient magnetic circuit and low armature mass. The opposing solenoid configuration described makes these features ])ossible. The magnetic circuit used in the J-7 valve has very low reluctance for a sliding armature type actuator. This low reluctance is accom- plished by providing ample thickness in the iron parts and employing 720 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 Fig. 8 — Internal view of the J-7 valve body. very short gaps of considerable cross-sectional areas. It has been sho^\^l elsewhere^ ■ ^ that if the distribution of reluctance of the magnetic structure is symmetrical along its longitudinal axis, minimum leakage flux and hence maximimi force would be developed if the working gap were at the exact center of the coil. To a close approximation, the valve solenoids are symmetrical in this manner. The references show that the maximum pull is not sensitive to small changes from the optimum loca- tion of the working gap. The gap in the J-7 valve is displaced toward the center of the valve from the location of maximum pull. The slight reduction in magnetic force was accepted as a suitable compromise for the resulting reduction in the mass of the moving pole piece and the corresponding increase in resonant freciuency. The gap between the solenoid pole faces is 0.01-i inch when there is no signal and the valve is centered. The two fixed faces have 0.004 inch non-magnetic shims attached so that the maximum motion of the arma- ture is limited to ±0.010 inch. The shims prevent the armature from sticking against the fixed faces l)y maintaining appreciable gaps. To further compensate for the inverse square law of magnetic attraction, the moving pole pieces have a reduced section that saturates under high flux or large forces. This neck can be seen plainly in Fig. o. The saturating AN ELECTRICALLY OPERATED HYDRAULIC CONTROL VALVE 721 sections limit the flux and tend to reduce the pull for short gaps so that the centering spring can be a simple linear member and still not lose control when the armature is near the fixed pole face. The flat surfaces on the neck permit the use of wrenches for assembly. Placing the necks on the moving pole pieces further reduces the mass of the armature as- sembly. To illustrate the saturation action, Fig. 9 shows the pull of one of the magnets plotted against gap length for quiescent and maximum current. The shim line and curves from a solenoid without a saturation neck also \ t \ 1 / / / / / / / 1 TYPICAL CURVES FOR * 1 A NON-SATURATING ARMATURE ^ 1 1 \ 1 \ 1 1 1 t 1 ly f t / / 1 /^ / J / // / / y / / X / / y / / / / / / y / > t J y y • • y / / / y ,^^ / ^ r ^^ -^\^W[A ^y ^.^ j^ y LU o ^^ v' < ^^^^ y u. y 5 ^ y^ I ^^^^1 (0 ^OMA 3600 3400 3200 3000 2800 2600 2400 2200 „ CO 5 < 2000 cc O z 1800 _i 1600 1400 1200 1000 800 600 400 200 3 Q. 24 22 20 IB 16 14 12 10 8 GAP IN LINEAR MILS Fig. 9 — Magnetic pull curves for a coil of the J-7 valve. 722 THIO HELL SYSTKM TECHNICAL JOUKXAL, MAY 1957 1800 1600 1400 01 5 < 1200 cr O z - 1000 I— X °^ 800 O ^ 600 CL 400 200 200 400 - to < 600 a. o - 800 1000 D 1200 a. 1400 1600 1800 / .«y / k. 1 .^ / \ \ .^ c^ ^ \ S \ \9 VA^ ^ v-^ r^ A \ K ,< / / \ ^^^:^- 1 ^^-l"** \ :'/i^ <-^" A <>^ / \ ^ liJ u < U < / / ~^?. ^■i«»** ^--^"" ^ LU u LLI O < LU 0_ 5 I (/5 / '1e^° r/^^ VA^ ^ \ 5 X to LU _] o a ,/ / / 1 vA"^ ^ \ ^^ k V 1>> — ^ ^^^ \ \ ,^^^ c^ V j/*^ \ \ Y 4 y^ N / / 10 8 642024 68 10 -« LEFT RIGHT >- ARMATURE POSITION IN LINEAR MILS Fig. 10 — Spring and magnetic forces on armature of J-7 valve. are shown to illustrate the need for these restrictive measures. The need is better appreciated when Fi^'. 10 is (examined. This graph shows the differential pull of the two coils ])lotted against armatiu'c movement for extreme signals and foi' the balanced condition. There is also a line repre- senting the spring force and one representing its reflection. The latter permits direct comparison of the magnitude of the o]:)posing magnetic and spring forces. AN ELECTRICALLY OPERATED HYDRAULIC COXTROL VALVE 723 It is important that the spring be able to center the valve when the coil currents are balanced. This means that the stiffness of the spring must be greater in magnitude than the negative stiffness created by the magnetic fields when 10 ma is flowing in each coil. On the other hand, the 19-ma current should be able to pull the armature against the pole piece and therefore must produce more force than the spring. If the shim and saturation limiting were not used it would be impossible to find a straight spring line that would fulfill both these rec[uirements; i.e., its reflection would be between these curves without crossing either of them. The family of curves representing the net magnetic forces for the various intermediate values of current unbalance fall between the extreme cases shown. The intersection of one of these curves and the reflection of the spring line is the position which the armature will assume for that par- ticular coil current. The reason for the relatively large margin of force shown for the 19-ma wide-open condition will be explained later. Fig. 11 is plotted to show the net forces on the armature. The curves are the difference between the spring line and the two magnetic pull curves of Fig. 10. It can be seen that the forces are such as to cause the armature to move to the center in the balanced condition. In the case of maximum signal, it will move all the way to the shim stop in the direc- tion of the coil which is carrying the current. When there is no magnetic field present the armature resonance is about 320 cps. When measured statically, or at very low frequencies, with the coils energized, the negative stiffness of the field greatly reduces the effective stiffness of the spring, as seen in Fig. 1 1 . However, when the valve is driven experimentally to find resonance, it occurs near 320 cps. This apparent increase in stift'ness with frequency results from eddy currents that retard the change in flux to the extent that the negative stiffness virtually disappears. Eddy currents reduce the effective in- ductance of the coils from about 40 henries at very low frequency to less than 10 henries at 000 cps. It is difficult to locate the resonance experimentally because of the large amount of damping provided by the extremely thin oil film be- tween the plunger and the inserts. High resonance frequency of the vaWe is desired so that it is safely above any frequency encountered in the servo operation, thereby eliminating one consideration in the eciuali- zation. Also, a high resonance means that missile acceleration along the valve axis causes little displacement of the unbalanced mass of the armature. A 250 cps differential dither voltage is superimposed on the push-pull dc signal to overcome the effects of static friction. The resulting 1 ma differential current produces a magnetic force about equal to that re- 724 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 6 4 2 0 2 4 6 -* — LEFT RIGHT *■ ARMATURE POSITION IN LINEAR MILS Fig. 11 — Resultant forces on armature of J-7 valve. quired to move the armature in breaking the friction of the stationary armature assembly. Thus, the signal threshold is reduced by the amount of the dither current and the resulting increase in sensitivity to small signals greatly reduces the phase lags at low amplitude. STEADY STATE HYDRAULIC CHARACTERISTICS The J-7 valve is designed to operate from an oil supply having a pres- sure of 2,000 psi, which is somewhat higher than eaily valves of this AN ELECTRICALLY OPERATED HYDRAULIC CONTROL VALVE 725 type. The increase in working pressure is a great advantage for a guided missile application because it results in lower weight, higher gain, and faster response. For example, doubling the pressure permits actuating cylinders of one half the size, an oil reservoir of one half the volume, and an increase in both response and gain by a factor of about three. Such features are sufficiently attractive to be worth a great deal of develop- ment effort. However, reliable and stable operation can be achieved under these high-gain conditions only if parasitic forces are kept ex- tremely small. It was found that the relation between pressure drop and flow is not so simple as one might expect from a sharp-edged, orifice-type control. For large openings of the control orifice, the pressure losses in the fixed orifices and passages of the valve body become an important factor. The following law is an adequate representation of pressure-flow characteris- tics : p = lOg + (^2 -f ^) q' (1) where p = pressure drop, psi q = rate of flow, cu in/sec X = valve opening, linear mils This equation was derived from test data from a model valve. These data confirmed a computational analysis of the hydraulic circuit. Fig. 12 graphically illustrates the equation. It is a plot of flow against valve position for various pressure drops. It will be noted that there is 0.001 inch difference between valve position and valve opening because of this amount of overlap at the ports. Equation (1) provides the information necessary to compute the maximum output power of the valve. If all the pressure drop were across the control orifices, all the pressure would be utilized to accelerate the oil at this point and only the square term of (1) would exist. If this were the case, the maximum output power would occur when the pressure drop across the valve was one-third of the supply pressure. The other two-thirds of the pressure would be used to produce work in the C34inder. If laminar flow existed throughout the valve the square term would drop out, leaving a linear equation. If this were the case, maximum power would occur with the total pressure equallv divided between valve and load. \Vhen both the linear the square terms are present, maximum power will occur when the pressure drop across the valve is somewhere 726 THE. BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 Q Z o u LU in LU a ui UJ I u z o (D D U 5 o 16 14 12 10 8 6 -I -6 -8 -10 -12 ■14 -16 PRESSURE DROP--, IN PSI J // ^^ Y. 'f /, u^ ^ / y y 222- #^ /^ ^ ^ -^ i ^ f -^oo y ^ f -^0 A /J // 4 ;Z 4^ ^^PRESSURE DROP ^ IN PSI -10 -8-6-4-2 0 2 4 6 VALVE POSITION IN LINEAR MILS 8 10 Fig. 12 — Flow characteristics of J-7 valve. between one-third and one-half the supply pressure. The exact point is dependent on the magnitude of the supply pressure as well as the co- efficients in the equation. The valve will be wide open, an opening of 0.009 inch, when maximum power is produced. In this situation, (1) becomes: p = IO9 + 7.6g2 (2) Useful output power at the load is the product of the flow rate and the pressure exerted on the piston. where W = {P - p)q W = Output power P = Suppl}^ pressure, psi (3) AN ELECTRICALLY OPERATED HYDRAULIC CONTROL VALVE 727 Therefore W = Pq - lOr/ - 7.i)q^ This expression can be differentiated and equated to zero to find the point of maximum power. -^ = P - 20q - 22.8r/ =0 .,. dq (4) q = V'O.192 + 0.0439P - 0.439 Substituting for q in ecjuation (2) we find that for maximum power p = 0.333 P + V2.15 + 0.49P - 1.46 (5) The normal supply pressure for the J-7 valve is 2,000 psi. Substituting this value for P in (4) and (5) q = 8.95 cu in/sec and p = 696 psi When these values are substituted in (3), we find TFmax = 11,700 in lb/sec = 1.77 horsepower Examination of the above equations will show that if the valve is used with a very low supply pressure, the linear term in (1) is dominant. In this case the maximum power output occurs when the pressure drop is nearly one-half the supply pressure. In the case of a veiy high supply pressure, the squared term is dominant and maximum power occurs when the pressure drop across the valve approaches one-third the supply pressure. The ratio between the electrical (juiescent input power to the coils and the maximum hydraulic out power is about 1,600, or a power gain of 32 db. Based on maximum signal the gain is 29 db. All forces must be precisely balanced and tolerances on parts be carefully controlled in order to realize this amount of gain in a single stage mechanical device. DYNAMIC HYDRAULIC EFFECTS Examination of the illustrations of the valve will show that it is statically balanced; i.e., pressure on any of the ports does not tend to translate the plunger. However, the flow of oil through a valve of this t,vpe produces a force on the plunger which tends to close the ports or 728 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 center the annature. Tlii.s force creates a stilTiie.ss tluit adds to the elTecl of the mechanical centering spring. The; magnitude of the force is (juite nonhnear, it varies with pressure drop, and hence, with load as well as with armature displacement. Such variations tend to upset the stability of the servo loop in which the valve is used. Fig. 13 is a simplified drawing of a valve w^hich can be used to explain the dynamic effect. It will be noted that when the valve plunger is displaced in either direction, the fluid flow is metered by two control orifices in series. The oil flows from oil supply, through the valve body, into a groove in the plunger via the first of the two orifices. The second SUPPLY ENLARGEMENT OF SUPPLY ORIFICE Fig. 13 — Simple valve with rectangular lands. orifice meters the flow from the other groove in the plunger into the exhaust part of the valve body. Most of the pressure drop in the valve appears across the two orifices and is equally divided between them. The maximum fluid velocity occurs immediately downstream from the ori- fices at the vena contracta of the jet. This point is labeled "A" in the enlarged insert on Fig. 13. The velocity at this point can be computed by use of Bernoulli's Theorem. In the case of the J-7 valve, where the valve opening is small compared to other passage dimensions, many of the terms of the equation that formulates this theorem can be neglected. In this way the eciuation becomes h = V 29 V = V2gfi (0) (7) AN ELECTRICALLY OPERATED HYDRAULIC CONTROL VALVE 729 where V = fluid velocity at the vena contraeta, ft/sec h = pressure drop across orifice, feet g = acceleration of gravity, ft/sec^ Von Mises' has shown that the departure angle of the jet from a small orifice, such as in the configuration shown in Fig. 18, is 69° from the longitudinal axis. Tests made with an orifice, shaped like those in a simple valve, showed that the jet continues at this angle for a short distance only. Further downstream the jet turns to hug the radial sur- face on the plunger. This action is depicted by the dotted lines in the insert on Fig. 13. Bernoulli's equation explahis that pressure is ex- changed for velocity. The low pressure within the jet stream pulls it toward the nearest wall of the cavity. The flow of oil over this surface reduces the pressure on that wall and unbalances the distribution of forces on the surface of the annular grooves in the plunger. The area of reduced pressure causes a net longitudinal force in the direction to center the plunger or close the valve. Examination of the situation around the exhaust orifice shows that a similar action will occur, but will not result in a comparable force on the plunger. The area of high velocity lies along a surface in the valve body rather than acting on the plunger. The velocity upstream from the orifice is not localized and hence produces forces that are small with respect to those downstream. The fact that the exhaust port forces on the plunger are small compared to those of the intake was confirmed by tests.* There is a small time lag between the opening of the ports and the dynamic centering force which is proportional to the rate of change of oil flow. This lag results from the fact that finite time is required to change the velocity of the oil mass in the system. At high frequencies, the delay results in a considerable phase lag between the plunger posi- tion and the dynamic force. This delay means that fluid velocity, and hence the force, is higher during the quarter cycle in which the valve is closing than it is during the cjuarter cycle in which the valve is opening. * Considerable work has been conducted on valve theory and design elsewhere since the J-7 valve was developed. Reference 4 is an excellent example of a thor- ough analysis of valve d3'namics with an approach to the i)rol)lem from a thtferent viewpoint. This reference reports on tests and theories which show the secondary forces from the exhaust and intake orifices to be equal. This is in direct contradic- tion to the experience with the J-7 valve and remains as an unresolved problem in the mind of the writer. 780 THE lilOLL SYSTEM TECHNICAL JOURNAL, MAY 1957 Therefore, more energy is exerted on accelerating the mass of the plunger during the closing operation than is absorbed in slowing the mass during the opening phase. If the net gain in momentum is larger than can be absorbed by the viscous damping of the oil film in the lapped fit, oscillation^ will occur. In the case of the J-7 this oscillation tended to occur at slightly over 400 cps. The Bernoulli force described above was recognized and measured early in the development of this series of valves, but was considered unimportant due to the high stiffness and large damping inherent in the design. The experimental models and the early production models showed no indication of oscillation. Later in the production program, the lapped clearances were increased and high ambient temperatures at the missile test locations were encountered. These tW'O factors combined to reduce the damping, due to the working fluid, to the point where hydraulic oscillation occurred. An external damper was added to alleviate this problem. The damper consisted of an aluminum piston closely fitted to an aluminum cylinder. A viscous fluid (polyisobutylene) between these two parts provided sufficient damping to stabilize operation. This fluid also has the advantage of a relatively small decrease in viscosity with temperature. This type of damper is illustrated on the valve in Fig. 3. (Subsequent improvement in the internal design of the valve reduced the dynamic effect to the point where the need for the external damper has been eliminated.) Fig. 14 shows a compensated intake orifice configuration correspond- ing to the insert picture on Fig. 13. It represents the first attempt to balance the dynamic or Bernoulli force. The depth of the annular groove P'ig. 14 — A compensated vtilvc orifice. AN ELECTRICALLY OPERATED HYDRAULIC CONTROL VALVE 731 in the plunger is reduced and a curved surface added to direct the flow parallel to the valve axis. This configuration reduces the dynamic force for two reasons. First, the amount of radial surface exposed to the low pressure is greatly reduced. Second, the cur\'ed surface acts much like a turbine blade in deflecting the oil stream and developing a reaction thrust that opposes the Bernoulli force. The reaction thrust increases as the longitudinal component of the high-velocity jet is increased. If the jet can be turned to become parallel with the longitudinal axis without appreciable loss in velocity, the maximum reaction thrust is obtained. In this case, the force is equal to the increase in the longitudinal component of momentum over the conditions of the free jet as shown in Fig. 1.']. F = ^ (1 - cos 69°) (8) where F = force, lb p = fluid density, Ib/cu in q = flow rate, cu in/sec V = fluid \'elocity, ft/sec g = acceleration of gravity, ft/sec* Calculations of the dynamic forces in accordance with the above reason- ing yield only approximate results because the local velocities and their gradients are functions of passage shape as well as pressure drops. The contour of the plunger grooves were computed for use in the first experimental model, whose design was intended to alleviate this problem. Refinements to the initial model were made by cut-and-try methods. Since the forces involved are relatively small, and their magnitude changes so rapidly with plunger position, specialized measuring instru- ments had to be developed whose sensitivity was high and compliance very low. A certain amount of contradiction was apparent in the force measure- ments made. To better understand the action of the oil within the valve, a transparent replica of the cross section of a yaXxe port was used under a microscope. Figs. 15, 16, and 17 are illustrations of typical tests. Fig. 15 is two views of an early type valve with rectangular ports at different openings and pressure drops. The arrows indicate a portion of the cylindrical sliding surface separating the plunger and body. The lower left shadow is the sharp corner at the edge of the annulus in the plunger. Fig. 15 — Oil flow through simple port. Fig. 16 — Flow through port with decreased Bernoulli effect. Fig. 17 — Flow through port with decreased Bernoulli effect and increased flow. 732 AN ELECTRICALLY OPERATED HYDRAULIC CONTROL VALVE 733 The lower light area is oil in the annular groove of the plunger. The oil is flowing from top to bottom. It will be noted that the flow on the downstream side of the orifice hugs the radial surface of the plunger, as discussed above and depicted in Fig. 13. The crosshair and the comb- like scale are a part of the microscope. Fig. 16 shows two views of a subsecjuent trial model quite similar to that shown in Fig. 14. Here, the bottom shadow is the insert and the top is the plunger. The flow is from bottom left to top right. This particular design reduced the Bernoulli force but resulted in a serious reduction in flow. This reduction was caused by the large cavitation bubble visible in the right view. This bubble was the result of rapid rotation of oil in the chamber. It prevented the orderly release of the oil through the in- ternal passage to the actuating cylinder (not visible in pictures) , Fig. 17 shows a trial model similar to the J-7. The left illustration 520 480 440 400 < o 360 cc UJ O 320 D _l Q. 2- 280 O oi U 240 O IL _l < z Q h; O z o 200 1 60 120 80 40 ^ ^^ PRESSURE drop/ IN PSI / r \ \, 2000 / \ / / 1600 " " V / / / \ / 1000 I / — / i / \ J l\ ^ \ / / L -/■ — ^"^ ^-- 500 I / // / (j y^ ^ / 2 3 4 5 6 7 VALVE POSITION IN LINEAR MILS Fig. 18 — Force on plunger of J-7 valve due to Bernoulli effect. 784 THE BELL SYSTEM TECHNICAL JOTTRNAL, MAY 1957 «hu\vs the oil flowing from left to right and simulates the intake port of the valve. The extra land on the plunger directs the oil stream toward the escape passage to reduce turbulence and cavitation and increase oil flow. The right illustration illustrates the reverse flow of oil, right to left, and represents the exhaust port of the valve. Fig. 18 is a plot of the measured Bernoulli force on the J-7 valve. It will be noted that there is little relation between the curves for various pressure drops. No simple ecjuation has been formulated to account for the forces observed. Although Fig. 18 shows the Bernoulli force to be large, Fig. 11 shows that full signal produces enough net force on the armature to overcome this force at any valve position. A large part of the development effort on the J-7 model was expended on the problem of reducing the forces caused by oil flow. For the same flow conditions, the J-7 has about one-fifth the Bernoulli force of earlier designs with simple rectangular grooves in the plunger. Subsequent to the initial manufacture of the J-7 valve, the design of the annular grooves and body inserts has been improved continually. Consequently, the Bernoulli force has been further reduced to permit higher operating pressure, and hence more gain, without creating a hy- draulic oscillation problem. THE J-7 VALVE AS A SERVO ELEMENT For any given set of operating conditions, the transfer function (ex- pressed as cubic inches of oil flow per milliampere of control current unbalance per lb per square inch of pressure drop) can be extracted from the information presented above. However, the resulting family of curves for various load torques would be of little use to the servo designer. The pressure drop available for use by the valve is different for each curve, and they are all ciuite nonlinear, as is apparent from the data. The overlap of the valve ports results in another type of nonlinearity that complicates the loop equalization problem. Examination of Fig. 12 will show that the effect of the overlap is a small dead area in the region of zero output of the valve. Small signal levels will cause the valve arma- ture to operate in and around the vicinity of the dead zone, resulting in very little oil flow. Thus, the gain of the valve for very small signals is lower than for signals of greater magnitude. As mentioned earlier, the effect of the nonlinearities of the valve is greatly reduced by use of the relatively fast-acting local loop which encompasses the valve, actuating cylinder, and amplifier. This inner, or secondary, loop contains sufficient gain to insure that, in spite of the AN ELECTRICALLY OPERATED HYDRAULIC CONTROL VALVE ■35 iioiilinearities, the fin position is controlled in strict accordance with the summation of the input signals applied to the amplifier. The first design of the servo circuits was made by using the slopes and magnitudes of typical and extreme points of operation as obtained from Figs. 11 and 12. The design of the servo equalization networks was obtained by successive refinements made during actual tests of the complete servo systems. These tests were performed with the aid of rather elaborate simulators that subjected the systems to the condi- tions of actual flight. The characteristics of the valve and the amplifier which drives it, as applied to a servomechanism, can best be illustrated by plotting gain and phase shift versus fretjuency in an open loop. Fig. 19 is such a graph. This information was gathered by applying an input signal to the servo amplifier from an oscillator. The valve was driven by the amplifier in the usual manner. The valve controlled the flow of oil to a piston which operated a load that was equivalent to a typical aerodynamic load as seen by the control surface. The voltage from the fin-position potenti- ometer was compared to the amplifier input. Fig. 19 shows the phase and amplitude comparison of these two voltages. A small amount of feedback was used to prevent the piston from drifting to one end of the cylinder. 40 36 32 28 -" 24 m u S 20 ? 16 < o 12 \ \ SsGAIN \ V \ \ \, PHASE / \ \ s. \ \ s. y > \, ^ y y \ s. ^ \ 1 1 1 1 -180 -170 -160 ai LLI a. -150 O LU Q Z -140 - -130 '^ LD If) < -120 ? -110 -100 0.6 0.8 1.0 2 3 4 5 6 8 10 FREQUENCY IN CYCLES PER SECOND 20 30 - 90 Fig. 19 — Frequencj- characteristics of J -7 valve. 736 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 The data were adjusted to correct for the errcjr introduced in this manner, so that open loop conditions are represented. The etiualization networks have compensating leading characteristics to prevent the oscil- lation suggested by the increasing phase shift at the higher frefiuencies. If the servo acted in strict accordance \\ ith minimum-phase network theory, the slope of the gain curve would have started to increase at the high frequenc}^ end of Fig. 19. The effects of nonlinearities caused by such things as overlap and dither action cause this departure from classical theory. Actually, the slope does start toward 12 db per octave just above the frequency range shown. Part of the phase shift shown on Fig. 19 is due to the inductance of the coils and the relatively low source impedance of the amplifier used. Later amplifier designs have much higher output impedance, which has greatly reduced this effect. CONCLUSION The series of hydraulic valves developed for use in the NIKE missile provide a light-weight, high-performance control element for positioning aerodynamic control surfaces. Although these electrohydraulic trans- ducers provide a high power amplification, they are relatively simple single-stage devices. Their successful application in the XIKE missile has caused hydraulic servos to be considered for many other military control systems, some of which are under active development at this time. The hydraulic servo has many advantages to offer in the high power field that cannot be provided by other conventional types. It is expected that these advantages will foster a great increase in the use of hydraulic servos in high performance applications in the next few years. ACKNOWLEDGMENT The writer wishes to thank E. L. Norton w^ho contributed greatly to all phases of the valve development and V. F. Simonick of the Douglas Aircraft Company who provided valuable consultation on the hydraulic problems involved. REFERENCES 1. Peek, R. L. and Wagar, H. N., Magnetic Design of Relays, B. S.T.J. , Jan., 1954. 2. Ekelof, Stig, Magnetic Circuit of Telephone Relays — A Study of Telephone Relays — I, Ericsson Technics, 9, No. 1, pp. 51-82, 1953. 3. Von Mises, R., Berechnung von Ausfluss — and Ueberfallzahlen, Zeitschrift des Vereines Deutscher Ingenieure, 61, pp. 447-452, 469-474, 493-498, Mav- June, 1917. 4. Lee, Shih-Ying, and Blackburn, John F., Axial Forces on Control-Valve Pis- tons, Meteor Report No. 65, Mass. Inst, of Tech., Jvuie, 1950. 5. Holoubeck, F., Free Oscillations of Valve-Controlled Hydraulic Servos, Royal Aircraft Establishment, Technical Note Mechanical Engineering-100, Nov., 1951. Strength Requirements for Round Conduit By G. F. WEISSMANN (Manuscript received October 16, 1956) Underground conduits arc subjected to external loads caused by the weight of the backfill material and by loads applied at the surface of the fill. These external loads will produce circumferential bending moments in the conduit wall. The magnitude and distribution of the bending moments have been determined by measurements of the circumferential fiber strains in thin-walled metal tubes subjected to the external loads. The effects of different backfill materials, different trench width, and trench depth have been investigated. Bending moments caused by static and dynamic loa^s have been compared. The bending moments are finally expressed in terms of the required crushing strength. INTRODUCTION For many years, vitrified clay has been the principal material for underground conduit used as cable duct by the Bell System. Vitrified clay conduit has, in general, given excellent service. It has more than adeciuate strength and durability for the wide variety of conditions under which it must be used and for the long service life expected of it. For this reason, relatively little attention has been given to the formula- tion of special strength reciuirements for this type of conduit during the period in which it has been standard for Bell System use. For some time other types of conduit, mainly in the form of single duct, h&ye appeared on the market. Many of their properties make them attractive enough to be considered for Bell System use. However, to prevent possible failure or excessive deformation of the conduit under field conditions each type of conduit should meet minimum strength requirements, in order to provide the same reliable service that clay conduit has given. The main purpose of this investigation was to deter- mine the minimum strength reriuirement for round conduit under vari- ous field conditions. An extensive investigation of the effects of external loads on closed conduits has been conducted at the Iowa Engineering Experiment Sta- 737 .S8 THE HELL SYSTEM TEf'HXirAL JOURNAL, MAY 1057 tion.'- Ilowexcr, duo to the liir^v (lianu'ter.s of the coiiduits ii.scd and the particular test eonditions employed, tJie test results obtained were not directly applicable for the determination of strength reciuirements for conduits for the Bell System. Underground conduits under service conditions are subjected to external loads. These external loads are caused by: a. The weight of the backfill material. b. The loads applied at the surface of the fill. The magnitude and distribution of the external loads around the con- duit are affected by: 1. The properties of the backfill material. 2. The magnitude of the applied load at the surface of the fill. 3. The height of the backfill over the conduit. 4. The trench width. 5. The bedding condition. 6. The diameter of the conduit. 7. The flexibility of the conduit. 8. Impact. 9. Arrangements of conduits in the trench. 10. Consolidation and compaction of the backfill material. 1 1 . Auxiliary protection of the conduit. Fig. 1 — Thin-walled tube with SR-4 strain gages. STRENGTH REQUIREMENTS FOR ROUND CONDUIT 739 Fig. 2 — Test set. External loads acting upon the conduit produce circumferential bend- nig moments in the conduit wall. The magnitude and distribution of these bending moments have been determined in tests conducted recently at the Outside Plant Development Laboratory, Chester, New Jersey, and at Atlanta, Georgia. These tests were made with gravel, sand, and clay as backfill, in trenches of ^'arious width and depth and under con- ditions simulating, as nearly as possible, those encountered in the field. TEST APPARATUS AND PROCEDURE A test method was developed which permitted the determination of the circumferential bending moments in thin-walled conduits under field conditions. The test device consisted of thin-walled aluminum or steel tubes of one foot length. The steel tubes used had an outside diameter of 4 inches and a wall thickness of 0.062 inches; the aluminum tubes had an out- side diameter of 4.5 inches and a wall thickness of 0.065 inches. SR-4 strain gages were attached to the inside surface of the tube. Each tube was efjuipped with four equispaced SR-4 strain gages (type A-o), (Fig. 1). One aluminum tube contained, in addition, sixteen SR-4 strain gages (type A-8), which were ec^ually distributed around the internal circumference of the tube. By means of an SR-4 strain indicator and an Edin brush recorder it is possible to measure the strains caused by static, as well as by dynamic loads. The strains could })e measured with an accuracy of drlO X 10~^ inch per inch. 740 THK BKLL SYSTEM TECHNICAL JOURNAL, MAY 1957 C/2 O O O Eh xn H H Q &H W O III T3 o XI "a. a < J3 ■a .a c > o O n o x) a a;) oj Qj) iD J ^ n.0^ iM O O C^ (M Q o ""^ ■— 1 1— 1 >— 1 ;-i t-t S3 JDJ2 1—1 1— ( OO OO lOiO OO ^_^ coco t/1 u c^f (m'im m ■<*< ^ .s CS(M(MC^»OiO(M »% ^ ^ (M « ,J=! COCOCOCOOOCDCD cocococococococo ^ o' o" o" o" -t^~ -*" o o CO CO CO CO (M IM CO CO '*" "* ^"^ -rjT cc oo" ^" '*" OaC^MCMr^rtlMC^ Ti -73 -o-o S fl c fl fl S c3 (rf o3 o3 t^ 02 M 0202 bC >>ai>-)«>iQ;(U- _^ G_^ c:_^ 0 d.S o E o E o E S <^i^ >>>.>.>> cj c3 cj c3n2::::z;:;3 — . — 1 , — ' — ' O o o o OOOOccMccM 03c3e3cjtHfc<(Ht-i .rt .„ ._ .„ 4) aj jj dj bC bC bC bO->S +S ^ ^ tHi-ctHi-itca2cc[C ooooa>Q;Q;a) 0; o q; (Uj3j:3j3-i3 OOOOOOOQ 1 to a> H o oi o JO 03 pq bO CI -a ^° 0 a — ' o "o ^ 1 m O 0) ^ & STRENGTH REQUIREMENTS FOR ROUND CONDUIT 741 The test equipment used is shown in Fig. 2. Each tube was laid length- wise on the trench bottom between two pieces of plastic conduit of the same outside diameter. The tubes were oriented so that one of the strain gages was at the top of each tube. The trench was then filled with the backfill material. The loads at the surface of the fill were applied by using trucks with various measured wheel loads. The trucks were either moved slowly to a stop in position over each tube, or driven at moderate speed across the trench. Additional impact tests were made with a Hydrahammer, which consists of a 500-pound-weight dropped from different heights onto the surface of the fill. Each tube was subjected, 4000 3 800 3600 3400 3200 3000 *Q 2800 X C 2600 2400 z a 22001- \- 2000 ■ STRAIN MEASUREMENTS TAKEN AT THE INSIDE SURFACE OF THE CONDUIT STRAIN GAGE CONDUIT X =1 O r2 i =3 • =4 STRAIN MEASUREMENTS VS. APPLIED LOAD CONDUIT OUTSIDE DIAMETER CONDUIT WALL THICKNESS HEIGHT OF COVER WIDTH OF TRENCH CONDUIT MATERIAL BACKFILL MATERIAL 4.5 IN. 0.065 IN. 30 IN. 22 IN. ALUMINUM CLAY j_ 2000 4000 6000 8000 10000 APPLIED LOAD [lBS] 12000 14000 Fig. 3 — Strain measurements versus applied load. 742 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 ill the laboratory, to various two-point loads (two edge bearing loads). Strain readings were taken during each test. Table I lists the tests conducted and the test conditions investigated. TEST RESULTS Field and laboratory measurements obtained from each strain gage were plotted as a function of the applied load. A typical example for a field measurement is shown in Fig. 3. For this example, as well as for several hundreds of similar measurements, a linear relationship between the measured strains and the applied loads could be observed. For each case this linear relationship was derived from the data using the method of least squares. The straight line in Fig. 3 was plotted by this method and is shown with the data obtained in the test. MOMENT DISTRIBUTION Soil pressure acting upon a thin-walled tube will cause circumferential forces and bending moments in the wall of the tube. Furthermore, it is assumed that the strains caused by the compressive forces are small compared with those caused by the circumferential bending moments and are therefore neglected. For pure bending, the following relation- ship for circumferential bending moments and fibre strains is established. M =lh'E, (1) where M = circumferential bending moment per unit length (in lb/in) h = wall thickness of tube (in) E = modulus of elasticity (psi) € = circumferential fibre strains (in/in) The circumferential bending moment of a thin-walled tube of unit length subjected to a two-point load is determined analytically: •) M = — - - sin d (2) where M = circumferential bending moment per unit length (in lb/in) F = applied two-point load (lb/in) r = radius of the tube (in) 6 = angle with vertical axis of tube The calculated circumferential bending moments (2) and those deter- STRENGTH REQUIREMENTS FOR ROUND CONDUIT 743 niiued by strain measurements and Equation (1) are compared in Fig. 4. The agreement is very close. Fig. 5 shows the theoretical moment distribution in a thin-walled tube subjected to a uniformly distributed vertical pressure; Fig. 6 is the theoretical moment distribution in the same tube subjected to a uniformly distributed vertical pressui'e at the top of the tube and a point load at the bottom of the tube. Fig. 7 shows the typical experimental moment distribution in a thin- walled tube in an 18-inch wide and 40-inch deep trench with a backfill (36-inch cover) of moist Georgia clay subjected to an applied surface load of 10,000 lb. Fig. 8 shows the moment distribution under the same conditions but with a backfill of moist fine sand. F=IOLBS/lN = l20 LBS/FT E = IO X 10* PSI LOAD DISTRIBUTION lOr 5-4 z z 5-4 2 UJ <^-6 MOMENT DISTRIBUTION M = 4- pr2cos2e Fig. 5 — Theoretical moment distribution in a thin-walled tube subjected to uniformly distributed vertical pressure. STRENGTH EEQUIREMEXTS FOR ROUND CONDUIT 745 bedding, the moment at the l^ottom may vary up to 235 per cent, and the moments at the side points maj^ change a maximum of 12 per cent.^ The field data indicate that l)edding is of particular importance with moist clay backfill, and to a lesser degree for moist fine sand. However, bedding did not appear to affect the moment distribution of the tube for a dry sand or gravel backfill. TRENCH WIDTH The effect of the trench width on the magnitude of the bending mo- ments in a conduit has been investigated. The presently available test results indicate the following: a. Xo significant difference in the magnitude of the bending moments of the tube (4.5-inch diameter) could be observed for a trench width MMM ,, p =2.22 PSI LOAD DISTRIBUTION M = pr2 M = pr2 ■icosae + 3^00594-1-] _3^cose-siNe + | + i] o^e<90 90£e m 1000 _i o O 1300 1200 1100 1000 900 800 700 600 500 400 300 200 100 a < o Z a. backfill: fine sand WIDTH OF trench: I8-30IN. CONDUIT MEAN D I A M ETE R : 4 IN. 3000 LBS BACKFILL ( LOOSE) X 10 _L 20 30 40 HEIGHT OF COVER (IN) 50 60 Fig. 13 — Equivalent two-point load versus height of cover for sand backfill. STRENGTH REQUIREMENTS FOR ROUND CONDUIT 753 l)edding eft'ect, the possible maximum bending moment at the bottom of the tube was obtained by doubling the values of the side points. Figs. 12 and 14 show clearly that the maximum bending moments occur in wet claj^, and also that improvement is obtained by an increase in the height of backfill or a decrease of the applied load. These figures apply to 4-inch diameter tubes. In conversion of results obtained using 4.o-inch diameter tubes, it was assumed that the eciuivalent two-point load is directh' proportional to the tube diameter. DYNAMIC LOAD A study was made to determine the effect of moving loads on the maximum bending moment of the conduit. For this purpose trucks were driven over the backfill at a speed of approximately 20 miles per hour, the strains measured and then compared with those obtained by static loads. The results show that for a clay backfill, the bending moments due to dynamic loads were equal to or even smaller than those obtained by static loads. For sand backfill, however, the dynamic loads caused an increase of the maximum bending moments of approximatel}^ 10 per cent. These results are in close agreement with dynamic load tests con- lOOOr 900- 600 u. \ CD - 700 o < o z o 0. 1 o 9 z UJ > § 200 600 500 400 300 100 CO o I r^ r*— VsuSTAIN I ^OUT ± TIME — (b) Fig. 1 — Simplified gas diode switching circuit. COLD CATHODE GAS TUBES FOR TELEPHONE SWITCHING SYSTEMS 757 tions, however, it is desired to apply the output voltage directly to other tubes without impedance transformation. In this case, voltage gain is of more interest than current gain. The maximum voltage gain per stage, defined as the maximum output voltage divided by the minimum input signal, is limited by variation in tube characteristics as will now be shown. The bias voltage E of Fig. 1 is expected never to cause breakdo\\'n during times when the input voltage is zero. This establishes the upper limit of E as 1^1^ V, ,„in (1) where Vb min is the minimum breakdown voltage at any point in the life of any tube to be used in the circuit. As the bias voltage E approaches breakdown, the input signal voltage required for triggering approaches zero, and if there were no variation in breakdown voltage or bias voltage, and no noise voltages, the gain could be made to approach infinity. The input signal, added to the bias, must be made large enough always to cause breakdown. Thus the minimum input signal is determined by Vb max , the maximum breakdown voltage at any point in the life of any tube to be used in the circuit: Combining (1) and (2) or ein ^ Vb max " E (2) a = ' B max ' B min ein ^ AFb (3) where AVb is the maximum variation in breakdown voltage among all tubes to be used in the circuit. The output signal is the difference between the bias voltage and the sustaining voltage of the tube: gout = E - T^sVlS (4) The minimum output voltage corresponds to the maximum sustaining voltage, Fsus max . It is this value that must be used in calculating the maximum gain per stage as limited bj^ the tube characteristics. The gain is then calculated as f, , E—V Vr. ■ — V /~i «'Out -«-' ' sus max ' B mm ' sus max ff\ ein AT B AFb This gain cannot be realized in practice because additional allowances 758 THE BELL SYSTEM TECHNICAL JOIJRXAL, MAY 1957 must be made for the variation in power supply voltages and protection against noise. In some cases the need for higher speed reduces the gain still further, as will now be shown. In Fig. 1 a delay, t, is indicated between the application of the trig- gering signal and the appearance of the output signal. Part of the delay is statistical in nature and part is occasioned by the building up of ioniza- tion within the tube. As will be discussed later, the delay can be reduced by tube design technicjues. Howe\'er, for any gi\'en tube, the delay is a function of the excess of the tiggering voltage over the breakdown volt- age. The larger this overvoltage, Fov , the shorter is the breakdown delay. Since this overvoltage must be added directly to the input signal, the gain is reduced. Although not shown in Fig. 1, the tube is turned off by applying a sig- nal that reduces the anode-to-cathode voltage below the sustaining value. This turn-off signal must have sufficient duration so that the tube does not again break down at the return to normal bias conditions. If the turn- off pulse duration is less than that needed for complete recovery, the ef- fective breakdown voltage is reduced. Ecjuation (5) can be modified to show the effect of this reduction in turn-off time by defining a quantity Vr , the reduction in breakdown voltage resulting from incomplete recovery of the tube. The combined effects of Vr and Fov are then /-> \' B min • r) ' sus max /^.x AT B + Fov Equation (6) shows that faster turn-on obtained by increasing the over voltage Fov and faster turn-off obtained by allowing for decrease in breakdown voltage by an amount Vr , both result in a reduction in volt- age gain. Thus the familiar trade of speed for gain extends to gas tube switching circuits. Summarizing, it can be seen by (5) that constant breakdown voltage and large difference between breakdown and sustain are desirable switching properties. Also, as shown in (6), the tube should be designed so that the overvoltage needed to cause fast breakdo\m is small and the recovery of breakdown voltage after the tube is turned off is fast. It is useful to consider now the internal physical processes of a cold-cathode glow-discharge tube in order to see how the desired external properties can be obtained. PHYSICAL PROCESSES OF A COLD CATHODE GLOW DISCHARGE Since the gas particles are neutral and the cathode does not spon- taneously emit electrons, current flow requires an auxiliary supply of charged particles. A small amount of radioactive material to ionize some COLD CATHODE GAS TUBES FOR TELEPHONE SAVITCHING SYSTEMS 759 B C 1 -Vb / ^ ■ 1 UJ < O > / Vsus- L _E^ F F' K F" ID 1- / 1 1 1 1 1 1 10 10 '2 10-'° 10-« 10"^ 10"^ TUBE CURRENT IN AMPERES 10 Fig. 2 — Voltage versus current curve of typical gas diodes. of the gas or very small photoelectric emission of electrons from the cathode are commonly used for this auxiliary supply. A typical voltage- current curve is shown in Fig. 2. At low voltage, the current is very small, often being in the range of lO^^"* ampere or less. The current in- creases with the voltage because collisions of electrons with neutral gas atoms produce additional excitation and ionization in the gas. Some of the new ions and excited gas atoms release new electrons by secondary emission when they strike the cathode. The rate of increase of current with voltage depends on the kind and the pressure of the gas filling, the cathode material, and the tube geome- try. An important characteristic of the gas is defined by an ionization coethcient rj, which represents the number of new electrons (and ions) produced by a single electron moving through the gas a distance corre- sponding to one volt of potential difference.^ This coefficient is a function of the kind of gas and of the ciuantity E/po where E is the voltage gradi- ent and po is the normalized gas pressure. The fact that there is an opti- mum E/po at which tj is a maximum will be important to later discussion. The electron current at the anode, 4 , produced by gas amplification of a photoelectric current I'n at the cathode is^ ?u U>c Jvo '"'^■ (7) 7(50 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 wlicre r is the aiicxie vollajijc and W Is the initial voltage through which the electrons must travel l)efore they can ionize. The ions produced in the space by this process flow back toward the cathode. The ion current ip resulting from this process is = io(e^ '» - 1 ioie-' "» - 1) (8) As mentioned above, new electrons are released at the cathode by posi- tive ions, neutral atoms excited to a metastable state, and photons gen- erated in the gas. These secondary processes can be grouped together by defining a coefficient y as the number of new electrons released at the cathode by all of these processes for each positive ion generated in the cathode-anode space. Thus each electron passing from cathode to anode, on the average, results in the release of M new electrons where M = 7(e-''^*' - 1) (9) Each new electron from the cathode is also amplified in the gas so that after n multiplication cycles, the electron current at the anode is^ in = ioe^''" ''\l + ill + ^/2 + • • • + M-) (10) When M is less than unity and n -^ x (the eciuilibrium state), (10) re- duces to a steady state value of . _ ioe ° (11) * 1 - M Since the current is dependent on the initial current iu , the discharge is said to be non-self-sustaining. This corresponds to the portion AB of the curve of Fig. 2. If the applied voltage is made high enough, the multiplication factor approaches unity, the current of (11) becomes independent of the initial current, and the tube is said to have broken down. This condition cor- responds to the horizontal portion BC of Fig. 2. To control this break- down voltage, the cathode secondary emission coefficient 7 and the gas ionization coefficient rj must be controlled. The secondary emission coefficient is highly sensitive to the surface conditions of the cathode. Pure metals such as molybdenum are often preferred to coated surfaces because they permit highly stable and repro- ducible emission. With the cathode surface determined, the breakdown voltage can be adjusted by changing the gas filling and tube geometry. Fig. 3 show^s the breakdown voltage for a tube having parallel-plane COLD CATHODE GAS TUBES FOK TELEPHONE SWITCHING SYSTEMS 7(31 220 210 200 In 190 o > J 180 O Q 5 170 a. 160 150 MO / / f / / / / J / / MOLYBDENUM CATHODE NEON FILLING GAS AT 50 MM Hg \ / Vl 1 23456789 SPACING, d, IN CM X PRESSURE, po, IN MM OF Hg 10 Fig. 3 — Breakdown voltage as a function of spacing and pressure for parallel plane anode and cathode. anode and cathode geometry, a molybdenum cathode, and neon filling gas. The curve is plotted as a function of the product of pressure po in mm Hg and electrode separation d in cm. Approximately the same plot would obtain for other pressures because both 77 and 7 are functions of (E/po) and, for uniform fields, E is simply the voltage divided by the separation (E) ^1^1. (at breakdown Cl Po (Po). (12) Since the variation of 7 with E/po is small and may be ignored in this elementary discussion, the minimum breakdown ^'Oltage corresponds ver}^ nearly to the optimum value of the ionization coefficient rj. At spacings or pressures less than optimum, t/ is reduced because some elec- trons strike the anode without colliding with gas atoms. At spacings or pressures greater than optimum, rj is reduced because electrons do not gain enough energy between collisions to ionize efficiently. It can be seen that a way of meeting the switching reciuirement of constant breakdown \'oltage would be to design the tube to operate at the minimum of Fig. 8. Minor changes in spacing or filling pressure from one tube to another and changes in pressure with tube operation would result in small changes in breakdown voltage. The advantages of op- 762 THE BELL SYSTEM TECHNICAL JOURNAL, MAY H).17 250 7 8 9 SPACING, d, IN CM X PRESSURE, po, IN MM OF Hg Fig. 4 — Breakdown voltage as a function of spacing and pressure for small wire anodes parallel to cathode surface. eration at the minimum of the p^d curve can be retained and the breakdown voltage made higher by resorting to non-uniform geometry. Typical curves are shown in Fig. 4. The cathode was a small rectangular plate and the anode was a wire placed parallel to the cathode surface. It is seen that as the anode diameter is decreased, the minimum of the breakdown curve is increased. The practical limit is set by mechanical stability of the anode and by transmission requirements, as will be dis- cussed later. The rise in minimum breakdown voltage as the anode size is reduced can be explained on the basis of the distortion of the electric field. Near the cathode, E is lowered, and near the anode, E is increased, as com- pared to the parallel plane case. If the spacing is adjusted for optimum E/pi) with parallel planes, then rj is necessarily less than optimum for the distorted fields. Returning now to Fig. 2, we note that, as the current is increased beyond breakdown, the tube voltage falls to a lower sustaining value and again is relatively constant with current. This lowei' voltage corresponds to the development of a space-charge layer of positive ions near the cathode and an increased voltage gradient at the cathode. This highei" COLD CATHODE GAS TUBES FOR TELEPHONE SWITCHIXG SYSTEMS 763 field results in an increase in the ionization coefficient rj, and, in some cases,'^ a larger effective value of the secondary emission coefficient 7. This is because electrons released by the secondary emission processes may strike neutral gas atoms and be reflected back to the cathode. A higher gradient increases the probability of escape of such an electron. Thus the multiplication factor M of (9) can ecjual unity at a lower total applied voltage. Practical tubes filled with neon or argon gas have sustaining voltages near 100 volts when pure molybdenum or tungsten cathodes are used. Cathodes coated with barium and strontium oxide may sustain at 60 volts. However, since this lower sustain is accompanied by a lower breakdown voltage, the difference between them is not increased. Also, since the coated cathode surface is more variable between tubes and with tube operation, the switching voltage gain may be reduced with such cathodes. The gas pressure and cathode geometry determine the length of the flat portion DE of Fig. 2. Over this current range, the area covered by the glow discharge increases with current until at E the cathode is completely covered. Increasing the cathode area or gas pressure increases the total current required for coverage. At still larger currents, the sus- taining voltage increases rapidly as indicated by the solid curve EF. Broken curve EF' applies to a special cathode geometry called a hollow cathode.* Such a cathode may be formed by the interior of a cylinder or by placing two plane cathodes close together so that the negative glow regions overlap. Under this condition electrons, ions, and excited atoms generated near one cathode can aid in current flow from the other cathode. Dotted curve EF" applies to a particular form of hollow cathode^ in which cathode shape and gas pressure have been selected to give a negative slope in the high current region. This negative slope represents a negative resistance and permits audio-frequency signals to be transmitted through the tube without loss. Anode effects have not been discussed. In general, the anode shape and location do not affect the sustaining voltage or the ability of the dis- charge to transmit audio frequency unless the anode-cathode spacing is too large. The basic requirement is that the anode should be large enough to intercept enough electrons to carry whatever current is re- (luired by the external circuit. Even a small anode placed near the cathode space-charge region can meet this requirement. Thus the sus- taining voltage of a tube designed to have a breakdown voltage near the minimum of Fig. '.] or Fig. 4 will not in general be sensitive to the anode size or shape. 764 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 The transition from low current to high current in a gas diode can thus be thought of as the process of introducing a space charge of positive ions in the region near the cathode. This is done by raising the voltage tem- porarily above the breakdown value. To switch back to the low current, it is necessary to decrease the multiplication factor M below unity by temporarily lowering the voltage and allowing the ions and excited atoms to diffuse out of the cathode and anode region. Both the turn-on and the turn-off processes impose time restrictions on the switching character- istics. The multiplication factor M of (9) applies to an average process. Thus, even though M is greater than unity, it is possible that the ioniza- tion and excitation produced in the gas by any individual electron msLj not release a new electron at the cathode. It is therefore necessary on the average to wait for more than the time between initiating electrons before the discharge starts to build up. The average statistical delay is then equal to the average time between successful starting events. If .Vo photoelectrons per second are emitted from the cathode and W is the fraction of these which successfully initiate a discharge, the average statistical delay is^ The fraction W -would be expected to increase with an increase in the multiplication factor M and hence with the overvoltage above break- down. It has been shown theoretically and experimentally^ that this is the case. For voltages only slightly in excess of breakdown, i.e., small overvoltages, Fov , the expression for average statistical delay can be approximated by ^AV ^ ^ (14) ' ov In practical tubes with overvoltages of 10 volts, the average statistical delay may be of the order of milliseconds with radioactive sources of ionization. Short delays of the order of microseconds are obtained by providing an auxiliary "keep-alive" discharge to a separate electrode or by illumination that provides a photoelectric current in the range of 10~^^ amperes, A formative delay in breakdo^\Ti also occurs because time is required for current to build up to the final value. This time is equal to the product of the number of multiplication cycles and the time per cj'cle. The number of multiplication cycles recjuired is reduced as multiplica- COLD CATHODE GAS TUBES FOR TELEPHOXE SWITCHING SYSTEMS 765 tion factor M is increased with increasing overvoltage. The multipHca- tion factor M inchides electrons released at the cathode by slow moving metastable gas atoms as well as those released by the faster positive ions. At very low overvoltages, these slow components must be included before the current can build up.^ At higher overvoltages enough positive ions are produced so that M is greater than unity without waiting for the slow components. Thus the effective time per multiplication cycle is reduced with increasing overvoltage. Since the number of cycles and the time per cycle are both decreased the formative delay decreases rapidly with increasing overvoltage. A typical formative delay for a neon filled, molybdenum cathode switching tube at 5 volts overvoltage might be of the order of 100 microseconds. APPLICATION TO A TALKING-PATH SWITCHING DIODE The principles discussed above have been applied in the development of a cold-cathode gas diode for use as a switch in series with the speech path in an electronic switching system. The objectives were a switching voltage gain as high as possible, a breakdown time of less than a few hundred microseconds, and a low transmission impedance for audio- frequency signals. A sketch of one version of the resulting tube is sho^vn in Fig. 5. The cathode is a molybdenum rod which has a small hollow cathode portion in the upper end. The anode is a small molybdenum wire placed near the minimum breakdown distance and slightly to one side of the opening in the end of the cathode. A barium getter is flashed to one side of the bulb wall and a small tungsten wire spring is arranged to make electrical contact with the getter flash. A neon filling gas at a pressure near 100 mm Hg is used. The cathode geometry has several interesting properties. It was found that the shape of a cylindrical hollow cathode is unstable at very high current densities and that it will rapidly grow into a spherical cavity with a small orifice.* Typical dimensions are a sphere diameter of 0.0:^0 inch and an orifice diameter of 0.008 inch. At an operating cur- rent of 10 milliamperes, the current density in the orifice is of the order of 50 amp/cm^. Once the sphere has stabilized it will operate many thousands of hours with relatively small changes in shape. The trans- mission properties of the stabilized spherical cavity cathode are similar to the earlier negative resistance hollow cathode tubes.* Typical im- * This cathode was developed by A. D. White of Bell Telephone Laboratories and will be described more completely by him in a forthcoming publication. 766 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 pedance values are 800 ohms negative resistance and 50 ohms inductive reactance at 10 milliamperes operating current, with a superimposed audio-frequency signal of 3,000 cycles per second. Even though the cathode geometry is stable, some cathode material escapes through the orifice and will rapidly collect on an anode placed directly over the opening. It is therefore necessary to locate the anode to one side of the orifice. The extremely high ionization density near the cathode orifice allows considerable flexibility in anode location without affecting the sustaining voltage or destroying the negative resistance. High switching-voltage gain is obtained by using a small anode formed by a 0.005-inch diameter molybdenum wire placed perpendicular to the end of the cathode at a spacing of approximately 0.005 inch. Breakdown voltage is nominally 190 volts with a range of ±10 volts over all tubes and over the nominal operating life of 4,000 hours. The sustaining volt- GETTER FLASH — _ SPRING CONTACT BARIUM GETTER BULB- ANODE CATHODE SHIELD FOR SPUTTER PROTECTION Fig. 5 — A talking-path switching diode. COLD CATHODE GAS TUBES FOR TELEPHONE SWITCHING SYSTEMS 707 age at the operating current of 10 nia is U!) ± 2 volts. Thus the .switching gain from (5) is (180 101)/20 or o.9. In practice, switching is often done without allowing the full 100 milliamperes operating current to flow. Under these conditions, the sustaining voltage may be 10 or 15 \-olts higher, with a conseciuent reduction in switching ^'oltage gain. Short breakdown times were desired for this tube. It was not desirable to use enough radium to obtain the needed initial ionization, since it is expected that large numbers of these tubes will be concentrated in a relatively small space. Also, the molybdenum cathode does not emit photoelectrons unless short wavelength ultraviolet illumination is used. The solution chosen was to use the barium getter flash as an auxiliary photocathode. An electrical contact is made to the getter deposit and this is connected through a high resistance to the main cathode. Visible light or long wave ultraviolet light is readily transmitted through the bulb and produces photoelectric current in the auxiliary gap. This cur- rent is amplified b}^ the gas, but remains a non-self-sustaining discharge. Currents of 10"^" amperes are readily available with a few foot-candles of illumination. This current is too small to afi'ect the breakdown voltage of the main gap, but produces enough residual ionization to allow break- down times of the order of 100 microseconds to be obtained with a few volts overvoltage. The high resistance connection to the main cathode may be of the order of 20 to 50 megohms. It protects the photocathode from deterioration which might result from high currents when the main gap is conducting. Recovery of breakdown voltage following conduction is rapid. Meas- urements indicate that the breakdown \'oltage is within the limits of 190 ± 10 volts in less than 500 microseconds. The relatively high gas pressure and close spacings speed up the deionization process. The tube described has not been designed for large scale manufacture although several hundred models have been made and tested to establish the feasibility of the design. SUMMARY Some useful switching properties of gas diodes can be described by defining the switchiug-voltage gain. This gain is shown to be equal to the difference between the breakdown and the sustaining voltage divided by the variation in the breakdown voltage. The gain is reduced if faster switching times are required. The switching-voltage gain is discussed in terms of the physical processes in a gas discharge. It is shown that a high gain can be obtained by using an inefficient anode operating at the minimum of the curve 768 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 of ])reakdo\vu voltage versus the i)roclu('t of gas pressure and anode distance. A tube is described which uses these principles to achieve a high gain over a useful operating life of 4,000 hours, and which has a negative re- sistance to audio fretiuency signals superimposed on the dc operating current. Fast switching is obtained by an auxiliary photoelectric cathode formed by making an electrical connection to a barium getter flash. Satisfactory tube operationg has been obtained for continuous operation for times which are ecjuivalent to 20 to 40 years of intermittent operation in switching systems. ACKNOWLEDGEMENT The author is indebted to many members of the gas tube and switching systems development groups at Bell Telephone Laboratories. Among these special mention should be made of A. D. White who originated the cavity hollow cathode and V. L. Holdaway, B. T. McClure, A. M. Wit- tenberg and C. Depew who made important contributions to the success- ful development of the tubes. BIBLIOGRAPHY 1. M. J. Druvvestevn and F. M. Penning, Rev. Mod. Phys., 12, p. 97-102, 1940. 2. Ibid., page 105. 3. R. N. Varney, Phys. Rev. 93, p. 1156, 1954. 4 RcfBrcncG 1 p. 139. 5. M. A. Town'send, W. A. Depp, B.S.T.J., 32, pp. 1371-91, 1953. 6. Reference 1, p. 116. 7. F. G. Hevmann, Proc. Phys. Soc, 63, Sec. B, 1950. 8. H. L. Von Gugelberg, Helvetica Physica Acta, 20, pp. 307-340, 1947. Activation of Electrical Contacts by Organic Vapors By L. H. GERMER and J. L. SMITH Unrcproducibiliti) of earlier work on the erosion of relay contacts has been traced to the effects of organic vapors in the atmosphere. Carbon from de- composition of these vapors greatly alters the conditions under which an electric arc can be initiated and can be sustained. The importance from the standpoint of erosion comes from the fact that for many circuit conditions contacts activated by this carbon cannot be protected against severe arcing by any conventional capacitance-resistance network. This paper reports investigations which have enabled us to understand the activation of contacts by organic vapors. TABLE OF CONTENTS Introduction 770 Part I. Electrical Effects 772 1. Observations on Activation 772 1.1 Striking Field 774 1 .2 Arc Voltage 775 1 .3 Minimum Arc Current 777 1 .4 Erosion 778 1.4(a) Palladium and Platinum 778 1.4(b) Silver and Gold 779 2. Interpretation of Activation 780 2.1 Striking Field 781 2.2 Arc Voltage 784 2.3 Minimum Arc Current 785 2.4 Erosion 786 2.4(a) Palladium and Platinum 786 2.4(b) Silver and Gold 788 2.4(c) Anode Arcs and Cathode Arcs 790 3. Recapitulation 794 Part II. Activating Carbon 796 4. Composition of Activating Powder and Rate of Production 796 4.1 Composition 796 4.2 Rate of Production 797 5. Surface Adsorption 798 5.1 Benzene ^lolecules on Contact Surfaces 798 5.2 Inhibiting Surface Films 801 5.3 Alloys 802 769 770 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 6. Activation in Air 803 6.1 Burning of Carbon 804 6.2 Diffusion of Activating Vapor 806 6.3 Sputtering and Burning in a Glow Discharge 807 6.4 "Hysteresis" Effects 800 7. Brown Deposit 810 7.1 Composition 810 7.2 Rate of Production 811 7.3 Brown Deposit and the Carbon of Activation 811 INTRODUCTION Contamination of surfaces by organic vapors is a subtle factor that influences the electrical erosion of relay contacts. Because of this con- tamination, contacts in the telephone plant sometimes erode very much more than one would expect from simple laboratory life tests. This caused considerable confusion until about 1945 when the influence of organic vapors was recognized. The term "activation" is used here to describe changes in the surfaces of electrical contacts which give rise to greater arcing when an electrical circuit is completed or broken than would occur if the metal surfaces were clean.* Although its cause is generally carbon from organic vapors, there are occasionally other causes. This paper is an account of recent research^ on activation produced by organic vapors, t It has been found that the carbon that causes activation is formed on the electrode surfaces by decomposition of adsorbed organic molecules. Microscopic examination of contacts gives a very sensitive way of de- tecting incipient activation, since the carbon can easily be seen before any electrical effects are observed. The minimum amount of carbon necessary for activation is of the order of 0.05 microgram. Activation has been produced on noble metals only, and only b}' un- saturated ring compounds. When experiments are carried out on clean noble metal surfaces under controlled conditions which do not permit burning of carbon, it is found that the amount of carbon formed by an arc corresponds to approximately a monolayer of organic molecules on the area heated by the arc. After a surface has become active, the amount of carbon formed by each arc is considerably increased and corresponds to the decomposition of several monolayers of molecules. In air, the situ- * The term "activation" has sometimes been used heretofore to signify en- hanced erosion resulting from organic vapors. This is a different definition from that used in this paper, due to the fact that in some cases, long sustained arcs produce less erosion than arcs of shorter duration. This is often true for silver surfaces, as described below. In a case of this sort, a surface may have a great deal of carbon on it and be very "active" by our definition, when it would be considered not active at all by the definition that relates activation to rate of erosion. t Other causes of activation will not be considered here. See Reference 2, page 961. ACTIVATION OF ELECTRICAL CONTACTS BY ORGANIC VAPORS 771 ation is much complicated by burning of carbon and by the impedance offered by air to diffusion of molecules to the electrode surfaces. Because of these complicating factors, activation will not occur in air if the vapor pressure is too low or if the time between arcs is too short. Arcs at the making and breaking of clean contacts — clean in the sense that they are free from carbon — produce transfer of metal from one con- tact to the other with a resulting pit and mound of about equal volumes. The situation is greatly changed by carbon. The presence of carbon causes increased arcing, alters the characteristics of the arcs, and greatly changes the resulting erosion both in character and amount. With carbon present, some or even all of the eroded metal does not stick to the elec- trodes, and there is often loss of metal from both of them, the missing metal turning up mixed with carbon in a loose black powder. With car- bon on the surfaces, successive arcs occur at different places, and the resulting erosion tends to be smooth with the electrodes worn down uni- formly all over their surfaces. This is because each arc burns off carbon at its center, while it produces more around its periphery where the metal is cooler, and each new arc strikes on a newly carbonized surface. Everj^ arc, of either the active sort or of the "inactive" sort which occurs at clean surfaces, is predominantly an arc in metal vapor. The active arcs, as well as the arcs at clean surfaces, are of one or the other of two quite distinct types which have been called, respectively, "anode arcs" and "cathode arcs" (Reference 3 and 4 which are concerned with palladium electrodes only). In an anode arc, most of the metal of the arc is vaporized from the anode by electron bombardment, but in a cathode arc the metal is supplied from the cathode by the explosion of small areas due to Joule heating by field emission currents of enormous densities flowing through them. In an anode arc, the erosion is predom- inantly from the anode, and in a cathode arc from the cathode. Whether a particular arc is of the anode or of the cathode type is de- termined by the electrode separation and the contact metal. For pal- ladium electrodes, an arc is an anode arc if the separation is less than about 0.5 X 10~^ cm, but a cathode arc if the separation is greater than this \-alue. The corresponding critical distance for silver is 3 or 4 X 10~* cm. The carbon particles producing activation permit breakdown at separations for which it would not occur in the absence of carbon, and thus favor cathode arcs. The critical distance of palladium is so small that all active palladium arcs are cathode arcs, with the greater loss of metal from the cathode. For silver, on the other hand, the critical dis- tance is so large that active arcs at silver surfaces are in many cases anode arcs, with the greater loss of metal from the anode as in the case of inac- tive silver arcs. 772 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 Part I — Electrical Effects 1. OBSERVATIONS ON ACTIVATION Just how different the behavior of contacts can be in the clean or inacJ tive condition, and in the active condition, is shown strikingly by the oscilloscope traces of Fig. 1. Each trace represents a plot against time of the voltage across a pair of protected relay contacts when the contacts are pulled apart to break a current through an inductive load. The cir- cuits used with the two pairs of palladimn contacts were identical, the only difference of an}^ sort being in the conditions of the surfaces of the contacts produced by exposure of the second pair of contacts to organic vapor. In the trace of Fig. 1 (a) , the potential across the contacts If) 60 O > 0 (0 50r o > 400 0 100 TIME IN MICROSECONDS 200 300 400 500 Fig. 1 — Oscilloscope traces of the voltage across relay contacts breaking a current of half an ampere through an inductive relay load. In each case a stand- ard protective network of a 0.5 fii capacitor in series with 100 ohms is in parallel with the contacts, (a) Clean or "inactive" contacts, with no observable arc. (b) Active contacts, with a sustained arc lasting 400 microseconds. rises abruptly on break from zero to 50 volts, and then continues to increase as the capacitor of the protective network is gradually charged up; there is no arc or other discharge at the contacts. In the trace of Fig. 1(b), the potential rises on break to about 14 volts and remains at this value for 400 microseconds. This represents an electric arc that oc- curred across the contacts, the 14 volts being the potential characteristic of arcs over short distances at pallaium electrodes (Reference 2, Table II). The energy dissipated at the contacts by this arc was about 25,000 ergs. A number of worth while experiments upon activation can be carried out with no better method of measuring, or detecting, activation than the observation of oscilloscope traces like those of Fig. 1, or correspond- ing traces obtained from contacts discharging a small capacitor on closure (Reference 2, Fig. 1). One can find what organic vapors produce activa- tion, and what metals can be activated. This can be extended to discover ACTIVATION OF ELECTRICAL CONTACTS BY ORGANIC VAPORS 773 what vapor pressure is needed and how the minimiun pressure depends upon the conditions of the test; for example, upon the electrical test circuit. Some results of simple tests of this sort will be given before going on to present anything more fundamental about what is happening when contacts become active. Activation is produced, in general, by repeated operation of a pair of contacts closing or breaking an electric circuit in air containing an organic ^'apor. At the beginning of a test of this sort, oscilloscope traces look the same as they would look in the absence of the vapor, but with continued operation, arcs may begin to occur when there were initially no arcs, or the durations of arcs may become greater. Activation is not produced b}' simply allowing contacts to stand idle in an activating vapor even for very long times, and even when the partial pressure of the vapor is extremely high. Nor is activation produced unless currents are made or broken. Operating contacts "dry" in a high pressure of an activating vapor does indeed make them temporarily active,* but this condition is unimportant from the standpoint of erosion. Under conditions that are effective in producing acti\'ation, the number of operations required before increased arcing can be detected is usually greater than 100, and often greater than 10*. In general, noble metals can be activated by organic vapors and base metals cannot. Vapors of unsaturated ring compounds produce activa- tion and other organic vapors do not. Tests have been made upon the metals Ag, Au, Cu, Pd and Pt which can be activated and upon Co, Cr Fe, Mn, Mo, Ni, Sn, Ta, Ti and W which have not been activated. f The vapors of nearly 50 organic compounds have been tested, about half of them unsaturated ring compounds which produce activation, and about half other compounds which do not. (These are listed, in part only, in Reference 2, Table 1). A very large number of tests have been carried out upon benzene, limonene and styrene. For these three compounds the minimum partial pressures which just produce activation of silver electrodes in air under certain standard conditions, and of platinum electrodes in air, for which the results are the same as for sih'er, were found to be respectively 0.1, 0.03 and 0.003 mm Hg. Some insight into activation is obtained by direct examination of active contacts. Black soot can always be seen on active contacts, and if they have been operating for some time in activating vapor, the amount of soot may be great enough to produce a visible deposit under- * See the Section 7.3 on "Brown Deposit." t Ni and ]V have been activated in the presence of an organic vapor in a con- tainer in which the pressure of air was reduced to 0.01 mm Hg, Reference 5, page 1090. 774 THE BELL SYSTEM TECHXIf'AL JOl'KXAL, M\Y 1957 neath the electrodes. It is clear that the increased arcing of activation is caused by solid carbonaceous material made b}' decomposition of organic vapor and not by the vapor itself. Clean metal contacts can, in fact, be made to show all of the symptoms of activation by allowing soot from a flame to settle on their surfaces.*! Activation produced in this way is, of course, temporary, lasting only until the deposited soot is burned away. When one looks for characteristics of arcs between active surfaces to which numerical values can be attached, four features come at once to mind — the electric field at which an arc strikes, the voltage across the arc after it is established, the minimum arc current (which is just the current at which the arc goes out), and finally, after the arc is over, the amount of metal that was gained or lost by each of the electrodes during the arc. All of these ciuantities have been measured for active arcs as well as for arcs at clean surfaces, and a brief summary of the results of the measurements is given here. 1.1 Striking Field To measure the electrode separation at which an arc strikes between closing electrodes, relay contacts were operated repeatedly, discharging on each closure a capacitor charged to a measured voltage. An arc at each closure was assured by using short leads between the capacitor and the contacts to keep the circuit inductance very low. The time from the initiation of the arc to the touching of the contacts was measured on an oscilloscope. J Fig. 2 illustrates the results of measurements made b}^ F. E. Ha- worth^ upon palladium electrodes closing at 30 cm sec to discharge a veiy small capacitor charged to 50 volts. Before the start of the experi- ment the electrodes had been cleaned by repeated arcing in air, and the first experimental point represents the closure of these clean electrodes. All of the other measurements were made in air containing a fairly high partial pressure of limonene vapor. Each point plotted on the curve rep- * Unpublished work of P. P. Kisliuk. t It is interesting to point out that a surface is not made active by rubbing petrolatum upon it, although activation will occur very quickly if an electric current is made or broken at such a greasy surface, so that some of the grease is decomposed. t For inactive arcs, it is necessary to make a correction for the height of the mound of metal thrown up by the arc (Reference 6, page 1136). After the contacts become active, there is no appreciable mound thrown up (at palladium surfaces), and the electrode separation at the initiation of the arc is calculated at once from the closure time and the previously measured electrode velocity. The height of the mound produced before the contacts are active was minimized b.y using a capacitance of only 40 X 10^'^ farad. ACTIVATION OF ELECTRICAL CONTACTS BY ORGANIC VAPORS 775 10 XlO" LU u z < I- ^<" I" ? UJ , -4n6 uu. ID Z O < UJ cc CD 5X106 200 400 600 800 1000 1200 1400 NUMBER OF OPERATIONS IN LIMONENE VAPOR 1600 Fig. 2 — Breakdown distance, and apparent striking field, for arcing at relay contacts on closure in the presence of limonene vapor, plotted against number of operations. Each closure discharges a very small capacitor charged to 50 volts. Contacts are clean and inactive at the beginning of the test. resents the average of 100 separate measurements. During tests of this sort, it was discovered that, with frequent microscopic examination of the electrodes, black sooty material could easily be seen after the first 30 closures, before certain evidence of activation could be obtained in any other known way. In Section 4.1, it is shown that this material is carbon. The average electrode separation at which an arc struck between clean electrodes at the beginning of the curve of Fig. 2 was about 1 X 10~* cm and after the electrodes became covered by sooty material, about 8 X 10~^ cm. The apparent striking field was decreased by activation from 5 X 10^ to 0.6 X 10* volts/cm. When measurements were made at 250 volts, rather than 50 volts, the striking field in the active condition was only slightly higher, 0.8 X lO"' volts/cm. Activation produces a lowering of the apparent striking field, regardless of the value of the applied voltage.* 1.2 Arc Voltage The observed voltage across an arc at active palladium contacts agrees in general with that of palladium cathode arcs, which is about 16 (Refer- ence 4, Fig. 7 and Reference 2, Table II), whereas the arc voltage of * This apparent contradiction of the conclusion of F. E. Haworth^ is clarified in Section 2.1. 77(5 TII1<: BELL SYSTEM TECHNICAL JOUUNAL, MAY 1!)57 26 24 < K _) O 20 > o a. < t 8 16 14 / ,^ ) /cneg ^ O 1 ( /C NEG \ L Apt NEG \ ^ / C NEG /C NEG i V r 1 ^ \w NEG >S- £k 20 10 20 30 40 50 60 0 X 103 NUMBER OF OPERATIONS 40 60 80 100 120 140 X 103 Fig. 3 — Measurements of arc voltage at cathode arcs between a carbon-plati- num pair of electrodes, and between a carbon tungsten pair — at successive rever- sals of striking potential. carbon is much higher and quite \'ariable in the range from 20 to 30. One is tempted to conckide from this that the vapor in an arc between active palladium contacts is predominantly the metal of the electrodes, not carbon vapor. A more sound conclusion, however, as will be pointed out later, is that the source of electrons on the cathode of an active arc is palladium metal rather than carbon.* When contact surfaces are very heavily carbonized, an arc voltage substantially higher than that characteristic of the metal of the elec- trodes is sometimes observed for a short time at the beginning and at the end of an active arc occurring at the discharge of a capacitor into an inductive circuit. An example of this is shown in the oscilloscope trace of Fig. 4. The higher arc voltage at the beginning of this arc, when the current was extremely small, is interpreted as the initiation of the arc between carbon surfaces, and the enhanced voltage at the end is evidence * A very simple experiment has been carried out which proves conclusively that the character of an arc of the type which we call a cathode arc (see below, and Ref . 3 and 4) is determined by the properties of the cathode, and not by those of the anode. This is perhaps self evident, l)ut a direct test is reassuring. Tlie test is simply the observation that, for an arc of the cathode type Itetween electrodes of different materials, the arc voltage is sul)stantially the same as it would be if both electrodes were of the cathode material. The test is made by reversing the potential between the electrodes rejieatedly, and after each reversal observing that the arc voltage changes gradually from that characteristic of the anode to that characteristic of the cathode. After each reversal the arc begins to clean from the cathode the anode material that was deposited there before the reversal, when wluit is now the cathode was the anode. Accompanying this cleaning, the arc voltage goes uj) or down until it reaches the value characteristic of the cathode itself. Measurements obtained in this way are reproduced in Fig. 3 for a carbon- platinum pnir of electrodes and for a carbon-tungsten pair. ACTIVATION OF ELECTRICAL CONTACTS BY ORGANIC VAPORS 777 that when the curreiit was again small the arc was localized at a new position on a fresh carbon surface so that it was again a carbon arc; during most of the arc time, when the current was larger, the cathode surface was maintained so free from carbon that the source of electrons at the cathode was palladium metal rather than carbon. For lightly carbonized surfaces, which may be just as active as judged by arc dura- tion or any other test that we know of, no such enhanced arc voltage at the beginning or at the end of an arc has been observed. It may well be that for lightly carbonized surfaces the arc voltage is characteristic of carbon for a time too short to be detected by this crude means. 1.3 Minimum Arc Current The current at which an arc goes out is readily found by observing on an oscilloscope the potential across closing contacts discharging a capacitor through a non-inductive resistor R. At extinction, the potential rises from the arc voltage v to that across the capacitor Vi . The mini- mum arc current is then (Fi — v)/R. An oscilloscope trace showing such a determination of minimum arc current at the arc initiation potential of 400 ^•olts is reproduced as Fig. 5. (See also Reference 2, Fig. 5 and Fig. 4 — Oscilloscope trace rep- resenting the voltage across an arc at the closure of very heavily car- bonized electrodes. Discharge through an inductance of 10~% of a capacitor of 10~^*f charged to 50 volts. Near the beginning and near the end of the arc the source of electrons at the cathode was a carbon surface. 50 r- _) O > TIME IN MICROSECONDS Fig. 5 — Voltage across clean palladium contacts when a capac- itor charged to 400 volts is dis- charged through a resistor of 200 ohms. The closure arc went out at the minimum arc current 0.42 amp. 400 1- o > 0 5 10 TIME IN MICROSECONDS 778 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 Reference 8, Fig. 1). The minimum arc current is much lower for active contacts than for inactive or clean contacts, and one can perhaps think of the decrease of the minimum aic current for noble metal contacts from a vahic of the order of 1 ampere for clean surfaces to 0.1 ampere or less for active surfaces as the chief characteristic of activation. 1.4 Erosion Active contacts of palladium and of silver transfer metal in cjuite different ways. The transfer at active silver contacts is the more complex, and for this reason the transfer that occurs at acti\'e palladium contacts -1.5 15 U O -4.0 (a) LIMONENE AT 1 MM PRESSURE ANODE -T- CATHODE ••o- 0.07 0.2 (b) NAPTHALENE AT ROOM TEMP J L .-O- 0 0.51 1,03 0.07 0.2 0.51 ARC TIME IN MICROSECONDS 1.03 Fig. 6 — Results of measurement l)y weighing of the erosion of palladium elec- trodes produced by active arcs in limonene vapor (a) and in napthalene vapor (b). will be taken up first. The behavior of platinum is in general like that of palladium, and gold is like silver. 1.4 (a) Palladium andPlatimim. It is found that arcing on closure at ac- tive contacts of palladium or platinum causes loss of metal at the cathode of the order of 4 X 10~^^ cc/erg. The anode often loses metal also, but the loss at the anode is considerably less and may be zero in some cases. The results of two sets of measurements upon active palladium contacts are plotted in Fig. 6. These data represent changes in volume (calculated from weighings) per unit of arc energy after repeated arcs in limonerie vapor at a vapor pressure of 1 mm Hg, Fig. 6(a), and in the vapor of napthalene saturated at room temperature. Fig. 6(b). Tests were made by closing electrodes to discharge on each closure a properly terminated fixed length of cable charged always to 200 \'olts, to gi\-e in each case a constant arc current of 4 amperes, with the arc lasting for the time de- termined by the cable length. For the shortest arc time, the energy of ACTIVATION OF ELECTRICAL CONTACTS BY ORGANIC VAPORS 779 each of the individual arcs was 40 ergs, and for the longest arc time 600 ergs. The results indicate no significant variation of the erosion per unit of energy over this range. There is some evidence that arcs at the break of active palladium sur- faces give significantly lower cathode erosion per unit of energy (1 or 2 X 10""'* cc/erg) than do arcs at closure. The reason for the difference is not clearly understood, but widely different currents and electrode sepa- rations may be significant factors. By examining contacts of palladium or platinum after many active arcs (on either break or closure), it is found that the erosion tends to be uniform over the surface, wearing each electrode down smoothly, with much less loss from the anode than from the cathode. This type of wear is quite different from that produced by arcs at clean surfaces. Erosion by arcs at clean surfaces always gives a mound of metal on one electrode, with a corresponding pit in the other ; the loss of metal from one electrode is not appreciably greater than the gain by the other, the entire erosion consisting simply of transfer of metal between the contacts. Now the inactive arcs at clean surfaces are known to be of two types which have been called "anode arcs" and "cathode arcs."^- "^ In anode arcs, the transfer of metal is about 4 X 10~^* cc/erg and is from anode to cathode, with a resulting pit in the anode and a matching mound on the cathode (Reference 9, page 1085-1086). In inactive cathode arcs, measurements made in the same way and not yet published have shown that the transfer is smaller — about 1 X lO"'* cc/erg — and is in the opposite direction, from cathode to anode, with a resulting pit in the cathode and a matching mound on the anode.'** It will be shown later. Section 2.4(a), that arcs at active palladium surfaces are of the cathode type, each individual arc being not readily chstinguishable from an inac- tive cathode arc in the effect it produces on the cathode surface. The reason for the net cathode loss being greater in an active cathode arc than in a cathode arc at clean surfaces is due, at least in part, to some reverse transfer in an arc at clean surfaces. 1 .4 ih) Silver and Gold. The erosion of silver surfaces is quite complex, and an adequate description of all of the phenomena encountered is re- served for later publication.'" A simplified description of the main fea- tures of the erosion of silver contacts is given here. Tests upon acti\'e gold contacts have been less extensive than upon active silver contacts, but as far as the observations go, gold has been found to behave just Hke silver. At active silver surfaces the erosion is, in most cases, from the anode, as it is at inactive surfaces. The arcs are active anode arcs, see Section 780 THE BELL SYSTEM TECHNICAL JOURXAL, MAY 1957 2.4(b), which have never been observed at palladium contacts. The metal lost from the anode after a great many active anode arcs tends to be eroded smoothly over the entire surface, like the cathode loss in arcs of the cathode type at palladium contacts. At a moderate pressure of activating vapor, almost all of the metal eroded from a silver anode is transferred to the cathode, but at a high pressure much of it is lost. Whether the metal from the anode is transferred or lost is correlated with the amount of carbon formed by the active arcs; if the production of carbon is small, metal is transferred, but in the presence of much carbon, the metal does not stick to the cathode and is lost. The amount of carbon formed (in air) by active anode type arcs at silver surfaces is very much less than the amount formed by active cathode type arcs at ' palladium surfaces, and this difference accounts for the fact that a great deal of the eroded metal is transferred at active sih'er surfaces, although there is always very little transfer at active palladium surfaces.* The erosion of a silver anode by active anode arcs may be as great as 10~^^ cc/erg, but is lower than this whenever the carbon formation is suffi- ciently slight to permit much transfer of metal. Long, sustained break arcs at active silver surfaces become cathode arcs when the electrode separation becomes sufficiently great. Such arcs give cathode erosion resembling that at active palladium surfaces. For a long sustained break arc, the cathode erosion suffered when the electrode separation becomes very large may be greater than the anode erosion occurring when the electrodes are closer together, so that the net loss from the cathode may be the greater. There may even be a small net anode gain. ^ Measurements of transfer at electrical contacts have sometimes been very confusing in the past, both because of their complexity and because of their apparently erratic character. Now, with well developed insight into the mechanism of short arcs, this complexity of transfer and its varied character have been most useful in improving our understanding of short arcs and of the transfer of metal to which they give rise. The over-all picture of activation will be given in the following pages. 2. INTERPRETATION OF ACTIVATION ■ After one has concluded that activation is due to solid carbonaceous material, it is natural that tests should be made upon contacts of solid * At extremely low pressures of activating vapor, active anode arcs at silver surfaces may not only transfer to the cathode practically all of the metal lost from the anode, but the type of erosion may even he changed to the mound anfl pit type characteristic of inactive arcs.' I ACTIVATION OF ELECTRICAL CONTACTS BY ORGANIC VAPORS 781 carbon, and upon metal surfaces on which carbon particles have been dusted. The results of these tests have supplemented measurements upon active noble metal contacts and have led to a great increase in our knowl- edge of activation. In fact they open the way to a fairly thorough under- standing of the subject. 2.1 Striking Field Five different experiments have been carried out, which were designed to discover the reason for the low striking field at active contacts. Al- though the results of these experiments do not establish the reason for the low striking field in any definitive fashion, they do lead to an ex- planation which seems entirely satisfying. The simplest of these experiments has already been reported at the end of Section 1.1. It is the observation that the striking field at active contacts is much the same at different striking voltages, of course below air breakdown only. In another experiment, not heretofore published, W. S. Boyle and P. Kisliuk produced active spots at various points along a palladium wire. The wire, which lay on the axis of a glass cylinder, was made active at these selected points by repeated short arcs in an atmosphere containing limonene vapor. The other electrode was operated by an elec- tromagnet outside the cylinder, with the magnet arranged so that the electrode could be placed at any location along the wire or withdrawn completely at anytime. After activating a number of points, as determined by continuous oscilloscopic observation, the cylinder was exhausted and field emission currents were drawn from the wire to the cylinder. From observation of a fluorescent coating on the inside of the cylinder, it was found that the positions along the wire, which gave the largest currents, were quite unrelated to the active spots. From this experiment, one can conclude that the work function of active spots along the wire was not lower than the work function of other parts of the wire, and also that there was no significant enhancement of field emission at these spots because of roughness. Thus, the activation of contacts by organic vapors is not due to enhanced field emission currents because of lowering of the work function or because of greater surface roughness. In a third experiment by F. E. Haworth,^ measurements were made of the electrode separations at which an arc strikes between a palladium electrode and a smooth palladium surface upon which carbon particles had been deposited. For this experiment, solid carbon particles of fairly uniform size were obtained by blowing air at a low controlled rate 782 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 Table I — Effect of Carbon Particles upon Striking Distance Range of Particle Size (by microscopic measurement) Average Striking Distance at 50 Volts Apparent Striking Field No Particles 0 to 1 X 10-^ cm 0 to 2.5 4 to 5 0.10 X 10 -J cm 1.4 2.5 4.3 5 X 10" volts/cm 0.36 0.20 0.12 through agitated carbon dust and collecting the particles that had been carried upward for a considerable distance in the air stream. The time of deposition of these particles upon the smooth surface was adj usted to give an average distance between particles of about 10 times their di- ameters. The smooth palladium surface with a fairly uniform, but sparse covering of carbon particles was made the cathode in measurements of striking distance by the oscilloscope method, Section 1.1. For a particular size of particle, 100 measurements were made of striking distance, each measurement at a different point on the surface, so as not to include any measurement of striking distance at a place on the surface where the original particles had already been burned off.* Table I gives the ranges of particle size as found microscopically and the corresponding average measured values of striking distance. The increase of striking distance was just equal to the particle size. At each arc, a particle was destroyed so that the time to closure measured on the oscilloscope corresponded, not to the true striking distance, but to the distance from the anode to the cathode surface upon which the particle rested. The electric field at which the arc struck was very much higher than the calculated \'alues of the third column of Table I, and was not significantly different from the striking field for inactive surfaces. In the fourth experiment, the striking field was measured between electrodes of solid carbon. One of these was mounted upon a cantilever bar in such a way that it could be moved through extremely small meas- ured distances by pushing on the end of the cantilever bar using a mi- crometer screw (Reference 4, page 33). The zero point was found by touching the contacts through a high resistance galvanometer circuit; then the contacts were separated and the striking distance found after applying the voltage. Measurements made in this way by M. M. Atalla (Reference 11, Table I) have given, for the striking field for carbon elec- * A correct measure of striking distance is obtained only when the arc energy is sufficient to burn up the carbon particles completely. Xo appreciable mound of metal is thrown up to falsify the distance measurement, because the arcs are of the cathode type, see Section 2.4(a). ACTIVATION OF ELECTRICAL CONTACTS BY ORGANIC VAPORS 783 trodes, 2.4 X 10*^ volts/cm, and our unpublished measurements agree with this. The striking field for carbon surfaces is thus only a little less than that found for cathode arcs at clean metal surfaces (Reference 4, Fig. 8), and very different from the field at which arcs strike between active surfaces.* In another experiment, tests were carried out upon carbon particles in the 4 to 5 X lO"** cm range of diameters, deposited sparsely upon a palladium surface as before. A careful comparison was made of the elec- trode separations at which an arc struck at 50 volts and at 250 volts. At the higher ^'oltag■e, the distance was greater than at the lower voltage by the factor of only l.o, offering confirmation that the isolated carbon particles act chiefly as chunks of material, partially closing the electrode gap. The one Avay in which the carbon that produces activation differs from other carbon, and in particular from small ca^^bon particles dusted sparsely upon a smooth metal surface, is in the very large number of its particles and in its state of subdivision. This gives an eminently plausible clue to the great electrode separation at which breakdown occurs between active surfaces. According to this model, breakdown occurs at a great separation between active surfaces because, at the electric field corresponding to this separation, electrostatic forces become sufficient to cause motion of small particles which decreases the separa- * In measuring the striking field at carbon surfaces for low voltages by the oscilloscopic method, a value of the order of 0.6 X 10" volts/cm was found earlier (Reference 6, Table I). This result was certainly in error, because of burning of carbon in the arc, so that the separation of the electrodes when the arc ended was greater than it was at the arc initiation. To check this explanation of the earlier incorrect result, an experiment was carried out in which the time to closure for carbon electrodes was measured as a function of the energy in the arc. In successive tests, a number of different capaci- tors, each charged to 50 volts, were discharged on the closure of carbon electrodes. The time to closure was foiuid to increase progressively with capacitance for the values 10^, 10', 10' and 10^ /ifii. Carrying out the measurements man\' times and taking average values, it was found that the time to closure increased linearly with the cube root of the capacitance. This suggests strongly that a hole was being burned in one of the electrodes and the increased time to closure was just the time for one electrode to move the depth of the hole. A quantitative value for the volume of the hole can be obtained from the data, on the basis of an as- sumed hole shape. In earlier work (Reference 9, page 1088), a pit on a metal elec- trode was assumed to be a spherical segment with the depth equal to one-half of the pit radius. Making the same assumption for the hypothetical hole in the present tests, and assinuing an electrode velocity on closure of 30 cm/sec, it turns out that the relationship between volume of the hole and energy of the arc is V = 4.5 X 10^'2 emVefg- The agreement of this resvdt with that for the erosion of the metal anode in an anode arc (Reference 9, page 1088), is remarkable and must be largely fortuitous. The agreement does, nevertheless, make almost cer- tain that burning of one of the electrodes (the cathode, as we know from other work) is the reason for the oscilloscopic method giving incorrect values for the electrode separation at which an arc strikes l)et\veen carbon elect roiies (Refer- ence 6, Tatile I). 784 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 tion. The experimentally observed field of O.G X 10^ volts/cm is the field at which this motion becomes appreciable lor the very small sooty particles. With the start of motion of this sort the field is increased, and further motion is assured making the situation imstable. The gap is greath^ decreased in length before electrical breakdown takes place, and the field at electrical breakdown is probably as high as it is at any carbon surface. 2.2 Arc Voltage At the beginning of an active arc, at least one carbon particle is always exploded by the arc current, but only when the surface is very heavily carbonized is an enhanced arc voltage observed. Fig. 4. It must not be thought that the higher arc voltage occasionally found at the beginning of an arc is to be attributed directly to the presence of carbon vapor in the arc during its ear^ stages, because carbon does not have an excep- tionally high ionizatioii potential. P. Kisliuk has showii'^ that, in a field emission short arc, the arc voltage should be just slightly larger than the sum of the ionization potential of the metal of the electrodes and of its thermionic work function. Now this result holds c^uite well for a num- ber of different metal arcs, but does not hold at all for carbon. The short carbon arc is apparently of a different type, and has no well defined arc voltage. On the other hand, although carbon, unlike the noble metals, gives out thermionic electrons copiously long before it is hot enough to vaporize, a true thermionic arc cannot have the enormous current densi- ties that occur in short arcs. (It does not seem impossible that thermi- onic emission may help to maintain an arc when the current is lower near its end.) The high arc voltage at the beginning and end of an active arc between heavily carbonized surfaces may be due to a dearth of positive ions, requiring a higher applied field to maintain the field emission. In any case, it is like the higher arc voltage of carbon which w^e do not under- stand. When the higher arc voltage is not detected, the vaporization of metal must be profuse, and only when vaporization is reduced, as it is when the current is very small near the beginning and end of an arc at the discharge of a capacitor into an inductive circuit, is the higher arc voltage observed. On rare occasions heavily carbonized surfaces show a suddenly enhanced arc voltage for a short interval near the middle of an arc. That this should occur very much less often than at the beginning or end of an arc is understandable. The observation that the arc \'oltage sometimes becomes high near the end of an arc suggests strongly that an active arc is moving con- tinually during its life. Only when the current is insufficient to vaporize carbon and underlying metal freely, and thus to maintain the large ion I ACTIVATION OF ELECTRICAL CONTACTS BY ORGANIC VAPORS 785 density necessary for the low voltage field emission arc, does one observe the high and erratic arc voltage characteristic of carbon. 2.3 Minimum Arc Current Values of minimum arc current for carbon electrodes have already been published. They are of the order of 0.02 to 0.06 ampere and agree fairl}^ well with measurements of minimum arc current for very active metal contacts (Reference 2, Table V) . The very low value of the mini- mum arc current for carbon, either in solid form or dispensed upon the surfaces of active contacts, is related to the low electrical and thermal conductivities of carbon. These low conductivities permit explosion of carbon particles on the cathode by currents too small to vaporize any metal. It has already been pointed out that it is this very low value of minimum arc current which accounts for the greatly enhanced energy that is dissipated at active relay contacts. From the low value of minimum arc current for active surfaces, one concludes that near its end an active arc is always located at a fresh point on the electrode surfaces, one from which carbon was not burned off earlier in the life of the arc. It had already been concluded from oc- casional high values of arc voltage near the end of an active arc that this is sometimes true, but the minimum arc current values extend this earlier conclusion to indicate that it is always so. An active arc cannot remain in a fixed position as does an inactive anode arc (For example, Reference 4, Fig. 1). The implication is thus suggested that any arc between active palladium contacts is a cathode arc. Further presumptive evidence for this is, of course, furnished by the very much greater elec- trode separation in the case of active arcs; it is well known'^ that large distances favor cathode arcs, because at great distances the anode cannot be efficiently heated by electron bombardment. The interpretation of minimum arc current of active cathode arcs to which we have been led can be written down in words, but we have not succeeded in any quantitative formulation. It is well known that every cathode arc is made up of a great number of small arcs moving continu- ally over the electrode surfaces and exploding one point, or one particle after another on the cathode.^' * In the case of an active arc, the end comes when the current gets so low that it will no longer explode a car- bon particle, or when no suitable particles are available.* The much * This is a necessary criterion for the end of an active arc only in the case of very short arcs. For electrodes that are being pulled apart to break a current larger than the minimum arc current, an arc will, of course, finally fail because of the great electrode separation, even though the current is al)ove the minimum arc current, as in the final failure of the arc in the oscilloscope trace of Fig. 1(b). For inactive anode arcs the minimum arc current arises in a quite different waj' and has been interpreted in fairly satisfactory quantitative fashion. '^ 786 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 higher minimum arc currents for cathode arcs at clean surfaces is attrib- uted to the higher thermal and electrical conductivities of metals and to the absence of loose material making poor contact with the surface. This picture is supported by the observation that metal contacts are made temporarily active by almost any kind of loose surface particles of very small size (Reference 2, Page 961). 2.4 Erosion 2.Jf{a) Palladium and Platinum. Further evidence that an active arc at palladium or platinum surfaces is always a cathode arc is furnished by the fact that the cathode loses much more metal in an active palladium arc than does the anode. (See also Reference 4, Table I). The direct way of proving that an active arc at palladium or platinum surfaces is a cathode arc would, of course, be microscopic examination of the contact surfaces after a single arc. This is not practicable because surfaces become active only after repeated arcs, but one can do what is apparently quite equivalent by looking at the damage done by a single arc to surfaces on which small carbon particles have been dusted. Ex- periments by Haworth do indeed prove that arcs at such surfaces are cathode arcs, even at the Ioav striking potential of 50 volts, and when the maximum diameter of the carbon particle is only 1 X 10~^ cm. Fig. 7(b) is typical of many examinations by Haworth of palladium cathodes after a single arc at surfaces upon which carbon particles had been de- posited. The striking potential was 50 volts and the capacitance that was discharged was C = 10~^ /, so that the energy C{Vo — v)v was 50 ergs. For comparison, photographs are reproduced in Figs. 7(a) and .if. ^ ^ .\^ .*»•- •»■ ' -*^ ■ '^'*i*^'^ ^J\ ■ W^ ^ -ei 1 (c) ^ *" 1 1 : Fig. 7 — Photomicrographs of palladium cathode surfaces after single cathode arcs. The photograph of (b) was obtained after a 50 erg arc with 50 volt striking potential at a surface upon which carbon particles has been deposited. This sort of cathode damage was observed for all of the different sizes of carbon particles which were tested, even for the smallest having diameters of onlj^ 10"'* cm. The comparison photographs (a) and (c) represent the damage done respectivelj' by 40 erg and 80 erg arcs to palladium surfaces without carbon particles, each arc at the striking potential of 400 volts. ACTIVATION OF ELECTRICAL CONTACTS BY ORGANIC VAPORS 787 7(c) which show clean palladium cathodes after constant current cathode arcs of 4 amperes lasting, respectively, for 0.072 microsecond and for 0.14 microsecond. The striking potential in each of these arcs was 400 volts, the total arc energy being 40 ergs and 80 ergs. The three photo- graphs of Figs. 7(a), 7(b) and 7(c) represent then the markings made on the cathode by arcs of 40, 50 and 80 ergs respectively. The voltage of 400 was chosen for the two comparison photographs of Figs. 7(a) and 7(c) because this is above the minimum air breakdown potential, and arcs on closure at striking potentials above this value are known to be always cathode arcs (Reference 4, Fig. 4). Cathode markings such as those of Fig. 7(b) are occasionally pro- duced by arcs at 50 volts on relatively clean palladium surfaces. In gen- eral, however, an arc at this low striking potential between clean surfaces is an anode arc, leaving a single well defined pit on the anode, and on the cathode, a single roughened area with considerable metal spattered over from the anode (Reference 9, Fig. 6). While a cathode arc, making on the cathode the type of markings shown in Fig. 7, is rather rare between clean palladium surfaces at a striking voltage as low as 50 (Reference 4, Fig. 4) it is the usual kind of arc between surfaces upon which carbon particles have been dusted, and by implication, it is the sort of arc that occurs between active surfaces. That this arc should cause loss of metal from the cathode is clear from the photographs of Fig. 7, and from the fact that the damage done to the anode sometimes cannot be detected and is always rather sUght.*^" Between clean surfaces, this sort of arc occurs more frequently at higher striking voltages, and invariably on closure when the potential is above the minimum breakdown potential for air. It is the greater striking distance that favors the cathode type of arc, and for active arcs also it is just this enhanced electrode separa- tion, resulting from carbon particles, which can be thought of as the reason for the arc being of this type. There is obviously a critical distance above which arcs are of the cathode type, and for palladium electrodes this critical distance is less than 1 X lO""* cm. Earlier experiments can be used to define this critical distance better. From the data of Fig. 8 of Reference 4 it appears that this distance for palladium is about 0.5 X 10-'^ cm. Markings made on the cathode by a single arc between active pal- ladium surfaces are doubtless not easily distinguishable from those re- sulting from a single arc that has been constrained to be of the cathode tj^pe only by a high striking potential and the resulting great electrode separation. Nevertheless, when many times repeated, the over-all results * See the footnote relating to Fig. 3, see page 776. 788 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 of cathode arcs between active surfaces, and of cathode arcs between inactive surfaces, are markedly different, as has been pointed out eadier. The fact that erosion by inactive, or clean-surface, arcs takes the form of a mound on one electrode and a crater in the other means simply that successive arcs tend to occur at the same place on the electrode surfaces. This is because each arc must occur where the electric field between approaching electrodes is highest, and the roughening from one arc will be the site of the highest field before the next discharge occurs. With carbon particles on the surface, the situation is different. In the case of active cathode arcs, the electric field between approaching electrodes is highest at a point where a group of carbon particles, perhaps pulled up by electrostatic forces, closes a large part of the electrode gap, and an arc must necessarily strike at such carbon particles. In the ac- tivating process, carbon is always being formed by an arc, but only at its periphery; at the hottest parts of the arc, carbon which was formed earlier, is completely removed. Not only does each arc move during its lifetime, continually searching out new carbon which was formed earlier, but a later arc will not strike at a point from which carbon was just cleaned by an earlier arc. This restless movement from point to point results finally in erosion that spreads over the surface in a way which is likely to be statistically uniform. 24ib) Silver and Gold. Although the character of the erosion at silver (and gold) surfaces, and also its magnitude, are drastically altered by activation. Section 1.4(b), the "direction" of the erosion is still in most cases that characteristic of anode arcs. The predominant loss of metal on closure is usually from the anode for active silver electrodes at voltages too low for air breakdown, just as it is for inactive silver electrodes at low striking voltages. This is in marked contrast to the behavior of pal- ladium surfaces when they become active ; for active palladium surfaces, loss of metal is always chiefly from the cathode. The behavior of silver leads naturally to the hypothesis that even when the surfaces are active arcs at low striking voltages are anode arcs, as they are when the surfaces are inactive. This hypothesis has been subjected to test by F. E. Ha worth by the same method used in the case of palladium surfaces. Small carbon parti- cles were dusted on a polished silver surface, and the surface was ex- amined microscopically after it had been subjected to a single arc under the circuit conditions used in similar tests at palladium surfaces. When the maximum particle diameter was 5 X 10~^ cm, it was found from the microscopic examination that all arcs were of the cathode tj^pe (see, for example, Fig. 7), but when the maximum diameter was 2.5 X 10"'* ACTIVATION OF ELECTRICAL CONTACTS BY ORGANIC VAPORS 789 cm all arcs were of the anode type with the characteristic pit on the anode and a roughened spatter of metal on the cathode. It is clear from these tests that active arcs at silver surfaces are of the anode type if the layer of carbonaceous material responsible for activation is not heavy enough to permit an arc to strike at a separation greater than 2.5 X 10~^ cm, but that they are of the cathode type when the layer is sufficiently thick to permit arcs at 5 X lO""* cm. The electrode separation at which an arc takes place determines the character of the arc* The critical distance for silver surfaces lies between 2.5 and 5 X 10~^ cm. Erosion at active silver surfaces on closure must be predominantly from the anode unless the layer of activating carbonaceous material is so heavy that arcs strike when the electrode separation is greater than 2.5 X 10~^ cm. After long continued operation at very high pressures of activating vapor it is sometimes, but not always, found that arcs on closure result in erosion that is chiefly from the cathode. The conclusion drawn from these measurements is that the striking distance at active surfaces on closure at low voltages can sometimes, with considerable difficulty, be made greater than 2.5 X 10~'* cm. Unless great pains are taken to keep surfaces very heavily carbonized, the striking distance on closure at active surfaces at low voltages is of the order of 2.5 X 10~^ cm or less. On closure at voltages that give air breakdown, the erosion of silver is predominantly from the cathode whether the surfaces are active or inactive, because the minimum distance for air breakdown (15 X 10~* cm) is much above the critical distance for silver. On breaking active silver contacts in an inductive circuit, erosion is chiefly from the anode unless the arc lasts long enough for the electrode separation to exceed the critical distance of 3 or 4 X lO""* cm. During the time an arc persists at distances greater than this, the loss is pre- dominantly from the cathode. For velocities typical of a U-type relay, the critical distance may be reached in 10 or 20 microseconds, and equal erosion may be attained in a time of the order of 40 microseconds. If the partial pressure of activating vapor is very high and the surfaces unusually heavily carbonized, much of the eroded metal will be lost. Under more usual conditions of lower vapor pressures, most of the eroded metal is transferred to the opposite electrode. Thus there may be a criti- cal arc duration for which the erosion of each silver electrode is nearly * Similar tests were carried out upon polished gold surfaces upon which sparse layers of carbon particles had been dusted. For particles of maximum diameter 2.5 X 10-^ cm all arcs were found by microscopic examination of the electrodes to be anode arcs, and for particles in the range of diameters from 4 to 5 X 10~* cm all arcs were found to be of the cathode type. These results are identical with those found for silver. 790 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 zero, and for an arc lasting longer than this time, there may be cathode loss and actual net gain by the anode. No such balancing effect is possible for palladium. 2.4{c) Anode Arcs and Cathode Arcs. The model of an active cathode arc to which we have been led seems fairly clear and rather well estab- lished, but the model of an active anode arc is more poorly defined. From electron micrographs of the damage done to the cathode by an arc of the cathode type (Reference 4, Fig. 3), it is kno\Mi that an arc of this type is intermittent, striking over and over again. In an active arc of the cathode type, a carbon particle on the cathode is blo^vn up each time the arc strikes, but always there is metal vaporized from the cathode at the site of the particle and the amount of vaporized cathode metal is greater than the amount of vaporized carbon, so that the arc is an arc in metal vapor. We know less of an active anode arc, and it may well be that some experiments described above seem to imply a model which is not con- sistent with other observations. The facts that we know are, that at a lightly carbonized silver surface an arc strikes at an electrode separation much greater than the separation at which it would strike if there were no surface carbon, that the resulting arc produces loss of metal pre- dominantly from the anode, and finally that the minimum arc current is very low. The arc is a true anode arc by our implied definition of such an arc, yet it is certainly an active arc. When the arc current is high, a crater is being produced on the anode as in the case of an inactive anode arc, and also in the case of an active anode arc at a surface on which a few carbon particles of diameters not greater than 2.5 X 10~* cm have been dusted. When the current becomes too low, or is too long sustained, one presumes that the arc is extinguished as in the case of inactive anode arcs." It may then restrike at another carbon particle. One speculates that an anode arc is intermittent when the arc current is very low, being initiated over and over again as are cathode arcs throughout their lives. A carbon particle is exploded repeatedly on the cathode. Yet, because the separation is less ^than the critical distance, at each re-ignition of the arc, metal vapor is derived from the anode rather than from the cathode, and possibly the over-all anode erosion results in a single anode pit produced when the current was sufficient 1}^ high, plus an array of very small anode pits formed while the current was small and intermit- tent. This model must be regarded as a plausible speculation without support in direct observation. The existence of the active anode arc is well established although the course of such an arc is speculative. Some insight into the reason for the existence of a critical electrode ACTIVATION OF ELECTRICAL CONTACTS BY ORGANIC VAPORS 791 separation, determining whether an arc is of the anode type or of the cathode type, can be obtained from a simpHfied picture of the evapora- tion of metal in an arc. One assumes a field emission arc just being estab- lished between a cathode point and the anode surface, the initial ions being supplied by oxygen and nitrogen of the air with as yet no metal vaporization. The electrons from the point are assumed to travel in straight lines to the anode and cover uniformly an area 7r(L tan dY where L is the electrode separation. If i is the total electron current and v the arc voltage, the power density on the anode is iv/iriL tan oy, decreasing with increasing separation. A lower limit for the power put into the cathode point is (p/d)i~ where d is the diameter of the point and p the resistivity of the cathode metal. Whether the anode begins to vaporize before the cathode, or vice versa, is determined in some way by the ratio of these quantities BUp/d, where parameters unimportant for the present discussion are grouped together in B. For Up/d greater than some critical value, we shall have cathode evaporation and an ensuing cathode arc, but for Up/d less than this value, the anode will begin to evaporate first with a resulting anode arc. The resistivity that probably counts is the resistivity at the melting point. At the temperature of melting, the resistivity of palladium is nine times greater than that of silver. Thus one can expect from this simple model that the critical distance which determines whether an arc is of the cathode or anode type will be three times greater for silver than for palladium. If a silver point is less sharp than a palladium point, d greater for silver than for palladium, as it may be because of the well knowii propert}^ of silver atoms to migrate at room temperature, the factor will be greater than this value of three. Now we have the experimental esti- mate of 0.5 X 10~^ cm for the critical distance for palladium. This simple theory predicts that the critical distance for silver shall be greater than this by a factor of three, or perhaps more. The experimental critical distance for silver is between 2.5 and 5 X 10~* cm. Quantitative measures of the erosion of contacts of palladium and of silver, which were given in Section 1 .4, are collected in Table II for ready reference. From additional experiments, not reported in Section 1.4, it is kno^^^l that these values of transfer apply approximately for potentials both above and below the minimum breakdown potential for air. Not all types of arcs occur, however, for both palladium and silver at potentials above and below the minimum breakdown potential. At potentials that give air breakdo^^^l, all arcs on closure are of the cathode type for both metals whether active or inactive. At potentials that do not give air 792 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 Table II — Loss or Gain of Metal from Arcing for Palladium or Silver (in units of 10-" cc per erg) Inactive Arcs Anode Tj-pe . . . Cathode Type. Active Arcs Anode Type . . . Cathode Type. Cathode 4 gain 1 loss (loss) 4 losst Anode 4 loss 1 gain 10 loss* (loss) mound and pit mound and pit smooth erosion smooth erosion * This high figure refers to arcs on closure at very heavily carbonized surfaces; for lightly carbonized silver surfaces the anode loss is less and most of the metal is transferred to the cathode. t This figure refers to arcs at closure of palladium surfaces. The rate of cathode loss at break of palladium surfaces is significantly less, as pointed out in Section 1.4(a) ; and in cathode arcs at active silver surfaces the rate of loss is still less. Table III — • Occurrence of Different Types of Arcs Below Air Breakdown Air Breakdown Inactive Arcs Anode Type Cathode Type Active Arcs Anode Type Cathode Tvpe Palladium, Silver Palladium Only Silver Only Palladium, Silver No* Palladium, Silver No* Palladium, Silver * This applies to arcs at closure. Between separating electrodes, air break- down often occurs when the electrodes are too close together for air break- down over the shortest path. Under such conditions, arcs between silver surfaces, which are initiated by air breakdown, can become anode arcs, and the transfer resulting from such arcs gives dominant anode erosion. breakdown, all inactive arcs at silver surfaces are of the anode type, and active arcs of the anode type occur for silver only. These facts are tabu- lated for reference in Table III. All of them are at once predictable from the values of the critical distances for palladiimi and silver, and from knowledge of the way in which breakdown distance is changed by activa- tion.* * The difference between the transfer behavior of palladium and silver elec- trodes in the active condition suggested to R. H. Gumle}- that the damaging ef- fects of activation can be greatly reduced by constructing a relay with negative contacts of silver and positive contacts of palladium. He tried out this idea and found it to be effective. In the absence of activating vapor, a relay in which the negative contacts are silver and the positive contacts palladium has no merit over a relaj^ in which all contacts are palladium, but when vapor is present, the erosion can, under some circumstances, be much reduced by replacing the nega- tive palladium contacts by silver contacts. ACTIVATIOX OF ELECTRICAL CONTACTS BY ORGANIC VAPORS 793 The sort of erosion produced by the different types of ares is shown in the somewhat conventionahzed sketches of Fig. 8. These sketches represent cross-sections of the square mating areas (about 1.3 mm on a side) of heavj^ type U relay palladium contacts. The contact contours are drawni to scale after the metal transfer resulting from repeated arcs with a total energy of 10^ ergs, using the values of Table II to convert this energy into volumes of metal. The mounds and pits produced by inactive anode arcs and by inactive cathode arcs are assumed to be spherical segments, each having a height equal to half its radius. The smooth erosion resulting from active arcs would have depths which do not show up at all on the scale of this figure. For each electrode in each of the four cases, the erosion is less than 2 per cent of the total volume of the metal of the contact, and represents a fairly early stage in the ex- pected contact life. The electrode separations at which arcs occur corre- spond respectively to fields of 8 X 10^ 4 X 10^ and 0.5 X 10^ volts/cm. The striking voltage is assumed to be 50 and the separations are drawn SEPARATION SCALE CATHODE S INACTIVE ANODE ARCS ^ANODE CATHODES INACTIVE CATHODE ARCS ; ANODE ACTIVE ARCS Fig. 8 — Erosion produced by anode arcs at clean surfaces, bj^ inactive cathode arcs and by active arcs of either type, the total energy in each case being 10^ ergs. The electrode separations at which these arcs strike correspond to 50 volts and are represented here on a greatly expanded scale. 794 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 to a scale 200 times greater than the scale of the electrodes. For poten- tials that give air breakdown, the scale of separation would be changed by large factors. The sketches of Fig. 8 are of assistance in understanding some of the qualitative erosion differences observed in the four types of arcs (Ta- ble II). All of the metal lost from one of the electrodes in an inactive arc of either type comes from the surface of a pit, and from the figure it seems clear that all of it must obviously be intercepted by the other electrode because there is no way for it to escape. This is true even for the case of air breakdo\vn where the electrode separation is much greater {-^Id X 10~^ cm). But for active arcs some of the metal coming from each electrode is permanently lost and not transferred to the other side, even though the separation is much less than it is for the case of air breakdown. The permanent loss of metal in the case of active arcs is due to the presence of carbon. When there is carbon on the surfaces, the metal simply does not stick. Chemical analyses have been made of the black powder produced by active cathode arcs at palladium surfaces, and these analyses show palladium metal as well as carbon. The pal- ladium metal lost from the electrodes turns up in this black powder rather than at new locations on the electrodes. At palladium surfaces, the net loss amounts to most of the eroded metal, but at silver surfaces, most of the metal is transferred. This differ- ence is related to the amount of carbon left on the surfaces. Carbon is found much more abundantly on palladium than on silver, which ac- counts for the failure of eroded metal to stick to palladium. The greater net carbon production on palladium is due to the low efficiency of cathode arcs (at active palladium surfaces) in burning carbon; the anode arcs, which occur in general at active silver surfaces, are more effective in burning off carbon. It is to be presumed that the amount of organic vapor decomposed per unit of energy at a silver surface is not so very much less than that decomposed at a palladium surface, even though the net carbon left on the surface is tremendously less in the case of silver. 3. RECAPITULATION We are ready now to state briefly some of the conclusions about active arcs which have been developed above. All of the observations refer to contacts of palladium or of silver. Less extensive tests upon platinum and upon gold have indicated that platinum behaves the same as pal- ladium, and gold the same as silver. An active arc is an arc that strikes between one electrode and car- ACTIVATION OF ELECTRICAL CONTACTS BY ORGANIC VAPORS 795 bonaceous material lying upon the other. If one calculates striking field by dividing the potential by the separation between the metal electrodes, a very low value is obtained, but this is the field at which electrostatic forces cause movement of carbon particles to decrease the separation; the true field at which the arc finally strikes between carbonaceous mate- rial and the opposing electrode is not significantly lower than the striking field for arcs at clean surfaces. Some or all of the local carbonaceous material is burned up by the arc, and metal vaporized from one of the electrodes is soon fed into the arc so that for most of its life the ions of the arc are metal ions supplied by atoms from one or the other of the electrodes. This is true for even the most heavily carbonized electrodes. There is a critical electrode separation, characteristic of the metal of the electrodes, which determines whether the arc is an anode type of arc with metal supplied by the anode or an arc of the cathode type with metal supplied by the cathode. If the separation is greater than this critical value the arc is a cathode arc, and less than this value an anode arc. This critical distance is about 0.5 X 10"'* cm for palladium electrodes and of the order of 3 or 4 X 10~* cm for electrodes of silver. The ratio of these distances is somewhat greater than the ratio of the square roots of the electrical conductivities of the metals at their melting points. The critical distance for palladium is so small that all arcs at active palladium surfaces are cathode arcs. For silver, on the other hand, the critical dis- tance is so large that most arcs at low voltages at silver surfaces are anode arcs. In any practical application of silver electrodes, the car- bonaceous material formed is rarely or never in a sufficiently thick layer to result in cathode arcs for closure at low voltages. In the case of sepa- rating silver electrodes, an active arc may last until the electrode separa- tion is beyond the critical distance for silver; the erosion occurring after this distance is reached is predominantly from the cathode, and the larger net loss may, on occasion, be from the cathode. The erosion resulting from repeated arcing at active surfaces is differ- ent in character from that produced by inactive arcs. Inactive arcs give rise to a crater on one electrode and a matching mound on the other, with most of the metal from the crater transferred to the mound. Active arcs, on the other hand, produce smooth erosion without craters and mounds, often with considerable net loss of metal which appears mixed with carbon as a black powder. This smooth erosion is accounted for by the striking of each new arc on carbon formed by preceding arcs, to- gether with the burning off of carbon at the center of each arc and the formation of new carbon around its periphery. 796 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 Part II — Activating Carbon 4. COMPOSITION OF ACTIVATING POWDER AND RATE OF PRODUCTION Experiments have been carried out designed to discover the chemical composition of the carbonaceous material responsible for activation, how much is made per unit of energy in an arc, and where it is made. Now it has been pointed out above that the reason for the uniform erosion in an active arc is the burning off of this black powder by arcs and the consequent continual wandering of successive arcs always to neighboring spots from which the powder has not been burned. This burning off of black powder makes quantitative measurements in air of its rate of formation quite impractical. Activation in vacuum avoids the destruc- tion by burning, and makes possible direct measures of rate of forma- tion; in these tests, the chemical composition of the powder can be found also. All of the quantitative studies of activation in vacuum were made by P. Kisliuk, but the results have not been previously pu))lished. In Kisliuk's experiments two electrodes, which were of platinum, were mounted in a glass chamber so they could be operated by the magnetic field of a coil placed outside the chamber, in the manner of a dry reed switch. The electric circuit was arranged to discharge on each closure a capacitor charged to a fixed voltage, with no current flowing in the cir- cuit as the platinum contacts are separated. Air was pumped out and the contacts operated in benzene vapor at a constant rate, discharging the capacitor a convenient number of times per minute. Every experi- ment consisted of measuring the pressure in the system, from which was deduced the rate of disappearance of benzene and the rate of evolu- tion of hydrogen resulting from its decomposition, hydrogen being dis- tinguished from benzene by freezing out the latter in liquid nitrogen. The pressures were measured by an RCA thermocouple gauge (1946) which was sho^^^^ in control tests not to produce benzene decomposition. The benzene, which had been distilled repeatedly to remove water vapor, was used at initial pressures not to exceed 10~- mm Hg determined by a dry ice-acetone bath. The experimental arrangement is sho^Mi in Fig. 9. 4.1 Composition In the first experiments with this system it was found, as had been expected, that with continued operation of the contacts in benzene vapor, the pressure rose steadily, although benzene continued to disappear. The pressure changes corresponded to the evolution of 3.2 ± 0.6 mole- cules of H2 for each vanishing molecule of benzene, agreeing well with \ A ACTIVATIOX OF ELECTRICAL COXTACTS BY ORGANIC VAPORS 797 the theoretical value of 3 for complete decomposition of benzene into carbon and hydrogen. The conclusion from this experiment is that the organic material in the black activating powder is just carbon. The pre- cision allows one to say that, if there is any hydrogen at all left in the black powder, it does not exceed 2 hydrogen atoms for every 15 carbon atoms. 4.2 Rate of Production In experiments in which the energy in individual arcs was varied, by using different capacitors in the range from 610 fxixi to -10,000 txjii and by using the two potentials 58 volts and 232 volts, it was found that a particular arc energy gives the same carbon formation per erg whether the striking voltage is 232 or 58, from which one deduces that formation of carbon depends upon energy rather than upon capacitance or voltage separately. The amount of carbon formed per individual arc increases with the energy of the arc but not so fast as linearly. The experimental values M of amount of carbon formed can be related to arc energy E by the empirical formula M = KE'^'^, over the range studied from 5 ergs to 1,250 ergs. A tentative explanation of this f power relation is given in the next section. Starting with clean electrodes and measuring the total amount of carbon formed as a function of number of arcs, it was found that the rate of production of carbon is initially low but increases with time, soon TO PUMPS RCA 1946 >- THERMOCOUPLE GAUGE Pt BUTTONS IN / MAGNETIC REEDS VOLUME 115 CC DRY ICE- ACETONE BATH COLD TRAP FOR FREEZING BENZENE DURING MEASUREMENT OF Hj PRESSURE Fig. 9 — Diagram of apparatus used by P. Kisliuk in quantitative measure- ments of the decomposition of benzene vapor at arcing contacts. 798 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 becoming constant. One such set of measurements is plotted as Fig. 10. In this experiment the striking voltage was 232 and the energy in each arc 1,250 ergs. The final slope of the curve of Fig. 10 corresponds to the production of 4.5 X lO"^^ gm of carbon per arc — 3.5 X 10~^^ gm/erg, 1.8 X 10^ atoms/erg — which is 0.04 carbon atom for every electron flowing in the arc, or the decomposition of 3.7 X 10^^ benzene molecules per arc, 3 X 10^ molecules per erg, or 70 X 10"'* molecule per electron. The lower slope, before the break in the curve, represents the decompo- sition of 1.1 X 10^^ molecules of benzene per arc, or the production of 5 X 10^ carbon atoms per erg. From continuous oscilloscopic observations it was found that the contacts were inactive up to the point where the slope of the curve in- creased. Here they were slightly active, and beyond this point they were fully active, exhibiting the usual apparent low striking field and low minimum arc current. The amount of carbon required to make the con- tacts fully active was about 5 X 10~^ gm (2.5 X 10^^ atoms) which, if it were in a single spherical speck, would have a diameter of 3.5 X 10~* cm. Such a speck can be seen quite easily with the naked eye, although an actual deposit of this volume probably could not be seen without a microscope because of its dispersed state. 5. SURFACE ADSORPTION 5.1 Benzene Molecules on Contact Surfaces In an early experiment, the rate of formation of carbon (from meas- ured rate of evolution of H2) had been found to be independent of ben- zene pressure down to the lowest pressure tested, which was of the order of 10~^ mm Hg. For this reason it was unnecessary to mention absolute pressures in describing the above tests. This lack of dependence on pres- sure suggests strongly that benzene had been adsorbed on the electrode surfaces and decomposed there, rather than in the space between the electrodes, and that the lowest pressure tested was sufficiently high to keep the surfaces completely covered. This tentative conclusion is con- firmed by other considerations given below. At the pressure of 10~^ mm Hg and an electrode separation of 10~^ cm, one calculates that only one electron in 3 X 10* can collide with a benzene molecule in the space between the electrodes in the experiment of Fig. 10. The discrepancy between the measured decomposition (70 X 10~* benzene molecule per electron) and the possible frequency of col- lision (0.3 X 10~*) is proof that most of the carbon responsible for activa- tion comes from benzene adsorbed on electrode surfaces rather than from molecules in the space between them. ACTIVATION OF ELECTRICAL CONTACTS BY ORGANIC VAPORS 799 One gets some insight into the adsorbed films responsible for activa- tion from estimates of the cross-section of an arc and of the amount of benzene adsorbed in a monolayer over an area of this size. A reasonable estimate of the number of molecules in a monolayer of benzene is 7 X 10^^ cm~2 (Ref, 16), or 14 X 10^^ cm"^ taking into account the two electrodes. Estimates of cross-sectional size have been published for ! anode arcs, but for cathode arcs the areas are quite different. Since all I of the arcs after a surface has become active are certainly cathode arcs, ! our first concern is with the cross-sectional areas of cathode arcs. It has been observed that the over-all area of the cathode markings made by inactive cathode arcs increases somewhat less rapidly than linearly with total arc energy, and seems to be independent of arc current and arc duration except as they influence the total energy. In one series of ex- periments, the areas observed (Ref. 10) for low energy arcs corresponded to somewhat less than 10^ ergs/cm-, and to somewhat more than this value for high energy arcs. Assuming for an average value 10^ ergs/cm^, we obtain 1.2 X 10~'* cm^ for the area of the arcs of the curve of Fig. 10.* This area should have adsorbed on it 1.7 X 10" benzene molecules. The observed rate of decomposition is 3.0 X 10^ benzene molecules per erg or 3.7 X 10" molecules per arc. Looking at photographs such as those of Fig. 7, one does not feel at all confident that all of the surface in the over-all area of the arc ever became hot enough to decompose benzene. If all of it did become hot enough, the surface must, on the average, have been covered by 2 layers of molecules, and if all of the surface did not become sufficiently hot, by more than two layers. For lower energy arcs, when the number of benzene molecules decomposed per erg is appreci- ably greater, it is natural to assume that the surface must, on the aver- age, be covered by a still deeper layer of benzene. At least part of the difference between the estimated thicknesses of the layers of benzene molecules for high energy arcs and for low energy arcs can, however, be attributed to the fact that the energy per square centimeter increases with increasing energy, 10^ ergs/cm- being only an average value. The data indicate only that the adsorbed benzene layer is several (greater than 2) molecules thick. The observed expression M = KE'^i^ of the above section, relating amount of carbon formed M to total arc energy E, can be accounted for if, in the particular experiment in which this relation was found, the over-all arc area increased with the f power of the energy. In various tests * One should note that the energy density measurements were made upon clean surface or inactive cathode arcs, but are being applied here to active cathode arcs. Some justification for this is afforded by the fact that the active 50 erg cathode arc of Fig. 7(b) had an over-all area of about 3 X 10~^ cm^ giving for the energy density 1.5 X 10' ergs/cm^. 800 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 it has been noted that area increases less rapidly than linearly with •energy, but it is certain that no universal rule applies in all cases; for example, by restricting the total electrode area, the over-all arc area can be forced to be constant independent of energ3^l° One can conclude only that all of the facts are accounted for by a benzene layer several mole- cules thick on the electrode surfaces with decomposition by each arc of all of the benzene within its over-all area. We are now in a position to consider the much lower rate of decompo- sition of benzene during the initial period before the electrodes became active. In Fig. 10, this lower initial rate is 1.1 X 10^^ molecules per arc. This is somewhat less than the number of molecules calculated to lie in a monolaj^er on the surface covered by an arc. The area used in this cal- culation was that of a cathode arc, but it is well kno\vn that before con- tacts become active a large proportion of the arcs are anode arcs which have smaller areas (Reference 9, page 1088). The estimated area may, however, be about correct because in the case of an anode arc, carbon is decomposed by heat over an area larger than that of the arc itself. Within the precision of the estimates we are able to make, it can be said that for inactive contacts operating in benzene vapor each arc de- composes a single layer of adsorbed molecules of benzene. After the contacts become active, the amount decomposed by each arc is greater and is the equivalent of several layers of molecules. It was surmised long ago that much of the vapor adsorbed on active contacts is held by carbon already on the surface rather than by the surface metal. The increased ylO 16 Q UJ (X. o z O 4 CD a. < LU 03 2 Z y V^ ^ y .<\~ r i^ 5 y^ 10 15 20 25 30 THOUSANDS OF OPERATIONS 35 40 Fig. 10 — Measurements by P. Kisliuk of the amount of carbon formed at arc- ing platinum contacts, each arc 1,250 ergs. The final slope represents the produc- tion of 3.5 X 10~'^ gm of carljon per erg of arc energy, or one benzene molecule decomposed for every 150 electrons flowing in the arc. ACTIVATION OF ELECTRICAL CONTACTS BY ORGANIC VAPORS 801 Table IV — Benzene Decomposition in Active and Inactive Arcs Measurements Carbon required for full activitj' 1 Carbon formed in active arcs 2 Carbon formed in inactive arcs 3 Benzene decomposed in active 4 arcs 1250 erg arcs (232 volts) 15 erg arcs (58 volts) 2.5 X 1015 atoms 1.8 X 10" atoms/erg 5 X 10« atoms/erg 3.0 X 10« molecules/ erg 70 X 10-^ molecule per electron No data 7 X 109 atoms/erg No data 13 X 108 molecules/ erg 300 X 10-^ molecule per electron Calculations Absorbed benzene in a mono- 6 14 X 10'* molecules 14 X 10" molecules layer (Ref. 16) per cm2 per cm^ Benzene molecules struck in 7 0.3 X 10-* molecule 0.03 X 10-* molecule space (Compare lines 5 & 7) per electron at 10"^ per electron at IQ-^ mm Hg mm Hg Active Arcs Arc area at 10^ ergs/cm^ 8 1.2 X 10-" cm2 0.015 X 10-* cm2 Number of molecules in one 9 1.7 X 10" molecules 0.02 X 10" molecules monolayer on arc area Decomposed per arc (from 10 3.7 X lO'i molecules 0.2 X 10" molecules line 4) of benzene of benzene Effective* thickness of adsorbed 11 2.2 molecules 10 molecules layer on basis of 10^ ergs/cm^ Inactive Arcs Arc area 12 <1.2 X 10-* cm2 Number of molecules in one 13 <1.7 X 10" mole- monolayer on arc area cules Decomposed per arc (from 14 1.1 X 10" molecules No data line 3) Thickness of adsorbed layer 15 1 molecule No data * The benzene is probably adsorbed on spongy carbon of much greater true area. adsorption for contacts already active is doubtless due to the greater surface area resulting from the presence of this carbon. Many of the numerical values considered here are collected in Table IV for ready reference. These data refer to arcs at platinum surfaces. It is our present opinion that the amount of carbon formed at silver surfaces in similar experiments would be found to be only slightly smaller per unit of energ}^, although unfortunately no experiments were carried out upon silver. 5.2 Inhibiting Surface Films One concludes from the above experiments that activation bj^ benzene vapor is the result of firm adsorption of benzene molecules on the elec- 802 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 trode surfaces, with heat producing decomposition into carbon and hydrogen rather than evaporation of undamaged molecules. Surface ' films prevent such strong adsorption, and metals with surfaces that are normally covered by oxide films cannot be activated. In some very recent experiments in extremely high vacuum, P. Kis- liuk has found^'' that benzene molecules are strongly adsorbed upon a tungsten surface that is perfectly clean, but if there is on the surface just one single layer of oxygen molecules, benzene molecules are not ad- sorbed. M. M. Atalla has reported (Reference 5, page 1090), on the other hand, that tungsten (and nickel also) can be activated if the pres- sure of air is as low as 10~* mm Hg. It seems probable that arcs at op- erating contacts remove adsorbed oxygen temporarily, and at sufficiently low air pressures this may be replaced in part by organic molecules rather than by oxygen. ^ Even at palladium surfaces, some cleaning by arcs seems to be neces- sary before benzene molecules can be adsorbed. This conclusion is reached in unpublished adsorption experiments carried out by W. S. Boyle upon palladium surfaces in air containing benzene vapor. In this work, two optically flat palladium surfaces are separated by an exceedingly small distance to make an electrical capacitor. With a very sensitive capaci- tance bridge, one can detect the change in capacity that would be produced by the adsorption on the palladium surfaces of even a small fraction of a monolayer of benzene molecules. In experiments carried out with this equipment it was found that benzene molecules are not adsorbed upon a palladium surface in air at atmospheric pressure. To reconcile this conclusion with the well known facts of activation, it seems necessary to conclude that even a palladium surface can adsorb benzene molecules only after it has been partly cleaned by arcing. 5.3 Alloys When a base metal is mixed with a noble metal, the result can be an alloy which is activated less readily by organic vapors than would be the noble metal constituent alone. In the curve of Fig. 11 is plotted the number of operations required under a particular set of standard condi- tions to activate a series of alloys of palladium and nickel. In air, nickel itself cannot be activated at all. The amount of carbon formed from benzene decomposition on the surface of a palladium-nickel alloy is always less than the amount which would be formed under the same conditions upon pure palladium. One does not know whether benzene is held less firmly on the alloy sui'face so that there is more likelihood i ACTIVATION OF ELECTRICAL CONTACTS BY ORGANIC VAPORS 803 106 > < O Q UJ D a UJ cr 10 z o ^' UJ a o a. UJ CD 2 D Z :10= 10* 10 20 30 40 ATOMIC PER CENT OF NICKEL 50 60 Fig. 11 — Resistance to activation of various alloys of nickel and palladium. that a heated molecule will evaporate rather than decompose, or whether there are just fewer sites on the surface which can take molecules. C. ACTIVATION IN AIR Electrical contacts are not so readily activated by organic vapors in the presence of air as they are when air is absent. Air inhibits the acti- vating process in at least three different ways, and sometimes in a fourth way. These are: 1. Covering up the metal surface so that activating molecules cannot be adsorbed upon it until some of it has been cleaned temporarily by arcing. 2. Offering obstruction in the path of organic molecules on their way to an adsorption site on the metal, so that the molecules diffuse slowly through air up to the surface, whereas in the absence of air, an adsorbed film is formed much more quickly at the same pressure of the organic vapor. 804 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 3. Burning off in each arc some of llic carbon formed on the surface- in preceding arcs. 4. Sputtering and lun-ning off carlxjii from the cathode in a glow dis- charge, when such a discharge occurs. The first of the.se effects of air has made itself evident in the experi- ments of Kisliuk, Atalla and Boyle described above. It will not be dis- cussed further. Observations and experiments have been made upon the other three effects of air, and these will be described below. Burning off of carbon in an arc is mentioned first because it can be most nearly sepa- rated from other effects and studied individually. 6.1 Burning of Carbon On a surface uniformly covered by organic molecules, carbon must be burned off on the area covered by an arc, but new carbon can be formed on an annular ring surrounding the arc where the metal tem- perature is lower. As a consequence of this, whereas in the absence of air contacts are activated very much more promptly by high energj^ arcs than by low energy arcs, in air the situation is less simple. The gen- eral result of many experiments is that in air high energy arcs are less efficient in producing activation than are low energy arcs. On the other hand, arcs of extremely low energy are also quite ineffective. There seems to be an optimum arc energy at which contacts can be activated most promptly, w^hich may be of the order of 100 ergs. Activation can be ex- pected to be most prompt when the difference between the area of the arc and the area of the annular ring around the arc is a maximum. The outer edge of this annular ring is the position on the metal surface at which the maximum temperature just reaches the decomposition temperature of adsorbed organic molecules, about 600°C for the case of benzene. If the width of the ring is A and its inner radius R, each arc can be assumed to burn carbon from an area irR'^, and to form new carbon on an area 7r[(7? -f AY — R-]. Now A certainly increases with increasing energy (being zero for zero energy), but on the simplifying assinnption that it is independent of energy, the difference area, which is A = ir[{R + A)'^ - 2R2] (1) will be a maximum for that energy that makes R equal to A. It is in- teresting to find the value R = Ri for a 100 erg arc, which is knoAMi to be very efficient in producing activation, and then to estimate the max- imum temperature reached at the outer edge of the annular ring for A = 7^1 . The simple model predicts that this maximum temperature should be 600°C. When the calculation is carried out in rough fashion, the I ACTIVATIOX OF ELECTRICAL CONTACTS BY ORGAXIC VAPORS 805 temperature is found to ])e of the order of ;)00°C, rather than ()00°C. The correct order of magnitude gives support to the general ideas behind the theory. According to this very simple model, activation takes place most promptly for arcs of 100 ergs energy, and for such arcs the net carbon formed per arc corresponds to the benzene molecules adsorbed on the area 2-kR{^, which is obtained from Ecj. (1) by setting R = A = Ri . In vacuum at the same energy, the carbon formed per arc would come from benzene on the area 4x7?!-. Thus for 100 erg arcs activation will occur almost as quickly in air as in vacuum, but for arcs of greater energy, much more slowly than in vacuum. Qualitative observation has con- firmed this general conclusion. That this picture is, however, over simplified in a fundamental man- ner is clear from the effect of electrode contours upon ease of activation. For flat electrodes, activation is very much more prompt when the sur- faces make good contact over a large area than when misalignment re- sults in contact on a rather small area. Furthermore, flat contacts can often be activated very promptly under conditions for which crossed wires cannot be activated at all. (Reference 8, page 335). In a ciualitative way this is understood, but the inhibiting effect of restricted areas is not amenable to quantitative consideration. This effect makes quite clear that the model of an annular ring about an arc is too idealized to be of much quantitative value. One might expect tliat the burning off of carbon would be greatly influenced by atmospheric conditions, and thus the ease of activation would depend upon such conditions. This is indeed found to be the case in experiments in which the air contains water as well as the activating vapor. In unpublished experiments F. E. Haworth determined the num- ber of operations required to activate contacts under a particular set of standard conditions for a wide range of relative humidity. In the range from 10 to 88 per cent relative humidity, the number of operations to make contacts fully active increased exponentially from 1.4 X 10^ to 1.0 X 10^, and at relative humidities of 95, 98 and 100 per cent, activa- tion was not attained at all. Furthermore the process of activation could be reversed by water vapor, and contacts that had been made fully active in dry air containing an organic vapor were made completely inactive by continued operation in the same vapor after the addition of water. The effect of water in these experiments may have been due to covering the surfaces so thoroughly with water molecules that the activating vapor could not be adsorbed, or to burning carbon by the water gas reac- tion, C -f- H2O -^ CO -j- H2 . The exponential relationship between num- 806 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 1)01' of operations required to make contacts active and relative humidity has no clear interpretation in our present state of knowledge. 6.2 Diffusion of Activating Vapor In Ivisliuk's vacuum experiments the amount of carbon formed and the degree of activation attained was independent of benzene vapor pressure. This is not at all the case when activation is produced by op- erating contacts in air. In fact, one of the earliest observations was a minimum vapor pressure below which contacts could not be activated (Reference 2, Table I). In more careful later tests it was found that the minimum vapor pressure is a function of rate of operation of the con- tacts, the minimum pressure being actually proportional to the rate of operation over a factor of 100 which was the range tested (Reference 8, Fig. 2). Obstruction offered by air supplies the explanation of this rate effect. Activation cannot occur if electrodes are separated between one arc and the next for a time which is short in comparison with the time required to cover the surface with one monolayer of organic molecules. A rough order of magnitude calculation confirms this conclusion. As an approximation, one assumes one dimensional diffusion to an electrode surface from the space in front of it, with all molecules reaching the surface sticking to it. Boundary conditions for the solution of the diffusion equation, dC/dt = Dd-C/dx^, are then: C = Co at t = 0 ioY X > 0 C = 0 at a; = 0 for all values of t The concentration of activating molecules in the space in front of the electrode is then C = Co erf [x/2 (Dt)^'-]. The total number of molecules to have reached the surface at any time ti is, dt = 2Co{D/Ty'W expressed in molecules/cm-, when Co is given in molecules/cm^. We are interested in the value of ^i for which 7W is the number of molecules in a monolayer, and the maximum rate of operation of contacts for ac- tivation to occur can be expected to be comparable with n = i^i = 2Co^ D/Tm'- = 8.1 X 10^^ D(p/mY, (2) where p is the partial pressure of activating vapor in mm Hg. The factor I in n = ^ti appears because diffusion to the surface can occur only when the electrodes are separated, and it is assumed that they are separated for half of the time. The best data we have for testing this relation are represented by ex- ACTIVATION" OF ELECTRICAL CONTACTS BY ORGANIC VAPORS 807 periments upon activation in vapor of the organic compound fluorene.^ According to the observations, the critical rate of operation was found to be proportional to the partial pressure of fiuorene rather than to its square as in (2). This is a discrepancy which must be overlooked in our present state of knowledge. To test (2) for fiuorene at 20°C, we require values of D, the diffusion coefficient of fiuorene in air, p, the partial pressure of fiuorene at 20°C, and m, the number of adsorbed fiuorene molecules per cm- of surface. The value of D == 0.067 cm-/sec. was ob- tained from a linear relation between ID and (molecular weight)^''-, which holds quite well for a number of organic compounds. The value p — 0.0-1 mm Hg is the geometrical mean between 0.23 and 0.007 mm Hg, respectively the vapor pressures of napthalene and anthracene at 20°C. We have estimated m = 3.3 X 10^"* molecules/cm-, which is related to the corresponding number for benzene, 7 X 10^^ in the inverse ratio of the molecular weights. ^^ These numerical values give from (2) n = 0.75 operation/second as the critical rate that vnW just permit one monolayer in the time the contacts are separated. The observed critical rate for activation at 20°C from Fig. 2 of Reference 8 is 3. The agreement is pretty good when the crudeness of the model is considered. 6.3 Sputtering and Burning in a Glow Discharge If both arcs and glow discharges occur when electrical contacts are operated in an atmosphere containing an activating organic vapor, the activation of the contacts resulting from the arcs is inhibited by the occurrence of the glow discharges.* This effect is sometimes very bene- ficial in extending the life of telephone relay contacts. In fact a very simple protective network, consisting only of an inductance of the order of 10"^ henry placed very close to one of the contacts, has been devised which, under some conditions, will increase the contact life by a factor of about 10. Quantitative measurements have been made of this inhibiting action of a glow discharge, and from them it has been concluded that the effect is attributable to sputtering and burning of carbon in the discharge. In making these measurements, a pair of contacts was operated in an at- mosphere containing limonene vapor in such a way that arcs and glow discharges occurred alternately in controlled fashion. A charged capaci- tor was discharged in an arc at each closure. By the use of an auxiliary synchronized relay in series with one of the contacts, the circuit was * It should be pointed out incidentally that a glow discharge in air can also activate silver electrodes. It produces silver nitrite on their surfaces, ^^ and silver electrodes with a layer of nitrite are fully active until the layer is burned off. 808 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 changed periodically so that a glow discharge could be made to occur at each contact break, or at every 6th, 60th, or 600th break. The glow (air- rent was always 0.04 ampere lasting for a time that could be accurately set by means of a synchronized shunt tube. In all of the tests, the energy in each closure arc was 190 ergs. Meas- urements were made at partial pressures of limonene of 0.05 and 1 mm Hg. At the lower pressure it was found that the contacts remained inac- tive indefinitely whenever the time of glow discharge on break was on the average more than 0.25 microsecond for each closure arc, and activa- tion would ultimately take place if the average glow time per closure arc was less than this value. (At the limonene pressure of 1 mm Hg there was a corresponding critical glow time of about 1 microsecond). The obvious interpretation of these tests is that a glow discharge of 0.04 ampere lasting for 0.25 microsecond sputters and burns off as much carbon as is made by an arc of 190 ergs under the conditions of the ex- periment. To test this conclusion, one needs to know how much carbon is produced by an arc of 190 ergs, and one needs to know the sputtering rate of carbon in a normal glow in air at atmospheric pressure. Measurements of the sputtering of carbon in a normal glow discharge were undertaken by F. E. Haworth, since such data are not available in published literature. Carbon and graphite electrodes were weighed before and after a normal glow discharge of 0.006 ampere lasting for various lengths of time. The loss of the carbon or graphite negative elec- trode in nitrogen was found to amount to about 0.15 atom per ion of the discharge. In air the loss was much greater, four times larger for graphite and 15 times larger for carbon (2.3 carbon atoms/ion for carbon in air). The increase in air was attributed to burning, and the difference between carbon and graphite losses in air was believed to be due to smaller crystal size and looser bonding in the carbon case.* If we use the highest loss figure of 2.3 carbon atoms/ion we find that a glow discharge of 0.04 ampere for 0.25 microsecond should remove 14 X 10^" carbon atoms. From Table IV, one finds that a 190 erg inactive arc in activating benzene vapor produces 9.5 X 10^° carbon atoms in the absence of air (line 3), and an active arc produces 34 X 10^° carbon atoms (line 2).t The net carbon which is left after each arc in air is, of course, considerably less than it would be in the absence of air (Section 6.1), but the order of magnitude agreement between these numerical * The sputtering rate of 0.15 atom/ion for carbon in nitrogen in the normal glow is about what is reported by Guiithersoliulzei" for silver in the ahnormal glow Init is greater by a factor of about 400 than that found for silver in the nurmnl glow in experiments by Hawortli."* ()l)viousIy sputtering rates for carbon are exceptionally high. t It is believed that these figures are substantially the same for linioncMic and for benzene. ACTIVATION OF ELECTKICAL CONTACTS BY ORGANIC VAPORS 809 values leaves little doubt that we have correctly interpreted the in- hibiting effect of glow discharges upon activation. 6.4 ''Hysteresis'^ Effects Sometimes a pair of completely inactive electrical contacts of a noble metal can be activated very quickly, and an apparently identical pair of contacts cannot be activated at all under exactly the same experi- mental conditions. In the first case a great amount of carbon may be formed, and in the second case no detectable carbon at all. In order to clear up this confusion, some controlled experiments were carried out upon the activation and deactivation of silver and palladium electrodes in air containing benzene vapor at various partial pressures. From these experiments, it has been possible to relate the variability of earlier results to previous history of the contacts, and the entire behavior is now quite well understood. In these tests adjustable benzene vapor pressure was obtained by first bubbling air at a controlled rate through benzene maintained at constant temperature by a bath of acetone and dry ice, and then mixing the saturated air with clean air in the proper proportions. In certain tests silver contacts were operated in air flowing from this apparatus, discharging a capacitor on each closure. The number of operations re- quired to produce complete activation was measured for many different values of the benzene vapor pressure. With contacts that had been cleaned in a standard way before each test, it was found that the number of closures required for activation rose extremely rapidly with decreasing vapor pressure over a narrow range of pressures. There was always a lower pressure limit below which it seemed impossible to activate the contacts at all. All of the tests were made at the high operating rate of 60 closures per second. When the contacts had been cleaned by abrasion before each indi- vidual test, the minimum pressure below which activation could not be attained was of the order of 2 mm Hg. (This pressure was exceptionally high because of the high operating rate, see Section 6.2.) A different re- sult was found for contacts that had been previously activated and then cleaned only by repeated arcing; for these contacts the minimum pressure for activation was about 0.7 mm Hg. The factor of 3 between these minimum pressures is doubtless related to the fact that, for those electrodes which had been cleaned by arcing only, there existed neigh- boring carbonized areas which were never cleaned. Each such area can be expected to hold about three times as much adsorbed benzene on the average as does the same area of clean metal, see Section 5.1, and espe- cially lines 2 and 3 of Table IV. Thus for such surfaces more carbon can 810 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 be expected to be formed by each arc. The model is not sufficiently well defined to permit any more exact conclusions. In another experiment, silver electrodes, which had first been com- pletely activated, were operated for a long period at a greatly reduced benzene vapor pressure. It was found that they remained completely active unless the pressure was very much less than the minimum of 0.7 mm Hg at w^hich activation could be produced. In repeated tests at a variety of low benzene vapor pressures, the number of operations re- quired for the contacts to become inactive was recorded. This number was found to increase very abruptly with increasing vapor pressure, and above about 0.02 mm Hg the contacts remained active indefinitely. This result must again be related to the capacity of a mass of spongy carbon to hold a great amount of adsorbed benzene. Very probably the upper limit of pressure below which contacts cannot be deactivated, depends upon the thickness of the carbon layer produced before the benzene pressure is lowered. Similar but less extensive experiments were carried out with palladium electrodes. These hysteresis effects observed in the activation and deactivation of contacts seem capable of explaining the erratic observations that had been made previously. If the immediate history of contacts is sufficiently well known, behavior can perhaps be predicted fairly well for various experimental conditions. 7. BROWN DEPOSIT Closely related to the activation of relay contacts is the formation of polymerized layers of organic material upon contact surfaces as a result of friction. This material, which is commonly kno\^^l as "bro\Aai deposit", is produced at contacts which do not make or break current. Its mode of formation is thus entirely different from that of the carbon which is the cause of activation. Both have, however, a common origin in layers of organic molecules adsorbed upon surfaces. Discovery of broAMi deposit and most of the investigation of it were carried out elsewhere (Ref. 20), but some discussion of brown deposit is appropriate here because of its relation to the carbon of activation and because of a study of its forma- tion by P. Kisliuk. 7.1 Composition The composition of brown deposit was determined by Kisliuk in an apparatus similar to that used to investigate the carbonaceous material responsible for activation, Fig. 9, and by the same analytical procedure. The apparatus was modified so that a palladium or platinum electrode I ACTIVATIOX OF ELECTKICAL COXTACT.S BY ORGANIC VAPORS 811 could be rubbed back and forth upon another electrode of the same mate- rial. The driving force was a magnet outside the glass apparatus. In tests carried out in benzene vapor in the absence of air, it was found that the deposit formed on the electrodes contained 65 per cent as much hydrogen as was in the original benzene, about 2 atoms of hydrogen for every 3 carbon atoms, this figure having a possible experimental error of as much as 20 per cent. The bro^\^l deposit formed by friction thus differs significantly from the pure carbon produced by arcing which is responsi- ble for activation.* The experimentally determined composition of the brown deposit does not, of course, distinguish between hydrogen or benzene simply adsorbed in the deposit and hydrogen existing in it in some combined form, 7.2 Rate of Production In Kjsliuk's experiments, which were carried out in the absence of air, the rate of production of bro^\^l deposit was found to be independent of benzene vapor pressure do^^'^l to 3 X 10~^ mm Hg, which was the lowest pressure tested, just as was the case in the formation of carbon bv arcs. When air is present, the rate of formation of bro^^^l deposit maj^ de- pend upon vapor pressure of the organic molecules. Unpublished experi- ments have indicated, furthermore, that there may be a limiting vapor pressure below which the deposit does not form, with this pressure de- pendent upon the idle period between operations.-" In some of Kisliuk's vacuum tests a palladium electrode was rubbed back and forth over an area determined microscopically to be about 4 X 10~* cm^, and produced the polymerization on each rub of 2.1 X 10^" molecules of benzene, or 5 X 10^- molecules per cm- of rub. This is smaller than the nvmiber of molecules in a monolayer (7 X 10^^ per cm^, Reference 16) by a factor of 140. Part of the discrepancy is certainlj^ due to the fact that the true area of contact of the electrodes is less than the apparent area as seen under the microscope. From more careful estimates of area it has been found bj^ other observers that the amount of benzene that is polymerized by friction is, in general, comparable with that ad- sorbed as a monolayer on the rubbing surfaces. 7.3 Brown Deposit and the Carbon of Activation Although both bro^ni deposit and the carbon of activation are pro- duced from the decomposition of adsorbed organic molecules, there are * In this connection, it is interestinj^ to point out, however, that any metal surface, ui)on wliich l)ro\vii (le])osit has been prothicetl l)y friction in an appro- priate atmosphere, is found to l)e fully active when tested in a suitable circuit. This activity naturally does not last after the brown deposit has been burned off. In this characteristic, the brown deposit behaves like any foreign more or less insulating laj-er upon a contact surface. 812 THE BELL SYSTEM TECHNICAL JOUKNAL, MAY 1957 several differences in the conditions necessary for formation. The carbon is produced on a noble metal but not on a base metal (in air) ; brown deposit, on the other hand, has been formed on vanadium, molybdenum and tantalum, but it has never been produced on silver and only spar- ingly on gold.'-" The failure of electrodes of silver and of gold to form brown deposit has been associated with the high thermal conductivities of these metals, with the idea in mind that polymerization of organic molecules to brown deposit requires frictional heat. Whether this is true has not been established. Both brown deposit and the carbon of activation can be formed from any of a great variety of unsaturated ring compounds. Various unsatu- rated aliphatic compounds which have been tested, and some saturated aliphatic compounds (for example, pentane), can be made to produce brown deposit to a limited extent, but activation has never been attained with any aliphatic compound. It seems probable that some activating carbon is produced from these compounds but the burning off in the arc makes activation impossible. ACKNOWLEDGMENT The work reported here is the joint effort of a number of persons whose contributions are acknowledged in the appropriate places. The authors coordinated the investigation and are responsible for its general plan. The authors are indebted furthermore to R. H. Gumley for many helpful criticisms. REFERENCES 1. R. H. Gumley, Bell Lab. Record, 32, p. 226, 1954. 2. L. H. Germer, J. Appl. Phys., 22, p. 955, 1951. 3. L. H. Germer and W. S. Boyle, Nature, 176, p. 1019, 1955. 4. L. H. Germer and W. S. Boyle, J. Appl. Phys. 27, p. 32, 1956. 5. M. M. Atalla, B.S.T.J., 34, p. 1081, Sept., 1955. 6. L. H. Germer, J. Appl. Phys. 22, p. 1133, 1951. 7. F. E. Haworth, J. Appl. Phys., 28, p. 381, 1957. 8. L. H. Germer, J. Appl. Phys. 25, p. 332, 1954. 9. L. H. Germer and F. E. Haworth, J. Appl. Phys., 20, p. 1085, 1949. 10. L. H. Germer, to be published. 11. M. M. Atalla, B. S.T.J. , 32, p. 1493, Nov., 1953. 12. P. Kisliuk, J. Appl. Phys., 25, p. 897, 1954. 13. L. H. Germer, Electrical Breakdown between Close Electrodes in Air, to be published. 14. W. S. Boyle and L. H. Germer, J. Appl. Phys., 26, p. 571, 1955. 15. J. J. Lander and L. H. Germer, J. Appl. Phys., 19, p. 910, 1948. 16. B. M. W. Trapnell, Advances in Catalysis, Vol. Ill, Academic Press, New York, 1951, pp. 1-24. 17. P. Kisliuk, to be pul)lished. 18. F. E. Haworth, J. Appl. Phys., 22, p. 606, 1951. 19. A. Giinthcrschulze, Z. Physik, 36, p. 563, 1926. 20. H. W. Hermance and T. F. Egan, 1956 Electronics Symposium, Electrical Engineering, to be published. \ i i Bell System Technical Papers Not Published in this Journal Aaron, M. R} The Use of Least Squares in Network Design, Trans. I.R.E., PGCT, CT-3, pp. 224-231, Dec, 1956. Anderson, J. R.' A New Type of Ferroelectric Shift Register, Trans. I.R.E., PGEC, EC-5, pp. 184-191, Dec, 1956. Anderson, P. W., see Clogston, A. M. Andreatch, p., Jr.,1 and Thurston, R. N.^ Disk-Loaded Torsional Wave Delay Line. I — Construction and Test, J. Acous. Soc Am., 29, pp. 16-19, Jan., 1957. AuGUSTYNiAK, W. M., See Wertheim, G. K. Bala, V. B., see Matthias, B. T. Bashkow, T. R.,' and Desoer, C. A.^ A Network Proof of a Theorem on Hurwitz Polynomials and its Generalization, Quarterly Appl. Math., 14, pp. 423-426, Jan., 1957. Bond, W. L., see McSkimin, H. J. Bozorth, R. M.i Magnetic Properties of Materials, Am. Inst. Phys. Handbook, Chap- ter 5, pp. 206-244, Feb., 1957. Breidt, P., Ju.,1 (Ireiner, E. S., and Ellis, W. C.^ Dislocations in Plastically Indented Germanium, Acta Met., Letter to the Editor, 5, p. 60, Jan., 1957. ' Bell Telephone Laboratories. 813 81-i THE BELL SYSTEM TECllMCAL JUUKXAL, MAY l'J57 Bridgers, H. E., see tabulation at the end. Bridgers, H. E., see tabulation at the end. Burke, P. J. . The Output of a Queueing System, Operations Research, 4, pp. G99- 704, Dec, 1956. Clemency, W. F.,^ Romanow, F. F.,^ and Rose, A. F.- The Bell System Speakerphone, Elec. Engg., 76, pp. 189-194, March, 1957. Clogston, a. M.,1 Suhl, H.,i Walker, L. R.,' and Anderson, P. W.^ Ferromagnetic Resonance Line Width in Insulating Materials, J. Phys. Chem. Solids, 1, pp. 129-136, Nov., 1956. CoRENZWiT, E., see Matthias, B. T. D'Amico, C.,^ and Hagstrum, H. D.^ An Improvement in the Use of the Porcelain Rod Gas Leak, Rev Sci. Instr., 28, p. 60, Jan., 1957. Desoer, C. a., see Bashkow, T. R. Dillon, J. F., Jr.' Ferrunagnetic Resonance in Yttrium Iron Garnet, Phys. Rev., Letter to the Editor, 105, pp. 759-760, Jan. 15, 1957. Ditzenberger, J. A., see Fuller, C. S. DoBA, S., Jr.* The Measurement and Specification of Nonlinear AmpHtude Response Characteristics in Television, Proc. I.R.E., 45, pp. 161-165, Feb., 1957. Edelson, D., see tabulation at the end. ' Bell Telephone Lalioratories. 2 American Telephone and Telegraph Conipan\- 1 I TECHNICAL PAPERS 815 Ellis, W. C, see Breidt, P., Jr. Evans, D. H.^ A Positioning Servomechanism With A Finite Time Delay and A Signal Limiter, Trans. I.R.E., PGAC, AC-2, pp. 17-28, Feb., 1957. Flaschen, S. S., see tabulation at the end. Flaschex, S. S., see Garn, P. D. Fry, T. C: Automatic Computer in Industry, Am. Stat. Assoc. J., 51, pp. 565-575, Dec, 195G. Fuller, C. S.,^ and Ditzenberger, J. A.^ Effect of Structural Defects in Germanium on the Diffusion and Acceptor Behavior of Copper, J. Appl. Phys., 28, pp. 40-48, Jan., 1957. Fuller, C. 8.,^ and Morix, F. J} Diffusion and Electrical Behavior of Zinc in Silicon, Phys. Rev., 105, pp. 379-384, Jan. 15, 1957. Fuller, C. S., see Reiss, H. GaLT, J. K.,1 AXD KiTTEL, C.^ Ferromagnetic Domain Theory, Solid State Physics; Advances in Research and Applications (book), 3, pp. 437-564, 1956, Academic Press, Inc., New York. Garx, p. D./ and Flaschen, S. S.^ Analytical Applications of Differential Thermal Analysis Apparatus, Anal. Chem., 29, pp. 271-275, Feb., 1957. Garn, P. D., and Flaschen, S. S. Detection of Polymorphic Phase Transformations by Continuous Measurement of Electrical Resistance, Anal. Chem., 29, pp. 268-271, Feb., 1957. ^ Bell Telephone Laboratories. ^ University of California, Berkeley. 81G THE BELL SYSTEM TECHNICAL JOUKNAL, MAY 1957 Garn, p. D., see tabulation at the end. Gast, R. W.s Field Experience with the A2A Video System, Elec. Engg., 76, pp. 44-49, Jan., 1957. Geballe, T. H., see Kimzler, J. E. Gibbons, J. F.^ A Simplified Procedure for Finding Fourier Coefficients, Proc. I.R.E., Letter to the Editor, 45, p. 243, Feb., 1957. Greiner, E. S., see Breidt, P., Jr. Gross, W. A} The Second Fundamental Problem of Elasticity Applied to a Plane Circular Ring, J. Appl. Math, and Phys., 8, pp. 71-73, 1957. I I Gould, H. L. B., and Wenny, D. H.' Supermendur — A New Rectangular-Loop Magnetic Material, Elec. Eiigg., 76, pp. 208-211, March, 1957. Hagstrum, H. D.^ 1 Effect of Monolayer Adsorption on the Ejection of Electrons from Metals by Ions, Phy.s. Rev., 104, pp. 1510-1527, Dec. 15, 1950. Hagstrum, H. D., see D'Aniico, C. Hamming, R. W.^ I Harnessing the Digital Computers, Columbia Engg. Quarterly, 10, pp. 16-19, 54, March, 1957. Hanson, R. L.,' and Kock, W. E.' Interesting Effect Produced by Two Loudspeakers Under Free Space Conditions, J. Acous. Soc. Am. Letter to the Editor, 29, p. 145, Jan., 1957. 1 Bell Telephone Laboratories. ^ New York Telephone Company. I TECHNICAL PAPERS 817 Hawkins, W. L., see tabulation at the end. Herring, C.^ Theoretical Ideas Pertaining to Traps or Centers, Photoconductivity Conference (book), pp. 81-110, 195G. John Wiley & Sons, New York. Hull, G. W., see Kunzler, J. E. Karp, A^ Japanese Technical Captions, Proc. I.R.E., Letter to the Editor, 45, p. 93, Jan., 1957. King, B. G.i Discussion on "An Investigation into Some Fundamental Properties of Strip Transmission Lines with the Aid of an Electrolytic Tank", Proc. I.R.E., 104, p. 72, Jan., 1957. KiTTEL, C, see Gait, J. K. KocK, W. E., see Hanson, R. L. KowALCHiK, M., see Thurmond, C. D. Kunzler, J. E.,i Geballe, T. H.,' and Hull, G. W.^ Germanium Resistance Thermometers Suitable for Low-Tempera- ture Calorimetry, Rev. Sci. Instr., 28, pp. 96-98, Feb., 1957. KuLKE, B.,^ and Miller, S. L.^ Accurate Measurement of Emitter and Collector Series Resistances in Transistors, Proc. I.R.E., Letter to the Editor, 45, p. 90, Jan.. 1957. Kunzler, J. E., see tabulation at the end. Lander, J. J., see Thomas, D. G. Law, J. T., see tabulation at the end. ^ Bell Telephone Laboratories. 818 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 LuNDBERG, C. v., see tabulation at the end. LuNDBERG, J. L., see tabulation at the end. Matthias, B. T.,' Wood, E. A.,^ Corenzwit, E.,i and Bala, V. B.^ Superconductivity and Electron Concentration, J. Phys. Chem. Solids, 1, pp. 188-190, Nov., 1956. McMillan, B.^ Two Inequalities Implied by Unique Decipherability, Trans. I.R.E., PGIT, IT-2, pp. 115-116, Dec, 1956. McSkimin, J. H.,1 and Bond, W. L.^ Elastic Moduli of Diamond, Phys. Rev., 105, pp. 116-121, Jan. 1, 1957. Mendizza, A.^ The Standard Salt Spray Test — Is It A Valid Acceptance Test?, Plating, 44, pp. 166-175, Feb., 1957. Mendizza, A.^ The Standard Salt Spray Test — Is It A VaUd Acceptance Test?, Symposium on Properties, Tests and Performance of Electrodeposited Metalhc Coatings, A.S.T.M. Special Tech. PubUcation 197, pp. 107- 117, 1957. Miller, R. C, see Smits, F. M. Miller, S. L., see Kulke, B. MoRiN, F. J., see Fuller, C. S. Nelson, L. S., see Tabulation at the end. Palmquist, T. F.^ Multiunit Neutralizing Transformers, Elec. Engg., 76, p. 201, March, 1957. i 1 Bell Telephone Laboratories. ^ Bell Telephone Company of Canada, Montreal. TECHNICAL PAPERS 819 Paterson, E. G. D.i Some Observations on Quality Assurance and Reliability, Proc. Third National Symp. on Keliability and Quality Control in Electronics, pp. 129-132, Jan., 1957. PiETRuszKiEwicz, A. J., 866 Reiss, H. Potter, J. F., S66 tabulation at the end. Prince, E.,^ and Treuting, R. G.' The Structure of Tetragnal Copper Ferrite, Acta Crys., 9, pp. 1025- 1028, Dec, 1956. Read, M. H., see Van Uitert, L. G. Read, W. T., Jr.i Dislocation Theory of Plastic Bending, Acta Met., 5, pp. 83-88, Feb., 1957. Reiss, H.^ Theory of the Ionization of Hydrogen and Lithium in Silicon and Germanium, .1. Chem. PM's., 25, pp. (381-686, Oct., 1956. Reiss, H., see tabulation at the end. Reiss, H.,^ Fuller, C. S.,^ and Pietruszkiewicz, A. J.^ Solubility of Lithium in Doped and Undoped Silicon, Evidence for Compound Formation, J. Chem. Phys., 25, pp. 650-655, Oct., 1956. Romanow, F. F., see Clemency, W. F. Rose, A. F., see Clemency, W. F. Rose, D. J.i Microplasmas in Silicon, Phys. Rev., 105, pp. 413-418, Jan. 15, 1957. ScuLABAcii, T. D., see tabulations at the end. 1 Bell Telephone Laboratories. 820 THE BELL SYSTEM TECHNICAL JOUKXAL, MAY 1957 ScHNETTLER, F. J., SGG Van Uitert, L. G. Seidel, H.' Ferrite Slabs in Transverse Electric Mode Wave Guide, J. Appl. Phys., 28, pp. 218-226, Feb., 1957. Slighter, W. P., see tabulation at the end. Smits, F. M.,1 and Miller, R. C.^ Rate Limitation at the Surface for Impurity Diffusion in Semicon- ductors, Phys. Rev., 104, pp. 1242-1245, Dec. 1, 1956. SUHL, H.i The Theory of Ferromagnetic Resonance at High Signal 'Powers, J. Chem. and Phys. of Solids, 1, pp. 209-227, Jan., 1957. SuHL, H., see Clogston, A. M. Tien, P. K.^ The Backward -Traveling Power in the High Power Traveling -Wave Amplifiers, Proc. I.R.E., Letter to the Editor, 45, p. 87, Jan., 1957. Thomas, D. G.,^ and Lander, J. J.' Hydrogen as a Donor in Zinc Oxide, J. Chem. Phys., 25, pp. 1136- 1142, Dec, 1956. Thurmond, C. D.,' Trumbore, F. A.,' and Kowalchik, M.^ Germanium Solidus Curves, J. Chem. Phys., Letter to the Editor, 25, pp. 799 800, Oct., 1956. Thurston, R. N.^ Disk-Loaded Torsional Wave Delay Line. II — Theoretical Interpre- tation of Results and Design Information, J. Acous. Soc. Am., 29, pp. 20-25, Jan., 1957. Thurston, R. N., see Andreatch, P., Jr. 1 Bell Telei)hone Laboratories. TECHNICAL PAPERS 821 Treuting, R. G., see Prince, E. Trumbore, F. a., see Thurmond, C. D. Van Uitert, L. G.,^ Read, M. H.,^ and Schnettler, F. J.^ Permanent Magnet Oxides Containing Divalent Metal Ions — I, J. Appl. Phys., Letter to the Editor, 28, pp. 280-281, Feb., 1957. Van Uitert, L. G.,^ see tabulation at the end. Walker, L. R., see Clogston, A. M. Wenny, D. H., see Gould, H. L. Wernick, J. H., see tabulation at the end, Wertheim, G. K.,1 and Augustyniak, W. M.^ Measurement of Short Carrier Lifetimes, Rev. Sci. Instr., 27, pp. 1062-1064, Dec, 1956. Wood, E. A., see Matthias, B. T. Yerkes, E. P.7 Comfort A. Adams 1956 Edison Medalist — Medal History, Elec. Engg., 76, p. 224, March, 1957. The Encyclopedia of Chemistry — Book Published by Reinhold Press, New York, January, 1957. Bridgers, H. E., Germanium and Its Compounds, p. 445, and Semiconductors, pp. 852-583. Edelson, D., Polar Molecules, pp. 767 769. Flaschen, S. S., Calcination, pp. 161-162. Garn, p. D., Electrolysis, pp. 341-342. Hawkins, W. L., Autoxidation, p. 116. ' Bell Telephone ivalioratories. ' Bell Telephone C'ompanj- of Pcnnsylvaiiia, Phihulelphia. 822 THE BELL SYSTEM TECIIMCAL JOURNAL, MAY 1957 KuNZLER, J. E., Calorimetry, pp. l()o~165. Law, J. T., Vacuum Techniques, pp. 964;-9()5. LuNDBERG, C. C, Antiozonants, pp. 97 98, and Solutions, pp. 873-874. Nelson, L. S., Olefin Compounds, pp. G(31 0(33. Potter, J. F., Porosity, pp. 775-776. Reiss, H., Thermodynamics, pp. 930-933. ScHLABACH, T. D., Photometric Analysis, pp. 735-73G. Slighter, W. P., Paramagnetism, p. 700. Van Uitert, L. G., Equilibrium, pp. 363-364. Wernick, J. H., Carbonates, pp. 173-174. lecent Monographs of Bell System Technical Papers Not Published in This Journal* I Allison, H. W., see Moore, G. E. Arnold, S. M. Growth and Properties of Metal Whiskers, Monograph 2635. AuGUSTYNiAK, W. M., See Wertheim, G. K. Bashkow, T. R. Effect of Nonlinear Collector Capacitance on Rise Time, ^Monograph 2742. BoMMEL, H. E., see Mason W. P. BOZORTH, R. M. Ferromagnetism, Monograph 2679. Brattaix, W. H. Development of Concepts in Semiconductor Research, ^Monograph 2743. Bridgers, H. E., and Kolb, E. D. Distribution Coefficient of Boron in Germanium, Monograph 2684. Chen, W. H., see Lee, C. Y. COMPTON, K. G. Potential Criteria for Cathodic Protection of Lead Cable Sheath, Monograph 2655. * Copies of these monographs may be obtained on request to the Pul)lication Department, Bell Telephone Laboratories, Inc., 463 West Street, New York 14, N. Y. The numbers of the monographs should be given in all requests. 823 824 THE BELL SYSTEM TECHNICAL JOUKXAL, MAY 11)37 David, E. E., and McDonald, H. S. Note on Pitch-Synchronous Processing of Speech, ^Monograph 2744. Dehn, J. W., and Hersey, R. E. Recent New Features for No. 5 Crossbar Switching System, Mono- graph 2745. Fay, C. E. Ferrite-Tuned Resonant Cavities, Monograph 2713. Fry, T. C. The Automatic Computer in Industry, Monograph 2755. Gilbert, E. X. Enumeration of Labelled Graphs, ^Monograph 2G80. Goldey, J. M., see ]\Ioll, J. L. Hagstrum, H. D. Auger Ejection of Electrons from Molybdenum by Noble Gas Ions, Monograph 2716. Hagstrum, H. D. Metastable Ions of the Noble Gases, ^Monograph 2714. Hersey, R. E., see Dehn, J. W. HoLONYAK, N., see Moll, J. L. Jaycox, E. K., and Prescott, B. E. Spectrochemical Analysis of Thermionic Cathode Nickel Alloys, Monograph 2756. KoLB, E. D., see Bridgers, H. E. Krusemeyer, H. J., and Pursley, 'SI. V. Donor Changes in Oxide-Coated Cathodes, Monograph 2717. MONOGRAPHS 825 Lander, J. J., see Thomas, D. G. Lee, C. Y., and Chen, W. H. Several-Valued Combinational Switching Circuits, Monograph 2746. LovELL, L. C, see Vogel, F. L., Jr. Mason, W. P. Internal Friction and Fatigue in Metals at Large Strain Amplitudes, Monograph 2758. Mason, W. P. Physical Acoustics and Properties of Solids, Monograph 2761. Mason, W. P., and Bommel, H. E. Ultrasonic Attenuation at Low Temperatures for Metals, Normal and Superconducting, Monograph 2748. Matlack, R. C. Role of Communications Networks in Digital Data Systems, Mono- graph 2678. Metreyek, W., see Winslow, F. H. McDonald, H. S., see David, E. E. McSkimin, H. J. Wave Propagation and Measurement of Elasticity of Liquids and Solids, Monograph 2749. Merz, W. J. Switching Time in Ferroelectric BaTiO:, and Crystal Thickness, Monograph 2721. Miller, R. C, and Savage, A. Diffusion of Aluminum in Single -Crystal Silicon, Monograph 2722. Moll, J. L., Tanenbaum, M., Goldey, J. M., and Holonyak, X. P-N-P-N Transistor Switches, Monograph 2723. 826 THE BELL SYSTEM TECHNICAL JOUKNAL, MAY 1957 Moore, G. E., and Allison, H. W. Emission of Oxide Cathodes Supported on a Ceramic, Monograph 2724. MosHMAN, J., see Tien, P. K. Ohm, E. a. A Broad-Band Microwave Circulator, Monograph 2726. Owens, CD. Modern Magnetic Ferrites and Their Engineering Applications, Monograph 2709. Owens, C. D. Properties and Applications of Ferrites Below Microwave Frequencies, Monograph 2727. Paterson, E. G. D. Nike Quality Assurance, Monograph 2728. Pierce, J. R., and Walker, L. R. Growing Electric Space -Charge Waves, Monograph 2729. Pierce, J. R. Instability of Hollow Beams, Monograph 2751. Prescott, B. E., see Jaycox, E. K. Pursley, M. v., see Krusemeyer, H. J. Rose, D. J. Townsend Ionization Coefficient for Hydrogen and Deuterium, Monograph 2731. Savage, A., see Miller, R. C. Slepian, D. Note on Two Binary Signaling Alphabets, Monograph 2733. monographs 827 Sproul, p. T. A Video Visual Measuring Set with Sync Pulses, Monograph 2752. Tanenbaum, M., see Moll, J. L. Thomas, D. G., and Lander, J. J. Hydrogen as a Donor in Zinc Oxide, Monograph 2753. Tien, P. K., and Moshman, J. Noise in a High -Frequency Diode, Monograph 2735. TORREY, M. N. Quality Control in Electronics, ^lonograph 2736. Van Uitert, L. G. Dielectric Properties of and Conductivity in Ferrites, Monograph 2737. VoGEL, F. L., Jr., and Lovell, L. C. Dislocation Etch Pits in Silicon Crystals, Monograph 2738. Walker, L. R., see Pierce, J. R. Weinreich, G. Acoustodynamic Effects in Semiconductors, Monograph 2764. Weiss, M. T. Improved Rectangular Waveguide Resonance Isolators, Monograph 2739. Wertheim, G. K. Carrier Lifetime in Indium Antimonide, ^lonograph 2740. Wertheim, G. K., and Augustyniak Measurement of Short Carrier Lifetimes, Monograph 2754. WiNSLOAv, F. H., and ]\Iatreyek, W. Pyrolysis of Crosslinked Styrene Polymers, Monograph 2741. Contributors to This Issue Kenneth Bullington, B.S., University of New Mexico, 1936; M.S., Massachusetts Institute of Technology, 1937; Bell Telephone Labora- tories, 1937-. Mr. Bullington's first work with the Laboratories was on systems engineering on wire transmission circuits, and since 1942 he has been concerned with transmission engineering on radio systems, particu- larly over-the-horizon radio propagation. In 1956, he was awarded the Morris Liebmann Memorial Prize of the I.R.E. and the Stuart Ballen- tine Medal from the Franklin Institute for contributions in tropospheric transmission and the application of those contributions to practical communication systems. He is a Fellow of the I.R.E. , and a member of Phi Kappa Phi, Sigma Tau and Kappa Mu Epsilon. Arthur B. Crawford, B.S.E.E. 1928, Ohio State University; Bell Telephone Laboratories 1928-. Mr. Crawford has been engaged in radio research since he joined the Laboratories. He has worked on ultra short wave apparatus, measuring techniques and propagation; microwave apparatus, measuring techniques and radar; microwave propagation studies and microwave antenna research. He is author or co-author of articles which appeared in the Bell System Technical Journal, Proceed- ings of the I.R.E., Nature and Bulletin of the American Meteorological Society. He is a Fellow of the I.R.E. and a member of Sigma Xi, Tau i Beta Pi, Eta Kappa Nu, and Pi Mu Epsilon. Harold E. Curtis, B.S. and M.S., Massachusetts Institute of Tech- nology, 1929; Department of Development and Research of the Ameri- can Telephone and Telegraph Company, 1929; Bell Telephone Labora- tories, 1934-. Mr. Curtis has been concerned with transmission prob- lems related to multi-channel carrier telephony. He has also been i engaged in studies of transmission engineering aspects of the microwave radio relay system. His work at the Laboratories has also included pioneering transmission studies of the coaxial cable, the shielded pair and quad, and the waveguide. Mr. Curtis holds ten patents relating to car- rier telephony. Harald T. Friis, E.E., 1916, D.Sc, 1938, Royal Technical College (Copenhagen); Western Electric Company, 1919; Bell Telephone Lab- 828 CONTRIBUTORS TO THIS ISSUE 829 oratories, 1930-. Dr. Friis, Director of Research in High Frecjueney and Electronics, has made important contributions on ship-to-shore radio reception, short-wave studies, radio transmission (inchiding methods of measuring signals and noise), a receiving system for reducing selective fading and noise interference, microwave receivers and measuring equip- ment, and radar eciuipment. He has published numerous technical papers and is co-author of a book on the theory and practice of antennas. The I.R.E.'s Morris Liebmann Memorial Prize, 1939, and Medal of Honor, 1954. ^"aldemar Poulson Gold Medal by Danish Academy of Technical Sciences, 1954. Danish "Knight of the Order of Dannebrog," 1954. Fellow of I.R.E. and A.I.E.E. Member of American Association for the Advancement of Science, Danish Engineering Society and Danish Academy of Technical Sciences. Served on Panel for Basic Research of Research and Development Board, 1947-49, and Scientific Advisory Board of Army Air Force, 1946-47. Lester H. Germer, B.A., Cornell, 1917; M.A., Columbia, 1922; Ph.D., Columbia, 1927; Western Electric Co., 1917-24; Bell Telephone Laboratories, 1925-. With the Research Department, Dr. Germer has been concerned with studies in electron diffraction, structure of surface films, thermionics, contact physics, order-disorder phenomena, and physics of arc formation. He has published about seventy papers and has three patents. Li 1931 he received the Elliott Cresson medal of the Franklin Listitute. He is a member of the American Physical Society, Sigma Xi, the New York Academy of Sciences, the A.A.A.S., and the American Crystallographic Society of which he served as president in 1944. David C. Hogg, B.S., ITniversity of Western Ontario, 1949; M.S. and Ph.D., McGill University, 1950 and 1953; Bell Telephone Laboratories, 1953-. Mr. Hogg has been engaged in studies of artificial dielectrics for microwaves, antenna problems, and over-the-horizon and millimeter wave propagation as a member of the Radio Research Dept. During World War H, Mr. Hogg served with the Canadian Army in Europe and from 1950-51 did research for the Defense Research Board of Canada. He is a member of Sigma Xi, and a senior member of the LR.E. Stephen 0. Rice, B.S., Oregon State College, 1929; California In- stitute of Technology, Graduate Studies, 1929-30 and 1934-35; Bell Telephone Laboratories, 1930-. In his first years at the Laboratories, Mr. Rice was concerned with the non-linear circuit theory, with special 830 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 emphasis on methods of computing modulation products. Since 1935 he has served as a consultant on mathematical problems and in investiga- tions of the telephone transmission theory, including noise theoiy, and applications of electromagnetic theory. Fellow of the I.R.E. J. W. ScHAEFER, B.M.E., Ohio State University, 1941 ; Bell Telephone Laboratories, 1940-. Mr. Schaefer has worked on dial design and dial test equipment, and during the war years contributed to the design and development of anti-aircraft fire control equipment and guided missiles. After the war, Mr. Schaefer proposed a means of steering missiles from which evolved NIKE. He is now working on anti-aircraft guided missile systems. He is a member of A.S.M.E., the Army Ordnance Association, Tau Beta Pi and Sigma Xi. Bernard Smith, B.S., City College of New York, 1948; A.M., 1951, and Ph.D., 1954, Columbia University; Lecturer, City College of New York, 1948-1954; Bell Telephone Laboratories, 1954-. In addition to the transmission studies in which he has been engaged since joining the Lab- oratories, his present duties include teaching information theory in the Communications Development Training Program. He is a member of the American Physical Society, Phi Beta Kappa, Sigma Xi and Kappa Delta Pi. James L. Smith, B.S., Newark College of Engineering, 1956; Bell Telephone Laboratories, 1941-. Mr. Smith worked on problems con- cerned with relay contact erosion as a technical aide, and in 1956 began his work on solid state switching networks. He is a member of the A.LE.E. and Tau Beta Pi. Mark A. Townsend, B.S., Texas Technological College, 1936; M.S., Mass. Institute of Technology, 1937; Bell Telephone Laboratories, 1945-. Mr. Townsend's early work with the Laboratories was on the development of gas discharge tubes for use in telephone switching sys- tems. More recently, his work has been in the exploratory development of systems for digital data transmission and of a small electronic switch- ing system. He is a member of the A.I.E.E., and senior member of the I.R.E. Gerd F. Weissmann. Dipl.-Ing. Technical University of Berlin, 1950; M.S. Pennsylvania State University, 1953; Bell Telephone Laboratories, 1953-. Mr. Weissmann 's work at the Laboratories has been in stress analysis, engineering mechanics, strain measurements, soil mechanics and metals properties and testing. He also has worked with outside plant problems and metallurgical engineering. HE BELL SYSTEM nical ournal CVOTED TO THE SC I EN TIFIC^^^ AND ENGINEERING liPECTS OF ELECTRICAL COMMUNICATION LUME XXXVI JULY 1957 NUMBER 4 Noise Spectrum of Electron Beam in Longitudinal Magnetic Field w. w. rigrod AUij vo , "" '^'^ 195/ Part I — The Growing Noise Phenomenon 831 Part II— The UHF Noise Spectrum 855 Distortion Produced in a Noise Modulated FM Signal by Non- linear Attenuation and Phase Shift s. o. rice 879 Self-Timing Regenerative Repeaters e. d. stjnde 891 A Sufficient Set of Statistics for a Simple Telephone Exchange Model V. e. benes 939 Fluctuations of Telephone Traffic v. e. benes 965 High-Voltage Conductivity-Modulated Silicon Rectifier H, s. veloric and m. b. prince 975 Coincidences in Poisson Patterns e. n. gilbert and h. o. pollak 1005 Bell System Technical Papers Not Published in This Journal 1035 Recent Bell System Monographs 1043 Contributors to This Issue 1045 COPYRIGHT 1967 AMERICAN TELEPHONE AND TELEGRAPH COMPANY THE BELL SYSTEM TECHNICAL JOURNAL ADVISORY BOARD A. B. GOETZE, President, Western Electric Company M, J. KELLY, President, Bell Telephone Laboratories E. J. McNEELY, Executive Vice President, American Telephone and Telegraph Company EDITORIAL COMMITTEE B. MCMILLAN, Chairman S. E. BRILLHABT B. I. GREEN A. J. BUSCH R. K. HONAMAN L. B. COOK H. R. HUNTLEY A. C. DICKIESON F. R, LACK R, L. DIETZOLD J. R, PIERCE K. E. GOULD G. N. THAYER EDITORIAL STAFF w. D. BULLOCH, Editor R. L. SHEPHERD, Production Editor T. N. POPE, Circulation Manager THE BELL SYSTEM TECHNICAL JOURNAL is published six times a year by the American Telephone and Telegraph Company, 195 Broadway, New York 7, N. Y. F. R. Kappel, President; S. Whitney Landon, Secretary; John J. Scan- Ion, Treasurer. Subscriptions are accepted at $5.00 per year. Single copies $1.25 each. Foreign postage is 65 cents per year or 11 cents per copy. Printed in U. S. A. THE BELL SYSTEM TECHNICAL JOURNAL VOLUME XXXVI JULY 1957 number 4 Copyright 1957, American Telephone and Telegraph Company Noise Spectrum of Electron Beam in Longitudinal Magnetic Field By W. W. Rigrod (Manuscript received January 21, 1957) Measurements of induced noise currents along drifting cylindrical elec- tron beams have shown that noise fluctuations propagate as space-charge waves in the same fashion as RF signals of the same frequency. On many such beams, however, the regular standing-wave noise pattern is interrupted, after some drift distance, by a smooth steep increase in noise current, fol- lowed by slow, shallow undulations. This "growing noise" phenomenon, discovered by Smullin and his co-workers at M.I.T. several years ago, is the subject of study in this paper. Its importance is considerable, in a nega- tive way, because it has hampered the development of medium-power travel- ing-wave-tube devices with acceptably low noise figures. The experimental measurements show the growing noise pattern to be the result of a two-stage process. Its primary cause is rippled-beam amplifica- tion of noise fluctuations over a wide band of microwave frequencies, much higher than the usual observation frequency. This explains its elusiveness. In the second stage, noise energy is transferred to lower frequencies, due to intermodulation and other non-linear processes within the gain band. As the beat- frequency noise increments are excited by continuous arrays of fre- quency pairs, their standing-wave patterns overlap one another, resulting in a smooth growing-noise pattern. 831 832 THE BELL SYSTEM TECHNICAL JOURNAL, .IITLY H)57 In Part II of this 'paper, measurements of the noise spectrum of a rippled beam in the UHF region are described. These measurements reveal the presence of additional forms of instability. Calculations are made to account for some of these, and for aspects of rippled-beam amplijication not previously understood. Part I — The Growing Noise Phenomenon* I INTRODUCTION When an RF probe is moved along a magnetically -focused electron beam in a drift region, the noise power is at first found to vary periodi- cally with distance from the electron gun. For a sufficiently long beam, however, the periodic pattern is succeeded by an exponential rise, culmi- nating in an irregular plateau. This so-called "growing noise" phenome- non has been extensively investigated by its discoverers, L. Smullin and his colleagues at the M.I.T. Research Laboratory of Electronics.^' ' They have established that this noise will begin to grow at a plane nearer the gun, and tend to grow at a faster rate, for electron beams (a) of higher perveance, (b) with less space-charge neutralization by positive ions, and (c) issuing from convergent, partly-shielded guns, rather than those immersed in the magnetic field. The growth of microwave noise power in drifting beams has hampered the development of high-power, traveling-wave tubes with acceptably low noise figures,, as such devices generally have convergent, partly- shielded electron guns. The problem has been evaded in the design of low-noise, low-power traveling-wave tubes, by resort to confined-flow, parallel beams. Several theories have been proposed to explain the growing-noise wave: (1) Excitation of higher-order modes with complex propagation con- stants, by electrons threading the beam transversely; (2) Slipping-stream amplification, due to either longitudinal or trans- verse velocity gradients; (3) Rippled-beam amplification; ' ' and (4) Electron-electron interactions leading eventually to equipartition of thermal energy, and thus an increase in longitudinal velocity fluctua- tions. In Part I of this paper, measurements are presented which sho\\- that the principal cause of growing noise appears to be space-charge wave * Presented at the I.R.E. Electron Tube Research Conference, Boulder, Colo- rado, June 27-29, 1956. PART I — THE GROWING NOISE PHENOMENON 833 amplification due to beam rippling. The mechanism is studied in some detail, as its connection with the usually-observed exponential rise of noise is not immediately apparent. In Part II, the UHF noise spectrum and its spatial distribution in beams with large-amplitude, long wave- length ripples, are described. In addition, some of the underlying proc- esses are analyzed. II APPARATUS As sketched in Fig. 1, the heart of the apparatus consists of an electron gun, drift tube, and movable probe, all enclosed in a demountable, con- tinuously-pumped vacuum system. Outside of the vacuum envelope there is a shielded solenoid, extending the entire 18-inch length of the drift tube. The annular gap between the solenoid pole face and the mag- netic shield about the gun is nearly all taken up by a soft-steel section of the vacuum envelope. The electron gun is of the convergent Pierce type, with oxide-coated cathode and a coiled-coil filament heater producing negligible flux at the cathode surface. Surrounding the gun, and inside of the magnetic shield, is a small copper- wire coil that permits variation of this flux over a small range, either aiding or opposing the leakage flux due to the main focusing solenoid. The flux density at the cathode has been approxi- mately calibrated in terms of currents in both coils. Throughout the ex- periments described below, the gun is pulsed with a 1,000 cps square wave of 2,200 volts on its anode, supplying 38 ± 1 ma peak current in space-charge-limited emission. The novel feature of the probe is that its annular RF pickup gap couples to a 50-ohm coaxial line leading to the receiver, rather than to a resonant cavity. This permits RF power measurements over a wide range of frequencies. The inner conductor of the coaxial line serves as current-collector, being isolated and biased positively about 40 volts with respect to the outer conductor to prevent escape of slow secondaries. An adjustable vane can be locked in position in front of the probe (whose entrance aperture is 0.100 inch in diameter), so that circular apertures of various smaller sizes are fixed on the probe centerline, about 0.070 inch in front of the probe. With these apertures, measurements of col- lector-current variations along the beam furnish a rough picture of beam-ripple amplitudes and locations. In addition, the current-density variation across the beam can be estimated by moving a pinhole aperture in a broad arc through the beam centerline. Both the inner conductor of the probe and the intercepting vane are liquid-cooled. The noise powers coupled to the coaxial probe are considerably smaller 834 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 than for a tuned coaxial cavity, because of the lower RF gap impedance of the former. To compensate for this drawback, a sensitive noise re- ceiver is employed, similar in principle to the radiometer invented by R. H. Dicke. The input noise power is replaced periodically by a matched load at room temperature by pulsing the beam on and off with a 1,000 cps scjuare wave, and placing an isolator in front of the re- ceiver. A synchronous detector eliminates gain-fluctuation noise and converts the receiver output to a dc voltage. Noise power variations at various microwave frerjuencies are measured in terms of the changes of attenuation, between probe and receiver, re- quired to keep the receiver output constant. These rapid adjustments in attenuation are performed by a servo amplifier-motor loop, and recorded on a chart, whose speed (1| inches per minute) is synchronized with that of the moving probe. In the same way, records of collector current as a function of probe position can be obtained, and correlated with those of noise power. The probe can be moved a distance of about 17 inches, its position nearest the gun (2 = 0 inches) corresponding to a distance of 0.95 inch between the anode and the input plane of the RF gap. VACUUM '''ENVELOPE 50 OHM COPPER COAXIAL DRIFT TUBE ^LINE .,,, V/////////A, I ,, COLLECTOR / -O^O DIA.^ \ /'I \ i .050 DIAn \ \ "^ top DIA I ( ,531 R Fig. 1 — Cress-section of experimental tube, showing electron gun, probe, and two solenoids. The isolated current-collector electrode serves as inner conductor of a coaxial line. The induced RF power can be measured over a wide range of frequencies. PART I — THE GROWING NOISE PHENOMENON 835 III EXPLORATORY MEASUREMENTS The electron gun used in these experiments had been designed for use in a helix traveling-wave tube with a longitudinal focusing field of 600 gauss. Noise-power and collector-current curves, therefore, were first taken with 600 gauss to study a typical state of affairs in an operational beam. As seen in Fig. 2, the noise power at 3.9 kmc varies periodically with distance for about 4 inches from the gun, then climbs rather smoothly by nearly 23 db to an irregular plateau, where it undulates slowly, and finally levels off. The initial part of the growing noise curve at 10.7 kmc is missing because of inadequate receiver sensitivity, but its later portion is similar to that at 3.9 kmc, with about half the rate of noise climb. With the 0.020-inch aperture, the collector-current varia- tions decrease in amplitude chiefly in the drift region preceding the noise climb; whereas those for the 0.100-inch aperture decrease afterwards. Both curves show a flattening in the growing-noise region itself, as well as a decrease in their average values after that region, signifying an in- crease in the average beam diameter. A similar set of curves is shown in Fig. 3, for a focusing field of 279 gauss (about twice the nominal Brillouin field). Noise growth at 3.9 kmc starts later, and proceeds less steeply, than at 600 gauss. The noise-power curve for 10.7 kmc is much more articulated, with a semblance of peri- odicity, throughout the drift region. Collector-current curves for both 0.020- and 0.050-inch apertures show considerable reduction in current- ripple amplitude with distance, reaching virtually zero in the former case. Another type of survey measurement is illustrated in Fig. 4. With the probe stationary at the far end of the drift space (about 18 inches from the gun anode), the main solenoid current is varied smoothly to change the focusing field from 0 to over 600 gauss, and synchronized records are made of collector current and noise power. (In this instance, the current in the auxiliary solenoid was +3.2 amperes.) At low mag- netic fields, both the current and noise-power curves have large ampli- tude variations, which diminish as the field increase. At first glance, the noise peaks and valleys seem to coincide with those of collector current; certainly, some do. Closer inspection, however, reveals significant mis- alignments which cannot be accounted for by experimental error. When the three noise curves, at 3,050, 3,930, and 4,730 mc, respectively, are compared with each other, some characteristic features emerge: (1) An average curve drawn through each pattern has one or two broad maxima, which tend to move toward higher field strengths with increasing frequency. 836 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 45 40 m u lU Q Z a. Ill 5 o Q. LU (/I O liJ > < _l 35 30 25 20 15 10 -^ —*.— H.9 Db/nCH-J ^ ^^ ^*— ^ y / / . .-J r SHOT NOISE LEVEL 20.8 DB 1 , . — .— _. — . — .. /^ k^ ^ y ' L.O. AT 3930 MC (a: i ,^^ 5.0 D&/lNCH-^^-> /^ V ^^ '^ ^^ "^ -^^ --^ ^^ ■- ^ L O. AT 10,690 MC (b: < ? > z 0 1- 20 z III cc 18 cc 3 u 16 n- O t4 u LU _l 1? _) o o 10 LU I') < a cc LU > 6 Ay 1 V v\ r^ v^ \A A/ ^A. ^A A/ ^/v '\/V /^^ r- ->^/-> -^V VN / 0.020" DIA APE .RTU RE r\^'\/ ^X\ ^^ ''V-n ^^ V^ ^^ "•^^ /"s..*^ ^ ' 0 100" DIA, APERTURE (dl 10 12 14 16 18 Z IN INCHES ALONG DRIFT TUBE (0 IS 0.95 "FROM ANODE) B=600 GAUSS, B(-=25.6 GAUSS, V=2200 VOLTS, 1 = 38 MA Fig. 2 — Typical smooth steep growing-noise patterns, near 4 and 10.7 kmc, respectively, with customary focusing field of about four times the Brillouin value. Collector-ciu'rent traces through small and large apertures reveal decreases in ripple amplitude and increase in average beam diameter. / ^ -''"^u -^ - ( 5.7 DB/iNCH— ^ Ny 1/ y -V J. 7-^^ SHOT NOISE LEVEL 20.8 DB - ^- . — — -._ « _ — • 1 1 L.O. AT 3930 MC 1 _(a) J A f\ / / J V /■ A ^ JA / -\ 8.0 DB/INCH--.^' J V J "* '\j\ J \j L.O. AT 10,690 MC J \j (b) \ ' 0.020" DIA. APERTURE A ( \ f\ \ \ 1 ^ i \ r s r\ ^ J t: / ^ \ J \J c) \ A 0.050" DIA. APERTURE l\ / r \ , -^ n /\ \ J \ / 1 / \; ^1 J ^ ^ — A < 0 ^ /■ ^ ^ y „^ y r\l ^ A \f\A f\r \ V r o.ioo"dia. aperture ni\l \|V« AM /IT*- /v" (a) to -J UJ m o UJ o UJ o Q. UJ o Z UJ > I- < _l UJ 35 30 25 20 15 10 5 0 40 N -. fll/' ^'^L / X;iv ''\ X^ L.O AT 3930 MC a/ vw y s V. IP V VH ^ K\ fv s. r ~^ / (c) 450 500 550 600 635 MAGNETIC FOCUSING FIELD IN GAUSS V=2200 VOLTS, 1-38 MA, Z=17.10 INCHES Fig. 4 — With the probe stationary at about 18 inches from gun anode, collec- tor current and noise powers in bands about 1 kmc apart are recorded, as current in the main solenoid is varied from 0 to 1.5 amperes (0 to 635 gauss). 838 PART I — THE GROWING NOISE PHENOMENON 839 (2) The lower the frequency, the lower the field strengths at which noise amplitudes change most violently with field. (3) The three noise curves resemble each other in small details. The results of a great many records of the kind illustrated by Figs. 2 and 3 can be summarized as follows: (1) There is always a decrease in beam-ripple amplitude associated with noise growth at any frequency. (Sometimes the ripple amplitude increases afterwards, as in Fig. 3.) (2) The higher the frequency, for a given field, the more articulated or scalloped the noise pattern. (3) No correlation can be found between rate of noise growth and either (a) distance from gun to take-off plane, or (b) net gain at the end of the drift region. The trends, as a function of magnetic field, are differ- ent at different frequencies. (4) Greatest noise growth does not, as a rule, occur with zero flux threading the cathode. Sometimes two nearly equal peaks occur for two values of Be , each of opposite polarity, referred to the sense of the main field. (5) The noise-distance patterns change very slowly with frequency. (6) No beam entirely ripple-free throughout its length has ever been observed by the writer. IV ORIGIN OF GROWING NOISE If noise growth is due to some amplification process, it should be possible to adjust the beam-focusing conditions so that the noise currents start increasing at the anode, and attain the greatest possible over-all gain at the end of the drift space. The enhanced activity of the unknown gain mechanism should presumably help identify it. The curves of Fig. 4 show that maximum noise occurs at different values of the focusing field, for different values of field at the cathode, and different probe posi- tions. With the anode voltage and receiver freciuency fixed, therefore, the conditions for greatest net noise growth can only be found by a series of trial settings of both magnetic fields, each followed by a recording of the noise-distance pattern. Eventually, a set of fields can be found for which the greatest total gain occurs; and such patterns are usually found to show fairly steady noise-amplitude increase, on the average, over the entire length of probe travel. The results of this procedure for noise power near 4 kmc, as well as the patterns of collector-current versus distance with the same fields, using the 0.1 00-, 0.050-, and 0.020-inch apertures fixed at the probe centerline, are shown in Fig. 5. A similar set of records, for noise power < 2 cc z> o cc o I- u _) _] o u UJ ID < (T UJ > < 1^: 10 T\ A 1 1 / 1 \ / \ J r \ ^"^ \ \ / \ / / \ / \ / \ ( V y V J V i \ / \i J V V vj / V- / v. / \ J 0.100" DIA. APERTURE 12 10 (b) A 1 A 0.050" DIA. APERTURE r\ / \ r \ r^ \ fN k V } / / \ y 1 \ 1 / V >w 1 / \ V y V_ y v_ y \ J \-J (c; b 1 5 T 4 3 2 ■ o.c 20" DIA. { / r\ APERTURE \ [^ I /■^ V /^ r \ 1 0 _J \ ^ ^. / \ r fv ^^ J\ \i ^ (d) 8 10 12 14 16 Z IN INCHES ALONG DRIFT TUBE (0 IS 0.95" FROM ANODE) B=134.7 GAUSS, 8^=18.24 GAUSS , \/=2200 VOLTS, 1 = 36 MA Fig. 5 — The magnetic fields in drift tube and at the cathode have been adjusted empirically to expand the growing-noise region over the entire drift region, with the L.O. at 3,990 mc. The field is slightly less than the Brillouin value, but the beam is strongly rippled because the gun was designed for best focusing at a much higher field. The noise-current maxima align with the average collector currents on their increasing slopes, for all three aperture sizes. 840 PART I — THE GROWIXG NOISE PHENOMENON 841 near 10.69 knic, is shown in Fig. 6. The significant features of both sets of records can be summarized as follows: (1) In both cases, the beam-ripple periods are equal to the RF scallop periods; i.e., the half-wavelengths of the space-charge standing waves. The noise minima tend to occur at planes where the collector currents are at their average values and decreasing; i.e., where the beam diame- ters are at their average values and increasing. The noise-current maxima occur where the beam diameters are about to decrease. These are the classical conditions for rippled-beam amplification. ' ' (2) In Fig. 5, the ripple amplitudes and peak values of all three col- lector-current curves decline appreciably with distance, the rate of de- cline being greatest for the smallest aperture. (Similar curves, not shown here, have displayed little or no such decline in the absence of noise growth.) This suggests that the RF noise power is amplified at the ex- pense of do energy associated with radially-directed electron velocities. (3) In Fig. 6, the disparity among rates of decline of current-ripple amplitudes and their peak values, for the three aperture sizes, is even more pronounced. In addition, the ripple wavelength barely changes for the^ 0.100-inch aperture, but increases with drift distance for the smaller apertures, resulting in an increasing "phase shift" among them. Thus the current-density variations at different radii in the beam can contribute unequally to space-charge wave amplification, depending ori their local ripple amplitude and phase. In this instance, the variations in current density along the beam are initially greatest near the axis, and suffer the greatest reduction there. It is worth noting that this "inner rippling" would be missed entirely in beam-size measurements with a large aperture.* The decrease of beam ripple and the increase in average beam diame- ter, shown in Figs. 5 and 6, has been found to accompany rippled-beam amplification of impressed signals by T. G. Mihran. Another corrobora- tion of the identity of this gain mechanism can be obtained by comparing the measured noise gain per scallop with that predicted by theory for idealized conditions. ' For a beam with stepwise alternations of maxi- mum and minimum beam diameters (ratio r2/ri), and with noise maxima and beam-diameter maxima coinciding, the gain per scallop is as follows: Gr,. = {;^ - ^. (1) Here, V is the beam potential, and p the reduction factor w^/ajp . Al- though the actual rippled beam is far removed from either Brillouin or * More information about "inner rippling" will be presented in Part II. to LU a lU Q. < J _J I- z UJ a. oc D U DC O I- o u i AA 3.3DB/iNCH^ X' J ■^c* .< < \/ r\ 7 \ 1 v o«. / \'', n vf '^n M\ i Ai V 1 41k ^n r J 1 (a) L.O.AT 10,690 MC lA ^^ 'X / \! c, ^^ ^^x' / J 0 J M 1 A i O i^> '^'^ /^ V .<~^ ^^ 1 1 1 f\l ^^ \/ A r V ■\ r \/ ^ r s^ X ^ <— - o 1 1 1 1 1 1 (b) 0.100" DIA APERTURE — ^ 1 1 1 o 1 1 1 0 1 1 1 4 A _ii_ A / 1 1 1 1 f A 1 \i A > \ 1 o I \ \ A ri r 1 1 1 \ r L , N y \ r /I M/ \ P I / \ r J \ / \j 1 1 (C) 0.050" DIA APERTURE J^ ' o' v^ ^ 1 ^ ' \j 1 1 1 0 1 1 1 7 ft A 1 ! c A i 1 1 (d) 0.020" DIA APERTURE 1 1 1 1 \i r\ 1 1 1 O 1 . 1 \ \\ A 1 1 1 A / y \ jl J \ .\ , ; V / L^ 1 ^ ~\ _^ 0 y v: ' \y v- ^ 1 / w V / 1 1 2 IN 4 6 8 10 12 14 INCHES ALONG DRIFT TUBE (0 IS 0.95" FROM ANODE) 16 18 8= 260 GAUSS, Be = 31.2 GAUSS, V= 2200 VOLTS, 1=38 MA Fig. 6 — The fields have been adjusted as in Fig. 5, for maximum extension of the gain region, for noise power near 10,690 mc. Collector current measured with the smallest aperture shows the greatest decline in amplitude of variations, as well as advance in ripple phase relative to the current through the largest aperture. 842 PART I — THE GROWING NOISE PHENOMENON 843 Table I — Measured Versus Calculated Maximum Noise Gain Freq. mc. Ripple Data Gain in db per Scallop Iris Dia. Inches rilr\ Brillouin Flow Confined Flow Measured 3,990 10,690 0.020 0.050 0.100 0.020 0.050 0.100 3.4 3.2 1.9 2.5 1.8 1.1 6.1 6.3 4.0 6.4 4.8 <1.0 5.0 5.4 3.3 5.6 4.4 <1.0 4.3 4.9 confined flow, the published values of reduction factor for both extremes can be used as first approximations. ' ' The ratio ri/ri can be estimated by assuming the current density to be uniform over the beam cross- section near the middle of the drift region, for each of the three apertures used. The potential variations can be neglected. The results of such cal- culations are given in Table I. As the computed gains are expected to be somewhat greater than those measured, because of the optimum conditions assumed, the best cor- respondence between measured and computed gain rates appears to be for the ripple data taken with the 0.050-inch iris at 3,990 mc, and that with the 0.020-inch iris at 10,690 mc. This distinction is in accord with previous qualitative comparison of Figs. 5 and 6, showing that most of the beam cooperates in the ripples of the former, but that "inner rip- pling" characterizes the latter. Another calculation that reveals which part of the beam is interacting with the RF noise field in each case is that of the space-charge half- wavelength, as follows: 2 where /3p6 17^I"'/V"\ (2) (3) Here ^p is the plasma wave number, b the beam radius, and p the reduc- tion factor, which can be evaluated as previously for the smooth beam in either ideal Brillouin or confined flow. For the gun used here, the square root of the perveance is or X»/2 ^ 29.8 h/p. (4) 844 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 Table II — Measured VERstJs Calculated Space-Charge Half-Wavelengths Iris used, inches dia. Avg. beam radius ro inches 7 rad./in. Xj/2, inches Ripple 1 Freq. mc. Brillouin Flow Confined Flow Meas'd Wavelength ■ L, meas'd 3,990 10,690 0.050 0.020 0.057 0.033 22.9 61.2 3.2 1.6 2.7 1.3 3.0 1.47 3.06 1.52 1 Thus, agreement between this expression and the measured value requires the correct choice of the effective beam radius, h. It turns out that the suitable value for Fig. 5 (3,990 mc) is the average beam radius obtained from ripple data taken with the 0.050-inch iris, and that for Fig. 6 (10,690 mc) is obtained with data taken with the 0.020-inch iris. The results are summarized in Table II. With this mechanism as the primary source of the noise gain, it be- comes clear why nearly equal noise maxima were found, with some values of the main focusing field, B, for two values of cathode flux den- sity Be of opposite polarity. From approximate analyses of beam ripples when flux threads the cathode, such as those provided by McDowell^^ and others, it is found that the ripple wavelength depends nearly alto- gether on B. Its amplitude and spatial phase, however, depend on Be , as this affects the beam geometry at the drift-space entrance. For a sufficiently wide range of variation of 5c , the spatial phase of the ripples can be varied from the proper relation wdth the space-charge standing wave for gain, through the positions for de-amplification, and back to gain again. I V THE GROWING-NOISE MECHANISM Although many earlier noise records can be understood in the light of the rippled-beam amplification (RBA) process, this is not yet true of the smooth, steep noise growth usually observed, as in Figs. 2 and 3. The simple theory predicts that a space-charge wave will be amplified when, for small ripples, a "resonance" condition exists between the rip- ple wavelength, L, and the space-chai'ge half-wavelength L ^ nXs/2, (5) where n is an integer, usually unity. In addition, as mentioned earlier, there is an optimum phase relation between ripple and standing wave for maximum gain. These conditions are not satisfied by the records of PART I — THE GROWING NOISE PHENOMENON 845 Figs. 2 and 3, except possibly for the 10.7 kmc noise current in Fig. 3 (at a relatively low magnetic field). To establish a connection between the two types of noise growth, the noise record of P'ig. 6 (for 10.7 kmc with greatly expanded gain region) is compared with that near -4 kmc under the same conditions, in Fig. 7. The growing noise region for 4 kmc does not start until at least four scal- lop wavelengths past the earliest observed 10.7 kmc noise growth. More- over, the 4-kmc noise pattern resembles that for 10.7 kmc in many de- tails. (The resemblance in details of noise patterns at nearby frec^uencies has been remarked before, in connection with Fig. 4.) cr UJ o Q. LU _l LU NOISE POWER NEAR 1 .■' r 10,690 MC .',< / 1 -^ < / \/ 3 J DB/lNCHj ^^' i V / v J \ ( ' /^ r v --i h- 30 < -I 111 cr 2b 20 15 10 ii J'*^ . L l«J J.. „ui # 0fr^ .„# w lT''iH,#ri 1 ruT " """"" JiJL 'i % rilTri lUll^ T (C) WITHOUT BEAM MODULATION L.O. AT 3120 MC Fl r F T r 6 8 10 12 14 Z IN INCHES ALONG DRIFT TUBE (0 IS 0.95" FROM ANODE) B = 954 GAUSS, Bc = 37 GAUSS, V=2200 VOLTS, 1 = 36 MA 15 18 Fig. 9 — Two strong klystron signals are impressed on the beam as in Fig. 8, and noise power at their difference-frequency recorded, both with and without these signals present. The deep noise minima in (b) are due to destructive inter- ference between trains of waves excited by intermodulation at different positions along the beam. 850 Jil PART I — THE GROWING NOISE PHENOMENON 851 is simultaneously modulated as before with two klystron signals (8,400 and 11, 590 mc, respectively), but now at fairly high level; and the fo- cusing field is made large. The interference dips in the pattern of 3,120-mc noise are quite deep, and are spaced irregularly and farther apart than the space-charge wavelength of any of the three frequencies involved. The third dip is shallower than the previous two because of the growth of 3,120-mc noise other than that due to the signals, as shown in Fig. 9(c). The latter pattern of noise in the absence of the two high-level, high-frequency signals suggests that the characteristic first gentle dip following the growing-noise region is indeed of the same nature as the artificially-produced interference dips, and has nearly the same cjuasi- period. The pattern of dips agrees with simple calculations, based on this model, in which the amplitude of the difference-frequency intermodula- tion product, excited at any plane f , is assumed proportional to the prod- uct of the amplitudes of the two high-frequency space-charge standing waves, as follows: \di,\ oc |ti(f)-z2(r)(^rl, (7) where in = In sin p„l3p^- sin co„(^ - t/u), (n = 1,2). The total current at f = ^ is the sum of contributions from all the stand- ing waves excited to the left of it : 1 f^ I t3 I cc -/1/2 / COS P3(3p(2 - f)[C0S (pi - 7)2)i3pf 4 Jo (8) - cos (pi -{- P2)0p^] f/f . This expression is readily integrated and evaluated. VI CONCLUSIONS Synchronized measurements of electron-current density and noise currents at several microwave frequencies have shown that the "growing noise" pattern in drifting cylindrical beams is the result of a two-stage process. In the first stage, rippled-beam amplification of noise fluctua- tions takes place over a very broad band of microwave frequencies, much higher than the usual observation frequency. In the second, noise energy is transferred to lower frec^uencies by intermodulation and other non-linear processes within this band. The element of non-linearity is supplied when primary noise gain is sufficient to make electron bunching 852 THE BELL SYSTEM TECHNICAL JOUKNAL, JULY 1957 non-sinusoidal. Other sources of non-linearity are thermal velocities, non-laminar beam flow, etc. As the beat-frequency noise increments at any plane are produced by continuous arrays of freciuency pairs, in- creasing in numbers and amplitude in various ways as primary amplifica- tion proceeds, the multiple standing-wave patterns at the observation frequency progressively overlap one another. This results in the smooth steep rise of noise power usually observed. Phase correlation among the space-charge waves excited at succes- sive planes on the beam by the same set of frequency pairs is indicated by gentle dips, due to their destructive interference, in the plateau following the initial noise rise. Rippled-beam amplification occurs whenever the ripple wavelength and half the space-charge wavelength are nearly ecjual, and bear a favorable spatial relation to each other. However, this "phase" relation becomes less critical with an increase in either the number of ripple Avavelengths over which synchronism persists, or the ripple amplitude, or both. Noise amplification by this mechanism, therefore, is probably present to some degree in all rippled streams, particularly at high fields. The extreme difficulty encountered in focusing ripple-free beams from convergent, shielded guns has to this date prevented the detection of any other primary gain mechanism, which may conceivabh' co-exist in such beams. A conspicuous feature of rippled-beam amplification is the decrease in ripple amplitude due to conversion of dc into ac kinetic energy. Such changes in beam structure emphasize the inadequacy of beam-flow com- putations based entirely on dc force eciuations. A more detailed descrip- tion of this dc-ac energy conversion is given in Part II. ACKNOWLEDGMENTS The experimental apparatus could not have been built without the combined efforts of man}- associates of the writer, principally A. R. Strnad, P. Hannes, J. S. Hasiak and J. AI. Dziedzic. The author is also indebted to R. Kompfner, C. F. Hempstead and K. M. Poole for valuable suggestions; and above all to C. F. Quate for constant encouragement and advice. REFERENCES 1. C. C. Cutler and C. F. Quate, Experimental Verification of Space-Charge and Transit Time Reduction of Noise in Electron Beams, Phys. Rev., 80, p. 875, 1950. 2. L. D. Smullin and C. Fried, Microwave Noise Measurements on Electron Beams, Trans. I.R.E. ED-1, No. 4, p. 168, Dec, 1954. PART I — THE GROAVING NOISE PHENOMENON 853 3. C. Fried, Noise in Electron Beams, Tech. Rep. 294, Research Laboratory of Electronics, M.I.T., May 2, 1955. 4 J. R. Pierce and L. R. Walker, Growing Waves Due to Transverse Velocities, B.S.T.J., 35, p. 109, Jan., 1956. 5. G. G. Macfarlane and H. G. Hay, Wave Propagation in a Slipping Stream of Electrons: Small Amplitude Theory, Proc. Royal Soc. (B) 63, p. 409, 1950. 6. C. K. Birdsall, Rippled Wall and Rippled Stream Amplifiers, Proc. I.R.E., 42, p. 1628, Nov., 1954. 7. R. W. Peter, S. Bloom, and J. A. Ruetz, Space-Charge-Wave Amplification along an Electron Beam by Periodic Change of the Beam Impedance, RCA Rev., 15, p. 113, March, 1954. 8. T. G. Mihran, Scalloped Beam Amplification, Trans. I.R.E., ED-3, No. 1, p. 32, Jan., 1956. 9. R. H. Dicke, The Measurement of Thermal Radiation at Microwave Frequen- cies, Rev. Sci. Instr. 17, p. 268, July, 1946. 10. W. W. Rigrod and J. A. Lewis, Wave Propagation Along a Magnetically- Focused Cylindrical Electron Beam, B.S.T.J., 33, p. 399, March, 1954. 11. G. M. Branch and T. G. Mihran, Plasma Frequency Reduction Factors in Electron Beams, LR.E. Trans., ED-2, No. 2, 3, April, 1955. 12. Informal communication from H. L. McDowell. 13. Informal communication from J. R. Pierce. 14. Informal communication from H. Hetfner. 15. S. Bloom, Space-Charge Waves in a Drifting, Scalloped Beam, unpublished RCA Research Laboratories report. 16. O. E. H. Rydbeck and B. Agdur, Propagation of Space-Charge Waves in Guides and Tubes with Periodic Structure, L'Onde Electrique, 34, p. 499, June, 1954. 17. P. V. Bliokh and Y. B. Feinberg, Space-Charge Waves in Electron Beams with Variable Velocity, Zhurnal Tekhn. Fiziki, 26, p. 530, March, 1956. 18. C. C. Cutler, The Nature of Power Saturation in Traveling Wave Tubes, B.S.T.J., 35, p. 841, July, 1956. 19. S. Lundquist, Subharmonic Oscillations in a Nonlinear System with Positive Damping, Quarterly of Appl. Math., 13, No. 3, p. 305, Oct., 1955. I Noise Spectrum of Electron Beam in Longitudal Magnetic Field Part II — The UHF Noise Spectrum By W. W. Rigrod (Manuscript received January 21, 1957) Sharp peaks are found in the UHF spectrum (10 to 500 mc) of an elec- tron beam, emanating from a shielded diode. In the presence of a longitudi- nal magnetic field, the strongly rippled beam displays an additional set of peaks whose frequencies are proportional to the field strength. The largest of these, just above the cyclotron frequency, is connected with the overlap of a dense cluster of particle orbits, passing close to the beam axis. It can attain amplitudes of 65 db above background noise. The transverse distribution of UHF noise power is found to agree with that for ideal Brillouin flow , even in rippled beams. With long ripple wave- lengths, two noise maxima are found to flank each beam waist. A small- signal wave analysis explains this pattern, and affords some insight into the energy-exchange processes in rippled-beam amplification. The reduction in "growing noise" due to positive ions is attributed to increased cancellation of net radial beam motion, due to overlap in particle orbits near the axis. I INTRODUCTION The reader is referred to Part V for a description of the experimental apparatus and its operation. In this paper, measurements of noise power in the same electron beam are described, with freciuencies chiefly in the 10- to 500-mc range, and relatively weak magnetic fields. For the UHF measurements, a calibrated coaxial step attenuator and a super-regenera- tive receiver (the Hewlett-Packard 417-A VHF Detector) are used. Rela- tive noise-power amplitudes at fixed freciuencies are measured as before, in terms of changes in attenuation between probe and receiver required to restore constant receiver output. To obtain qualitative information, however, such as the location of noise maxima along the beam, the series attenuation is fixed. The receiver output is amplified, rectified, and per- 855 856 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 mitted to register itself directly on the chart recorder, whose motion is synchronized with that of the probe. Very roughly, the detector output varies as the log of input power. Measurements are described (a) of the UHF noise spectrum in the beam, just outside the gun anode; (b) of this spectrum at the end of the drift region, in a longitudinal magnetic field; (c) of the noise-power dis- tribution along the axis; and (d) transverse to the axis of the rippled beam in the drift region. Two calculations are then outlined, one of wave propagation along the rippled beam (to explain the observed distribution patterns), and the other to account for some spectacular peaks in the beam spectrum (b). II FIELD-INDEPENDENT PEAKS When the noise spectrum of an electron beam is scanned by a tunable receiver, it is found that an irregular array of narrow-band peaks char- acterize the UHF region, below about 1000 mc. Of these peaks, some are due to spurious modulation effects," and can be eliminated as follows: (1) Transit-time oscillations due to positive ions, secondary electrons, or both. Such frequencies vary with probe (collector) position. (2) Resonances in the probe and receiver, excited by the pulsed- voltage supply. These are unaffected by changes in collector current. (3) Ion oscillations in the electron gun or beam. Their frequencies vary with anode voltage. The remaining narrow-band peaks fall into two classes, depending on whether their frequencies vary with the magnetic field. Well-defined peaks can be detected with the RF probe stationed one inch from the gun anode, with or without any focusing field. When the beam is focused by a longitudinal magnetic field, these disturbances propagate along the beam, and tend to increase in amplitude with dis- tance, but not to change in frequency. A typical set of such frequencies, within the range of the tunable receiver is as follows: 15.9, 24.3, 31.2, 34.0, 48.5, 63.4, 77.0, 108, 151, 166, 270.5, 372 and 481 mc. (During this measurement, the anode voltage was 2,200, and the peak current about 40 ma.) No consistent relation could be found between these frequencies and either the anode voltage or the cathode temperature, although unmis- takable frequency changes did occur when these parameters were ma- nipulated. Failure to establish such a relation may have been due to uncontrolled drift in cathode activity. In any case, the measurements did serve to narrow the field of possible mechanisms, by eliminating the following : PART II — THE UHF NOISE SPECTRUM 857 (1) Transverse positive-ion oscillations, for which the freciuencies vary as the square root of anode voltage. (2) Transverse electron plasma oscillations (near or beyond the anode), for which the frequencies would be too high. (3) Longitudinal electron plasma oscillations at the potential mini- mum, for the same reason (should be near 2,500 mc). (4) Longitudinal diode oscillations.'* When the electron transit angle through the diode is approximately (n -\- j) periods, where n is an in- teger, the real part of the diode conductance becomes negative, permit- ting oscillations to occur. Again the frequencies of such oscillations would be too high, (2,200 mc and higher) for the gun used, to conform to the observed values. There is, however, one published theory for which an order-of -magni- tude correspondence does exist between the measured and calculated frequencies. Klemperer^' ^ has shown that a strip beam tends to break up into clusters of "pencils" at the cathode. He ascribes these to standing waves resulting from transverse oscillations in the space-charge cloud, and offers an expression for the wave velocity in this medium. Applica- tion of his formula to the cathode used in the present experiments results in a least frequency of 3L3 mc. Other observers, such as Smyth' and \^eith,* have also reported evidence of interaction between electrons in a retarding-field region and RF fields, which may underlie these oscilla- tions, III FIELD-DEPENDENT PEAKS With the RF probe stationed ten or more inches from the gun anode, narrow-band peaks can be found in the noise spectrum of the beam. The amplitudes of these peaks increase and their frequencies decrease with decreases in the magnetic field. For each probe position, the process of finding the peak of greatest amplitude involves repeated adjustments of the focusing field, the magnetic field at the cathode, and the receiver frequency. When the fields have been so optimized, it is found that the probe is located at or near the first beam-diameter minimum, following that at the entrance to the drift space. When the field is doubled, and the "tuning" process repeated, the greatest peak is found to have about twice the frequency of the fir.st, and the probe is found to be located at or near the second beam waist. It is convenient, therefore, to think of these peaks as "proper" frequencies of the A'' = 1, etc., modes of the rippled beam, where A^ is the number of ripple wavelengths between gun and probe. 858 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 400 350 300 a z o o iJJ 250 a. o o 200 < z UJ a LU 150 100 Z= 15.00", 0.100" DIA APERTURE, OB READINGS NOT NORMALIZED. RIPPLE WAVELENGTHS, N = 4 BELOW 0 08 30 DB BELOW 0 DB CYCLOTRON FREQUENCY N = 2 40 DB , PLASMA FREQUENCY 40 60 80 too FOCUSING FIELD IN GAUSS 20 140 Fig. 1 — Frequencies and amplitudes of several narrow-band UHF peaks measured at a fixed probe position, about 16 inches from the gun anode. N is the number of beam-ripple wave-lengths between anode and probe. Other peaks have been observed at higher harmonics of the "proper" frequency (encircled points), and at about half that frequenc}'. As shown by the encircled points in Fig. 1, these frequencies range be- tween 1.03 and 1.06 times the calculated cj^clotron frequency, and have amplitudes as high as 65 db above the background noise. The amplitudes decrease with increasing ^V, falling off as the minus two-thirds power of the frequency. PART II — THE UHF NOISE SPECTRUM 859 At each of these optimum field settings, several weaker "satellite" peaks can also be detected, most readily those at the cyclotron frequency itself, and at 0.707 times the latter; i.e., the "plasma" frequency, as shown in Fig. 1. In addition, smaller peaks have been repeatedly ob- served at harmonics (up to the sixth) of the proper frequency, and one at slightly less than half of that frequency. (When a proper frequency was simulated by means of a signal generator, only its first harmonic could be detected in the receiver output.) At the fields corresponding to AT" = 4 in Fig. 1, the cyclotron frequency (312 mc) was found, but not the proper frequency. The highest proper frequency observed was 240.5 mc, in the A^ = 3 mode. The proper- frequency peaks decrease with increasing focusing field, whereas the field-independent peaks excited in the electron gun tend to increase, at the far end of the drift region. IV SPATIAL DISTRIBUTION OF UHF NOISE CURRENTS In Figs. 2 to 5 are shown synchronized chart records of collector cur- rent, one or more UHF narrow-band peaks, and microwave noise power near 4,000 mc — all as functions of distance from the electron gun, for the A'' = 1 to 4 modes, respectively. In all runs, the beam was pulsed with a 1,000-cycle square wave, and the collector aperture set at a 0.100 inch diameter. The magnetic fields at the cathode and in the drift space were adjusted before each set of readings, with the probe at a common reference position, for greatest amplitude of some UHF peak. In Figs. 2 and 3, these were proper frequencies, whereas in Figs. 4 and 5 they were field-independent frequencies. The content of these distribution curves can be summarized as follows: (1) At the low fields employed (none quite equal to the nominal Brillouin value), the beam ripples are quite large, both in amplitude and wavelength. (2) The proper-frequency traces have two or three maxima near each beam waist, and their amplitudes grow more rapidly with distance from the gun than any of the satellite frequencies. (3) The patterns of the cyclotron and "plasma" frequencies do not differ significantly from those of the field-independent frequencies, and usually display two peaks near each beam waist. (4) The collector-current maxima decrease with distance from the gun, although their minima change little. (The first maximum is sometimes flat-topped due to beam interception before it enters the drift space.) The rate of decrease of these maxima, and the rate of increase of proper- frequency amplitude, are greater, the longer the ripple wavelength. UJ (t UJ o. 2 < _i _i 2 Z - 2 a. D (a ) COLLECTOR CURRENT 0.100 DIA APERTURE \ \ /X \ V /A I \ J V. ' ' v_ ■ UJ z O Q- (O (r o (b) ^J ARROW- BAND NOISE POWER, °' BEFORE RECEIVER A / \ 1 \ 25 20 1 5 1 0 10 - 5 O UJ Q (C) RELATIVE NOISE POWER, L. 0. AT 3930 MC 1 1 fW* % A ^ I V 2 4 6 8 10 12 14 16 Z IN INCHES ALONG DRIFT TUBE (O IS 0.95" FROM ANODE) B=26.0 GAUSS, Bc=-2I.3 GAUSS, V=2200 VOLTS, 1 = 41.6 MA PEAK 18 Fig. 2 — The fields have been adjusted lor ma.ximuni amplitude of the .V = 1 proper frequency, 77.8 mc, at a reference probe position {z = 15 inches). The synchronized probe records indicate three distinct maxima of this proper fre- quency near the beam waist. 860 ■-'\ 8 (a) COLLECTOR CURRENT r 0.100" DIA APERTURE \ 6 1 j / \ lij 0. 1 \ / \ \ \ / \ 2 2 \ J ' \ / V \ \, y y K y \ 0 ' ' ■v — ■^ 10 z o Q. o lU I- UJ o (b) NARROW-BANC NOISE POWER, - ffiy — 157 MC Wl 1 M JU utJ BEFORE RECEIVER /i f\ 1 1 / 1 1 20 15 to m 5 m V lU o (C) NARROW- BANC ) NOISE POWER. Lj f = 76.2 MC \ UJ \ / h z o n ll / / \ m m a. / \ a. \ r \ o UJ I 1 ' o \ \ \ ; \ i v ^^ z^^- ^v^ J s, 'V •**s ^ "/ _ (d) RELATIVE NOISE POWER. L.O. AT 3930 MC f \ -. \ /' \\ \ 1 f \ 1 \ V ^ ( / V L \ J V J 2 A 6 6 10 12 14 16 Z IN INCHES ALONG DRIFT TUBE (O IS 0.95" FROM ANODE) B = 53.9 GAUSS, Be =" '5.2 GAUSS, V = 2200 VOLTS, I = 4 I MA PEAK 18 Fig. 3 — The longitudinal distributions of the A^ = 2 proper frequency-, 157 mc, as well as its "satellite" 76.2 mc, and microwave noise power, are shown here, with fields adjusted for greatest amplitude of the proper frequency at 2 = 15 inches. 861 20 16 UJ a. I 12 < 5 Z l- Z ui tr a. D O (a) COLLECTOR CURRENT 0.100" DIA APERTURE r-^ r K 1 \ , 1 \ /^ IL \ \ 1 \ V / \ V / \ 1 \ / / \ 'V \ s_ y \ V> ^ ' \ ,^ J UJ to z o 0. (U q: a o (- o UJ H UJ o (b) NARROW -BAND NOISf^ POWER kiu f=165 MC ^ \ 1 i / \ / If^ \ I A / \ \ 1 \ ii* ^ r\ III / 1 \ 1 1 / \ NLi / tW \ J 1 y ^W ^ ' Tvfp w M/< f 25 20 15 10 to _) UJ - 5 UJ O (C) RELATIVE NOISE POWER, L.O. AT 3930 MC 1 \\ n i^ii ^ aW^ M\ y / \, \ N / \ f \ liLn* / IT \ b / 1 V I; / ^Tjl" n' 4 6 8 10 12 14 16 Z IN INCHES ALONG DRIFT TUBE (O IS 0.95" FROM ANODE) 8 = 85.9 GAUSS, Be = 1.2 GAUSS, V = 2200 VOLTS, I =40.8 MA PEAK 18 Fig. 4 — The fields have been adjusted for maximum amplitude, at the same reference probe position, of a wave excited in the diode, with frequency unafTected by the magnetic field, 165 mc. The cyclotron frequency for this field is 240.2 mc. 862 16 If) S '2 < S. z a. cc o (a) COLLECTOR CURRENT \ r O.tOO" DIA APERTURE \ \ / N, / / 1 \ / \ \ / 1 \ \ / r V V y Nj J \ 1 \ / \ • *s_ V. u to z o Q. <0 UJ cr a. o I- o UJ H UJ O UJ w z o a. iij cc cc O H- O UJ t- UJ o (C) NARROW-BAND NOISE POWER, f=372 MC 20 15 10 10 _l UJ e 5 o UJ a ( d) RELATIVE NC )ISF POW FR 1 L.O. AT 3930 MC ,1 j/ ^f^ ^W •k *1 1 n^ ^ ^rpil Ai^fn tf* <^0|J /^>!^ n i^/f 1 1 f 'f ' T''p' 2 4 6 8 10 12 14 16 Z IN INCHES ALONG DRIFT TUBE (0 IS 0.95"FROM ANODE) B = 1ie.O GAUSS, B(- = +2.6 GAUSS, V=2200 VOLTS, I =40.4 MA PEAK 18 Fig. 5 — A procedure similar to that in Fig. 4 was followed, with four ripple wavelengths between anode and reference plane. The cyclotron frequency here is 329.5 me. 863 864 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 (5) The patterns of microwave noise power resemble blurred envelopes of the UHF traces. Some idea of the transverse distributions of UHF noise power and electron-current density, in a region of strong proper-frequency exci- tation, is given in Figs. 6 and 7. The measurements were taken by mov- ing a small aperture in a broad arc through the probe centerline, just in front of the probe aperture. In both illustrations, the relative noise power has been "normalized" to compensate for variations in electron current traversing the RF gap. The curves of Fig. 6 are typical of most such measurements. The beam- current density varies smoothly through a single broad maximum, and 50 45 40 in _l UJ cj UJ a a. UJ o Q- UJ 35 30 25 ^ 20 < cc o 2 15 1 0 148.5 MCS POWER Z=17.10 INCHES B = 51.30 GAUSS Bc=-90 GAUSS 0.250 0.225 0.200 0.175 0.150 0.125 2 0.100 0.075 0.050 0.025 0.05 0.10 0.15 0.20 0.25 0.30 0.35 TRANSVERSE IRIS POSITION IN INCHES 0.40 Fig. 6 — Simultaneous point -by-point measurements of collector current and relative noise power, obtained by moving an 0.013-inch diameter aperture in a broad arc through the probe centerline. The probe is stationary, about 18 inches from the gun anode, and the fields have been adjusted for maximum amplitude of the proper frequency, 148.5 mc. The cyclotron frequency is 143.8 mc. PART II — THE UHF XOLSE SPECTRUM 865 the noise-power density is greatest at the rim of the beam so defined, and least near its center. No evidence of azimuthal periodicity was found. The curves of Fig. 7, which are less typical, indicate five distinct peaks of RF power, despite a nearly symmetrical pattern of collector cur- rent. At the time of this measurement, cathode emission may have been uneven, due to coating damage by ion bombardment. In the rippled beam on which these measurements were made, the ratio of flux encircled at the cathode, to that in the drift space, was \er3^ small for most electrons. One would, therefore, expect the trans- verse noise-power distribution in this beam to resemble that in a smooth Brillouin beam.^ The noise power expected when a pinhole aperture is located at the beam center can be compared with that when the aper- 48 44 40 36 ^ 32 (J UJ O 28 - a. UJ Q. N 20 < 2 q: 16 O z 12 4- COLLECTOR CURRENT 0.020" DIA IRIS - Z = 15.00 INCHES B = 54.8GAUSS Bc=".4 GAUSS J_ J_ _L _L 0.05 O.IO 0.15 0.20 0.25 0.30 035 TRANSVERSE IRIS POSITION IN INCHES 0.24 0.22 0.20 -0.18 0.16 (o LU tr LU Q. 0.14 2 < -0.06 0.04 0.02 0.40 Fig. 7 — Transverse distribution measurements similar to those of Fig. 6. This pattern was obtained a week hiter than that of Fig. 6, and the cathode was operated at a higher temperature. The cyclotron frequency would be 153.2 mc for the field used. 860 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 tiire straddles the beam rim, by taking the beam area exposed in the first case to be that of a sector of angle 6, and the length of beam sur- face in the second case to be that of the corresponding arc: Rf current sample inside of beam ^^ dh'J^ _ h(u — /3i/) -hilSb) Rf current sample at rim of beam 2dbGz 2u/i(/36) Here b is the beam radius, and Jz , Gz the longitudinal components of volume and surface current densities, respectively. 7o and /i are modi- fied Bessel functions, (3 is the propagation constant, u the beam veloc- ity, and CO the radian frequency. For the frequencies and Vjeam radii employed in these measurements, this ratio is very much less than unity. Thus the pattern of Fig. 6 is in accord with this mode distribution. The multiple peaks of Fig. 7, however, do not conform to this picture, and are not understood at present. As most of the RF power is concentrated near the rim of the beam, the question arises whether the double and triple peaks, in the longi- tudinal distribution patterns of Figs. 2 to 5, are not due to the probe aperture breaking through the beam rim. However, the dip between adjacent noi.se peaks is too great to be explained on the basis of reduced partition noise or weakened gap coupling, assuming the beam diameter there to be less than the gap diameter (0.100 inch). Moreover, double peaks occur even when the beam diameter exceeds the RF gap diameter; for instance, near the last three beam w^aists of Fig. 5. (When all of the beam is transmitted by the 0.100 inch aperture, the collector-current peak is flat-topped.) It seems likely, therefore, that the double and triple peaks correspond to peaks of amplitude over the entire beam cross-section. V PROPAGATION ALONG THE RIPPLED BEAM To find an explanation for the multiple peaks of space-charge cur- rent, a small-signal, slow-wave analysis of wave propagation along the rippled beam can be made, in which the special features of these experi- ments are exploited: long ripple wavelength, effectively no flux at the cathode, and low frequencies. The first of these features suggests that the propagation constants can be evaluated at each cross-section plane as though the beam were uniform, despite the presence of radial ve- locities. In addition, the space-charge density is assumed constant at each cross-section, and the electron flow laminar. With these assumptions, the beam can be regarded as a fluid of mov- ing charge, with a single-valued velocitj^ at each point in space, as fol- lows: PART II — THE UHF NOISE SPECTRUM 867 Vo = {Vr , Ve , v^) (1) where Vr = r-f(z), or — ' = -^ (2) or r ve = rd = r |^ (3) V, = u. (4) Here, r, 6, z are the polar cylindrical coordinates, Wc = r]B the angular cyclotron frequency corresponding to the longitudinal focusing field B, and j{z) a function describing the amplitude and spatial periodicity of the beam ripple. The experimental data indicates that the potential variations along the beam axis are negligible, permitting the assumption that the longitudinal velocity, xi, is constant. MKS units are used. Consistent with the distribution pattern of Fig. 6, the ac field can be represented by an axially-symmetric potential function, similar to that for the smooth Brillouin-flow beam: V ~ 7o(7r) expjXwf - ^z), (5) E = -grad V. (6) The ac equations of fluid motion are obtained by adding a small ac increment to each of the steady-state velocity components. In addition to the space-charge field, the ac electric field contributes forces acting on the charged medium; those contributed by the ac magnetic field are neglected: {vo + y) = -77[-grad V - grad Vo + (vo + fJ) X B]. (7) at " - - - The ac velocity is distinguished by a tilde, and the dc velocity by a zero subscript. Here ri = e/m is the charge-mass ratio of the electron, a positive quantity. As all ac quantities are functions of spatial positions, their time differentiation (indicated by a dot) is equivalent to multi- plication by y(co — 0u), written jojfc for brevity. The components of the force equation are expanded as follows: ^ + (^. + v.) ^ (.. + Vr) + (U + V.) ~ (Vr -f r-,.) - ^^^1±^ dt dr az r dV , dVo f , . dr dr (8a) 868 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 >' + 'V (I, + -. r J. /M - 3F J- + 'v(^^ + ^ dd Ve = 0, ^i)^ , dv, . dv. -\- Vr -\- U dt dr dz V j^h + (V dr a7 dz' (8b) (9a) (9b) (10a) (10b) An expression for the ac space-charge density, jo, can be obtained in terms of its steady-state counterpart, po , by means of the charge-con- servation equation : dp dt — Vo-grad p — 5"grad po — po div v — p div ^o — Vo-grad po — po div Vo . (11) As the beam diameter changes slowly, the dc space-charge density at each plane is taken to be inversely proportional to the square of the radius, b: grad PC I = dpo ~dz 2podb^ b dz~ 2tv ^lr Po div Vo = — - yo-grad po •'■"' + "' (I + 7, ■po po '1 d 2Vr r (rvr) - jl3v, ( 1 - j i-- , r dr \ (311 r /_ (12) (13) (14) At low frequencies (the UHF region), dr r as {yrf « 1. This inequality is also true of other ac quantities pro- portional to V, such as V. and p, and with a small error can be assumed to be true for Vr . When the operator d/dr is omitted from (8), (9), (10), and (14), it is possible to solve explicitly for p in terms of po and T". PART II — THE UHF XOISE SPECTRUM 869 The laminar-flow rippled beam can be described by the particle trajectories, as follows: ri = ro,(l + 5 C0S|S,2), where ro, is the maximum radius for the paiticle considered, and 0 < 5 < 1. For this model of the beam, (15) r r dz h _ —boic sin (Sc2 h ~ 1 + 5cos/3,2' — ajci8c5(5 + cos ^cz) (Ki) (17) (1 + 5cosM- ■ The region of interest, judging from the observed peak locations, is not at the mid-plane of the beam waist, where Vr = 0, but on either side of that plane, where | Vr/r \ is greatest. It is readily found that, at these positions (I//-) (dVr/dz) is zero, and (14) can be written P = 7 J 0' fiu r / W6/ > (18) This can be combined with Poisson's Equation, AV = (y' - 0')V = -p/e, to furnish a relation between y and |8: (19) 7 R 1 (jibV/ _ = ^2 ini -J . 2 v., 1 - 0u r 1 mr (20) where R = Wp/wb and oij = — Tjpo/e, the square of the angular plasma fi'equency. At the beam boundary, r = h, the continuity of the tangential field components and the change in radial electric displacement can be ex- pressed in the form of an admittance equation: V \ dr a 1 ^J V di nil (21) Here I refers to the beam, 0 ^ ?• ^ b, and II to the space between beam and the concentric conducting tube, b ^ r ^ a. The surface charge layer, a, takes account of the surface ripple, of amplitude r: 870 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 por -ar/e = - __JPQVt R{dV/dr) (22) 1 - J . Vr cohr The appropriate potential functions in I and II are reduced by means of the low-frequency, or thin-beam, approximation, as follows: ']_dV'Y ^ yhjyb) ^ Yb V dr b hiyh) - 2 ']_dV V dr ~iii = /3 h{yb) ■ ^% _/o(/36)Ko(/3a) - h{l3a)Komj 1 (23) ~ 2 6 In a/6 where the following small-argument approximations have been used; Ko{x) ^ -In X, KiOr) ^^ln.T-f -, 2 X (24) , The boundary equation thus provides a second relation between 7 and (3: y% 1 - R 1 l3-'b 2 (■ cobr/_ 2 6 In a (25) For the smooth beam in Brillouin flow {vr = 0), the boundary equa- tion, to the same low-frequency approximation, is as follows: 2 (26) Re COj (« - i3ouy a im' In ~ To see how the beam ripple affects the propagation constant, it is sufficient to find its first-order effect; i.e., to assume relatively small radial velocities and find a solution for /3 which is not very different from its value, /3o , for the smooth beam: (27) /3 = /3o + 6 = /3e ± ^g + 5, where 5 I « /3o ; ^c COt u ^' /3e CO u PART II — THE UHF NOISE SPECTRUM 871 In addition, | Vrl (j^hf \ is less than unity, and | 2vr/^ur \ can be neglected entirely. With these assumptions, the boundary and characteristic equations can be combined to solve for ^ : ^ F{F -R) ^ - U) ^° (28) where 7_ _ _ ^2 F^ - R F - R CObV utilizing the low-frequency condition, \ R \ > \ R \ > 1, this equa- tion can be reduced and, after some algebra, solved: = 1 - j (00 + 5)(±/3,) — '' 2a;6r' /3.^/3e + ^« - i^, (29a) 2ur Pf^l3e- ^, + J:^. (29b) 2ur These expressions show that the current in the slow wave (IJ will grow when (vr/r) is negative; i.e., when the beam is contracting, and decrease during its expansion. The fast wave (I/) will do the opposite. In probe measurements along the beam, the detected ac power is pro- portional to the square of the total space-charge current, which has the following dependence on time and distance when the amplitudes of both waves are initially equal: (Is + //) = 2/max cos {cot - ^ez) -cos (13 gz) -sinh f ^ j . (30) In UHF noise-power measurements along beams with long ripple wavelengths, the two planes of maximum dz (vr/r) are separated by only a small fraction of a space-charge wavelength. Therefore, cos ^qZ at the first of these planes is only slightly larger than at the second. Thus, two peaks of current are observed, in agreement Avith (30). By contrast, in rippled-beam amplification at microwave frequencies, shorter ripple wavelengths and smaller ripple amplitudes are employed. Then (iv/r) varies nearly sinusoidally over the ripple wavelength. For maximum net gain per ripple, maximum negative (vr/r) is adjusted to coincide with the plane of cos ^gZ = 1 (maximum current), and maxi- mum positive (vr/r) at the current minimum, half a wavelength bej^'ond. 872 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 The gain constants in (29) are independent of frequency. The net gain per ripple wavelength, however, will vary with frequency, depending on how closely both the current maxima and minima coincide with the regions of maximum ± (vr/r), respectively. This is a statement of the "resonance" condition between ripple wavelength and half the space- charge wavelength, which emerges from one-dimensional analyses^" of this gain mechanism based on transmission-line analogies. Such analj^ses generally assume small-amplitude sinusoidal variations of the reduced plasma wave number, jS, , along a one-dimensional beam in a longitudinal ac field with no losses. Periodic variations in either beam or wall diameters, or beam velocity, cause the beam "impedance" to vary periodicallj^ imparting to it narrow-band filter-like properties equivalent to narrow-band signal gain. From another point of view, these periodic impedance changes couple the fast and slow space-charge waves to each other intermittently, thereby effecting an energj^ trans- fer from the fast to the slow wave. As this coupling is lossless, Is increases and // decreases with drift distance, in such a way as to keep their product constant. Then the product /max/min increases, and the ratio /max/min correspondingly decreases. In the case of noise-power amplification, two uncorrelated space-charge standing waves are present. Because the two slow waves cannot simultaneously be amplified at the expense of the two fast waves, the product /max/min must remain constant. The observed noise-current patterns in rippled-beam amplification, however, are characterized b}- a nearly constant ratio Imax/Imin , and an increase in the product /max/min along the beam, despite the fact that the beam voltage is fixed. This apparent contradiction can be resolved by a closer look at the energy-exchange processes. Chu'^ has shown that the kinetic power flow in space-charge waves (the major part of the total power) is equal to the difference in powers carried by the fast and slow waves. This is equally true of beams with transverse motions and fields. In rippled-beam amplification, whether analyzed as a modulated linear beam or at each beam cross-section sepa- rately, as here, the propagation constants are found to be complex con- jugate quantities, whose real parts describe the ordinary fast and slow waves of a uniform beam. From either point of view, therefore, a de- crease in // and an increase in /« signifies an increase in the negative kinetic power flow carried by the waves, or a decrease in the total kinetic energy of the beam. As shown in (29), the gain constants are proportional to tv , indicating that the dc energy transferred to the waves when the beam contracts could only have come from the radial kinetic energy, not the longitudinal. PART II • — THE UHF XOISE SPECTRUM 873 The direction of energj' transfer is reversed during the subsequent beam expansion. If the ripple were perfectly symmetrical, therefore, and the dc-ac energy exchange perfectlj^ reversible, the net effect of a beam ripple would be zero. Neither of these conditions is quite true in actual beams. Rippled flow is never truly laminar, and | Vrlr \ usually decreases with drift distance as the flow loses coherence; i.e., it is greater in beam con- traction than in the next expansion. This by itself would produce a net gain per ripple in /« , and a net loss in // , of equal amounts. In addition, however, unavoidable small non-linearities in electron motions prevent all of the ac energy in a de-amplified wave from being converted back to dc kinetic energj'. Thus it is possible for hoth the fast and slow waves to increase in a ripple wavelength, the latter always more than the former. The greater gain of the slow wave entails a loss of radial kinetic energy, in agreement with the observation that the ripple amplitude always decays more rapidly when rippled-beam amplification takes place. The incomplete reversibility of the ac-dc energy exchange probably accounts for the observed increase in /max/min for noise currents. Finally, the net amplification of all of the space-charge waves, fast as well as slow, is in accord with the observed near-constancy of the ratio /max/Zmin for microwave-frequency noise, despite increases in the product /max/min of 30 db and more. VI ORIGIN OF THE PROPER-FREQUENCY PEAKS Of the various peaks in the beam's noise spectrum, described in Sec- tion III and Fig. 1, those with "proper frequencies," slightly above the cyclotron value, are so large in amplitude that even an approximate analysis should be able to account for them. To do so, a "working model" of the beam is needed, which conforms to the experimental conditions which existed during the observations: (1) The peak intensities were greatest near the middle of each beam waist, and decreased with decrease in ripple amplitude. (2) The focusing field was below the nominal Brillouin \-alue. The field at the cathode. Be , was finite and opposed to the main field, B. (3) Collector-current measurements along the beam axis showed the ratio of maximum to minimum current to be greater, the smaller the aperture. (4) The gas pressure was about 10 ' mm Hg. The beam was pulsed with a 1,000-cycle square wave. Item (3) indicates that the flow was non-laminar; and Item (4) in- dicates the presence of positive ions. All the items are consistent with the following picture: 874 THE BELL SYSTEM TECHNICAL JOTTRXAL, JULY 1957 In a beam with large ripples, nearly all electrons have their maximum radii and zero radial velocity at the same z-plane. Those with sufficiently large maximum radius will have enough transverse kinetic energy to surmount the space-charge forces at the beam waist, and pass through or close to the axis. Others, with smaller maximum radii, will spiral about that axis. Bolder and Klemperer^ have observed a similar di- vision of electrons into "crossovers" and non-crossovers, in electron- optical systems without magnetic fields. Positive ions tend to neutralize the electronic space charge at the beam waists, broadening the region in which crossover occurs. The cross- over trajectories thereupon overlap one another, resulting in multi- valued transverse particle velocities in this region. In a first-order (linearized) study of wave propagation along the beam, one must re- place the actual multivelocity charge motions with a single "fluid" of charge, whose velocity at any point is the average of the particle ve- locities there. It is clear that the e-velocity of the stream is u, and the radial velocity zero. The tangential velocity, ve = (^r)av , however, is more complicated. Owing to the partial or total neutralization of electronic space charge at the beam waists, and their large radii elsewhere, the crossover elec- trons will encounter virtually no space-charge forces in their paths. Their transverse paths will consequently be circles about fLxed centers, de- scribed with angular velocity equal to the cyclotron frequency. Their angular velocity about the beam axis is given by Busch's Theorem: *=2 1 + 5 r- where K = -^M-^j = ^max?*min (3l) is a positive quantity, as Bc/B is negative. Here, Tc is the radius at which a particular electron left the cathode, and r is its radius in the drift region. The angular velocity, 6, is greater than coc/2 at all times, and exceeds coc in the waist region of the beam. The average value of ve at any point here, therefore, is greater than UcT and presvunabl}^ varies from point to point in some unknown way. If Ve is left unspecified, and the assumptions adopted of zero space- charge forces and radial velocity over a finite length of beam: ,^° = 0, r. =0, f=0, (32) the radial component of the force equation (7) in Euler coordinates can PART II — THE UHP NOISE SPECTRUM 875 be written as follows: ( dvo\ ve' _ . . dt r - -7 - - "^'« ' ^^^^ ve = 0 and UcV. (34) Thus, the radial "balance" conditions (32) are consistent with either of two values for ve , of the equivalent stream with single-valued velocities. As it develops that either of these values leads to the same result, the first one will be used here for simplicity, ve = 0. An ac traveling wave along this beam cannot have any 0-dependency, because the beam has no single value of angular velocity 6, which might remain in synchronism with that of the wave. Thus, the perturbed dynamics equation (7) can be expanded, wdth the assumptions of an axial-symmetric ac field given by (5) and (6), a stream with steady- state velocity (0, 0, u), constant space-charge density po , and no space- charge forces, as follows: dVr , d~r dV dt az or dve , dve dt az dv^ , dv^ dV dt dz dz These are solved for the ac velocity components: Ub — ojc or v,= -t^v,, (36) V, = -^ V. (37) COb With grad po = div ^o = 0, the charge-conservation equation (11) can be solved for p: A. = - Vo- grad p - po div v, at ^ = ^^ div .- = ,p. r^^^, - ^1 03b [_Oib — Wc 0}b J At very large ripple amplitudes, it is a fair assumption that the density of non-crossover electrons is negligible relative to that of crossovers in this region. Poisson's equation (19) can then be combined with the 870 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 above expression to obtain the characteristic equation : 2 1 "'P 2 ' ~ 2 2 _ (jJb — COe 2 ' ' 2 C06'' (39) In a frame of reference moving with the stream, u^ is 0, ^'u' is 0, and 03b = w. Then, ^/\2 / 2 2 2\ 2 and iS' becomes an infinite imaginary quantity when co is Wc . The phase velocity in the moving frame is infinite, as the real part of (3' is zero; therefore the phase velocity Vp in the rest frame is also infinite. Thus, there is no Doppler shift in the "resonant" frequency observed in the rest frame: _ ^g _ '^'observed — — ^c • / A1\ Vp As the actual beam has a 2- velocity spread, the field is never perfectly uniform, and as the calculation is valid for small ac quantities only, the discrepancy between this result and the observed "proper" frequencies, which were 1.03 to 1.06 times the cyclotron value, is not unexpected. The singularity in (40) is seen to disappear when Wp = 0. This indi- cates that an exact calculation would show the gain constant (— j/S) to increase with po , the density of the crossover electrons. Their tra- jectories, described by (31), and the absence of space-charge forces are such that K = rmax^min ; that is, the greater r^ax , the smaller rmin , the distance of closest approach to the axis. Thus, a larger ripple ampli- tude (permitted by a lower magnetic field) produces a greater electron density in the waist region, and accordingly a greater oscillation ampli- tude at the resonant frequency, as observed. The foregoing mathematics describes a form of resonance, the infinite phase velocity corresponding to longitudinal "cutoff" in a waveguide. Unlike a waveguide, however, the disturbance increases rather than attenuates along the axis, due to the transfer of dc kinetic energy (repre- sented by ve^/r) to the ac fields (excited by noise fluctuations at the cathode), at the cyclotron frequency Wc . Except for the direction of energy transfer, the situation is analogous to that of a low-pressure gas in a uniform magnetic field, when stressed by an impressed ac field of varying frequency. It has been found that the breakdown field at the cyclotron frequency is very much less than PART II — THE UHF XOISE SPECTRUM 877 at other frequencies. Here the energy suppHed by the ac field is coupled most effectively to the free electrons at the resonant frequency, increas- ing their dc kinetic energy until the gas breaks down. The circular ac charge motions due to the dc magnetic and the ac electric fields are superimposed on high-velocity random motions, similar to the radial motions in the drifting beam. The UHF peaks observed at harmonics of the proper frequency may simply be due to the non-linear character of the beam, when excited by the high-level fundamental oscillations. The other faint satellite peaks, near 0.5 coc and 0.707 Wc , seem to be associated with the unneutralized space-charge density at the beam waist. The conspicuous role played by crossover electrons in the waist region of rippled beams, due to the tendency of their orbits to overlap there, leads one to re-examine their influence on rippled-beam amplification. As seen in the previous section, this gain process depends on the average value of (vr/r) at each cross-section plane of the beam. The fraction of all electrons which penetrate to the beam axis depends on competition between the unneutralized space-charge forces and the particle's trans- verse kinetic energy. An increase in positive ion density tends to make the potential depressions at beam waists broader and shallower, and thereby increase the number of crossover electrons as well as the axial distance over which they reach the axis. The net effect is to reduce the average value of | fr | over a greater portion of the ripple wavelength, and thus reduce the net gain of the space-charge wave. This may explain why the "growing noise" phenomenon tends to be inhibited by an in- crease in positive ion density. VII CONCLUSIONS Evidence is found of oscillations with frequencies in the 10- to 500-mc region inside of an electron-gun diode. There is some basis for associating them with electron-field interaction in the retarding region of the diode. Another type of narrow-band noise peak is found near the waists of a strongly rippled beam in a longitudinal magnetic field, with frequencies proportional to the field strength. The strongest of these, at about 1.05 times the angular cyclotron frequency, co^ , as well as its harmonics, can be explained by the resonant behavior of a short section of the beam, in which the average transverse velocity is nullified by overlap in particle orbits. Fainter satellite peaks, near 0.5 Wr , 0.707 Uc , and o)^ , respectively, accompany the dominant frequenc3\ In a drifting beam launched from a shielded electron gun and focused by an axial field, the transverse distribution of noise (or signal) intensity is found to agree with that predicted for ideal Brillouin flow. Despite 878 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 the presence of thermal motions and beam ripples, the ac power is found to be concentrated chiefly at the rim of the beam. Occasionally, several concentric rings of noise maxima are found within the beam, possibly due to unusual cathode conditions. When the ripple wavelength is very long, two maxima of noise power are observed to flank each beam waist. A fir.st-order calculation of wave propagation along a rippled laminar-flow beam accounts for this pat- tern by showing that space-charge waves grow at the expense of dc kinetic energy in the radial charge motion. In rippled-beam amplifica- tion of noise, the product /max^min has been found to increase, and the the ratio /max/-^min remain nearly constant, because both fast and slow waves are amplified, the former less than the latter, and because the wave coupling is not lossless. Positive ions tend to collect at the waist of rippled beams, thereby extending the region in which electrons pass close to the axis, instead of circling about it. The overlap of their orbits leads to net cancellation of radial charge motion, and hence a reduction in rippled-beam ampli- fication. This may explain why positive ions tend to inhibit the "grow- ing noise" phenomenon. REFERENCES 1. W. W. Rigrod, Noise Spectrum of Electron Beam in Longitudinal Magnetic Field. Part I — The Growing Noise Phenomenon, p. 831 of this issue. 2. C. C. Cutler, Spurious Modulation of Electron Beams, Proc. I.R.PL, 44, p. 61, Jan., 1956. 3. K. G. Hernquist, Plasma Ion Oscillations in Electron Beams, J. Appl. Phys. 26, p. 544, May, 1955. 4. F. B. Llewellyn and A. E. Bowen, The Production of UHF Oscillations by Diodes, B. S.T.J. , 18, p. 280, April, 1939. 5. O. Klemperer, Lifluence of Space Charge on Thermionic Emission Velocities, Proc. Royal Soc. (London) (A) 190, p. 376, 1947. 6. K. T. Dolder and O. Klemperer, High Frequency Oscillations in the Space Charge of some Electron Emission Systems, Journal of Electronics, 1, p. 601 May, 1956. 7 C.N. Smyth, Total Emission Damping with Space-Charge-Lmiited Cathodes, Nature, 157, p. 841, June 22, 1946. 8. W. Veith, Electron Energy Distribution in Space-Charge-Limited Electron Streams, Zeit. f. angew. Physik, 7, No. 9, p. 437, 1955. 9. W. W. Rigrod and J. A. Lewis, Wave Propagation Along a Magnetically- Focused Cylindrical Electron Beam, B. S.T.J. , 33, p. 399, March, 1954. 10. R. W. Peter, S. Bloom, and J. A. Ruetz, Space-Charge-Wave Amplification Along an Electron Beam by Periodic Change of the Beam Impedance, RCA Rev., 15, p. 113, March, 1954. 11. J. R. Pierce, The Wave Picture of Microwave Tubes, B. S.T.J. , 33, p. 1343, Nov., 1954. 12. L. J. Chu, 1951 I.R.E. Electron Tube Conference on Electron Devices. 13. H. A. Haus and D. L. Bobroff, Small Signal Power Theorem for Electron Beams (to be published). 14. K. T. Dolder and O. Klemperer, Space-Charge Effects in Electron Optical Systems, J. App. Phys., 26, p. 1461, Dec, 1955. 15. S. J. Buchsbaum and E. Gordon, Highly Ionized Microwave Plasma, M.I.T. R.L.E. Quarterly Prog. Rep., p. 11, Oct. 15, 1956. Distortion Produced in a Noise Modulated FM Signal by Nonlinear Attenuation and Phase Shift By S. O. Rice (Manuscript received December 6, 1956) An expression is given for the FM distortion introduced by a transducer whose attenuation and phase shift depend upon the frequency in an arbitrary way. This expi'ession appears to be difficult to evaluate, but it yields useful approximations for the second and third order modulation terms. In all of the work, it is assumed that the distortion is S7nall compared to the signal, and that the signal can be represented by a random noise having the same power spectrum. INTRODUCTION A number of workers have been concerned with the problem of com- puting the distortion introduced by a transducer when an FM wave passes through it. Some of the earUest results were published by Carson and Fry and by van der Pol. Several contributions to the subject have been made recently in connection with studies of microwave radio systems. An excellent paper on this subject has been published recently by R. G. Medhurst and G. F. Small. Although their results differ consider- ably in form from those given here, they are nevertheless closely related to ours — their "sinusoidal variations of transmission characteristics" being special cases of our "nonlinear attenuation and phase shift." Here we treat the problem by applying a method used in a recent paper to study the distortion produced by an echo. Two assumptions are made, (1) that the distortion is small compared to the signal, and (2) that the signal can be represented by a random noise which has the same power spectrum as the signal. In Section I, we review some known results and put them in a form suited to our needs. Sections II and III are devoted to the derivation of our main formulas. The principal result is given by the triple integral (3.2) for the power spectrum of the dis- 879 880 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 tortion. Unfortunately, the integrals are difficult to evaluate. However, it is possible to obtain approximations for the second and third order modulation terms. These are given in Section IV. Some miscellaneous comments are made in Section V. I APPROXIMATE EXPRESSION FOR THE DISTORTION 6(t) Let the FM signal be '+^>''^ (1.1) where p = 2x/p is the carrier frequency. Let this wave pass through a transducer having attenuation a and phase shift /3, where a and ^ are even and odd functions, respectively, of the frequency /. When a unit impulse of voltage 8{t) is applied to the transducer input, the output is g(t) = r e-«-'-^+2.i/t ^^^_ ^2) J — 00 For physical systems, g{t) is zero for negative /. When Vi{t) is applied to the transducer input, the output is vo(t) = f vAt')g{t - t') dt'. (1.3) When V(i{t) is applied to an FM receiver, the detector output consists of the original signal ^'^^'^ ^ ^ Z J-00 J-« (2.7) The symbol R^ is chosen to agree as closely as possible with the notation of Reference 4. There R^ w^as the autocorrelation of the random func- tion, vii), where v{l + T) = ^(0 - ^{t + T), T being the echo delay. Here, R^ is the average value of the product, [+'^' cos px(e""^'"'^ - 1) . (4.5) This is the quantity which is to be subtracted from We-e{f) to obtain the interchannel interference spectrum wdf). The second order modulation term is handled in much the same manner. With the help of (4.3) it may be shown that /OO -| /«00 /?/ COS 27r/T rfr = Re - / du w^{u)w^{f — w) -00 t: ^ — 00 / — 27r»xu 1 ^ / ~2irtx(/— u) -i \ \'i."/ From this it follows that the second order modulation term in (3.2) is 1 /»00 /*00 2T2 j_ duw^{u)w^if - u) j dxg{x)e'"''''^'''' sinpx (4.7) / —ivixu , \ / — 2jrix(/— u) -i\ DISTORTION IN NOISE MODULATED FM SIGNAL 885 When ^0 — ^x is so small that exp ( — i^o + 1^2) may be replaced by- unity, as it is in some important practical cases, approximations may be obtained for (4.5) and (4.7). The integral in x may be expressed as the sum of integrals of the type / N —ipx—2iriax j r —a—tS-t g{x)e "^ dx = [e ^If^a+f,, -00 = Ga-{- iB, , (4.8) /" . _ . ' g{x)e'^'^ ^'^"^ dx = G-a — iB^a . -00 The values of the integrals follow from (1.2) and the Fourier integral theorem. G and B are, respectively, even and odd functions of frequency, and Ga , Ba are their values at the frequency f — fp -\- a where fp = p/2ir is the carrier frequency: G at frequency fp-\-a = Ga, B at frequency fp-{-a = Ba. In this way we get the approximation ^~'wM) KGf - 2(?o + G^ff + {B, - B_,f\ (4.9) for the first order modulation term, and 1 r" — - / duw^(u)w^{f - u)[{Gu - G-u + (j/-u - G-f+u - Gf 218J-00 (4.10) + G-ff + {Bu + B_„ + Bj.u + 5_/+„ - Bj - B^f - 2BoY] for the second order modulation term. Expression (4.10) is an approximation to the second order modulation term (4.7). When most of the interchannel interference is due to second order modulation products, (4.10) is also an approximation to wdf), the interchannel interference spectrum. The following remarks may be of some help in deciding whether (4.10) may be used. 1. For the case of phase modulation and a "flat" signal band, the first of equations (5.3) shows that \po and \//t may be made as small as we please b,y choosing the signal power (as measured by Po) small enough. Since /?,. is proportional to Po , Po may be chosen small enough to make P^. and higher order terms negligible in the expansion of the integrand of (3.2) (unless there is some sort of symmetry which causes the second order terms to vanish). In this case the interference is mostly second order modulation and (4.7) is a good approximation to wdf)- Fvu'thermore, as Po approaches zero, exp ( — i^n + v^x) approaches unity 886 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 and (4.10) becomes a good approximation to (4.7). Just how small Po has to be depends upon the signal bandwidth, fb , and the characteristics of the transducer. 2. For the case of FM and a flat signal band, the second of equations (5.3) shows that even if Po is small, the difference \po — \pr approaches co as I T I approaches =» . To justify the use of (4.10) in this case it is neces- sary to take into account the behavior of g{t), the response of the trans- ducer to the unit impulse b{t). For example, if the duration of g{x) in (4.7) is so brief that g{x) becomes negUgibly small before —\}/o-\- ypx be- comes appreciably different from zero (which may be achieved by mak- ing Po small enough) then (4.10) is a good approximation to (4.7). 3. When the attenuation, a, and phase shift, /S, are given for any particular transducer, the corresponding g{t) may be obtained from (1.2). Once g{t) and ypo — ^t are known, the conditions under which exp ( — i/'o + yp^ may be replaced by unity in (4.7) and 0{Rv) terms neglected in (3.2) may be determined by direct examination of the integrals. As might be expected, the third order modulation results are quite complicated. The third order modulation term in (3.2) is Qii f ^/' f drwM')wM">M"') o!4 J — 00 J— 00 , . (4.11) cospxe-^°+^^(2'' - 1)(/" - 1)(/"' - 1) /oo dxgix) -00 where /'" = f — f — J" and z = exp ( — i2Trx) . When i/'o is small this is approximately ^ f df r drwM')wM")^M'")[H' + K'] (4.12) 3! lb J-oo ^-00 where H = 7n{n + mXn + mif) + m{f - f - f") - ni{f - n - m{f - n - m(0) - m(f' + /"), m{f) = Gf + (?_/, n(/) = Bj - 5_,, and K is an expression obtained from H by replacing n by m. V MISCELLANEOUS COMMENTS Here we make some miscellaneous comments related to the foregoing results. DISTORTION IN NOISE MODULATED FM SIGNAL 887 If the transducer is perfect except for an echo, its response to a unit impulse 8(t) is g(t) = 8(t) + r8(t - T) (5.1) where r and T are the amplitude and the delay of the echo. The results obtained using (5.1) agree, as they should, with the results obtained in Reference 4. Of course, r must be assumed small compared to unity in order that condition (1.5) may hold. When the power spectrum of the signal is equal to a constant Po over the band (/„ , /&) and zero elsewhere we have for phase and frequency modulation, respectively, PM: w^{j) = Po, fa. When fa = 0 the autocorrelation functions are (5.2) (5.3) PM: lAr = PoMsmv)/v, FM: yPo - ypr = A[-l + cos v + vSi{v)], V = 27rf,T, A = Po.U2Th)-' = ( L and would be omitted if P(/o) < L. With this method the timing deviations in regenerated pulses would be limited to iAT, regardless of the timing deviations in received pulses. There would be no cumulation of timing deviations in a repeater chain. However, the tolerance of the repeaters to noise would be somewhat reduced by the timing deviations dzAT. 1.3 Regeneration with Partial Retiming Partial retiming is obtained by a combination of the above two methods, by triggering regenerated pulses without sampling at instants ta determined by P(/o) + R{i,) = L. (1.3) To permit regeneration without sampling and without a marked reduc- tion in the tolerance of the repeaters to noise, the timing wave R(t) must meet certain conditions illustrated in Fig. 1. One is that it must be a nearly periodic function as for complete retiming. The second condi- tion is that R{t) must be zero near the sampling points to obtain sub- stantially the same tolerance to noise in the presence of a pulse as in the absence of a pulse. A third condition is that R{t) must have sub- stantial negative values between sampling points in order that the repeater be rather insensitive to noise between sampling points, as ^xith complete retiming. It will be recognized that, in general, the maximum value of R{t) need not necessarily be zero, as in the above illustration. It can be greater or smaller than zero, provided the triggering level i> SELF-TIMING REGENERATIVE REPEATERS 895 modified accordingly. A maxiniiiin value of zero is, however, convenient from the standpoint of instrumentation. A limiting shape of retiming wave that would result in complete re- timing, iuit without the need for special sampling is also illustrated in Fig. 1. 1 ..'i Derivation of Timing Wave from Pulse Train As shown abo\'e, the retiming wave must be essentially periodic, with a fundamental frequency equal to the pulse repetition frequency./' = 1/T, where T is the interval between pulses. The simplest form is a sinusoidal wave, which can be derived from the pulse train at repeaters with the aid of a narrow band-pass filter, such as a simple resonant circuit cen- PULSE TRAIN COMPLETE RETIMING Fig. 1 — Principle of partial retiming method. 896 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 tered on the pulse repetition frequency. This possibility resides in the circumstance that a random "on-off" pulse train can be resolved into two components. One is an infinite sequence of pulses of the same polarity and equal amplitude, the other a sequence of randomly positive and negative polarity. The response of a resonant circuit to the first component is a steady state sinusoidal wave of the pulse repetition fre- quency. The second component gives rise to random variations in ampli- tude and phase, which in principle can be limited to anj^ desired extent by limiting the band of the resonant circuit and the deviation in the resonant frequency from the pulse repetition frequency. A principal feature of this method of "self -timing", aside from its simplicity, is that the timing wave becomes a slave of the pulse train. Thus, if there is a fixed delay in pulse regeneration at a repeater, the same delay is imparted to the timing wave derived from the pulse train at the next repeater. This prevents a cumulation of such fixed delay.^ with respect to the timing wave, but not with respect to an absolute time scale; i.e., with respect to an ideal timing wave transmitted along the repeater chain and independent of the pulse train. 1.5 Self -Timed Repeaters with Partial Retiming A timing wave derived from the pulse train with the aid of a resonant circuit can be used in conjunction with complete or partial retiming. With complete retiming, pulses could be regenerated at the zero points in the timing wave, and the effects of amplitude variations in the timing wave can thus be avoided. Timing deviations in the regenerated pulses would in this case depend only on phase deviations in the timing wave, caused partly by the component of randomly positive and negative polarity in the pulse train and parth' by timing deviations in the pulse train from which the timing wave is derived. With partial retiming the situation is more complex. Timing de^•ia- tions in regenerated pulses in this case depend not only on amplitude and phase variations in the timing wave, but also on the regeneration characteristics of the repeaters. 1 .6 Types of Timing Deviations In a regenerated pulse train there will be fixed and random timing deviations. Of the latter there are three types. One is the timing devia- tion taken in relation to an exact timing wave with a period T equal to the nominal pulse interval. The second is the timing deviation taken in relation to the timing wave derived from the pulse train, which in itself SELF-TIMING REGENERATIVE REPEATERS 897 will contain random deviations. The third type is random deviations in the interval of adjacent pulses. If the first type is held within tolerable 1 limits, this will also be the case for the second and third types. For this reason only the first type is considered herein. ' II REGENERATION CHARACTERISTICS WITH PARTIAL RETIMING 2.0 General With partial retiming, there will be timing deviations in the re- generated pulses as a result of timing deviations, amplitude variations and distortion by noise of both the received pulses and the timing wave. Fig. 2 — Reduction in tolerance to noise by displacement in timing wave. 898 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 The conversion of these variations into timing deviations in the re- generated pulses depends on certain relationships between the pulse , train and the timing wave, discussed in the following sections. I 2.1 Tolerance to Noise From Fig. 2 it can be seen that if the timing wave is displaced by to , " the value of P{t) -{- R{t — to) in the presence of a pulse exceeds the triggering level by a maximum amount [P(0 + Rit - to) - L]„,ax ^ [P(ro) - L]. (2.1) j It will be recognized that the right-hand side of this equation represents i the tolerance to noise of negative amplitudes with instantaneous sam- ' pling at t = To , as in an ideal repeater with complete retiming. With partial retiming, the tolerance to noise will be less than the above maximum value. However, it will be greater than the average of P{t) + R{t — To) — L in the range where the latter difference is positive. Let it be assumed that it is smaller than the maximum by a factor k somewhat smaller than unity. The tolerance to noise with a displacement to in the timing wave is then smaller than without a displacement (i.e., to = 0) by the factor ^ k[P(ro) - L] ^ P(to) - L ..^ .^ ^ k[P{0) - L] P(0) - L ■ The tolerance to noise will thus be reduced in a way similar to that for an ideal repeater with complete retiming. The absolute tolerance to noise will be less than for a repeater with complete retiming by a factor A; somewhat smaller than unity, say in the order 0.8, corresponding to about 2 db. 2.2 Conversion of Timijig Deviations With partial retiming, timing deviations in received pulses and in the timing wave are converted into smaller deviations in regenerated pulses. Let Tp be a time displacement in a received pulse and Tr in the timing wave, both in the positive direction. Pulses will then be regenerated . at a time to' given by I P(to' - T;0 + R{t,' - Tr) = L (2.3) where the minus signs are used since this corresponds to a displacement of P and R in the positive direction. Subtracting (1.8) from (2.8), P(/o' - Tp) - P{to) + R{to' - Tr) - R{to) = 0. (2.4) SELF-TIMING REGENERATIVE REPEATERS 899 i By adding and subtracting P(/(/) + R{tu') and rearranging terms, (2.4) can also be written [P(/o') - P{h)\ + [R{un - Hit,)] I = [7^(/n') - P{h' - T,)\ + [R{h') - R{h' - Tr)]. ; For small values of Tp and r^ , such that br = to' — ^o is sufficiently small, I both sides of (2.8) can be represented in differential form as ' 8r[P'ito) + R'ito)] = T,P'{h) + TrR'ih) (2.6) where P'{h) = dPo{t)/dt at t = to , and R' is correspondingly defined. Equation (2.9) can be written in the form 5t = PrTp + l-rTr (2.7) where P'(to) R'ito) .28) ^' P'ito) ^ R'itoV '' P'{to) + R'itoY ^'^ and Vr + /v = 1. (2.9) With random uncorrelated displacements of rms values fp and f, , the rms value of 5t is 8r = iprri + rrrry" (2.10) Eciuation (2.9) and (2.10) give the timing deviations in regenerated pulses in terms of the deviations tp and r^ in the received pulses and in the timing wave. To limit timing deviations in the regenerated pulses, it is necessary to make pr and the product VrTr small. This will entail the use of a timing wave comparable in amplitude to that of the pulses, or greater, in conjunction with a small timing deviation r^ in the timing wave. 2.3 Conversion of Amplitude Variations Into Timing Deviations With partial retiming there is a conversion of amplitude variations I in the received pulses and in the timing wave into timing deviations in the regenerated pulses. Let the pulses have an amplitude variation Op and the timing wave Or expressed as fractions of the normal values. Pulses will then be regen- erated at a time /(/ given by (1 + ap)P{t,') + (1 + ar)R{t^') = L. (2.11) 900 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 Subtracting (1.3) from (2.11), [P(/o') - P{to)] + [R{to') - Rm = -a,P(/o') - arPiUn. For small values of Op and ttr , such that 5„ = to' — /o is sufficiently small, the same procedure as in Section 2.2 gives 5„ = iPattp + rattr), (2.12) and V - ~^^^"^ r - -^^^'^ (2 13) For uncorrelated variations of rms amplitude g^ and Qr the correspond- ing rms timing deviation is L = (Pa'ai + iVq;Y\ (2.14) Equations (2.12) and (2.14) give the timing deviations in regenerated pulses resulting from amplitude variations in the pulses and in the timing wave. 2.4 Resultant Timing Deviations in Regenerated Pulses For small variations in the pulses and in the timing wave as considered previousl}^ the resultant timing deviation in a particular regenerated pulse is A - 5, + 5„. (2.15); Considering a large number of pulses, the resultant rms timing devia- tion in terms of the rms deviation in the received pulses and in timing wave is A = (5/ + 8jf\ (2.16) These expressions can also be written A = A;, + A. , (2.17) A = (A/ + ArY\ (2.18) ^P = PrTp -\- Pattp , Ap" = Pr'fp' + Pa'Qp', (2.19) Ar = IrTr + faar , A/ = rr'ir' + ra'Qr'. (2.20) SELF-TIMING REGENERATIVE REPEATERS 901 III ILLUSTRATIVE REGENERATION CHARACTERISTICS 3.0 General In this section the general equations given in the preceding sections are applied to a particular case, in order to obtain specific expressions for the regeneration characteristics and illustrative curves, as an aid to further analysis. The particular case selected for illustration approxi- mates the conditions in experimental Wrathall repeaters, and may be regarded as an idealized model of such a repeater, in which certain effects to be discussed later are ignored. 3.1 Pulse Shape It will be assumed that the pulses are transmitted at intervals T and that the shape of the received pulses after equalization is given by : TT t Pit) - I 1 + cos (3.1) This is the familiar "raised cosine" type of pulse. With rj = I the pulse width is the maximum that can be tolerated without intersymbol inter- ference. With 7? = f , the amplitude of a pulse train at a point midway between two success pulses is equal to half the peak amplitude of a pulse. The latter assumption will be made here, for reasons discussed later. 3.2 Retiming Wave The retiming wave is assumed to be given by R{t) = --cosiA cos (3.2) This type of retiming wave can be obtained if a sinusoidal wave of the pulse repetition freciuency / = 1/ T is applied to a resonant circuit to reduce distortion of the timing wave by noise. The resonant circuit would have a nominal resonant frequency/ = l/T", but because of mis- tuning it would actually be /o . The output of the resonant circuit after appropriate adjustment of amplitude would be of the form [Appendix I, equation (2)]: i?o(0 = ^ cos ,A cos {2r ^ - ^), (3-3) where \p is the phase shift of the resonant circuit at the frecjuency /, 902 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 given by: tan \p = Q h JV (8.4) and Q is the loss constant of the resonant circuit. If the peaks of the wave given by (3.3) are held at zero potential, a retiming wave as given by (3.2) is obtained. This type of retiming wave can also be obtained b}- applying an infinite secjuence of rectangular pulses of equal amplitudes Avith spacing T to a resonant circuit. 3.3 Triggering Instants With a pulse shape and retiming wave as assumed above, the resul- tant wave is given by Pit) + Rit) = 1 1 + cos-- cos yp 1 - COs(27r- - \l/ (3.5) This wave is shoA\ii in Fig. 3 for xj/ = 0 and ±60°. For i^ = ±90° the retiming wave disappears, so that the combined wave is P{t). cos p 2 1-cos [zrr Y - ¥'] Fig. 3 — Illustrative example of j)ulse shape and retiming wave. SELF-TIMING REGENERATIVE REPEATERS 903 The triggering instants ^o are obtained from the relation P{to) + Rito) = L. (3.6) With complete retiming the optimum performance, with positive and negative noise amplitudes of cfjual probabilities, is obtained with a triggering level ^. With partial retiming, optimum performance is ob- tained with a somewhat lower triggering level, but this is of secondary importance in connection with the present analysis. For this reason L = ^ is assumed, in which case the following equation is obtained for determination of ^o : TT to , cos - ^ — COS \p 1 — COS I '2ir r = 0 (3.7) 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 -0.1 -0.2 •0.3 \ ,^ ■ > N, />J / / \ / '"-X /to L 7 \ .^ JL-. <: \ r 1 // / >? s \ ' / / f N. ^^^. :\ k N K t / 1 / / ^^x '^C --.^ 1 /I 1 4 , -J^ ^^ xq: X / l^-^>.^ ^dT, ^ <-J-, \*-6, ^3\*- ^3h- 1 STEADY STATE OR SYSTEMATIC COMPONENT "7 RANDOM COMPONENT 1 + 2 "ON -OFF" PULSE TRAIN WITHOUT PULSE DISPLACEMENTS DIPULSE COMPONENT 1 + 2 + 3 "ON -OFF" PULSE TRAIN WITH PULSE DISPLACEMENTS Fig. 7 — Resolution of "on -off" pulse train with timing deviations into sys- tematic component (1), random component (2), and time displacement compo- nent (3). 010 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 nearly the same for other pulse shapes, provided the frequency spectrum / of the pulses can be regarded as approximately constant over the im- I portant portion of the band of the resonant circuit. This approximation ; is legitimate for resonant circuits with a loss constant Q and pulse shapes '■ at the input of repeaters as considered here. 4.1 Resonant Circuit Response to Steady State Coniponent 1 The first component consists of an infinite sequence of impulses of ^ amplitude ^ and all of the same polarity, at intervals T. This sequence ! has a fundamental f requeue}^ / = 1/T. When it impinges on a resonant circuit with resonant frequency /n = / — Af and loss constant Q, the < response is of the form 1 As{t) = cos \f/ cos (o)/. — \p), (4.1) and tan ,A = Q(///n - M) ^ 2Q ^. (4.2) ^ The response is thus a steady state sinusoidal wave of frequency / displaced from the fundamental component of the input wave by the phase shift xp and reduced in amplitude by cos \p. This is the phase shift and amplitude reduction of the resonant circuit at the frequency f when the resonant frequency is /n . .2 Resonant Circuit Response to Random Signal Component The second component consists of an infinite random sequence of im- pulses of amplitude ±§, at intervals T. The response of the resonant circuit to this component will be a randomly fluctuating wave Ar{t) of mean value 0. The maximum positi^'e amplitude is obtained when all impulses of the second component are positive and is Arit) = As . The maximum negative amplitude is Ar{t) = — *4s . Owing to the presence of this component the total output of the resonant circuit .4,. + Ar{t) can thus fluctuate between the limits 0 and 2.4s , but the actual fluctua- tions of significant probability will be smaller. The above fluctuations can be resolved into a component in phase with the steady state response given by (4.1) and another component at quadrature with the steady state timing wave. The rms values of these components taken in relation to the amplitude of the steady state wave are (4.3) cos ^ SELF-TIMING REGENERATIVE REPEATERS 911 and / \ 1/2 I I I (4.4) 4Q/ cos xp These relations apply for small values of x// and for t/Q « 1. The resultant rms amplitude variation in the timing wave is Qr = g/ as given by (4.3). The rms phase error ipr resulting from the quadrature component a," is given by tan ^r = ^r = a/'. (4.5) The corresponding rms time deviation is {T/2Tr)ipr or rr / \l/2 2ir \4Q/ cos \l/' (4.6) With regard to the probability of exceeding the above rms values by various factors the normal law can probably be invoked with reasonable accuracy. As mentioned before, the maximum possible amplitudes are Ar{t) = ±As which would correspond to a peak factor {'IQ/tY '. With Q = 100, the factor is about 8, while with Q = 1000 it is about 25. Based on the normal law the probability of exceeding the rms value by a factor of 4 is about 5 X 10~^ and by a factor of 5, about 10~'. The normal law would be expected to apply, since the limiting peak values are substantially greater than the peak values expected with significant probabilities. 4-3 Resonant Circuit Response to Pulse Displaceme7its Because of the random components given by (4.3) and (4.4), the timing wave will contain small random amplitude and phase deviations from a sinusoidal wave represented by (4.1). This will result in small random deviations in the positions of regenerated pulses triggered from the timing wave, which is represented by the third component shown in Fig. 7. When the rms deviation in the pulse positions is 5, there will be an additional random cjuadrature component in the timing wave which, when taken in relation to the steady state component, is given by a/' = As" /A. = co8 (|^Y . (4.7) The corresponding rms phase de^'iation is given by ip, ^ a,". (4.8) 912 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 The resultant rms time deviation is (T'/2x)(^5 or h = 52, (4.9) and « = {T^/Qf- (4.10) The above factor a appHes to a single resonant circuit. When the rms timing deviations represented by (4.9) are present in the regenerated pulse train, the rms deviation at the output of the second resonant circuit is ^5,2 = 5aia2 , where Si = ^• With n resonant circuits in tandem, Ss.n = daiaoQCs ■ ■ ■ a,, . (4.11) The factors q:„ are given by si - « = (tt/QY", (4.12) ^j [ai-ao-as • • • a„J = a = a «2 = (1 - hr\ «3 = (1 - ir, Qi = (I - iY'^, etc. 2 1-3-5 ••• [2(n - 1) - 1] 2.4.6 ••• 2(w - 1) (2n)! (4.14) (4.15) 22"(n!)- = a' ( — ) when n » 1. (4.16) The factors ay for j ^ 2 represent the reduction in timing deviations resulting from the reduction in bandwidth as resonant circuits are added in tandem. If resonant circuits with a narrow flat pass-band were used, the bandwidth of any number of resonant circuits in tandem would be the same as for a single resonant circuit. In this case 22 = 23 = a„ = 1. SELF-TIMING REGENERATIVE REPEATERS 913 44 Deviations in Timing Wave The timing wave derived from an "on-off" pulse train \\ith the aid of a resonant circuit will in accordance with the expressions given in the previous sections contain three types of amplitude and timing devia- tions. The first type is a fixed amplitude reduction by a factor oo and a fixed time deviation to given by ao = cos^, (4.17) and TO = 1^ ^, (4.18) where yp is given by (4.2). The second type is a random amplitude and time deviation resulting from the random amplitude component of the pulse train, which have rms values a.^(^y'[l-^V2r'^-^, (4.19) \2Q/ cos 4/ and §,-f(^)"^. (4.20) 27r \4Q/ cos ^ The third type is a random amplitude and time deviation resulting from random timing deviations fp = 5 in the pulse train. The amplitude variation can be disregarded and the rms time deviation is (\l/2 The total rms amplitude variation is accordingly given by (4.19). The total rms timing deviation obtained by combining (4.20) and (4.21) is fr =bj + a%y\ (4.22) The expressions for br and fr are the quantities appearing in (2.20) for Ar , the total rms timing deviation in regenerated pulses resulting from random amplitude and timing deviations in the timing wave. 914 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 V SELF-TIMED KEPEATEKS WITH PARTIAL RETIMING 5.0 General As shown in the preceding section, timing for pulse regeneration can be derived from the pulse trains, with certain random phase and ampli- tude variations in the timing wave that can be reduced by increasing the loss constant Q of the resonant circuit. This method of "self-timing" can be combined with partial retiming, and the regeneration charac- teristics of this type of repeater will be discussed in the following sections. For purposes of numerical illustration, the same type of pulse shape and timing wave will be assumed as in the previous numerical illustration in Section III. This pulse shape and timing wave closely approximates those in experimental Wrathall repeaters, in which timing is derived from the regenerated pulse train. In the following discussion timing from the received pulse train will also be considered. 5.1 Timing from Received Pulse Train It will be assumed that the timing wave is derived from the received pulse train with the aid of a resonant circuit and that random timing deviations are absent. The response of the resonant circuit is then a sinusoidal wave as given by (4.1). From this wave it is possible to obtain a retiming wave of the form R{t) = -cosiA 1 — cos (5.1) This can be accomplished by holding the peaks of the timing wave from the resonant circuit at zero potential with a diode. This is the form of retiming wave previously considered in Section III, in conjunction with a pulse shape given by (3.1). As shown in Section 3.7, the tolerance to noise will vary with the phase shift \p of the resonant circuit, in accordance with (3.21). If a reduction in the tolerance to noise of about 2 db is allowed, the maxi- mum permissible phase shift would be about \J/ — 1 radian (57.6°). On this basis the maximum permissible deviation A/max in the resonant fre- cjuency from the pulse repetition frequency / as obtained from (4.2) with \p = 1 radian becomes A/max ^ tan \J/ ^ L58- , -,v ./■ 2Q 2Q • ^ ^^^ For various values of Q in the range that can he realized by simple SELF-TIMING REGENERATIVE REPEATERS 915 resonant circuits, the permissible deviations are as follows: Q 10 25 50 100 200 ^fm^Jf 0.08 0.030 0.016 0.008 0.004 This assumes that there are no random timing deviations and that the tolerance to noise is reduced by not more than 2 db. 0.2 Timing from Regenerated Pulse Train It will again be assumed that there are no random timing deviations. Without a phase shift in the resonant circuit, let the regenerated pulses be triggered at a time to . When there is a phase shift \f/', the pulses will be triggered at a time ^o'. The timing wave derived from the regenerated pulses will then have a time shift A = t,' - to^-^ rP'. This time shift will cause pulses to be regenerated with a time shift /3'A, which must equal ^n' — ^o • Accordingly, U>' - to = ^' (to - to +^'/''), and to to = T /SV 2x 1 - /3'" (5.3) With timing from the received pulse train with a phase shift ^ in the resonant circuit, the following relation applies: to T to = — W- (5.4) If to — to is to be the same in both cases, so that the timing wave and tolerance to noise is the same, the following relation must exist between the phase shifts in the resonant circuit: ,A' = ^(1 - 0') I (5.5) In this expression, (3 and (3' are the factors shown in Fig. 4. It will be recognized from (5.5) that the smallest permissible phase shifts are ob- tained for large values of /3'. From Fig. 4, it is seen that the largest 916 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 values of /3 are for phase shifts between 0 and —60°. For t? = f , (3 ^ 0.7 and for r; = 1,8^ 0.9. For J? = f and rj = I the tolerable maximum phase shifts \p' in the resonant circuit with timing from the regenerated pulse train, in rela- tion to the maximum tolerable \{/ with timing from the input, are ^P' ^ 0.3^p for V — 4, (5.6) and ^' ^ 0.1x1/ for 7? = 1. Although greater phase shifts can be tolerated when 4/ is positive, and /?' is smaller than above, the requirements on the resonant circuit must be based on the worst condition that can be encountered, as above. From (5.6) it follows that for ?? = 1 the requirements on the per- missible phase shift in the resonant circuit are much more severe than for 17 = f . For this reason the latter value of rj is decidedly preferable for the particular case in which the peak amplitudes of the pulse train and the timing waves are equal, as assumed here. A value 77 = f is also desirable from the standpoints of avoiding intersymbol interference between adjacent pulses at the triggering instants, to permit the timing wave to be derived from the pulse train and to permit self-starting of the repeaters, as discussed later. In accordance with (5.6) the maximum tolerable frequency deviation for 77 = f will be less than with timing from the received pulse train by a factor of about 0.3. The maximum permissible frequency deviation for a phase shift of about one radian in the timing wave and 0.3 radian in the resonant circuit, will accordingly be about as follows: Q 10 25 50 100 200 A/max// 0.025 0.009 0.005 0.0025 0.0012 For a repeater with complete rather than partial retiming, the factor |8 would be unity, and timing from the regenerated pulse train would not be possible. 5.3 Random Timing Deviations In combining random timing deviations from various sources at a particular repeater, it will be assumed that there is no correlation be- j tween the various deviations, so that they will combine on a root -sum- square basis. SELF-TIMING REGENERATIVE REPEATERS 917 In accordance with (2.21) the rms timing deviation at the output is then : • 2 / 2 2 I 2 2\ I / 2 2 , 2 2\ /,- ^\ A = (Pr Tp + Pa flp ) + {Vr fr + r„ Qr ), (5.7) where in accordance with (4.13) and (4.16) ttr L2Q ^' - ''^'\ 1/2 ^ (5.8) cos \p Tr = {^r + afj,") , (5.9) « = (i) . (5'«) When (5.9) is inserted in (5.7) .2 / 2 , 2 2x_ 2 I 2 2 I 2. 2 , 2 2 /t- , r>\ A = {Pr +Qcrr)Tp + PaQp + fr 6, + Ta tt^ . (5.12) This expression gives the rms timing deviation at the output in terms of the rms deviation fp at the input and the various repeater parameters. With timing from the output, rather than the input as assumed above, Tp is replaced by A in (5.9), and the following relation is obtained: .2/, 2 2n 2_ 2 I 2 2 I 2-2 , 2 2 /- , r,\ A (1 - a fr ) = Pr Tp + Pa Qp + /> 5^ + r„ tt, . (5.13) In the above expressions p/ = 0.15, 7\' ^0.4 and a' = 0.03 {Q = 100) . The term a rj can thus be neglected in comparison with pi in (5.12) and in comparison with 1 in (5.13). The following expression is thus obtained with timing from either the input or the output: A = {pr fp" + PaQp') -j- (r/5r" + riqr') = A/ + A.-. 5.4 Magnitude of Random. Timing Deviations The first two terms of (5.14) represents the rms timing deviations in the regenerated pulses resvilting from timing deviations and ampUtude variations in the received pulses. The last two terms represent the timing deviations resulting from timing deviations and amplitude variations in the timing wave. The conversion factors pr , Pa , 'V and ?•„ are discussed in Section II and representative values given in Figs. 5 and 6. The values of Qr and 8r are obtained from (5.8). 918 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 Table IV — Rms Devlvtions from Timing Wave Distortion for Q = 100 1! (().()) , , „ 2(,i-l) 2 2 2 The rms deviation at the output of repeater n thus becomes A,,' = (Ap' + A,.')7„" + a"/v'fp'p-,'"- (6.7) In the case of repeaters with partial retiming the last term in (6.7) can be neglected, in which case the cumulation of timing deviation will be virtually the same when the timing wave is derived from the regenerated as when it is derived from the received pulse train. The above expressions apply for resonant circuits consisting of a coil and capacitor which have a gradual cut-off. If resonant circuits with a flat pass-band and sharp cut-offs were used, a2 = as = «„ and (6.5) can be simplified to 7;' = (i - a{)vi""'' + ahp; -f uT'"'- (6.8) 6.3 Cumulation of Timing Deviations The cumulation of random timing deviations from various repeaters in a chain can be determined from the propagation constant given above for any prescribed law of combination of timing deviations from various repeaters. When equal rms deviations are contributed by each of A'^ repeaters, and they are combined on a root-sum-square basis, the rms :! deviation at the end of a repeater chain is greater than for a single repeater by the cumulation factor ! / N \ 1/2 c = ( E yn . (6.9) i H=l An upper limit to (' is obtained by taking a-2 = a-i = a„ = 1 in (6.5) in which case 7,," is given by (6.8) ; (6.9) then becomes for A^ = oc C (1 — ai") :; -, + af 1/2 (6.10) I - Pr^ 1 - Pr- - >-_ 1/2 (6.11) where the terms in gf have been neglected in (6.11), since gi" = a « 1, about 0.03 for Q = 100. From Fig. 5 it will be seen that when \p < ±60°, pr < 0.6. Hence | (' < 1 .25. Cumulation of random timing deviations can thus for practical SELF-TIMING REGENERATIVE REPEATERS 923 purposes be disregarded, with root-sum-square combination as assumed above. The value of C obtained from (6.11) will differ from that obtained from (6.9) when 7,, is given by (6.5), by a small fraction of one per cent. Although root-sum-square combination appears justified for reasons given before, it is of interest to determine an upper limit to the cumula- ! tion based on direct addition of random timing deviations. The maxi- mum cumulation factor thus obtained is I If 1 n = l Cxnax = Z 7. . (6.12) Employing (6.8) for 7„ and neglecting the terms in ai', the upper limit to the cumulation factor for A^ = x becomes Cmax = :; ■ (6.13) With Pr < 0.6 for ^ < ±60°, C„,ax < 2.5. If the above maximum cumulation factor is applied to random timing deviations resulting from amplitude variations in the timing wave, as given in Table I^' of Section 5.4, the resultant rms phase deviation at the end of a long repeater chain could be as great as 25°, rather than 10° for a single repeater, when i^ = 60° and Q = 100. To attain satisfactory performance it would in this case be necessary to limit the maximum fixed phase shift to substantially less than ±60°, which would entail greater freciuency precision than indicated in Sections 5.1 and 5.2. li \p < ±15°, Pr < 0.40 and Cmax < 1-7- Ii^ this case the rms phase deviation as given in Table I for a single repeater is ^r = 4°, and the rms phase deviation in a long repeater chain would be less than 7°. In a long repeater chain the rms phase deviation resulting from pulse dis- tortion would be greater than given in Table II by an rms cumulation factor C = 1.08 for pr = 0.4, and would thus be about 8° when \{/ < ±15°. The total rms phase deviation would thus be about (7" + 8')^ " = 11°. Random phase deviations exceeding 4 times the latter value, or about 45°, would be rather unlikely. The sum of the fixed and random phase deviations would thus be limited to about 60°, so that satisfactory performance would be expected when the fixed phase deviation is limited to about ±15°. With the approximations for 7,, employed above, the rms cumulation factor for a chain of A" repeaters as obtained from (6.9) is less than for N = oc by the factor (1 - p.'-'Y'" ^ 0.99 for p. = 0.5 and A' = 3. The maximum cumulation factor obtained from (6.12) is less than for A' = y- by the factor 1 — p/^ = 0.99 for A' = (i. Thus, cumulation of random 924 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 timing deviations is virtually completed in a chain of 3 to 6 repeaters, I so that for experimental determinations of the degree of cumulation it I suffices to operate a few repeaters in tandem. f ^.4 Repeaters with Complete Retiming I In the particular case of complete retiming, pr = 0 and Tt = 1 in , (6.5) and (6.6) so that j 7« = aia^s • • • On-i , (6.14) ' Pn = mm • ' • Qin ■ (6.15) i ! For w » 1, approximation (4.16) can be employed, in which case ' 7. = s (— ) ' , Pn = f-Y . (6.16) ■ In this case (5.14) simplifies to ^p + A.' = 5^ (6.17) since pa = 0, ?•„ = 0, pr = 0 and fr = 1. Hence (6.7) becomes A„ = 8r~yn' + fpapn'. (6.18) With approximations (6.16), A,;^ = i8j + f^h' (J^J'\ (6.19)1 At the output of the first repeater, Ai' = 5; +«V- (6-20)1 For n » 1 the sciuared propagation factor is accordingly An'/^r'-a\^:^'z(^T. (6.21) Qr" + Qc-Tp~ \Trn/ The squared rms cumulation factor for A^ » 2 repeaters becomes C'^ 1 = 1 + a= ^' + ''' '■t.V\"= /8\"=' IT I VTT, In the particular case of perfect tuning of all resonant circuits 6^ = 0 ' and ;_^i SELF-TIMIXG REGENERATIVE REPEATERS 925 (A„/Ai)^ ^ Q:J'\ (6-23) (6.24) The last expression gives the factor by which the rms timing devia- tion at the output of repeater N is greater than at the output of the first repeater. The rms deviation at the output of the first repeater is greater than at the input by the factor a. The rms deviation at the output of repeater .V is thus greater than at the input of the first repeater by the factor, C\=a (~y \ (6.25) For this particular case {8r == 0) expressions equivalent to those above have been derived in unpublished work by H. E. Rowe of Bell Telephone Laboratories. In accordance with (6.22) and (6.24) the cumulation of random timing deviations increases indefinitely with ^V when retiming is complete. The icumulation factor as given by (6.24) is in fact the same as would be ob- jtained if a timing wave were transmitted on a separate pair, with a iresonant circuit at each repeater to limit noise and with amplification of the timing wave at each repeater to obtain the same amplitude of the timing wave as when it is derived from the pulse train. With partial retiming cumulation is limited, for the reason that there is partial re- generation of both the pulse train and the timing wave. Although with complete retiming the cumulation factor increases indefinitely with N, this is of but little practical significance, because of jthe slow rate of cumulation. At the output of a chain of .V repeaters an rms deviation approximatelj^ equal to that at the input of the first re- peater could be tolerated, in which case Ci = 1. On this basis the per- missible number of repeaters would be (6.26) ^ 800 when Q = 100. This assumes exact tuning of all resonant circuits. With mistuning of the resonant circuits, the permissible number of repeaters in tandem for a specified rms deviation at the output of the final repeater can be 926 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 determined with the aid of the cumulation factor given by (6.22). For example, if the rms deviation at the output of repeater iV is assumed the same as at the input of the first repeater, the permissible number of repeaters in tandem is less than given by (6.26) by the factor [(1 — m"), (I + nOf, m = b,;fp . When the fixed phase shift is 30°, m ^ 0.5 and N ^ 300. 6.5 Self- Starting of Self-Timed Repeaters With self-timing it is necessary that repeaters be self-starting if the timing wave should be absent for any reason. If each repeater is self- starting, this will also be the case for a repeater chain, since starting will be progressive along the chain. Initially, before the timing wave has reached the appropriate amplitude at all repeaters, there will be a high rate of digital errors. With timing from the recei\-ed pulse train, the resonant circuit will be excited by every pulse and the timing wave will reach its normal ampli- tude in about n ^ Q pulses. With timing from the regenerated pulse /'l \\ / \ >' \ \ /' \ //,' \ 1 1' \\ hi > \ 1 1 \ \ /'' '. \:i. /i'l \ 'i ' \ 1 ii \ ' r? 1 \ / 'm r? \J PULSE TRAIN TIMING: WAVE ■ Fig. 9 — Progression of repeater .starting in absence of timing wave when timing is derived from regenerated pulse train. O Triggering points with timing wave absent. Xoise prevents triggering at cer- tain points, n. Timing wave reaches fraction of normal value, Ri . A Triggering i^oints with timing wave Ri. Timing wave increases to norma! am- plitude R. • Triggering points witli normal timing wave. SELF-TIMING REGENERATIVE REPEATERS 927 train the resonant circuit will not be excited by every pulse, unless the shape of the received pulses is such that there are virtually no overlaps between pulses so that the triggering level will be penetrated by each pulse. With a pulse shape as assumed in the previous analysis, the amplitude of a pulse train midway between pulses is half the peak amplitude of the pulses, as indicated in Fig. 9. In the presence of noise, triggering will in this case occur on the average for every second pulse, as indicated in the above figure. If it is assumed that the resonant circuit has the maximum permissible phase shift of about 20° allowed with timing from the output, the amplitude of the timing wave with excitation from e\'ery pulse will be -^-irtually equal to the peak pulse amplitude. With excitation from half the pulses, the amplitude of the timing wave ^vill rapidly reach half the peak amplitude of the pulses. When this initial timing wave is com- bined with the pulse train, triggering will occur for virtually all pulses, as indicated in Fig. 9. It will thus reach its normal value. If the phase shift is greater than 20° as assumed above, say 60°, the initial amplitude of the timing wave will be | the peak pulse amplitude. Combination of this initial timing wave with the pulse train will increase the number of pulses exciting the resonant circuit, which in turn increases the amplitude of the timing waves, etc. Self-starting with a pulse shape as assumed in this analysis is thus insured. VII SUMMARY In self-timing regenerative repeaters as considered here, a timing wave is derived from either the received or regenerated pulse train with the aid of a simple resonant circuit tuned to the pulse repetition fre- quency. This timing wave is combined linearly with received pulse trains as indicated in Fig. 1, and pulses are regenerated when the combined wave penetrates a certain triggering level. It is concluded that if these timing principles are implemented bj^ appropriate repeater instrumentation, a performance can be realized that approaches that of ideal regenerative repeaters. To this end it is necessary to meet certain requirements with regard to the loss constant Q of the resonant circuit, its frequency precision, the shape of received pulses and the amplitude of the timing wave in relation to that of re- ceived pulses. Equalization of each repeater section should preferably be such that the received pulses have a shape and duration in relation to the pulse 928 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 interval as indicated in Fig. 3, and the peak amplitude of the timing wave should be about equal to that of the received pulses. Under these conditions the pulse repetition frequency will be present in the received pulse train in sufficient amplitude to permit derivation of the timing wave from the received pulse train, and to permit rapid self-starting in the absence of a timing wave if it is derived from the regenerated pulse train. A loss constant of the resonant circuit Q = 100 appears desirable. This value is sufficiently low to be readily realized with simple resonant circuits consisting of a coil and capacitor in series or parallel, without unduly severe requirements on its frequency precision. It is also ade- quately high from the standpoint of avoiding excessive random timing deviations in regenerated pulses from amplitude and phase deviations in the timing wave. The tolerable deviation in the resonant frequency from the pulse repetition frequency with Q = 100 is about 0.2 per cent when the timing wave is derived from the received pulse train, and about 0.06 per cent when it is derived from the regenerated pulse train. These frequency precisions correspond to a maximum fixed phase shift of 15° in the timing wave, and allow for the possibility that random timing deviations resulting from amplitude variations in the timing wave maj- cumulate directly along a repeater chain, rather than on a root -sum- square basis. With root-sum-square cumulation of timing deviations from all sources, the frequency deviations could be about twice as great. "V^Tien the above requirements are met the reduction in the tolerance to noise owing to timing deviations in a repeater chain is limited to about 2 db. If the requirements on freriuency precision of the resonant circuit are met, substantial degradation or improvement in performance would not be expected as a result of moderate changes in the other design parameters. VIII ACKNOWLEDGMENTS In this presentation the writer had the benefit of unpublished work, referred to pre^'iously, b^' W. R. Bennett and .1. R. Pierce on the deriva- tion of a timing wave from a pulse train with the aid of a resonant cii- cuit, and by H. E. Rowe on the cumulation of timing deviations in a chain of repeaters with complete retiming. Bennett, Pierce and Rowe are at Bell Telephone Laboratories. He is also indebted to H. E. Rowe for a critical review that resulted in several improvements in the analy.sis. SELF-TIMING REGENERATIVE REPEATERS 929 Appendix ix resonant circuit response to random binary pulse trains / General In the following analysis of the response of a resonant circuit to a binary "on-off" pulse train, the pulses are assumed of sufficiently short duration to be regarded as impulses. This is a legitimate approximation when the duration does not exceed about half the interval between pulses. The pulse train is regarded as made up of three components, as indi- cated in Fig. 10. The first is a systematic component consisting of pulses of amplitude \. This component gives rise to a steady state response at the fundamental frequency of the pulse sequence. The second com- ponent consists of pulses of amplitude ±^, with random ± polarity. This component gives rise to a random component in the resonant cir- it rh iii r+i [k [] [] jn II -T— ♦ ^ ^ ^ ? A=B + C B FIRST COMPONENT C SECOND COMPONENT 1 ♦— T— ♦! THIRD COMPONENT F = A+D Fig. 10 — Components of random binary on-off pulse train. A. — Transmitted "on-off" pulses. B. — Stead}'- state pulse train of fundamental frequency/ = l/T. C. — Random pulse train with zero mean value. I). — Random pulse train with displacements ±5. F. — "On-off" pulse (rain with displacements ±5 from av- erage pulse interval T . 930 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 oiiit response; i.e., a fluctuation about the steady state value derived from the first component. The third component consists of a train of dipulses. Eacli dipulse consists of a pair of pulses of amplitude 1 and —1, displaced by an interval ±5. The response of the resonant circuit to this component gives the effect of random displacements ±5 in the oiiginal "on-off" pulse train. 2 Im'pedance of ResonaJit Circuit The impedance of a resonant circuit consisting of R, L and C in parallel is Ziiw) = Z{.i>> 1 is of the form P(t) = P(0) cos wo^e"""'''*', (6) where P(0) = c^o8oR/Q. (7) P{t) designates voltage in response to an impulse current in the case of a parallel resonant circuit, or the current in response to an impulse voltage in the case of a series resonant circuit. SELF-TIMING REGENERATIVE REPEATERS 931 4 Response to Steady State Impulse Train Let a long sequence of impulses of amplitude ^ and the same polarity- impinge on a resonant circuit at uniform intervals T. The response after N impulses is then AM) =li:P(t- nT) (8) 2 r!=0 = — ^ 2^ COS coo(« - nT)e . (9) The subscript s indicates a systematic component. The above series is conveniently summed by taking the real part of the series 2 ri=0 With t = NT -V t,,Q ,=o 2 The rms value of the (juadrature component becomes Z shr [4. - Ac.T{N - n)]e-"°^*-^'-"^'*^]''" i; ^ (1 - cos 2[,A - Acor(.V - ;OF""'*''~"^'')T "• _ n=0 2 These expressions can be transformed into sums of geometric series by writing cos.r = i(e'' + e-'O, x = 2[rP - AvoT{X - n)]. Evaluation of (25) and (26) by this method gives 1 (26) , . P(0) 1 2 21/2 |_1 - e g-wor/Q ' D 1/2 , // _ P(0) 1 (2) 2''2 1 1 - e-"or/Q D 12 (27) (28) 934 THE BELL SYSTEM TECHNICAL JOURNAL, JILY 1057 where A^ = cos 2,^(1 - cos 2AcoTe~"'''"'"=') + sin 2^ sin 2AcoTe~"'''"-'^, (29) 2) = 1 + e-2"or/Q _ 2g-"o^/Q p^jg 2Acor. (30) With the same approximations as used previously in connection with (12) and with cos 2AcoT ^ 1 - 2(Acor); sin 2Acor ^ 2AcoT, iV^|, (31) D ^ (^ly [1 + n (32) 1 _ e-"or/Q ^ 2x/Q. (33) With these approximations in (27) and (28), a; ^ ^ (I)'" [1 - ^V21'", (34) which apply when }p is small and (27r/Q) « 1 . 6. Response to Random Dipulse Train Each dipulse is assumed to consist of two impulses of unit amplitude and opposite polarity, displaced by an interval 5, which in general will be a function of the pulse position; i.e., 5 = d{n). The response of the resonant circuit to a train of such dipulses, obtained by taking the dif- ference in response to the two impulses, is given by .V A,{t) = P(0) cos oiaij, — nJ )e (36) — cos oiM — nl + b[ri)\e In determining the response, mistuning of the resonant current can be disregarded; i.e., coo = co. Furthermore, in the second term of (36) it is permissible to take exp [-wo5(n)/2Q] ^ 1. SELF-TIMING REGENERATIVE REPEATERS 935 With the following further approximations cos uoit — nT) — cos wo[f — nT + 5(n)] = sin wo[/ + 5(w)/2] 2 sin M(n)/2], ^ coo5(w) sin cooi, expression (36) becomes: A,{t) = P(0)coo sin coi E 5(n)e-"°^'-"^^^''^ (37) 71 = 0 N (38) = P(0)a;o sin coo^ Z 5(n)e-"''^^^-"^''^ n=0 where the substitution t = NT -\- to has been made as in previous ex- pressions. The above expression shows that the resonant circuit response will be at quadrature vnih. the steady state timing wave cos w^o • In the above expressions, the dipulses are assumed to be present at intervals T, whereas in a random pulse train they will be present at average intervals 2T. The rms value of the quadrature component ^^'ith randomly positive and negative dipulses at intervals 2T, with an rms displacement 5, is 11/2 Al = P(0)a;o5 P(0) JV y^ ^-2uQT{N-n)IQ H=0 ] - C005 (^ 1/2 (39) In (38) the function e ""''"^ will be recognized as the impulse response function of a circuit with impedance /3 + iw Z(2co) = ^ .1 + CO-//32J 1/2 tan i/' = co//3. (40) (41) (42) (43) It will also be recognized that (39) corresponds to the rms response of such a circuit, when impulses 5(n) of random amplitude with an rms value h are applied to average intervals 2T. Thus (39) can alternately be ob- tained from 936 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 A" = P(0)a;„5 = P(0)a;o5 = P(0)coo6 '^IjyzMf.,: 1 _47rT/32 / 1 \^'^- /3(tan 'a)/j8) 1/2 1/2 (44) .4Ti3, P(0) ,/qY'^ (45) Let the output of the first resonant circuit be appUed to a second resonant circuit, and in turn to n successive resonant circuits, with an ampHtude amphfication ^ between successive resonant circuits. At the output of the 71* resonant circuit, the rms amplitude of the response is then obtained from Aa,/' = P(0)coo5 r /j2(n - 1) /•« 47rT f [z\ico)T V — 00 d CO 1/2 = P(0)coo5 P(0) 1 r ■TB'~ i-oc (1 du 1/2 coo5 I — _47rr/32 J-oc (1 + wV/32)"J (46) where r ^ = 1 ["^ _ f/, CO 9 l02\r,.^ ^ j_=c (1 + CoViS^) (47) 1, 2n - 3 2(w - 1) n In-\, n >2, (48) 1 2{n - 1)/' // = (1 - i), /a"^ = (1 - l)h\ li = (1 - D/sl Thus (46) can be written: As^n = As^a-yQiz ' ' ' «« , (49) where 1 a> 1 - 2(i- D' (50) 0 0 SELF-TIMING REGENERATIVE REPEATERS 937 1 ^.^3 ...^„- = (l-,){l-,)(l-^.J...(^l-2-^— -^j (51) 1-3-5-7 ••• [2{n - 1) - 1] 2-4-G-8 2(w - 1) (2«) ! 22"(n!)2 When n » 1, (51) approaches the value (52) (53) o •> 1 1/2 a2'ai ■ ■ ■ a,- ^ — . (54) Vxn/ The latter approximation is based on the following expression, for X = —^, giveninWhittaker and Watson's: "Modern Analysis" page 259: lim (1 + .r)(l + .r/2)(l + .r/3) •••(!+ x/n) = — ^V^' (55) n~^x r(l + X) where T is the gamma fmiction, r(~j + 1) = tt''". The above analysis assumes that the timing wave at each resonant circuit is applied directly to the next resonant circuit, except for the amphfication between resonant circuits. This would be the case if the timing wave were transmitted on a separate pair, in which case A'l^n would be the rms cjuadrature component owing to noise in the timing circuit. In regenerative repeaters, deviations in the timing wave resulting from the cjuadrature component are imparted at intervals T into the next repeater section as deviations in the spacing of pulses. These timing deviations occurring at intervals T will have a certain random amplitude distribution, which can he regarded as having a certain frequency spectrum. When the deviations are discrete and occur at inter- vals T, the spectrum will extend to a maximum frequency /max = l/2r, or co„,ax = T^/T = wo/2. In this case the upper and lower limits of the integrals above would be replaced by ±coo/2, except for the first repeater section. The recurrence relation (48) is then no longer exact, but the resultant modification is insignificant and can be disregarded. This will be seen when the value wn/2 is inserted for co in the integrand of (47), which then becomes 1/(1 + Q ), as compared with 1 for w = 0. Thus the contribution to the integrals for w > a)n/2 can for practical purposes be disregarded. A Sufficient Set of Statistics for a Simple Telephone Exchange Model By V. E. BENES (Manuscript received October 17, 1956) This paper considers a simple telephone exchange model which has an infinite number of trunks and in which the traffic depends on two parameters, the calling-rate and the mean holding-time . It is desired to estimate these parameters by observing the model continuously during a finite interval, and noting the calling-time and hang-up time of each call, insofar as these times fall within the interval. It is shown that the resulting information may, for the purpose of this estimate, be reduced without loss to four statistics. These statistics are the number of calls found at the start of observation, the number of calls arriving during observation, the number of calls terminated during observation, and the average number of calls existing during the interval of observation. The joint distribution of these sufficient statistics is determined, in principle, by deriving a generating function for it. From this generating function the means, variances, covariances, and correlation co- efficients are obtained. Various estimators for the parameters of the model are compared, and some of their distributions, means, and variances pre- sented. I THEORETICAL PROBLEMS AND METHODS OF TRAFFIC MEASUREMENT Four important kinds of theoretical problems arise in the measurement of telephone traffic. These are: (1) the choice of a mathematical model, containing parameters characteristic of the traffic, to serve as a descrip- tion; (2) the devising of efficient methods of estimating the parameters; (3) the determination of the anticipated accuracy of measurements; and (4) the assessment of actual accuracy, after measurements have been made. The present paper deals with aspects of the second and third kinds of problem, for the simplest and least realistic mathematical model of tele- phone traffic. Specifically, for this model, we treat the problems of (i) complete extraction of the information fiom a given observation period, 939 940 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 without regard to costs of observation, and (ii) determination of the anticipated accuracy of certain methods of estimation which arise natu- rally from the discussion of complete extraction. The method by which we attack problems (ij and (iij in this paper has three stages. First we choose a small number of significant properties of, or factors in, the ph^ysical system we are studying. Then we abstract these properties into a mathematical model of the physical system. Fi- nally, from the properties of the model, we derive results which may be interpreted as answers to the two problems treated. The advantage of this method is that we can use the precise, powerful apparatus of mathe- matics in studying the model; its limitation is that it yields results which are only as accurate as the model in describing reality. A method similar to the above forms the theoretical underpinning of telephone traffic engineering itself. To design equipment effectively, the traffic engineer needs a description of the traffic that is handled by central offices. He decides what properties of the entire system of telephone equipment and customers will be most useful to him in describing the traffic. He then designates certain parameters to serve as mathematically precise idealizations of these properties, and in terms of these parameters constructs a model of the traffic, upon which he bases much of his engi- neering. In choosing a mathematical model for a physical system, one is con- fronted with two generally opposed desiderata: fidelity to the system described, and mathematical simplicity. The model may involve impor- tant departures from physical reality; a model that is sufficiently amena- ble to mathematical analysis often results only after one has introduced admittedly false assumptions, ignored certain effects and correlations, and generally oversimplified the system to be stvidied. However, the abstract model will be an exact and simple tool for analysis. We can construct a simple mathematical model for the operation of a telephone central office by leaving out of consideration many impor- tant facts about such systems, and by concentrating on factors most relevant to operation. Since we are interested in telephone traffic and in the availability of plant, it seems natural to require that a realistic model take account of at least the following five significant factors: (1) the demand for telephone service; (2) the rate at which requests for service can be processed and connections established; (3) the lengths of conversations; (4) the supply of central office equipment; and (5) the manner in which the first four factors are interrelated. I'nfortmiately, the mathematical complexity of such a realistic model precludes easy investigation. Therefore, the model used in this paper is based only on factors (1) and (3). STATISTICS FOR A SIMPLE TELEPHONE EXCHANGE MODEL 941 The demand for telephone traffic is usually made precise by describing a stochastic process which represents the way in which requests for tele- phone service occur in time. A realistic description will take account of the facts that, the demand is not constant, but has daily extremes, and that in small systems, the demand may be materially lessened when many conversations are in progress. Since taking account of the first fact leads to a more complicated model in which our investigations are more difficult, we ignore it, with the proviso that the results we derive are only applicable to systems and observations for which the demand is nearly constant. The second kind of variation in demand becomes insig- nificant as the number of subscribers increases and the traffic remains constant. Hence, we further confine the applicability of our results to systems with large numbers of subscribers, and we assume that the de- mand does not depend on the number of conversations in existence. With these assumptions, a mathematically convenient description of the demand is specified by the condition that the time-intervals between requests for service have lengths which are mutually independent posi- tive random variables, with a negative exponential distribution. A telephone central office contains two kinds of equipment: control circuits which establish a desired connection, and talking paths over which a conversation takes place. The time that a reciuest for service occupies a unit of equipment, be the unit a control circuit or a talking path, is called the holding-time of the unit. A request for service affects the availability of both kinds of equipment but, except for special cases, the holding-times of talking paths are usually much longer than the holding-times of control units such as markers, connectors, or registers. In view of this disparity, we assume that the only holding-times of con- sequence are the lengths of conversations; i.e., the holding-times of talking paths. We assume also that these lengths are mutually inde- pendent positive random variables, with a negative exponential distribu- tion. For the simplest mathematical model of telephone traffic, we may consider the arrangement of switches and transmission lines which con- stitutes a talking path in the physical office to be replaced by an abstract unit called a "trunk". A trunk is then an abstraction of the equipment made unavailable by one conversation, and we may measure the supply of talking paths in the office by the number of trunks in a model. The word "trunk" is also used to mean a transmission line linking two central offices, but as long as we have explained our use of the word there need be no confusion. Often the number of transmission lines leading out of an office is a major limitation on its capacity to carry conversations, and in this case the two uses of the word "trunk" are verv similar. Un- 942 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 fortunately, we do not take advantage of this similarity, since we make the mathematically convenient but wholly unrealistic assumption that the number of trunks in the model is infinite. The model we investigate thus depends on only two of the factors j previously listed as essential to a realistic model: namely, (1) the demand for service, and (3) the lengths of conversations. In view of the simplicity and inaccuracy of this model, the question arises whether much is gained from a detailed analysis. Such scrutiny may indeed reveal little that is of great practical value to traffic engineers. It is important methodologi- cally, however, to have a detailed treatment of at least one approximate case. We undertake this detailed treatment largely for the insight that it may give into methods which could be useful in dealing with more complex and more accurate models. Once a designer has chosen a model and has specified the parameters he would like to have measured, it is up to the statistician to invent effi- cient means of measurement, by choosing, for each parameter, some function of possible observations to serve as an estimate of that parame- ter. One measure of efficiency that is of mostly theoretical interest is the observation time required to achieve a given degree of anticipated ac- curacy ; the most reafistic measure of efficiency is in terms of dollars and man-hours. It may often be more efficient, in the sense of the latter measure, to spread observation over enough more time to compensate for the inability of an intrinsically cheaper method of measurement to extract all of the information present in a fixed time of observation. For example, periodic scanning of switches in a telephone exchange is usually less costly than continuous observation. As a result, telephone traffic measurement is usually carried out by averaging sequences of instan- taneous periodic observations of the number of calls present, rather than by continuous time averaging, although it can be shown that continuous observation is more efficient at extracting information. Thus statistical efficiency, which may be expensive in terms of measuring equipment, can be exchanged for observation time, which may be less costly. This exchange brings about a reduction in cost without impairing accuracy. Our concern in this paper is with the less practical problems of com- plete extraction, and of the anticipated accuracy of estimation methods based on complete extraction. Let us consider how our mathematical model can shed light on these problems. A mathematical model may or may not be a faithful description of the behavior of real telephone sys- tems. Nevertheless random numbers, with or without modern computing machines, enable one to make experiments and observations on physical situations which approximate, arbitrarily closely, any mathematical model. Thus we can speak meaningfully of events in the model, and of STATISTICS FOR A SIMPLE TELEPHONE EXCHANGE MODEL 943 making measurements and observations on the model. The mathematical model elucidates our problems in the following ways: (1) it enables us to state precisely what information is provided by observation; (2) it enables us to explain what we mean by complete extraction of informa- tion; and (3) it enables us to derive results about the anticipated ac- curacy of measurements in the model. These results will have approxi- mately true analogues in physical situations to which the model is applicable. The calls existing during the observation interval (0, T) fall into four categories: (i) those which exist at 0, and terminate before T; (ii) those which fall entirely within (0, T) ; (iii) those which exist at 0 and last beyond T; and (iv) those which begin within (0, T) and last beyond T. For calls of category (i), we assume that we observe the hang-up time of each call; for category (ii), we observe the matching calhng-time and hang-up time of each conversation ; for category (iii) , we observe simply the number of such calls; and for category (iv), we observe the caUing- times. Table I summarizes the kinds of calls and the information ob- served about each. What we mean by the complete extraction of information is made precise by the statistical concept of sufficiency. By a statistic we mean any function of the observations, and by an estimator we mean a statistic which has been chosen to serve as an estimate of a particular parameter. Roughly and generally, a set S of statistics is sufficient for a set P of parameters when S contains all the information in the original data that was relevant to parameters in P. If S is sufficient for P, there is a set E of estimators for parameters in P, such that the estimators in E depend only on statistics from S, and such that an estimator from E does at least as well as any other estimator we might choose for the same parameter. Thus we incur no loss in reducing the original data (of speci- fied form) to the set »S of statistics. It remains to state what it means for S to contain all the relevant information. We do this in terms of our model. The mathematical model we are adopting contains two distribution Table I — • Information Observed Types of Calls Start in (0, T) Start before 0 End in (0, T) (ii) , matching calling-times and hang-up times known, num- ber of calls known (i) , hang-up times known, num- ber of calls known End after T (iv), calling-times known, num- ber of calls known (iii), number of calls known 944 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 functions, that of the intervals between demands for service, and that of the lengths of conversations. We have supposed that these distribu- tions are both of negative exponential type, each depending on a single parameter. Thus we know the functional form of each distribution, and each such form has one unknown constant in it. Since the mathematical structure of the model is fully specified except for the values of the two unknown constants, we can assign a likelihood or a probability density to any sequence S of events in the model during the interval (0, T). This likelihood will depend on the parameters, on 2, and on the number of calls in existence at the start 0 of the interval. If the likelihood L(2) can be factored into the form L = FH, where F depends on the param- eters and on statistics from the set S only, and H is independent of the parameters, then the set S of statistics may be said to summarize all the information (in a secjuence 2) relevant to the parameters. If L can be so factored, then S is sufficient for the estimation of the parameters. The mathematical model to be used in this paper is described and discussed in Sections II and III, respectively. Section IV contains a summary of notations and abbreviations which have been used to sim- plify formulas. In Appendix A we show that the original data we have allowed our- selves can be replaced by four statistics, which are sufficient for estima- tion. In Appendix B and Sections Y-VIII we discuss various estimators (for parameters of the model) based on these four statistics. To determine the anticipated accuracy of these methods of measurement, we consider the statistics themselves as random variables whose distributions are to be deduced from the structure of the model. A primary task is the determination of the joint distribution of the sufficient statistics. In view of the sufficiency, this joint distribution tells us, in principle, just what it is possible to learn from a sample of length T in this simple model. By analyzing this distribution we can derive results about the anticipated accuracy of measurements in the model. The joint distribution of the sufficient statistics is obtainable in prin- ciple from a generating function computed in Appendix C, using methods exemplified in Section X. This generating function is the basic result of this paper. The implications of this result are summarized in Section IX, which quotes the generating function itself, and presents some statistical properties of the sufficient statistics in the form of four tables: (i) a table of generating functions obtainable from the basic one; (ii) a table of mean values; (iii) a table of variances and covariances; and (iv), a table of squared correlation coefficients. (The coefficients are all non-negative.) STATISTICS FOR A SIMPLE TELEPHONE EXCHANGE MODEL 945 II DESCRIPTION OF THE MATHEMATICAL MODEL Throughout the rest of the paper we follow a simplified form of the iiotational conventions of J. Riordan's paper" wherever possible. A sum- mary of notations is given in Section IV. The model we study has the following properties: (i) Demands for service arise individually and collectively at random at the rate of a calls per second. Thus the chance of one or more demands ill a small time-interval A^ is aAt + o{At), where o{At) denotes a quantity of order smaller than A^ The chance of more than one demand in At is of order smaller than A^ It can be shown (Feller,' p. 864 et seq.) that this description of the demand is equivalent to saying that the intervals between successive demands for service are all independent, with the negative exponential distribution 1 —at I — e . This again is equivalent to saying that the call arrivals form a Poisson process;" i.e., that for any time interval, t, the probability that exactly ?i demands are registered in / is —at / ,\n e {at) nl Thus the number of demands in t has a Poisson distribution with mean at. (ii) The holding-times of distinct conversations are independent vari- ates having the negative exponential distribution 1 - r^"\ where y is the reciprocal of the mean holding-time h. This description of the holding-time distribution is the same as saying that the probability that a conversation, which is in progress, ends during a small time- interval A^ is yAt + o{At), without regard to the length of time that the conversation has lasted Feller, p. 375). (iii) The model contains an infinite number of trunks. Thus, at no time will there be insufficient central office equipment to handle a demand for service, and no provision need be made for dealing with demands that cannot be satisfied. 940 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 The original work on this particular model for telephone traffic is in Palm,^ and Palm's results have been reported by Feller^ and Jensen.* The results have been extended heuristically to arbitrar}^ absolutely con- tinuous holding-time distributions by Riordan," following some ideas of Newland* suggested by S. 0. Rice. Let Pijit) be the probability that there are j trunks busy at t if there were i busy at 0. And let Pi{t, x) be the generating function of these probabilities, defined by PAUx) = T^x^PiM)- Then Palm^ has shown (pp. 56 et seq.) that PiiU x) = [1 + (.r - 1) e-''X exp {(.r - \)ah (1 - e"^')}. This is formula (12) of Riordan" with his g replaced by e""^*. It can be verified that the random variable N{t) is jMarkovian; the limit of Piit, x) as ^ ^ 2c is exp !(.r - 1) ah], so that the equilibrium distribution of the numl)er of trunks in use is a Poisson distribution with mean h = ah. The shifted random variable [N{t) — h] then has mean zero, and covariance function 6e~^'. For additional work on this model the reader is referred to F. W. Rabe,^° and to H. Stormer.^' Ill DISCUSSION OF THE MODEL Let us envisage the operation of the model we have described by con- sidering the random variable N{t) ecjual to the number of trunks busy at time t. As a random function of time, N{t) jumps up one unit step each time a demand for service occurs, and it jumps down one vmit step each time a con^-ersation ends'; If N{t) reaches zero, it stays there until there is another demand for service. If N{t) = ?t, the probabilit}' that a con- versation ends in the next small time-interval M is h-yM + o(A0, because the n conversations are mutually independent. A graph of a sample of A^(0 is shown in Fig. 1. The model we described departs from realitj^ in several important ways, which it is well to discuss. First, the assumption that the number of trunks is infinite is not realistic, and is justified only by the mathe- matical complication which results when we assume the number of trunks STATISTICS FOR A SIMPLE TELEPHONE EXCHANGE MODEL 947 220 215 N(t) 210 205 - 200 TIME, t *- Fig. 1 — A graph oi Nit). to be finite. It can also be argued that unlimited office capacity is ap- proached by offices with adequate facilities and low calling rates, and therefore, in some practical cases at least, the model is not flagrantly inaccurate. Second, the choice of a constant calling rate for the model ignores the fact that in most offices the calling rate is periodic. Thus, the applica- bility of our results to offices whose calling rates undergo drastic changes in time is restricted to intervals during which the normally variable calling rate is nearly constant. Finally, although the assumption of a negative exponential distribution of holding-time afl'ords the model great mathematical convenience, it is doubtful whether in a realistic model the most likeh' holding-time would have length zero, as it does in the present one. IV SUMMARY OF NOTATIONS a = Poisson calling rate h = mean holding-time 7 = h^^ = hang-up rate per talking subscriber h = ah = a\'erage number of busy trunks N{t) = number of trunks in use at f {0, T) = interval of observation n = N{0) — number of trunks in use at the start of observation .1 = number of calls arriving in (0, T) H = number of hang-ups in (0, T) K = A + H 948 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 Z = f N(t) dt Jo M = Z/T = average of A^(^) over (0, T) \p„\ = the (discrete) probability distribution of n, the number ot trunks found busy at the start of observation An estimator for a parameter is denoted t)y adding a cap (*) and a subscript. The subscripts differentiate among various estimators for the same parameter. We use d,. = ^■^/T, jc = H/Z, di = K/2T, yi = K/2Z, and 72 = A/Z. Also, it is convenient to use the following abbreviations: r for yT, and C for (1 — e~'')/r, where r is the dimensionless ratio of observation-time to mean holding-time. The symbol E is used throughout to mean mathe- matical expectation. V THE AVERAGE TRAFFIC We have adopted a model which depends on two parameters, the calling rate a, and the mean holding-time h, or its reciprocal 7. Before searching for a set of statistics that is sufficient for the estimation of these parameters, let us consider the product ah = b. This product is important because, as we saw in Section II, the equilibrium distribution of the number of trunks in use depends only on 6, and not on a and h individually. Indeed, the equilibrium probability that n trunks are busy is — bin e 0 n! ' and the average number of busy trunks in equilibrium is just b. The average number of trunks busy during a time interval T is M - f r -^'<" "'' i.e., the integral of the random function Nit) over the interval T, divided by T. This suggests that for large time intervals T, M will come close to the value of b, and can be used as an estimator of b. Since M is a ran- dom variable, the question arises, what are the statistical properties of M? This question has been considered in the literature, the principal references being to F. W. Rabe^° and to J. Riordan." Riordan's paper is a determination of the first four semi-invariants of the distribution of M during a period of statistical equilibrium, but without restriction on the STATISTICS FOR A SIMPLE TELEPHONE EXCHANGE MODEL 949 assumed frequency distribution of holding-time. It follows from Rior- dan's results that M converges to 6 in the mean, which is to say that lim^ {[3/ - 6 1'} = 0. r->oo It also follows that M is an unbiased estimator of b; i.e., that E{M\ = h, and that M is a consistent estimator of b, which means that lim pr{\ M - b \ > £} = 0 T-»QO for each f > 0. VI MAXIMUM CONDITIONAL LIKELIHOOD ESTIMATORS As shown in Appendix A, the likelihood Lc of an observed sequence, conditional on N{0), is defined by In L, = A In a -{- Hhiy - yZ - aT. According to the method of maximum likelihood, we should select, as estimators of a and y respectively, cjuantities dc and -y^. which maximize the likelihood Lc . Now a maximum of L,. is also one of In Lc , and vice versa. Therefore Oc and 7^ are determined as roots of the following two ecjuations, called the likelihood e(iuations: I- In L. = 0; ^ In L, = 0. da oy The solutions to the likelihood equations are . _ A '^ ^H These are the maximum conditional likelihood estimators of a and 7. The estimator dc is the number of requests for service in T diA'ided by T; this is intuitively satisfactory, since d,. estimates a calling rate. Since maximum likelihood estimators of functions of parameters are generally the same functions of maximum likelihood estimators of the parameters, we see that AZ HT is a maximmn likelihood estimator of b. VII PRACTICAL ESTIMATORS SUCJtiESTED BY MAXIMIZING THE LIKELIHOOD L, DEFINED IX APPENDIX A We obtain as likelihood ecjuations — In L = 0, — In L = 0. da oy 950 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 These may be written as n -\- A and y= ^. 7 The first of these shows the estimated calling rate as a pooled combination of the conditional estimate A/T, considered in the last section, and an estimate n/h based on the initial state. This latter estimate has the form calls in progress mean holding time ' and so is intuitively reasonable, since b/h = a. The second equation exhibits our estimate of 7 as a pooled combination of the conditional | estimate H/Z and the ratio a/n. This ratio is acceptable as an estimate ; of 7, since a/b = 7 and b = E{n\ is the average value of n. If we substitute, in the right-hand sides of these eciuations, the condi- tional estimators A/T, H/Z, and Z/H for a, 7, and h, respectively, we obtain simple, intuitive estimators which include the influence of the initial state ?i, and show how it decreases with increasing T. Thus n + A H^ ^^ H estimates a, estimates 7. VIII OTHER ESTIMATORS Additional estimators may be arrived at by intuitive considerations, or by modifying certain maximum likelihood estimators. Some estimators so obtained are important because they use more of the information available in an observation than do the conditional estimators dc and 7c , without being so complicated iunctionally that we cannot easily study their statistical properties. STATISTICS FOR A SIMPLE TELEPHONE EXCHANGE MODEL 951 It seems reasonable, and can be shoAni rigorously (Appendix C), that for an interval (0, T) of statistical equilibrium, the distribution of .4 and that of H are the same. Thus we can argue that, for long time inter- vals, A and H will not be ^-ery different. This suggests using / =±±£ = ^ ' 2T 2T as an estimator of a. This estimator does not involve y, and it uses not only information given by A, but also information supplied by arrivals occurring possibly before the start of observation. Similarly, since b = a y, and .1/ is a consistent and unbiased estimator of 6, we may use -^ = ^ = L to estimate 7, and its reciprocal to estimate h. Finally, since for long {0,T) we have .4 ^ H, we may try A 1 as an estimator of 7, and its reciprocal as an estimator of h. IX THE JOINT DISTEIBUTION OF THE SUFFICIENT STATISTICS The basic result of this paper is a formula for the generating function E{z''x'''''w\"e:'''\ (9.1) for the joint distribution of the random variables n, N(T), A, H, and Z. This formula is derived in Appendix C, by methods illustrated in Section X. For an initial n distribution {p„ j , the generating function is V- n [U-r + y-r - yu)e~^^^^^^ + 7^* ""^ 1 (r + 7)' f + 7 /■ It is proved in Appendix A that the set of statistics [n, A, H, Z} is sufficient for estimation on the basis of the information assumed, which was described in Section I. Thus the generating function (9.2) .specifies, at least in principle, what can be di.sco^•ered about the process from an observation interval (0, 7"), for which N{0) has the distribution |p„}. All the results summarized in this section are consequences of (9.2). T 952 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 Table II 1. e-fz 2. e-f^ 3. y^ 4. e~f«i 5. y^e~^^ In E[X] -f T + r'T fHl - e-(f+^>r)' S" + 7 (r+7)' .r f2(l - e-(r + r))' 2aTC(y - 1) + ar(l - C)iy^ - 1) 2arC(e-f«^ - 1) + aT{l - C)(e-f/r - 1) V f + V [e-!-(+r) _!]_,- (■- j.yi r + r. By substitution, and by either letting the appropriate power series variables — > 1, or letting f -^ 0, or both, we can obtain from (9.2) the generating function of any combination of linear functions of the basic random variables 7i, N{T), A, H, and Z. Some of the generating func- tions thereby obtained are listed in Table II, in which the entries all refer to an interval (0, T) of equilibrium. Since, for eciuilibrium (0, T), the generating functions are all exponen- tials, it has been convenient to make Table II a table of logarithms of expectations, with random variables X on the left, and functions In E{X} on the right. C as a function of r is plotted in Fig. 2. Entry 1 of Table II is actually the cumulant generating function of Z for ecjuilibrium (0, T) ; similarly, Entry 2 is that of il/, and depends only on the average traffic b and the ratio r. The form of the general cumulant of M is A-, n{n — 1) 2^n i {T - .r)x"-V dr. This result coincides with a special case (exponential holding-time) of a conjecture of Riordan. ' This conjecture was first established (for a general holding-time distribution) in unpublished work of S. P. Lloyd. The cumulant generating function permits investigation of asymptotic properties. We prove in Section X that the standardized variable ,1/2 V = (77726)"-= (iM - b) = {:r/2hf- {M - b) is asymptotically normally distributed with mean 0 and variance 1. STATISTICS FOR A SIMPLE TELEPHONE EXCHANGE MODEL 953 1.0 0.8 0.6 0.4 0.2 i-e-'" c = ~ — 6 8 r 10 12 14 Fig. 2 — C as a function of r. From Entry 3 of Table II it can be seen that K is distributed as 2u + V, where u and v follow independent Poisson distributions with the respective parameters aT{l — C) and 2aTC. The probability that K = n for an interval of equilibrium is r„ = exp {aTiC - 1)} £ (^ _ 2^)! Jl ' where the sum is over j's for which 0 ^ 2j ^ n. The estimator di for a is equal to K/2T, and has mean and variance given by E{di} = a, var {d,} = ^ (2 - C). The distribution of di is given by pr{di ^ x} = X) ''" , the summation being over /( ^ 2Tx. From (9.2) one can obtain, by substitution of the stationary n distribu- tion for [pn], and subsecjuent differentiation, the means, variances, covariances, and correlation coefficients of the sufficient statistics, for 954 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 Table III — E{X, Y] 1 n A H K Z 1 n A H K Z 1 b 6(1 + 6) aT baT aT(\ + aT) aT aT(C + 6) aT{,\ - C + aT) aT{\ + aT) 2aT aT(C + 26) aT(2 - C + aT) aT(2 - C + aT) 2aT(2 - C + 2aT) bT bT(C + b) bT(l - C + aT) bT{l - C + aT) 2bT{l - C + aT) bTh(2 - 2C + aT) Table IV — gov Z,F} n A H K Z n A H K Z b 0 aT aTC aTH - C) aT aTC aT{2 - C) aT{2 - C) 2aT{2 - C) bTC bTH - C) bT{\ - C) 267(1 - C) 2bTh{l - C) equilibrium intervals (0, T). It has been convenient to display these in three triangular arrays, the first consisting of expectations of products, the second comprising the variances and covariances, and the third exhibiting, for simplicity, the squared correlation coefficients, since the correlation coefficients are never negative for these random variables. In Table III, the entry with coordinates (X, Y) is£'{A'F} foreciuilib- rium (0, T). All three tables are expressed in terms of a, 6, T, h, r, and C, the last of which is plotted in Fig. 2. The variances and covariances of the sufficient statistics are listed in Table IV; the entries are of the form: cov {X, F} = E{XY\ - E{X\E{Y\. Table \', finally, lists the squared correlation coefficients; i.e., the quantities cov' {X,Y} AX, Y) = var \X\ var {F} For any time interval (0, T), A has a Poisson distribution with param- eter aT, so that Tdc does also. Therefore the distribution of dc is given by pr {(te < •r! = E n! where the summation is over ;/ < xT. Evidentlv STATISTICS FOR A SIMPLE TELEPHONE EXCHANGE MODEL 955 E{dc} = a, and var lad = a T' so that dc is an unbiased and consistent estimator of a. We now compare the variances of estimators dc and di. From Table IV we have var {di} = |f 1 2" ) < jT = var {ttcl, so that di is a better estimator of a for any T > 0, in the sense that its variance is less. X THE DISTRIBUTIONS of Z AND M Since we have defined = [ N{t) dt, we can regard Z as the result of growth whose rate is given by the ran- dom step-function Nit) ; when N{t) = n, Z is growing at rate n. An idea similar to this is used by Kosten, Manning, and Garwood , and by Kos- ten alone. Now the Z{T) process by itself is not Markovian, but it can be seen that the two-dimensional variable \N{t), Z{t)\ itself is Marko- vian. Let Fn{z, t) be the probability that N{t) = n and Z{t) ^ z. Since the two-dimensional process is Markovian, we can derive infinitesimal relations for Fn{z, t) by considering the possible changes in the system during a small interval of time A^ Table V — p\X ,Y) n A H K Z 1 0 1 - e-' 2 - C rC 2(1 - C) A 1 1 - C 2 - C 2 1 - C 2 H 1 2 - C 1 - C 2 2 K 1 1 - C 2 - C Z 1 95G THE BELL SYSTEM TECHNICAL JOUKXAL, JULY 1957 If A''(0 = n, then the probabiHty is [1 — ytiAt — aAt — o{At)] that there is neither a request for service nor a hang-up during A^ following t, and that Z{t + AO = Z{t) + 7iAt. Therefore the conditional proba- bility that N{t + AO = fi and Z{t + At) ^ z, given that no changes occurred in At, is Fn{z - nAt, t). For N(t) = (n -f 1), the probability is 7(/i + 1)A^ + o(At) that one conversation will end during At following /. The increment to Z{t) during A^ will depend on the length x of the interval from t to the point within A^ at which the conversation ended. The increment has magni- tude (n -\- l)x -f n{At — x) = x + nAt, as can be verified from Fig. 3, in which the shaded area is the increment. Since x is distributed uniformly between 0 and A^ the increment x + nAt is distributed uniformly be- tween 71 At and (n + 1)A^ Therefore the conditional probability that A^(^ + At) = n and Z{t + At) ^ z, given that one conversation ended in At, is — / Fn+i(z — u, t) du. At J,iAt By a similar argument it can be shown that the probability that one reciuest for service arrives in At is a At -f o(At), and that the conditional probability that A^(^ -f At) = n and Z(t -f At) ^ z, given that one request arrived during At, is 1 It nAt At J{ n-l)At Fn-i{z - u,t) du. Define Fniz, t) to be identically 0 for negative n. Adding up the probabil- n + 2 - t + At Fig. 3 — Increment to Z in At. STATISTICS FOR A SIMPLE TELEPHONE EXCHANGE MODEL 957 ities of mutually exclusive events, we obtain the following infinitesimal relations for Fn{z, t): F„(z, t -\- At) = y(n + 1) / F„+i(2 - u, t) du + a / F„-i{z - ?/, /) du + F„(z - riAt, t) J(n-1)A( •[1 — A((yn -\- a)] + oiAf), for any n. Expanding the penultimate term of the right side in powers of nAt, and the left side in powers of At, we divide by At, and take the limit as At approaches 0. Now lim — / F„+iiz - u, t) du = F^+i(z, t). At->0 At J r,M Thus, omitting functional dependence on z and / for convenience, we reach the following partial differential eciuations for F,Xz, t): iF„ = ,(„ + l)F.,,, + aF,._,-„|F. ^^^^^ — [yn + a]Fn , for anj^ n. Since Z(0) = 0, we impose the following boundarj^ conditions: Fn{0, 0=0 for n > 0 and t > 0, Fniz, 0) = p„ for z ^ 0, (10.2) Fn{z, 0) = 0 for z <0, where the sequence }p„} forais an arbitrary iV(0) distribution that is zero for negative n. To transform the equations, we introduce the Laplace-Stieltjes in- tegrals 0, Jo- in which the Stieltjes integration is understood always to be on the variable z. We note that ' " 1 / e~^'Fn{z,t) dz = -<^„(f, 0, Jo- C and that ^«(r, 0 = F„{0,t) + / e-'=^F,. {z,t) Jo dz dz. 958 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 Applying now the Laplace-Stieltje.s transformation to (10.1), we obtain dt = y(n -\- \)(pn+i + a 0; in (10.8) we may therefore omit this term in the region / > 0. Let

- 1 m" + r which approaches f /2 as T -^ oo . It follows that the normalized variable is asymptotically normal with mean 0 and variance 1, and that (r/2by{M — b) is also asymptotically normal (0, 1). STATISTICS FOR A SIMPLE TELEPHONE EXCHANGE MODEL 961 Appendix A PROOF THAT {u, A, H, Z} IS SUFFICIENT. We observe the system during the interval (0, T), and gather the in- formation specified in Section I, and summarized in Table I. From this information we can extract four sets of numbers, described as follows: Sa the set of complete observed inter-arrival times, not counting the interval from the last arrival until T Sh the set of complete observed holding times Si the set of hang-up times for calls of category (i) Si the set of calling-times for calls of category (iv) In addition, our data enable us to determine the following numbers: n the number N{0) of calls found at the start of observation k the number of calls of category (iii); i.e., of calls which last through- out the interval (0, T) X the length of the time-interval between the last observed arrival and T In view of the negative exponential distributions which have been assumed for the inter-arrival times and the holding-times, and in view of the assumptions of independence, we can write the likelihood of an observed sequence of events as utSa ~tSh wlSi V^Si SO that hi L = —ykT — ax + In p„ + A In o — ^ au u(Sa + H \n y - Y, yz - Y, yw - ^ y{T - ij) ziSh wtSi ytSi It is easily seen that the summations and the two initial terms can be combined into a single term, so that we obtain In L = In pn + .1 In a -{- H hi y - yZ - aT. This shows that L depends only on the statistics n, .4, H, and Z; it follows that the information we have assumed can be replaced by the set of statistics {n, .4, H, Z\, and that these are sufficient for estimation based on that information. The likelihood is sometimes defined without reference to the initial state, by leaving the factor p„ out of the expression for L. Strictly speak- ing, this omission defines the conditional likelihood for the observed 962 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 sequence, conditional on starting at n. We use the notation : Vn A definition of likelihood as Lc has been used by Moran. Clearly \nLc = A\na + H\ny - yZ - aT. Appendix B unconditional maximum likelihood estimates The definition of likelihood as L leads to complicated results which are of theoretical rather than practical interest. For this reason these results have been relegated to an appendix. The results of setting d/dy In L and d/da In L equal to zero lead, re- spectively, to the likelihood equations a - y{n - H) - y'Z = 0, yn — a + 7-i — ayT = 0. Considered as a system of equations for y and a, this pair has the non- negative roots H - n - M + {{H - n - Mf + 4MK}''' 7 = a = ^ - W. 2Z These are the unconditional maximum likelihood estimators for y and a. Although dc depended only on A and T, and 7c only on H and Z, the unconditional estimators depend on all of n, A, H, Z, and T. We may obtain a maximum unconditional likelihood estimator for b as well, either by considering L to be a function of b and 7, or from general properties of maximiun likelihood estimators. Since b = a/y, we expect that b = d/y, as can be verified by an argument similar to that used above for a and 7 . The estimators d, b, and 7 obtained in this Appendix may turn out to be useful in practice, but their complicated dependence on the sufficient statistics n, A, H, and Z makes a study of their statistical properties difficult. As a first step along such a study, we have derived the gen- erating function of the joint distribution of the sufficient statistics in Appendix C. The greater simplicity of the conditional estimators of Section VI makes it possible to study their statistical properties. This STATISTICS FOE A SIMPLE TELEPHONE EXCHANGE MODEL 963 fact gives them a practical ascendancy over the unconditional estimators, even though the latter may be more efficient statistically by dint of using all the information available in an observation. Appendix C the joint distribution of n{t), tl, a, h, and z By methods already used in Section X one can obtain a gen- erating function for the joint distribution of all the random variables n, N(t), A, H, and Z. Let ^ = L[x w u e \. Then $ satisfies the differential equation ^ + [f.i- + 7.i- - yu]— = aiwx - 1)^, dt dx whose solution has the form /aw[^x -i- yx — yu][l — e"^^"^^^'] , aywut \ ■^H o^^r + r+^ - "V- where the function R is determined by the initial distribution {p„} through the relation ^ + yu n^O L r + 7 J From these results it follows that the generating function E\z X w u e ^ \ is given by 2^ PnZ ( — r ) "go \ f + 7 / fawi^x + 7.r - yu)[l - e'^^^'^^] . aywuT „\ If {p„\ forms the stationary distribution, this reduces to 2(fx + 7.T — 7tOe~^^^^'^ + yiiz \ R{^\ = E Pn exp r + 7 / awj^x + yx - yu)[l - e~^^+"^^] aywuT _ ■^ (f + 7)^ "^ f + 7 "" 96-1 THE BELL SYSTEM TECHXICAL JOURNAL, JULY 1957 If, ill this last expression, we let x approach 1, z approach 1 , and u ap- proach 1, we obtain exp ^ _ ^i^Y^rie---- - 1) _ ,,; (C) r + 7/\ r + 7 as the generating function E\w^e^^^] for an interval of equiUbrium. Alternately, if instead we let x approach 1, z approach 1, and w ap- proach 1, we obtain (C) with u substituted for w; this implies the not- surprising result that for an interval of equiUbrium, the two-dimen- sional variables {A, Z\ and [U, Z\ have the same distribution. From this and (C) it follows that for eciuilibrium (0, T), (i) .4 and E both have a Poisson distribution with mean oT, and (ii) the estimators Ac and Ao have the same distribution. ACKNOWLEDGEMENT The author would Uke to express his gratitude for the helpful com- ments and suggestions of E. N. Gilbert, S. P. Lloyd, J. Riordan, J. Tukey, and P. J. Burke. REFERENCES 1. H. Cramer, ■Mathematical Methods of Statistics, Princeton, 1946. 2. W. Feller, An Introduction to Probability Theory and its Applications, John Wilev and Sons, New York, 1950. 3. W. Felier, On the Theory of Stochastic Processes with Particular Reference to Applications, Proceedings of the Berkeley Symposium on Math. Statistics and Probability, Univ. of California Press, 1949. 4. A. Jensen, An Elucidation of Erlang's Statistical Works Through the Theory of Stochastic Processes, in The Life and Works of A. K. Erlang, Copenhagen, 1948. 5. L. Kosten, On the Accuracy of Measurements of Probabilities of Delay and of Expected Times of Delay in Telecommunication Systems, App. Sci. Res., B2, pp. 108-130 and pp. 401-415, 1952. 6. L. Kosten, J. R. Manning, F. Garwood, On the Accuracy of Measurements of Probabilities of Loss in Telephone Systems, Journal of the Royal Statistical Society (B), 11, pp. 54-67, 1949. 7 P A. P. Moran, Estimation Methods for Evolutive Processes, Journal of the Royal Statistical Society (B), 13, pp. 141-146, 1951. 8 W. F. Newland, A Method of Approach and Solution to Some Fundamental Traffic Problems, P.O.E.E. Journal, 25, pp. 119-131, 1932-1933. 9. C. Palm, Intensitatsschwankungen im Fernsprechverkehr, Ericsson Tech- nics, 44, 1943. 10. F. W. Rabe, Variations of Telephone Traffic, Elec. Comm., 26, 243-248, 1949. 11. J. Riordan, Telephone Traffic Time Averages, B.S.T.J., 30, 1129-1144, 1951. 12. H. Stormer, Anwendung des Stichprobenverfahrens beim Beurteilen von Fernsprechverkehrsmessuugen, Archiv der Elektrischen Ubertragung, 8, pp. 439-436, 1954. Fluctuations of Telephone Traffic By V. E. BENES (Manuscript received November 9, 1956) The number of calls in progress in a simple telephone exchange model characterized by unlimited call capacity, a general probability density of holding-time, and randomly arriving calls is defined as N{t). A formula, due to Riordan, for the generating function of the transition probabilities of A^{t) is proved. From this generating function, expressions for the co- variance function of Nif) and for the spectral density of N{t) are determined. It is noted that the distributions of N(t) are completely specified by the co- variance function. I INTRODUCTION The aim of this paper is to study the average fluctuations of telephone traffic in an exchange, by means of a simple mathematical model to which we apply concepts used in the theory of stochastic processes and in the analysis of noise. The mathematical model we use is based on the following assumptions : (1) requests for telephone service arise indi^'idually and collectively at random at an average rate of a per second; (2) the holding-times of calls are mutually independent random variables having the common probability density function h{u); and (3) the capacity of the exchange is effectively unlimited, and no call is blocked or delayed by lack of equipment. This telephone exchange model has been described by J. Riordan.^ As a measure of traffic, it is natural to use the number of calls in prog- ress in the exchange. We are thus led to consider a random step-function of time N(t), defined as the number of calls in progress at time t. iV(/) fluctuates about an average in a manner depending on the calling-rate, a, and the holding-time density, h{u). II PROOF OF RIORDAX'S FORMULA FOR TRANSITION PROBABILITIES Let Pm.n(t) be the probability that w calls are in progress at t if m calls were in progress at 0. Define the generating function of these prob- 965 966 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 abilities as and let f{u) = [ h{x) dx, so that the average holding-time, h, is given by h = j f{u) du. Jo Riordan" has given the following formula for P,„{t, x) : P,M, x) = [1 + (.r - \)g{t)]"' exp {{x - l)ah[l - git)]], (1) with git) = ^ fin) du. For exponential holding-time density, this formula had alread}' been derived (as the solution of a differential equation) by Palm." In private communication, J. Riordan has suggested that his proof of (1) is incomplete. We therefore give a new proof of (1). We seek the generating function of N{t), conditional on the event JSfiO) = m. We obtain it by first computing the joint generating function of 7^(0) and A^(^) ; that is, ^{/^V^'M- (2) The desired conditional generating function is then the coefficient of I/'" in (2), divided by the probability that A^(0) = m. To obtain a formula for (2), we exhaust the interval {— --^ , 0) by division into a countable set of disjoint intervals, /„ , the n^ having length Tn > 0. Let S„ be the sum of the first n lengths, Tj . Let ^„(0, f or ^ > — »S'„_i , be the number of those calls which arrive in /« and are still in progress at /. And let ri{t) be the number of calls arriving during (0, t), t > 0, and still in existence at /. Then NiO) = Z UO), (3) «>i Nit) = vit) + E Ut), t > 0. (-i) "SI Since calls arri\-ing during disjoint intervals are independent, we know FLUCTUATIONS OF TELEPHONE TRAFFIC 967 that 7]{t) is independent of all the ^'s, and that ^n{t) is independent of ^y(r) if Ji 9^ j. Of course, ^„{t) and ^nir) are not independent. It follows that if the infinite product converges, then for / > 0 ^^{/%-^''^l = E\x''"} ni?h/"%-'"^'^}. (5) We now compute the terms of the product. If a call originates in in- terval /„ , it still exists at 0 with probability Qn =~ [ " fiu + Sn-l) dU = ^ f " /(m) du. -f n •'0 1 n •'S„_i Hence if k calls arrived in /„ , the probability that m of them are still in progress at 0 is pr{^n(0) = m I A- calls arrive in /„} M QZd - Qn)'-"\ m ^ k. Similarly, if a call originates in /„ and exists at 0, it also exists at ? > 0 with probability T Kn = {QnTnV f ^ fin + t + Sn-i) du. Jo Therefore Eix^"'''^ I ^„(0) = m and A- calls arrive in /„} = [1 + {x - l)Knr, and so - {1 + (^[1 + {x - 1)K„] - 1)Q,}' k = a . The number of calls arriving during /„ has a Poisson distribution with mean aT„ ; hence £;{2/«"'V«^'^} = exp {aT.ia - 1)} (6) = exp {aTnQn{y{l + {x - 1)K„] - 1)}. By reasoning like that leading to (6), it can be shown that 968 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 Eix"'"'] = exp L(.r -!))-{ /(") diX = exp \ah{x - 1)[1 - git)]}. (7) Now /»00 ^ aT„Qn = a I f{u) du = ah, 71 gl Jo -. T E aT„Q„/C = a E / "/('' + ^ + ^"^'n-i) du, /(?/) du = ahg{t). Therefore the infinite product is convergent, and ^{/oo 1 then /*C0 w{f) = 4 / R{t) COs27r/Vf/r, Jo rtOO R(t) = wU) COS 2irfTdf. Jo (Ci. Rice,' p. 312 ff.) At the same time, we have R{r) = E{[Nit) - b][N{t+ r) - b]\ = 'A(r) - b' = bg{r). Let X(t) be any stochastic process which is known to be the occupancy of a telephone exchange of unlimited capacity, having a probability density of holding-time, and subject to Poisson traffic. From the pre- ceding result it can be seen that the covariance function of .Y(/) deter- mines the distributions of the X{t) process completely, since dR' dn t=0 -rdR dr' If the holding-times are bounded by a constant, k, then readings of A^(^) taken further apart than k are uncorrelated . In fact, such values /(r) = f^ h{u) du = -a FLUCTUATIONS OF TELEPHONE TRAFFIC 971 are independent, because no call which contributes to N{t) can survive until {t -\- k), with probability 1. Using (11), we see that w /•OO (/) = 4 / cos 27r/r/?(r) dr Jo = 46 / cos 27r/rgr(T) dr Jo = 4a / cos 27r/r / / h{u) du dy dr (12) vQ J J Jy = —. I sin 27r/r / h{u) du dr irj Jo Jt r ,'« = ^Tf^ 1 - / COS 27r/r/l(T) C?7 Equation (12) expresses the mean square of the frequency spectrum of the fluctuations of the traffic away from the average in terms of the call- ing-rate and the cosine transform of the holding-time density, h{i(). The calling-rate appears only as a factor, and so does not affect the shape of w{f). The function iv(j) is what Doob^ (p. 522) calls the "spectral density function (real form)." V EXAMPLE 1. N(t) MARKOVIAN Let the frequency h{u) be negative exponential, so that h{u) = ^ e-'\ (13) where /) is the mean holding-time. It is shown in Riordan" p. 1134, that N{t) is Markovian if and only if h{u) has the form (13). From page 523 of Doob^ we know that the covariance function of a real, stationary Markov process (wide sense) has the form R{t) = R{0)c~"\ a constant. (14) Under the assumption (13), the covariance of N(t) is Rir) = bgir) = ^^ f^ f h{u) du dy = he -Tlh 972 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 in agreement with (14). The spectral density can now be obtained from (11) or (12); it is w(f) = 46/1 1 + 47r2/2/i2- This is the same as would be obtained for a Markov process that alter- nately assumed the values + \/ah, — y/ah at the Poisson rate of (2/1)"^ changes of sign per sec. (Cf . Rice p. 325.) VI EXAMPLE 2. HOLDING-TIME DISTRIBUTED UNIFORMLY IN {a,0) Let h{u) be constantly equal to (|S — a)~^ in the interval (a, /3), and constantly 0 elsewhere. Then by (12), w{f) = a a TT*-;- 1 f 1 — / cos 2irft dt 1 - Now we see that J{ij) = \ h{u) du sin 27r//3 — sin 27r fa 27r/(/3 - a) . 1 for y ^ oc ^ - y ^ - a [0 for 7/^/3 for a ^ y ^ 0 so that Rir) = a a + 13 - a 0 < r < a g (^ - tY 2 0 - a 0 a ^ r ^ /i (15) T ^ l3 is the covariance function of the process N{t) when holding-time is dis- tributed uniformly in (a, (3). If, formally, we let (/3 - a) approach 0 while keeping §(a + /3) fixed, then the holding-times become concentrated in the neighborhood of the mean, h; in the hmit, as h{i() tends to a singular normal distribution ^ with mean, h, and variance zero, we obtain ' a w{f) = -^, [1 - cos 2irfh] (16) FLUCTUATIONS OF TELEPHONE TRAFFIC 973 as the spectral density function for the N(t) process with constant hold- ing-time, h = ^{a 4- |(3). Similarly, from (15), we note that as the hold- ing-times become singularly normal with mean, h, and variance zero, the covariance function becomes f = a{h - t) 0 ^ t ^ h R(r) = \ [= 0 T ^ h. We can express (16) as ,2 /■j-\ .-. j2 /sin -irfh , and note that this is exactly like the power spectrum of a random tele- graph wave constructed by choosing values + -s/ah, — -y/ah with equal probability and independently for each interval of length, h. (Cf. Rice,* page 327.) REFERENCES 1. J. L. Doob, Stochastic Processes, John Wiley and Sons, New York, 1953. 2. C. Palm, Intensitatsschwankungen im Fernsprechverkehr, Ericsson Technics, 44, pp. 1-189, 1943. 3. F. W. Rabe, Variations of Telephone Traffic, Elec. Commun., 26, pp. 243-248, 1949. 4. S. O. Rice, Mathematical Analysis of Random Noise, B. S.T.J. , 23, pp. 282-332, 1944, and 24, pp. 46-156, 1945. 5. J. Riordan, Telephone Traffic Time Averages, B.S.T.J., 30, i)p. 1129-1144, 1951. High- Voltage Conductivity-Modulated Silicon Rectifier By H. S. VELORIC and M. B. PRINCE (Manuscript received May 1, 1957) Silicon power rectifiers have been made which have reverse breakdown volt- ages as high as 2,000 volts and forward characteristics comparable to those obtained in much lower voltage devices. It is shown that the magnitude and temperature dependence of the currents can be explained on the basis of space-charge generated current with a trapping level 0.5 eV below the con- duction band or above the valence band. The breakdown voltage of a P IN'^ diode is computed from avalanche multiplication theory and is shown to be a function of the width of the nearly intrinsic region. A simple diffusion process is evaluated and shoivn to be adequate for diode fabrication. The characteristics of devices fabricated from high-resistivity compensated , floating-zone refined, and gold-doped silicon are presented. The surface limi- tation to high inverse voltage rectifiers is discussed. I IXTKODL'CTION The desire for high voltage rectifiers in the electronic industry has pushed the peak inverse voltage of solid state rectifiers to higher and higher values. The purpose of this paper is to present some of the con- siderations necessary in designing a device with a high iuA^erse voltage and an excellent forward characteristic. In many cases the device charac- teristics are predictable. Conversely, high Noltage diodes are excellent tools for studying many solid state phenomena. It has been shown^ that it is possible by the use of the conductivity modulation principle to separate the design of the forward current-volt- age characteristic from the reverse current- voltage characteristic of a silicon p-n junction rectifier. Units have been fabricated by the difTusion of boron and phosphorus into high resisti\'ity material, that have reverse breakdown voltages in the range of 1,000 to 2,000 volts. The reverse currents are of the order of a microampere per scjuare cen- timeter at room temperature and increase approximately as the square 975 976 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 root of the applied voltage. The magnitude, voltage dependence, and temperature dependence of the reverse currents can be explained as due to space-charge generated current- with a trapping level 0.5 eV from either the conduction or valence band. These effects will bo discussed in Section II. In Section III the breakdown \'oItage and its dependence on the re- sistivity and width of the high resistivity region of the rectifier will be considered. In the next section the forAvard current is discussed and explained by considering both a space-charge region generated current and a diffu- sion current that takes into account high levels of minority carrier in- jection.^ Device processing information is given in Section V, together with an evaluation of different sources of high resistivity silicon. The devices to be discussed in this paper have been processed with high resistivity p-type material, although some devices have been made with ?i-type ma- terial. Finally, a discussion of some surface problems associated with high voltage rectifiers is given in Section VI. Although this paper is entitled "High-Voltage Conductivity-Modu- lated Silicon Rectifier", the theoretical arguments are applicable to all semiconductor diodes. However, the experimental results have been limited by considering only high A'oltage diodes. II REVERSE CURRENT-VOLTAGE CHARACTERISTIC 2.1 Theory The simple theory* for a p-n junction yields an expression for the re- verse saturation current density (Id) which is: h = q (2-1) where q is the electron charge, np is the equilibrium electron density in p-type material, pn is the equilibrium hole density in /i-type material, D„ and Dp are the diffusion constants for electrons and holes, and r„ and Tp are the minority carrier lifetimes for electrons and holes. When reasonable numbers are substituted into (2-1), h at room tem- perature is of the order of 10"^" amperes per square centimeter. This quantity doubles with every increase of 4° C. The theory also contains no voltage dependence of this current. Even when breakdown multi- plication^ is taken into account, there is essentially no voltage dependence CONDUCTIVITY-MODULATED SILICON RECTIFIER 977 at voltages less than half the breakdown voltage. The magnitude and temperature and voltage dependences of measured diodes do not agree with these theoretical values at room temperatures. Recently, Pell*^ has shown that the reverse currents at low temperatures in germanium, and at room temperatures in silicon, are dominated by space-charge generated current. The space-charge generated current density (Isc) is given by /,, = qWG M, (2-2) where W is the width of space-charge region, G is the generation rate of hole-electron pairs in the space-charge region, and M is the breakdown multiplication {M ~ 1 except near the breakdown voltage). G is given by-^ G = '^ , (2-3) where iii and pi are the densities of electrons and holes respectively if the Fermi levels were at the energy level of the recombination centers, and r„n and Tpo are the minority carrier lifetimes of electrons and holes respectively in heavily doped p-type and ?i-type silicon. This expression assumes constant generation over the space-charge region. Thus, and n, = Nc exp ^ (Vr - W) = n, exp ^(F. - Yd, (2-4a) pr = N. exp ^ (7. - Vr) = m exp - /3(F. - F,), (2-4b) where Vr is the recombination level above the valence band edge T'\ , Vi is the midband intrinsic level, /S = q/kT, Nc and A^„ are the effective densities of states in the conduction and valence bands ^ 2.4 X 10 (T'/300)^ Vc is the conduction band edge, k is the Boltzmann's constant, and T is the absolute temperature. Substituting (2-4) into (2-3), one obtains: rii 1 G = 2V TnOTpO cosh /3(F. - Vi) + h In "^ TnO_ (2-5) For the diffused silicon junctions under consideration, it has been found' that T„ri equals 1.2 X 10"^ seconds and Tpo equals 0.4 X 10"" seconds. Also, iii = 3.74 X 10'' r^'V''""'' and F.- = 0.54 vohs. Using these 978 THE BELL SYSTEM TECHNIC'AL JOUU.NAL, JULY 1U57 numbers, (2-6) becomes: 1.25 X 10'« (; = — ;^oo g20.8(l-30O/r) 'osh .8.02 (^)(r,.- 0.54) 0.55 (2-6a) aiitl where a = G:miV,M\T, Vr), (7:51)0 (» r) — 1.25 X 10 16 cosh [38.62(T^ - .54) - 0.55]' and f{T, Vr) (2-6b) (2-7a) (2-7b) ' rp \3;2 J \ 20.8(1-300/7') c osh [38.62 (F, - 0.54) - 0.55] cosh 38.62 (-^^^^ [Vr 0.54) - 0.55 In (2-6b), G-m{yr) is the generation rate for a recombination level at Vr equal to 300° K, and f{T, T,) is the temperature variation of G for a recombination level at 1', normaHzed to :^00° K. Curves of /(T, Vr) are gi\-en in Fig. 1 for several \alues of W with a curve g{T) which is the temperature variation of the reverse saturation current (/o). Table I gives values for Gm for various Vr . In the reverse biased diffused junctions made with high resistivity ma- terial, the junction may be considered abrupt. Therefore, the width (IF) of the space-charge region, when the junction is rtn-erse biased to a volt- age V, is given by ir = :V 1/2 :2qN = 3.14 X urirp,,) 1 2 cm (2-8) where the units after the first equal sign are electrostatic, and k is the di- electric constant. In the second expression, 1' is in volts, and pp , the base material resistivity, expressed in ohm-centimeters. Thus, /,,. = 4 X 10"''G';uH,(r,.)/(7', l',.)[rpj' - amperes-cnF (2-9) It is seen that /«< varies theoretically as the square root of the reverse voltage for values of V less than h Va , the breakdown voltage, in which range avalanche multiplication is negligible. The (luantity /,,. varies in- versely with Na^^' and will be large for high \'oltage de\'ices with small Na . The Isc at 300° K for a rectifier with 40 ohm-centimeter base ma- CONDUCTIVITY-MODULATED SILICON RECTIFIER 979 terial and a reverse bias of 100 volts is given in Table I as a function of Vr . The numbers compare with 8 X 10"^° ampere per square centimeter for /o . Thus, from diode measurements at room temperature and above, one could not observe Vt less than 0.3 eV from either the conduction or valence band. In fact, from a measurement of the temperature depend- ence of the reverse currents, one can determine only the recombination level lying closest to the center of the forbidden band. This can be seen more clearly from the folloAving argument: There will be a contribution to the reverse current from the diffusion current hmgiT) which varies with temperature as g{T). There will be contributions to the reverse cur- 105 5 5 10^ > 102 10' 10° 10" \ ^^ — q (T), Vr = 0 \ Vp = 0.20, 0.88 V > V Vr = 0.30, 0.78 \ Vr = 0.40, 0.68 Vp = 0.54 \ > \ \ k \ \ \ \ N \ \ \ ^ > S \ \ \ ^. \ \ \ \ \ \ \ N \ \ k k, '^^ ' \ \ \ \ A k s 'V \ s s A ^k^ \ ^> §^^ ^ ^ N 2.2 2.4 2.6 2.8 1000 T°K 3.0 3.2 3.4 Fig. 1 — The temperature variation of the generation rsite,f{T, Vr), for several values of the recombination level, Vr . 980 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 Table I — Values of G and Space Charge Generated Current at 300° K for Various Values OF the Trapping Level Vr T = 300° K Eg = l.OSeF np = 3 X 10'° cur^ r„o = 1.2 X 10-« sec Tpo = 0.4 X 10-« sec Vt Volts above Valence Band G300 cm"3 sec"' /»e (7 = - 100 volts, p = 40 ohm-cm) microamperes/cm^ 0.10 5.92 X 108 1.88 X 10-' 0.20 2.84 X IQio 9.03 X 10-6 0.30 1.35 X 1012 4.29 X 10-" 0.40 6.5 X 10" 2.06 X 10-2 0.50 3.02 X 1016 0.96 0.54 1.08 X 1016 3.43 0.58 8.1 X 10" 2.58 0.68 1.95 X 101" 6.2 X 10-2 0.78 3.96 X 1012 1.26 X 10-3 0.88 8.45 X IQio 2.69 X 10-5 0.98 1.78 X 10« 3.75 X 10-' rent by the individual trapping centers given by IscdooiVr)f(T, Vr), where hcsooiVr) is the current at 300° K due to generation at recombmation centers located at the level Vr , and/(T, T^) is the temperature variation of the generation rate. Thus, the total reverse current is given by = lomgiT) + Z^.cm{Vr)KT, Vr), (2-10) where the summation is over all recombination levels. The relative cur- rents at 300° K are given in Table I. The greatest contribution at 300° K is due to the level nearest the center of the forbidden band. As the tem- perature increases, all the terms under the summation sign approach each other. Before a second recombination level contributes significantly to the reverse current, however, the saturation current will ha"\'e become the most important component. 2.2 Experimental Results To evaluate the theory for the reverse currents in silicon N^P junctions, careful measurements were made on five typical units for the reverse current-voltage characteristics at various temperatures from 300° K to 435° K. The curves were taken with a X-Y recorder. The voltage ranged from 0 to 200 volts so that multiplication effects were completely negligible. From the recorded data, curves of Ir versus 1,000/T° K were plotted for V = —10, —40, and —160 volts. The set of curves for diode No. 3 CONDUCTIVITY -MODULATED SILICON RECTIFIER 981 10' 102 If) Ml a. UJ a 5 < O a. u 5 z 10' 10° 10" 10-2 V _,, o 10 VOLTS ^o A 40 VOLTS X 160 VOLTS N^ xs:) , N i>^. i i ^ \, 1 \ ;^> : \ 1 NXX. \S $; \ N ^ ^v S^ 1 x 2.2 2.4 2.6 2.8 1000 T" K 3.0 3.2 3.4 Fig. 2 — The temperature variation of "reverse current" for a typical diode at -10, -40, and -160 volts. is given in Fig. 2. The slope of these curves indicates that the recombina- tion level lies near 0.5 eV below the conduction band or above the val- ence band. The junction area of this device is 0.015 cm^; thus, the cur- rent density at 300° K and at - 100 volts is 4.4 microamperes per square centimeter. This compares with the order of one microampere as listed in Table I. This suggests that the (t„ot„o)' is overestimated. The agree- ment of this measurement with theory is reasonable. The voltage variation of the reverse currents does not agree with theory as well as the magnitude and temperature dependence. The ex- perimental results give, as the voltage dependence, an expression: /, ~ V \IN where N equals 2.9. This compares with the theoretical value of N = 2. 982 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 Some of this discrepancy can be attributed to the fact that the junction is not truly an abrupt junction. A "graded" junction would yield A^ equals 3. Measurements of capacitance versus voltage, which essentially measure the width of the space-charge region, yield A^ equals 2.4. Thus, these devices in the relatively low voltage range still have some contri- bution from the gradation of the diffused junction. The highest temperature points in Fig. 2 deviate above the straight lines. This deviation can be attributed to the onset of the contribution from the h component. Calculations indicate that, by T = 220° C, the contribution to the reverse current by the space-charge current is equaled by the saturation current and that, by T = 820° C, the space-charge- generated current is negligible compared to the saturation current. Ill BREAKDOWN VOLTAGE OF PN AND PIN JUNCTIONS 3.1 Theory It has been demonstrated that, in germanium ' and silicon, reverse biased junctions breakdown as a result of a solid state analogue of the Townsend ^ Avalanche Theory. Multiplication and breakdown occur when electrons or holes are accelerated to energies sufficient to create hole-electron pairs by collisions with valence electrons. The breakdown phenomena in silicon for graded and step junctions has been previously considered.*' ^^ Depending on the impurity distribution, the field in the junction will be a function of distance and will have a maximum value in the region of zero net impurity concentration. The breakdown voltage is a critical function of the space-charge distribution. In this section the existing multiplication theory is extended to the case of PIN junctions. It is shown that relatively wide intrinsic regions are required to obtain breakdown voltages greater than 1000 volts. Fig. 3 is a plot of the impurity, charge, and field distributions in PIN and PttN junctions. Fig. 3(a) schematically illustrates the geometry of the three region devices considered, and Fig. 3(b) is a plot of the impurity distribution. In this analysis step junctions will be assumed. For the PIN junction there are no uncompensated impurities in the intrinsic region, and no net charge. At low reverse voltage, the field will sweep through the intrinsic layer and will increase with increasing reverse bias until the breakdown field is reached. Absolutely intrinsic material is not yet available, and devices are made from high resistivity x-type material. In this class of devices there is some uncompensated impurity and charge in the center region. The field will have a maximum value at the N^ tt junction and will decrease CONDUCTIVITY-MODULATED SILICON RECTIFIER 983 with increasing distance into the tt region. At sufficiently high reverse bias the field may sweep into the P^ region. Breakdown in silicon^ is a multiplicative process described by 1 r (3-1) where M is the multiplication factor, W is the space-charge width, and ai is the rate of ionization which is a strong function of the field in the junction. For a PIN structure, the field is constant, at breakdowTi M approaches x , and aiW = 1. (3-2) The ionization rate at breakdown is then a simple function of the wddth of the intrinsic region. McKay and Wolf^^ have considered a^ as a func- Na-No < — W ^ p+ I OR 7T N+ (a) - P+TN+ p+;7N+ (b) p 0 (C) E 0 (d) Fig. 3 — Impurit}^ charge and field distribution in PIN and PttN junctions. 984 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 tion of the field. If ai is fixed, the field at breakdo\ni can be determined. The breakdo\\ii voltage is / Ed.> Jo Fig. 4 is a plot of breakdown voltage as a function of space-charge p width for PN and PIN diodes. The PIN values are calculated; the PN data is previously unpublished data supplied by K. G. McKay. Some interesting observations can be made from Fig. 4: 1. The plot of breakdown voltage versus barrier width for a PN step \ junction assumes that the space-charge region does not extend through ; the high resistivity side of the junction. For this class of junctions the breakdown voltage is determined by the impurity concentration as shown in Fig. 5. The plot of breakdown versus space-charge width for a PIN diode assumes that the space-charge region extends from the P to N region at very low bias, and that it is limited by the width of the I re- gion. If a constant field is assumed in the I region, the breakdown volt- age is a function of the barrier width. 2. Although the space-charge region can reach through the I region at low bias, the avalanche breakdo^\^l voltage is a function of the width of the I region. 3. For the devices considered here with tt regions in the order of 10' ' cm, the maximum breakdown voltage is in the order of 2,000 volts. 10' o > < o > z 5 o 10^ 5 102 10 ^~ ' ^ WIDTH OF I REGION FOR PIN DIODES / / / / y ,/ r / r / /.. y ^y ,'' / / ^ x ^^ MCKAY'S DATA FOR PN JUNCTIONS y ,^ ' /y • y\ / 4 6 8,^-2 2 4 6 8, 10"" " " "10"^ " " " "10""^ " "" " "10"' BARRIER WIDTH FOR PN AND PIN JUNCTIONS IN CM Fig. 4 — Breakdown vohage as a function of barrier width for PN and PIN junctions. CONDUCTIVITY-MODULATED SILICON' RECTIFIER 985 lU^ MAXIMUM BREAKDOWN VOLTAGE 5 FOR UNITS WITH 0.018 CM I REGION EXTRAPOLATED DATA >^ 2 5 \, w O EXPERIMENTAL POINTS i i c 0 N N. f r' ^. ^< ) v. V 2 I02 5 ' - \ ^ ^ \ ^ 2 10' x| ^ ^ 1012 lO'S 2 5 ,Q,4 2 5 ,Q,5 2 5 ,q,6 Nj IN ATOMS PER CUBIC CENTIMETER 10'7 Fig. 5 — Breakdown voltage versus impurity concentration for silicon step junctions. S.2 Experiment Fig. 5 is a plot of breakdo\\'ii voltage versus impurity concentration for silicon step junctions. The plot above 300 volts is extrapolated from the data of Miller^" and Wilson.' Capacity data, discussed in Section V, indicates that many devices show body breakdown. A few rectifiers break down at voltages as high as 2,000 volts. In many high voltage devices the breakdo^^^l voltage is not limited by geometry but by surface problems. IV FORWARD CURRENT-VOLTAGE CHARACTERISTIC 4-1 Theory It will be shown in this section that the forward current- volt age char- acteristic as well as the reverse characteristic can be completel\' explained by considering both a space-charge region generated current and a diffu- sion current. The diffusion current component must also take into con- sideration the effect of high injection levels of minority carriers. According to the Shockley-Read- theoiy, the rate of recombination, U, of holes and electrons in a semiconductor is given by: U = -G = pn 71 i Tpo{n + rii) 4- Tno(p + Pi) (4-1) 98G THE BELL SYSTEM TECHNICAL JOUENAL, JULY 1957 where 7?, and n are the mstantaneous concentrations of holes and elec- trons, respectively. When a PN junction is forward biased, holes and electrons are injected into the space-charge region which has been re- duced in width. Some of these carriers diffuse through the space charge region and give rise to the normal diffusion current when the excess minority carriers recombine with majority carriers in field free regions. The other carriers recombine according to (4-1) in the space-charge re- gion giving rise to what is called the space-charge generated current. In the reverse biased junction, the current is due to carriers generated in the space-charge region; whereas, in the forward biased junction, the current is due to recombination of carriers. The quantity U is large in the space- charge region since both p and n are large in this region. In the field free regions, however, one of these quantities is usually small and the product deviates only slightly from rii . The space-charge generated current, Igc , is given approximately by:'" V 2qWn, ^"^^^2 ,,,, (4-2) where Vb is the built-in potential of the junction, and /(6) is discussed in Reference 12 and is approximately 1.5 for recombination centers near the intrinsic level as is the case for the diodes under consideration. For shallower recombination levels the function f(b) is much smaller and de- pends strongly upon the forward applied voltage. For the forward-biased junction, the space-charge region is narrow, the concentration gradient can be considered linear and W is given by the following expression: W = 4.35 X io'(lj^^\ ' cm, (4-3) where Fjunction is the total potential across the junction in volts and a is the concentration gradient at the junction in cm^^ These are given by: ' junction ' built-in ' = kT/q In (NANn/nf) - V (4-4) = 0.792 - V. Also, a = — ^ 6-^^/"°' for diffused junctions, (4-5) 'VirDt where Cc = surface concentration of diffusant = 3 X 10 cm , CONDUCTIVITY-MODULATED SILICON RECTIFIER 987 D = diffusion constant = 3 X 10~ " cm /sec, / = diffusion time = 5.7 X 10 sec, Xj = junction depth below surface = 0.003 cm. When these numbers are substituted into the equations, at 300° K: W = 9.25 X 10"'(0.792 - Vf'^ cm. (4-6) For the diodes under consideration : r„c = 1.2 X 10"' sec, r^o = 0.4 X 10"' sec. When these expressions are substituted into (4-2) , one obtains at 300° C : T oo v/ in-7 sinh 19.31 F ,2 /, ^.^ /.e = 2.8 X 10 ^Q ..^2 - Vyi^ amp/cm . (4-/) In order to fit the experimental data, it is necessary to multiply (4-7) b}^ a factor of 5. This may be due to an overestimation of (r„oTpo)'- There- fore, the eciuation which shall be used in the remainder of tliis section Avill be: T 1 t w in-6 si"l^ 19.31 F , 2 (. ON he = 1.4 X 10 ^ojQ2 - Vyi^ amp/cm . (4-8) A plot of this expression is given in Fig. 6. The normal diffusion current for low level diffusion, /dl , is given by /dl = h{e'''"' - 1) (4-9) where U is given by (2-1). /o for the diodes under discussion is approxi- mately 8 X 10"'^ ampere/cm" at 300° K. ^\Tien the injected minority carrier densit}^ approaches the equilibrium majority carrier density, the form of (4-9) changes. The high injection level diffusion current, /dh , is then given by /dh = /DHo(e^"^''" - 1), (4-10) where /dho equals qnis/r, and s eciuals the A\'idth of the high resistivity region. For the diodes under discussion, /dho is approximately 2 X 10" amperes/cm at 300° K. A current-voltage plot of these currents at 300° K for Vr = 0.50 is given in Fig. 6 together with their sum. It can be observed that the resulting characteristic starts with slope of qV/kT and bends over to a slope of qV/2kT near 0.10 volt. The slope increases again to near qV/kT at 0.35 volts and decreases once more to qV/2kT above 0.40 volts giving a bump to the over-all characteristic. 988 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 Next, consider the temperature dependence of the coefficients of the forward current components and IscQ ~ ni{T), /o ~ rii — — ~ miT) , I DHO o b cr LU CL 01 LU rr 10" 3 lU a 5 < z ^ 1/1 10 -4 ^ 7- 5 in a. a. ~) o 10" •5 5 10" 6 5 10" 1 /■ /' / I TOTAL/ / / // / Y/y / /I/ I SPACE f /^ CHARGE /7 y/j I / • 1 )1FFUS10N / / r / / / / / / > / 9 1 1 / / 1 / 1 / / / / / / i 1 t 1 / 0.1 0.2 0.3 0.4 V IN VOLTS 0.5 0.6 Fig. 6 — The two components of current for a forward biased junction. CONDUCTIVITY-MODULATED SILICON KECTIFIER 989 Ui with temperature. Fig. 7 gives a plot of this variation. The tempera- ture variations of the other parameters are all small compared to that of Wi . Thus, as in the case of the reverse currents, at sufficiently high temperatures, the diffusion current makes the more important contribu- tion. In the case of the forward current, I^c is relatively insensitive to the distribution of impurities; therefore, the results of this section are im- portant for all forward-biased diodes. In high-voltage diodes, to keep the resistive voltage drop small, it is necessary to maintain high minority carrier lifetime in the center region. The diffusion length of injected 10' 10'2 10' lO'O o c 10^ 108 107 10 6 2.0 2.5 3.0 3.5 1000 T°K d.O 4.5 5.0 Fig. 7 — The variation of tii with temperature. 990 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 minority carriers should be the order of or larger than the center region width. 4.2 Experimental Results The forward characteristics of the five typical high voltage rectifiers mentioned in Section 2.2 were measured with a X-Y recorder, and all showed similar shapes. Diode No. 8 will be discussed in detail in this sec- tion. The forward current- voltage characteristic was measured at three temperatures: 220° K, 300° K, and 375° K. Measurements below cur- 10-2 10-3 5 lO"'* ui a. Ml I 10-5 < 5 5 10-6 a. o 10-7 5 10-8 10-9 O EXPERIMENTAL T=300° K / / / / / /" / / / I y f / / / / / / / / / / 0.1 0.2 0.3 0.4 V IN VOLTS 0.5 0.6 Fig. 8 — The calculated and observed current-voltage characteristic of a for- ! ward biased junction at 300° K. CONDUCTIVITY-MODULATED SILICON RECTIFIER 991 rents of one microampere were made only at 300° K. Currents above 10 milliamperes were not measured since internal power losses would cause temperature variations. The unit has a junction area of 0.015 cm", junc- tion lifetime of 4 microseconds at 300° K, S equal to 0.008 cm, and Na equal to 3 X lO" cm~l When these numbers are substituted into the expressions for the coefficients, one obtains, at 300° K, I SCO = 1.4 X 10~* amperes, /o = 1.2 X 10~" amperes. DHO = 3.0 X 10 * amperes. Fig. 8 shows a semilogarithmic plot of the current -voltage characteristic at 300° K over a range of 6| decades. The circles represent measured points and the solid line is the theoretical curve. Using the variation of rii given in Fig. 8 and the temperature variations as given in (4-11), one can obtain the coefficients for any temperature. This has been done for two temperatures, 220° K and 375° K. Figs. 9 and 10 show the theoretical and experimental plots at 375° K and 220° K 10-2 5 10-3 ifl in a. UJ a. < z z UJ cr a. D O 10-^ 5 10-s IQ-® 10-7 / r O EXPERIMENTAL T = 375° K / / / y / / /^ X /° / / / / c / / / 0.2 0.3 V IN VOLTS 0.4 0.5 0.6 Fig. 9 — The calculated and observed current-voltage characteristic of a for- ward biased junction at 375° K. 992 THE BELL SYSTEM TECHNICAL JOURNAL, JULY J 957 respectively. The circles represent measured points and the solid lines are the calculated theoretical curves. It is observed that the fit in Fig. 9 is quite good; whereas, the fit in Fig. 10 is not as good as at the other temperatures. However, even this figure shows good quahtative agree- ment of the deviation from a straight line. Some of the factor of two dis- crepancy in Fig. 10 can be ascribed to the temperature variation of the other parameters, and some to a possible error in the measurement of temperature which would be reflected in the value of rii . It should be noted that at all temperatures the IR drop in the high resistivity region is not observable to the limits of the experimental measurements of forward current, 10 milliamperes. This is due to the fact that the region has been conductivity modulated by the forward current. This requires a sufficient minority carrier lifetime in the region so that most of the injected carriers diffuse across the region before re- combming. Such lifetimes can be maintained in diffused junctions 10-' 5 10-2 5 IQ-^ OJ Q. < -10" cr ct D U 10- 10'^ 5 10" O EXPERIMENTAL T = 220°K / f /' / A ' o / / / ' y Kl J / / r y ro / / 0.3 0.4 0.5 0.6 0.7 V IN VOLTS 0.8 0.9 Fig. 10 — The calculated and observed current -voltage characteristic of a forward biased junction at 220° K. CONDUCTIVITY-MODULATED SILICON RECTIFIER 993 to permit the high resistivity region to be at least as wide as 0.025 cen- timeters. Thus even in high voltage rectifiers it is still possible to design the forward and reverse current voltage characteristics independently. V DEVICE PROCESSING 5.1 Silicon Material Fig. 5 shows that step junctions which break down at over a thou- sand volts must have a background impurity concentration ^ 10^^ atoms/cm^ The highest grade commercial semiconductor silicon has 5 X 10^* impurities/cm^ (20-50 Q cm P type). This material must be processed to reduce the impurity level. To date, high voltage devices have been processed from four types of high resistivity material: float- ing zone refined, compensated, gold diffused, and horizontal zone refined silicon. Some silicon was prepared by adding N-type impurities to reduce I Nd — N A I < lO'*. Maintaining this delicate balance in material where Nd ^^ Na is difficult. The boron is relatively uniformly distributed since the distribution constant is close to unity. N-type impurities are less uniformly distributed in the crystal since the distribution constants are considerably less than unity. High resistivity compensated silicon is full of N- and P-region striations. The units processed from this material generally had poor electrical characteristics. Table II is a typical contour of a compensated crystal. The resistivity varies around the crystal and changes along the length of the crystal. At the bottom of the crystal the resistivity goes through a maximum. The tail end is converted from P to N type. A number of devices have been fabricated from silicon processed with Table II — ^ A Typical Contour of a High Resistivity Compensated Crystal Crystal A-161, Oriented 111, Rotated ^ RPM Resistivity (r cm) at Angle Distance from Impurity Type seed (inches) 0° 90° 180° 270° 1 2 28 33 23 30 P 3 4 25 31 31 32 P n 41 22 27 34 P If 57 51 63 37 P 2 160 160 87 200 P 2\ 510 520 — — — 2h — — 1200 — — 2f 2.9 1.2 0.8 0.8 N 994 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 Table III — The Characteristics of Some High Voltage Rectifiers Processed from Gold Diffused and Zone Refined Silicon Silicon-Type Er (volts)2 Ef (volts )' TTnit«5l lO/iO lOO/id 1 ma 10 ma 100 ma lA Me-512 30 120 500 0.8 1 1.3 1.61 513 22 200 600 1.0 1.2 1.5 0.6 514 300 600 1000 0.8 1 1.5 2.1 515 300 500 1000 0.8 1 1.4 I.2J Me -375 1200 1500 2.5 3.5 1020-9 x lo2o] SURFACE CONCENTRATION IN CM"^ Fig. 12 — Distribution of surface concentration of 28 P2O5 diffusions bj^ the open tube deposition technique. 18 centrations were calculated assuming an erfc distribution."* All the diffusions are on lapped silicon surfaces in the temperature range of 1 ,200 to 1,300° C. Fig. 12 shows the distribution of surface concentration of 28 P2O5 diffusions by the open tube process. The surface concentrations vary from 10^^ to 5 X 10"° atoms/cm . These values are about a decade lower than the closed tube values of surface concentrations reported by Fuller.^^ The measured diffusion depths were in the order of 2 X 10"^ to 5 X 10"^ cm. Fig. 13 shows the distribution of diffusion depths normalized with the calculated diffusion depth as unity. The diffusion depths were calculated from the measured surface concentration assuming an erfc'^ distribution. The observed variation in diffusion depth is difficult to explain. Some of the possibilities which have been considered are: 1. The diffusion temperature from lot to lot would have to be from 0 to 50 degrees below the expected value to explain the variations. Dis- crepancies this large have not been observed. 2. One impurity distribution which may explain some of the results is a modified Gaussian with considerable out diffusion. There are some runs with high sheet resistance and diffusion depths which are consistent with this picture. Generally the sheet resistances are so small that there could not be much out diffusion. 3. Some workers have suggested the possibility of the diffusion con- stant being a function of the surface concentration. Fig. 13 does not 998 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 indicate any correlation between surface concentration and diffusion constant. The variations in diffusion process control have not been observed to effect the production of rectifiers. If better geometry control is necessary, more sophisticated diffusion tochniriues are required. VI PULSE PROPERTIES AND RELIABILITY Important considerations in all diode applications are the pulse prop- erties and reliability in operation. In this section some problems which are associated with avalanche breakdown are described and the result." related to recent work on surface and body breakdown. 6.1 Theory Several workers" have considered the possibility of a negative resist- ance in the avalanche region for reverse biased junctions in which one side is either intrinsic or so weakly doped that the space charge of the carriers cannot be neglected. A negative resistance might be observed at very high current densities in an N'^tt junction. One possible source of a negative resistance would be a large tempera- ture rise due to current concentration at a few points instead of a uni- a. CD 5 1.3 X 1020 2 X 1020 2 x1020 2 X 1020 5x 10'® 1020 10'^ 1.2 X 10'^ 8x 10'9 1020 2x 1020 4x 10'9 1020 8x10'® 1.3 X tO'5 10'^ 1.2 X 1020 1.2 X 10'9 6 X 10'® 4 x10'5 3 X 1020 3x 1020 6 X 10'® 10'9 3 x10'9 3 X 10'5 0.4 0.5 0.6 0.7 0.6 Xj [OBSERVED] Xj [CALCULATED] 0.9 1.0 Fig. 13 — Distribution of diffusion depths for diffusion by the open tube depo- sition technique. CONDUCTIVITY-MODULATED SILICON RECTIFIER 999 form flow through the junctions. This case is of particular significance in high voltage rectifiers where small reverse currents result in relatively large power. It has been pointed out in Sections 3.2 and 5.1 that body avalanche breakdown is frequently not observed in these devices. A\'alanche breakdown current in silicon is carried by discrete pulses of about 50 ^la at their onset and increasing with increasing current to about 100 /ua. Approximate calculations"^ show that the ionizing regions o of these microplasmas are about 500 A in extent, have a current density ?^ 2 X 10*' amp/cm^, and have a net space-charge density ?^ 10 /cm . These pulses for junctions with ii'm.ix less than 500 kv/cm appear to be independent of junction width and built-in space-charge. Rose considers the statistical problem associated ^^^th a large number of pulses and pre- sents a picture which is consistent with most of the experimental data. He calculates the temperature rise, assuming the avalanche power is 1 X 10 " watts and is dissipated uniformly in a sphere. The maximum temperature rise for a cluster of two or three pulses is in the order of 25° C. For the picture Rose presents, the temperature rise due to, the microplasma should be relatively insensitive to the breakdown voltage. Thermal collapse of rectification, i.e., increase of temperature until the silicon is intrinsic, will probably not occur in the region of avalanche multiplication. Two important conclusions can be obtained: 1 . Avalanche breakdown should occur as a random process with a uni- form probability over the junction. Large temperature rises due to a breakdown of microplasma will probably not occur since the resulting temperature rise would cause the breakdown voltage in that spot to increase. The power is dissipated throughout the path of the current pulse in the space-charge region. 2. A thermal effect in silicon due to heating by the small plasma has a very short time constant of the order of lO""^" seconds.'^ It is not possible to separate a thermal effect of this type by reducing the pulse width. The heating and cooling time is short compared to the pulse time in these experiments. The pulse properties of a junction would be ciuite different if the break- down occurred at one spot instead of many spots distributed over the junction. Breakdown at a single spot on the surface has been observed. " 6.2 Experimental Results Many rectifiers were given a voltage pulse which carried them into breakdown. There was a wide distribution of V-I characteristics. Many diodes did not show a negative resistance up to the maximum instan- 1000 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 taneous power the pulser could deliver, okw. These diodes are not con- sidered in the subsequent analysis. The diodes were subjected to 50 yusec triangular voltage pulses which would send them into breakdown. Variations in pulse conditions did not effect the I-"\^ characteristic until large pulses destructively damaged the unit. Fig. 14 is a sketch of a typical Y-l characteristic and Fig. 15, shows the voltage- versus-time characteristic for a diode with a negative resistance. The V-I curve can be broken into four regions: V IN VOLTS 10" 10"^ UJ CC UJ Q. < z 10-2 - LU CC a: 10-' 3 10'^ Fig. 14 — A typical V-I characteristic for a diode in which a negative resistance is observed. TIME REQUIRED TO GO IN ^--'' LOW IMPEDANCE STATE -r^ BREAKDOWN VOLTAGE t 1 o > I RISE TIME OF PULSE j z I > J LOW IMPEDANCE /-■ STATE yi- PULSE WIDTH >iV TIME Fig. 15 — A tj'pical V-T characteristic for a diode in which a negative re- sistance is observed. CONDUCTIVITY-MODULATED SILICON RECTIFIER 1001 1. A high impedance state before the breakdown voltage is reached. 2. A current required to turn on the negative resistance; this cur- rent varies from 10~ to 1 amp. 3. The transition to a low impedance state. 4. The low impedance region in which the current is probably limited by the circuit impedance. The V-T curve can be broken in four regions: 1. The time it takes the pulse to reach the breakdown voltage. 2. The time the diode can maintain the breakdown voltage less than 1 jusec. This is beyond the resolution of the oscilloscope. 3. The time required to fall to the low voltage (low impedance) state, is less than 1 /isec. 4. The remainder of the pulse in the low voltage state. Fig. 16 is a plot showing the current and voltage required to turn on a negative resistance in several power rectifiers (area -^ 10~" cm). To 10' a. LU Q. < z UJ cc a. D (> •- 1» • It 4) • 200 400 600 V IN VOLTS 800 1000 Fig. 16 — Current and voltage required to turn on a negative resistance in several power rectifiers (A '-^ 10~^ cm^). 1002 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 consider the spread of breakdown voltage, the data was normalized to the instantaneous power required to turn on a negative resistance. This turn-on power was the turn-on power multiplied by the voltage. Fig. 17 is a plot of the distributions of turn-on power for the rectifiers which had a negative resistance plotted as a log normal distribution on probability paper. The median value for the turn-on power is 1.2 watts. Eighty per cent of these diodes went into a negative resistance condition at powers between 0.1 and 10 watts. Many diodes could dissipate several kilowatts with no negative resistance. These were not included. Experiments show that devices which show surface breakdown will collapse at power levels which are orders of magnitude below that ob- served for devices in which body breakdo^Mi is observed. The picture is more cloudy with smaller area rectifiers (area •^ 10"^ cm"). In these devices it was not possible to predict the pulse properties < OI 5 o a 40 20 0.2 0.1 0.08 0.06 i _ . , o / > A - / - / / / / / / / - / - / o / / / / / / - / - y 1 10 20 30 50 70 80 90 95 99 DISTRIBUTION Fig. 17 — The distribution of turn-on power for rectifiers {A ^^ 10~^ cm^) in which a negative resistance is observed plotted a.s a log normal distribution on probability paper. CONDUCTIVITY-MODULATED SILICON RECTIFIER 1003 of the device from the reverse I-V characteristic. This may be attributed to the decrease in poAver capabilities of the body breakdown process in the smaller devices. This also suggests that the smaller devices have a less severe surface problem. The distribution of turn-on power for a few hundred small area recti- fiers (A '^ 10~ cm") is shown in Fig. 18. The median of the distribution occurs at 40 watts. Eighty percent of the miits will show a negative re- sistance when pulsed at power levels between 3 and 500 watts. VII CONCLUSION High voltage rectifiers have been fabricated using several sources of high resistivity material employing an uncomphcated diffusion process. < 5 tr UJ O a. 1000 800 600 500 400 300 200 100 80 60 50 40 30 20 10 8 6 5 4 3 - / - i f s ) / / / 1 / 1 f - / - i 1 / 1 1 1 i / f\ - i - / P / / / ; ' 5 10 20 30 50 70 80 DISTRIBUTION 90 95 99 Fig. 18 — The distribution of turn-on power for small area rectifiers {A cm^) plotted as a log normal distribution on probability paper. 10-" 1004 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 The most consistent results were obtained using horizontal zone refined silicon. The open tube diffusion technique has sufficient control to satisfy the fabrication requirements. j The magnitudes, voltage and temperature dependences of both the j forward and reverse currents of silicon rectifiers can be explained by in- < eluding a recombination level near the middle of the forbidden energy ; gap. Design equations for the forward and reverse characteristic of a j diode are presented for several important cases. The breakdown voltage { of the high voltage devices was shown to be a function of the width of i the high resistivity region. One unsolved problem is the surface limitation of breakdown voltage ' and reverse currents. This has been observed to decrease the breakdowTi voltages and increase the reverse currents to undesirable levels. ACKNOWLEDGEMENT The authors wish to thank their colleagues for many helpful discus- sions. Thanks are due Dr. R. N. Noyce of the Shockley Semiconductor Laboratory for making his paper available before publication. The work on zone refuied and compensated silicon was done by S. J. Silverman. The floating zone material was supplied by H. E. Bridgers. Much of the experimental work was done by A. R. Tretola, T. J. Vasko and F. R. Lutchko. G J. Levenbach assisted with the statistical aspects. REFERENCES 1. M. B. Prince, B.S.T.J., 35, p. 661, 1956. R. N. Hall, Proc. I.R.E., 40, p. 1512, 1952. 2. W. Shockle}% and W. T. Read, Jr., Phys. Rev., 87, p. 835, 1952. 3. R. N. Hall, Proc. I.R.E., 40, p. 1512, 1952. J. S. Saby, Proc. Rugby Con- ference on Semiconductors, 1956. 4. W. Shockley, B.S.T.J., 28, p. 435, 1949. 5. K. G. McKay, Phys. Rev., 94, p. 877, 1954. 6. E. M. Pell, J. Appl. Phys., 26, p. 658, 1955. E. M. Pell, and G. M. Roe, J. Appl. Phys., 27, p. 768, 1956. 7. B. Ross, and J. R. Madigan, Bull. A.P.S., 2, p. 65, 1957. 8. K. G. McKay, Phys. Rev., 94, p. 877, 1954. 9. S. L. Miller, Phys. Rev., 99, p. 1234, 1955. 10. S. L. Miller, Phvs. Rev., 105, p. 1246, 1957. 11. P. A. Wolff, Phj-s. Rev., 95, p. 1415, 1954. 12. C. T. Sah, R. N. Noyce, and W. Shockley, "Carrier Generation and Recombi- nation in p-n Junctions and p-n Junction Characteristics", to be published in the Proc. I.R.E. 13. H. C. Theuerer, J. Metals, p. 1316-1319, Oct. 1956. 14. J. A. Burton, Physica, 20, p. 845-854, 1954. 15. C. J. Frosch and L. Derick, J. Elec. Chem. Soc, to be published. 16. K. D. Smith, P.G.E.D. Conference of the I.R.E. , Washington, 1956. 17. F. M. Smits and R. C. Miller, Phys. Rev., 104, p. 1242-45, 1956. 18. G. Backenstoss, to be published. 19. C. S. Fuller and J. A. Ditzenberger. J. Appl. Phys., 27, p. 544-53, 1956. 20. W. T. Read, Jr., B.S.T.J., 35, p. 1239, 1956. 21. D. J. Rose, Phvs. Rev., 105, p. 413, 1957. 22. C. G. B. Garre'tt and W. H. Brattain, J. Appl. Phys., 27, p. 299-306, 1956. Coincidences in Poisson Patterns By E. N. GILBERT and H. O. POLLAK (Manuscript received August 3, 1956) A number of practical problems, including questions about reliability of Geiger counters and short-circuits in electric cables, reduce to the mathe- matical problem of coincidences in Poisson patterns. This paper presents the probability of no coincidences as well as asymptotic formulas and simple bounds for that probability under a variety of circumstances. The probability of exactly N coincidences is also found in some cases. IXTRODUCTIOX A number of practical problems are questions about what we call "coincidences" in Poisson patterns. In c?-dimensional space, a Poisson pattern of density X is a random array of points such that each infinitesi- mal volume element, dV, has probability \dV of containing a pomt, and such that the numbers of points in disjoint regions are independent random variables. Then a volume, V, has probability (xy)' e of containing exactly k points. A coincidence, in our usage of the word, is defined as follows: We imagine a certain fixed distance 8 to be given in advance; two points are then said to be coincident if they lie within distance 8 of one another. Examples The best-known case of a coincidence problem concerns Geiger coun- ters. In the simplest mathematical model, there is a short dead-time 5 after each count during which other particles can pass through the counter without registering a count. In our present terminology, a count is missed whenever two particles traverse the counter with coincident times of arrival. The same problem is encountered with telephone call registers. lOUo 1006 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 Another example arises in the manufacture of electric cable. Each Avire in a cable is covered with an insulation which contains occasional flaws. When the cable is assembled it will fail a short circuit test if it contains a pair of wires such that a flaw on one wire Ues within some distance 5 of a flaw on the other wire. In a similar way, coincident flaws , in the insulation of the wire from which a coil is wound can lead to fail- ! ure of the coil. There are also some problems in the development of certain military systems which lead to the consideration of coincidences in Poisson pat- terns. Outline of Work Our primary aim is to study the probability of no coincidences under various circumstances. In Part I, we examine coincidences of two differ- ent Poisson patterns, of densities X and n respectively, on a line of length L. Here we do not count two points of the sa?ne pattern within a distance 8 as giving a coincidence. A set of integral equations yields the probability of no coincidences as well as an asymptotic formula and upper and lower bounds. In Part II, we study the probability, Fo{L), of no coincidences for a single one-dimensional Poisson pattern of density X. These results may also be interpreted as the distribution function for the minimum distance between pairs of points of a Poisson pattern. Sample formulas are the asymptotic formula (for large L) ^«(^) ^ T^ mAtJK ^1 ^~"^ (X - a)[l + 6(X - a)] and the bounds (vaUd for all L) where s = —a is the largest real root of The problem of n Poisson patterns, all of the same density X, is ex- amined in Part III. Coincidences are now counted between points of any two distinct patterns. The one-dimensional problems of Parts I-III succumb readily to ana- lytic techniques. We can find exact expressions for the probabilities of no coincidences in Parts I-III. Two entirely different met hods of deriving COINCIDENCES IN POISSON PATTERNS 1007 exact results are available and are illustrated in Parts II and III. Un- fortunately, the exact formulas, although they are finite sums, contain a luunber of terms which grows with L. Much of our effort has been di- rected toward finding good, easily computed bounds and asymptotic formulas. The probabilities of having exactly iV coincidences are also obtainable but they have more complicated formulas. A detailed derivation is given only in Part II. In Part IV, we consider the probability of no coincidence in higher dimensional problems. The methods of Parts I-III fail in higher di- mensions, but we are still able to derive some bounds. An exact formula is derived for the probability of no coincidences within a single two- dimensional Poisson pattern in a rectangle with sides ^ 25. We also give particular attention to coincidences in a three-dimensional cylinder. Part V contains numerical results. Reduction of the Examples to the Theory We now wish to see how answers bearing on the practical problems previously listed may be found from this stud3^ The literature on Geiger counters (see bibliograph}^ in Feller ) is con- cerned with statistics of the number of counts registered in a given long time, /. The basic problem is to test the hypothesis that the particles arrive in a Poisson sequence. To this problem, then, are relevant the formulas for the probability of N coincidences in one pattern given in Part II, and the bounds and asymptotic results there derived. The problem of coincident flaws in an electric cable is three-dimen- sional, and we have various approaches leading to the probability of no coincidences which are valid under different circumstances. If the cable contains only two wires (with possibly different flaw densities), then the problem reduces to the one-dimensional case of coincidences between two Poisson patterns treated in Part I. If the diameter of the cable is small with respect to 8, and if the density of flaws is the same on each of the n wires in the cable, we have the situation of )i identical patterns treated in Part III. If, in addition, n is very large, we may ignore the fact that coincident flaws on a single wire do not cause short circuits, and think of coincidences within a single pattern (Part II). AVithout the assumption that the diameter of the cable is small with respect to 8, the problem is no longer reducible to a one-dimensional form. Section 4.4 is especially devoted to thick cable, and to producing a lower bound for the probabilit}^ of no coincidences in this three-dimensional situation. The literature on Poisson patterns in a line segment contains the fol- 1008 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 lowing related papers. C. Domb' finds the distribution function for the total length of the set of points lying within distance 5 of a pattern point. P. Eggleton and W. O. Kermack' and also L. Silberstein" consider ag- gregates, Avhich are sets of k pattern points all contained in an interval of length b. In the special case k = 2, aggregates are our coincidences. These authors find the expected number of aggregates but not the prob- ability of A^ aggregates. I CONCIDENCES BETWEEN TWO PATTERNS 1.1 Integral Equation Consider two Poisson patterns of points on the real Une, the first \nth density X (points per unit length) and the second with density n. We want the probability F{L) that in the segment from 0 to L there is no coinci- dence between a point of pattern No. 1 and a point of Pattern No. 2. F{L) will be formulated in terms of the conditional probabilities Pi(L) = Prob (no coincidence, given Pattern No. 1 has point at L), P^iL) = Prob (no coincidence, given Pattern No. 2 has point at L). If L ^ 5, Pi(L) and P2{L) are the probabilities that patterns No. 2 and No. 1 are empty: Pi(L) = e-'\ Po(L) = e-'\ if L ^ 5. (1-1) If L > 6 and Pattern No. 1 contains a point at L, there are two ways that no coincidences can occur. First, Pattern No. 2 may fail to have any points anywhere in the interval [0, L]. The probability of this event is exp — ijlL. The second possibility is illustrated in Fig. 1 (using circles for points of Pattern No. 1 and crosses for points in Pattern No. 2). Pattern No. 2 has points in (0, L) ; the one closest to L is at ?/ < L — 5. Since the interval {y, L) contains no points of Pattern No. 2, the probability of finding this closest point, y, in an interval, dy, is exp l-niL - y)]iJL dy. The interval (y, y + b) must be free from points of Pattern No. 1 (prob- NO COINCIDENCES EMPTY NO CROSSES _j . I . 1 ■ ^/ — ■^'pXs), ( N _ s -\- \ -\- y.e , X 'P^^^^ - (s + x)(s + m) - XMe-'(x+M+«)a ' ^'■''^ and I I >. — (X+/j+s)5 ^'^^^ (s + \){s + m) - XMe-2^^+''+^^*" Likewise, using (1-4), the Laplace transform /(s) of F{L) is 1 + X/>i(s) + M?>2(s) /(s) = A + M + s As one might expect from the piecewise analytic character of Pi{L) and Pi{L) there is no convenient way of transforming /(s) back to F{L). By evaluating residues of /(s) exp (sL) at the poles of /(s) one might ex- press F{L) as an infinite series of exponential terms. The most slowly damped term in this series can be expected to approximate F{L) when L is large. The poles of /(s) are at the zeros of the denominator D{s) of ' Pi(s) and p2(s): D{s) = (s -F X)(s + m) - \tJ^c-''^-"'^''\ (1-9) Since D{x) > 0 for x ^ 0 and both D{ — X) and D{ — ix) are negative, it follows that D{s) has a real zero s = —a ^^■ith a < IVlin (X, ^x). The zero s = —a of Z)(s) is the one with the largest real part. For, letting s = .T + iy, we have in the half plane .r ^ —a (s + X)(s + m) I - Xm i e" -2(\+M+s)« ^ (.r + X)-(.i- + m) - Xiie"''^^"^''' ^ 0. Also, if !j ^ 0 the ^ sign in the above proof can be replaced by > and one concUides that all other zeros of D{s) = 0 satisfy Re 6' < - h COINCIDENCES IN POISSON PATTERNS 1011 for some h > a (note that the left hand side of the preceding inequahty does not approach 0 as ?/ approaches ± co ) . The pole of /(s) at s = —a contributes to F{L) a dominant term F(T) ~ X' + m' - (X + M)a + 2X^6"^'^'''°^^ -aL ^ jQS ^ ^ ^ (\-\- n - a)[K + M - 2a + 25(X - a)(n -a)] In (1-10) the error is 0(exp — bL) for large L. When 8 is small, we find a = 2\n8 + 0(5") and (1-10) becomes F(L) ^ [1 + 0(6')] exp - [2Xm5 + 0(5')]L. (1-11) It is interesting to note that a simple heuristic argument also leads to a formula like (1-11). When 5 is small and L is large, one expects that the intervals of length 25 which contain points of Pattern No. 1 at their cen- ters will comprise a total length near (XL) (25) of the line segment (0, L) . The probabiUty that a set of length 2XL5 shall be free of points of Pat- tern No. 2 is exp — 2Xm5L. 1.3 Bounds In this section we derive some relatively simple expressions which are good upper and lower bounds on F(L) . Both bounds have the same func- tional form: K{A, B; L) = h±±J^ e-- + fi _ ^^^ ^ ^^ ) e'''^^''. (1-12) X-f-ju — a \ \ -\- ti — a/ In (1-12), a is again the smallest real solution of D( — a) = 0. .4 and B are positive constants which are related by A _ M -(X+M-a)S _ X — g (X+^_a)5 (1-13) B n — a X K{A, B; L) becomes an upper bound or a lower bound depending on ad- ditional restrictions which will be placed on A and B. To get the lower bound, we restrict .4 and B by the inequalities A < e'"-"', B < e'"-^'', (1-14) and A<(l-f\e''\ B<(\-^^e'\ (1-15) We first prove that (1-13), (1-14), and (1-15) imply Pi(L) > Ae-''\ PoXL) > Be'"''. (1-16) 1012 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 When 0 ^ L ^ 5, (1-16) holds because of (1-1), (1-14), and the in- equaUties a < \, a < fi. li (1-16) were not true for all L there would be a smallest value, say L = X > 6, at which at least one of the inequali- ties (1-16) would become an equality. Suppose the inequality (1-16) on Pi(Z) fails. Usmg (1-16) for L < X, and (1-2), Pi(X) > e-"^ ( 1 + B^jie-'' ) \ n - a / > Ae-'' + ( 1 - 5 J^^— ) e-'"" by (1-13), > Aq-""^ by (1-15). This contradicts our assumption that (1-16) fails for Pi(X). A similar proof shows (1-16) cannot fail for PiiX). Having proved (1-16) we now substitute these bomids into (1-4) and integrate to get F{L) > K(A, B; L). To make (1-12) into an upper bound it is only necessary to replace (1-14) and (1-15) by ^ > 1, B > 1, (1-17) and A>(l-^ e'\ B>(l-^ e^'. (1-18) The proof that now F(L) < K{A, B; L) proceeds exactly as before but with all the inequality signs reversed. Both bounds are dominated by an exponential term exp — aZ, as is the asymptotically correct formula (1-10). In typical numerical cases the coefficients multiplying this term in the three formiilas agree closely. A numerical case is given in Part V. 1 4 Probability of N Coincidences The methods of Sections 1.1 and 1.2 can also be used to find the prob- ability Fn{L) that there be exactly N coincidences in the interval (0, L). It might appear most natural to define N to be the number of pairs of points (x, z), X from Pattern No. 1, z from Pattern No. 2, such that I .r - .- I < 6. (i) However, we add the additional requirement that x and z be "adjacent" points; i.e. the interval {x, z) is empty. (ii) COINCIDENCES IN POISSON PATTERNS 1013 For example, in Fig. 3, we would count iV = 6 coincidences even ! though there are 18 pairs which satisfy (i). In cable problems it appears I reasonable to count coincidences as above. If we assume that all flaws are equally bad, then a short circuit is likely to develop only across an , adjacent coincidence; our N is the number of places on the cable at which a short circuit can form. Another interpretation is that the cable can be cut into exactly iV + 1 pieces each of which contain no coinci- dences. Let Pi,n{L) be the conditional probability of having N coincidences in (0, L) knowing that there is a point of Pattern No. 1 at L. The Lap- lace transform of Pi,n{L) turns out to be the coefficient of t^ in a generat- ing function of the form '& VAt, s) - (X + s)(m + s) - X/xfi^' where 0 = g-(^+''+«^^Q _/)_!_/ Interchanging X and /x one gets the gen- erating function p2{t, s) for the Laplace transform of the probability P2,n{L) of A^ coincidences, given a point of Pattern No. 2 at L. Finally the Laplace transform of F.w{L) is the coefficient of t^. in the generating function 1 - 6-^^+^+^^^ + \p,(t, s) + mit, s) fit, s) X + /i + s Since /(/, s) is a rational function of /, it is easy to find the coefficient of t' . The poles of this function are again just zeros of D(s). Now, however, the poles are higher order poles. For large L an asymptotic formula for Fn{L) has the form exp — aL times a polynomial in L with degree de- pending on N. For more details about this method we refer the reader to Part II where a similar, but less involved, calculation is carefully done. II SELF-COINCIDENCES IN ONE POISSON PATTERN 2.1 Integral Equation In this part we shall consider a single one-dimensional Poisson pattern with density X and ask for the probability Fn{L) that in the interval (0, L) the pattern have exactly iV coincidences. We count comcidences I ^^ ^ — I (T:0 X )( )( 0 *e@ 1 0 (T L Fig. 3 — Patterns with six coincidences. ^-; e-", alliV. (2-1) }!:^]Z.e-'\ Nil. (2-2) 1014 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 as in Section 1.4; a pair (x, z) of pattern points contributes one coinci- dence to the total number A^ only if both | a; — 2 | < 5 and the interval between x and z is empty. Note that Fo{L) is related to the distribution function for the mini- mum distance between the points of the pattern in (0, L) : Prob (min. dist. ^6) = 1 -Foil), where it must be remembered that Fo(L) is a function of 8. As in Part I, we first define the conditional probabilities Pn{L) = Prob (exactly A^ coincidences in (0, L), given a point at L). We then have the following equations: UL a, PAL) = If L > 6, and A'' ^ 1, the probability of exactly N coincidences in (0, L) equals the probability of A^ coincidences up to the last point of the pat- tern in the interval (0, L) — and if there are to be any coincidences, there must be points of the pattern in (0, L). Hence, if L > 5, A^ ^ 1, Fn{L) = \' PAL - y)e-^'X dy. (2-3) If A^ = 0, the same argument applies, but there is also the possibility that there are no points at all of the pattern in (0, L). Hence, if L > 5, F,{L) = e-^' + f ' Po(L - y)e-^\ dy. (2-4) : Now let us consider the case where there is a point of the pattern at L. Then if the last point preceding L is between L — 8 and L, this point and the point at L will create a coincidence; if there is no point within (L — 8, L), then all coincidences are within (0, L — 8). Hence, if L > 5, and A^ ^ 1, p^L) = [ Ps-x{L - y)\e-'"dy + f-'V^(L - 8). (2-5) Jo For the case A^ = 0, we cannot allow a point in the interval (L — 8, L), and hence, if L > 8, P,(L) = e-^'F,{L - 8). (2-6) COINCIDENCES IN POISSON PATTERNS 1015 2.^ Laplace Transform of Fn{L) To analyze the system of equations which is given by relations (2-1) through (2-6) , we introduce the generating functions f{L,t) = ZFAL)^, and p(L,t) = f:PAL)f. If L > 5, we obtain from (2-3) and (2-4) the relation e^'-fiL, 0 = 1 + f v(w, Oe'^X dw, (2-7) and from (2-5) and (2-6) the relation (again if L > 8) 'p{L, 0 = \t C p{w, Oe'" dw + e^''-''f{L - 5, 0- (2-8) XL e If we differentiate (2-7) and (2-8) with respect to L, and then apply (2-7) differentiated to simphfy the last terms of (2-8) differentiated, we obtain, still only f or L > 8, f'iL, t) + X/(L, 0 = ^P(L, i), (2-9) p'(L, 0 + X(l - t)p{L, t) = \e-^\l - t)p{L - 8, t). (2-10) It is easy to check from (2-1) and (2-2) that if L ^ 5, then /T ,N -XL (1-0 p{L, t) = e and and hence (2-9) is valid for all L, but the left side of (2-10) vanishes if L ^ 8. Hence we may take Laplace transforms of (2-9) and (2-10). If we define and Ais,t) = r f{L, t)e-'' dL, Jo . B{s, 0 = [ p{L, Oe-^" dL, JO 1016 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 we obtain from (2-9) , which we now know to be valid for all L, [ (X + s)A{s, t) - I = XB{s, t), (2-11) and from (2-10), by recalling that the left side vanishes for L ^ d, sB(s, 0 - 1 + X(l - t)B{s, t) = X(l - t)e~^'^^^'B{s, t). (2-12) Hence B(«. ') = , + x(i - m - .-<.+».| • (2-13) and A{s, t) = -4- (1 + XE(s, 0). X -f- s If we denote the Laplace transforms of Pn{L) and Fn{L) by Pn{s) and /jv(s) respectively, then P»W = ;, ^ , _ ,,-,.^»y.. . (2-14) and jNis) =-^pAs) for .V = 1,2, X + s (2-15). ;g.5 JS'aracf Formula for Fo{L) It is possible to solve (2-1) through (2-6) in piecewise analytic form by computing recursively from each interval of length 5 to the next one. We shall obtain the piecewise analytic form for Fo{L) by a direct derivation essentially due to E. C. Molina. Suppose k is the number of pattern points which fall into (0, L). Let Xi denote the distance between the i — 1^* point and the i' point (xi is the distance from 0 to the first point) as shown in Fig. 4. The configura- Xk -®^ ±-zf — a '..L' -^-± 0 1 2 L-1 Fig. 4 — Definition of Xi COINCIDENCES IX POISSON PATTERNS 1017 tion of points 1, • • • , k on the line is represented by a single point (xi , • • ■ , Xk) in the polyhedron T in ^--dimensional space defined by the inequalities T: 0 ^ .Ti , • • • , 0 ^ Xk , xi -\- X2+ ■■• + Xk -^ L, , and the probability distribution of the point (xi , • • • , Xk) in T is uni- j form. The configurations with no coincidences lie in a smaller polyhedron T' consisting of all points of T for which 8 ^ xo , ■ ■ ■ , d ^ Xk . Given k, I the conditional probability that there be no comcidences is the ratio of two A'-dimensional volumes Vol (T")/Vol (T). Vol (r) =0 if L S (k - 1) 8. For larger \-alues of L let yi — Xi , yo — X2 — 5, y^ = .Ts — 8, ■ • • , yk = Xk — 8. Then T" becomes a polyhedron of the form T": 0^yi,0^y2,---,0^yk, yi + y2 ■ ■ ■ + yk ^ L - (A: - 1)5. Since the transformation from x's to y's has determinant equal to one, T" has the same \^olume as T'. However, T" is now seen to be similar to T but with, sides of length L — {k — 1)8 instead of L. The volume ratio sought must be /L- (k- 1)8Y Since k has the Poisson distribution with mean XL we obtain finally The piecewise-analytic character of Fo(L) is evident; increasing L by an amount 8 increases the upper limit on the sum bj'^ one and thereby adds a new term to the analytic expression for F(L). 24 Asymptotic Formula for F.x(L) Similar exact formulas could be found for all the Fx(L), but they are both complicated and inconvenient for computing if L/8 becomes large. It is thus natural to aim for asj^mptotic results and for bomids connected with them. The Laplace transform of Fa(L) is given through (2-14) and (2-15) above. The pole of f^■{s) with largest real part is a pole of order A^ + 1 1018 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 at a real negative point s = —a > —X. For large L, the asymptotic behavior is given by -aL r, /T\ Xe "^ r aL (X - a)[l + 5(X - a)]N<. Ll + S(X - a). N where the error term is 0(L^~^ e~"^) if A" ^ 1. Such a formula, then, is a good approximation for fixed N as L increases; for fixed L, however, it will fail to be good for sufficiently large A^. If iV = 0, the asymptotic form is Fo(L) ^ 7- rr- j -TT r-, 6 , (X — a)[l + 5(X — a) J but the error term now decreases at a more rapid rate, as may be seen by including the contributions of some of the complex poles of /o(s). To find these poles, set s + X = Xe . If s = —X + r exp (id), one obtains the simultaneous real system 2irm — 6 = 8r sin 6 (m integer), log (r/X) = —6r cos 6. The first equation defines an infinite family of curves in the s-plane (see ! Fig. 5). The second equation defines a single curve which intersects the family at poles of p{s). 2.5 Bounds on Fo(L) As in Part I, we may derive bounds on Fo{L) from the integral equa- , tion, and obtain ] (l --^ e^^'-e-^"-^^' g Fo(L) ^ e'^'^e-^''-^^'. Since a = X^5 + 0(5") for small 5, the bounds are very close if X5 is not too large. COINCIDENCES IX POISSOX PATTERNS 1019 Fig. 5 — Solution of s + X = Xe -(s + X)o III COINCIDENCES BETWEEN n POISSON PATTERNS 3.1 Integral Equation In this part we consider n one-dimensional Poisson patterns and ask for the probability, F{L), that in the interval (0, L) no pair of points from different patterns are coincident. Unlike Part I, we now consider only the case in which all n patterns have the same density X. Let P{L) be the conditional probability, given that Pattern No. 1 has a point at L, that there are no coincidences in (0, L). If 0 ^ L ^ 5, P{L) = exp - (» - l)\L. If 5 < L, by the same sort of argument used in Part I. Then F{L) will be given bv P{L) = e -(n-DXL ( 1 -\- in - l)\e -u I L-S F{L) = g-"'"' (l + nX I"" e"'"P(.T) dx\ 1020 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 3.2 Bounds and Asyynptotic Formula The Laplace transform of P{L) is . I p(s) = {s + (n - 1)X(1 - e-("^+«>^)pi (3-1) i which has one real pole at a negative point s = —a, a < (n — 1)X. Again it is this pole which contributes the dominant term to both P(L) and F{L) for large L. We find ^ —aL F{L) - ''^' (1 + [{n - 1)X - a]b){ii\ - a)' To bound P{L) by expressions of the form A exp( — aL) one finds that .4 > 1 will gi\'e an upper bound and will give a lower bound. The corresponding bounds on F{L) are of the form /^ nXA \ -n\L I n\A -aL (1-— le +— e . \ n\ — aj nh — a 3.3 Exact Solution As in Part II an exact formula for F(L) may be given as a finite sum. We now derive it from the Laplace transform, j\s) = (s + nXf (1 + nXpis)), of F{L). We may use (3-1) to expand /(s) into the series /r ^ 1 /i , ,,x V ((^^ - i)xe-^"^+-^y\ ,. _. lis) = — ■ — r U + nX 2^- — ,...,., >. (3-2) s + n\ [ t=o (s + (w — l)\y+^ J The identity (s + n\y\s -f (n - 1)X)"''~' = 7 i: (-A)-'^^(s + in - 1)X)-^'-^ + (-X)-^-^(s + n\r' X ;=0 provides a partial fraction expansion for the k term of the series (3-2). Transforming (3-2) term by term with the help of (3-3) we find F(L) = e~"'^[-(n - 1)]^"^"^+' [lU] k Z [-in-De-^'rZ This is the desired formula for F{L). + ne'"'-'>''- "Z [-in -Dc^'Y' E ^~^^^.~ ^^^^' COINCIDENCES IN POISSON PATTERNS 1021 IV MULTIDIMENSIONAL PROBLEMS j 4.1 Two-Pattern Lower Bound } We now derive some results on the probabilities of no coincidences in ! some multi-dimensional situations. The simplest one is a lower bound for the case of two Poisson patterns. Theorem: Consider a d-dimensional region of volume T' cordaininej two Poisson patterns ivith densities X and n. Let S{8) he the volume of the d-di- mensional sphere of radius 5. The probability of tio coincidences between the two patterns has the lower hound e Proof Let the pattern with density X be called the X-pattern and the other the ju-pattern. Given any X-pattern of k points there will be no coinci- dences provided only that a certain region T contains no points of the ju-pattern. T consists of all points of the volume V which lie in any of the spheres of radius 5 centered on the k points of the X-pattern. Since these spheres may overlap and may extend partly outside the volume T'^, we have volume of r ^ /.■ S{b), and Prob (no coinc, given k points) = exp ( — yu volume of 7") ^ exp (- kn S{8)). Since the number, k, of points of the X-pattern has the Poisson distribu- tion with mean W the (unconditional) probability of no coincidences has the lower bound E(XF) -\v -k^siS) -^-r- e e k =0 kl Summing the series one proves the theorem. Interchanging X and yu in the theorem gives another lower V)ound. The one stated above is the better of the two if X < /x. The difference between the lower bound and the true probability comes from two sources: (a) The overlap between the k spheres; this will be a small effect if \^S{28)V is small, and (b) the spheres which extend partly outside the volume V; there will be relatively few such spheres if only a small fraction of the volume V lies \A-ithin distance 8 1022 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 of its boundary. Hence in some cases the lower bound will be a good approximation to the correct value. It may also be noted that no real use was made of the spherical shape of the volumes S{8). If one wants to consider a point of the ^-pattern to be coincident with a point of the X-pattern if it lies in some other neighborhood, not of spherical shape, the same lower bound applies but with S{8) replaced by the A'olume of the neighborhood. 4.2 Single-Pattern Lower Bound A similar derivation in the case of a single Poisson pattern leads to: Theorem: Let a Poisson pattern of density X he distributed over a d-di- mensional region of volume V. Let S{8) be the volume of the d-dimensional sphere of radius 8. Then the probability of no coincidences is at least as large as g-^^{l ^ xS(8)}'"'''\ The theorem will follow from another bound which is slightly more accurate but much more cumbersome. Lemma Ln the above theorem a lower bound is e-'' 1 + XF + E ^ n [1 - JS{8)/V] . (4-1) Proof of Lemma The probability sought is of the form Z e-''' ^' p. , (4-2) k Kl where pk is the probability that, when exactly A- points are distributed at random over V, there are no coincidences. To estimate pk , imagine the k points to be numbered 1,2, • • • k and placed in the region one at a time. If no coincidences have been created among points 1, ••■, j (which is an event of probability Pi) the probability that the addition of point ./ + 1 creates no coincidence is just the probability that this new point lies in none of the j spheres of radius 8 centered on points 1, ■••,,/. The union of these J spheres intersected with the ^■olume T^ COINCIDENCES IN POISSON PATTERNS 1023 is always of volume ^ jS{8). Hence pj^, ^ pj[l - jSi8)/V], or fc-i P^ ^ n [1 - jS(8)/V]. (4-3) 3 = 1 When {k — l)S(8) > T" the above argument fails because the later terms of the product are negative; in this case we use the trivial bound Ph ^ 0. Combining (4-2) with. (4-3) the lemma follows. Once more the bound may be expected to be almost correct if \'VS{28) is small and if most of the region T^ lies farther than 8 away from its boundary. The bound is also correct for non-spherical neighborhoods (see discussion of previous theorem). When V/S{8) is large, the sum (4-1) is unwield}'. If we let H equal V/S{8), we may rewrite the typical term in the sum as ^^lia-j/H) =^^^i/(//-i) ... (//-A- + 1). If H happens to be an integer, this equals (f ) (mnr, so that the complete sum (4-1) eci[ua]s e-"' (l - ^y. (4-4) We will now prove that if ^ is not an integer, the sum always exceeds (4-4), so that (4-4) is a lower bound in all cases. We ^^ish to prove that [H] + l k 1 + E r, ^(^ - 1) • • • (// - A- + 1) ^ (l-f .r)^ (4-5) fc=l Kl for any positive H, in which event the theorem follows with X = ^ and H = T7^(5). The inequahty (4-5) will be proved by induction on [H]. If [H] = 0, then we are required to show that 1 + Hx ^ (1 + •r)'' 1024 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 for 0 S H < 1. This follows immediately from the concavity of (1 + xr. Suppose now that (4-5) holds for a value H. If we integrate both sides of (4-5) from 0 to x, we obtain '"'''' -i-'^' rr^rr .^ ^rr , , .^ ^ (1 + :c)"+^ - 1 X + Z ,, , ,^, H{H-1) ■■• (H - k + 1) ^ ,^ (/.• + 1)! ^ ' ^ ' ' - H +\ which may be rewritten as {H+Vi+l k 1 + Z n (^ + l)(^) •••(/?- A: + 2) ^ (1 + xr+\ This completes the induction, and the proof of the theorem. 4-3 Another Lower Bound {Any Number of Patterns) Another kind of lower bound can be derived which sometimes will be better than the above bounds when the region V has a large fraction of its volume within 5 of the boundary. For example, V might be a three-dimensional circular cylinder (a cable) with a radius which is com- parable to 5. To derive this bound one first finds the expected number, E, of co- incidences in V. An upper bound on E will also suffice. Then it is noted that 1 — £" is a lower bound on the probability of no coincidences. For if Qiv is the probability of finding A'' coincidences, 00 E = T. NQ^ ^ E Qiv = 1 - Qo . (4-6) iV=l 44 Thick Cable For example, we now give a lower bound which is of interest in con- nection with the problem of a cable mth many wires. Theorem: Let a Poisson pattern of points with density X be placed in a cylinder of length L and radius R > 8. The probability of finding no co- incidences in the cylinder is at least as great as ^5 \ 1 - XV-^L ( ::^^ - i:;! -f- L Proof Introduce cyUndrical coordinates r, (p, Z so that the cylinder is de- scribed by r < R, 0 < Z < L. COINCIDENCES IX POISSON PATTERNS 1025 Consider first any pattern point (r, (p, Z) with Z-coordinate satisfying d ^ Z ^ L — 8. Let arrows be drauTi from this point to all other pat- tern points (if any) within distance 8. The expected number of arrows drawn from this point will be XG(r) where G(r) is the volume of the intersection of the cylinder with a sphere of radius 5 centered at the point. For points near the ends of the cylinder {Z ^ 8 or L — 8 ^ Z), the expected number of arrows will be less than XG{r). Since the proba- bility of finding a pattern point in a little volume element dV is XdV, we conchide that the expected number of arrows drawn in the entire cylinder will be less than /// ^'«« '^^' cyUnder If the cylinder has A^ coincidences, there will be 2A^ arrows (each point of a coincident pair appears once at the head of an arrow and once at the tail). Hence the expected number of coincidences is E n ft ^ xVL / Gir) r dr. (4-7) Since an exact formula for G{r) is rather cumbersome, we are content with a simple but close upper bound, li r ^ R — 8 then clearly G(r) = 47r5 /3. If r > R — 8 we get an upper bound on G{r) by computing the shaded volume in Fig. 6; the intersection of the sphere with a half-space. G{r) ^ [28' + 3(7? - r)5' - (R - /•)'] tt/B. Substituting these expressions for G{r) in (4-7), integrating, and using (4-6) the theorem follows. The approximation to G{r) which was made above is bad when R is much less than 5, but in this case good estimates may be obtained from the one-dimensional results of Part II. Note also that if X is large enough, the bound becomes negative and is therefore useless. ,-SPHERE PLANE Fig. 6 — A region for estimating G(r). 1026 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 li-.B Upper Bounds Good upper bounds appear even harder to get than lower bounds. One procedure i.s to divide the region V into a number of smaller cells. If each cell has probability, p, of no coincidences and if there are A' cells, then p'^ is the probability of no coincidence in any cell. If there is no coincidence in V there will be none in any cell; hence p^ is an upper bound on the probability of no coincidence in V. Of course, p^ is too large because of the possibility of a coincidence between two points in different cells. It follows that p will be a close bound only if the cell size is made large; but then p becomes hard to compute. For example, consider self -coincidences in a single Poisson pattern in a large region of area V in the plane. Cover this area with an array of hexagonal cells of side 5/2 as shown in Fig. 7. The area of each hexagon is 3\/3 sVS so the number of cells used will be about K = 87/3\/3 5l A cell has no coincidence if it contains at most one pattern point, hence p = (1 + X3V3 SVS) exp - 3a/3 XS'/S. The upper bound is P = e { 1 + — g— X5 1 which has an interesting resemblance to the lower bound e""'^(l + 7rX6") 2x V7jr52 Fig. 7 — Pattern for studying coincidences in a plane region. COINCIDENCES IN POISSON PATTERNS 1027 1^.6 An Exact Calculation The upper and lower bounds in Section 4.5 are not very close, largely because of the small size of the hexagonal cells. An improved upper bound may be obtained using square cells of side 26. We can calculate p for small rectangular cells but only if we redefine our notion of coin- cidence in terms of square neighborhoods instead of circular neighbor- hoods. That is, points (xi , yi) and (.r2 , 7/2) are now considered coincident if simultaneously I xi — X2\ ^ 8, and | ^1 — ^2 | ^5. The result we get is the only exact calculation of a non-trivial multi- dimensional coincidence probability known to us. Consider the rectangle 0^x^L,0^y^M with L and M both ^ 26. If L is less than 5, two points are coincident if and only if their //-co- ordinates differ by less than 6. The problem then reduces to a one-di- mensional coincidence computation such as we gave in Part IL There- fore, suppose both L and M are greater than 6. There is probability (XLMf -xz,./ that the rectangle contains k points. We therefore subdivide the problem into cases of the form "given k, find the probability that the A- points have no coincidences". Only five of these cases have a non-zero answer. To show this, divide the rectangle into four rectangles of sides L/2, M/2; if /o ^ 5 one of these rectangles must contain more than one point, and so a coincidence. The remaining cases k = 0, 1, 2, 3, 4 may be further subdivided according to which pairs of .r-coordinates are less than 5 apart. Let us number the k points (.ri , yi), • • •, (.ta; , yk) in such a way that the .r-coordinates are in order Xi ^ x^ S^ • • • ^ .t^ . If, for some i, Xi+2 ^ Xi -f 6, then the subcase in question contributes zero to the probability of no coincidences because all of | .r, — .r,+i [, | Xi+i — .r,:+2 |, I Xi+2 — Xi I are ^ 6 and at least one of | /y, — yi+i |, \ yi+i — yi+o |, I ?/,+2 — yi I is ^6. The only subcases which remain to give a non-zero contribution are the nine listed in Table I. The number in the "subcase" column is k. The next column contains the a--ineciualities which define the subcase. The probability that the k ordered .r-coordinates satisfy the stated inec^ualities is listed as prob^ . If the r-inequalities are satisfied there will be no coincidences if and only if | ^6 — //„ | > 6 for every in- equaUty | Xb — Xa \ ^ 6 given in the a;-inequality column. These y-in- 1028 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 Table I Subcase X inequ. probx y inequ. probj/ 0 — 1 — 1 1 — 1 1 2(a) 2(b) ^2 - xi > 8 X2 — Xi ^ 8 U - ^/LY 28L - 52 L2 \ yi - yi \ > s 1 (1 - 8/ MY 3(a) X2 — Xi ^ 8 X3 — Xo > 8 f (1 - 5/Lr \ y- - yi \ > 8 (1 - S/MY 3(b) X2 — Xi > 8 1(1 - s/Ly 1 2/2 - 2/3 1 > 6 (1 - 8/ MY 3(c) X2 — Xi -^ 8 Xz - X2 ^ 8 Xi — xi > 8 1(1 - 8/Ly (1^ - 0 i 2/2 - 2/3 1 > 5 1 2/1 — 2/2 1 > 5 §(1 - 5/M)3 4(a) Xi — Xi -^ 8 Xi — Xi > 8 Xi — X2 > 8 Ki - 5/Ly \ y2 - yi \ > 8 1 '2/3 - 2/2 1 > 5 1 2/4 - 2/3 1 > 5 A(l - 8/My 4(b) Xi — X2 > 8 Ki - 5/Ly 1 2/2 - 2/1 1 > 5 1 2/4 - 2/3 1 > 5 (1 - 5/M)^ equalities are listed in the third column and the probabilities that they are satisfied are hsted as prob^^ . The probability of no coincidences is J2 Qk prob^ proby where the simi is over all nine subcases. The sum is exp (-XLM) \ 1 + \LM + ^ [L'il/' - b\2L - 8)mi - 5)] 4- ?^ (L - 8)\M - 8y-{2LM + L5 + M8 - 45') If L = M = 26, this reduces to exp ( — 45'X) 1 + 45'X + I 8V + 1^ 8\' + ij- 6^' 2 2/ 8o4 J COIXCIUEXCES IX POISSOX PATTERXS 1029 A sample of one of the above computations may be instructive. Con- sider, for example, Case 4(a). We have 0 ^ .ri ^ .1-2 ^ .r? ^ X4 ^ L, and require: ^'3 — .<"2 ^ 6, X3 — xi > 5, Xi — .r2 > 5. The probabilitj' of this is (L*/8)"^ / / I dxi dxi dx2 dxz = y^ / / (L - .ra - 5) (.1-3 - 5) (^a^g dr2 _ S (L- SY _1( _8\ L' 24: 3\ L/' In the ?/-direction we require \ 1/2 — Ui \ > 5, I i/3 — i/2 | > 8, \ iji — y-i I > 8, and there are no order restrictions. Assume first that tjo < i/z ■ Then the probability that yi and 1/4 satisfy their restrictions is ( ?/3 — 5\ /M — y-2 — 8^ M /\ M /■ Hence, the probability for satisfying all the conditions is 6 Jo V M J\ M J M M 24 V M ' Interchanging 7/2 \x\\\\ y-^ and yi with ?/4 shows that the assumption y-z > yz yields the same answer, so that the required probability is A(i-AY. 12 V M V XUMERICAL WORK 5.1 Coincidences between Two Patterns 5.1.1 Machine Computation of F(L) To compute the probability of no coincidences in a hue of length L directly, it is convenient to transform equations (1-2) through (1-4) into 1030 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 the following differential difference equations: [O if X < 8 P^ix) + nP,{x) = P,'{x) + \P,{x) = -(a+m) 5, if X > 5, P2{x - 8)fjLe 0 if X ^ d Prix - 8)\e~''^''' F'(x) + (X + M)/^(.r) = \P,{x) + fiP.ix), Pi(0) = P2(0) - F(0) = 1. These have been solved on a general purpose analog computer with i the aid of a lumped-element approximate delay line for a number of : cases. We have chosen for illustrative purposes the parameters A = 5, M = 10, 5 = 0.02, and L ^ 1. The exact solution, together with various approximations to be described in the sequel, is plotted in Fig. 8, where the exact solution is labelled yi . 1.0 0.9 0.8 LU (J z 111 9 u z o o o z IL o 0.7 0.6 0.5 0.4 0.3 0.2 0.1 \ \ yi = y2- EXACT SOLUTION ASYMPTOTIC SOLUTION -^ ^ y4= UPPER BOUND y5= DISCRETE MARKOV BOUND ^ \, \ ^ ^v yi& [X V \ s v, •\ ^ :\ ^ ^v ^-- ::::; 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 L Fig. 8 — Probability of no coincidences between two one-dimensional Poisson patterns with X = 5, m = 10, if 5 = 0.02. COINCIDENCES IN POISSON PATTERNS 1031 5.1.2 The Asymptotic Formula All approximation to the probability F{x) of no coincidences is given by the asymptotic formula (1-10) which, of course, becomes a better approximation the larger L becomes. If X = 5, /x = 10, and 5 = 0.02, the smallest value, a, such that (X - a){n - a) = Xixe--^^^'-"'' is a = 1.548. The asymptotic formula for F{L) now becomes F{L) ^ 1.013e"'•'''^ which is found in Fig. 8 as ?/2 . 5.1.S Bounds Using the Asymptotic Exponent Formulas (1-12) through (1-18) give a scheme for computing both upper and lower bounds for F(L) which have the right behavior for large L, and also agree with the solution at L = 0. They become F(L) ^ 1.007e~' •'*'"' - 0.007e"''^ and FiL) ^ 1.195e~' •'''"' - 0.195^''^ respectively, and are represented by ^3 and yi in Figure 8. 5.1.4 An Upper Bound by a Discrete Markov Process If we mark on the positive a;-axis the points nb/2, ?i = 0, 1, 2, • • •, we can assign to each interval of length 6/2 thus created a state (z^), i, j = 0 or 1, as follows: t = 0 if no point of the X-process is present in the interval, i — 1 if one or more points of the X-process are present, and similarly for j and /x. An interval of length 5, made up of two adjacent intervals of length 5/2, may then be represented by a number between 0 and 15 in binary notation, where 3, 6, 7, 9, and 11-15 represent a coincidence within the interval of length 5. We now define a Markov process as follows: in the interval 0 ^ / < 5, let p/°\ z = 0, 1, 2, 4, 5, 8, 10, be the probabilities of occurrence of the i state, so that, for exam- pie, p^ = e-'''e-''\ and p/°' = e-'''e-'\\ - e-''). These are the states in which there is no coincidence in (0, 5). In addition, let g^°^ represent the probability of all the other states put together; i.e., of a coincidence in (0, 5). We now define pi'"\ i = 0, 1, 2, 4, 5, 8, 10 as the probability of the i state in the interval {nb/2, (n + 2)5/2), where we 1032 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 require in addition that all states in the intervals (k8/2, (I: + 2)8/2), /,■ < n, are from the same "no coincidence" index set. We define q " as, lli(> probability of a state 3, 6, 7, 0, or 11-15, in some interval (A"5/2, (/)■ + 2)5/2), k ^ n. There are then transition probabilities from states in the ?} — f to states in the /;* interval. For example. (n) and An) (n-1) Po + (1 = e -\d -m5 (P^ (n-1) 0 + P4 (n-1) + V""''), -\5 )(1 „-mS (»-l) A8n + (1 - e )(P; («-i) + Pi )(po (.-!)) + (1 (n-1) )(P2 (n-l)N -M«\ (n-1) + P (n-1) in ). The quantity 1 — g^"^ is then an upper bound for the probability of no coincidences (upper because it is possible for a coincidence to occur in the process which is not counted in this subdivision of it). The curve 2/5 in Fig. 8 is drawn through points at L = n8/2 computed in this manner. To summarize the results, we see that the asymptotic formula and the lower bound are both indistinguishable from the right answer; the upper bounds are fairly far off. The upper bound derived by the Markov process is better than that derived from the integral eciuation until 1.0 (n 0.6 LU o Z LU Q U z o o o z U- o > 0.4 0.6 CD < m o CE a. 0.2 0 ^^r--^ N ^^^^>^^ ^^ x^ X, "\ \N \, ^^.^ORRECT •e-^V[,^^s((;)]^/s('"-- K^ \ \ .1-E \ v^ \ \ \ 0 0.1 0.4 0.5 0.2 0.3 Fig. 9 — Prol)ability of no coincidences in a 25 X 25 square; neighborhoods are square. COINCIDENCES IN POISSON PATTERNS 1033 about L = 0.5 (25 iterations), when the integral equation upper bound becomes better. 5.2 A Single Pattern in a Square To test our higher-dimensional bounds, we consider again coincidences in a single Poisson pattern in a square of side 25. The exact probability of no coincidences was given in l^art JV assuming square neighborhoods. The lower bound (Sec. 4.2) e-'''{l + \S{8)V"''> applies using T^ = (25) and aS(5) = (26)' for square neighborhoods. To use the lower bound 1 — E we note that the exact expected number of coincidences is 1 , r'-^ r" £; = -X' / / A{x, y) dxdij where A{x, y) is the area of the intersection of the given sc^uare with the square neighborhood centered at (x, y). The lower bound is 1 — £" = 1 — 9X"5 /2. The upper bound p can be used if the square is cut into /v = 4 squares of side 5, each with a probability?? = (1 + X5") exp — X5" of no coincidence. These bounds, together with the exact probability, are plotted as functions of X5' in Fig. 9. When X5"' is small, the 1 — E bound is correct to terms of order 0(X'^5 ). This might have been predicted from (4-6) since it seems reasonable that Q2 , Qi , • ■ • should be of higher order in X than Qi when X is small. Ultimately the first lower bound becomes a better estimate. It must be recognized that this other lower bound is being tested under very severe conditions. Since every point of the square has a neighborhood which intersects the boundarj^, the errors from source (b) of Part ^" are considerable. The authors wish to thank D. W. Hagelbarger and H. T. O'Neil for their assistance in the course of the calculations reported in this section, and Aliss D. T. Angell for preparing some of the figures. REFERENCES I.e. Domb, The Problem of Random Intervals on a Line, Proc. Cambridge Phil. Soc, 43, pp. 329-341, 1947. 2. P. Eggleton and W. O. Kermack, A Problem in the Random Distribution of Particles, Proc. Royal Soc. Edinburgh, Sec A, 62, pp. 103-115, 1944. 3. W. Feller, On Probabilit}' Problems in the Theor}' of Counters, Studies and Essays presented to R. Courant, Interscience, pp. 105-115, 1948. 4. E. C. Xlolina, The Theory of Prol)abilitv and Some Applications to Engineering Prol)lems, Trans. A. I.E. E., 44, pp. 294-299, 1925. 5. L. Silberstein, The Probable Number of Aggregates in Random Distributions of Points, Phil. INIag., Series 7, 36, pp. 319-.336, 1945. Bell System Technical Papers Not Published in this Journal Anderson, 0. L., see Andreatch, P. Andreatch, p., and Anderson, 0. L.^ Teflon as a Pressure Medium, Rev. Sci. Instr., 28, p. 288, April, 1957. BoYET, H.,^ and Seidel, H.^ Analysis of Nonreciprocal Effects in an N-Wire Ferrite -Loaded Trans- mission Line, Proc. I.R.E., 45, pp. 491-495, April, 1957. BoYET, H., see Seidel, H. BOZORTH, R. M.i Review of Magnetic Annealing, Proc. of 1956 A.I.E.E. Conf . on Mag- netism and Magnetic Materials, T-91, pp. 69-75, April, 1957. Burns, F. P.^ Piezoresistive Semiconductor Microphone, J. Aeons. Soc. Am., 29, pp. 248-253, Feb., 1957. Carruthers, J. A., see Geballe, T. H. ClOFFI, P. P.i Rectilinearity of Electron-Beam Focusing Fields from Transverse Component Determinations, Commun. and Electronics, 29, pp. 15-19, March, 1957. Cook, R. K.^ Absorption of Sound by Patches of Absorbent Material, J. Aeons. Soc. Am., 29, pp. 324-329, March, 1957. 1 Bell Telephone Laboratories, Inc. 1035 10;^g the bell system technical jouknal, july 1957 Cook, R. K.^ Variation of Elastic Constants and Static Strains with Hydrostatic Pressure: A Method for Calculation from Ultrasonic Measurements, J. Acous. Soc. Am., 29, pp. 445-449, April, 1957. Dewald, J. F.i The Kinetics of Formation of Anode Films on Single Crystal Indium Antimonide, J. Electrochem. Soc, 104, pp. 244-251, April, 1957. DOWLING, R. C.4 Lightning Protection on the Stevens Point-Wisconsin Rapids Inter- city Telephone Cable, C/ommim. and Electronics, 28, pp. G97-701, Jan., 1957. Feher, G.^ Electron Structure of F Centers in KCl by the Electron Spin Double - Resistance Technique, Phys. Rev., Letter to the Editor, 105, pp. 1122-1123, Feb. 1, 1957. Foster, F. G.^ The Unconventional Application of the Metallograph, Focus, 18, pp. lG-20, April, 1957. Garn, p. D.i An Automatic Recording Balance, Anal. Chem., 29, pp. 839-841, May, 1957. Gast, R. W.^ Field Experience with the A2A Video System, Commun. and Elec- tronics, 28, pp. 710-716, .Jan., 1957. Geballe, T. H.,1 Carruthers, J. A.," Rosenberg, H. M.,*^ and Ziman, J. M.^ The Thermal Conductivity of Germanium and Silicon Between 2 and 300°K, Proc. Royal Soc, A238, pp. 502-514, .Jan. 29, 1957. ' Boll Telephone Laboratories, Inc. ■' Wisconsin Telephone Companj-, Madison. ^ New York Telephone Company, New York. •^ Oxford University, England. ' Cambridge University, England. TECHNICAL PAPERS 1037 Geller, S.^ Crystallographic Studies of Perovskite-Like Compounds. — IV. Rare Earth Scandates, Vanadites, Galliates, Orthochromites, Acta Crys., 10, pp. 243-248, April 10, 1957. Geller, S.^ Crystallographic Studies of Perovskite-Like Compounds. — V. Rela- tive Ionic Sizes, Acta Crys., 10, pp. 248-251, April 10, 1957. Geller, S.,^ and Gilleo, M. A.^ Structure and Ferrimagnetism of Ythium and Rare -Earth -Iron Gar- nets, Acta Crys., 10, p. 239, March 10, 1957. Gilleo, M. A.^ Crystallographic Studies of Perovskite-Like Compounds. III. La(M,, , Mni_x)0 with M = Co, Fe and Cr, Acta Crys., 10, pp. 161-166, March, 1957. Gilleo, M. A., see Geller, S. Green, E. I.^ Nature's Pulses, I.R.E. Student Quarterly, 3, pp. 3-5, Feb., 1957. Grossman, A. J.^ Synthesis of Tschebycheff Parameter Symmetrical Filters, Proc. I.R.E., 45, pp. 454-473, April, 1957. Hagstrum, H. D} Thermionic Constants and Sorption Properties of Hafnium, J. Appl. Phys., 28, pp. 323-328, March, 1957. Haworth, F. E.^ Breakdown Fields of Activated Electrical Contacts, J. Appl. Phys., Letter to the Editor, 28, p. 381, IMarch, 1957. Heidenreich, R. D.,^ and Xesbitt, E. A.^ Stacking Disorders in Nickel Base Magnetic Alloys, Phys. Rev., Letter to the Editor, 105, pp. 1678-1679, March 1, 1957. 1 Bell Telephone Laboratories, Inc 1038 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 HoLDEN, A. N., see Wood, Elizabeth A. Huntley, H. R.^ Where We Are and Where We Are Going in Telephone Transmis- sion, Commun. and Electronics, 29, pp. 54-63, March, 1957. Joel, A. E.^ Electronics in Telephone Switching Systems, Commun. and Elec- tronic, 28, pp. 701-709, Jan., 1957. lappEL, F. R.2 Three -Dimensional Engineers, Elec. Engg., 76, pp. 267-270, April 1957. Karlin, J. E., see Pierce, J. R. KjlRp, A.^ Backward-Wave Oscillator Experiments at 100 to 200 Kilomegacy- cles, Proc. I.R.E., 45, pp. 496-503, April, 1957. Kelly, M. J.^ The Work and Environment of the Physicist Yesterday, Today, and Tomorrow, Phys. Today, 10, pp. 26-31, April, 1957. Law, J. T.,1 and Meigs, P. S.^ Rates of Oxidation of Germanium, J. Electrochem. Soc, 104, pp. 154-159, March, 1957. Law, J. T.,1 and Meigs, P. S.^ The High Temperature Oxidation of Germanium, Semiconductor Surface Physics (book), pp. 383-400, 1957, Univ. of Penna. Press, Philadelphia. LlEHR, A. D.^ Structure of Co(CO)4H and Fe (00)^2, Zeitschrift Fiir Naturfor- schung, 12b, pp. 95-96, Feb., 1957. 1 Bell Telephone Laboratories, Inc. 2 American Telephone and Telegraph Company. TECHNICAL PAPERS 1039 LlEHR, A. D.^ Structure of 7r-Cyclopentadienyl Metal Hydrides, Natunvissenschaf- ten, 44, p. 61, Feb. 1, 1957. LuNDBERG, C. \., see Vacca, (i. N. LuNGBERG, J. L.,^ and Nelson, L. S.^ The High Intensity Flash Irradiation of Polymers, Nature, Letter to the Editor, 179, pp. 807-368, Feb. 16, 1957. Marrison, W. A} A Wind-Operated Electric Power Supply, Elec. Engg., 76, pp. 418- 421, May, 1957. McCall, D. W.i Nuclear Magnetic Resonance in Guanidinium Aluminum Sulfate Hexahydrate, J. Chem. Phys., Letter to the Editor, 26, pp. 706-707 March, 1957. Meigs, P. S., see Law, J. T. MendizzA; A.,1 Sample, C. H.,« and Teel, R. B.^ A Comparison of the Corrosion Behavior and Protective Value of Electrodeposited Zinc and Cadmium on Steel, Sjniiposium on Proper- ties, Tests, and Performances of Electrodeposited Metallic Coatings, A.S.T.M. Special Tech. Publication 197, pp. 49-64, 1957. Miller, S. L.' The Ionization Rates for Holes and Electrons in Si, Phys. Rev., 105, pp. 1246-1249, Feb. 15, 1957. Nelson, L. S., see Lundberg, J. L. Nesbitt, E. a., see Heidenreich, R. D. ' Bell Telephone Laboratories, Inc. * International Nickel Company, Xew York City. ^ International Nickel Company. Wrightsville Beach, North Carolina. 1040 THE BELL SYSTEM TECHNICAL JOUKXAL, JULY 1957 Palmquist, T. F. 10 Multi-Unit Neutralizing Transformers, Commun. and Electronics, 28, pp. 717-721, Jan., 1957. Pierce, J. R.,^ and Karlin, J. E.^ Information Rate of a Human Channel, Proc. I.R.E., Letter to the Editor, 45, p. 368, March, 1957. Rea, W. T.i The Communication Engineer's Needs in Information Theory, Com- mun. and Electronics, 28, pp. 805-808, Jan., 1957. Rosenberg, H. M., see Geballe, T. H. Sample, C. H., see Mendizza, A. Seidel, H.,^ and Boyet, H.^ Form of Polder Tensor for Single Crystal Ferrite with Small Cubic Symmetry Anisotropy Energy, J. Appl. Phys., 28, pp. 452-454, April, 1957. Seidel, H., see Boyet, H. Slichter, W. P.^ Nuclear Magnetic Resonance in Some Fluorine Derivatives of Poly- ethylene, J. Poly. Sci., 24, pp. 173-188, April, 1957. Smith, K. D., see Veloric, H. S. Suhl, H.i Proposal for a Ferromagnetic AmpUfier in the Microwave Range, Phys. Rev., Letter to the Editor, 106, pp. 384-385, April 15, 1957. Swanekamp, F. W., see Van LTitert, L. G. Teel, R. B., see Mendizza, A. 1 Bell Telephone Laboratories, Inc. 10 Bell Telephone Company of Canada, Montreal, Quebec. TECHNICAL FAPERS 1041 Treuting, R. G.^ Torsional Strain and the Screw Dislocation in Whisker Cyrstals, Acta Met., Letter to the Editor, 5, pp. 173-175, March, 1957. Vacca, G. N.,1 and Lundberg, C. V.^ Aging of Neoprene in a Weatherometer, Wire and Wire Products, 32, pp. 418-457, April, 1957. Van Uitert, L. G.^ Magnesium -Copper — Manganese -Aluminum Ferrites for Microwave Applications, J. App. Phys., 28, pp. 320-322, March, 1957. Van Uitert, L. G.^ Magnetic Induction and Coercive Force Data on Members of the Series BaAl:^Fei2-xOi9 and Related Oxides, J. Appl. Phys., 28, pp. 317-319, March, 1957. Van Uitert, L. G.,^ and Swanek.\mp, F. W.^ Permanent Magnet Oxides Containing Divalent Metal Ions, .T. Appl. Phys., 28, pp. 482-485, April, 1957. Veloric, H. S.,1 and Smith, K. D.^ Silicon Diffused Junction Avalanche Diodes, J. Electrochem. Soc, 104, pp. 222-227, April, 1957. Walker, L. R.^ OrthogonaUty Relays for Gyrotropic Wave Guides, J. Appl. Phys., Letter to the Editor, 28, p. 377, March, 1957. Weber, L. A.^ Influence of Noise on Telephone Signaling Circuit Performance, Commun. and Electronics, 28, pp. 636-643, Jan., 1957. Weibel, E. S.i An Electronic Analogue Multiplier, Trans. I.R.E., PGEC, EC-6, pp. 30-34, March, 1957. ' Bell Teleuhone Laboratories, Inc. 1042 THE BELL SYSTEM TECHNICAL JOUKXAL, JULY 195 ( Weiss, J. A} An Interference Effect Associated with Faraday Rotation, and Its Application to Microv/ave Switching, Proc. Coiif. on IMagnetism and Magnetic Materials, pp. 580-585, Feb., 1957. Wertheim, G. K.^ Energy Levels in Electron-Bombarded Silicon, Phys. Rev., 105, pp. 1730-1735, March 15, 1957. Willis, F. H.^ Some Results with Frequency Diversity in a Microwave Radio System, Commun. and Electronics, 29, pp. 63-67, March, 1957. Wood, Elizabeth A.,^ and Holdex, A. X.^ Monoclinic Glycine Sulfate: Crystallcgraphic Data, Acta Crys., 10, pp. 145-146, Feb., 1957. YOUNKER, E. L.^ A Transistor Driven Magnetic Core Memory, Trans. I.R.E., PGEC, EC-6, pp. 14-20, March, 1957. Zimax, J. M., see Geballe, T. H. 1 Bell Telephone Laboratories, Inc. lecent Monographs of Bell System Technical Papers Not Published in This Journal* Bashkow, T. R., and Desoer, C. A. A Network Proof of a Theorem on Hurwitz Polynomials, Monograph 2614. Beach, A. L., see Thurmond, C. D. Biggs, B. S., see Lundberg, C. V. Cutler, C. C. Instability in Hollow and Strip Electron Beams, Monograph 2711. Desoer, C. A., see Bashkow, T. R. Elias, p., Feinstein, A., and Shannon, C. E. A Note on the Maximum Flow Through a Network, jMonograph 2768. Feinstein, A., see Elias, P. GuLDNER, W. G., see Thurmond, C. D. Haring, H. E., see Taylor, R. L. Ingram, S. B. Role of Evening Engineering Education in the Training of Technicians, Monograph 2771. Kramer, H. P., and Matheavs, M. V. A Linear Coding for Transmitting a Set of Correlated Signals, Mono- graph 2757. * Copies of these monographs may be obtained on request to the Publication Department, Bell Telephone Laboratories, Inc., 463 West Street, New York 14, N. Y. The numbers of the monographs should be given in all requests. 1043 1044 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 Lewis, H. W., Smith, De Witt H., and Lewis, M. R. Ballistocardiographic Instrumentation, Monograph 2747. Lewis, M. R., see Lewis, H. W. Lundberg, C. v., Vacca, G. N., and Biggs, B. S. Resistance of Rubber Compounds to Outdoor and Accelerated Ozone Attack, Monograph 2773. Mathews, M. V., see Kramer, H. P. McMillan, B. Two Inequalities Implied by Unique Decipherability, Monograph 2774. Robertson, S. D, Recent Advances in FinUne Circuits, Monograph 2759. Shannon, C. E. Zero Error Capacity of a Noisy Channel, Monograph 2760. Shannon, C. E., see Elias, P. Smith, De Witt H., see Lewis, H. W. Taylor, R. L., and Haring, H. E. A Metal-Semiconductor Capacitor, Monograph 2776. Theuerer, H. C. Removal of Boron from Silicon by Hydrogen Water Vapor Treatment, Monograph 2762. Thurmond, C. D., Guldner, W. G., and Beach, A. L. Hydrogen and Oxygen in Single -Crystal Germanium Determined by Gas Analysis, Monograph 2777. Trumbore, F. a. Solid Solubilities and Electrical Properties of Tin in Germanium Single Crystals, Monograph 2779. Vacca, G. N., see Lundberg, C. V. Contributors to This Issue Vaclav E. Bexes, A.B., Harvard College, 1950; M.A. Ph.D., Prince- ton University, 1953. Instructor in logic and philosophy of science, Princeton University, 1952-53; Bell Telephone Laboratories, 1953-. Since joining the Laboratories, Mr. Benes has been engaged in mathe- matical systems research, involving stochastic processes describing the passage of traffic through a switching system. He is the author of a number of papers on mathematical logic and analytic philosophy. Member of the Mind Association, the Association for Symbolic Logic, the Listitute of Mathematical Statistics, American Mathematical Society, and Phi Beta Kappa. E. X. Gilbert, B.S., Queens College, 1942; Ph.D., Massachusetts Institute of Technology, 1948; Mr. Gilbert's early employment was with the M.I.T. Radiation Laboratory. He joined Bell Telephone Labora- tories in 1948. His work has been on studies of the information theory and on the switching theory. He now is part of the communication fundamentals group. Mr. Gilbert is a member of the American Mathe- matical Society. H. 0. PoLLAK, B.A., Yale University, 1947; M.A., Harvard Univer- sity, 1948; Ph.D., Harvard University, 1951; Bell Telephone Labora- tories, 1951-. Mr. Pollak has been engaged in mathematical research and mihtary systems analysis. He is a member of Phi Beta Kappa, Sigma Xi, American Mathematical Society and Mathematical Association of America. M. B. Prince, A.B., Temple University, 1947; Ph.D., Massachusetts Institute of Technolog}^, 1951; Bell Telephone Laboratories, 1951-1956; Hoffman Semiconductor Division of Hoffman Electronics Corporation, 1956-. Between 1949-51 he was a research assistant at the Research Laboratories of Electronics at M.I.T. Avhere he was concerned with cryogenic research. At Bell Telephone Laboratories, Mr. Prince was concerned with the physical properties of semiconductors and semicon- ductor devices and was associated with the development of silicon de- vices, including the Bell Solar Battery and the silicon power rectifier. 1045 1046 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 Mr. Prince is a member of the I.R.E., the American Physical Society, the Association for AppHed Solar Energy, the Electrochemical Society and Sigma Xi. W. W. RiGROD, B.S. in E.E., Cooper Union Institute of Technology, 1934; M.S. in Engineering, Cornell University, 1941; D.E.E., Poly- technic Institute of Brooklyn, 1950; State Electrotechnical Institute, Moscow, U.S.S.R., 1935-39; Westinghouse Electric Corporation, 1941- 51; Bell Telephone Laboratories, 1951-. His work has been related principally to the study and development of electron tubes, both the gaseous-discharge and the high-vacuum types. He is a member of the American Physical Society, I.R.E. and Sigma Xi. Stephen O. Rice, B.S., Oregon State College, 1929; California In- stitute of Technology, Graduate Studies, 1929-30 and 1934-35; Bell Telephone Laboratories, 1930-. In his first years at the Laboratories, Mr. Rice was concerned with the non-linear circuit theory, with special emphasis on methods of computing modulation products. Since 1935 he has served as a consultant on mathematical problems and in investiga- tions of the telephone transmission theory, including noise theory, and applications of electromagnetic theory. Fellow of the I.R.E. Erling D. Sunde, E.E., Technische Hochschule, Darmstadt, Ger- many, 1926; Brooklyn Edison Company, 1927; American Telephone and Telegraph Company, 1927-1934; Bell Telephone Laboratories, 1934-. My. Sunde's work has been centered on theoretical and experimental studies of inductive interference from railway and power systems, lightning protection of the telephone plant, and fundamental transmis- sion studies in connection with the use of pulse modulation systems. Author of Earth Conduction Effects in Transmission Systems, a Bell Laboratories Series book. Member of the A.I.E.E., the American Mathematical Society, and the American Association for the Advance- ment of Science. Harold S. Veloric, B.A., University of Pennsylvania, 1951; M.A., 1952, Ph.D., 1954, University of Delaware; Bell Telephone Labora- tories, 1954-. Between 1951-4 he was a research fellow concerned with the synthesis and analysis of boron and silicon compounds. Since joining the Laboratories, Mr. Veloric has been concerned with the properties and development of solid state devices. He has been associated with the de- velopment of several classes of silicon diodes, including power rectifiers, voltage-reference and computer diodes. Dr. Veloric is a member of the American Chemical Society and the Electrochemical Society. HE BELLSYSTEM Jechnical journal VOTED TO THE SCI ENTIFIC^W^ AND ENGINEERING PECTS OF ELECTRICAL COMMUNICATION LUME XXXVI SEPTEMBER .1957 NUMBER 5 " ■ . Oceanographic Information for Engi'Hcering Submarine Cable Systems c. h. elmendorp and b. c. heezen 1047 Resistance of Organic Materials and Cable Stnictm-es to Marine Biological Attack l. r. snoke 1095 Dynamics and Kinematics of the Laying and Recovery of Sub- marine Cable E. E. ZAJAC 1129 Theory of Curved Circular Waveguide Containing an Inhomo- geneous Dielectric s. p. morgan 1209 Circular Electric Wave Transmission in a Dielectric-Coated Wave- guide H. G. UNGER 1253 Circular Electric Wave Transmission Through Serpentine Bends H. G. UNGER 1279 Normal Mode Bends for Circular Electric Waves h. g. unger 1292 Bell System Technical Papers Not Published in This Journal 1308 Recent Bell System Monographs 1313 Contributors to This Issue 1317 COPTBIGHT 1967 AMERICAN TELEPHONE AND TELEGRAPH COMPANY THE BELL SYSTEM TECHNICAL JOURNAL ADVISORY BOARD A. B. GOETZE, President, Western Electric Company u. J. KELLT, President, Bell Telephone Laboratories E. J. McNEELY, Executive Vice President, American Telephone and Telegraph Company EDITORIAL COMMITTEE B. MCMILLAN, Chairman k. e gould 8. E. BRILLHART E. I. GREEN A. J. BUSCH R. K. HONAMAN L. R. COOK H. R. HUNTLEY A. C. DICKIE80N F. R. LACK R. L. DIETZOLD J. R. PIERCE EDITORIAL STAFF w. D. BULLOCH, Editor B. L. SHEPHERD, Production Editor T. N. POPE, Circulation Manager THE BELL SYSTEM TECHNICAL JOURNAL is published six times a year by the American Telephone and Telegraph Company, 195 Broadway, New York 7, N. Y. F. R. Kappel, President; S. Whitney Landon, Secretary; John J. Scan- Ion, Treasurer. Subscriptions are accepted at $5.00 per year. Single copies $1.25 each. Foreign postage is 65 cents per year or 11 cents per copy. Printed in U. S. A. THE BELL SYSTEM TECHNICAL JOURNAL VOLUME XXXVI SEPTEMBER 1957 number 5 Copyright 1957, American Telephone and Telegraph Company Oceanogr^phic Information for Engineering Submarine Cable Systems* By C. H. ELMENDORF and BRUCE C. HEEZEN (Manuscript received June 4, 1957) Information on the environment in which submarine cable systems are placed is of vital interest in designing, selecting routes for, placing, and repairing this type of communications facility. Existing data are sum- marized and evaluated, and their application to submarine cable systems is considered. I. INTRODUCTION 1.1 General Oceanography, broadly defined, includes the study of all aspects of the oceans. As a science, it is concerned with gathering data and de- vising theories which describe and explain the past, present, and the fu- ture of the oceans. Oceanography includes physical description of the topography, sediments, and teinperatiu-c of the ocean bottom; investi- * This is T^amoiit (loolo^ical Oliservatory Cont ril)iiti()n No. 251. Dr. Hoozcn is a meml)er of the Ijamoiit Cicological Observatory of Columbia University. Addi- tional information on this sul)ject is being presented by Dr. Heezen in a publica- tion by the Geological Society of America. 1047 1048 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 gation of currents and circulation; study of the geology of the earth's crust under the ocean; and investigation of biological factors. In designing, in finding the best route for, in laying, and in repairing a submarine cable system one can benefit from as detailed a knowledge of the ocean floor as can be obtained. However, the vastness, complexity, and inaccessibility of the ocean bottom make its study difficult. One must depend on limited data, interpreted with the aid of a knowledge of the earth sciences. The acquisition of specific engineering information is further complicated by the inaccuracies of much of the existing data, and the rudimentary nature of many present theories. Yet, by culling, codifying, interpolating, and interpreting the data gathered during the past hundred years, much can be learned that is applicable to particular cable routes. Further, methods now exist for surveying and describing a route with a thoroughness and accuracy that will permit many refine- ments ui the engineering of future submarine cable systems. In this paper specific problems of immediate interest in the engineer- ing of submarine cable systems are discussed in order to give a perspec- tive of the use of such data in current applications. Emphasis is placed on the state of existing knowledge and on the accuracy of available data. The work reported forms a foundation for more detailed studies of spe- cific routes and for the application of knowledge which will be derived from rapidly expanding oceanographic studies to the particular problems of submarine cable systems. 1.2 Application To Submarine Cable Systems How are oceanographic information and technique applied in the se- lection and description of the detailed path of a new cable? First, vari- ations on a direct route must be examined to avoid ocean bottom condi- tions which may result in cable failures. Studies of telegraph cable fault records indicate that many of the deep sea cable breaks occur where cables pass over sea mounts, canyons and areas susceptible to turljidity currents, and an effort must be made to avoid such hazards. Topographic studies form the basis for both initial route selection planning and for a preliminary description of the selected route. This description will include, where data are available, an exag- gerated depth profile uncorrected for angle of the sound beam of the sonic depth recorder, a corrected 1 :1 depth profile where necessary, and a temperature profile. Also, bottom characteristics, including photo- graphs, can be collected for the particular route. These data will be essential in planning a detailed survey of the route, and they will provide OCEANOGRAPHIC INFORMATION FOR SUBMARINE CABLES 1049 preliminary information for the determination of the amount of cable required, for system transmission planning and for studies of cable- placing techniques. One of the fundamental requirements in cable laying is the deposit of a sufficient amount of cable to cover irregularities of the bottom ! without introducing dangerous suspensions and without laying a waste- ful amount of excess slack. Satisfaction of this requirement will require the most detailed possible knowledge of bottom topography, coupled with knowledge of the kinematics of the cable laying process.^ A determination of required cable strength does not directly call for an extremely accurate knowledge of bottom depth and contour. The re- quired cable strength is determined by cable tension during recovery, which is two or more times that experienced during laying. Although the required strength is directly proportional to the depth, it is also affected to a major degree by the ship speed, cable angle during recovery, and the ship motion caused by waves. The ship motion can be controlled to some extent by seamanship and choice of the time at which the re- cover}^ is to be made. Further, the design strength of the cable is in large measure deter- mined by the strength of available steel and the amount of steel that can be accommodated in an economical over-all design. Thus, uncer- tainties of 5 to 10 per cent in the maximum depth of the water on a route would not affect the cable design. Yet, during a critical recovery situ- ation, a more accurate knowledge of depth would be useful in planning and executing the operation. The integrity of the cable will depend on the choice of materials to withstand biological factors and wear on the ocean bottom. A companion paper- discusses the resistance of likely cable-sheath materials to attack by marine borers and bacteria. II. TOPOGRAPHY 2.1 General Mapping the ocean bottom involves depth measurements coupled with a knowledge of the location on the earth's surface of the points at which these measurements are made. There exists a vast store of data on the depths of the oceans taken by hundreds of observers and expeditions over the past hundred 3^ears. It is not surprising that many of these data are of questionable accuracy due to errors in navigation, soundings, plotting, and interpretation. Thus, before existing data can be used for the engineering of submarine cable systems, it is essential 1050 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 O O 1— ( <1 m u m < O U er N. Atlan ; spotty el iround Br cally nil el a tempora 3r special ] North Atl 'a CZ2 '3 >! o o .5 c d >. >/" — . ^ QJ > o3 Oh 03 ::; s- 4J oodov routes 11 ood a practi sed as tion f( astern "S ^^ £ £ 03 >• o 03 a o3 a;t^_ +J j^ O :2; O t) w w P W -fj rH ^ u '3- ^ o ji X .i "io >^ 03'« "IT S C t*=3 s < »3 cS O O O lO e 03 G OJ rtiN ^H lO ^^ lO C -f -H -H ^^ 41 4^ ^ 4^ tf +3 03 ^1 +J 0) .5P 03 M CC Ml M K: Q; s ^^ * cr a (D o; 0) ^^ Pi •| 'S I 1 -£ C a; « C o o O 03 O +J g o; Q C! o O O o o-=^ c 5 J 5: "^^ "^ o i?5 ■" ^ CO ^ ajO as Cr- G^, o3c 4) -no c^ o-~ 0/.- 1 o ss^ .a ^a 'T^ ^ O -t^ Qi O ires time difference betw es transmitted by two e shore .station groups. system: shipljoard eqi t triggers two shore stati etermine position, ires phase difference in c ous waves transmitted or more shore stations, res phase difference in c ous waves transmitted e shore stations. determination of gr e iiearing of transmitt a si 1h t: -; iH O t- y. .H'*^ o; 2-^ -a EC tn ■;:: bc CC' 03 0) a g. 1- IJ ^ 5 C 03 £ o3 £ c losition ini es distance of two sho pulse techi and bearin t/1 "" ii P -3 O o .o x-s bcM t: =?_C g 03 ^ Q C 03 t: t» ill 43 c o3 ^ O; fl, .^ 03-*.^ ? a ^ T. i~ *^ oj-:r o =s 5 '^' ^ .° tc 2 '-•-- l: =3 - c-c S o 03.:: $ o3.5^-a-= .^ ;-< -t-' .f^ o3 o; ;/: ■*j n. •-'. 73 o '^j::-^ O > 03 aj&iG/.jC-i-ia;-i^-i.^a)-w-iJ^ij ■/: X -/. ■c ■ S rt S § P3 w < Pi < o hH > E < ^ ^ ^ ^ ^ ^ < Pi ^^ < w o ffi S^ o o ^ ^ < Ph o o <»: K^! M Q ►-) Q CO W H 03 bC C o3 ^^ o3 03 o; 'a o 03 o o o3 -o o; 03 c Sh o O +j 03 C3 -c 3 S-> -G -^ *j 03 Xi IS o rn o 0) ^ a 8 1-H bC O & o O 4^ T-J O-fl ^ o3 03 rH bl .^1 c3 0. 03 > O a 03 ? ^5 >> Ol M >-. mxi oT > 73 f^ ^ != ■o '"' rt 43 -( bC o C b 03 o« OCEANOGRAPHIC INFORMATION FOR SUBMARINE CABLES 1051 that it be compiled, evaluated, and culled with due regard for the sources, inherent errors, and possible misinterpretations. The data remaining after this type of review can then be combined with other knowledge from the earth sciences to provide the best available maps and profiles. 2.2 Instrumentation for Topographic Studies 2.2.1 Navigation Celestial navigation, depending on hand sextant sights of heavenly bodies and subsequent solution of an astronomical triangle, is the only method available in all parts of the world. It is, of course, useless during periods of poor visibility. Positional accuracy of ±| mile can be obtained, although the usual accuracy is ±2 to 5 miles. During the interval between sights, an estimated position is computed by dead-reckoning methods, assuming the ship's speed and course to be known. Speed determined by propeller revolutions or by a pitometer log is subject to the influence of winds, seas, and currents. The ship's heading is indicated by compass, but the course actually traveled by the vessel is affected by all the same variables that affect the speed. Starting from a celestial or radio fix, a good navigator can plot a dead-reckoning track with little error over short periods of time under ideal conditions. The probable error increases rapidly with elapsed time under less than ideal conditions. Some of the existing radio navigational systems and their limitations are listed in Table I. 2.2.2 Echo Sounding Errors and Corrections Present-day echo sounders, operating with a total beam angle of about 60 degrees, indicate the chstance to the best reflectors within the effective cone of sound. Neglecting scattering layers, which can usually be eliminated from consideration by interpretation, the best reflector will coincide with the bottom immediately below the transducer if the bottom is horizontal or if the highest point on the bottom is immediately below the transducer. Under any other condition the echo sounder indicates less than the true depth. Where the bottom is very une\'en or rocky, a multiplicity of echoes are returned and recorded. These considerations necessitate careful evaluation of the data and its correction for slope. Since the echo soimder actually measures the time interval between transmission of a pulse and receipt of an echo, the timing mechanism 1052 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBEK 1957 is the heart of the indicating and recording equipment. However, many types of echo sounders have poor timing mechanisms which depend upon mechanical governors, poorly regulated AC power supplies, and friction drives. Recently, a Precision Depth Recorder (FDR) havmg an instrument accuracy of better than one fathom in 3,000 has been de- veloped.^ The equipment is used with standard deep-sea sounding equip- ment. This PDR will perform the timing function with an accuracy bet- ter than one part in a million. After obtaining a record of the time between the outgoing and re- ceived pulses the data must be converted to depth, employing velocity corrections and slope corrections. True sound velocity is obtained by SURFACE SEA BOTTOM-' Fig. 1 — Slope correction of echo soundings. reference to tables, or by computation based on simultaneous sea water temperature and salinity measurements. The distance traveled by the echo, obtained from the velocity-corrected data, is converted to depth by the slope correction. The PDR sends out a ping and records an echo once each second. If the sounding vessel is under way at 10 knots, the individual soundings are about 17 feet apart. When the outgoing ping exactly coincides with the returning echo, a gating circuit reduces the frequency of soundings to once in 2 seconds corresponding to a spacing of about 34 feet at 10 knots. Fig. 1 illustrates the proljlem of slope correction on an ideal slope, where the ship is steaming at right angles to the slope. At sounding position A, the echo is returned from B, the nearest point on the bottom. On the uncorrected profile, this would be interpreted as a vertical sound- ing AC. To obtain the true vertical depth at A, an amount CD must OCEANOGRAPHIC INFORMATION FOR SUBMARINE CABLES 1053 be added to the depth read from the echo trace. This is done graphically by swinging arcs representing the echo distances, using the cUstance between soundings as the arc center spacings. The envelope of a suc- cession of such arcs is the best approximation to the actual bottom con- figuration that can be made. This method, of course, reciuires that the sounding track l^e run approximately at right angles to the slope, and thus, that the trend of the topography be determined. In addition, when the relief becomes more complicated, constructing and interpreting the en^■elope becomes much more difficult. Although all hills are shown on echograms, small \'alleys are often completely missed because their width is much less than the breadth of the cone of sound. This problem is partly eliminated by the use of a PDR, where second echoes indicate the exist- ence of valleys not recognized on standard echo sounders. Fig. 2 (a) shows the trace made by a PDR in passing over a rugged slope in mid- Atlantic. The multiple echo on the left hand side of the figure illustrates how echoes from the wide sound cone are returned from different parts of a steep slope. Similarl}^, the multiple echoes in the center show a deep valley with energy from the same pulse reflected from the steep slopes as well as the bottom. Fig. 2 (b) shows a corrected profile constructed from the echogram illustrated in Fig. 2 (a), and Fig. 2 (c) is a profile of the same track with 40: 1 vertical exaggeration, which is typically used in describing bottom topography. To construct a profile and interpret each sounding taken would re- quire a prohibitive amount of work. Thus, in preparing contours and uncorrected profiles for ordinary mapping purposes, a sufficient number of the initial echoes are taken to allow a reasonably accurate profile to be constructed. Where 1 : 1 corrected profiles are required, all the echoes are used and the best possible envelope representing the bottom is constructed. 2.3 CHARACTERISTICS OF AVAILABLE INFORMATION 2.3.1 Sources of Data The \-ast majority of data for a study of submarine topograph}^ are obtained as a series of "soundings," or depths below sea level.* Prior to the development of echo sounding apparatus, soundings were made by measuring the length of either a weighted piano wire or hemp line which was lowered to the bottom. This method of line or wire sounding * Features to be studied by detailed soundings can often be located by measure- ments of the earth's magnetic and gravitational fields and by acoustic methods. o o <\l II Mii6^il3A5 sa^^ 1 rt u .^ G ;3 00 C ^^ "^ — . ^-^ o ■7. ° 5 3 -^ ■7-73-- C £ 0 ^^ 4) 03 73 — - I- I s tJD-G j^ -, » - '»' X c3 I ^ :3 0 CD'S 0 £ O 03 t- •So--; ■> M •- «-^ii-= - Q^Pi r/^ -u +- ' q; ' x ^H c; -1 ^0 S i:"*^ S •• S 0 tjtCN C rt 0 0 C • 0 2 ?^C^.H i; Qj I)-- 0 r. 0 3 by 24 in al lines ntervals ith no ve with . (c) Pro tion plo aes show c miles izont iiom i file w ation slope ggera t ech *. 0 - J w t< l^ 13 X ^ J- — o J o o SlMOHIVd Nl Hidaa 1054 OCEANOGRAPHIC INFORMATION FOR SUBMARINE CABLES 1055 was fraught with error because there was no adequate sensing device to indicate when the bottom was reached, and because the sounding line might be swept far from a true vertical by the action of currents between the surface and the bottom. These difficulties could cause errors as great as 50 per cent. Echo sounding was thus a tremendous improvement despite its own inherent inaccuracies. Ocean bottom soundings are available from a number of sources including, in this country, government agencies such as the Navy's Hydrographic Office and the U. S. Coast and Geodetic Survey, and private oceanographic institutions. Abroad, national hydrographic offices, such as the British Admiralty's Hydrographic Department, the Japanese Hydrographic Office, and the International Hydrographic Bureau, collect and publish soundings. Depending upon the organization which compiles the soundings, various corrections are applied to the raw data, each organization selecting both the corrections it wishes to apply and the method of application. If all soundings for an area off the continental shelf of the United States were compiled, there might be available soundings in feet, corrected for velocity, supplied by the U. S. Coast and Geodetic Survey; uncorrected soundings in fathoms supplied by the U. S. Navy Hydrographic Office; similar soundings supplied by Lamont Geological Observatory; corrected soundings in fathoms supplied by the British Admiralty; and corrected soundings in meters supplied by the Inter- national Hydrographic Bureau. In addition, there would be a quantity of hemp, wire and discrete echo soundings on published charts. One difficulty in using the soundings printed on the published charts arises from the fact that hemp line, wire, and echo soundings of all types, both corrected and uncorrected, are all plotted on the same chart usually without designation as to method or corrections. Table II summarizes the methods of presenting sounding data used by various agencies. Several methods of recording continuous depth records are used. The most common, and least satisfactory, is to read the echo sounder and plot the sounding at the appropriate point on the chart at discrete intervals, say every 10 or 20 minutes. This achieves an orderliness in printing but has the disadvantage that canyons, mountains, or other features which cannot be adequately represented by such spacing are ignored and obscured in the plotted soundings. Better results are ol)- tained by use of the "texture method," where soundings are recorded at each crest, valley, or chajige of slope, and soundings at uniform time intervals are only used in ai-eas where a continuous slope extends for 1056 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 Table II — Methods of Presenting Sounding Data Source Coast and Geodetic Survey, U. S. Dept. of Com- merce Hydrographic Of- fice, U. S. Navy. . . Lamont Geological Observatory British Admiralty Hvdrographic Dept.. International Hy- drographic Bu- reau Japanese Hydro- graphic Office ... Depth Units Fathoms Fathoms Fathoms Fathoms Meters Meters Sounding Velocity 820 or 800 fm/sec 800 fm/sec 800 fm/sec 820 fm/sec Note D 1500 meters /sec Velocity Correction Note A No No — Note E Yes — Note C Yes ? Slope Correction NoteB No No — Note E No Note D ? 1. All agencies use Mercator projection charts. 2. All deep sea soundings on 4" = 1° longitude charts; various larger scales used near shore. A. use & GS usually makes velocitj^ correction according to data taken at time of sounding. B. use & GS makes slope and drift corrections where deemed necessary. C. Admiralty data velocity corrections are made according to D. J. Matthews.* D. International Hydrographic Bureau takes no data of its own, but publishes data received from various surveyors. E. Although corrections are made in surveys of specific areas, soundings are first compiled in uncorrected form. many miles. This produces an uneven spacing of numbers on the chart, and in some areas the soundings have to be crowded together to show all crests and valleys. In this method the sounding is written alongside a dot which represents the location of the soimding. Another method is to write the sounding without a dot but centered over the place where the sounding was taken. This produces a more pleasing drawing but all detail must be left out in complicated areas since the physical size of the letters limits the number of soundings that can be so recorded on the chart. 2.3.2 Methods of Evaluation Evaluation of topographic data starts with a comparison of data | from all the different sources, with all the soundings plotted to the same scale on one set of charts. Soundings from different sources must be reduced to a common base. When the soundings from all sources are compiled on the same sheet, many ob\-ious discrepancies will be noted. A great number of these OCEAXOGRAPHIC INFORMATION FOR SUBMARINE CABLES 1057 cases can be traced to either gross mistakes in plotting or poor accuracy in na\'igation which may cause errors in position of up to 25 miles. Usuall3' these gross errors are fairly easy to spot. For example, a large shoal area was shown for many years in deep water east of Georgia, but it now appears that this particular shoal resulted from the misplotting, by one-half degree of longitude, of a series of continental shelf soundings. Lines of soundings from different sources should indicate the same depth at their intersections, providing a check on the reliability of both or an indication that one or both is suspect. Where there is lack of agreement the sounding and navigational methods should be checked in an effort to find a basis for choosing one set of soundings rather than the other. However, without special knowledge about the individual sounding lines, it is often impossible to decide which line is correct. I'ncertainties of 2 to 25 miles in position combined with possible errors in depth determination of 10 per cent and possible gross errors in plotting are indicative of the difficulties that may be encountered. The extent of the coverage of the Atlantic Ocean with precision sound- ing tracks is shown on Fig. 3. Sounding tracks taken by the Lamont staff prior to the availability of the PDR are shown on Fig. 4. 2.3.3 Methods of Presentation Relief is usually indicated on maps and charts by any one of a number of devices, including contour lines, profile views, and physiographic sketches. In contouring, after surveying a number of control points and obtaining their exact elevations, the land surveyor sketches in the con- tour lines between control points while standing on a ^'antage point such that he can actually see the terrain. In contrast, the oceanographer must sketch contour lines by applying his own interpretation of the submarine processes responsible for the relief in the areas between soundings. The accuracy of contour is, of course, determined by both the number, spac- ing, and accuracy of the soundings, and the skill and knowledge of the oceanographer. The International H3^drographic Bureau in Monaco publishes a colored contour chart for the entire world on a scale of 1 : 10 million, individual sheets of which are revised and republi-shed at 10-25 year intervals. Profiles, or elevation views along particular tracks, provide a detailed outline of the bottom. The usual practice is to construct exaggerated profiles (-40:1 or greater vertical to horizontal scale ratio), such as those illustrated in Figs. 2(c) and 5. Where accuracy of the highest order 1058 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 I 1— I I ^ 03 c3 -a o • I— I u 0) a c o o o c3 (4-1 "a S 03 > X! (- I 7' I I _LIGHT ■ I SOURCE -I I I I -f-SWITCH 3' 3*--^ — SPRING iV ARFA OF -^t^ /iLra'' ^.j ^^ ( AREA OF PHOTOGRAPH — >T<- -4-3"-- -^ CONTACT PLATE Fig. 11 — Diagram of miilti])lo-shot uiidorwalor camera taking a bottom picttire. 1070 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 Television is being used in shallow waters by various organizations. However, picture resolution is poorer than that obtained photographi- cally, and nothing has been done in depths greater than 110 fathoms. Physical sampling is accomplished by corers, grab samplers, and rock dredgers. Earliest samples were obtained by "arming" a sounding lead with tallow, to which some of the bottom sediment would adhere. Coring is the most important source of bottom composition data. Specimens up to 70 feet in length are obtained by dropping a weighted tube vertically into the bottom sediments. About 1,200 sediment cores have been ob- tained in the Atlantic. The locations of most of these stations are shown in Fig. 10. Rock dredging has produced much evidence on the nature of the continental slope, the Mid-Atlantic Ridge, and on the various sea- mounts. Lamont's rock dredge stations are shown in Fig. 10. Not shown are a large number taken by French workers off the Bay of Biscay and off Georges Banks. Sounding data can provide a wealth of detail in addition to the depth if an experienced operator evaluates the fathogram. The least skilled operator can differentiate between rough and smooth bottoms, while the most experienced can interpret a fathogram in terms of bottom smooth- ness, sediment thickness, and the location of interfaces in the sediment. 3.2 Present Knowledge 3.2.1 General Characteristics Navigation charts sometimes include a short notation alongside a sounding, indicating the type of bottom, ranging from common terms such as sand, mud, or ooze, through the less familiar foraminifera or globigerina ooze (shells of microscopic marine life). These notations are most abundant in shallow coastal waters where they provide informa- tion for piloting and anchorages. In the less frecjuented depths, bottom notations on navigation charts are very rare — charts of bottom sediments commonly published are based on sparse and incomplete data and, as a result, are generalized. Deep sea sediments have been divided into two main classes, terrig- enous and pelagic. Terrigenous sediments are those derived from the erosion of the land and are found adjacent to the land masses, while the pelagic deposits are found in the deep sea and are distinguished as either organic ooze or inorganic clay. The organic oozes are composed princi- pally of fossil remains of planktonic animals. Distribution of types of sediment is by no means static. Such factors as deposition by turbidity currents, land slides or slumps, bottom scour by ocean currents, and climatic changes continually cause changes. OCEANOGRAPHIC INFORMATION FOR SUBMARINE CABLES 1071 3.2.2 Sediment Densities Quite accurate density determination can be made by laboratory analysis of sediment from core tubes. Densities of 1.35 to 1.55 gm/cc are characteristic of the gray and red clays which cover most of the deeper parts of the ocean. The globigerina oozes which are abundant on the Mid-Atlantic ridge have densities from 1.60 to 1.75 gm/cc. Sand layers which maj^ occur in abyssal plains at or near the sediment surface range in density from 1.65 to 2.00 gm/cc. An increase in density as a function of depth in the core would be expected. However, after an initial increase in the first 1 or 2 meters the density usually fails to show further regular increase in cores up to 10 meters in length, and deep in the core the density often falls to within 0.1 gm/cc of the initial value. The sediment averages about 300 fathoms in thickness over the deep ocean floor, except for the bare rock surfaces on the steeper parts of the continental slopes and submarine peaks where sediment is thin or absent. Thicknesses exceeding 100 fathoms may be reached on the continental rises. Fig. 12 — Continental -shelf photographs taken off Cape Cod. Each pho- tograph shows an area of approximately 2.4 ft by 3.3 ft. Dials are compas- ses. Tassel beneath dial indicates current. Note small ripple marks in left photograph. Depths : 64 and 54 fathoms, respectively. 1072 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 Fig. 13 — Continental-slope photograph taken at 550-fathom depth at 44°43'N, 54°30'W. Area shown in each photograph in Figs. 13-16 is about 40 square feet. 3.2.3 The Bottom in the North Atlantic The continental shelf at depths less than about 70 fathoms was dry land for a considerable period prior to 11,000 years ago. Thus, the sedi- ments of the continental shelf resembled the sediments of the coastal plain from Cape Hatteras to Cape Cod. A deposit of sand continues along the shelf edge and is generally thought to be an old beach. Land- ward of this is a series of irregularities generally considered to be old dunes and beaches. Photographs of the continental shelf are shown in Fig. 12. Hardened sandstones and limestone have been recovered from the walls of submarine canyons off Georges, Browns and Banquero Banks. A rock outcrop has been photographed at a depth of 500 fathoms in a small gully south of Block Island. In other areas the continental slope is covered with low-density gray clay in which the coring rig completely buries itself. Gravel and sand form the floors of some continental slope canyons while others are deeply covered with low density mud. In many areas ancient, partly consolidated clay crops out on canyon walls. The Western Union Company, when plowing in their continental- slope cables, had widely different experience along closely parallel cables. '^ Presumably the differences in the depth to which the plow would penetrate were due to differences between ancient and recent compaction of sediments. Although rock was probably not en(^ountered on these runs, it is known from dredging experience that rock can be expected. A photograph (Fig. 13) of the bottom at 550 fathoms depth south of the Grand Banks reveals huge ripple marks. It is not difficult to imagine that cable chafe would be appreciable in such an area. Beneath the nearly flat abyssal plains alternate layers of sand, silt, OCEANOGRAPHIC INFORMATION FOR SUBMARINE CABLES 1073 and red clay make up the approximately 300 fathoms of sediment. A photograph (Fig. 14) .shows the bottom at a depth of 3,000 fathoms in the abyssal hills. This remarkable shot .shows ball-shaped objects that have been identified as mangane.se nodules. The most interesting feature of this photo is the scour marks around the objects, implying an ap- preciable current at a depth of 3,000 fathoms. Seamounts present extremely varied conditions. Rocks, from crystal- line basalt through hardened limestone to soft marl, are encountered. Sediments, including sticky ancient formations, deep sea oozes, and shell sand are found. Photographs show all types from tranquil mud bottom through wave-rippled silt and sand to craggy rock. Some of these types are illustrated in Fig. 15. The flanks of the Mid-Atlantic Ridge are areas of irregular topog- raphy. The steeper .slopes are probably bare rock and the sediment removed from these .slopes probably is deposited in the intermountain basins. Cores are usually of globigerina ooze, but the different rates of sedimentation on steep slopes and on basin floors cause changes in thick- ness of sediment and relatively great changes in physical properties over short distances. The deeper flanks of the ridge are covered by red clay. A very similar bottom is found on the Bermuda Rise. Fig. 14 57°22'W. Abyssal-liills photograph taken at 3,190-fatliom depth at 29°17'X, 107-1 THE BELL SYSTEM TECHNICAL JOUKNAL, SEPTEMBER 1957 Fig. 15 — Seamount photographs taken near summit of seamount on Bermuda Rise at 34°38'N, 56°53'W at depth of 1,370 fathoms. The two photos were taken about 100 feet apart, indicating the rapid alternation of ooze and rock bottom over short distances. The crest of the Mid-Atlantic Ridge is similar, as a bottom type, to j the seamounts previously described. Dredge hauls have brought up | mostly basalt, although a few fragments of limestone have also been | retrieved. The photographs shown in Fig. 16 were taken about 60 feet ' apart on the Mid-Atlantic Ridge. They illustrate a change from smooth to rocky conditions in this short distance. Fig. 16 — Mid-AtLantic Ridge photographs (1,500-fathom depth at 48°30'N, 28°48'W). The two pictures were taken about 60 feet apart. Out of 60 photographs taken at simihir intervals in this location three were similar to that on the left and the remainder resembled that on the right. The dark l)and in the right-hand pic- ture is probably composed of gravel and sand of the dark-colored rock of the peaks, while the white underlying layer is clay or ooze. The dark bantl was produced by a current which swept the dark material over the light-colored material. OCEANOGRAPHIC INFORMATION FOR SUBMARINE CABLES 1075 IV. TEMPERATURES* 4.1 General The temperature of a given point on the deep sea floor is determined by the system of ocean circulation. Study of deep sea circulation is still in an early stage and theories which would permit prediction of changes are still in a rudimentary form. In addition, observations of actual bot- tom temperature are few. Thus, a study of the temperature environment of submarine cables must proceed by evaluating those data that exist and striving for increased understanding of the underljdng circulation processes. The new electronic thermometer under development at the Lament Geological Observator}^ determines temperature with an accuracy of 0.01 °C by the frequency of an oscillator employing thermistors in an RC network. The oscillator is lowered on the end of a cable and its fre- quency is monitored by equipment installed aboard ship. Bottom-temperature changes might be predicted if the rate and direc- tion of circulation of the sea water could be determined. This is being studied by sonar tracking of a submerged blimp designed so that it has negative buoyancy at the surface but is neutrally buoyant at the level where the measurement is desired. This method has been used down to depths of 3,000 meters. Results have indicated much higher velocities than hitherto suspected. Near the base of the continental slope off the eastern United States near-bottom currents of -g- knot have recently been observed by this method. Another method depends on the measurement of the time elapsed since a given water mass was at the surface by radiocarbon dating of sea-water samples. At the surface, water is in free exchange with the atmosphere and acquires a radiocarbon concentration in equilibrium with that of the atmosphere. As the water sinks from the surface to enter the deep sea circulation system, it is cut off from the supply of fresh radiocarbon, and radioactive decay reduces the content of Carbon 1-1 at a rate given by its half life. Thus, the measurement of the radiocarbon content of a given sea water sample ideallj^ will give the time at which this sample left the surface of the ocean. * In this section dealing with temperature, depths are given in meters rather than in fathoms. Temperature has largely been of interest in physical oceanog- raphy where volume is of concern. This has led to the vise of meters. Since a nauti- cal mile is approximately 1,000 fathoms, the fathom has been widely used in topo- graphic work. One fathom equals approximately two meters. 107G THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 4.2 Characteristics of Available Information 4.2.1 Sources of Data Observations of temperature in the deep sea were first made in the mid-nineteenth century. The early observations were made with crude instruments and are now of purely historical value. The Challenger expedition of 1872-1876 made several hundred observations but with maximum-minimum thermometers unprotected from pressure. In the late nineteenth century the Richter reversing thermometer was invented and by the turn of the century they were used by nearly all scientific expeditions. Cable ships have taken many observations but almost al- ways with maximum-minimum thermometers. Major expeditions have published volumes which included tabulated lists of temperature, salinity, oxygen, etc., for each station occupied, while the shorter expeditions and those institutions which continually collect oceanographic data in the North Atlantic publish their observa- tions in the "Bulletin Hydrographique," a journal published by the International Commission for the Exploration of the Sea, Copenhagen. In addition, unpublished data are available from the files of oceano- graphic institutions. Expedition reports give estimates of the reliability and accuracy of' their data and usually describe the calibration tests used to determine ' the accuracy. The "Bulletin Hydrographiciue" merely publishes the data: without comment. The scarcity of data and the tendency to systematic errors in single sets of data coupled with the temperature changes now. being demonstrated for deep ocean water masses tend to frustrate efforts to evaluate the accuracy of data. 4.2.2 Methods of Evaluation Evaluation of temperature data involves comparison of nearby obser-^ vations, verification of the original data sheet, and checking for errors in computation. The calibration of the thermometers is ordinarily done with great care, and observations are generally accurate to ±.05°C. When the thermometer fails to function properly, the temperature is usually so far off that the observation is not reported. The main error comes in the determination of depth of observations. The length of wire paid out to reach a stated depth varies with the magnitude of winds and currents in the area. On early expeditions this led to large errors in observation. The use of two thermometers, one in a pressure case and one unprotected from pressure, allows the calculation of depth of obser- vations with relatively great accuracy. OCEANOGRAPHIC INFORMATION FOR SUBMARINE CABLES 1077 One method of understanding temperature changes is to consider the movement of the water masses. These movements depend on density gradients which are directly dependent on the sahnity and temperature. This type of study is apphcable in shallow water where circulation of the surface layers is brisk. For the deep sea, however, dynamic calculations are ambiguous; different investigators ushig the same data not only arrive at different values for velocity but often arrive at opposite direc- tions of flow. Thus, continuity considerations and the conservation of volume are the primary factors in studies of the deep-water circulation. It is important when evaluating temperature data and studying tem- perature change and rate of bottom water circulation to study the entire process and not be limited to temperature observations, even though the temperature is the desired final answer. 4.3 Temperature in the North Atlantic 4.3.1 General Ocean-bottom temperatures in shallow water (less than 200 meters deep) are affected by seasonal air temperatures and movements of local masses of water. Thus, each specific area exhibits its own pattern of temperature changes. Data are fairly abundant in shallow water areas, so that despite the large and often erratic changes, it is generally pos- sible to determine roughly the bottom-temperature cycle from existing data. However, the local nature of the phenomena makes it desirable to concentrate any detailed studies on areas of immediate interest rather than to attempt broad generalizations. In deep water (depth greater than 200 meters) bottom temperatures and their variations result from large-scale, oceanwide topographical and \ circulation phenomena. At the same time, the paucity of data makes an analysis of any particular locale quite difficult. Thus, a general study of deep-water bottom temperatures in the North Atlantic presents the best hope of obtaining at least some useful data. 4.3.2 Shallow Water (Depth less than 200 Meters) In many shallow-water areas near shore (depth less than 50 meters) there are predictable seasonal chang(\s in temperatuio of the order of 10°C. In harbors and bays where interchange with open ocean water is restricted the seasonal temperature cur\'e will approximate the seasonal air-temperature curves except that the amplitude of the sea bottom temperature changes will be smaller and the peaks and troughs will be 1078 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 slightly retarded. In the open water of the continental shelf there is often a strong stratification of water masses and the vernal cycle is either strongly retarded (by several months) or completely obscured. On the open shelf the bottom-temperature cycle is controlled by shifting currents and wedges of water which flow in along the bottom from the open ocean. In some areas these changes go through essentially the same cycle each year. The Irish Sea and the continental shelf west of Scotland are areas where the cycle is so regular that one can safely predict the bottom temperature for a given month within an accuracy of ±1.5-2°C. On the other hand, the bottom temperature on the Grand Banks changes radically from day to day and week to week. It is possible to show that on the Grand Banks summer temperatures are on an average 2° colder than winter bottom temperatures. The day-to- day temperature changes can amount to 5°C or more. In one particularly well-studied area off Halifax, Nova Scotia, an in- teresting complication has been discovered. In this 10,000-sciuare mile area the bottom temperatures had been studied for about twenty-five years, observations having been taken at different times of the year. The bottom temperature was considered known to 1°C. It has more recently been found that on occasion, the 8°C water is displaced upward by an underflow (incursion) of 2°C water which suddenly lowers the bottom temperature by 6°C. However, after a few weeks the bottom temperature again approaches the usual value of 8°C. Such incursions of contrasting water (both cold and warm) from the open ocean are as yet only partially understood. The maximum amplitude of temperature changes in bays and near shore areas of both seasonal and erratic nature often approaches 20°C. On the outer shelves 8°C would be the maximum change expected. It is now well established that the average temperature over wide areas in the North Atlantic has undergone a gradual increase for the past one hundred and fifty years. The average bottom temperature on the Nova Scotian shelf increased 2°C between the early and mid-nine- teen thirties and the late nineteen forties. Similar changes have beeni reported for the area near Iceland. At present, no sure way of predicting! the future longterm changes of temperature is available. Changes of 1° per decade may be experienced. 4.3.3 Dee/p Water {Depth more than 200 Meters) A search was made for all deep sea temperature measurements taken with accurate thermometers in depths greater than 2,000 meters, from I OCEANOGRAPHIC INFORMATION FOR SUBMARINE CABLES 1079 70 60 60 40 30 20 10 "T" OB o o o oo > fV-^ '='^ v.". • NEAR-BOTTOM TEMPERATURE MEASUREMENTS WITHIN 100 METERS OF BOTTOM IN DEPTHS GREATER THAN 2000 METERS o DEEP-WATER TEMPERATURE MEASUREMENTS IN DEPTHS GREATER THAN 2000 METERS /■ 60 30 20 10 1 1" — Accvirate (leep-wuter temperature measurements in depths greater than 2,000 s. Points marked by solid circles indicate observations within 100 meters of the bottom. the Equator to the Icelaud-Faeroe-Greenland Ridge (which divides the Atlantic Ocean from the Norwegian Sea). Approximately 600 observa- tions (Fig. 17) were found after a search of all data up to 1950 and much of the data up to 1954. (The "Bulletin Hydrographique" is 5 to 6 years behind in publication.) Since the temperature at intermediate depths is of interest to the cable engineer onl}^ to the extent that he can use it to determine l^ottom temperatures, the observations in depths greater than 2,000 meters which lay within 100 meters of the bottom were sorted out. Only about 150 observations (Fig. 17) were found in this 1080 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 1000 2000 a: '^ 3000 UJ 5 4000 Q. a 5000 6000 / 1^ _^ / , 1-NEAR GREENLAND 2-OFF RECIFE 3-OFF NATAL 4- OFF SURINAM 5- OFF BARBADOS 6- OFF MOROCCO ^ BOTTOM / / 4 7 f 6 Lh- ■ — -, 012345678 TEMPERATURE IN DEGREES CENTIGRADE Fig. 18 — Deep-sea temperature gradients. Mean gradient in the sediments is indicated by the dashed line. category and most of these were either between Greenland and Labrador or near the Equator. The number of actual bottom observations is limited by inability to determine when the bottom was reached and a reluctance on the part of observers to risk losing expensive equipment by having it snagged on the bottom. At the present time there are insufficient data or knowledge of the | mechanism involved to permit reliable extrapolation of bottom temper- i atures from a series of mid-depth observations. Fig. 18 illustrates the- problem. Here are six different near-bottom gradients observed in dif- ferent parts of the Atlantic. Assuming these gradients terminated 500 . meters above the bottom (as do many of the observed data), it is ap-j parent that extrapolating such data to the bottom is not feasible. ]\Ieas- '< urements of gradients to the bottom at stations for which near-bottom data exist, coupled with a knowledge of the processes causing the gra- j client, may make it possible in the future to make use of manj^ of the old mid-depth observations in studying bottom temperature. From the compilation of available data, the three profiles (Figs. 20- 22) whose locations are shown in Fig. 19 were prepared. More recent studies indicating that deep water temperatiu'es may vary a few tenths of a degree Centigrade with time make it probable that some of the ripples in the isotherms are not real but instead reflect the fact that the data were taken at widely different times. The data for Profile 1 were OCEANOGRAPHIC INFORMATION FOR SUBMARINE CABLES 1081 taken in the same year and do not show these effects. The large fluc- tuation on Profile 3 is probably due to variations with time. At a certain depth, often about 1,200 meters, a sharp change in tem- perature takes place. An interface known as the main thermocline separates the warm surface waters from the cold (2°-4°C) deep water. This boundary shifts slightly from time to time and is affected by sub- surface (internal) tidal waves. Thus, cable laid near the main thermo- cline may undergo temperature changes of a few degrees. These changes may be of different periods depending on their causes, e.g., subsurface waves, seasonal changes, or long term changes in ocean regime. It is not known if a long-term change in depth of the thermocline has occurred but such change seems probable. The greatest percentage of any transatlantic cable route lies in depths ! greater than 2,000 meters and thus the temperature changes in the I deep sea are of primary importance to the engineering of a cable. The I temperatures are low, averaging 3°C, and the temperature changes are Fig. 19 — Positions of Temperature Profiles 1, 2, and 3. o o z o a LU o < X 5 o CO (N OS o n o3 Sh ■ r-t O o CQ o3 O w 03 o y3 o Oh o o o o o o o o o o "- f\J (O sa3l^^N ni Hidaa 1082 o o z g cc LU 0) o < LU < o I- cr LU > o3 > Sfcl3i3l^ Nl Hld3a saaiakN ni Hidaa c3 Q '-3 d O CC a> 5b o CO 5 5 O o u 1083 til a. O a t\j- :] o :] r\ I — ' ^=N: H 1- h o o o o o o o o o o o o o o o o o o o o () o C5 <> o o o o o o o o o o o o o *" w <^ ^ >n (0 OJ n ^ in vW<.%\ HILLS AND MOUNTAINS. BERMUDA RISE, WESTERN FOOTHILLS OF THE MID-ATLANTIC RIDGE Fig. 26 — The 1929 Grand Banks turbidity current. OCEANOGRAPHIC INFORMATION FOR SUBMARINE CABLES 1091 barriers. The arrows show some modern turbidity currents which have been documented through the breakage of telegraph cables. This chart is not yet complete and it is expected that many more arrows can be added, each representing one or more currents, and some representing as many as 20 documented cases. Areas which have experienced turbidity current flows in the past can be determined by a careful study of the nature of the bottom. From a study of sediments and topography of areas along a proposed route it is possible to delimit areas where turbidity current could and could not Fig. 27 — Cable breaks in the submarine canyons off the Magdalena River, Colombia, South America. 1092 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 OCEANOGRAPHIC INFORMATION FOR SUBMARINE CABLES 1093 occur, and in some cases to outline areas where they occur at frequent intervals. If, after the completion of such a study, it is decided to take the risk of laying a cable across a dangerous area and at a later date a turbidity current does occur, it will be possible to predict the length of cable to be replaced under various conditions. VI. CONCLUSIONS The application of the rapidly developing science of oceanograph}- to the development and engineering of submarine cable systems will per- mit refinements in design, cable placing techniques, route selection, and repair operations. Existing knowledge, when evaluated and codified, pro- vides many useful data for immediate application. Continuing study of topography, the nature of the bottom, causes of cable failures, and deep sea circulation will permit further advances in the engineering of sub- marine cable systems. It is to be expected that the value and usefulness of submarine cable oceanographic studies will be substantially extended as geologic and oceanographic researchers broaden the understanding of the natural laws and processes which govern and produce the ocean- bottom environment. Through such knowledge, the data of many fields can be coordinated, permitting better explanation of past events and more accurate prediction of future conditions. ACKNOWLEDGEMENTS The authors wish to acknowledge the contributions of Marie Tharp, W. Fedukowicz, and H. Foster of Lamont Geological Observatory, and A. L. Hale and H. W. Anson of Bell Telephone Laboratories. The en- couragement and guidance of Dr. Maurice Ewing has been of great value. REFERENCES 1. E. E. Zajac, Dynamics and Kinematics of Laving and Recovery of Submarine Cable, pp. 1129-1208, this issue._ 2. L. R. Snoke, Resistance of Organic Materials and Cable Structure to Marine Biological Attack, pp. 1095-1128, this issue. 3. B. Luskin, B. C. Heezen, M. Ewing, and M. Landisman, Precision Measurement of Ocean Depth, Deep-Sea Research, 1, pp. 131-140, April, 1954. 4. D.J. Matthews, Tables of the Velocity of Sound in Pure Water and Sea Water for Use in Echo Sounding and Sound Ranging. Admiralty, London, 1939. 5. C. S. Lawton, The Submarine Cable Plow, A.LE.E. trans., 58, p. 685, 1939. 6. B. C. Heezen and M. Ewing, Turbidity Currents and Submarine Slumps, and the 1929 Grand Banks Earthquake, American Journal of Science, 250, pp. 849-873, Dec, 1952. 7. B. C. Heezen and AL Ewing, Orleansville Earthquake and Turbidity Currents, Bull. Am. Assoc. Petroleum Geologists, 39, pp. 2505-2514, Dec, 1955. Resistance of Organic Materials and Cable Structures to Marine Biological Attack By LLOYD R. SNOKE (Manuscript received June 6, 1957) The increasing use of submarine telephone cable has resulted in the need for information on the performance of organic materials and cable structures under marine conditions. Recently, Bell Telephone Laboratories initi- ated a program to acquire fundamental data on the resistance of a wide range of organic materials, as well as immediately applicable engineering information. The present progress report describes the program which in- cludes accelerated, laboratory-microbiological tests, as well as the ac- quisition of data from actual marine exposures. In biochemical oxygen de- mand-type tests conducted to date polyethylene was not utilized as a carbon source by marine bacteria. Polyvinyl chloride plastics served as a source of energy for the organisms depending on the way in which the materials were plasticized. Five elastomers were utilized by the bacteria. There has been a steady rise in capacitance values for GRS-insidated conductors exposed in sea water and sediment under laboratory conditions for thirteen months. These increases appear due to biological activity on the insulation. The gen- eral performance of materials undergoing marine exposure is reported in- cluding reference to penetration of a few synthetic materials by marine borers. Brief mention is made of the examination of submarine cable samples from service. I. INTRODUCTION As a result of the increasing use of submarine telephone cable, there is a growing demand for information on the performance of organic materials and cable structures under marine conditions. Particularly im- portant is the need for data on the resistance of materials to attack by marine organisms. Although considerable published information exists on the behavior of natural organic materials such as wood, jute, hemp and the like, there is virtually no data on plastics, elastomers, casting resins or similar materials. 1095 1096 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 About three and a half years ago, the Laboratories initiated a program to determine the resistance to marine biological attack of materials which might find application in submarine cable. The program has two primary objectives: (1) acciuisition of fundamental information regarding the biological resistance of a wide range of selected organic materials, and (2) accumulation of immediately applicable engineering information on materials. II. OUTLINE OF PROGRAM It seemed evident that marine borers or microorganisms, particularly bacteria, might be expected to be the major agents of deterioi-ation. Marine borers are mollusks or crustaceans which bore into a material for food or shelter depending on the particular organism involved. Of the crustaceans, the gribble, Limnoria, is the most outstanding. Cellulose material such as wood and cordage form its food supply and natural habitat. There are a few references which suggest that members of the genus Limnoria have bored into gutta percha. One by Chilton' refers to the activity of Limnoria in the splice of a submarine cable in about 60 fathoms off New Zealand. Preece- identifies Limnoria as the organism responsible for failure of the Holyhead-Dublin cable in 1875. Jona^ states that he frequently found Limnoria in cables in the Adriatic Sea. Menzies* points out that no American species is known to occur in depths exceed- ing 50 feet; however, one species is known to occur off Japan at a depth of 163 fathoms. He suggests that the absence of wood probably limits the distribution of the animals in deep water. In the bibliography by Clapp and Kenk,^ there are ten, separate cita- tions to the attack of submarine cables by molluscan borers belonging to the family Teredinidae. In most cases, attack was confined to cellulose constituents such as jute and hemp, although in a few instances mention is made of attack on gutta percha insulation. Although the teredine borers, along with Limnoria, are considered to be relatively shallow water organisms, Roch,^ in his paper on Mediterranean teredos, refers to Teredo utricnlus being obtained from depths as great as 3500 meters. There is one reference^ to teredo attack of lead-co\'ered submarine cal)le. The other important family of boring mollusks is the Pholadidac. Members of this family are sometimes referred to as the "burrowing clams" and include rock, shell and wood borers. Some genera, such as Xylophaga, are found in water up to 1 ,000 fathoms or more deep.'' Bartsch and Rehder*^ report the penetration of the lead sheath of a sulv marine cable by one of the Martesia, another genus of the family Pholidi- RESISTANCE OF MATERIALS TO MARINE BIOLOGICAL ATTACK 1097 dae. Members of the same family were reported by Snoke and Richards^ to have bored through the lead sheath of a submarine telephone cable. The bacteria generally are single-celled organisms, a large number of which are heterotrophic, that attack organic matter and use it as a source of carbon or energy. The bacteria play an important part in the biology of the sea, their most important function being to decompose organic material into carbon dioxide, water, ammonia and minerals. The characteristics, distribution and function of the marine bacteria have been described in great detail by ZoBell.'" Bacteria are found in sea water and sediment from shallow depths to the deepest portions of the sea. During the Danish Galathea Deep-Sea Expedition from 1950 to 1952, bacteria were found in depths as great as 10,280 meters." Many of these bacteria have been found to be barophilic-^ growing exclusively or preferentially at pressures approximating 15,000 psi. ZoBell and Morita^" have reported experiments performed with these bacteria to determine the effects of high pressure on such factors as viability and enzyme production. Marine bacteria have been found capable of oxidiz- ing rubber products,^^ as well as a wide variety of gaseous, liquid and solid hydrocarbons.^'' Although evidence to date indicates that among the microorganisms, the bacteria are particularly likely agents of de- terioration in the ocean, it is possible that the fungi may also be con- tributors. Barghoorn and Linder^^ report the physiological behavior and growth on various media of seven species of marine fungi isolated from wood continuously submerged in the sea. Deschamps-" has discussed the role of fungi and bacteria in aiding the attack of wood by marine borers. Also, the occurrence of marine fungi in wood test panels, driftwood and piling in Biscayne Bay has been reported by Myers. ^^ A program designed to provide fundamental and engineering data on the susceptibility of organic materials to marine borers and microorgan- isms in an environment that covers about 70 per cent of the earth's sur- face could be almost unlimited. The practical parameters which finally were established were based on a number of considerations. Funda- mental data on the basic inertness or relative rates of attack by micro- organisms could best be determined under controlled laboratory condi- tions; however, more than one procedure would be needed to determine performance in the environments of water and sediment. Because of the relatively rapid activity of marine borers under natural conditions, and their critical requirements as far as laboratory culture is concerned, it was decided that any borer tests would be conducted in the field. This meant that the natural exposure tests would serve as correlative tests i 1098 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 for the laboratory microbiological portion of the program, as well as a means of evaluating the relative performance of materials in the physical and chemical conditions of the ocean. The integrated program, shown in Fig. 1, involves a series of three laboratory tests on the one hand, and actual marine exposure on the other. Eventually, more than fifty different materials including plastics, elastomers, natural and synthetic fibers, as well as sections of cable will be tested. The present paper is in the nature of a progress report in which only a portion of the data to be acquired are presented. The results of the program to date will be examined beginning with the laboratory experi- ments. III. LABORATORY TESTS 3.1 Biochemical Oxygen Demand Type Test The BOD (biochemical oxygen demand) type of test as applied in this study is really composed of two separate bioassay procedures. In one case, the oxygen consumed by aerobic bacteria is determined, and in the other a metabolic by-product resulting from anaerobic activity is meas- ured. With a few changes, both methods follow those which have been employed by ZoBelP^ in tests of elastomers and various natural organic materials. There is one point which should be emphasized regarding both the aerobic and anaerobic procedures used in this accelerated sea water test. It is considered primarily a screening test which provides basic data on BIOLOGICAL TEST PROGRAM LABORATORY TESTS BOO TEST MEASURE RESPIRATION OR BY-PRODUCTS OF ATTACKING ORGANISMS (WEEKS) CONDUCTOR TEST MEASURE BREAKDOWN OF DIELECTRIC (MONTHS OR YEARS) SOIL BURIAL ELECTRICAL OR PHYSICAL MEASUREMENTS (MONTHS OR YEARS] MARINE EXPOSURE I MARINE BORER TESTS WRIGHTSVILLE BEACH, N.C. DAYTONA BEACH, FLA ANALYSIS OF CABLE SAMPLES FROM SERVICE Fig. 1 — Outline of marine biological test program. RESISTANCE OF MATERIALS TO MARINE BIOLOGICAL ATTACK 1099 the abilit}^ of marine bacteria to utilize a compound as a carbon source at the time of test. It will not reflect changes brought about in the ma- terial clue to prolonged exposure in sea water, or ecological relationships which might make the material more or less susceptible to attack by certain bacteria. The other laboratory tests and natural exposure test will help furnish data on c^uestions involving changes in materials due to long-term marine exposure. Table I — Materials Tested Against Aerobic and Anaerobic Marine Bacteria Designation Polyethylene^ 2.0 melt index^ 0.2 melt index (Source A) 0.2 melt index (Source B) 0.2 melt index + 5% butj-l rubber + antioxidant 0.2 melt index + antioxidant 0.7 melt index (high den.sity) nat. + antioxidant 0.7 melt index (high density) + carbon black and antioxi- dant Poly {Vinyl Chloride^ Plasticizer Polyester A Di-2-ethylhexyl phthalate (DOP) Shore A 88 Tricresji phosphate (TCP) None (rigid) None^ None^ Tri-2-ethylhex3^1 phosphate Nitrile rubber/polyester C Di-2-ethylhexyl phthalate (DOP) Shore A 62 Nitrile rubber Polyester E/DOP (BTL 46-55) None (PVC resin) Casting Resins Epoxide (cast), unfilled straight epoxy resin cured with amine hardener Stj-rene poljester, silica-filled Elastomers^ GR-S jacket GR-A jacket Butyl jacket Natural rubber jacket Neoprene jacket Jute Type P53 10466 P5304156 P53 12587 P5308396 P5308390 P5503135 P5503133 BTL 24-54 BTL 23-54 BTL 529-53 P5503087 P5502078 P5502077 P5502081 P5502074 P5502082 P5502076 P5503115 P5510645 BTL 54-14 BTL 54-18 BTL 54-19 BTL S4-23 BTL 54-164 1 Except where noted polymers are low density grades manufactured by the high pressure process. 2 ASTM D1238 ' With the exception of P5510645 all PVC compositions contained typical or- gano-metallic type stabilizers (such as Ba, Cd, and Pb), fatty acid lubricants in low concentrations, and in some cases small quantities of inorganic fillers. '' Semi-flexible PVC copolymer. ^ These compounds all contain, in addition to the basic elastomers, sulfur, accelerators, waxes, processing oils, and reinforcing ciuantities of carbon black. (54-164 also contains clay.) 1100 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 AGED SEA WATER OCEAN BOTTOM SEDIMENT RAW SEA WATER TEST MATERIAL (a) SATURATE WITH FREE OXYGEN OR (b) REMOVE ALL FREE OXYGEN ^ ENRICHMENT CULTURE (INOCULUM) ^ TEST BOTTLE Fig. 2 — Flow chart of biochemical oxygen demand (BOD) ty-pe test. The materials which have been tested thus far by the BOD type pro- cedure include polyethylene, polyvinyl chloride plastics, casting resins, elastomers and jute. The individual materials are listed in Table I. Other plastics and elastomers are still to be tested. The general features of both the aerobic and anaerobic parts of the test procedure are shown in the flow chart in Fig. 2. Certain features of the test are common to both parts. These features will be described first. The four primary constituents of the test are aged sea water, test ma- terial, ocean bottom sediment, and raw (unaltered) sea water. Aged sea water is raw sea water which has been filtered through Millipore filters of 0.5 micron pore size, and then aged in the dark until the biochemical oxygen demand (BOD) is quite low; i.e., until the water contains about 1 ppm of organic matter. This usually requires about eight weeks of aging. In the first tests which were run, materials were finely ground so as to expose a large surface area, and so accelerate attack. However, it soon became apparent in efforts to relate the rate of oxidation to surface area exposed that only crude estimates could be made of the irregular surface areas. Consequently, after the first few tests, thin sheets of ma- terial were employed whei'ever possible so that a measured amount of surface area could be exposed in each case. The inoculum for the test comes from specially prepared enrichment cultures. Approximately 90 cc of marine sediment is placed in a 250 ml RESISTANCE OF MATERIALS TO MARINE BIOLOGICAL ATTACK 1101 prescription bottle. About 1 gram of a finely divided test material is also placed in the bottle which is then filled about three-quarters full of raw sea water. To include as heterogeneous a population of marine bacteria as possible, another inoculum is prepared for addition to the enrichment culture. The additional inoculum is made by placing in a vial a small particle of each of seven different sediments furnished by Dr. ZoBell of the Scripps Institute of Oceanography. These sediments are identified in Table II. Following this, one or two drops of liquid are added to the same vial from each of twenty-nine different enrichment cultures which also were provided by Dr. ZoBell. These cultures are identified in Table III. Transfers from eight different cultui'es of marine sulfate-reducing bacteria are included, and the vial shaken thoroughly. About five drops of pooled inoculum are added to the eniichment culture prepared for each test material. The completed enrichment cultures are incubated at 25° C for a minimum of six weeks prior to use. During the incubation period those bacteria in the culture which are capable of utilizing the test material tend to develop preferentially. The same enrichment culture is used whether the test procedure is aerobic or anaerobic since both conditions prevail in this type of enrich- ment cultiu'e — aerobic in the water and upper sediment, and anaerobic in the deeper, compacted sediment. From this point on, in describing the method used in the material tests, it is necessary to describe the aerobic and anaerobic procedures separately. In the aerobic tests, 0.01 per cent ammonium phosphate is added to sufficient sea water (usually about 7 liters) for a given test run. Oxygen is bubbled through the sea water in a carboy for a minimum of sixteen hours at which time the oxygen content of the sea water is about 25 ppm. Since as many as four or more test materials may be included in a test run, the inoculum is prepared by combining in one vial a small amount of liquid from the enrichment culture for each material to be Table II — Sources of Sediments* used in Preparing Enrichment Cultures Ref. No. Source XG 17-4 (surface) Gulf of Mex., Rockport, Texas Gulf of Mex., Miss. Delta Gulf of Mex., Rockport, Texas Gulf of Mex., Miss. Delta Pacific, 1° 22.2'N, 127° 17'W Pacific, 19°02'N, 174° 58'W Pacific, 7° 03.8'N, 126° 24.3'W 5403-1 (surface) XS-384 (surface) 5402-7 (0-5 cm) 56:180 (4520 fathoms) 56:184 (2650 fatlumis) 56:177 (4550 fathoms) * Obtained from Dr. C. ZoBell, Scripps Institute of Oceanography 1102 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 included in the run. Once in the vial, the inoculum is shaken and added to the aged sea water at the rate of 1 ml per 10 liters of medium. This amount of inoculum was calculated to give the maximum number of bacteria, consistent with a minimum addition of organic matter. The carboy is then placed under slight, positive oxygen pressure. The test is run in 60 ml glass-stoppered bottles. A small amount of test material is placed in each bottle. At the outset of the experiments, when ground material was used, this amounted to 0.05 gram, or a surface area of 4 to 45 sq cm, depending on the material. Later, when thin sheets of about 4 mils thickness were used, the samples were cut to a size of 2.54 cm square. The samples are placed in the bottles the night before, and enough aged sea water added to permit surface wetting. With many materials this seems to result in less accumulation of air bubbles on the surfaces of the materials during subsequent filling with the medium. Table III — Enrichment Cultures* Used as Supplementary Sources of Inoculum in Preparation of Enrichment Cultures for Current Program Ref. No. 34-134 34-134 .34-134 34-134 34-134 34-132 34-134 34-134 25-143 34-134 34-134 34-1.34 25-141 34-134 34-134 34-134 34-134 34-134 34-134 34-134 34-134 Description rubber in distilled water anthracene in sea water sewage outfall, rubber in sea water mixed hydrocarbons in sea water garden soil, rubber in sea water Athabaska tar sand, hydrocarbon-oxidizing bacteria and sulfate-reducers in sea water tricresol in sea water mixed hydrocarbons in sea water 0.10% phenol in sea water 0.25% phenol in sea water cork in sea water Shell oil No. 10 in sea water lignin in sea water sewage outfall, rul)ber in sea water sawdust and mud in sea water garden soil, rubber in sea water rubber in tap water mi.xed crude oil in sea water kerosene in sea water paraffin in sea water rubber in tap water Athabaska tar sand, mixed crude oil in sea water i; thiokol in sea water neoprene in sea water cellulose acetate in sea water butadiene (Buna A) in sea water pooled aerobic hydrocarbon-o.xidizing bacteria in sea water crude coal tar in sea water shellac in sea water * Obtained from Dr. C. ZoBell, Scripps Institute of Oceanography. RESISTANCE OF MATERIALS TO MARINE BIOLOGICAL ATTACK 1103 Of course, air bubbles would be a source of error in later oxygen deter- minations. Usually, sufficient test bottles are made up to provide duplicates for analysis after each period of incubation. Oxygen pressure, maintained on the sea water in the carboy, assures no loss of oxygen from the me- dium and forces it through tubing into the test bottles. Since incubation periods of 0, 1, 2, 4 and 8 weeks are used as a general guide, and two test bottles must be sacrificed for analysis after each interval, ten test bottles are used for each material. One set of ten control bottles containing only inoculated, aged sea water suffices for a test run, as long as the bottles for materials and controls are made up from the same batch of sea water and incubated at the same time. Incubation is carried out in the dark in a constant temperature water bath maintained at 20° dz 0.5°C. Incubation in the water bath minimizes the fluctuation in ox^'gen content of the sea water which might be encountered as the result of "breathing" of the bottles in atmospheric incubation. After the various incubation periods, the free oxygen content of the sea water in the bottles is deter- mined by a modified Winkler procedure. In the anaerobic portion of the test, the procedure is essentially the same as for the aerobic part, the only differences being in the prepara- tion and handling of the sea water medium, the incubation times, and the analytical method. Of course, with the anaerobic bacteria it is necessary to remove all free oxygen from the sea water medium if the organisms are to function. Consequently, instead of bubbling oxygen through the medium, the sea water is boiled for ten minutes and placed hot in a Table IV — Oxygen Consumption by Marine Bacteria IN BOD Test with Polyethylene as the Only Source of Organic Carbon Test Material- 2.0 melt index^ 0.2 melt index (Source A) 0.2 melt index (Source B) 0.2 melt index + antioxidant 0.2 melt index -j- 5% butyl rubber -|- antiox. 0.7 melt index (High Density) -f- antiox Controls (inoculated sea water) O2 Consumption .\fter Weeks of Incubation ppm 2.2 0.8 1.4 0.9 0.2 0.9 1.5 ppm 3.7 1.6 3.4 3.0 3.8 4.3 5.3 ppm 6.0 2.4 5.2 6.2 5.8 7.4 8.3 8 ppm 10.2 10.9 10.8 8.5 1 9.3 11.2 ' Samples accidentally destroj-ed. - Except where noted polymers are low density grades manufactured by the high pressure process. 3 ASTM D123S 1104 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 Table V — Oxygen Consumption by Marine Bacteria in BOD Test WITH Poly(Vinyl Chloride) Plastics, Epoxide Casting Hesin OR Jute as Only Sources of Organic Carbon Test Material PVC — no plasticizer (rigid) PVC — tricresvl phosphate (TCP) PVC — di-2-ethvlhexvl phthalate (DOP) Shore A" 88 PVC — polyester A Epoxide casting resin Jute Controls (inoculated sea water) * All free O2 in sea water consumed. O2 Consumption After Weeks of Incubation 1 2 4 8 ppm ppm ppm ppm 11.1 12.9 11.6 18.7 9.5 13.2 21.6 22.2 9.1 13.4 19.7 20.7 19.3 22.2 * * — 4.1 5.1 4.2 10.0 15.0 16.5 * 6.8 6.8 7.7 7.7 carboy containing 0.01 per cent ammonium phosphate. Nitrogen is introduced into the carboy immediately. When the sea water is cool, inoculum, which is prepared as described for the aerobic procedure, is added and additional nitrogen pressure placed on the carboy for filling the test bottles. Since anaerobic activity is usually slower than aerobic, the time in test is increased. Analysis for hydrogen sulfide in the sea water is carried out at 0, 4, 8, 12 and 16 weeks. Since the sulfate-reducing bacteria are ubiquitous anaerobic marine species, the hydrogen sulfide produced by them in the course of breaking down organic material is used as an indicator of their activity. The sulfide in the sea water is de- termined volumetrically according to the method described in the Oflficial Table VI — Oxygen Consumption by Marine Bacteria in BOD Test with Poly (Vinyl Chloride) Plastics as the Only Source of Organic Carbon Plasticizer Nitrile rubber/polyester C Nitrile rubber None' None' Tri-2-ethvlhexyl phosphate Di-2-ethvlhexvl phthalate (DOP) Shore A 62 Polyester E/DOP (BTL 46-55) Controls (inoculated sea water) * All free O2 in sea water consumed. ' Semi-flexible PVC copolymer. O2 Consumption After Weeks of Incubation ppm 10.3 9.2 3.7 4.0 11.7 6.4 * 3.5 ppm 12.9 12.3 4.2 5.5 14.4 8.4 4.5 ppm 21.4 18.7 6.5 8.4 23.1 11.5 7.1 ppm * * 10.5 11.0 * * 9.7 RESISTANCE OF MATERIALS TO MARINE BIOLOGICAL ATTACK 1105 Table VII — Oxygen Consumption by Marine Bacteria in BOD Test with Polyethylene, Polyester Casting Resin or Poly- (ViNYL Chloride) Resin as Only Source of Organic Carbon Test Material Polyethylene 0.7 melt index (High Dens.) Nat. + antio.xidant Polyethylene 0.7 melt index (High Dens.) Blk Styrene polyester, silica-filled Poly(Vinjd Chloride) resin Controls (inoculated sea water) Oz Consumption After Weeks of Incubation ppm 3.1 2.9 5.5 4.2 2.5 ppm 3.3 4.1 7.0 4.1 3.8 ppm 6.1 7.1 9.3 7.3 6.7 ppm 6.5 7, 12 7 6 and Tentative Methods of Analysis of the Association of Agricultural Chemists. The results of the aerobic test procedure are presented in Tables IV to VIII inclusive. In these tables the oxygen consumption values ob- tained with materials which went through the same test run are included in the same table. The materials included in Tables IV and V, with the exception of jute, were exposed in finely ground or shaved form. Since it was not possible to obtain reliable estimates of the surface areas exposed to attack in this case, the oxygen consumption ^'alues in these tables are not directly comparable with respect to rate. The data serve the im- portant basic purpose of indicating whether these materials can serve as a source of energy for the bacteria. However, data in Tables VI to VIII inclusive are based on the use of equally thin sheets of material with about 12.9 sq cm of surface area exposed to attack. Two exceptions Table VIII — Oxygen Consumption by Marine Bacteria in BOD Test with Elastomers as the Only Source OF Organic Carbon Elastomer GR-S jacket (54-14) GR-A jacket (54-18) Butvl jacket (54-19) Natural rubber jacket (54-23) Neoprene jacket (54-164) Controls (inoculated sea water) * All free O2 in sea water consumed 0-2 Consumption After Days of Incubation 3 7 14 28 ppm ppm ppm ppm 15.8 * 6.1 10.9 23.5 * 13.9 * 14.1 * 1.9 4.1 10.3 * 0.0 -0.4 0.0 1106 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 to this are the polyvinyl chloride resin and styrene polyester in Table VII which could not be prepared in sheet form. Results for polyethylene are described in Tables IV and VII. The oxygen consumption values in these tables are almost identical to the control values obtained using only inoculated sea water. There is no evidence in any of these tests of polyethylene being utilized as a source of carbon by the bacteria. In fact, in Table IV, all of the eight week values for polyethylene are slightly below those for inoculated sea water alone. The results with the polyvinyl chloride plastics vary according to the manner in which the compounds are plasticized. The data are contained in Tables V, VI and VII. First, as may be noted in Table Yll, there is no attack on the polyvinyl chloride resin. This indicates that the sus- ceptibility of these plastics can be attributed to materials added in com- pounding. Every polyvinyl chloride plastic tested shows some evidence of attack; (distinct oxygen consumption above the control rate), ex- cept the semi-flexible copolymers which contain no added external plasticizer. In these compounds, acrylates are employed as copolymers. The most severe attack occurred on the plastic in Table Yl which con- 2 Q. 32 28 24 20 O 1 6 Z o Q. D iri Z o U 12 -' ' (\PPROX 0 2 co^ gTENn ■ AT STAR! >^ y.^^^X .^ ^ C 5 LYES E/DO TER P / / r ^ -^ / ^ J\ /^ / —fid c^ ?^ — — ■"*? 1 1 / ---< ^^ --^ ..-^ ■^ p^ CONTROL- ' INOCULATED SEA WATER 1 >i<='^ "" f ^ 3 4 5 INCUBATION TIME IN WEEKS Fig. 3 — Examples of O2 consumption by marine bacteria in BOD test with Poly (Vinyl Chloride) plastics as carbon source. RESISTANCE OF MATERIALS TO MARINE BIOLOGICAL ATTACK 1107 tains a combination of polyester E and di-2-ethylhexyl phthalate (DOP), and one in Table V plasticized with polyester A. These polj^esters are fatty acid-type compounds. Typical oxygen consumption values for three different polyvinyl chloride plastics, representing different rates of utilization by the bacteria, are plotted in Fig. 3. As noted in Table I, \ery low concentrations of organo-metallic stabilizers and fatty acid lubricants were in all the compounds tested except the resin alone. How- ever, of the three materials which contained no added external plas- ticizer only the rigid plastic is utilized. This material contained about 8 to 10 times as much fatty acid lubricant as the other two compounds. Two casting resins were tested, one an epoxide (Table V), and the other a silica-filled styrene polyester (Table VII). Under the conditions of this test, the epoxide resin is not utilized by the organisms. In the case of the styrene polyester, results are less conclusive. After eight weeks, an oxygen consumption value 5.4 ppm higher than that for the controls suggests the possibility of attack. Additional tests are planned with this material to obtain more data on which to base a final decision. . As might be expected, the jute fibers are quite susceptible to attack ; all oxygen was consumed from the test medium between the fourth and I eighth week (Table V) . The fact that results in the same test run with I the polyvinyl chloride compound plasticized with polyester A show that j all oxygen was consumed from the test medium in 17 days does not mean I that this latter compound is more susceptible to attack than jute. In I the jute, bacterial attack is necessarily restricted to a progressive surface attack, but with the polyvinyl chloride compound, leaching of the sus- Table IX — Hydrogen Sulfide Production by Marine Bacteria IN Anaerobic Sea Water Test with Polyethylene as the Only Source of Organic Carbon Test Material' 2.0 melt index2 0.2 melt index (Source A) 0.2 melt index (Source B) 0.2 melt index + antioxidant 0.2 melt index + 5% but 3d rubber -f- antiox. 0.7 melt index (High Density) -f- antiox.. . . Controls (inoculated sea water) H2S Production After Weeks of Incubation ppm 0.22 0.22 0.22 0.22 0.22 0.22 0.10 8 ppm 0.32 0.29 0.32 0.64 0.32 0.22 0.64 12 ppm 0.22 0.45 0.26 0.35 1.31 0.29 0.70 16 ppm 0.38 0.58 0.24 0.45 0.58 * Except where noted polymers are low density grades manufactured by the high pressure process. 2 ASTJM pi 238 ' Insufficient samples 1108 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 ceptible plasticizer into the sea water medium might greatly accelerate utiHzation of that material and be reflected in rapid oxygen consumption. Five different elastomers have been evaluated by the BOD test to date. The results with aerobic bacteria are presented in Table VIII. First, it is apparent that all of the elastomers tested can serve as a source of carbon for the bacteria. As may be noted in the table, GR-S jacket (54-14), butyl jacket (54-19) and natural rubber (54-23) are oxidized at about the same rate — all oxygen being consumed from the test me- dium between the third and seventh day analyses. GR-A (54-18) and neoprene jacket (53-164) are more resistant than the other three elas- tomers in the test. During the fourteen-day test period, approximately twice as much oxygen was consumed in the case of the GR-A as with the neoprene. The results of anaerobic bacterial activity, as reflected by analyses for hydrogen sulfide in the sea water medium, are contained in Tables IX to XII, inclusive. As with the results of the aerobic test, materials in a given test run are included in the same table. No polyethylene is utilized as a source of carbon by the sulfate-reducing bacteria. In no case is the production of hydrogen sulfide, with different polyethylenes Table X — Hydrogen Sulfide Production By Marine Bacteria IN Anaerobic Sea Water Test with Poly (Vinyl Chloride) Plastics, Epoxide Casting Resin, or Jute as Only Sources of Organic Carbon Test Material Poly (Vinyl Chloride) Plastics No plasticizer (rigid) Tricresyl phosphate (TCP) Di-2-ethylhexvl phthalate (DOP) Shore A 88 ^ Polyester A Nitrile rubber/polyester C Nitrile rubber No plasticizer^ No plasticizer' Tri-2-ethvlhex3d phosphate Di-2-ethylhexyl phthalate (DOP) Shore A 62 Polyester E/DOP (BTL 46-55) Epoxide casting resin Jute Controls (inoculated sea water) 1 Semi -flexible PVC copolymer H2S Production After Weeks of Incubation ppm 1.90 0.22 0.26 2.60 1.50 4.10 0.22 0.32 0.26 0.22 12.20 0.16 1.90 0.10 ppm 3.50 0.22 0.26 38.40 7.00 9.60 0.22 0.64 0.96 0.22 61.40 0.64 13.40 0.64 12 ppm 4.20 0.64 0.26 38.40 19.98 12.40 0.90 1.89 1.86 1.09 94.10 0.86 38.60 0.70 16 ppm 5.60 0.38 0.61 47.70 18.60 11.50 0.51 1.02 0.99 0.58 82.90 0.48 52.20 0.58 RESISTANCE OF MATERIALS TO MARINE BIOLOOICAL ATTACK 1109 Table XI — Hydrogen Sulfide Production by Marine Bacteria IN Anaerobic Sea Water Test with Polyethylene, Polyester Casting Resin or Poly(Vinyl Chloride) Resin as Only Sources of Carbon Test Material Polyethylene — 0.7 melt index (High Dens.) Nat. + antioxidant Polyethylene — 0.7 melt index (High Dens.) Blk. + antioxidant Silica-filled styrene polyester Poly (Vinyl Chloride) resin Controls (inoculated sea water) HjS Production After Weeks of Incubation ppm 0.35 0.26 0.83 0.48 0.45 ppm 0.58 0.48 0.83 0.58 0.86 12 ppm 0.90 0.38 1.02 0.58 0.91 16 ppm 1.12 0.74 1.02 0.58 0.91 as the test material (Tables IX and XI), significantly greater than in j the control bottles. In fact, in most cases it is actually less than that for I the controls. Four polyvinyl chloride plastics appear to have served as a source of carbon for the anaerobic organisms. In order of decreasing susceptibility they are the compounds plasticized with (1) polyester E/DOP, (2) poly- ester A, (3) nitrile rubber/polyester C, and (4) no plasticizer (rigid). Just as in the case of the aerobic procedure, the plastic plasticized with polyester E/DOP is used much more rapidly than any of the other polyvinyl chloride compounds. There is no e\'idence of attack on poly- \'inyl chloride resin, again indicating that the attack is on the plasticizers, not the polyvinyl chloride itself. In this regard, it should be pointed out again that although the polyvinyl chloride compound listed as "no plas- ticizer (rigid)" in the tables and text does not contain an external plas- Table XII — Hydrogen Sulfide Production by Marine Bacteria IN Anaerobic Sea Water Test with Elastomers as the Only Sources of Organic Carbon Elastomer GR-S jacket (54-14) GR-A jacket (54-18) Biitvl jacket (54-19) Natural rubber jacket (54-23) . . Neoprene jacket (54-164) Controls (inoculated sea water) HzS Production after Weeks of Incubation ppm 0.66 0.96 1.52 1.62 1.06 0.37 8 ppm 0.77 0.95 6.64 2.48 1.20 0.43 12 ppm 0.56 0.72 8.03 3.58 0.99 0.43 16 ppm 0.75 0.87 9.65 3.74 0.96 0.42 1110 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 lOOr 2 d CL I (T UJ < < LU z o u r 6 8 10 12 INCUBATION TIME IN WEEKS 14 16 18 Fig. 4 — Examples of H2S production by marine bacteria in anaerobic sea water test with Poly (Vinyl Chloride) plastics as carbon source. ticizer, fatty acid lubricant probably serves as a source of nutrient. For comparative purposes, the examples of hydrogen sulfide production plotted in Fig. 4 are for the same plastics included in Fig. 3 which relates to the data from the aerobic procedure. Jute is attacked by the anaerobic bacteria just as it is utilized by the aerobic organisms. However, neither the epoxide casting resin (Table X) or the polyester casting resin (Table XI) seem to serve as a source of carbon. The results of the anaerobic test with the elastomers are presented in Table XII. It is interesting to note that early attack occurs on the natural and butyl rubber jackets, but that none of the other elastomers is utilized by the organism. It is somewhat surprising that attack on GR-S did not progress at about the same rate as on natural and butyl rubber. The data which have been obtained in the aerobic and anaerobic parts of the BOD-type test are summarized in Table XIII. There is one out- standing fact about the data — no material was utilized by the anaerobic bacteria which was not utilized also by the aerobic organisms. Under the conditions of the test, however, materials did serve as a carbon source for aerobic bacteria and not for the anaerobes. 3.. 2 Conductor Test It is apparent that the BOD test provides considerable fundamental information on the ability of halophilic bacteria to utilize organic ma- RESISTANCE OF MATERIALS TO MARINE BIOLOGICAL ATTACK 1111 terials as a carbon source in sea water. There is little or no opportunity for ecological factors to come into play, however, particularly with re- gard to marine sediment. In the conductor test, sea water and marine sediment form a part of the test environment, and the test is run over a much longer period of time, thus encouraging more natural and dy- namic organism associations. Likewise, the natural relationship between material and environment is simulated more closely than it is in the more accelerated test. In these respects, the conductor test is intermediate to the BOD-type test and natural marine exposure. The material to be tested is coated on a conductor to provide about 10 mils of insulation. A standard coil of this insulated conductor is then exposed in a 16-ounce bottle so that half of the coil is in marine sediment, and half is in sea water. The ends of the coil are brought through holes in the bottle cap and attached to terminals in the cap. The general features of the test setup are shown in Fig. 5. The bottle is incubated at 20°C. Capacitance and conductance measurements, taken monthly, in- dicate any change in the insulation. Some conductors are placed in sterile sea water and sediment to serve as controls. This type of test can be continued for months or years if necessary. Most of the conductor tests are now being initiated. Two materials, however, GR-S and a rigid polyvinyl chloride, have been under study Table XIII — Summary of Materials Utilized as Source of Carbon by Aerobic or Anaerobic Marine Bacteria IN BOD-Type Test Utilized as Source of Carbon by Aerobic Bacteria Anaerobic Bacteria PVC - - no plasticizer (rigid) PVC — no plasticizer (rigid) PVC - - tricre.syl phosjjhate (TCP) PVC - - di-2-et"hylhexyl phthalate (DOP) Shore ASS PVC- - polyester A PVC — polyester A PVC - - nitrile rubber/polyester C PVC — nitrile rubber/polyester C PVC- - nitrile rubber PVC — nitrile rubber PVC- - tri-2-ethylhexyl phosphate PVC - - di-2-ethvlhexyl phthalate (DOP) Shore A 62 PVC - - polyester F./DOP (BTL 46-55) PVC — polyester E/DOP (BTL 46-55) Styrene polyester GR-S J acket (54-14) GR-A jacket (54-18) Butyl acket (54-19) Butyl jacket (54-19) Natur: il rubber jacket (54-23) Natural rul)l)er jacket (54-23) Neoprene jiieket (54-164) Jute • Jute 1112 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 for .several months in a "dry" run to establish the biological procedure, as well as the techniques of measurement which are to be employed. The capacitance and conductance data which have been obtained on these two materials to date are presented in Figs. 6 and 7, respectively. In the case of the test samples, each point represents the average value for four test coils, but for the controls each point represents only one j coil. With the GR-S test samples, there is a sharp rise in the capacitance values between the second and third month, amounting to about 110 jujuf • Thereafter, the rise in the curve continues, the slope decreasing some- what at about the eighth-month point. Over the entire test period, the capacitance ranged from 632 nt^f at the start to 850 MAtf after 13 months Fig. 5 — General setup of conductor test showing a coil half in sediment and half in sea water. RESISTANCE OF MATERIALS TO MARIXE BIOLOGICAL ATTACK 1113 860 840 820 800 780 760 740 720 10 Q < cr < O q: u o cr o 2 700 o z < o < u 680 660 640 620 U-4-4 ^,-< U--ri > r y / f 1 GRS INSULATION-10 MILS PVC INSULATION -12 MILS 0 -o GRS TEST / t i ^ A -A PVC TEST • • GRS CONTROL 1 1 1 — t 1 1 1 1 1 — i k i L p\ /c cc NTRO L 1 1 1 1 1 -t — / ; ,— — ' ^^^i 1 — » ' — d ) — 1 ^^ f ' — 1^-1 4 5 6 7 8 9 TIME IN TEST IN MONTHS 10 11 12 13 Fig. 6 — Capacitance changes resulting from exposure of GR-S (51-92) and Poly (Vinyl Chloride) (BTL 172-54) insulated conductors in sea water and sediment. exposure — a total change of 218 \iiii. If it is assumed that the insulating materials were removed equally along the length of the coil, it can be computed that this change in capacitance represents a loss of 8.1 mils of insulation. The following formula is used to arrive at this figure: D - If ' ^t ^B - >' ■ ^Jl." '* "J" 1° " ', . , ^ B f/'V- B ^^'.*i* B ''*w^^ ^K- -■. J^^Sr ^^H '■i .."'-^ .; '^^HH ^,^5^" ^ > ^ '■ ' ^' 1 Fig. 11 — ("olhilose acetate after 60 days in laboratory soil burial. Note charac- teristic surface erosion comparable to that shown in Fig. 10 for marine test sample. Original magnification 500X. Photo by F. G. Foster. 1120 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 Fig. 12 — Test rack being lifted from water at Wrightsville Beach. Heavj^ ac- cumulation of fouling on test rods in water-exposed area stops at point where rods entered the sediment. structures and coatings, is referred to the report of the investigations conducted at the Woods Hole Oceanographic Institution during the years 1940 to 1946.^^ The restricted areas beneath fouHng, particularly under the Imses of calcareous organisms such as barnacles, provide ideal cells for l)acterial activity. Conditions of pH and aeration may be mai'k- edly different in these confined areas from those in the surrounding water. Some of the test rods made of polyvinyl chloride plastics contain- ing basic lead stabilizers, illustrate the fact rather dramatically. Ana- erobic, sulfate-reducing bacteria are common marine organisms which release hydrogen sulfide in the process of breaking down organic ma- terial. Under tightly adhering fouling, aerobic bacteria can utilize the free oxygen much more rapidly than it can be replaced by diffusion from the surrounding water. Once the oxygen has been depleted, the anaerobic organisms begin their activity and cause relatively high concentrations of hydrogen sulfide to be built up. The hydrogen sulfide reacts with the basic lead salts used as stabilizers and produces black lead stilfide. The sharp l)()undaries of the different envii'oimiental conditions existing ])('ii(>atli tlu> base of a barnacle on one of the polyvinyl chloride test rods are illustrated in Fig. 13. Here the pattern of the barnacle base has literally been reproduced b.y the sulfiding which occurred under it. The black border and black radiating lines correspond to areas of exception- RESISTANCE OF MATERIALS TO MARINE BIOLOGICAL ATTACK 1121 ally close contact. The radial extent of this sulfiding in the bottom end of the rod which was embedded in the sediment, as compared to the top or water end, is shown in Fig. 14. It must be emphasized that there has been no indication to date of any adverse effect on the physical properties of plastics which have been sulfided in this way. VI. CABLE SAMPLES FROM SERVICE The samples of submarine cables which have been examined to the present time represent both telegraph and telephone cables. The samples of telegraph cable have been obtained through the cooperation of the Western Union Telegraph Company. It takes considerable time to as- semble a large number of specimens during the course of routine repair operations. As a result, although some 22 different samples, the majority from the North Atlantic, have been examined, it is possible to make only Fig. 13 — Sulfiding of Poly(Viu3'l Cliloricle) plastic test rod beneath barnacles. The black, circular border and center area represent sulfiding at points of excep- tionally close contHct. Original magnification 2X. Photo bj^ J. B. DeCoste. 1122 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 Fig. 14 — Cross-section of Poly (Vinyl Chloride) rod showing sulfiding due to j sulfate-redvicing marine bacteria. Bottom end was in sediment — top in water. I E.\posed at Daytona Beach for two years. Original magnification 1.6X. • general observations and broad comparisons. The locations and depths i from which the samples were obtained are given in Table XIV. In most cases, a sample 3-feet long is obtained. Twenty-two different pieces of such size represent a rather small sample with respect to the total marine environment. Here again the program assumes more value as additional samples are obtained. The procedure employed in examining one of these cable sections is about as follows. First, the over-all external condition is observed and recorded. Then, the outer jute covering, armor wires, inner jute bedding, and cloth and metallic tapes, if any, are removed progressively. The armor wires are examined in detail by electrochemists to determine the extent and kind of corrosion. The jute is tested in various ways. If sufficient material is available tensile strength is measured. Microscopic examination of representative fibers is also made. In the case of the inner jute which is not treated with tarry materials, damage counts are run according to the procedure of MacMillan and Basu.^^ According to this method, deoiled and dewaxed fibers are permitted to swell in 10 per cent sodium hydroxide solution. Following this they are treated in a bath of 133 per cent weight to volume, aqueous zinc chloride solution over steam. Undamaged fibers swell as tight helices while damaged fibers swell as bundles of parallel fibrils. The fibers are mounted in zinc chloride solu- tion on a microscope slide and counted to determine the per cent of damaged fibers. To examine the integrity of the insulation on the conductor, the elec- trolytic procedure of Blake, Kitchin and Pratt^^ is used. An electrolytic RESISTANCE OF MATERIALS TO MARINE BIOLOGICAL ATTACK 1123 cell is set up with 20 per cent copper sulfate solution as the electrolyte, and a copper plate as the anode. The cathode is a loop of the insulated conductor from the cable. Any plating out of copper on the cathode indicates a break in the insulation. In this way the integrity of a rela- tively long length of conductor can be examined critically and simply. One of the outstanding facts apparent from the examination of cable samples has been the evident importance of the outer jute in limiting the corrosion of armor wires. Galvanized steel armor wires which still retain the protection of flooding compounds, such as asphalt, tar or pitch, together with outer servings of impregnated jute, have shown negligible steel corrosion within 40 years, and in one case for as long as 66 years. On the other hand, most of the corrosion of armor wires which has been observed has occurred in cable from which a major part, or all, of the outer jute has been lost. Table XIV — Locations and Depths from W' high Submarine Cable Samples have been Obtained for Laboratory Examination BTL No. Location Depth Latitude Longitude Fathoms 110 approx. 81° 30' 00"N 24° 30' 00"W 5 approx. 111 approx 81° 30' 00" N 24° 30' 00"W 5 approx. 112 approx. 81° 30' 00"N 24° .30' 00"W 5 approx. 113 approx. 81° 30' 00"N 24° 30' 00"W 5 approx. 114 approx 81° 30' 00"N 24° 30' 00"W 5 approx. 135a 23° 45' 00"N 81° 57' 30"W 830 136 Several mil es south of Long Island, N. Y. Exact 1 ocation unknown. 90 137 40° 13' 40"N 71° 07' 25" W 90 163 48° 36' 06"N 36° 23' 36" W 2460 164 51° 53' 42"N 10° 37' 18"W 54 165 51° 40' 42"N 13° 02' 12"W 630 166 51° 55' 21 "N 11° 58' 18"W 387 167 47° 52' 24"N 38° 23' 12"W 2460 168 47° 22' 06"N 42° 14' 12"W 2175 169 36° 41' 46"N 25° 38' 09"W 1180 195 45° 28' 21"N 60° 20' 24"W 106 196 46° 41' 36"N 56° 18' 18"W 37 197 47° 00' 32"N 56°51'40"W 100 200 44° 25' 40"N 63° 25' 15"W 46 212 45° 08' 38"N 54° 33' 06"W 82 281 43° 38' 10"N 55° 07' 00" W 2090 282 39° 17' 24"N 70° 12' 15"W 1450 283 53° 57' 00"N 165° 50' 00"W Unknown 1124 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 Fig. 15 — Corrosion pockets in galvanized steel armor wires of submarine cable after 12 years of service. Of special interest is a particular type of corrosion which has occurred in two separate cable samples — one from Alaskan waters, the other from off the southern coast of Newfoundland. In one case the age of the cable was 12 years, and in the other 36 years. The Alaskan sample was located in an area characterized by water velocities of 5 to 9 knots. In both instances, the outer jute and most of the flooding compound was | gone. Corrosion, instead of starting and progressing on the outer sur- ■ face of the wires, had started, and been confined largely to the sides of , the wires. Usually there are corresponding areas of corrosion on two ! adjacent wires to form "corrosion pockets." These pockets are illustrated in Fig. 15. In the case of the 12 year old cable, corrosion caused failure of the armor wires. In the case of the cable which was in service 36 years, failure was reported to have occurred from chaffing on a rocky bottom. Close examination suggests that failure may more reasonably be at- tributed to sevei'e corrosion of the type just described. The exact cause of the corrosion pattern is still to be determined. Sufficient samples have not been examined as yet to form a coordi- nated picture with respect to the inner jute. In the case of cable samples from the North Atlantic, the inner jute bedding w^as in good condition in cables which had been in service for as long as 30 or 40 years. Samples more than 40 years old showed the effect of deterioration. Although only a limited number of samples have been examined from the Caribbean, most of them from water about 50 feet deep, jute and cotton tape com- ponents were in poor condition in certain spots. It was evident that microbiological deterioration of the jute had occurred. In no case has there been any evidence of deterioration of the insulation of the central conductor of any of the cable samples. In the case of the older cable samples the insulation was gutta percha, but in the most recent samples it has been polyethylene. RESISTANCE OF MATERIALS TO MARINE BIOLOGICAL ATTACK 1125 VII. SUMMARY A progress report has been presented on the results of a test program designed to determine the relative resistance of materials to marine bio- logical attack. Specific test i-esults have been reported wherever possible, predominanth^ from the laboratory test procedures. In the case of the natural exposure tests, which are intended to provide correlative data for the laboratory program over longer periods of time, the information which has been assembled thus far is of a more general nature. There follows a summary of the more important information which has been obtained : 1 . In the biochemical 0x3' gen demand-type test it has been found that polyethylene is not utilized by the aerobic bacteria or the anaerobic suKate-reducing bacteria. Polyvinyl chloride plastics are attacked ac- cording to the way in which they are plasticized. All of the samples tested which had an added external plasticizer, mcluding the rigid plastic, were attacked to some degree. In the latter case the attack was apparently due to lubricants. The semi-flexible polyvinyl chloride copoljaiiers, and the polj^vinyl chloride resin alone, were not utilized by the bacteria. The five elastomers assayed were all attacked by aerobic bacteria, neo- prene being the most resistant. The epoxide casting resin did not serve as a source of carbon for the organisms, but further testing is re- quired with a polyester casting resin. 2. Coiled conductors insulated in one case with a rigid polyvinyl chloride, and in the other with GR-S, have been exposed half in sea water and half in marine sediment in the laboratory for thirteen months. Capacitance measurements show that a considerable change has oc- curred in the GR-S insulation apparently as a result of bacterial attack. Although there has been a slight rise in the capacitance values for the polyvinyl chloride-insulated conductors during the last five months, further observations are necessary before attack can be considered defi- nite. 0. In three years of actual marine exposure of plastics, elastomers and pasting resins, there have been definite penetrations by marine borers of onl}^ three materials — a test rod of silicone rubber, a 0.0035-inch film of poljanonochlor-trifluoroethylene wrapped on a Lucite rod, and on Lucite rods themselves. The first two cases represent single instances of penetration — both by pholads. The Lucite rods were penetrated at many places bj^ pholads as a result of the organisms getting started in an asphalt-impregnated jute wrapping and then progressing into the Lucite. Secondary cellulose acetate yarn and tow have been deteriorated badly, apparently by bacteria, in as short a time as six months. 1126 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 Natural fibers, notably jute, have been degraded extensively by borers and microorganisms. There is considerable evidence of fiuigus attack. Under fouling and in the sediment area, rods of polyvinvl chloride plastics containing basic lead stabilizers have been blackened as the re- sult of hydrogen sulfide produced by sulfate-reducing bacteria reacting with the lead salts to give black lead sulfide. This sulfiding has caused no apparent degradation of the physical properties of the plastics. 4. The examination of cable samples from service has indicated that the impregnated outer jute serves an important function in limiting cor- rosion of armor wires. Generally, when corrosion is present the outer jute has been lost. Two unusual cases of extensive corrosion have been reported • — one in a cable 12 years old, the other in a cable which was in service 36 years. In both cases, corrosion occurred in pockets between adjacent armor wires rather than on the outside surfaces (water side) of the wires. The performance of the inner jute in samples from service has been generally good for as long as 30 or 40 years in deep water. In samples from relatively shallow water in the Caribbean, inner jute bedding was l)adly deteriorated in as short a time as five years. ACKNOWLEDGMENTS The data which have been acquired in this program are the result of teamwork by many different members of the Laboratories. Special thanks are due to Priscilla Leach for obtaining much of the data in the BOD test, and her general assistance on many phases of the program. Madeline L. Cook is responsible for the majority of the electrical meas- urements in the conductor tests. T. D. Kegelman, formerly of the Laboratories, and W. C. Gibson gave considerable assistance in setting up the equipment and establishing the procedures for measurement of capacitance and conductance. Many members of the Chemical Research Department cooperated in furnishing the materials which have been tested. J. B. DeCoste has been particularly helpful in assembling the recjuired information on the materials. From outside the Laboratories, Professor Claude E. ZoBell of the Scripps Institute of Oceanography has made many helpful suggestions and comments with regard to the labora- tory portion of the program, and provided supplementary enrichment cultures and samples of sediment. The marine borer test program has been executed with the cooperation of A. P. Richards, William F. Clapp Laboratories, Inc., who has furnished nuich valuable information in many discussions of the tests. The cooperation of C. S. Lawton, Western Union Telegraph Company, and the personnel of C. S. Lord Kelvin in RESISTANCE OF MATERIALS TO MARINE BIOLOGICAL ATTACK 1127 obtaining samples of telegraph cable from service is gratefully acknowl- edged. REFERENCES 1. C. Chilton, The Griblile {Limnoria Ugnorum, Rathke) Attacking a Submarine Cable in New Zealand. Annal.s and Mag. Natural History, Ser. S, 18, p. 208, 1916. 2. G. E. Preece, On Ocean Cable Borers, Telegr. Jour, and Electr. Rev., 3, pp. 296-297, 1875. 3. E. Jona, I cavi sottomarini dall 'Italia alia Libia, Atti della See. ital. per il Progr. delle Sci., 6, pp. 263-292, 1913. 4. R. J. Menzies and Ruth Turner, The Distribution and Importance of Marine Wood Borers in the United States, presented at Second Pacific Area National Meeting, A. S. T. M., Paper 93, 1956. 5. W. F. Clapp, and R. Kenk, Marine Borers, A Preliminary Bibliography, Parts I and II, The Library of Congress, Tech. Inform. Div., Washington, D. C;., 1956. 6. F. Roch, Die Teredinidae de Mittelmeeres. Thalassia 4, pp. 1-147, 1940. 7. Notes on Everyday Cable Problems. Distribution of Electricity, 8, pp. 1896- 1898, W. T. Henley's Telegraph Works Co., Ltd., London, November, 1935. 8. P. Bartsch and H. A. Rehder, The West Atlantic Boring Mollusks of the Genus Martesia, Smithsonian Inst. Misc. Collections 104, Washington, D. C, 11, 1945. 9. L. R. Snoke and A. P. Richards, Marine Borer Attack on Lead Cable Sheath, Science, 124, p. 443, 1956. 10. C. E. ZoBell, Marine Microbiology, Chronica Botanica Co., Waltham, Mass., 1946. 11. R. Y. Morita, and C. E. ZoBell, Bacteria in Marine Sediments. Off. of Na- val Res., Research Reviews, p. 21, July, 1956. 12. C. E. ZoBell and R. Y. Morita, Effects of High Hydrostatic Pressure on Physi- ological Activities of Marine Microorganisms, Off. of Naval Res., Contr. N6 onr-275 (18) Project NR 135-020, Semi. Ann. Prog. Rept., July, 1955. 13. C. E. ZoBell and Josephine Beckwith, The Deterioration of Rubber Products by Micro-Organisms, Jour. Amer. Water Works Assoc, 36, pp. 439-453, 1944. 14. C. E. ZoBell, Action of Microorganisms on Hydrocarbons, Bact. Rev., 10, Nos. 1-2, March-June, 1946. 15. E. S. Barghoorn and D. H. Linder, Marine Fungi, Their Taxonomj' and Bi- ology, Farlowia, 1, pp. 395-467, Jan., 1944. 16. S. P. Myers, Marine Fungi in Biscayne Bav, Florida. Bull, of Marine Sci. of the Gidf and Caribbean, 2, pp. 590-601, 1953. 17. Marine Fouling and Its Prevention. United States Naval Institute, Annapolis, Md., 1952. 18. W. G. MacMillan and S. N. Basu, Detection and Estimation of Damage in Jute Fibers — Part I: A New Microscopic Test and Implications of Certain Chemical Tests. Jour. Text. Inst., 38, pp. T350-T369, 1947. 19. J. T. Blake, D. W. Kitchin and O. S. Pratt, The Microbiological Deterioration of Rubber Insulation. Presented at A.I.E.E. General Meeting, New York, Jan., 1953. 20. P. Deschamps, Xylophaga Marins. Protection de Bois Immerges contres les Animaux Perforants. Peint.-Pigm.-Vern., 28, pp. 607-610, 1952. 21. C. E. ZoBell, Some Effects of High H.ydrostatic Pressure on Physiological Activities of Bacteria, Proc. Soc. Amer. Bact., pp. 26-27, 1955. Dynamics and Kinematics of the Laying and Recovery of Submarine Cable By E. E. ZAJAC (Manuscript received June 5, 1957) This paper is an attempt to formulate a comprehensive theory with which the forces and motions of a submarine cable can be determined in typical laying and recovery situations. In addition to the fundamental case of a cable being laid or recovered with a ship sailing on a perfectly calm sea over a horizontal bottom, the effects of ship motion, varying bottom depth, ocean cross currents, and the problem of cable laying control are considered. Most of the results reduce to simple formulas and graphs. Their application is illustrated by examples. TABLE OF CONTENTS Page I. Introduction H'^^ II. Basic Assumptions H"^"^ III. Two-Dimensional Stationary Model 113-1 3.1 General 1134 3.2 Normal Drag Force and the Cable Angle a 1135 3.3 Tangential Drag Force 1139 3.4 Sinking Velocities and Their Relationship to Drag Forces 1141 3.5 General Solution of the Stationary Two-Dimensional Model 1143 3.6 Approximate Solution for Cable Laying 1146 3.7 Approximate Solution for Cable Recovery 1149 3.8 Shea's Alternative Recovery Procedure 1153 IV. Effects of Ship Motions 1154 4.1 Tensions Caused by Ship Motions 1154 V. Deviations from a Horizontal Bottom 1158 5.1 Kinematics of Laying Over a Bottom of Varying Depth 1158 5.2 Time-Wise Variation of the Mean Tension in Laying Over a Bottom of Varying Depth 1161 5.3 Residual Suspensions 1163 VI. Cable Laying Control 1165 6.1 General 1165 6.2 Accuracy of the Piano Wire Technique 1166 VII. Three-Dimensional Stationary Model 1169 7.1 General 1169 7.2 Perturbation Solution for a Uniform Cross-Ciu-rent 1172 Appendix A. Discussion of the Two-Dimensional Stationary Configuration for Zero Bottom Tension 1175 Appendix B. Computation of the Transverse Drag Coefficient and the Hydro- dynamic Constant of a Smooth Cable from Published Data 1177 1129 1130 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 Appendix C. Some Approximate Solutions for Laying and Recovery 1180 C.l Laying 1180 C.2 Recovery 1183 Appendix D. Analysis of the Effect of Ship Motion 1184 D.l Formulation of the Differential Equations 1184 D.2 Perturbation Equations 1187 D.3 Solution of the Perturbation Equations 1189 D.4 Transverse Response 1190 D.5 Second-Order Longitudinal Response 1191 D.6 Numerical Results 1194 Appendix E. Tension Rise with Time for Suspended Cable 1195 E.l Formulation of the Solution of the Problem 1195 E.2 Nomograph for the Solution of Equation (99) 1198 E.3 Numerical Example 1199 Appendix F. The Three-Dimensional Stationary Model 1202 F.l Derivation of the Differential Equations 1202 F.2 Perturbation Solution for a Uniform Cross Current 1204 Acknowledgments 1206 References 1206 Glossary of Symbols A Amplitude of harmonic ship motion Ci , C2 , C2 Longitudinal wave velocity; trans- verse wave velocity in air and water Cd , Cf Transverse and tangential drag co- efficients d Cable diameter, also distance be- hind the ship at which the cable enters the lower stratum Dn , Dt Normal and tangential unit drag forces e Sidewise distance from the laid cable to the ship KA Extensile rigidity h Ocean depth h = ^ Dimensionless ocean depth EA H Hydrodynamic constant L Inchned cable length from surface to bottom, also from ship to surface AT^ Reynolds number p^ q Longitudinal and transverse devia- tional cable displacements Po ^ Qo Longitudinal and transverse ship displacements Pi s,x X X ~ h t - Vt '=J DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 1131 Deviation from mean pay-out or haul-in rate Arc length and horizontal distance from the touchdown point to the ship Dimensionless forms of S and X Time Dimensionless time T, Ts , To Cable tension at an arbitrary point, at the ship, and at the bottom T = ^, Ts = '^, % = ^ Dimensionless forms of T, Ts and To wh wh wh Tp , Tq Cable tension due to longitudinal and transverse ship motion V, Vc Ship speed, pay-out or haul-in rate Vff , Vt Normal and tangential velocity of the water relative to the cable configura- tion Vt Tangential velocity of the water rela- tive to a cable element w, Wa Submerged and in-air vmit cable weight a, an Critical angle, approximate critical angle as Cable angle at the surface (S Descent angle, cross current orienta- tion (Section 7.1) 7 = - — r—: Constant, also ascent angle sm'^ a e Slack 6 Orientation of a cable element 6, \J/ Spherical polar coordinates for the three-dimensional model K, X Constants (see Appendix C) 1132 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 . CopdV cos a r~i 1 1^ A — — = -V-- — Constant i 2 sm- a fjL, V Constants V Kinematic viscosity $, -q, I Rectangular coordinates for the three- ' dimensional model p Mass density of water . Pc , Pw Mass per unit length of cal)le in air .' and water 0 Deviation from the stationary angle, ' also angle between ^ axis and V : (Section 7.1) I. INTRODUCTION In the summer of 1857, the first attempted laying of a transatlantic cable ended dismally when, after only a few hundred miles had been • laid, the cable broke and fell into the sea. Although fouling of the pay- ' out gear caused by a negligent workman was the principal suspected reasons for the failure, its occurrence aroused great interest in the de- tailed dynamics and kinematics of the laying of submarine cable, and leading British scientists such as Kelvin and Airy published analyses of i, this problem in late 1857 and early 1858.^ • ^ ■ » ■ ^ , & t However, after this initial activity, interest in submarine cable dy- i namics and kinematics evidently waned for there appear only sporadic subsequent investigations in the literature.^' '^' ^' ^' ^^ Further, the re- sults of the early and subsequent analytical investigations have been, by and large, little utilized in cable laying and recovery practice. One can conjecture several reasons for this. For one, because the early ana- lytical work was done before the advent of modern hydrodjaiamic theory, it did not rest on a secure base. Thus, as late as 1875, one finds vigorous debate over the nature of the tangential resistance of water to the cable.' For another, the results of the analyses could not all be expressed in terms of elementary functions and required the numerical evaluation of some definite integrals. In the 1850's this was a tedious and laborious process. However, these are probably secondary reasons. For, after another failure in the early summer of 1858, a transatlantic cable was successfully laid in August of that year. The mechanical problem of de- positing a cable was thus proved surmountable without complicated mathematical analyses, and the marriage of analysis and practice was never fully realized. DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 1133 However, a present-day submerged-repeater transoceanic cable is a delicate and expensive transmission system. Reducing the amount of cable deposited by as little as one per cent can result in a substantial saving in the first cost of such a system. Its repair is a costly operation requiring the sustenance of an ocean ship and its crew. Therefore, it is important to lay the cable without wasteful excess and with minimum chances for failure after laying. Further, it is important that repair, if necessary, be as efficient as possible. To accomplish these things, an un- derstanding of the djaiamics and kinematics of cable laying and recovery is essential. The purpose of this paper is to provide some of this understanding in as straightforward a way as possible. To this end concepts and results are stressed in the main part of the paper, mathematical details being given in the appendices. Moreover, we hope to show that the results of the analysis can pro^'ide a numerical basis for decision making in many of the laying and recovery operations. Most of these results can be ex- pressed in the form of simple formulas and graphs. Several numerical examples are included to illustrate concretely how the results can be applied in practice. The general plan of the paper is to proceed from simple to more re- fined models of the laying and recovery processes. Thus, we discuss first what we have called the two-dimensional stationary model. This model is appropriate for laying and recovery on or from a perfectly flat bottom while sailing on a perfectly still sea. As a preliminary to this discussion, we consider in some detail the hydrodynamic behavior of typical deep sea submarine cable. We then take up the effects of the ship motions which are induced by wave action and the effects of a bottom of ^-arying depth. These considerations are followed by a short discussion of the problem of controlling the cable pay-out properly during laymg and the associated problem of the accuracy of the present taut wire method of determining ship speed. Finally, we consider the three-dimensional sta- tionary model and the effects of ocean cross currents. II. BASIC ASSUMPTIONS Our analyses, like most analyses of physical problems, are based on idealizations or mathematical models of the actual phj^sical system. The extent of validity of these models must be ultimately determined by ex- periment and experience. However we shall tr}' to give the reader an idea of when they are clearly applicable and when they are not. All of the models we consider contain two basic idealizations, namely, (1) No bending stiffness in cable, i.e., it is a perfecth^ flexible string, (2) The average forward speed of the ship is constant. 1134 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 Bending effects are caused by locally large curvatures, and are significant mainly where the cable leaves the pa3^-out sheaves and at the ocean bottom. However, for a cable with a steel strength member, bending even to the small radius of the pay-out sheave typically does not ma- terially reduce the tension required to break the cable. Hence, in these cases we can expect an analysis based on the first idealization to give a reasonable idea of when cable rupture will occur. In laying, ship speeds are normally steady and, with the exception of the fluctuations caused by wave action which we consider later in the paper, the second idealiza- tion is reasonable also. In recovery, on the other hand, ship speeds are apt not to be steady, and the second idealization is more tenuous. But because of the very slow speeds usually employed, this idealization may in fact be meaningful in recovery as well. III. TWO-DIMENSIONAL STATIONARY MODEL 3.1 General Assume that the cable ship is sailing at a constant horizontal velocity, that the cable pay-out or haul-in rate is constant, and that the drag of the water on the cable depends only on the relative velocity between the water and the cable. Further, assume that in a frame of reference translating with the ship the cable configuration is time-independent or stationary. This idealized model of the cable laying or recovery pro- cess we call the two-dimensional stationary model. This is the model which has been considered in the previous analytical studies. ^'^^ As the early investigators quickly pointed out, when the tension at the bottom of the cable is zero, the cable, according to this model, can lie in a straight line from ship to ocean bottom. During lay- ing, when slack is normally paid out, the zero tension condition actually occurs, and hence this case is of considerable practical importance. The straight line can in fact be shown to be the only solution which can satisfy all the observed boundary conditions. This point is discussed in detail in Appendix A. That the straight line is a possible configuration can be seen from Fig. 1. In the vector diagram the velocity of the water with respect to the cable is resolved into a component Vn normal to the cable and a component Vt tangential to it. Associated with Vn and Yt are normal and tangential water resistance or drag forces Dn and Dt ■ In the straight line configuration, the cable inclination is such that Dn just balances the normal component of the cable weight forces. The situation is thus analogous to that of a chain sliding on an inclined plane, with the forces Dn corresponding to the normal reaction forces of the plane. Summing forces in the normal direction, we get, thei'efore. DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 1135 W COS a = Dn , (1) while the summation in the tangential direction gives for Ts , the ten- sion at the ship, 1\ = wL sin a - DtL. (2) Here iv is the weight per unit length of immersed cable, a is the cable's angle of incidence, Dn and Dt are the normal and tangential drag forces per unit length respectively, and L is the inclined length of the cable. For most submarine cable used currently the force DtL is negligible and we arrive at wL sin a = wh, (3) where h is the ocean depth at the cable touchdown point. Hence, during slack laying the cable tension at the ship is very nearly equal to the weight in water of a length of cable equal to the ocean depth. Fig. 1 — Forces acting on a cable in normal laying. The straight-line solution is the simplest and probably the most im- portant result to be obtained from the stationary two-dimensional model. We shall derive results for other important situations from this model also. As a preliminary, we study first, however, the nature of the normal and tangential drag forces D^ and Dt . .3.2 Normal Drag Force and the Cable Angle a The resistance at sufficiently slow speeds to the flow of a fluid around an immersed body varies as the square of the fluid velocity. This relation- ship is usually written as* (4) Jy.\ — Co ^: — , 2 * For towed stranded wire experimental verification of this relationship is reported in Reference 11. 1136 THE BELL SYSTEM TECHNICAL JOUUXAL, SEPTEMBER 1957 50 45 01 40 UJ LU cc ^ 35 Q 30 25 20 < O 16 CC U 10 \ LENGTH OF TOWED CABLE o 100' \ A 80' + 60' D 20' 1 1 ^ \ \ 1 1 1 1 1 EQUATION (6) WITH Co = 1.11 V 1 1 1 1 ' t\ J V r /! 1 ? 1,^ f |^^-^_ 2 3 4 5 6 7 8 TOWING VELOCITY IN 'KNOTS 10 Fig. 2 — Experimental and theoretical variation of critical angle with towing j velocity for cable No. 1. ! i where D^^ is the normal drag force per unit length, Co is the so-called drag coefficient, p is the mass density of the fluid, and d is the diameter of the cable. For the straight-line configuration, the vector diagram in Fig. 1 shows that Vn = V sin a. Substitution of (5) and (4) into (1) yields in turn CDpV'd . 2 w cos a = sni a. (5) (6) Eciuation (6) suggests how the value of the drag coefficient Co can be obtained experimentally. By towing a length of cable in water at a con- stant velocity, one can establish the straight-line configuration. The angle a can then be measured as a function of velocity, from which Cd can be computed by (6). Figs. 2 and 3 show the results of such tests together with plots of (6) for the indicated values of Co ■ These results are taken from an analysis by A. G. Norem of experimental data obtained by H. N. Upthegro^•e, J. J. Gilbert, and P. A. Yeisley. The properties of these cables are listed in Table I.* To eliminate end effects different lengths of cable were towed, * Cable No. 2 is very similar to present type D transatlantic telephone cable. For engineering calculations, type D can be considered the same as cable No. 2. DYNAMICS AND KINEMATICS OF SUBMARINE CABLE Table I — Properties of Cables No. 1 and No. 2 1137 Cable Diameter (inches) ;Wt. in water (lbs/ft.).. j Outer covering ' Surface condition EA (twist restrained). . . EA (twist unrestrained) No. 1 0.75 0.243 Polyethylene Smooth No. 2 1.25 0.705 Tar impregnated jute Rough 4 X 108 lbs 1.2 X 10« lbs as is indicated by the plotted experimental points. It is seen that (6) gives a good fit to the experimental data over the entire velocity range. If the cable has a smooth exterior, an estimate of the drag coefficient Cd can be computed from published values of resistance to flow about an immersed cylinder. This computation is described in Appendix B, where we have also tabulated computed ^-alues of Co • For the smooth cable No. 1, the value of Cd obtained from Appendix B is 1.00 which is in fair agreement with the experimentally determined value of 1.11. Although the drag coefficient Cd is a fundamental hydrodynamic para- meter, it is not the most convenient description of the effect of the nor- o 56 i 1 — ' \ LENGTH OF TOWED CABLE 50 \ O 80' \ A 75' 46 40 \ + 45' □ 2C )' \ T 35 \ I 1 1 1 1 1 \EQUATI0N (6) WITH Cd = '-55 30 \ \ 25 V 20 15 10 r \ , 1 \ "^^^ ^ s ^-^^ L ^ f1 n— -4^ i^ 5 — r^ 0 2 3 4 5 6 7 8 TOWING VELOCITY IN KNOTS 10 Fig. 3 — E.xperimental and theoretical variation of critical angle with towing velocity for cable No. 2. 1138 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 mal component of water velocit3^ For small values of the incidence angle a cos a ;^ 1, sin a 7^ a, and (6) is approximately 2w 1/2 cos a V-UfT-K9' (10) where ao is the approximate value of a. The quantity {2w/CDpdy is a constant for a given cable. It brings together all the cable parameters which influence the magnitude of the incidence angle a. If the angle a for a given speed is determined accurately, as can be done in a towing test or with a sextant during over-the-stern laying, this cjuantity is easily computed. Because of its importance, we shall call it the hydrodynamic constant of the cable and denote it by H, namely, » = (e&)" By virtue of (7) and (8) we may write a,y = H. (9) The constant H rather than the drag coefficient Cd ^^^ll be used from this point on. When the approximate relationship (9) is not valid, a can be obtained by solving (6). This gives where V is in knots and H in radian-knots. In terms of ao we obtain in J turn cos a = / that a can be thought of as a dimensionless parameter which embodies i DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 1139 a. O ou 1 ^ ^ ^ 60 ^ ^ y / 40 y / / r 20 / / 0 / 20 40 60 80 OCn IN DEGREES 100 120 Fig. 4 — Variation of a with ao . both the hydrodyiiamic properties of the cable and the ship speed. Thus, even when the configuration is not a straight fine, we shall find it con- venient to express results as a function of the single parameter a, rather than as a function of the two parameters H and T'. For this reason, following Pode, ^' ^■' we call a the critical angle. 3.3 Tangential Drag Force Over the range of velocities encountered m laying and recovery the I drag coefficient Cd in equation (6) is essentially constant. However, the corresponding coefficient for the skin friction force associated Avith Vt , I the component of flow along the cable, is not constant. For the cable of smooth exterior (cable No. 1), the expression Dt = Cf^pV^ir d, (12) with Cf = 0.0o5/{Nr) ' , was found to give good agreement with the experimental data, as is shown by Fig. 5. Here Dt is the skin friction or tangential drag force per miit length; Vt is the relative velocity of the water \\ith respect to a cable element gi\'en for straight-line lajdng by Vt = Vc — V cos a, (13) where Vc is the cable pay-out rate; p is the mass density of water; and Nr is the Reynolds number defined as Nr = Vi L/v, where v is the kine- matic viscosity of water. The data of Fig. 5 are for 100 foot lengths of cable towed in fresh water at a temperature of 60°F. 1140 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 From (12) we find 0.14n Dt = 0.055 v-''Vt 1.86 L 0.14 TT d. (14) This expression indicates that Dt for smooth cable depends on the in- clined length of the cable as well as the relative tangential velocity Vt . The form of (13) suggests that the flow tangential to a smooth cable is similar to flow past a smooth plate. In such flow a turbulant boundary layer develops which grows in thickness with distance from the leading edge, resulting in a length dependence of the type shown by (14). Since Fig. 5 refers to 100 foot cable lengths, (13) is probably not accurate for the magnitudes of L occurring in deep-sea laying, and should be used only to obtain the order of magnitude of C/ . Q Z 5 in 1 O TOWING TEST VALUES / i / A 5 ) EQUATION (12)^^ 7? / y\ i V ] i V — •-^O-C rT' ^ 012345678 TOWING VELOCITY IN KNOTS 10 Fig. 5 — Experimental values of the tangential drag force for cable No. 1 compared with those obtained by equation (12). For the cable with conventional jute outer covering, (cable No. 2); it was found that Z)^ = 0.01 Yl-'"' (15) fits the experimental data obtained by towing test (Fig. 6). Whereas Ie (15) the constant 0.055 is dimensionless, the constant 0.01 in this equa- tion has the dimensions necessary to give Dy in units of pounds per foo* when Y i is in feet per second. We note that for this cable Dt is inde-< pendent of the length of the cable. DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 8 7 6 5 1141 Q / o TOWING TEST VALUES V / 1 / E QUATION (i; 5)— / j 14 .A V k Y\ 2 3 4 5 6 7 8 TOWING VELOCITY IN KNOTS 10 Fig. 6 — Experimental values of the tangential drag force for cable No. 2 compared with those obtained by equation (15). The ratio of Dr to the tangential component of the cable weight force is given by Dt/w sin a. Ecjuations (14) and (15) indicate that even for small values of a. of the order of twelve degrees, Dt/w sin a is of the order of 6 per cent for relative tangential velocities Vt of 1.0 feet/sec. In many- situations V t will be less than this value, and we can neglect Dt compared to w sin a. As we shall see later, this approximation greatly simplifies the differential equations of the two-dimensional stationary model. Historically, the question of the variation of Dt with Vt is of some interest. In one of the early papers of 1858 Longridge and Brooks as- sumed a velocity squared dependence. In 1875, W. Siemens attacked this assumption stating that Dt actually varied linearly with Vt . There ensued a debate in which many bitter words but few experimental data were displayed.^ In view of our present knowledge that the skin friction force, even in the simplest case of flow past a smooth plate, is the result of complicated boundary layer phenomenon, the existence of this con- fusion is not surprising. 3.4 Sinking Velocities and Their Relationship to Drag Forces The studies of submarine cable forces in 1857 and 1858 preceded modern fluid mechanics by many years. To characterize the hydrody- namic forces acting on cal)le the eai-l}^ in\'estigators used sinLi'ng or \settling \'elocities rather than the more recently conceived drag coeffici- 'ents. The transverse sinking velocity Us was deflned as the terminal ve- locity attained by a straight, horizontal length of cable sinking in water. 1142 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 Similarly, the longitudinal sinking velocity v^ was the terminal velocity of a cable length sinking with its axis constrained to be vertical. If for a given cable the drag forces are functions only of velocity, the pa- rameters w, lis , and Vs , together with the laws of variation of the drag forces Anth velocity, completelj^ define the hydrodynamic behavior of the cable. Since sinking velocities are still used in submarine cable tech- nology, it is of interest to relate them to the more modern drag coeffici- ent viewpoint. In the case of transverse or normal flow around the cable, the variation of Z),v ^^'ith the square of the relative transverse velocity gives (Fat/Ws)^ = Dx/w, since at a transverse velocity equal to the sinking velocity the unit transverse drag force is w. Substituting for Djv from (4) we find Thus, the transverse sinking velocity Us is identical with the hydrody- namic consant H. We can therefore alternativelj^ write the approximate i relationship (9) as aoV = Us, (17) where ao is in radians and iis and V are in knots. For the tangential or skin friction flow along smooth cable, the sinking velocity concept is inadequate because the unit tangential drag force < Dt varies \nth length as well as ^^^th the relative tangential velocity *■ Vt . However, for cable with the conventional jute exterior (cable Xo. 2), we have (Vf/Vs) ' = Dt, w and from (15) the vertical sinking velocity : Vs is Vs = (46. Iw)^'^'^^, where Vs is in knots. j We note in passing that the cable does not, as is sometimes supposed, I sink vertically to the bottom at the transverse sinking velocity Us ■ '< Actually, the term "vertical cable sinking rate" is ambiguous. There are i in fact two vertical sinking rates which maj^ be important. Although both these rates are normallj^ approximately equal to Us neither is identi- cal to it. Relative to the earth, the resultant velocitj^ Y n of a cable element ha- two components: a horizontal component of the magnitude of the ship \'elocity, and a component inclined at the angle a of the magnitude of the cable pay-out rate Vc . These are shown in Fig. 7. The component Fvert of V K , given by T^v) 2iv sm- a where To is the tension corresponding to the angle 9^ 0 DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 1145 At the cable touehdowTi point on the ocean bottom only two conditions are possible. If the angled is not zero or tt there, the cable tension T must be zero. Otherwise a finite tension would act on an infinitesimal length of cable, producing an infinite acceleration. Hence, either the tension T must be zero or the angle 6 must be zero or tt. The first case normally implies a straight-line configuration (see Appendix A), which has al- ready been discussed. In other cases, we define To as the tension at the touchdown point, and we let ^o be zero or x, whichever is appropriate. If X, y are coordinates in the translating {x, y) frame of a point along the cable configuration, then dx = ds cos d, dy = ds sin 6. Combining these relations with (18a), we have I y 9q w(cos ^ — a sin f I sin ^ |) _ /•" {T - PeVc) COS ^ Jbq iy(cos ^ — A sin | | sin ^ |) _ [' {T - poV') sin ^ Jeo w{cos ^ — A sin ^ | sin ^ |) d^, (a) d^, (b) (20) dl (c) Equations (19) and (20) are an integral representation of the complete solution of the basic two-dimensional model. In general, the integrals appearing in these equations cannot be evaluated in terms of elementary functions, and the solution must be obtained by numerical integration. For towing problems where the pay-out velocity is zero, Pode " has tabu- lated these numerical integrations using the approximation that Dt has certain constant ^'alues. However, in towing problems the direction of Dt is opposite to what it is in normal laying and recovery problems. Be- cause small magnitudes of Dr were used, these tables nevertheless usually give adequate results in laying and recovery situations as well. At the same time, for submarine cable problems, other approximations allow more convenient ways of evaluating the integrals of (19) and (20). For example, it is more accurate simply to assume that Dt is zero. As we indicated in Section 3.2, this approximation gives a negligible devia- tion from the exact solution if the relative tangential velocity Vt is small. Furthermore, in this situation we obtain from (18b) dT . , dy -— = w sin 6 =^ w -f- , ds ds 1146 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 and hence the tension at the ship Ts is very nearly T. = To + wh, (21) where h is the depth at the touchdoAMi point. Thus, if the tangential drag force is neghgible, the tension at the ship is essentiaUy the bottom ten- sion plus wh, regardless of the nature of the normal drag forces. This is in fact a form of a well-known theorem which, as we shall see in Section 7.1, apphes in the three-dimensional case as well. In the next sections we make further simplifications of the general solution for the specific cases of laying and recovery. 3.6 Approximate Solution for Cable Laying On long cable lays ship speeds are normally of the order of 4-8 knots, with accompanying values of the critical angle a of the order of 10°-30°. For these small values of a, the assumption of zero tangential drag to- gether with some mathematical approximations allow further simplifi- cations of the general solution. These simplifications are derived in de- tail in Appendix C; here we indicate the results. The angle 6 which the configuration makes with horizontal is closely given by 1 - [%/{% + y)Y '^"' tan - = tan - l-f['ro/(n + ^)rtan^| (22) where y and To are dimensionless depth and bottom tension defined by y = y/h, To = To/wh. Here we use the cable angle a in the sense of Section 3.2, namely, as a parameter characterizing the hydrodynamic cable properties and the ship speed. The constant y is in turn defined by = (2 - «i"' ") . (23) sm^ a For small a, tan (a/2) is negligible and y is large. Further ° < ?rh < ^- Hence, the denominator in (22) is very nearly unity and 6 approaches the critical angle a at small values of y, even for relatively large values of To of the order of three or four. Thus in the laying case, the cable configuration is very close to a straight line except for a short distance at the ocean bottom. DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 1147 In Appendix C it is further shown that for small a >S = L + kT^/w, X = L cos a + \T,/w. (24) Here S and X are the distance along the cable and the horizontal dis- tances respectively from the touchdown point to the ship (Fig. 11), L and L cos a are the corresponding distances for straight-line laying at the same ship speed, and k and X are functions of the critical angle a which are plotted in Fig. 10. To illustrate the use of (24) we consider the following. Example: Cable No. 2 is being laid without slack onto a rough bottom from a ship moving at six knots. If the pay-out rate is decreased so the slack is 1 per cent negative, what is the subsequent rise of the tension with time at the ship? This is really a transient problem. However, we shall try to get an idea of the average behavior of the cable by assuming it passes through a se- quence of stationary configurations. Also, we assume that because of the rough bottom there is no slippage of the cable along the ocean floor. If d is the amount of negative slack and V the ship speed, then in a time t an amount V{1 — 8)toi cable will have been paid out. This amount plus the inclined length L will equal the amount contained in the curve AOC (Fig. 11). We then have L -f V(l - 8)t ^ S + Vt - {X - L cos a). (25) Substituting (24) into this equation and solving for To we find To = (w/(X — K))8Vt and that by (21) the tension at the ship is given by Ts = wh -\- w 8Vt. 0.4 0.3 0.2 0.1 (a) / ^ / [y^ / 0.016 0.012 I 0,008 0.004 (b) / / y / ^ / 5 10 15 20 a IN DEGREES 25 10 15 20 a IN DEGREES 25 Fig. 10 — Variation of k and X with the critical angle. 1148 THE BELL SYSTEM TECHNICAL JOUKNAL, SEPTEMBER 1U57 U- vt — 4 >!<- Lcos a. J X A t: Fig. 11 — Cable geometry at a time I after the onset of negative slack. For cable No. 2 a ship speed of six knots corresponds to a = 11.7 de- grees. By Fig. 10, this corresponds to X — k = 1.4 X 10~^ Also w = 0.705 lbs/ft by Table I. We get therefore n = wh + 3000 Thus, according to this calculation the tension in this example rises at the extremely rapid rate of 8000 Ibs/min. We note also that the rate of tension rise is here independent of the depth h. In the model which has been postulated, the cable is inextensible; that is, it is assumed not to stretch under load. Because the difference between the lengths of AOC and the sum of the hnear segments AD and DC (Fig. 11) is small, one might suspect that the effect of cable extensibility in the present example is important. We can account for this effect in a crude way by assuming that the curve AOC has an additional length cor- responding to the stretching caused by the load To acting over the length L. For a cable made of a single material, the stretching would be TqL/EA, where E is the Young's modulus of the material and A is the cross-sec- tional area of the cable. In analogy to this we denote the extensile rigidity of the cable by EA, using the bar to indicate that EA is actually a single number obtained directly by measuring the extension of a length of cable loaded in tension. With this notation (25) becomes L + 1^(1 - 6); + =^ = S + Vt - (X - L cos a), KA and repeating the previous computation we find w wh + r wh EA sin a -\- X - K V8I. It is to be noted that in this computation, unlike the inextensible case, the rate of tension rise depends on the depth h. DYNAMICS AND KINEMATICS OF SUBM.\IIINE CABLE 1149 For conventional helically armored cable, one cannot define a single extensile rigidity because of coupling between pulling and twisting. Thus, how such a cable extends under tension depends on how it is restrained from twisting at the ship and at the ocean bottom. Instead of trying to determine these end restraints, we consider the limiting cases of no re- straint and complete restraint to twisting. Data supplied by P. Yeisley indicate the values of EA for cable No. 2 in these conditions to be those given in Table I (Section 3.2). If we take h = 6,000 and 12,000 feet, we find with these values that h = 6000 feet: Ts = wh + 220 (Ib/min)/ (twist unrestrained), = wh -\- 640 (lb/min)i (twist restrained), h = 12,000 feet: Ts = wh + 120 (\h/mm)t (twist unrestrained), = wh -\- 360 (Ib/min)^ (twist restrained). Comparing with the inextensible computation, we see that the extensi- bility markedly reduces the rate of tension build-up. Nevertheless, even for the case of no restraint to twisting at a depth of 12,000 feet the rise rate is a relatively high 120 Ib/min. Hence, at least over a rough bottom, the tension would quickly indicate the onset of negative slack, although the sensitivity of this indication would decrease with increasing depth. 3.7 Approximate Solution for Cable Recovery Fig. 8 illustrates how cable is in present practice recovered from the ocean bottom. The cable is in front of the ship as it is brought in over the bow, and the ship pulls itself along the cable. In this process the cable tends to guide or lead the ship directly over its resting place on the ocean bottom. It is clear that during recovery by this procedure the tension at the ocean bottom is not zero and the cable configuration is not a straight line. Furthermore, in this situation the normal component of the water drag force Da- pushes down on the cable instead of buoying it up as in the case of laying. This in turn implies a higher tension at the ship during re- covery than during lajang. If the tangential drag is neglected, the tension at the ship Ts during recovery is given in dimensionless form by (see Appendix C) Ts - 1 2 cos a + cos Us tan a 1 — cos a cos a. l/T (26) 1150 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 wt 1 ^W \ V '^ ^^ \v \ \ \, _^ \y ^. \ s \^ as =40° ^^ ^ \ \, ^ >^ \ S: \, \ ^^ ., 50° \ \: h^ ^^ ^ ^. N \ ^v "^ ^^ ^--- __60^ ^ -^ b:; ^ 80° ^^ _90° - 10 20 30 40 50 60 a IN DEGREES 70 80 90 1 Fig. 12 — Variation of the tension factor for recovery with the critical angle a. ■ w h 4 2 3 4 5 SHIP SPEED IN KNOTS yig 13 _ Variation of exact and approximate tension factors for recovery of cable No. 2. DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 1151 where Ts is the tension factor defined by 7",. = T^/wh and y is given by (23). Equation (26) is plotted in Fig. 12 in the form of Ts versus a for various surface incidence angles as (Fig. 8). It is seen that the recovery tensions are in fact considerably higher than the laying tension of approx- imately wh. To illustrate the smallness of the error of neglecting the tangential drag force in this computation, we have plotted the approximate and exact curves of Ts versus ship velocity for cable No. 2 in Fig. 13. The dotted curves have been computed from (26), while the solid curves have been obtained by substituting Dt from (15) into (19) of the general solu- tion and integrating numerically.* (The curve labeled Shea's recovery method is discussed in the next section.) The distance along the cable S and the horizontal distance X from the touchdown point to the ship cannot be expressed in a simple form as in the case of laying. However, they can be obtained by numerical integra- tion from (20). The results of this computation for Dt = 0 are shown in Figs. 14 and 15. How Figs. 12, 14 and 15 can be used is illustrated in the following ex- ample. * The standard form of Simpson's rule was used for all the numerical integra- tions mentioned in the paper. In each case the interval of integration was chosen fine enough to obtain at least three significant figure accuracy. h ■J \ A ^ V ^ \ S^ 3 ^ s\ --^ ^ ^bi ^ «s = = 40° ? \ ^ ^ :^^ !».,;— ^ 50° ^ -^ . ..^ _60°_ 70° ^ -^ — , _ — ■ ■ ----- -^ 80° 0 90° --- ^ 10 20 30 40 50 60 OC IN DEGREES 70 80 90 Fig. 14 — Variation of the horizontal distance to the touchdown point during recovery with the critical angle. 1152 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 h \ V \ ^ s \ ^ \ ^ . , "5 = = 40° \ ^ ^ ^ ^ "^^■^ X ::< J:::::^ ^ . " ' — .50° __60^ _70°_ ~90^ — . "^ :::::: ^ — — — ■ — ■ — ^^ :^ — 10 20 30 40 50 60 a IN DEGREES 70 80 90 Fig. 15 — Variation of the distance along the cable to the touchdown point during recoverj' with the critical angle a. Example: A cable weighing 0.7 lb/ft in sea water and having a hj'dro- dynamic constant H of 70 degree-knots, is to be picked up from a depth of two thousand fathoms. If the ship speed is one knot what is the cable tension at the ship for surface angles as of 40°, 60°, and 90°? How far in front of the ship and how far along the cable will the touchdo\ra point be for these values of a^ ? As indicated by (9), an H value of 70 degree-knots together with a ship velocity of one knot yields ao = 70 degrees. Fig. 4 yields in turn a = 60 degrees. Entering Fig. 12 with this value of a, we can obtain Ts/wh. In this example the wh tension for a depth of two thousand fathoms is 8,400 lb, and hence the values of TJwh and 7',. are as follows: 40,700 lbs 21,700 lbs 12,900 lbs From Fig. 14 we get in turn for the horizontal distance from the ship to the touchdown point as X/h X 40° 2.65 5300 fathoms 60° 1.56 3120 fathoms 90° 0.66 1320 fathoms Otg Ts/wh 40° 4.85 60° 2.58 90° 1.53 DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 1153 Finally, from Fig. 15 we get for the distance along the cable to the touch- down point as S/h S 40° 2.88 5760 fathoms 60° 1.95 3900 fathoms 90° 1.33 2660 fathoms 3.8 Shea's Alternative Recovery Procedure The high tensions which result in the usual recovery operation require slow ship speeds of the order of one knot or less if the cable is not to be broken. One wonders if it is possible to mitigate these tensions and thus speed the recovery process. J. F. Shea discovered that this can theo- retically be done by allowing as to exceed 90°, thus establishing the straightline configuration (Fig. 16). As in laying, the normal drag forces in this scheme support the cable, rather than push down on it as in con- ventional recovery. However, in contrast to the laying situation we have Vt = Vc + V cos a. Thus Vt is the sum of Vc and V cos a instead of their difference and Dt is not necessarily negligible. Furthermore, the direction of Dt is now such as to increase rather than decrease the tension over the wh value. Hence, instead of (2), a summation of forces along the cable yields Ts = wh + DtL, and the tension at the ship can be consid- erably higher than wh. A curve of T^ as a function of ship speed for cable No. 2 is shown in Fig. 13 with the label "Shea's recovery method". This has been computed for the case of haul-in speed equal to ship speed by means of the above equation and (15). It is seen that the tensions com- puted for this method of recovery, at least for the cable No. 2, are never- theless considerably smaller than those which occur in the usual recov- ery procedure. It would seem that the straight-line recovery technique could fruitfully bear further examination, especially for application to the recovery of long stretches of cable. Fig. 16 — The present and Shea recovery methods. 1154 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 IV. EFFECTS OF SHIP MOTIONS 4.1 Tensions Caused hy Ship Motions 111 the basic stationary model a perfectly calm sea is postulated. However, in reality, wave action gives rise to a random motion of the ship which in turn induces variations in cable tensions around those cor- responding to the basic model. To analyze this effect, we assume that the mean forward velocity of the ship and the mean pay-out or haul-in rate are constant and that the mean tension at the ship and the mean direction of the cable as it enters water are those given by the stationary model. In a reference frame mov- ing with the mean velocity, we resolve the ship displacement into a longitudinal component Po (Fig. 17) along the mean or stationary direc- tion and a transverse component Qo perpendicular to the stationary di- rection. Fig. 17 — Longitudinal and transverse components Po and Qo of the ship displacement. Intuitively, one might e.xpect the tensions caused by the transverse displacement Qo to be negligible compared to those caused by the longi- tudinal displacement Po . An analysis we have carried through in fact yields this conclusion. Because of its complexity and length, this analysis and the model upon which it is based are given in Appendix D. The re- sults for the case of harmonic variation of Qo with time indicate, at least for cable No. 2, that the tension associated with the transverse com- ponent Qo is indeed negligible for all except ship motions so extreme as to rarely occur. In addition, this analysis indicates that for the transverse disturbance Qo , the amplitude of the responding transverse cable motion decreases exponentially after the cable enters the water because of the damping action of the water drag forces. The "half-life" distance for cable No. 2, that is, the distance along the cable at which the amplitude of a harmonic transverse motion is damped to one-half its surface value, is plotted in Fig. 18 as a function of the period of the motion for various depths h and ship velocities V. The striking feature of these figures is the rapidity of this damping. The analysis thus shows for cable No. 2 that the effect of a transverse disturbance penetrates only a short distance into the water. DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 1155 340 200 LL LU U z If) a 160 120 1 80 < I 40 OCEAN DEPTH = 1000 FATHOMS V n vl KN ^'V ^ 9^ y^ . / / / h l^ J fathoms/^ 300 ^ / r ^^ 1000 / /^ ^ y / 500^ ^ / _> ^ ^ X (b) 8 12 16 0 4 8 12 PERIOD OF TRANSVERSE SHIP MOTION IN SECONDS 16 = 0 (27) Fig. 18 — • Variation of half-life distance of cable No. 2 with the period of ship motion. As far as cable tensions are concerned, the important ship displacement then is the longitudinal component Po , directed along the stationary direction of the cable. The analysis of Appendix D leads to the basic one-dmiensional wave equation d ip 1 ^-p for the description of the longitudinal motion. In this equation p is the tleviation in longitudinal displacement from the mean pay-out or haul-in displacement, and the remaining symbols are defined as (Fig. 17) X = distance from the mean ship position along the stationary cable configuration, t = time, c\ = EAIpc . The additional tension Tp due to ship motion is in tiu'n given by dp ax (28) As in the example of Section 3.6, we ha\'e again assumed that bj^ using 115G THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 in (28) the limiting values of EA obtained by complete restraint to twist- ing and no restraint to twisting during pulling, one can obtain bounds on the actual displacements and tensions. The solution of (27) under arbitrary boundary conditions can be ob- tained from standard textbooks. Probably it is most representative to assume the cable is semi-infinite. That is, although damping of the cable is normally so small that we neglect it in (27), we may assume, because of the cable's great length, that the damping is sufficient to cause com- plete decay of a disturbance initiated at the ship, and that such a dis- turbance is not reflected from the ocean bottom. Under this condition the additional tension Tp is given by T,= -VeApc^, (29) where P = Po + Pi with dPi/dt being in turn the increment in pay-out rate or decrement in haul-in rate from the mean. For cable No. 2, Table I (Section 3.2) indicates that \^EApc ^ 220 Ib/ft/sec (twist unrestrained), = 400 Ib/ft/sec (twist restrained). Two examples will make clear the application of (29). Example 1: Steady- Slate Laying or Recovery in a Regular Seaway. Assume that in a frame of reference traveling at the mean horizontal ship velocity ship surging (to and fro forward motion) is zero and the combined heave and pitch motion is normal to the ocean surface and is given by W = Asin27r-. T If the period t is 6 seconds and the amplitude A is 15 feet find for cable No. 2, a) (^p)max for laying at a constant pay-out rate and at a ship speed of 6 knots, ^'>) (7'p)max for recovery at a constant haul-in rate and with a surface incidence angle of 60°. In l)oth cases (a) and (b), the deviation Pi in pay-out or haul-in rate is zero, hence P = Po = W sin a, , and (c?P/c?0,nax = (27r/r) .1 sin as . Since DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 1157 cable No. 2 has a hydrodynamic constant H of 70 degree-knots, we have in case (a) as = 11.7 degrees and ( -y- ) =2.12 ft/sec. \ (It /max From (29) we get therefore (7'p)max = 466 lbs (twist unrestrained), = 848 lbs (twist restrained). In case (b) we have as = 60°, (rfP/(/Omax = 13.6 ft/sec, and hence (Tp)inaK = 2,990 lbs (twist unrestrained), = 5,430 lbs (twist restrained). During recovery by conventional methods the surface incidence angle as is in general much larger than that which occurs during laying. The above example points up that one can expect correspondingly larger ship motion tensions during recovery than during laying in the same sort of seas. Since the stationary tensions are also much larger during recovery, recovery is the condition for which the strength of the cable should be designed. In this example we have considered a regular seaway, something which does not exist in nature. Recent work in the application of the theory of stochastic processes to the study of ocean waves and ship dynamics promises to develop into a realistic description of the behavior of ships at sea.'^ When such a description becomes available, we shall be able to obtain a better estimate of the magnitudes of ship motion tensions. As far as data presently available are concerned, the maximum storm condition vertical velocity at the bow or stern recorded by the U.S.S. San Francisco during her research voyage of 1934 was 22 feet/sec. Since this ship was roughly the size of a cable ship such as the H.M.S. Monarch, this figure might indicate the order of the maximum velocities to be expected in cable practice. In terms of our example, for six knot laying this vertical velocity would imply Tp = 980 lbs (twist unrestrained), = 1,780 lbs (twist restrained). For recovery at a surface incidence angle of 60°, it would imply in turn Tp = 4,200 lb (twist unrestrained), = 7,600 lb (twist restrained). 1158 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 However, it is to be cautioned that these numbers are merely indicative and might differ considerably from those which occur on a particular cable ship. Example 2: Brake Seizure While laying cable No. 2 at six knots in a perfectly calm sea, a sudden seizure of the brake occurs. What is the resulting initial rise in tension? Because of the calm sea we have Po = 0. Therefore —- = Pi = —V cos as . at With the value of T" = (3 knots and a corresponding «« of 11.7° (see Ex- ample 1) we have dP/dt = 9.9 ft/sec and hence from (29) Tp = 2180 lbs (twist unrestrained), = 3970 lbs (twist restrained). These values of Tp pertain only to the transient values occurring while the tension wave is being transmitted to the ocean bottom. If the seizure in this case occurred at a depth of three thousand fathoms, the time of transit to the ocean bottom would be only of the order of nine seconds. After reaching bottom our initial assumption of no reflection from the bottom w^ould be violated and (29) would no longer hold. In reality the cable tension would continually increase at the ship and reversing ship engines or some other action would be required to avoid rupture of the cable. V. DEVIATIONS FROM A HORIZONTAL BOTTOM 5.1 Kinematics of Laying Over a Bottom of Varying Depth Ocean bottom topography is not everywhere flat and horizontal as postulated in the basic model. In the Mid-Atlantic ridge, for example, there exist bottom slopes of thirty or forty degrees. In other places sub- marine canyons with almost vertical sides have been found. Further- more, where the bottom is steepest it is most likely to be rocky and craggy since erosion tends to smooth out a sandy or muddy bottom. Therefore, it is important to know how the cable should be paid out to cover a bottom of varying depth. To help determine this, we extend here the stationary model to the case of a non-horizontal bottom. In Section 3.1 we indicated that if the cable tension at the touchdown point is zero the configuration according to the basic model is a straight line, regardless of how the cable is paid out. If the cable is paid out with DYNAMICS AND KINEMATICS OF SUBM.\RINE CABLE 1159 slack with respect to the bottom, the zero touchdown tension condition is fulfilled. Hence, under the proper slack pay-out, the cable geometry and, as we shall see, the cable kinematics are particularly simple. Essentially, we must consider two deviations from the horizontal bottom, namely, downhill or descent laying and uphill or ascent laying. We consider these situations in turn, confining ourselves to bottoms of constant slope since any bottom contour can be approximated by straight-line segments. To cover a descending bottom, the cable pay-out rate must exceed the ship speed, Fig. 19(a). To cover an ascending bottom, the angle of in- cidence a of the cable, which as we have seen in Sections 3.1 and 3.2 de- pends only on the ship speed, must exceed the ascent angle 7, Fig. 19(b). Otherwise, the situation shown in Fig. 19(c) develops. Hence the critical parameters are pay-out speed and ship speed. (b) ASCENT (a > 7) (C) ASCENT {yxx) Fig. 19 — Cable geometry during straight-line descent and ascent laying. During descent laying we see from Fig. 20 that in a time / an amount of cable equal to a + 6 must be paid out. Hence the required paj'-out rate Vc is (a -f- h)/t. But by straightforward trigonometry y _ ct + 5 _ sin a + sin /? y. " t sin (a + &) ' (30) where jS is the angle of descent and a is the straight-line incidence angle. IIGO THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 Fig. 20 — Kinematics of straight-line descent laying. In accordance with usual terminology we define the slack e as 6 = (F. - V)/V. (31) i We shall think of the slack as being composed of two parts: a fill f, which is the amount of slack required for the cable to cover the bottom, and an excess, equal to e — /, which will normally be laid to provide a margin of safety. Substituting Vc from (31) into (30) we get the expression for the fill /. The result can be transformed to the form I / tan - tan - = .^^^. (32) The quantities a, 13 and / are normally all small quantities and we may make the approximations a a tan-^-. tan / 2+/ f For a, 13 < 30° and / < 0.06, the error in each of these approximations is less than 3 per cent. Hence, with good accuracy we write (32) as f = ^ J 2' (33) where a and jS are expressed in radians. Further, we have from (9) that a in radians is very nearly a = H/V, where H is in radian knots. Sub- stituting this expression into (33), we get for the fill DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 1161 f = §. (34) Finally, using this expression for/ in (31), we arrive at* Ve - V = ^. (35) Thus, the increment in required pay-out rate is essentially a function only of the descent angle 13 and is independent of ship speed. In the case of an ascending bottom for which a > y, Fig. 19(b), posi- tive bottom slack may be obtained with a pay-out of less than the ship speed. The allowable decrement in pay-out rate is given by V-Vo = ^, (36) that is, the same as the required increment for ascent laying. Likewise, the fill / in this case is simply / = — {Hy/2V). The only way to avoid the situation shown in Fig. 19(c) where a < y is to sail slowly enough to maintain an incidence angle a greater than the angle of rise y. By (9), we have for most laying speeds aV ^ H. With good accuracy the condition a > y thus implies V <-. (37) 7 Therefore, for a given rise y the limiting ship speed is simply H/y. 5.2 Time-Wise Variation of the Mean Tension in Laying Over a Bottom of Varying Depth In the cases where the cable is paid out with excess onto a bottom of constant slope, the variation of the mean tension at the ship with time is easily computed. During descent laying the increase in depth 8 after a time t is by elementary trigonometry (Fig. 20) _ sin a sin /3 „ sm (a -}- (8) Hence, the rate of rise of the mean shipboard tension is dT w8 sin a sin j8 ^r /oo\ — - = -- = ^— — ■ — r wV. (38) dt t sm {a + 13) Similarly, during an ascent lay for which the bottom is less steeply * Note that in (33), (34) and (35), // nuij- he replaced by the numerically identi- cal transverse settling velocity Us (see Section 3.4). 1162 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 inclined than the cable (a > 7), the rate of decrease in shipboard ten- sion is dT sin a sin 7 ,7- at sm {a — 7) Like negative slack laying on a flat bottom, the variation of tension with time depends greatly on the frictional characteristics of the bottom in cases other than the above. We therefore limit ourselves to situations , where the cable does not move with respect to the ocean floor. This case ! might be approximated by rough bottoms, where the cable might wedge itself between rocks. A nomograph giving a rough estimate of the rise of mean tension with time when a cable becomes completely suspended is worked out in Ap- pendix E. In deri^dng this nomograph it is assumed that the cable takes i on a sequence of stationary configurations. This assumption is probably ] reasonable if the time span of the tension rise is large compared to the - time of passage of a tension wave from the ship to ocean floor and return, which as mentioned in Section 4.1 is of the order of 18 seconds. However, j because of this assumption and others mentioned in Appendix E, we | regard the tension variation computed by the nomograph only as a crude approximation. i Fig. 21 shows the mean ship-board tension versus time computed by means of the nomograph for various slacks e, where e is defined by (31). The values which were used for the other parameters entering the calcu- lation were ^^ = 3.1 X lO-l EA a = 12°. Also shown on this curve is the tension rise computed for the case of laying down a vertical slope without excess. The rise for this case is given by (38) with /3 = 90°. It is seen that as the slack e is increased the curves for a complete suspension approach the |S = 90° curve. Indeed, it can be shown that under the assumptions made in computing Fig. 21 the (8 = 90** curve gives a lower bound on the tension rise with time in the case of a complete suspension. A tension rise rate greater than the j8 = 90° rate is thus an indication of unsatisfactory covering of the bottom. In the case of too rapid a ship speed resulting in a < 7 (Fig. 19c) re- straint of movement of the cable along a rough bottom would cause the tension on the high side of the crest to be zero. There would thus be a sudden drop in tension corresponding to the sudden decrease in depth at the touchdown point after the cable was laid over the crest of the hill. DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 1163 7000 4000 TIME 15 20 N MINUTES Fig. 21 pended. Variation of tension with time when cable No. 2 is completely sus- On the other hand, in the case of a frictionless bottom, the removal of the supporting water drag forces would cause the cable to seek a catenary equilibrium position on the low side of the crest. But in doing this, the cable would drag itself over the crest, with an accompanying increase in shipboard tension. Thus for the case of a bottom rise steeper than the cable inclination (a < 7) either an increase or a decrease of tension with time is possible, depending on the nature of the bottom. 5.3 Residual Suspensions If the cable is not paid out rapidly enough, or if the ship speed is ex- cessive, the cable will be left with residual suspensions after it has been laid. To get an idea of the possible magnitudes of the tensions accom- panying these suspensions, we consider here some numerical examples pertaining to cable No. 2. As before, we assume for definiteness the ex- treme case of a bottom rough enough to prevent movement of the cable. In Fig. 22 is shown the profile of a 85 fathom (210 feet) increase in depth with a maximum slope of 45°. This profile was obtained from 1164 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 fathometer records of the Mid-Atlantic Ridge provided by Professor Bruce C. Heezen of the Lamont Geological Observatory. Laying down this slope at a ship speed of six knots requires a slack of 8.5 per cent (see Section 5.1). If the slack were only 5 per cent, the successive cable con- figurations as calculated by the methods of Appendix E would be those shown in Fig. 22(a).* The cable would touch bottom after 2.6 minutes, t IN minutes: 0 (a) DESCENT 2710 LBS -990' *\ 1320' (b) ASCENT Fig. 22 — Successive cable configurations during a 35-fatiiom descent and as- cent lay of cable No. 2 at a 6,000-ft depth with an assumed 5 per cent slack and 6-knot ship speed. leaving a residual suspension with a half-span of 480 feet and a tension of 525 lbs. The mean tension at the ship would correspondingly increase i by 525 lbs during the 2.6 minute time interval. In even moderately^ rough seas, this tension change could be obscured by the ship motioni tensions. Consider this profile next to represent an ascending lay under a shipi speed of six knots. Fig. 22(b) shows the initial {t = 0) and residual cable* configuration. Because of the small incidence angle of the initial straight- line shape, the residual half -span of the catenary is a quarter of a mile (1820 feet) long, and the accompanying residual tension is 2,710 lbs, or roughly that which normally occurs in laying at a depth of f of a nautical mile. At the ship, there would be a decrease in the mean tension of 130^ lbs. corresponding to the 35 fathom decrease in depth. Again, a tension change of this magnitude would be difficult to discern because of ship motion tensions. * We have further taken the ratio wh /EA to be 3.1 X 10"^ in this computation. However, the results are very insensitive to change in the wh /EA ratio. DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 11G5 If the above 35 fathom change occurred at a depth of say three thous- and fathoms, a very sensitive fathometer would be required to detect it. Thus, although complete restraint of cable movement along the bottom is an extreme and unlikely condition, the above examples indicate that long residual suspensions can occur with essentially no manifestation at the ship, especially in deep water. VI. CABLE LAYING CONTROL 6.1 General We have seen that the mean cable tension at the ship reflects the amount of slack which is being paid out and how the cable is covering the bottom. However, in most cases this reflection is not sensitive. For example, the tangential drag force Dt varies with V t , the longitudinal velocity of the cable relative to the water. In theory, as (2) shows, one can therefore determine the amount of slack being paid out from ship- board tension measurements. For cable No. 2, we have plotted in Fig. 23 the variation of the mean tension at the ship as a function of slack for a ship speed of six knots and a depth of two thousand fathoms. At three per cent slack the tension is 8,240 pounds, while at six per cent slack it is 8,020 pounds, a difference of only 220 pounds. This amount of tension 9000 8600 IT) a z D O Q- 8200 Z 7800 O 5 7400 h- 7000 ^wh , . ^ -^ -.^ "^ 3 4 5 6 7 PER CENT SLACK 10 Fig. 23 — Variation of shipboard tension with per cent slack for hiving cable No. 2 at a ship speed of 6-knots in a depth of two thousand fathoms. could be easily obscured by the effect of ship motion. Thus, to measure slack accurately by relating it to cable tensions one would have to know the depth and cable parameters very precisely and, in addition, would need a veiy efficient filter to separate out the "noise" tension caused by ship motion. Similarly, it has been shown that residual suspensions can occur with essentially no reflection in th(> tension readings at the ship. Hence, al- though tension readings can give a valuable check on how the cable is 11G() THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 covering the bottom, it would seem difficult for them to provide exact enough data for the control of cable laying. At the same time we have seen that if the bottom contour is known in advance, then for a given ship speed one can compute the required cable pay-out rate. Also with foreknowledge of the bottom, one can anticipate steep bottom ascents and decrease the ship speed accordingly. Such a purely kinematic attack on the cable laying problem would seem more fruitful than an attack which depends on measurements of ship- board cable tensions. Possibly the simplest way of measuring the bottom contour is by means of a fathometer located at the ship. Since the cable ship is nor- mally far forward of the touchdown point of the cable, one could in theory obtain in this manner the reciuired advance knowledge of the contour. In present practice, a taut piano wire is used to obtain the ground speed of the ship. We examine briefly the accuracy of this method in the next section. 6.2 Accuracy of the Piano Wire Technique The taut wire is laid simultaneously with the cable, but under a con- stant mean shipboard tension. If the bottom is perfectly horizontal, the speed of the wire coincides with the ground speed of the ship. However, when the bottom depth is variable and the wire is laid up and down hill, the wire's pay-out speed deviates from the ship speed. By (31), it is seen that the error in the ship speed which is indicated by the wire is just equal to the slack e with which the wire is paid out. This slack, which may be positive or negative, can in turn be estimated by the methods of the previous sections. Consider the beginning (denoted by (1) in Fig. 24) and end (denoted by (2) in Fig. 24) of a downhill lay of the piano wire. As before we neglect the tangential drag force. Then, the condition that the tension at the ship remains constant gives, by (21), (Tn)i + wh, = (Toh + wh2 , (39) where the subscripts 1 and 2 refer to the configurations at the beginning and end of the downhill lay. If e is the average slack or error of the piano wire during the descent, then (1 + e)F is its average pay-out rate, and we have by Fig. 24, S, -f (1 -f e)Vt = ^-^^-1^ + .S'2 , (40) sm /3 DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 1167 where Sy and S2 are lengths along the cable from the touchdown point to the ship. Also, from Fig. 24 Zi + Vt = (/i2 - /ii)/tan 13 + X. . (41) ^m^>^^<^^#s^^^^<<^^^^^^'^ Fig. 24 — Piano wire configurations at the beginning and end of a descent lay. Equations (39), (40), and (41), together with the general equations (Section 3.6) s = h sin a + K To X = h tan a + X To (24) allow one readily to solve for the average error e in the piano wire indi- cation of ship ground speed. The result is sin a + sin ^ — k sin a sin /3 e = — 1 '. : 7T : ; ; — — i- (42) sin {a + ^) — \ sm a sm ^ For the small values of a and ^ which normally occur during the lajdng of the piano wire, the terms X sin a sin ,8 and k sin a sin /3 are negligible. Hence, the average error e is thus very nearly sin a + sin ^ . /,q\ sin (a + p) which, as (30) indicates, coincides with the amount of fill which would be required to lay downhill with the straight-line or zero touchdown tension configuration. Equation (43) is in turn closely approximated by (Section 5.1) a/3 27' (■14) 1168 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER IfloT Similarly, for ascent laying of the wire on a bottom which rises less steeply than the inclination of the wire (19b), we get sin a — sin 7 + « sin a sin 7 sin (a — 7) + X sin a sin 7 1, which is very nearly — a7 //7 27 (45) : (4G) Thus, in both the above cases, the error in the piano wire technicjue can be closely obtained by assuming that the configuration of the wire is a straight line during ascent and descent laying. This is not surprising since, as we saw in Section 3.6, the deviation from the straight-hne con- figuration during piano wire laying is normally small. Because of its smooth exterior, the normal or transverse drag coefficient of the piano wire probably can be obtained from published curves for flow past a smooth right circular cylinder as shown in Appendix B. For typical 12 gauge (0.0290 inch diameter) piano wire, these curves yield a value of Co of 1.45 and an //^ value of 25.0 degree-knots. However, these values of Co and H must be considered tentative until confirmed expe- rimentally. Ivnowing the wire's H value, we can compute the error of the ground speed caused by descent and ascent laying of the piano wire by means of (44) and (46). The result of this computation for H = 25.0 degree- knots is showTi in Fig. 25. When the ascent angle of the bottom exceeds the incidence angle of the wire, suspensions result and the error cannot be computed without 6 8 10 0 2 SHIP SPEED IN KNOTS Fig. 25 — Error during descent and ascent laying of 12-gauge piano wire. DYNAMICS AND KINEIVIATICS OF SUBIVLIRINE CABLE 1169 knowledge of the frictional properties of the bottom. For an H value of 25.0 degree-knots, (37) indicates that suspensions will occur for ship speeds V greater than V = 25.0/7, where V is in knots and the ascent angle 7 is in degrees. Hence, for a typical laying speed of 6 knots, ascent angles greater than 4.2 degrees will cause suspensions of the piano wire. These magnitudes indicate that suspensions of the piano wire probably actually develop in practice. It is seen from Fig. 25 that for the usual small ascent or descent angles, the piano-wire technique is quite accurate, while for large bottom slopes it can be considerably in error. Again, however, if the bottom contour is known in advance, these errors can be estimated in the cases plotted in Fig. 25 and therefore can be corrected for. In this manner, the piano wire could be improved to give accurate ground speeds in all two-dimen- sional situations, with the exception of the case of a suspension caused by a too steeply ascending bottom. Such suspensions can be avoided only by maintaining a sufficiently slow ship speed. However, as seen by the small computed H value of 25.0 degree-knots, the ship speeds recjuired to avoid piano wire suspensions on uneven bottoms are probably pro- hibitively slow. Hence, for steeply ascending bottoms it is likely that some other means of determining the ship ground speed is necessary. VII. THREE-DIMENSIONAL STATIONARY MODEL 7.1 General Thus far we have assumed that the cable lies entirely in the plane formed by the ship's velocity vector and the gravity vector. Because of the symmetry of the cable cross-section, this assumption seems reason- able.* However in certain cases, as for example in the presence of ocean cross-currents, the assumption of a planar configuration is clearly un- tenable. We consider therefore the case where the cable configuration is not necessarily planar but is still time independent with respect to a reference frame translating with the constant velocity of the ship. In analogy with previous terminology, Ave call this the three-dimensional stationary model. Assume there is a constant velocity ocean current in each of a finite number of layers. Let the vector Vw denote the ocean-current velocity in a reference layer. In the stationary situation the velocity of the cable * Because of asymmetries caused by the helical armor wire or because of minor out-of -roundness, it is conceivable that a sidewise drag force might develop which would cause the cable to move out of the ship's velocitj'-gravitN' phme. For a re- port of experimental observations of such jawing in wire stranded cables, see Ref- erence 11. 1170 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBEll 1957 configuration is everywhere the velocity of the ship, which we denote by the vector V- Hence the velocity V' of the water with respect to the cable configuration in the reference layer is r = v^ + i-v) Vu V. Further, in this layer we choose a set of coordinate axes ?, r?, T translating at the velocity V as follows: The ^ axis has the direction of — V', while 77 is measured vertically upward, and f is perpendicular to rj and ^ so that the axes ^, ??, f form a right-handed system. A plan view of this configuration is shown in Fig. 26. We have denoted the angle between V and Vw by jS, while the angle between the ^ axis and V is denoted by (p. (The distances d and e refer to a subsequent section.) To describe the cable configuration with respect to the ^, r?, f axes, we use the spherical polar coordinates 6 and i/' shown in Fig. 27. (The t ,u ,v vectors are dis- cussed in Appendix F.) Fig. 26 — Plan view of the coordinate system for the three-dimensional sta- tionary model. As in the two-dimensional case, we resolve the velocity of the water with respect to a cable element in the reference layer into a component Vn normal to the cable and a component Vt tangential to the cable, and associate with Vn and Vt the drag forces Djv and Dt . The resulting differential equations, which are derived in detail in Appendix F, are the following: (T - p^^:) f as + i:;A'(cos^ x// sin" 6 + sin" i/')"" cos i/- sin d — w cos 0 = 0, (a) DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 1171 (T - PcVc) COS d (47) + wA'Ccos" \}/ sin' d + sill" \py''^ sin ^ = 0, (b) dT \ ds + Dt — w sin 6 = 0, (c) where A' = CDpdV'^/2, and V is the magnitude of F'. In addition, connecting the coordinates ^(s), v(s), and f(s) of a point s along the cable with the angles 6 and \p we have the geometric relation- ships dm ds dr](s) ds d^(s) ds = cos 6 cos ip, (a) = sin 6, (b) = —cos 6 sin \p. (c) (48) Two important general results follow from (47) and (48). For one, if the tangential drag force Dt is negligibly small, (48b) substituted mto equation (47c) yields upon integration T = To-\- wr,, (49) where To is the tension at r; = 0. Hence, if 77 is measured from the ocean "t DIRECTION OF CABLE Fig. 27 — Definition of the spherical pohir coordinates 6 and \p and the unit vectors t, u, and v. 1172 THE BP]LL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 surface, and if at the bottom (77 = —h) the tension is zero, the tension at the ship is essentially wh, regardless of the nature of the normal drag forces. Since in most laying situations for present cables, the tan- gential drag force can be reasonably neglected, this fact provides a con- venient over-all check on the laying process. That is, if the cable is being laid with excess, the tension at the ship for any stationary cable con- figuration, planar or non-planar, should be essentially wh. Any marked increase of tension over the wh value necessarily means the bottom ten- sion is non-zero and insufficient cable is being paid out. The second important result is derived in Appendix F. This result is that if the bottom ocean layer in our model is devoid of cross currents, and if the bottom tension is zero, then, for the boundary conditions which are normally observed, the cable configuration in the bottom layer is a straight line. Further, this straight line is in the plane formed by the ship's velocity vector F and the gravity vector. Hence, for example, in laying with excess in a sea which contains surface currents, the cable configuration in the lower, current-free portion will be a straight line in a vertical plane parallel to the resultant velocity of the ship. The laid cable will be parallel to the ship's path, but displaced a certain distance from it. Thus, because the lower portion is a straight line, our previous results about the kinematics of straight-line laying still apply. Only they now are pertinent to the displaced bottom contour rather than to the contour which hes directly beneath the ship. 7.2 Perturbation Solution for a Uniform Cross-Curreyit Cross-currents are commonly confined to a region near the ocean sur- face. It is of interest therefore to determine for such surface currents the distance e (Fig. 26) which the laid cable will be displaced from the path of the ship. In Appendix F we consider the problem for a cross-current of uniform but comparatively small velocity. In addition, we determine the distance d (Fig. 26) back of the ship at which the cable leaves the upper, cross-current stratum and assumes the straight-line configuration it has in the lower stratum. Let us assume for the sake of reference that the resultant ship velocity V is due east, and that the cross-current F„ is inclined at an angle jS to the north (Fig. 26). The resultant velocity V of the water with respect to the cable in the surface stratum has the magnitude therefore of V = \{V - F„, cos ^f + (F, sin /3)']', (50) and is incUned at the angle ip from due \vest, where DYNAMICS AND KINEMATICS OF SUBMAKINE CABLE 1173 tan

pcVc does not guarantee that the shipboard tension must be greater than pcVc . We might somehow contrive to lay at a zero bottom tension with T < pcVc and ^Wth the cable in one of the non-straight line configurations of Regions II or III. Consider the cable configuration lying in Region II. From Fig. 7 it can be seen that the vertical velocity of a cable element is given by 37 = - Fvert = - Vc sin d, at where y is measured upward. Hence, of the possible trajectories for which the bottom tension is zero only those for which the bottom cable angle do is between zero and tt correspond to cable laying. For region II, there- fore we need consider only the trajectories in the range 0 ^ ^u < a at To = 0. From (20c) the maximum value of y^ for these trajectories is given by ft PcVc' n sin^ Vm = w Jo \(cos ^ — A sin- ^) 'o IV sin 77 — Drir]) X exp w (cos 7; — A sin^ r?) dr) Let (-Dr)/^ be the maximum value oi Dt ,0 ^ 7? < a. With Dt set eciual to (Z)7-)m , the right-hand side of (54) gives an upper bound on y^ • This substitution further allows one to evaluate the right-hand side of this equation in terms of standard integrals. The result yields the following upper bound on y^: 2 1 y,n < 2.1 where P^ ■Vc w 1 — r (Dr), w sm a DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 1177 In general, this upper bound will be much less than the laying depth. For example, for cable No. 2 being laid with 6 per cent slack at 6 knots ?/,„ < 12.5 feet. That is, the cable configurations corresponding to Region II do not reach the ocean surface. Hence these solutions of the stationary model do not in general satisfy all the required boundary conditions and can be discarded. Similarly, in Region III, the laying trajectories for which To = 0 are in the range a < da ^ tt. Consider those for which ^o < 7r/2. We get for these trajectories Pcv: n j sin ^ • "'" w Jeo \(A sin^ ^ — cos ^) X exp f^ w sin 7] — Dri-n) 7 'flo w (A sin^ 7/ — cos 77) where 1/^/2 is the value of ^ at 0 = 7r/2. Let m be the minimum value of sin 7] — {Driv)/'^) in the range a < rj ^ t/2. If, as in the usual case, m is positive, we can obtain an upper bound on ij^/2 by replacing sin 1] — {DT{'n)/w) by m in the right-hand side of (55). By this means we find that ^ PcVc 2(1 + cos' a) yw/2 < 7 as — • w m tan a/2 For cable No. 2 being laid with G per cent slack at 6 knots this relation yields ?/x/2 < 1,100 feet. So in the usual laying depths, which are many times greater than y^rii , the configurations in Region III for which To = 0 correspond to a value of 6 at the surface greater than 7r/2, or to cable being paid out in front of the ship during laying. It is doubtful whether such configurations would be stable and, at any rate, doubtful whether cable would ever be laid in such a manner. Hence, we conclude that these To = 0 solutions of Regions II and III will in general be mathematical curiosities, and that the only realistic laying solution of the stationary model for which the bottom tension is zero is the straight line 6 = a. APPENDIX B Computation of the Transverse Drag Coefficient and the Hydrodynamic Constant of a Smooth Cable from Published Data From (6) of Section 3.2 we obtain the relationship 1178 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 Vcos a xCopd ' where H is the hydrodynamic constant. Also, we define the Reynolds number for flow normal to the cable in the usual way ; ,j dV sin a /,->. V being the kinematic viscosity of water. For smooth cable we now as- sume that the drag coefficient Cd depends on Nr in the same way as for flow around a smooth cylinder of infinite length. Experimental data for this relationship, namely, Co = Cn{Nu) (58) are available in the hterature and have been collated by Eisner. For a given velocity T^, (56) through (58) represent three equations for the unkno\\Tis a, Co , and Nr . In general, the solution of these equa- tions depends on V, thus contradicting the assumption made in Section 3.2 that Cd , and therefore H, are constants independent of T'. However, for sufficiently large T'^ we can expect the resulting a to be small so that \/cos a ;^ 1 . In this case (56) and (57) combine to give Cn = ?^^., (59) ■■' Nr'' which together with (58) yields two equations for Cd and Nr that are indeed independent of V. In laying, V will normally be large enough for this approxhnation to hold. Equations (58) and (59) are in turn easily solved graphically by find- ing the intersection on log-log paper of the curves, Cd versus Nr , that these equations represent. Since p and p are properties only of the water, we see that Cd is a function only of the product wd of the unit weight of the cable times its diameter. In Fig. 31 we have plotted the resulting values of Cd for wd ranghig from 10"^ to 10 pounds. For this computation we have assumed sea water at 32°F with an assumed density of 1.994 slugs per cubic foot and a kinematic viscosity of 2.006 X 10 ft^/sec. For other than large values of V, (56) through (58) can be readily solved if one interchanges the roles of a and V, that is, if one considers a as given and V as unknown. Equations (56) and (57) can again be com- bined in this case to give DYNAMICS AND KINEMATICS OF SUBALIRINE CABLE 1179 Cn = 2wd cos a 1 pi^ iV«2' (60) and with wd cos a a kno^^^l number, (60) and (58) can be solved for Co and Nr as before. Thus, one can obtain Co from Figure 31 by merely reading wd cos a rather than ivd on the abscissa. Knowing Co one can solve for V from (56). 3.0 2.0 1.5 1.0 0.9 0.8 '0-^ 2 4 6 8 10-6 wd IN POUNDS ( ) 10-5 2 468"-' 2 466''-' 2 468 10" ,10- N. -^--:- ^^^__^ ^^^^^^ """^ "*~- la ,-32 4 6 8,Q_2 2 4 6 8,^., 2 4 6 6, 2 4 6 8 ^^ wd IN POUNDS ( ) Fig. 31 — Variation of Co with wd for cables of smooth exterior. The results of such a computation are shown in Table II for cable No. 1. For V > 1.5 knots the experimentally determined H is 64.0 de- gree-knots. The corresponding computed values of H, ranging from 67.4 to 70.0 degree-knots, compare favorably with, this experimental value. Over the entire range of V, from 0.25 to 10.00 knots, the variation in H is about 4 per cent. This small variation makes the assumption of Section 3.2 that H is & constant for all T^ appear reasonable, especially since we can only hope to use this computation in a preliminary design before the hydrodynamic properties of a cable are established by experiment. Table II — Computed Values of Nr , Cd , AND H for Cable No. 1 V (knots) Nr Cd H (deg.-knots) 0.25 0.50 1.50 3.00 10.00 1.25 X 10^ 2.50 5.20 5.80 6.05 0.935 0.922 0.965 0.985 1.000 67.5 70.0 67.8 67.5 67.4 1180 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 In Table III we have indicated computed high- velocity H values as a function of the unit weight w and the diameter d of a cable. Table IV shows the computed high-velocity Co and H for various gauge piano wire. The American Steel and Wire gauge scale is used in this tabulation. Table III — Computed Values of the Hydrodynamic Constant H in Degree-Knots for Smooth Cable Submerged Diameter in Inches Weight in lb/ft 0.5 0.75 1.00 1.25 1.50 1.75 2.0 2.5 3.0 4.0 0.1 54.5 44.2 37.9 33.7 30.6 28.1 26.2 23.2 21.0 17.9 0.2 75.9 61.1 52.3 46.4 41.9 38.5 35.8 31.6 28.5 24.4 0.3 91.7 73.6 62.9 55.6 50.2 46.1 42.8 38.0 34.4 29.7 0.4 104.7 83.9 71.5 63.1 57.1 52.5 48.9 43.5 39.6 34.3 0.5 115.9 92.6 78.9 69.8 63.3 58.3 54.4 48.5 44.3 38.3 0.6 125.8 100.4 85.6 75.9 68.9 63.6 59.5 53.2 48.5 42.0 0.7 107.6 91.9 81.6 74.2 68.7 64.2 57.4 52.4 45.3 0.8 114.2 97.8 87.0 79.3 73.4 68.6 61.3 55.9 48.4 0.9 120.6 103.4 92.1 84.1 77.8 72.7 65.0 59.3 51.3 1.0 126.5 108.7 97.1 88.6 82.0 76.6 68.5 62.5 54.1 2.0 153.3 137.0 125.0 115.7 108.2 96.7 88.2 76.3 3.0 167.6 152.9 141.5 132.3 118.2 107.9 93.3 Table IV — Computed Cd and H Values of Piano Wire Gauge (Am. Steel & Wire) Dia. (inches) Cd H (deg- knots) 0 0.009 2.49 10.7 5 0.014 1.91 15.2 10 0.024 1.56 22.1 15 0.035 1.39 28.2 20 0.045 1.31 33.0 25 0.059 1.24 38.7 30 0.080 1.14 47.2 35 0.106 1.02 57.1 40 0.138 0.970 67.1 APPENDIX C Some Approximate Solutions for Laying and Recovery c.i Laying We assume that the tangential drag and the centrifugal forces are negligible. Then, since for laying 0 ^ d ^ t, (18a) by virtue of (21) be- comes w + 2/) \- A sm 6 as cos 9=0. (61) DYNAMICS AND KINENATICS OF SUBMARINE CABLE 1181 Let the origin of an x, y coordinate system be at the cable touchdown point (Fig. 8). Further, let x be the x coordinate of a point along the cable configuration and s the corresponding distance along the cable from the origin. If we define ^ = s - X, (62) then dA ds dx ^ 6 ._„. and ^ = sin 9. (64) as By means of (63) and (64), (61) transforms to .rp , .. dA d'A 1 {dAy (dA)' 1 „ ..,. dy dy'- 4 {dy) (dy) 4 where we have in addition introduced the non-dimensional variables To = To/wh, A = A/h, y = y/h. Here h is the ocean depth at the touchdown point. Using the condition that 6 = 0 a,t y = 0, which implies dA/dy = 0 at y = 0, we get upon integrating (65) dA ^ j^_^ a I 1 - [%/(% + yW Y" where 2 - sm a , . 7 = ^, . (67) sin^ a The usual range of the critical angle a is between 10 and 30 degrees. Also To 0 < = ■ < 1 - T, ^y= ' Therefore, we approximate the denominator of equation (67) by unity. 1182 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 With the boundary condition that A = s — .t = 0 at ?/ = 0, we thus obtain A(l) = S - X = tan ^ f (1 - [To/iTo + ^)]^)* d^, (68) Z Jo where S and X are the dimensionless values of s and x at the ship. Next we let CO — s -\- X, 0} = o:/h. Then we have do} _ I dA dy I dy' and, as can be seen from (66) through (68), J^d) =&^X = ctn ^ f (1 - [n/(n + ^)]')~^ dl (69) Z Jo For convenience we define u and R by u = ^ R = To + r To (70) ci(l) =foctn" r ,,/^ ... (71) 2 Jfl M^l — WT)^ 1 + To' In terms of m and R (68) and (69) become A(l) = To tan ^ f ' ^^^^^^ di^, 2 Jr v? du \i - u^y^ Further, integration by parts gives r (1 - u')' ,^. _ (1 - m' , 7 rOj::^ , _T r__^!^ i« ^^ "^'^ R "^ 2 i« ^^ '^'^ 2 i« 2^H1 - ^*^)^- Combining the above three ecjuations and making the approximation (1 - R'^f X 1, we find (l - fj A(l) + I tan^ ^ (1,(1) = (1 + To) tan ^ . (72) Thus A(l) and d)(l) are related, and we need evaluate only one of the quantities numerically by means of equation (70) or (71) in order to compute both A(l) and 0 and Af —> 0, we obtain the following ecjuations of equilibrium* Air: Tipx — Wa cos (e — (p) = pciqtt cos

2r(0, t), (d) which follow if we assume that at the point of entry into the water the cable is continuous and the tensions are finite and continuous. We consider only the problem of the tensions associated with a har- monic steady-state transverse disturbance. Ecjuations (86a) and (87a) show the transverse response to this disturbance to be independent of the longitudinal motion to fu'st order. The first-order transverse motion in turn can be thought of as a forcing action on the second order longi- tudinal motion, as (86c) and (87c) indicate. This suggests the program we follow to compute tensions. Namelj', we first determine the first- order steadj^-state transverse response, then the second-order steady- state longitudinal response which is excited by the first-order transverse oscillation, and finally, b}' (84c) the resulting tension caused by trans- verse motion. D.4 Transverse Response At the ship we assume a harmonic forcing function Qo{t) = A cos o:t, (90) and we introduce complex exponential representation DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 1191 gi = Re Qi{x) e'"', Vy = Re i^i(f) e'"', where the factor e'"' will be henceforth suppressed. The solution of (86a) and (87a) for the steady state may then be written ^ . s p ioiX . j^ ( ioix\ Qi{x) = Bi exp — + Bi exp I 1, Co \ C2 / ^i(f) = Fi exp (gif) + F^ exp (g.r), where the -B's and F's are complex constants and gi and 52 are the roots of the quadratic 2 q — 8q — icoy + -^ = 0. C2^ Throwing aw^ay the root of this equation which corresponds to the in- coming wave in water, we get /fi(f) = Fexp(g,f). where gi is the root corresponding to the outgoing wave. The three com- plex constants Bi , B2 , and F can now be determined from (89a), (89b) and (90) Bi -\- Bo = A/e, B, exp — + 52 exp (^- _-j - /^ = 0, ^^^^ — Bi exp i52 exp ( — C2 L C2 \ C2 /J - qiF = 0. We note that Bi , B2 and F are proportional to the amplitude A of the forcing motion. D.5 Second-Order Longitudinal Response From the preceding results, the right-hand sides of the equations of longitudinal motion (86c) and (87c) can be computed. This computation for (86c) results in 1192 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 -^ VittVu - ?'uxru = ::: I -4 — 1 CO Ci^ ,T X . 2a;.i: , 2co.r\ ,^ , /•i sm + }'2 COS J COS 2oof , C2 C2 / , / 2wx . 2wa;\ . ,^ , + I rs cos — r4 sin 1 sm 2wf \ C2 Co / (92) 2aja; . 2wx , + r5 sm + r2 cos C2 C2 where the r's, which are proportional to the square of the ampHtude A, are n = Re {B{ + Bo'), r-2 = Im (5r - B2'), n = Re {B{ - B2'), r4 = Im {B{ + 52"), rs = 2Re BS2 , re = rs + 2 2 e r2 ^2 [The quantity u will be used subsequently.] Similarly, for the right-hand side of (87c) we get 77if \ -^ 771U — vm = e " [(ai cos 2c7f + 02 sin 2o-f) cos 2wi (93) -f (ai sin 2(7^ — a2 cos 2o-f) sin 2cLi + — sm I r4 sm — re cos Ci C\ \ Cl Cl /_ sin 2: CO ('-0 + . 2coL , 2(joL , Cl . 2a}L I . 2coL r2 sin + r^ cos + — sin I re sm Cl Cl C2 Cl \ Cl + r4 cos 2coL Cl y COS 2u [ t — {■ - 9 ^|2C2^-2K Cl J D.6 Numerical Results Since the r's are each proportional to the square of the amphtude A, the above results indicate that the transverse motion tension varies as A squared also. It is additionally a function of the frequency of ship motion CO, the forward mean ship velocity V, and the stationary tension To . The computation of the transverse ship motion tension for the laying situa- tion was carried out for cable No. 2. The results are showii in Fig. 34. Here we have denoted the transverse motion tension by Tq and have plotted Tq/A^ against the period of ship motion t. Rather than the stationary tension To , we have used the depth h, which during laying is directly related to Tohy h = To/w. Fig. 34(a) is a plot of Tq/A~ versus the period t = 27r/co for h = ^, 2 and 3 nautical miles and for V = 6 knots. Figure 34(b) is a plot of Tq/A^ versus t for F = 3, 6, and 9 knots and h = one nautical mile. For representative laying, for example at 6 knots with a ship period of 6 seconds into a depth of one nautical mile. Fig. 34 gives DYNAMICS AND KINEMATICS OF SUBIVLIRINE CABLE 1195 TJA^ = 0.50 Ib/ft^ (twist unrestrained), Tg/A' = 0.93 lb/ft' (twist restrained). For an extreme value of A =20 feet, we get therefore that Tq is be- tween 200 and 370 pounds. Additionally, by means of the above analysis, one can compute the rate of damping of a transverse disturbance after it enters the water. The results of this computation are shown in Fig. 18 and are discussed in Section 4.1. 2.0 1.6 1.2 in 0.4 SHIP SPEED = 6 KNOTS TWIST RESTRAINED *^ TWIST UNRESTRAINED ^ (a) .V 1 \ ,\\ \ h IN FATH OMS \ « \ N^OC ) V; '^\- "*'», i^ *--.": OCEAN DEPTH = 1000 FATHOMS 1 \ \ \ \ \ \ \ \ (b) ''^^ \ \\ \ V IN knots: s^ 0-'^ k ^ t> ••- K; ^■**-, r ^•"^ ^^ 8 12 16 0 4 8 PERIOD OF TRANSVERSE SHIP MOTION IN SECONDS 12 16 Fig. 34 — Variation of the transverse ship motion tension of cable No. 2 with the period of ship motion. APPENDIX E Tension Rise with Time for Suspended Cable E.i Formidation of the Solution of the Problem, Let 0 be the lowest point of the cable at time t after the suspension has begun (Fig. 35). We make the following definitions: h = depth at onset of the suspension, Si = cable length from A to 0, S2 = cable length from ship at B to 0, Xi = horizontal distance from A to 0, 1196 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 X2 = horizontal distance from B to 0, 8 = vertical distance from A to 0, To = cable tension at 0. If the cable is being paid out with a slack e, then conservation of the total cable length gives the equation Si -\- Sz — h sin a + (1 -\- e)Vt + cable stretching. (95) Fig. 35 — Coordinate.s for the analysis of tension rise when a cable is com- pletely suspended. It is assumed that there is no cable pulled from the bottom. The cable stretching we evaluate as in the example of Section 3.6, viz., cable stretching = (*Si + *S2) EA This makes (95) read S,+S, = J^ + {\-\- e)Vl + (5i + S-^ ^ sm a EA (96) To obtain further relations for the unknowns appearing in (96), we assume that from the ship to point 0 the cable configuration is a station- ary one governed by the equations developed in Section 3.6, while from points 0 to A we assume that the cable configuration is a static catenary. These assumptions yield the following relations: (a) (b) Si = To . , — smh a, w S2 = h + 8 , sm a To DYNAMICS AND KINEMATICS OF SUBM.\RINE CABLE 1197 (c) (d) ^''^ (e) X2 hi- 8 ..To . -r A , tan a w 8 - ^' (cosh (7-1), w 2 + Xi -' +vt. tan a a wXi To ' Ts = n + w(h + 5). (f) (g) Here k and X are constants, defined and plotted in Section 3.6, which de- pend only on a, the critical angle corresponding to V. Equations (96) and (97) form a complete set of equations in the unknowns Xi , Xi , Si , S2 , To , Ts , 8, and a. They can be reduced to a set which contain only the unknowns a and Ts : ^■M 1 „;. (Pi{a) sin a — 6^2(0-) sin q; — Al 1 + \ ..t sin a 1 = 0, (a) \ ^2(0-) / f. = i+'j^, (b) (98) where h = wh/EA, t = Vt/h, Ts = Ts/wh, and "a f LiaCo-) VS (T — iS? ^ / 1 i UJ 5 0.004 I.C 0.003 0.002 I 0.001 (b) 1 (X-'c i ... >5° 20° f// \ 16° 14° \/ f / 7/ / 1 \ f/ / '// f 1 1/ w / Jl f y3( ■4^2 5' t VI 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.4 0.8 1.2 1.6 2.0 cr 2.2 2.4 Fig. 36 — Nomograph for the solution of equation (99). venience made an auxiliary plot on the right-hand sides of Fig. 3G of 2/3(0-) versus a, but with numerical values of the ordinate omitted. In addition, we have plotted in Figs. 37 and 38 the functions 1/^2 (cosh 0-) and (^'3/^2) sin a for various a. E.3 Numerical Example To illustrate the method of obtaining the tension rise with time described above, we consider a numerical example for cable No. 2. The 1200 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 f.5 1.4 1.3 1.2 1.1 1.0 ^0.9 5 0.8 1 1 1 1 [ 1 m \1 \ ) i\ |\ s. \^ w X s \ V oK fr -^ \ ^ \^ ^ ^ ^ ^ a = 25° „ \ \ ^ ^ ^ 16° -^ \ ^ ^ . ' ^14° 10° _ 5° ^ ^ 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 cosh a Fig. 37 — Variation of — j— with a. values we assume for the parameters which enter the calculation are thei following: e = 0.02, 7 = 6 knots, (a ;^ 12°), h = 6,000 ft, M = 1.2 X 10' lbs, A = 3.1 X 10"'. To solve (99), we connect on Fig. 36 the points e = 0.02 and h = wh/EA = 0.0031 with a straight edge and note the intersection with the intermediate y-i = y^ixs) curve for a = 12° (point A). We then locate the point on the y-i versus o- curve having the same ordinate (point B). DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 1201 Finally, we obtain the root of (99), a = 0.555 by reading off the cor- responding abscissa (point C) . This value of a now serves as the starting point in the iteration procedure by which we find the tension correspond- ing to a given t. For example, for I = 1.0 (t = GOO seconds) we have the following se- quence of values (To = 0.555 (Ti = 0.580 (72 = 0.580 ((P3 sin a)/(pi ^* = ^ [1 + (ang and recovery respectivel3\ Likewise, the expression for T shows that any non-straight line trajectory with zero bottom tension is bounded by PcTVV^- Hence, as in the case of the two-dimensional model, we con- clude that if the tension is somewhere greater than pcV^/w and the bot- tom tension is zero, the only possible stationary configuration is the' straight line lying in the plane of the resultant ship velocity and gravity vectors, and making the critical angle a with the horizontal. F.2 Perturhaiion Solution for a Uniform Cross Current i At the outset we assume the tangential drag force to be zero. This gives by (49) T = w{h + r,), (107) where h is the total ocean depth. Furthermore, we take pcVc to be zero.. If the angle (f (Fig. 26) is small compared to unity, we assume that 6 and \l/ will vary only slightly from the values they would have if the i DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 1205 upper, cross-current stratum extended all the way to the ocean bottom. That is, we take 6 and \l/ to be of the form 6 = a' ^ 6, (108) ,/. = ,/,, where a' is the stationary incidence angle corresponding to the velocity V, and 6 and ^ are assumed small compared to unity. Substituting (48b), (107), and (108) into (47a, b) and retaining only linear terms in 6, \p and their derivatives, we get the linear first order equations riff {h + 7?) -f + (2ctn'a' + 1)^ =0, (a) drj (109) (/i + ^) # + csc'a';/. = 0. (b) dr} Because in the lower stratum the cable is a straight line parallel to the path of the ship, we have as boundary conditions: ,= -/.',(^. = «-"'' (110) where h' is the depth of the upper, cross-current stratum and a is the stationary incidence angle corresponding to the velocity V. The solution of (109) for the boundary conditions (110) is ^^ + '^ (111) - fh-h'X where M = (2 ctn'ct' -[- 1), V = cscV, (112) Aa = or — a\ Equation (48) for the space-coordinates ^, r;, and f of the cable in turn can be written to terms of first order in the form -f = etna — 0CSC a , drj (113) -— = — ,A,ctnQ: . dj] I'iOli THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 Substituting (111) into (113) and integrating under the condition that at 7; = 0, ^ = 0 and f = 0, we find ^ , . {h - h')Aa 2 / I — rjCtna + — -, rr— CSC a (m- 1) ^ , . (h - h') f — etna 7^ (p 1 1 _{h + r^y-' /i^-ij ' 1 {v - I) [.{h + r))'-^ h"-'} (114) These equations describe the space curve formed by the cable in the cross-current stratum. To determine the distances d and e (Fig. 32), we transform (114) for the cable configuration to coordinates ^' and f' oriented along the ship's path and normal to it respectively ])y means of I' = ^ cos v? — f sin n X(m) where Yw,[m\[H] and Zy,,{m)(n) may be defined as the ratios of certain de- terminants involving Zy,,[m][n] and F^, („)(„) respectively.* We are now able to eHminate Vw,(m) and Iw,[m] from (14) and (17), and to write down the generalized telegraphist's equations for the curved circular waveguide filled with an inhomogeneous dielectric in the following form : dw = — 2-( [Z {m){n)I (n) + Z i^m)[n]I [n]\ , r^ = —/^ [Z[m\(n)I(n) + -^[m] [n]/[n]], aw n -^ = —Z^ [F(m)(n)F(„) + F(,„)[„]y[„]], (23) dw —r^ = — ZJ [Ylm]in)Vin) + Y [m] [n]V [n]] . dw n The impedance and admittance coefficients are defined by : Z(^;n)(n) = 10} / UBiigYSid T'(„o)-(grad T(„)) dS + Z^a.(m)(n), Z^,n)[n] = ioi \ M,) dS, (28) 5(m)(n) = X(,m)Xin) I 5T(,„) T(„) dS. The quantity 8mn is the Kronecker delta, and is not to be confused with 5(,«)(n) , which is defined by the last of equations (28). Note that ^[m][n] and ^(m)M are zero unless the angular indices of the two modes in- volved differ by exactly unity. It is not difficult to obtain approximate solutions of (20) in the forms (22), since the off-diagonal elements of the coefficient matrices of (20) are small compared to the diagonal elements. Using the expression de- rived by Rice'^ for the inverse of an almost-diagonal matrix (we shall not attempt to prove this result for infinite matrices), we find the first- order approximations ■17 X[m]X[n] fs r^ V 1 1 w.[m]ln] — : [Omn "T ^[m][n]i, iwHo , , (29) '7 — X(m)X{n) \^ _\ f ;■ 1 ^w,{m)in) — : \Omn "T C,{m^{n) 0(m)(n)J. tweo Approximate expressions for the impedance and admittance coeffi- cients appearing in the generalized telegraphist's equations (23) are: Z(m)(n) = ?COyUo[5m,j + H(m)(nU + Za',(m)(n) , Z{m)[n] — 'ZW/XoH(m)[rt] , Z[m]{n) = io:iJ.o'E[m]{n) , Z[m][n] = ta))Lio[5,„,j + H[m][n]], (30) ■ ^' (m)(.n) = io:eo[8mn + H(m)(n) + '^(»i)(n)], Y(m)[n] = ?'coeo[H(m)[„] + A(m)[«l], Y[m](,n) — ^''*^€o[H[m](n) + ^[mlC'oJ) y[m][n] = io)to[8,nn. + H[ml[«] + •^['«]["]] + ^ w,["']\ti] . C^i) (32) CIRCULAR WAVEGUIDE WITH INHOMOGENEOUS DIELECTRIC 1221 where H(m)(„) = / ^(gi-ad r(,„))-(grad T^) dS, H(.)W = f s^ (grad Tco) • (flux Tt,]) (/>S, H[,„](«) = /^(flux T[,„])-(grad T^) dS, H[,«][«] = / ^(grad r[„])-(grad T[n]) dS, and A(^)(„) = / 5(grad T (,„))• (grad T^n)) dS, •Is A(m)M = f digrsid r(,„))-(flux Tm) dS, •Is A[m](n) = f d{nuxT{,nj)-(grsidT^n)) dS, •Is ^Min] = / 5(grad T^) • (grad T[n]) dS. -Is The H's are zero unless the angular indices of the two modes involved differ by exactly unity. 1.2 Representation in Terms of Coupled Traveling Waves From now on Ave shall assume that the distribution of dielectric over the cross section of the curved guide is independent of distance along the guide, so that the impedance and admittance coefficients are con- stants independent of z. (We shall henceforth designate the coordinates by (p, i]J, = +/ Zl lK[»i](n)Ci(n) + K[„,](n)h(n) + K(,«][n]0[«l + f^lm][n]h[„]]. dz dz n , . (3/) dh[m\ dz The k's are coupling coefficients defined in terms of the impedance and admittance coefficients by *«(m)(n) = ■2[(-^(m)^(n))' Y (m)(n) ± {K(m)Kin)) ' Z(m)(»)], iK(m)[n] = 2[(-^(m)-^[n])' ^^("OI"! ± {K(m)K[n\) ' Z(„,)[h]], U[m](n) = |[(-K^[ml-K'(n))' 5" [„,](„) ± (K [m]-K^(n)) '2^[ml(n)], *'^[m][n] = ^[(i^[m]-K'[nl)' I^[m]ln] ± (/C[m]i^[„]) 'Z[m][„]]. (38) CIRCULAR WAVEGUIDE WITH INHOMOGENEOUS DIELECTRIC 1223 In these definitions the plus signs are taken together, likewise the minus signs. The factors of i are introduced in order that the k's may be real for pi'opagating modes in a lossless guide. For the small-coupling case discussed at the end of the preceding sec- tion, it is convenient to separate a typical coupling coefficient into two parts; thus, K = c + d. (39) Here c is the coupling coefficient due to curvature and is zero unless the angular indices of the two modes involved differ by unity. The coupling coefficient d is due to the dielectric. All c^'s vanish if the dielectric is homogeneous; otherwise particular symmeti'ies may cause certain classes of d's to be zero. The c's and d's may be expressed in terms of integrals written down in the preceding section if we substitute for the F's and Z's in (38) their definitions according to (30). The k''"'s which have equal subscripts {n){n) or [n][n] may be regarded as phase constants (of particular TM or TE modes) which have been modified by the presence of the dielectric. For the modified phase constants we introduce the symbols /3(„) and /?[„] ; thus, o _ + J, _i_ X(rt)'5(„)(„) -f /l(„)2A („)(„) 2/i( n) ^W K-[n\[n] — H[n] -p (40) 2h[n [n] The general expressions for the coupling coefficients between any two different modes are as follows: C{m)(n) d(m) (re) C(m)[7i] d(m)[n] C[m] (n) 1 2 vh(_m)h(n) i^(m)(n) ± ^ 'B(m)(n) — X(m)X{n)^(m)(n) X(m)X(n)5{m)(n) 1 /7 7 X(m)X(n)6(7re)(n) ^5 V«'(m)'i(n) '^(m)(n) ± /r 7 j - L V ll(m)H(n) _ 2 /3H(m)[n] [\/h(m)/h[n] ± \/ h[n\/h^,n)\ , 2 ^^{m)ln] V /i(m)//l[n]) I /^H[,„](«)[V/t(n)//l(m] ± V'h[,n]/h(n)]j d[m]U') — Clm][n] d[,n][n] 2 /3A[„,](„) y/h(n)/h[m] , /3^S[OT][n] — X[m]X[n]^M[n] i[ '\/h[m]h[n] >^[m][n] 'Vh[,n]h[n] , 0'^lm]ln] 2 '\/h[m]h[n] (41) 1224 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 where the symbols with double subscripts are defined by (28), (31), and (32). 1.3 Coupling Coefficients Involving the TEoi Mode I In Part II we shall consider a well-compensated bend in which the total power in all spurious modes is everywhere low compared to the power level of TEoi . (This is somewhat more restrictive than merely assuming that the power in any one spurious mode is everywhere small compared to the power in TEoi •) To first order, therefore, we may com- pute the power abstracted from TEoi by mode conversion by assuming that the TEm mode crosstalks into each spurious mode independently. For this calculation we need the values of the forward coupling coeffi- cients between TEoi and all other modes. The crosstalk into backward | modes will be negligible in all practical cases. We shall use the customary double-subscript notation for the various i modes in a round guide, but shall continue to denote TM waves with ; parentheses and TE waves with brackets. We assume that the distribution j of dielectric is symmetric with respect to the plane of the bend, so that TEqi j is coupled to a definite polarization of each spurious mode. The normal- ; ized T-f unctions are then: j J, ^ /en Jn{X(nm)p) SlTl nxp V TT n'(nm)J n-l{rC{nm)) Jn{x[nm]p) COS Hif (42) where and [nm]" n~)^Jn\K[nm]) k{nm) — X(nm)tt, JnV^\nm)) — 0, K[nm] = Xlnm](l, J n \k[nm]) — 0, 1, n = 0, (43); (44) 2, n ^ 0. 1.3.1 Coupling Coefficients due to Curvature We know that to first order the curvature of the guide can couple the TEoi mode only to modes of angular index unity. Let us calculate the CIRCULAR WAVEGUIDE WITH INHOMOGENEOUS DIELECTRIC 1225 coupling between TEoi and TMi,„ . Referring to (31), we have »-(lm)[01] = A[01](lm) = f ^(grad T(i„o) • (flux T[oi]) dS ^ f'' r '\/2./i(x[oi]p)-^i(x(im)p) cos^y (45) ^0 Jo Trahk(im)Jo{k[Ol])Jo(,k(im)) \a/\/2k[oi]h if m = 1, [O if 7W F^ 1. Hence the only transverse magnetic mode coupled to TEoi by the bend is TMn , and from (41) the forward coupling coefficient is: Cai)[oii = cfoiKU) = l3a/\/2k[oi]b = 0.18454,Sa/6. (46) To obtain the coupling between TEoi and TEi;„ , we must evaluate two integrals. From (28), the first is ^[01] [Im] = ^[lOT][01] X[01]X[lm] / ^T[oi]T[im] dS ^ Z"^" r \/2X[lm]pVo(x[01lp)'/l(x[]m]p) cos' (p , ^"1") Jo Jo Trab{k[un]^ — l)Uo(fc[oi])/i(/c[im]) _ '\/2a A;[im](/v[oi] + ^'[im]v and from (31), the second is A[01][]m] — A[lm][01] = f Kgrad Tio,]) • (grad l\un]) dS •Is 'S ^ ^ ^.T p \/2X[lm]P^Jl(xi0l]P)JliX[lm]p) cos' V? (-IS) Jo Jo ■7rab(k[lm]^ — l)'Joik[Ol])Jl{k[lm]) _ 2\/2a k[oi]k[im]' A short table of numerical values of the above two integrals follows: m i;[01I(lml A|01)|lmJ 1 0.23871 a/b 0.18638 a/b 2 0.32865 a/b 0.31150 a/6 3 0.03682 a/b 0.02751 a/b 1226 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 Putting these values into the expression (41) for the forward coupling coefficient, we obtain: "0.09319(^a)2 - 0.84204 C[01][ll] C[01][12] C[01][13] y/h[oi]ah[n]a '0.15575(^a)" - 3.35688 V/i;oi]a/i[i2]a "0.01376(/3a)2 - 0.60216 + 0.09319 VA[oi]a/i[n,a + 0.15575V^[oi]tt/i[i2]a + 0.01376\//i[oi]aA[i3]a 1 b' 1 b' (49) ■\/hioi]ah[i3]a 1.3.2 Coupling Coefficients due to Dielectric Depending upon the distribution of the dielectric material over the cross section of the guide, the TEoi mode may be coupled to any mode except those of the TMom family. The dielectric coupling coefficients, as given by equations (41), are d[0\](nm) = «(nm) [01] = 2/5^[01] (»'») V ^(nOT)/"[Ol] , ,+ ^"A [01] [nm] 7+ (50) dp d(p, d[01][nm] — d[„m][01] '— r,^/T T • ■^ V "[01]«'[nm] The A's are obtained from equations (32) ; thus, A[oi](nm) = / 5(grad T(„„o)-(flux T[cii]) f/*S •Is ^ r'" r 8{p,ip)n\/7„JniX(nm)p)Jl{Xm]p) COS thp Jo Jo '7rak^„m)Jn— l{K{nm)) J 0\k [01]) A[oi][n,«] = / 6 (grad T [„,„])• (grad T [01]) d*S Js ^ ^ ^2t -.a g(p^ i^ (7'i) e — -, r-„e (7o - 7i)-J (7o - 7i)^ CIRCULAR WAVEGUIDE WITH INHOMOGENEOUS DIELECTRIC 1231 Let US con.sider the case in which line 1 has a much higher attenuation constant than Une 0; that is, (Xi » QIu (74) The second term on the right side of (73) is provided with a small co- efficient, and also its exponential factor decays much faster than the exponential in the first term. The second term, therefore, rapidly be- comes negligible as z increases, and we may write, ao{z) 1 + (75) (to — 7i)"_ If the attenuation constant of line 0 is not modified* by the presence of the coupled lossy line 1, then in the absence of line 1 the amplitude of ao{z) would be e~"°% and the factor by which the amplitude is reduced owing to the presence of line 1 is 2 1 + K^zKyQ-yi) (76) (to — Ti)' The first factor on the right is very nearly unity, but not less than unity if K is real (lossless coupling mechanism) and (ar - a,)' ^ (^j - ^o)'. (77) Hence the factor by which the amplitude is multiplied is not less than (ao — aiJK'Z exp 9 K Z To Ti exp (ao - aiy + (/3o - ^iT (78) assuming that k is real. If the amplitude of the wave on fine 0 is not to be down by more than .V nepers, after a distance z, from what it would have been in the absence of the coupled line, it suffices to have oJkz ( "1 oco) {ay - a^y + (/3i - |8o)^ = AT, or «i - ao = h[{Kz/N) + V{K'z/Ny - 4(^1 - ^o)-^J. (79) (80) 2.2 TEoi-TMii Coupling in Plain and Compensated Bends In Jouguet's^ and Rice's^ analysis of propagation in a curved wave- guide, the curvature is treated as a perturbation and the field com- * The value of ao rnay very well be modified by the coupling; but if it is this can easily be taken into account when computing the over-all change in | ao(z) | due to the presence of line 1. 1232 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 ponents are developed in powers of the small parameter a/6, but the field perturbations are not expressed in terms of the modes of the straight waveguide. We shall now consider propagation in plain and compen- sated bends from the coupled-mode viewpoint. Denote the coefficient of coupling between the TEoi mode and the TM„,„ mode or the TE„« mode by (81) respectively, where as usual we indicate TM modes by enclosing the subscripts in parentheses and TE modes by enclosing the subscripts in brackets. In Part I the coupling coefficients are written with two pairs of subscripts, since in general they may refer to any two modes, but here one pair of subscripts would always be [01] and will be omitted. The co- efficient c represents that part of the coupling (if any) which is due to the curvature of the guide, and d represents the coupling (if any) which is due to the inhomogeneity of the dielectric. We assume that the dielec- tric loading, if present, is symmetric with respect to the plane of the bend, so that coupling to only one polarization of each mode need be considered. The phase constants of the TM„,„ and TE,j,„ modes in a straight, empty guide are, respectively, /l(nm) = -S/^- — Xinm)"^, h[nm] = a/jS^ — X[nm]^ (§2) where and Also X(nOT) = k(nm)/(l, Xl'im] — k[mn]/a, (83) /„ (A-(„„o) = 0, J/(A-[,„„]) = 0. (84) 0 = 2t/\, (85) where X is the free-space wavelength. As noted in the preceding section, the presence of coupling may cause the modified phase constants |8(„„o and lS[„m] of the coupled modes to differ slightly from the unperturbed phase constants /i(„m) and h[nm] • In a plain bend (curvature coupling only), the /3's are equal to the h's, and in most cases the effect of a small amount of dielectric coupling on the phase constants may be neglected. Exact values of I3[nm] and I3{nm) may be obtained if necessary from (40). CIRCULAR WAVEGUIDE WITH INHOMOGENEOUS DIELECTRIC 1233 The coupling coefficient between the TEoi and TINrn modes in a plain bend is given by equation (46) as Ciu) = 13a/ V2kioi]h = 0.18454 /3a/6 = 1.1595a/X6. (86) The (smallest) critical distance for maximum power transfer is given by (67) ^^•ith /3o = /8i , namely _ T k[oi] h\ _ 1.3o47bX ^"o ~ 2c(n) = 2V2a " a ' ^^^^ and the critical angle i?co is ^co = -co/b = 1.3547 \/a radians = 77.62 X/a degrees. (88) This expression agrees, as it must, with that obtained by Jouguet and Rice. (We write ■^cq for the uncompensated bend in order to reserve t?r for a bend with dielectric loading.) It should be pointed out that c^i) is not necessarily the largest of the coupling coefficients due to curvature. In a guide sufficiently far above cutoff, it appears from (49) that C[n] is approximately equal to C(u) , and C[i2] is one and two-thirds times as large as Cm) . If two transmission lines are coupled over a distance z which is small compared to the dis- tance required for maximum power transfer, then by (65) the relative power transferred to line 1 is Pi{z) ^ Kz\ (89) which is proportional to the square of the coupling coefficient. It follows that for a sufficiently small bending angle the largest amount of power will go into the mode which has the largest coupling coefficient to TEoi (in the above example, TE12). Each coupling coefficient, however, is proportional to 1/6, and can be made as small as desired by increasing the radius of curvature of the bend. Since the phase constants are unal- tered to first approximation by the curvature, the maximum power trans- ferred tends to zero with 1/6^ for every mode whose unperturbed phase constant differs from A[oi] . The only mode with finite power transfer for a finite bending angle with an arbitrarily large bending radius is TAIu , since /?(n) = /i[0]] . For the present we shall assume a bending radius so large that power transfer to modes other than TMn is negligible. Com- plete power transfer from TEoi to TAIn will then take place in a plain bend at odd multiples of the critical bending angle t^^o • We now consider a dielectric-loaded bend in which the permittivity e is a function of the transverse coordinates (p, 60° portions of the outer sectors counteract the effect of the rest of the compensator on TMu , and dielectric losses make the design inefficient. CIRCULAR WAVEGUIDE WITH INHOMOGENEOUS DIELECTRIC 1245 and if tan v? = 5 X 10^^, the dicleftric loss in a 90° bond is a])oiit 0.25 db. 2.4 Can Dissipation Be Used to Discourage Spurious Modes? It was shown in Section 2.1 that the effect of markedly increasing the attenuation constant of one of two coupled transmission lines is to re- duce the over-all attenuation of a wave introduced on the other line. One might wonder whether it would be practicable to decrease the per- missible radius of a compensated bend by introducing loss into the spurious modes. The answer is "No", at least for guides large enough to propagate 200 to 300 modes at the operating wavelength. One simply cannot get the required magnitude of loss into the spurious modes with- out simultaneously introducing intolerable loss into TEoi . A numerical example will make this clear. We found in Section 2.3.3 that with a three-sector compensator in 2-inch guide at 5.4 mm it would be possible to negotiate a bend of radius about 12 feet with a maximum loss of 0.1 db by mode conversion to TEi2 (the worst spurious mode). Let us now ask w^hat the attenuation constant of TE12 would have to be if we wished to transmit around a bend of radius 6 feet with a three-sector compensator, and have the mode conversion loss suffered by TEoi not greater than 0.1 db in a 90° bend. Preparing to substitute into (80) of Section 2.1, M'e have the following values: 'to 6 = 72 inches, K[i2] = C[i2] + f/[i2] = 2.54/6 = 0.0353 in"\ z — 7r6/2 = 113.1 inches, /3o — ^1 ^ /io — hi = 0.236 radians/inch, N = 0.1 db = 0.0115 nepers. From (80) we get «[i2] — «[oi] = 12.2 nepers/inch ^ 4200 db/meter. Since the maximum TE12 attenuation which can be achieved in a 2-inch guide by a mode filter which transmits TEoi freely is of the order of 10 db/meter,* the value of a[n] called for by the above calculation is ob- viously out of the question. * This estimate is based on calculations described in Reference 6 for modes in a helix surrounded by a lossy sheath; but it is doubtful that much greater loss could be produced by other types of filter, such as resistance card "killers". 1246 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 It should be noted that a moderate amount of loss in the spurious modes may be worse than none, so far as the effect on TEm is concerned. Miller^ has shown that the total power dissipated in the system goes through a maximum when (ai — ao)/K ^ 2. It appears that ai — ao must exceed k by a couple of orders of magnitude before the loss in the driven line (i.e., TEoi) becomes really small, if we are counting on dissipation to counteract the coupling to spurious modes. Since by use of the compensator we are attempting to make the TEoi - TM)i coupling coefficient zero, we may expect that this co- efficient, if not exactly zero, will at least be small compared to the cou- pling coefficients of spurious modes such as TE12 . Because K(ii) is very small, it may be that a practicable amount of loss in the TMn mode would improve the performance of the bend. But in view of the preceding para- graph we must be careful, when introducing loss into TMu , not to introduce the wrong amount of loss into some spurious mode which has a larger coupling coefficient to TEoi • ACKNOWLEDGMENTS I am indebted to S. E. Miller, A. P. King, and J. A. Young for stimu- lating discussions and several helpful suggestions relating to this work. APPENDIX Compensation of a Gradual Bend by a Dielectric Insert in the Adjacent Straight Pipe We shall discuss briefly three different ways of transmitting the TEoi mode around a plain (i.e., air-filled) bend with the aid of dielectric mode transducers inserted into the straight sections of guide on one or both sides of the bend. The first two methods involve converting the TEoi mode to a normal mode of the bend and reconverting to TEm on the other side.** In the third method, the input to the bend is pure TEqi , and the output mixture of TEoi and TMn , whatever it may be, is re- converted to TEoi by a dielectric transducer. A.i The TMn Normal Mode Solution One of the normal modes of the bend is a pure TMu mode (TMi/) which is polarized at right angles to the TMu mode (TMu") that the bend couples to TEoi • Clearly if one has a transducer in a straight guide which converts TEoi entirely to TMu , it is a mere matter of rotating the CIRCULAR WAVEGUIDE WITH INHOMOGENEOUS DIELECTRIC 1247 transducer about the guide axis to insure that the polarization which enters the bend is TMi/. We shall design such a transducer using a di- electric sector in a straight pipe. From Section 2.1, for complete power transfer from TEoi to TMn we must have /3[oi] - ^(11) = 0; (111) the transfer then takes place in a distance I = 7r/2|ic(n)|. (112) The modified phase constants /3[oi] and /3(ii) for a single dielectric sector of angle 6 are given by (103) of Section 2.3.2. Substituting these values into (111), we find that the only condition under which it is satisfied is sin e ^ 0, (113) e = 180°. The transducer must therefore be a half cylinder. From (104) we have K'(u) = c?(ii) = -0.12066^5, (114) and so (112) gives for the length of the transducer, I = 2.072 \/b. (115) The TEoi - TMi/ transducer should be placed on either side of the diametral plane of the straight guide which lies in the plane of the bend. An exactly similar transducer on the other side of the bend will reconvert TMi/ into TEoi • Since TEoi and TMu have the same velocity in a straight guide, the transducer can be made of a number of sections with arbitrary spacing and of total length /; but in practice one \\i\\ not wish to have too long a run of TMn in the empty guide because of the higher heat losses of this mode. A.2 The TEoi ± T:\rii" Normal Mode Solidi / / / / / / f / / J / / > / 0 / y^ 0123456789 COAT THICKNESS IN PER CENT OF THE RADIUS 10 Fig. 2(a) — Change in phase constant of the TMu wave in the dielectric-coated waveguide, e = 2.5; a/X = 1.03. DIELECTRIC-COATED WAVEGUIDE 1259 1.8 2 1.6 o £ 1.4 CL z 1.2 1 = o i 0.8 UJ u. u. 5 0.6 UJ 10 < 0.4 Q. 0.2 0 / / / / / f / / J / / / / / 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 COAT THICKNESS IN PER CENT OF THE RADIUS Fig. 2(b) — Change in phase constant of the TMn wave in the dielectric-coated waveguide, e = 2.5; a/X = 2.06. KJ.D ^ 1- § 0.4 tr Ul \^ ^ / a. z ) _0.3 / 1 / UJ o i 0.2 UJ u_ u. PHASE D p / f 0 1 0 0.4 0.8 1.2 1.6 2.0 COAT THICKNESS IN PER CENT OF THE RADIUS Fig. 2(c) — Change in phase constant of the TJNIn wave in the dielectric-coated waveguide. « = 2.5; a/X = 4.70. 1260 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 manner. Assuming the conductivity to be high though finite and the loss factor of the dielectric material to be small, we take the field pattern and wall currents of the lossless case and calculate the total transmitted power P and the power P m absorbed per unit length of the waveguide by the metal walls of finite conductivity. The wall current attenuation (13) In this expression «>/ is related to the TE^m attenuation constant aom of the plain waveguide. For 1 — p = 5 « 1 we introduce the series expansions of the functions Ui(x2, pXi) and Ri{x2, PX2), ^ = (e - 1) ^ 8\ (14) (Xom Vom Here Aa^ is defined as the change in wall current attenuation compared to the attenuation in the plain waveguide. III. PROPERTIES OF COUPLED TRANSMISSION LINES Wave propagation in gentle bends of a round waveguide can be de- scribed in terms of normal modes of the straight guide. ^ The bend causes coupling between the normal modes. The TEoi wave couples to the TMn wave and to the TEi„ waves and the propagation in the bend is de- scribed by an infinite set of simultaneous linear differential equations. An adequate approximate treatment is to consider only coupling between TEoi and one of the spurious modes at a time. Furthermore, only the forward waves need to be considered, since the relative power coupled from the forward waves into the backward waves is quite small. Thus, the infinite set of equations reduces to the well known coupled fine equations: ^ + 71^1 - JcE2 = 0, dz (15) ^ + 72^2 - JCE, = 0, dz DIELECTRIC-COATED WAVEGUIDE 1261 in which -£"1,2(2) = wave amplitudes in mode 1 (here always TEoi) and mode 2 (TMii or one of the TEi„), respectively; 7i,2 = propagation constant of mode 1 and 2, respectively (the small perturbation of 71,2 caused by the coupling may be neglected here) ; and c = coupling coefficient between modes 1 and 2. Subject to the initial conditions: EM = 1, E-,(0) = 0, the solution of (15) is: 1 1 + A7 VAt^ - 4c2 .-■ + 2 11 ^' A7 ^/Ay'^ — 4c2 ] 0-^22 Eo = jc (16) VA72 - 4c2 [e -Tz^ -Tiz I where A7 = 71 — 72 and ri,2 = 3^[ti + 72 ± \/A7- — 4c2]. Ti and r2 are the propagation constants of the two coupled line normal modes. Both coupled line normal modes are excited by the initial conditions. For I C/A7 I « 1, ec^uations (16) can be simplified: E, = 1 - 2-%sinh^A72e'^'' A7- 2 -(71 — Cc2/A7))2 E, = /^sinhJA7^e~^^"^+'^^^ A7 2 (17) We are concerned with a difference in phase constant which is much larger than the difference in attenuation constant. Consequently in A7 = jAjS + Aa we have | A,8 | » | Aa | and we may write : El = l+.Jsin^A^.-- •exp ^\^^+A^^^^>~ r'A^^'^V' 1 (18) E2 = i ^ -sin-AiSs exp - j- (pi + 13-^z --(«!+ a^^z We note that the amplitude A'l , apart from suffering an attenuation, varies in an oscillatory manner, the maximum being ^1 = 1 and the minimum £"1 = 1 — 2(cVA/5"). Accordingly^, the maximum mode conver- sion loss is given b}^ : 1262 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 20 log E, 10 E max _ 17 qc ^ (19) The attenuation constant of Ei is modified by the presence of the coupled wave. Compared to the uncoupled attenuation constant it has been changed by iV (20) Aq!c OCX ') The amplitude E2 varies sinusoidally. From our point of view it is an unwanted mode. The power level compared to the Ei power is 20 log,. %^ = 20 log,. I (21) So far we have considered only a constant value of the coupling co- efficient, c, corresponding to a uniform bend. The attenuation m such a uniform bend is increased according to (20), and the worst condition we can encounter at the end of the bend is a mode conversion loss (19) and a spurious mode level (21). A practical case of changing curvature and consequently changing coupling coefficient is the serpentine bend. A waveguide with equally spaced supports deforms into serpentine bends under its own weight. The curve between two particular supports is well known from the theory of elasticity. An analysis of circular electric wave transmission through serpentine bends^ shows that mode conversion becomes seriously high at certain critical frequencies when the supporting distance is a multiple of the beat wavelength between the TEoi and a particular coupled mode. The beat wavelength is here defined as ^b = — '2t AiS (22) In serpentine bends formed by elastic curves, mode conversion at the critical frequencies causes an increase in TEoi attenuation aoi W Co EI A/3-aoi_ Aa and a spurious mode level in the particular coupled mode E2 E, w Co EI Af^-'m OOl Aa (23) (24) where w = weight per unit length of the pipe, E = modulus of elasticity, I = moment of inertia. DIELECTRIC-COATED WAVEGUIDE 1263 and Co is the factor in the bend couphng coefficient c = Ca/R determined by waveguide dimensions, frequency and the particular mode. R is the bend radius. Equations (23) and (24) hold only as long as 4Aa, « I Aa 1 (25) is satisfied. The rate of conversion loss has to be small compared to the difference between the rates of decay for the unwanted mode and TEoi amplitudes. If (25) is not satisfied a cyclical power transfer between TEoi and the particular coupled mode occurs, and the TEoi transmission is seriously distorted. Another case of changing curvature of the waveguide is random de- viation from straightness, which must be tolerated in any practical line. Such deviations from straightness change the curvature only very gradu- ally, and since there is no coupled wave in the dielectric coated guide, which has the same phase constant as the TEoi wave, the curvature may be assumed to vary only slowly compared to the difference in phase constants. Under this condition the normal mode of the straight wave- guide, which here is the TEoi mode, will be transformed along the gradually changing curvature into the normal mode of the curved wave- guide, which is a certain combination of TEqi and the coupled modes. This normal mode will always be maintained and no spurious modes will be excited. The change in transmission loss is therefore given alone by the differ- ence between the attenuation constants of the TEoi wave and the nor- mal mode of the curved waveguide. The propagation constants of the normal modes of the coupled fines are Fi and r2 as given by (16). Only the mode with Ti will be excited here and consequently the attenuation difference is given by (20). IV. CIRCULAR ELECTRIC WAVE TRANSMISSION THROUGH CURVED SECTIONS OF THE DIELECTRIC-COATED GUIDE In curved sections of the plain waveguide the wave solution has been described in terms of the normal modes of the straight waveguide. In this presentation it has been found that the TEoi wave couples to the TMn and TEi„ waves in gentle bends. Likewise, the wave solution in curved sections of the dielectric-coated guide can be described in terms of the normal waves of the straight dielectric-coated guide. In a wa^'eguide with a thin dielectric coat the normal waves may be considered as perturbed normal modes of the plain waveguide. Consequently the bend solution of the plain waveguide may be taken as the first order approximation 1264 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 for the bend solution of the dielectric-coated guide. In this fii'st order approximation the TEoi wave of the dielectric-coated guide couples to the TMii and TEi„ waves of the dielectric-coated guide and the coupling coefficients are the same as in the bend-solution of the plain waveguide ■} TE 01 TM 11 TE 01 TE TE, 01 11 c — TEi2 c = 0.18454 ^ , "0.093 19(/3a)2 - 0.84204 \/|8oiajSiia "0.15575(^a)2 - 3.35688 TE 01 TE 13 V'i8oia/3i2a "0.01376(i3a)2 - 0.60216 \/l3oia^i3a + 0.09319 V/3oia/3„a + 0.15575 Vl3oiai3na + 0.01376 V^oia^isrt I R' 1 R' 1 R' (26) j8 = free-space phase constant. With the coupling coefficients (26) and the propagation constants as given by (10) and (14) the coupled line equations can be used to com- pute the TEoi transmission through curved sections. Since the absolute value of C/A7 is usually small compared to unity, the mode conversion loss is given by (19), the increase in TEoi attenuation by (20), and the spurious mode level by (21). The curves in Figs. 3, 4 and 5 have been calculated for the 2-inch pipe at a wavelength of 5.4 mm. They take into account the effects of the three most seriously coupled modes, TMn , TEn , and TE12 . In very gentle bends of a guide with a very thin coat, coupling effects to the TEim modes are small and only TMn coupling influences the TEoi transmission. The increase in TEoi attenuation in such bends is obtained by substituting the expression (10) for the TMn phase difference in (20). Aa, 0.034 11 aoi Vdl (« 1)252/22- (27) Note that (27) requires | C/A7 | « 1 and consequently {l/b){a/R) « 1. In Fig. 4, as well as in (27), losses in the dielectric coat have been neg- lected. Ecjuations (10) show that the dielectric losses are small com- pared to the wall current losses for a low loss dielectric coat. DIELECTRIC-COATED WAVEGUIDE 1265 UJ U UJ Q I.O 0.8 0.6 0.4 to (/) o 0.2 0.1 0.08 0.06 0.04 0.02 - < *N <, - s \ - « V \ \ > ::■> V - V\ \c OAT THICKNESS IN % )F THE GUIDE RADIUS - ■^^x V - \ \ 1 - 1 ovA ^ \ - \ \ \ - > ^ > \ - N \ \ V - \ \ 1 1 1 1 _L \ \\ ^ 1 6 8 10 20 40 60 100 200 400 600 BEND RADIUS IN FEET Fig. 3 — Maximum conversion loss of the TEoi wave in a vmiform bend of the dielectric-coated waveguide. 2a = 2 inches; X = 5.4 mm; e = 2.5. There are two different applications of the dielectric-coated guide, which require different designs: 1. Intentional bends These are relatively short sections and the increase in TEoi attenuation is usually small compared to the bend loss. Also, a high spurious mode level can be tolerated, because with a mode filter at the end of the bend we can always control the spurious mode level. Consequentlj^, the only limit set for this type of bend is the mode conversion loss of the TEoi wave. There is conversion loss mainly to TEn , TE12 and TMn . Increas- ing the phase difference of the TMn wave by making the dielectric coat thicker decreases the phase-difference between TEoi and TE12 and in- creases the phase-difference between TEoi and TEu . Apparently we get 1266 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 I 100 50 20 10 5- I- z CE UJ Q_ Z UJ CO < LU cm u z O 1.0 I- < g 0.5 UJ 0.2 0.1 \ \ \ \ \ \ \ \ 0 \ V \ N COAT THICKNESS IN PER CENT ^ \ \ \ OF THE GUIDE \^^ RADIUS — '-OX^ 0.75-^ Vo.sy \ 5.25 t \ \ \ A \ V \ \ \ s^ \ \ 10 10^ 10" 10** BEND RADIUS IN FEET 10° Fig, 4 — Increase in TEoi attenuation of a dielectric-coated guide in a uniform bend. 2a = 2 inches; e = 2.5; X = 5.4 mm. very near to an optimum design with a dielectric coat for which: C /tmu t (28) For this condition conversion losses to TMn and TE12 are equal, while the conversion loss to TEu is small. To find values which satisfy (28) we will generally have to solve (1) because the TMu phase difference required by (28) is too large to be calculated with the first order approximation. At a wavelength of X = 5.4 mm and a dielectric constant e = 2.5 the optimum thickness of the coat according to (28) is 5 = 1.25 per cent in the 2-inch pipe. In Fig. 6 the mode conversion loss in a dielectric-coated guide of this design is plotted versus bending radius. 2. Random deviations from straightness As mentioned before, random deviations from straightness change the curvature only gradually and only one normal mode propagates. Mode conversion loss and spurious mode level are very low. The normal mode attenuation depends on the curvature. The increase in normal mode attenuation as caused by curvature is obtained by adding the attenua- tion terms (20) of the various straight guide modes which are contained DIELECTRIC-COATED WAVEGUIDE 1267 -100 -80 -60 -50 10 _i eg o Q UJ > LU UJ Q O in D o ir Q. 10 -40 -30 -20- •10 -5 -4 -3 -1 - - ^ _,-^ S^ ^ COAT THICKNESS IN PER CENT ■^ ^^ $^ Ci^ RAC \ lUS / ^ ^ / ^ 0.75 P V. y/\ / -/^/ /0.50 y / v/ / V/ oV / 1 \ 1 1 10 20 30 40 50 60 80 100 200 BEND RADIUS IN FEET 300 400 600 1000 Fig. 5 — Spurious mode level in a uniform bend of a dielectric-coated guide. 2a = 2 inches; e = 2.5; X = 5.4 mm. in the normal mode. The bending radius R is a function of position and an average bending radius, 1 R Av = -7 z Jo ' dz R^ (29) has to be used in (20). All the attenuation terms (20) decrease with increasing coat thickness 5; the TEoi attenuation in the straight guide (10) and (14) increases with 6. Consequently there is an optimum thickness for which the total in- crease in attenuation is a minimum. This optimum thickness depends on the average radius of curvature. In Fig. 7 optimum thickness and the corresponding increase in attenuation have been plotted versus the average radius of curvature. In gentle curvatures the normal mode is a mixture of TEoi and TMn only and the attenuation increase as caused by the curvature is given by (27). In this case the optimum thickness and the corresponding attenuation increase are: 1268 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 Oont — 1 1 v; ■'opt a/2 7>oi W - iY" Aa V2 e y RJ a aoi J'oi VV^^iR (30) (31) Av We note that 5opt does not depend on frequency. So far we have listed only the useful properties of the dielectric-coated guide. There is, however, one serious disadvantage. Serpentine bends caused by equally spaced discrete supports and the elasticity of the pipe are inherently present in any waveguide line. At critical frequencies, when the supporting distance I is a multiple of the beat wavelength \h between TEoi and a particular coupled mode, an increase in TEoi attenuation (23) and a spurious mode level (24) result from the mode conversion. We evaluate (23) and (24) for a dielectric-coated copper pipe of 2.000- inch I.D. and 2.375-inch O.D. and a supporting distance I — 15 ft. The 1.0 0.8 0.6 0.4 0.2 0.1 0.08 "^ 0.06 an o 0.04 O z If) ir> O 0.02 0.01 0.008 0.006 0.004 0.002 0.001 !. \ \ V- 10 20 40 60 100 200 BEND RADIUS IN FEET 400 600 1000 Fig. 6 — Bend convension loss in a dielectric-coated guide of optimum design according to equation (28). 2a = 2 inches; 5 = 1.25%; € = 2.5; X = 5.4 mm. DIELECTRIC-COATED WAVEGUIDE 1269 result is for coat thicknesses which cause the wavelength X = 5.4 mm to be critical with respect to TEoi-TMn coupling: 5 = 0.002 I = \b — = 43.3 20 logio OiOl E2 = -1.29 dh = 0.004 = 2X6 = 2.70 = - 13.32 dh 0.006 = 3X6 = 0.169 = -25.37 dh. The values corresponding to 5 = 0.002 do not satisfy the condition (25). Therefore they cannot be considered as a cjuantitative result but only as an indication that the mode conversion is very high. We conclude from these values that the mode conversion is much too high for a coat thick- ness which makes the beat wavelength between TEoi and TMn equal to the supporting distance or half of it. If no other measures can be taken, such as remo\dng the periodicity of the supports or inserting mode filters, the lowest critical frequencies of TEoi-TMii coupling have to be avoided. A dielectric coat must be 10 a. HI a LU < UJ U 2 Z z o I- < 1.0 5 0.8 5 0.6 Q < 0.4 (/) (/> HI z y 0.2 < o •J 0.1 - N^ \, - \ - > \ \ s \ \ A* - \ - \ \ - ^^^ \^ \ - ^""^^ -^ "V *OPT \ k s. 1 1 1 1 ^ 1 N. 1 \ 1 AVERAGE RADIUS OF CURVATURE IN FEET 10" Fig. 7 — Optimum coat thickness and increase in TEoi attenuation of a dielec- tric-coated guide with random deviations from straightness. 2a = 2 inches; X = 54 mm; e = 2.5. 1270 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 chosen, which is thin enough or thick enough to keep these critical fre- quencies out of the band. Mode conversion from TEoi to the TEi,„ modes in serpentine bends is not changed substantially by the presence of the dielectric coat. Gener- ally these mode conversion effects decrease rapidly with the beat wave- length. When the curvature varies slowly compared to the difference in phase constant between coupled waves almost pure normal mode propagation is maintained. v. MODE CONVERSION AT TRANSITIONS FROM PLAIN WAVEGUIDE TO THE DIELECTRIC-COATED W^AVEGUIDE We consider a round waveguide, a section of which has a dielectric layer next to the walls. A pure TEoi wave incident on this dielectric- coated section will excite TE^m waves. For circular electric wave trans- mission it is important to keep low the power level of the higher circular electric waves which have low loss. In an evaluation of Schelkunoff's generalized telegraphist's equations for the TEoi mode in a circular waveguide containing an inhomogeneous dielectric^ S. P. Morgan describes the wave propagation in the dielectric- filled waveguide in terms of normal modes of the unfilled waveguide. The only restriction made in this analysis for the dielectric insert is \f\e-l\dS«l, (32) where S is the cross-sectional area of the guide. The dielectric-coated guide satisfies (32), and we may use the results of Morgan's evaluation here. The round waveguide is considered as an infinite set of transmission lines, each of which represents a normal mode. Along the dielectric- coated section the TEom transmission lines are coupled mutually. The coupling coefficient d between TEoi and one of the TEq^ waves is ob- tained by taking Morgan's general formula and evaluating it for the di- electric coat: V|Soi|8om 3 We mtroduce this coupling coefficient into the coupled fine equations (16). Since d/A^ « 1 for any of the coupled modes, the spurious mode level at the output of the dielectric-coated section is given by (21), 20 log 10 ^2n ^1 on 1 2 (e' - l)poiPoml3~ 3 ,oA\ 20 logic -^ ~ ^ — , 5 . (34; ^ (/3oi - iSom) V^OllSom DIELECTRIC-COATED WAVEGUIDE 1271 -130 -120 -110 -100 -90 LU ?-80 Z-70 a. UJ p-60 5-50 _i -40 -30 -20 -10 ^ — 1 ■^ ^ s. \ ^ % > ^ ^ ^v N ^ ^ 1 ^ \ \ ^ 1 ^ \ s %^ s ^ ^ s^ N ^ ^ a|o5 ^TEo3 ^TEo2 > ^ N 0.1 0.15 0.2 0.3 0.4 0.5 0.6 0.8 1.0 1.5 2 3 4 COAT THICKNESS IN PER CENT OF THE GUIDE RADIUS Fig. 8 — Higher circular electric waves at a transition from plain waveguide to the dielectric-coated guide, e = 2.5; a/X = 4.70. Fig. 8 shows an evaluation of (34) for a/X = 4.70 and e' = 2.5 correspond- ing to a 2-inch pipe with a polystyrene coat at X = 5.4 mm. VI. SUMM.\RY A theoretical analysis of wave propagation in the dielectric-coated guide is presented to provide information necessarj'- for circular electric wave transmission in this waveguide structure. The normal modes of a waveguide with a thin dielectric coat are perturbed modes of the plain waveguide. While the perturbation of the phase constant is only of third order of the coat thickness for the circular electric waves, it is of first 1272 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 order for all other modes. Thus, the degeneracy of equal phase constants of circular electric waves and TMim waves can be removed quite effec- tively. The additional attenuation to TEoi wave as caused by the dielec- tric loss in the coat and the increased wall current loss remains small as long as the coat is thin. The dielectric-coated guide may be used for negotiating intentional bends or for avoiding extreme straightness requirements on normally straight sections. For intentional bends of as small a radius as possible, an optimum thickness of the coat makes the mode-conversion losses to TMii and TE12 modes equal and minimizes the total conversion loss. For random deviations from straightness, an average radius of curva- ture is defined. For this average radius an optimum thickness of the coat minimizes the additional TEm attenuation as caused by curvature and dielectric coat. In random deviations from straightness, propagation of only one normal mode is maintained as long as only the rate of change of curvature is small compared to the square of the difference in phase constant between TEoi and any coupled mode. Serpentine bends, caused by equally spaced supports and the associ- ated elastic deformation of the pipe, increase the TEoi attenuation sub- stantially at certain critical frequencies, when the supporting distance is a multiple of the beat wavelength. The lowest critical frequencies of TEoi-TMii coupling corresponding to a beat wavelength, which is equal, to the supporting distance or half of it, have to be avoided by choosing} the proper coat thickness. At transitions from plain waveguide to dielectric-coated guide higher circular electric waves are excited by the TEoi wave. However, the power level of these spurious modes is low for a thin dielectric coat. ■ ACKNOWLEDGMENTS \ The dielectric-coated waveguide is the subject of two patents. Some of its useful properties were brought to the writer's attention by a com- munication between the Standard Telecommunication Laboratory, Ltd., England, and S. E. Miller. For helpful discussions the writer is indebted j to E. A. J. Marcatili, S. E. Miller, and D. H. Ring. APPENDIX I Approximate Solutions of the Characteristic Equation In the following calculation we will use the definitions: R„{x, px) = Jn{x) N„-i{px) — J„_i(p.-c)A'„(a;), Sn{x, px) = Jn-l{x) Nnipx) - J u(pX^ A'„_i(.t), DIELECTRIC-COATED WAVEGUIDE 1273 and their relation to the definitions (2) ; Wn{x, px) _ Rn{x, px) px Sn+l(x, px) -\- n = —px ^/^ ^ — n, Unix, px) Un(x,px) Un{x, px) Fn(.i-, px) ^ xUn-iJx, px) + nRnjx, px) Znix, px) ' xSn{x, px) + nUn{x, px) (36) To find solutions of (1) for 1 — p = 5 « 1 we first substitute for the functions (36) their series expansions with respect to 5. We have for instance Un{x, px) = Nn{x) Jn{x — 8x) — J n{x) Nn{x — 8x) where we introduce J nix - 8x) = JM + SxJ.'ix) + ^'.//'(.r) + •.. = J nix) + 8x ^ (5x0 " ./„+i(.r) - -J nix) X 1 X / N , /n' — n and Nnix - 8x) = Nnix) + 8x ' 2 Upon using the relation -Jn+xix) + Nn+yix) - -Nnix) X - l]jnix) + X X'- - l)iVn(a;)] + we get Unix, px) Jn+lix)Nnix) - Jnix)Nn+lix) = — TTX . ^+^¥(S^-' + 0(6"), (37) and by the same procedure _ , . 2 Rnix, px) = — 1 7r.f 1 - (/; - 1)5 + in - Din - 2) -)¥ n - 2/, , in - Din - 3)\ (6.r)" 1 + X 1-3 6 (38) + 0(5"). 1274 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 With these expressions the functions (36) are approximated by: Vn\X, pX) ,2 2\ I fs(f2\ ■f=- ^ = b\x - n ) + 0(6 ), Z„(.r, px) and for n = 0 especially: 1 Fo(a;, px) _ 1 U\{x, px) px~ Zo{x, px) X Ri(x, px) (39) -8 l+l + sM^o; a---i (40) + 0 (5^) Since for 5 = 0 the roots of Jn{pxi) = 0 and Jn(pxi) = 0 represent the solutions of (1) for the TM and TE waves respectively, we expand the Bessel functions of the argument pXi in series around these roots: pxi = (1 - 8)(pnm + Ax). The result for TM waves is JniPnm) - 0: :^4^ = ^ \^ ; (41) Jn{pXi) Ax — 8pnm for TE waves: //(p..) = 0 : -If^ = '^^^ (X - 6p.„.) ; and for TEom waves especially : Joipom) = 0: 'Jo {pXlJ 1 / . 2 , -2 2\ 5 /r, 1 >-. 2\ f-7 T- = Ax — dpom — [AX -\- 8 Pom) — -7 Pom{o + 2po,n ). Introducing (39 • • • 42) into the characteristic equation (1) and neglect-| ing higher order terms in 5 and Ax we get the following approximations for (1): TMnm waves: Ax = ( pnm — ) 8 2 2 2 ^ rrjTTt A X2 Pnm 'I' ^ Thnm waves: Ax = — - — ^— ^ ■ 5 n^O Pnm " ^ ^Pnm (42) ' DIELECTRIC-COATED WAVEGUIDE 1275 TEo^ waves: ^x = -^ {x{ - VoJ)h\ (44) If we write for the perturbed propagation constant we get with (3) and (4) : \ 2 §71711 A Ax = a Ay Pnm Vnm and in which X2 = (e — 1 + Pnm^) 2 _ X _ Pnm X Acnm ^TT 0, i Using these expressions in (43) and (44) we finally get approximate I formulae for the perturbation of the propagation constant as caused ! by the dielectric coat: TMnm waves : — = 5 TE„„ waves: — = ■ 5 (4o) n^O Tnm Pnn, — Tl^ C 1 — Vnm n^Tjy A7 Pom e — 1 .3 1 Eom waves : — = '-— 8 . Tom 'J 1 Vom' The series expansions used so far hold only when (1 — p)x « 1. Approxi- mate expressions which require only (1 — p) , 1 E2{z) = 2^ "' y^i(^) ^^P — A7 + Wiiz) exp A7 [z — 2 \ sn\ Cod dz j [z — 2 \ sin" Cod dz j (12) sin Ci)d cos Cod >. The solution (12) in combination with (11) is general and may be applied to any form of curvature as long as the converted power remains small compared to the original power in either of the modes. III. -WAVE PROPAGATION IN SERPENTINE BENDS If we apply (12) to a section of a serpentine bend with the length I we have 6(1) = 0. The output amplitudes are related to the input ampli- tudes of both modes by a transmission matrix EiH) = II r II Em. The elements of \\ T \\ are obtained from (11) and (12): (13) 1284 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 7^11 = 1 + f Uz) f i Jo Jo -,i{z) dzdz •exp - jil + 2A7 / sin^ CoO dz -'0 7^21 = - / ^1(2) dz exp Jo -jil + 2A7 / sin^co^d^ , Jo J 7^12 = - / ^2(2) dz exp -72^ - 2A7 / sin Cod dz Jo > 7^22 = 1 + I Uz) f ^liz) dz' dz _ Jo Jo •exp -y,l - 2A7 ( Jo sin^ CoO dz (14) For a line of iterative serpentine bends we apply the rules of matrix calculus. If £"10 = 1 and £"20 = 0 at the input of the first section, then the output amplitudes of the n section are : Eln = - 1 + 7^11 - T 22 V{Tn - T22y + 4ri2T2i_ Tn - T i J 11 ~ -t 22 "^ 2 L ~ VCTii - 7^22)^ + 4^127^21. -"02 , (15) Tn V(7^n - T,,y + 47^12^21 [e-"«i _ e-""'], Eon = where e~''- = hiTn + 7^22 ± V(rn - 7^22)^ + 4^12^21]. (16) Two limiting cases for the expressions (15) and (16) are of special interest: 1. I 7^11 - 7^22 r» 4 I 7^12^21! 7^12 7^21 -01 = 7^11 + -(72 _ i 11 — J 22 TriTii Tr^T Tn ~ T22 2. 4 I r 12 T21 I » I Tn - 7^22 r E^n = 12^21 ^^-„«i _ ^-na,j ^7) {Tn - T,,y Tn 7 n — 7 22 22 -0,., ^ Tn + 7^22 ^ ^jT^ 21 £i„ = hie-"'' + e-"^^) (18) CIRCULAR ELECTRIC WAVE IN SERPENTINE BENDS 1285 In case 1 the wave amplitude Ein is only affected by a slight change of the propagation constant. The small additional term in the expression for Ein can usually be neglected. The power in the wave E^n is small compared to the A\„ power; Tu is usually of the same order of magnitude as 2^21 . In case 2, however, a complete power transfer between Ein and E2n occurs cyclically if the loss is sufficiently low. Consequently, condition (18) has to be carefully avoided. Rather, condition (17) must always be satisfied. IV. SERPENTINE BENDS FORMED BY ELASTIC CURVES A section of the waveguide line between two supports deforms like a beam fixed at both ends. Under its own weight, w per unit length, such a beam will bend and form an elastic curve. Fig. 1, whose deflection from a straight line is given by: ,2 y = wl X 24:EI P 1 X (19) in which E = modulus of elasticity of the beam, and / = moment of inertia of the beam. Since we are concerned with small deflections y only, we have x = z and 6 = dy/dx. Hence, * = <'(i-3p+4'! (20) in which d = wl /12EI. Introducing the elastic curve (20) into the trans- mission matrix (10) and (14) and performing the integrations with sin Cod = Cod we get for the elements of the transmission matrix : 7^11 = exp T.,. = exp yj + A7/ + ? Ay'f - — y-J — Ayl 2 ,2-1 Cod l05 105 2 ,2 Cod 105 /i + Co d 9 3A7'/' + A7V' 4A7«/' A77' - (3 - 3A7/ + A7'^')V^"' Cod 1 1 + 4A7«/« 4,4 y - 'SAy-l- + Ayl (21) A7 1 + ~ Ay'r - (3 + 3A7/ + A7-/")-e 2,2\2 -2A7/ T12 = T,i = ./ . Cod 2AyH' 105 [(3 - 3A7/ + A7'/')e -72' - (3 + 3A7/ + A7''r)e"^^']. 1286 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 The expressions (21) are hard to evaluate, but for some special cases of interest they can be simplified greatly. To compute the coupling effects between the TEoi wave and the TMn wave we make use of | A7/ | « 1 and get the following approxima- tions : T. ^[,-g .yV] exp - (.. - <§ Ay) I, [, + g ,yr rp _ 1 1 , -u - , 3,3 J 22 — 2 ,2 Co a exp - 72 + ~ At I, (22) 105 m m ■ ^0^ A 2,2 -yl T12 = T21 = J ^r^ Ay I e ^ . 15 In (22) the condition | Tn - T^ | ' » 4 | TnT^i \ is satisfied; conse- quently the wave propagation is described by (17), Em = exp - [y, - ^" At) nl + g^' Ay't sinh AT^fe^^"', Ein = j ,-V ^T^ sinhAT/i/e~^" . 15 (23) In addition to small oscillations, which are negligible, the wave ampli- tude El suff'ers an additional attenuation A«. = - ^' Aa. (24) 105 Physically this means that to a first approximation there is no net power transfer from Ei to E2 . The power converted from Ei to E2 in one section of the iterative serpentine bends is all reconverted in the same section. But this power, which travels partly in the E2 wave, suffers the E2 attenuation and consequently changes the Ei attenuation. To evaluate (24) w^e introduce the coupling coefficient and the differ- ence in attenuation constants between the TEoi and TMu wave. Then, the relative increase of TEoi attenuation is: — ^ = 6.39 X 10-^ ^ / / - y /■ / - / / - / / / / / / / / / / IDEAL MODE FILTERS / IN A PIPE WITHaoi-(Xi2 / - / - / ^ - / / / / y 1 1 1 \ 1 1 1 1 1 1 1 10 20 40 60 100 200 400 600 1000 2000 SPACING OF MODE FILTERS IN FEET 4000 6000 10,000 Fig. 2 — TEoi attenuation increase of TE01-TE12 coupling in serpentine bends with mode filters; 2-inch I.D. 2f-inch O.D., X = 5.4 mm. Serpentine bends are caused by equally spaced supports and the elasticity of the copper pipe. The sup- porting distance is a multiple of the beat -wavelength between TEoi and TE12 . An alternative to control the coupling effects is insertion of mode filters into the line. Mode filters which pass the TEo„ waves ^nthout loss but attenuate all other modes have been developed in various forms. To estimate the amount of mode conversion control that can be achieved by mode filters, we make two different assumptions. Only the critical case of the supporting distance ecjual to a multiple of the beat wave- length is considered here. A. The mode filters are ideal; they present infinite attenuation to all unwanted modes. At the input of a section between two mode filters we have a TEoi wave only and at the output the spurious mode level has risen to w Co EI (2A/5)2 (34) 1290 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 _l LJJ o UJ Q UJ > a O (/) D O ' JC LU a. i a. 0 / 1 i 1 \ U--z,--J <- — -L--- ->l Fig. 1 — Normal mode bend with linear curvature taper. NORMAL MODE BENDS FOR CIRCULAR ELECTRIC WAVES 1297 amplitude is '(^■' I = 2- I i „,fe) I = i ^ «"'" dz dz (7) This amplitude represents mode conversion loss and therefore has to be kept as small as possible. In (7) the function ^(2), i.e., the taper function, is still undetermined. Obviously it can be chosen so as to optimize the taper performance. A taper of optimal design keeps the unwanted mode below a certain value with as short a taper length as possible. From (7) the relation between this optimizing problem and the problem of the transmission line taper of optimal design is at once evident. The transmission line taper is a low reflection transition between lines of different characteristic impedances. To minimize the length of the transition for a specified maximal reflec- tion, the characteristic impedance has to change along the transition according to a function which is essentially the Fourier transform of a Tschebj^scheff polynomial of infinite degree. The same procedure can be applied here and it will result in a curvature taper of optimal design. We are, however, at present not as much interested in a transition of optimal design as in a curvature taper which can easily be built. Suppose we bend the pipe to a bending radius Ro which causes only elastic defor- mation. We do this on a form of radius Ro , Fig. 1. The forces acting on both ends of the pipe cause a torque and hence a curvature of the pipe which increases approximately linearly from the pipe end (z = 0) to the point of contact (z = Zi) between pipe and form: k = ko-. (8) The corresponding curve which the pipe forms along the taper is Cornu's spiral. We shall evaluate (7) for a curvature as given by (8). In considering the mode conversion we may neglect all heat losses, that is 7 = jp, etc. With c = Co-, (9) Zl we get ^ _ 2co 1 dz A|82i . i4_£oV_' (10) 1298 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 and f V . A)8^2i r Co2 /, , . / CozY I 1 . , -1 2coZ 4co L^jS2i 'y ' • ' \Al3zi/ ' 2 A/3zi_ We introduce (10) and (11) into (7) and take advantage of A^ «1, (11) (12) which is satisfied for a gentle enough bend. The unwanted mode level is then given by 3\ ^2(^1) I = Co A/S^^i (1 - e'"''') + 0 8 Co A^3 (13) The general restriction (5) for the solution (6) in case of the linear taper is 2cn 1 +4 2 2 N CqZ A^, -3/2 «1, A/3221 and in view of (12) only I A^2i I ^ 1 (14) is required. The length of the transition has to be of the order or greater than the largest beat wavelength. In addition to mode conversion loss the normal mode suffers heat loss along the taper. From (3) and (6) this heat loss is given by the real part of [yz — p{z)]. If A/3 » Aa we get r' c R[-yz - p] = aiz -\- Aa -—- dz JQ AB^ (15) It follows from (15) that the attenuation of the coupled straight guide modes should not be too high for the normal mode bend to work properly. III. THE TOTAL BEND LOSS We will consider bends of the dielectric-coated waveguide only. The normal modes of the dielectric-coated waveguide have phase constants which are slightly different from the phase constants of the modes in the plain guide^ TM„^ A^ e' - 1 TE„m vith rif^O Aj8 n e - 1 ^nm Vnn? " W^ €'(1 - v') TEom A/3 yam e' — 1 -3 — = _-— - — . d . 5, (16) /3o„ 3 1 - VQn NORMAL MODE BENDS FOR CIRCULAR ELECTRIC WAVES 1299 The losses in the dielectric coat increase the attenuation constants by: // TM„m - — = — h, I3nm e ^ TE„OT - — = - — ^ 1 ~W\ 2^ ^' ^^^^ with n5>^0 pnm Pnm ^ € i-i i'nm ) 2 // i -b^Orn -^ = -^- :j ^ 0 . pOm O i — J-Om For the circular electric waves the dielectric coat increases the wall cur- rent attenuation by TEom — = (e' - 1) H 5^ (18) OCOm VDm" The various symbols in (16), (17) and (18) are: ^nm = plain guide phase constants of TM„m and TE„TO respectively; Vnm = wth root of Jn(a:) = 0 forTM„^ , andmthrootof /„'(a;) = 0 for TE„m waves respectively; Vnm = — = ^^ cutoff factor in plain waveguide of radius a; 8 = - relative thickness of dielectric coat; a e = e — je" relative dielectric permittivity of dielectric coat; aom = attenuation constant of TEom in the plain waveguide. The coupling coefficient between the straight guide modes in a curved waveguide is c = c'/R in which : TEoi ^ TMii c = 0.18454 I3a, , 0.09319(^a)2 - 0.84204 , TEoi ^ TEn c = /^ \ + 0.09319 V(3o,a^ua, TF ^ TT^ ' 0-15575(/3a)^ - 3.35688 ^-^ (19) TEoi ^ TEi2 c = /^ ^ + 0.1557O V^ovajSna, Vi8oiai8i2a , 0.01376(/3a)2 - 0.60216 , TEoi ^ TEi3 c = y ' ^ + 0.01376 Vl3oial3,za, where jS = free-space phase constant. We consider the bend configuration of Fig. 1, with the curvature being a trapezoidal function of length. The maximum power loss due to con- version to one of the unwanted modes in the first transition is, by (13), I ^2(2:1) A 2 ,2 _ 4 Co max (A/32i)2A/32" I 1300 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 I By the law of reciprocity the same conversion loss occurs in the second transition. Both conversion parts phase with each other. To get an aver- age total conversion we may add them in quadrature and the total con- version loss to one of the unwanted modes is, expressed in nepers, Under most unfavorable phase conditions the conversion loss may be twice this value, but it is veiy unlikely that such phase conditions will be satisfied for all coupled modes simultaneously. Besides mode conversion loss the local normal mode suffers attenuation in the bend. This attenuation is larger than the straight guide attenua- tion. Each straight guide mode contained in the local normal mode of the bend causes an increase in attenuation. From (15) the loss caused by one of these straight guide modes is: J 1.1 2 T^ ^^- (21) 0 Ap^ Where aim is the attenuation constant of the TEi^ and TMn waves respectively in the dielectric coated waveguide. Introducing the trapezoidal curvature function of Fig. 1 into (21) we get A, = 1^, (aim - «oi) (l-^ 2i). (22) The loss caused by the TEoi attenuation in the straight dielectric coated guide is from (17) and (18) As = aoil 1 + (e - 1)^5^ VOm~ + ^ ^!^ 8\ (23) 3 1 — foi The total bend loss is finally obtained by summing up all the terms of (20), (22), and (23), A = As-^ZA, + T.Ae. (24) The summation signs indicate that all coupled modes (TMn and TEi,;,) have to be taken into account. The effectiveness of the normal mode bend is best demonstrated by a practical example. A copper pipe now in experimental use at Bell Tele- phone Laboratories for circular electric Avave transinission near 5.4 mm wavelength has 2-inch I. D. and 2f-inch CD. Suppose we want to change the direction of a waveguide fine with this copper pipe bn an angle ^o • We can do this most easily by inserting a dielectric-coated section, which XOmL\L MODE BEXDS FOR CIRCUK\R ELECTRIC WAVES 1301 is bent around a fixed support in the center by forces acting on both ends. In order not to exceed elastic deformation the bending radius must not be smaller than E Rmin = 7 <^1 > (-5) Jm&x ¥ where /,aax = flexural stress at elastic limit, E = modulus of elasticity, Oi = outside radius of pipe. This minimum bending radius requires a minimum length to change the pipe direction by a specified angle ^o given by /.nin = 2eoi?min • (26) The total bend loss (24) has been evaluated for a bend configuration as specified by (25) and (26). The result is shoAAii in Fig. 2. The total addi- tional bend loss is only of the order of the TEoi loss in the plain straight ^va^'eguide. For small bending angles the curvature taper becomes .shorter and consequently the mode conversion loss mcreases. The mode conver- sion loss, however, does not go to infinity for zero bending angle. In this ca.se (14) is no longer satisfied, and the mode conversion loss is no longer described by (20). The level of the various miwanted modes which can be calculated from (20) is plotted in Fig. 2. For a practical waveguide one would decide on a .standard length of dielectric-coated pipe, one or several of which would be inserted whene\'er a change in direction has to be made. Take, in our example, a standard length of 15 feet. With one such section a change of direction up to 15° could be made. For a change in direction up to 30° two such sections would have to be inserted and bent around a fixed support at the center joint. The total loss of Fig. 2 is then a maximum value, which would only occur when the pipe is bent to the highest allowable bending angle. IV. A XORiL\L MODE BEXD OF OPTIMUM DESIGX The various terms of the total bend loss (24) depend on the bend geom- etry in quite different ways. It is therefore hkely that for a given bending angle ^o a bend geometry can be found, which minimizes the total bend lo.ss. The total bend loss can generallv be written as: &"■ -4. = SI -{- B y— r:, -1- C J-, ^ , /(I — u)- r(w — u-)- 1302 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 / DIELECTRIC COAT 0.005" THICK f' = 2.5 f"= 2.5x10"^ 1- Ul UJ ^ 60 Z t3 40 z UJ _l a 20 z UJ CD 0 ^ ^^ "^ , ^ -50 101 _iz 8^^-40 5 < OD z D< -20 -C^A^^ ■ -^^ - ^ -^VA^ in 0.040 20 25 30 35 40 BENDING ANGLE IN DEGREES Fig. 2 — Normal mode bend. Dielectric-coated copper pipe with 2-iiich I.D. and 2f-inch O.D. deflected to limit of elastic deformation (X = 5.4 mm). NORMAL MODE BENDS FOR CIRCULAR ELECTRIC WAVES 1303 in which S = aoi 1 + (e' - 1) ""{ «-^l /2 ^ ^ A3' ^^ ^°^^'" — aoi), A /2 - " o 6 1 — vqi (28) u = I Here again the summation signs indicate that all coupled modes have to be taken into account. The factors S, B, and C do not depend on the bend geometry, but only on the total bending angle, the waveguide prop- erties, and the frequency. Necessary conditions for A(u, I) to be a mini- mum are : dA _2(l - 2m) du B C with the two roots Z(l - u') L3 /V_ 1 = 0, u = 2' and '-i"i 4C — = S - 73 dl (1 - uY r- (u - u')- I' If u = h, the solutions of (32) are the roots of S f - iBf - 64C = 0. If {III) = ?){C/B), the solutions of (32) are the roots of Sufficient conditions for A{u, I) to be a minimum are: d'A ^ ^ d'A T^ > 0- ^ > 0> = 0. 6w2 dl' (29) (30) (31) (32) (33) (34) (35) (3()) h 1304 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 If w = I, we have: d'A d'A dudl 8/5 -0, C' M3+^^3y. (37) ^^(oC _B du" I \ I' 3. Substituting X '-4 B ■ (38) we get instead of (33) and instead of (37) x\dx'' - 1) - 2/ = 0, (39) d'A B "ar- = i«f(^^-i)- The positive root of (39) is plotted in Fig. 3. It follows that if r > 1 we have a; > 1, consequently d^A/du^ > 0; and if r < 1 we have a; < 1, consequently d^A/du < 0. Consequently if, and only if, r > 1 the values u = ^ and x from Fig. 3 minimize the total bend loss A. 3.0 2.5 2.0 X 1.5 1 .0 Ob/" ^ ^ -^ ^^ /" ^^^ y y / y \ \ 0' Fig. 3 — Positive root of a;3(32;2 _ i) - 2r^ = 0. NORMAL MODE BENDS FOR CIRCULAR ELECTRIC WAVES 1305 If {ulf is equal to 3(C/5), a^ al4 _ / al^Y ^ 4B^ i - 2u du^ dp \dudl) ~ l^u (l-uy and dA 2B 1 - 2u Bu- lu (1 -uY Hence, if w < | or, because of (31) and (34) r < 1, a minimum of A{u, I) is located at 25 LU LU Ll_ Z 20 Q Z UJ m 15 U- O f 10 (J) z LU 6 0 \ \ \ \ \ ^ --. ^ ^ 008 01 O _J - 0.06 0.04 0.02 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 30 COAT THICKNESS IN PER CENT OF THE GUIDE RADIUS Fig. 4 — 90° normal mode bend of |-inch I.D. copper pipe with a dielectric coat of e' = 2.5, e" = 2.5 X 10~^ Optimum design for 5.4-mm wavelength. 1306 THE BELL SYSTEM TECHNICAL JOUENAL, SEPTEMBER 1957 To fiiid the optimum bend geometry for a given dielectric coated guide and a specified bending angle we calculate r from (38). If r > 1 the opti- mum geometry is I = 2 with X from Fig. 3. If r < 1, and Zi = and A numerical example, the 90° bend of a |-inch I. D. copper pipe, is shown in Fig. 4. The total bend loss in the optimally designed bend de- creases steadily mth increasing thickness of the dielectric coat. This indicates that there is also an optimum coat thickness, which minimizes the total loss of the normal mode bend of optimum total length and taper length. Unfortunately, however, several approximations made in calcu- lating phase constants and coupling coefficients in the dielectric-coated 0.20 0.18 0.02 10 20 30 40 50 60 70 80 FREQUENCY IN KILOMEGACYCLES PER SECOND 100 Fig. 5 — 90° normal mode bend of |-inch I.D. copper pipe with a dielectric coat €.0075 inch thick (e' = 2.5, e" = 2.5 X 10~^), designed for optimum performance at X = 5.4 mm (55.5 kmc). NORMAL MODE BENDS FOR CIRCULAR ELECTRIC WAVES 1307 waveguide usually break down at smaller than optimum values of the coat thickness. It should be mentioned finally that the normal mode bend is an in- herently broad band device. Except for the oscillations of the mode con- version portion of the total loss as caused by spurious mode phasing, there is only a gradual change of the loss with frequency. P Some terms contributing to the total loss decrease with frequency, others increase. The over-all frequency dependence is of the same order as the frequency dependence of the loss in the straight waveguide. As an example, in Fig. 5 the bend loss has been plotted versus frequency for the normal mode bend of Fig. 4. ACKNOWLEDGMENT Mathematical analysis of tapered curvature in other forms of wave- guide has been made by others. S. E. Miller reports that Siemens & Halske A. G., Germany, have made an original treatment of this sub- ject. REFERENCES 1. H. G. Unger, Circular Electric Wave Transmission in the Dielectric Coated Waveguide, pp. 1253-1278, this issue. 2. S. E. Miller, Coupled Wave Theory and Waveguide Applications, B.S.T.J., 33, pp. 661-719, May, 1954. 3. W. H. Louisell, Analysis of the Single Tapered Mode Coupler, B. S.T.J. , 34, pp. 853-870, July, 1955. 4. R. W. Klopfenstein, A Transmission Line Taper of Improved Design, Proc. I.R.E., 44, pp. 31-35, January, 1956. 5. S. P. Morgan, Theory of Curved Circular Waveguide Containing an Inhomo- geneous Dielectric, pp. 1209-1251, this issue. Bell System Technical Papers Not Published in This Journal ASHKIN, A.^ Electron Beam Analyzer, J. Appl. Phys., 28, p. 564, May, 1957. Beck, A. C Communications Superhighways, Trans. I.R.E., PGMTT, MTT-5, pp. 81-82, April, 1957. Becker, G. E.' Dependence of Magnetron Operation on the Radial Centering of the Cathode, Trans. I.R.E., PGED, ED-4, pp. 126-131, April, 1957. BooTHBY, 0. L., see Williams, H. J. Bowers, F. K.^ What Use is Delta Modulation to the Transmission Engineer? Com- mun. & Electronics, 30, pp. 142-147, May, 1957. Brown, S. C, see Rose, D. J. Broyer, a. p., see Schlabach, T. D. Buck, T. M.,i and McKim, F. S.^ Experiments on the Photomagnetoelectric Effect in Germanium. Phys. Rev., 106, pp. 904-909, June 1, 1957. BlJEHLER, E.l Contribution to the Floating Zone Refining of Silicon, Rev. Sci. Instr., 28, pp. 453-460, June, 1957. Chilberg, G. L.^ Buried Cable Telephone Systems, Commun. & Electronics, 30, pp. 130-135, May, 1957. ^ Bell Telephone Laboratories, Inc. ^ American Telephone and Telegraph Company. 1308 TECHNICAL PAPERS 1309 Chynoweth, a. G./ and McKay, K. G.^ Internal Field Emission in Silicon P-N Junctions, Phys. Rev., 106, ^ pp. 418-426, May 1, 1956. Clemency, W. F.,^ Romanow, F. F.,i and Rose, A. F.^ The Bell System Speakerphone, Commun. & Electronics, 30, pp. ^ 148-153, I\Iay, 1957. COMPTON, K. G.^ Variability in Working Copper Sulfate Half Cells, Corrosion, 13, pp. 19-20, March, 1957. CowAx, F. a:- Transmission of Color Over Nationwide Television Networks, S.M.P.T.E., 66, pp. 278-283, May, 1957. Drenick, R.^ An Operational View of Equipment Reliability, Trans. Annual Con- vention, Am. Soc. Quality Control, 11, pp. 603-611, May 22, 1957. Easley, J. W.i The Effect of Collector Capacity on the Transient Response of Junc- tion Transistors, Trans. I.R.E., PGED, ED-4, pp. 6-14, Jan., 1957. Emling, J. W.i General Aspects of Hands -Free Telephony, Commun. & Electronics, 30, pp. 201-205, May, 1957. Fagen, R. E., see Hall, A. D. Feldmann, W. L., see Pearson, G. L. Ford, B. W.' Demand Increasing for Special Uses of Telephone Facilities, Teleph- ony, 152, pp. 22-24, 44, 48, June 8, 1957. Freericks, L.^ Semiconductors in Switching Circuits, General Engineering Bulletin (N. Y. Tel. Co.), 7, pp. 21-25, May, 1957. ^ Bell Telephone Laboratories, Inc. ^ American Telephone and Telegraph Company, ^ Illinois Bell Telephone Company, Cliicago. 1310 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 Freudenstein, F.,^ Warthman, K. L.,^ and Watrous, A. B.' Designing Gear-Train Limit Stops for Control of Shaft Rotation, Machine Design, 11, pp. 84-86, May 30, 1957. Galt, J. K.i Losses in Ferrites — Single Crystal Studies, J. Inst. Elec. Engrs. (London), 104, pp. 189-197, June, 1957. Gellkr, S.^ Comments on Pauling's Paper on Effective Metallic Radii for Use in the /^-Wolfram Structure, Acta Cryst., 10, pp. 380-382, May 10, 1957. Gerard, H. B.^ Some Effects of Status, Role Clarity and Group Goal Clarity Upon the Individual's Relations to Group Process, J. Personality, 25, pp. 475-488, June, 1957. Green, E. L^ Evaluating Scientific Personnel, Elec. Engg., 76, pp. 578-584, July, 1957. Gupta, S. S.,i Huyett, M. J.,' and Sobel, M.i Selection and Ranking Problems with Binomial Populations, Trans. Annual Convention, Am. See. Quality Control, 11, pp. 635-718, May 22, 1957. Hake, E. A.' A 10-Kw Germanium Rectifier for Automatic Power Plants, A.LE.E. Conf. Publication "Rectifiers in Industry", T-93, p. 119, June, 1957. Hall, A. D.,i and Fagen, R. E.i Definition of System, Yearbook Soc. Ad\ancement of General 83^3- tems Theory, 1, pp. 18-28, April, 1957. Harker, K. J.^ Non-Laminar Flow in Cylindrical Electron Beams, J. Appl. Phys., 28, pp. 645-650, June, 1957. Hennessey, T. M.^ A Dial Service and Community Relationships. Telephony, 152, pp. 22-24, 40, June 1, 1957. ^ Bell Telephone Laboratories, Inc. ^ New England Telephone and Telegraph Company, Boston, Mass. p technical papers 1311 Herrmann, G.^ Transverse Scaling of Electron Beams, J. App]. Phys., 28, pp. 474- 478, April, 1957. HuYETT, M. J., see Gupta, S. S. Levenbach, G. J.^ Accelerated Life Testing of Capacitors, Trans. I.R.E., PGRQC, p RQC-10, pp. 9-20, June, 1957. Lloyd, S. M.^ A New Water Rheostat for Testing Exchange Power Plants, Teleph- ony, 152, pp. 32-34, May 25, 1957. LUMSDEN, G. Q.^ P Wood Poles for Communication Lines, A.S.T.M. Bulletin, 222, pp. 19-24, May, 1957. McCall, D. W.i »Cell for the Determination of Pressure Coefficients of Dielectric Con- stant and Loss of Liquids and Solids to 10,000 psi. Rev. Sci. Instr., 28, pp. 345-351, May, 1957. McCall, D. W., see Slichter, W. P. McIvAY, K. G., see Chynoweth, A. G. McKiM, F. S., see Buck, T. M. McSkimin, H. J.' Use of High Frequency Ultrasound for Determining the Elastic Moduli of Small Specimens, Proc. National Electronics Conf., 12, pp. 351-362, April 15, 1957. i Miller, W. A.^ A Narrow-Band Experimental FM Mobiletelephone System, Com- mun. & Electronics, 30, pp. 98-100, May, 1957. Montgomery, H. C.^ Field Effect in Germanium at High Frequencies, Phys. llvx., 106, pp. 441-445, May 1, 1957. ' Bell Telephone Laboratories, Inc. ' Western Electric Company, Inc. ' Pacific Telephone and Telegraph Company, Los Angeles, Calif. 1312 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 O'Brien, J. A.^ Unit Distance Binary-Decimal Code Translators, Trans. I.R.E., PGEC, EC-6, pp. 122-123, June, 1957, Letter to the Editor. Pearson, G. L.,^ Read, W. T., Jr.,^ and Feldmann, W. L.^ Deformation and Fracture of Small Silicon Crystals, Acta Met., 5, pp. 181-191, April, 1957. Pederson, C. W.^ Crystal Clock for Airborne Computer, Electronics, 30, pp. 196-198 June 1, 1957. Read, W. T., Jr., see Pearson, G. L. Rider, D. K., see Schlabach, T. D. Romanow, F. F., see Clemency, W. F. Rose, A. F., see Clemency, W. F. Rose, D. J.,^ and Brown, S. C.^ Microwave Gas Discharge Breakdown in Air, Nitrogen, and Oxygen, J. Appl. Phys., 28, pp. 561-563, May, 1957. Schlabach, T. D.,^ Wright, E. E.,^ Broyer, A. P.,^ and Rider, D. K.' Testing of Foil-Clad Laminates for Printed Circuitry, Bull A.S.T.M., 222, pp. 25-30, May, 1957. Shenitzer, A.i On the Problem of Chebyshev Approximation of a Continuous Func- tion by a Class of Functions, J. Assoc. Computing Machiner}-, 4, pp. 30-35, Jan., 1957. Sherwood, R. C, see Williams, H. J. Snoke, L. R.i Some Needed Basic Research on Wood Deterioration Problems^ Appl. Microbiology, 5, pp. 188-193, May, 1957. SoBEL, M., see Gupta, S. S. 1 Bell Telephone Laboratories, Inc. * Massachusetts Institute of Technology, Cambridge. I monographs 1313 Van Uitert, L. G.^ Effects of Annealing on the Saturation Induction of Ferrites Contain- ing Nickel and/or Copper, J. Appl. Phys., 28, pp. 478-481, April, 1957. Warthman, K. L., see Freudenstein, F. Watrous, a. B., see Freudenstein, F. Whittemore, L. E.2 The Institute of Radio Engineers — Forty-five Years of Service, Proc. I.R.E., 45, pp. 597-635, May, 1957. Williams, H. J.,^ and Sherwood, R. C.^ Magnetic Domain Patterns on Thin Films, J. Appl. Phys., 28, pp. 548-555, May, 1957. Williams, H. J.,^ Sherwood, R. C.^ and Boothby, 0. L.^ Magnetostriction and Magnetic Anisotropy of MnBi, J. Appl. Phys., 28, pp. 445^47, April, 1957. Wright, E. E., see Schlabach, T. D. 1 Bell Telephone Laboratories, Inc. 2 American Telephone and Telegraph Company. Recent Monographs of Bell System Technical Papers Not Published in This Journal* Bennett, W. R. Synthesis of Active Networks, Monograph 2816. Dewald, J. F. Formation of Anode Films on Single -Crystal Indium Antomonide, Monograph 2802. DiTZENBERGER, J. A., 866 Fuller, C. S. Eigler, J. H., see Sullivan, M. V. * Copies of these monographs may be obtained on request to the Publication Department, Bell Telephone Laboratories, Inc., 463 West Street, New York 14, N. Y. The numbers of the monographs should be given in all requests. 1314 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 Flaschen, S. S., see Garn, P. D. Fuller, C. S., and Ditzenberger, J. A. Effect of Defects in Germanium on Diffusion and Acceptance of Copper, IMonograph 2803. Fuller, C. S., and Morin, F. J, Diffusion and Electrical Behavior of Zinc in Silicon, Monograph 2789. Garn, P. D., and Flaschen, S. S. Analytical AppUcations of a Differential Thermal Analysis Apparatus, Monograph 2769. Geballe, T. H., see Kunzler, J. E. Geballe, T. H., see Morin, F. J. Gohn, G. R., see Torrey, M. N. Gould, H. L. B., and Wenny, D. H. Supermendur: A New Rectangular-Loop Magnetic Material, Mono- graph 2780. Green, E. I. Nature's Pulses, Monograph 2770. Green, E. I. Science and Liberal Education, Monograph 2765. Green, E. I. Telephone, Monograph 2806. Hagstrum, H. D. Auger Ejection of Electrons from Tungsten by Noble Gas Ions, Monograph 2715. Hagstrum, H. D. Effect of Monolayer Adsorption on Ejection of Electrons from Metals, Monograph 2804. MONOGRAPHS 1315 Hagstrum, H. D. Thermionic Constants and Sorption Properties of Hafnium, Mono- ^ graph 2790. Herring, C, see Morin, F. J. Hull, G. W., see Kunzler, J. E. Klemm, G. H. Automatic Protection Switching for TD-2 Radio System, Monograph H 2772. KOHN, W. Effective Mass Theory in Solids from a Many-Particle Standpoint, Monograph 2791. Kunzler, J. E., Geballe, T. H., and Hull, G. W. Germanium Resistance Thermometers Suitable for Low-Tempera- ture Calorimetry, Monograph 2792. Lloyd, S. P., and McMillan, B. Jk Linear Least Squares Filtering and Prediction of Sampled Signals, P Monograph 2815. Lundberg, C. v., see Vacca, G. N. 1 McMillan, B., see Lloyd, S. P. I Mendizza, a. Standard Salt-Spray Test — Is It A Valid Acceptance Test?, Mono- graph 2807. Meszar, J. Full Stature of the Crossbar Tandem Switching System, ]\Ionogiaph 2750. Miller, S. L. Ionization Rates for Holes and Electrons in SiUcon, IMonograph 2794. Morin, F. J., see Fuller, C. S. 1316 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 MoRiN, F. J., Geballe, T. H., and Herring, C. Temperature Dependence of Piezoresistance of High-Purity Silicon, Germanium, Monograph 2797. MoRiN, F. J., and Reiss, H. Formation of Ion Pairs and Triplets Between Lithium and Zinc in Germanium, Monograph 2795. Reiss, H., see Morin, F. J. Rose, D. J. Microplasmas in Silicon, Monograph 2796. Smith, K. D., see Veloric, H. S. SUHL, H. Theory of Ferromagnetic Resonance at High Signal Powers, Mono- graph 2817. Sullivan, M. V., and Eigler, J. H. Electroless Nickel Plating for Making Ohmic Contacts to Silicon, Monograph 2808. Sullivan, M. V., and Eigler, J. H. Five Metal Hydrides as Alloying Agents on Silicon, Monograph 2775. ToRREY, M. N., and Gohn, G. R. A Study of Statistical Treatments of Fatigue Data, Monograph 2778. Vacca, G. N., and Lundberg, C. V. Aging of Neoprene in a Weatherometer, Monograph 2809. Van Horn, R. H. Experimental Evaluation of ReUability of Solderless Wrapped Con- nections, Monograph 2810. Veloric, H, S., and Smith, K. D. Silicon Diffused Junction "Avalanche" Diodes, Monograph 2811. CONTKIBUTORS TO THIS ISSUE 1317 VoGEL, F. L., Jr. Dislocations in Plastically Bent Germaniiun Crystals, Monograph 2763. Weber, L. A. Influence of Noise on Telephone Signahng Circuit Performance, Monograph 2812. Weibel, E. S. An Electronic Analog Multiplier Using Carriers, Monograph 2813. Wenny, D. H., see Gould, H. L. B. YOUNKER, E. L. A Transistor-Driven Magnetic-Core Memory, Monograph 2814. Contributors to This Issue C. H. Elmendorf, B.S., California Institute of Technology, 1935; M.S., 1936; Bell Telephone Laboratories, 1936-. Mr. Elmendorf was concerned with the development of coaxial cable transmission systems from 1936 to 1955, except for the period from 1941-1945 when he worked on airborne radar systems. In 1952 he started an exploratory program on submarine cable systems. As Assistant Director of Transmission Sys- tems Development since 1955, he has been responsible for development of submarine cable systems. He is a senior member of the I.R.E. Bruce C. Heezen, B.A., University of Iowa, 1948; M.A., Columbia University, 1952; Ph.D. 1956. After participating in a cruise of the Woods Hole research vessel Atlantis in the summer of 1948, Mr. Heezen held a fellowship in geology at Columbia, where he joined the staff of the Lamont Geological Observatory when it was founded in 1949. As submarine geologist, and now as senior scientist in charge of the sub- marine geology program, he has been a member of numerous deep-sea expeditions. In addition, he teaches a graduate course in submarine geology on the Columbia campus. His work includes deep-sea topogra- phy, sediments, and sedimentation processes; submarine photography and deep-sea research instrumentation; and geologic, geoph3^sical, and oceanographic exploration of the deep sea. 1318 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 Samuel P. Morgan, B.S., 1943; M.S. and Ph.D., 1947, California In- stitute of Technology; Bell Telephone Laboratories, 1947-. A research mathematician, Mr. Morgan has been concerned with the applicatiori of electromagnetic theory to microwave problems, and has also made studies in other fields of mathematical physics. Member American Physical Society, Tau Beta Pi, Sigma Xi and I.R.E. Lloyd P. Snoke, B.S. in For., 1948, Pennsylvania State L'niversity; Bell Telephone Laboratories, 1948-. Since joining the Laboratories, Mr. Snoke has specialized in the timber products used in the Bell System and their preservative treatment. He has been specifically engaged in the study of timber treatment theory, the application of radioactive isotopes to fundamental problems and the bioassay of wood preservatives. For the past four years Mr. Snoke has been concerned with microbiological testing of materials including laboratory bacteriological studies and actual marine tests. He heads the Environmental Protection Group of the Outside Plant Development Department. Member xA.merican Asso- ciation for the Advancement of Science, the Society for Industrial Microbiology, American Wood Preservers' Association, American Soci- ety for Testing Materials, Materials Advisory Board — Technical Panel on Miscellaneous Materials, Steering Committee of Microbiological Deterioration Section — Gordon Research Conferences and Zi Sigma Pi. Hans-Georg Linger, Dipl. Ing., 1951, Dr. Ing., 1954, Technische Hochschule Braunschweig (Germany); Bell Telephone Laboratories 1956-. Mr. Lunger's work at the Laboratories has been in waveguides, especially circular electric wave transmission. He holds several foreign patents on waveguides and has published in German technical maga- zines. Member I.R.E. E. E. Zajac, B.M.E., 1950, Cornell University; M.S.E., 1952, Prince- ton University; Ph.D., 1954, Stanford University; Bell Telephone Laboratories, 1954-. Since joining the Laboratories, Mr. Zajac's work has been in theoretical and applied mechanics in the Mathematical Re- search Department. Member of the American Society of ]\Ieehanical Engineers, Tau Beta Pi, Pi Tau Sigma, Phi Kappa Phi and Sigma Xi. PHYSIOGRAPHIC DIAGRAM OF THE ATLANTIC OCEAN SEE ELMENDORF AND HEEZEN ARTICLE PAGES 1047-1093 RHiMl^tfBfiiii^&i 80' 70' 65' 60= 45° ^mm ?^£^s??.&i»F I _ ^^I^LCl^ 'N^— "3"/ 7i fH--«=5=3F r;=- ^^-^^ '^'^yS,^:^' ^-'^'-''^vl -.„ ^V.--^T. :;^NS ^'" '-^^' ^tG^:^* — ~lf/ IX^."^ t^ =^ ~i^ -<^- ■i.^r Reprinted by permission of the I.amont Geological Observatory (Columbia Universiiyj, Copyri^bt © 19r»7. Hnire G. Heezen. THE BELL SYSTEM Jem / mem oumUi DEVOTED TO THE SC I EN TIFIC ^^^ AND ENGINEERING ASPECTS OF ELECTRICAL COMMUNICATION VOLUME XXXVI NOVEMBER 1957 NUMBER 6 A New Storage Element Suitable for Large-Sized Memory Arrays — TheTwistor J^7«.. a. h. bobeck 1319 PVJBL/-." 4 s-f. Non-Binary Error Correction Codes werner ulrich 1341 010 131957 Shortest Connection Networks and Some Generalizations r' R. C. PRIM 1389 A Network Containing a Periodically Operated Switch Solved by Successive Approximations c. a. desoer 1403 Experimental Transversal Equalizer for TD-2 Radio Relay System b. c. bellows and r. s. graham 1429 Transmission Aspects of Data Transmission Service Using Private Line Voice Telephone Channels p. mertz and d. mitchell 1451 Design, Performance and Application of the Vernier Resolver G. KRONACHER 1487 Bell System Technical Papers Not Published in This Journal 1501 Recent Bell System Monographs 1508 Contributors to This Issue 1511 COPYRIGHT 1957 AMERICAN TELEPHONE AND TELEGRAPH COMPANT THE BELL SYSTEM TECHNICAL JOURNAL ADVISORY BOARD A. B. Q oviTZ'E, President, Western Electric Company M. J. KELiiY, President f Bell Telephone Laboratorie* 15. J. McNEELY, Exccutive Vice President, American Telephone and Telegraph Company EDITORIAL COMMITTEE B. McMiiiiiAN, Chairman 8. E. BRILLHART A. J. BU8CH If. R. COOK A. C. DICKIH80N B L. DIETZOLD K. E. GOULD E. T. GREEN R. K. HONAMAN H. R. HUNTLEY F. R, LACK J. R. PIERCE EDITORIAL STAFF w. D. BULLOCH, Editor R. L. BBEPB.ERD, Production Editor T. N. POPE, Cir aviation Manager THE BELL SYSTEM TECHNICAL JOURNAL is published six times a year by the American Telephone and Telegraph Company, 195 Broadway, New York 7, N. Y. P. R. Kappel, President; S. Whitney Landon, Secretary; John J, Scan- Ion, Treasurer. Subscriptions are accepted at $6.00 per year. Single copies $1.23 each. Foreign postage is 66 cents per year or 11 cents per copy. Printed in U. S. A. THE BELL SYSTEM TECHNICAL JOURNAL VOLUME XXXVI NOVEMBER 1957 number 6 Copyright 1967, American Telephone and Telegraph Company A New Storage Element Suitable for Large-Sized Memory Arrays — The Twistor By ANDREW H. BOBECK Three methods have been developed for storing information in a coinci- dent-current manner on magnetic wire. The resulting memory cells have been collectively named the "twistor". Two of these methods utilize the strain sensitivity of magnetic materials and are related to the century old Wertheim or Wiedeynann effects; the third utilizes the favorable geometry of a wire. The effect of an applied torsion on a magnetic wire is to shift the preferred direction of magnetization into a helical path inclined at an angle of 1^5° with respect to the axis. The coincidence of a circular and a longitudinal magnetic field inserts information into this wire in the form of a polarized helical magnetization. In addition, the magnetic wire itself may be used as a sensing means with a resultant favorable increase in available signal since the lines of flu.v wrap the magnetic wire many times. Equations concerning the switching performance of a twistor are derived. An experimental transistor-driven, 330-bit twistor array has been built. The possibility of applying weaving techniques to future arrays makes the twistor approach appear economically attractive. I. IXTUODUCTION A century ago Wiedemann^ observed that if a suitable magnetic rod which carries a current is magnetized bj^ an external axial field, a twist 1319 1320 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 of the rod will result. The effect is a consequence of the resultant helical flux field causing a change in length of the rod in a helical sense. Con- versely, it was also observed that a rod under torsion will produce a voltage between its ends when the rod is magnetized (see Fig. 1). Recently, during an investigation of the magnetic properties of nickel wire, it was observed that a voltage was developed across the ends of a nickel wire as its magnetization state was changed. Both the amplitude and the polarity of the observed signal could be varied by movements of the nickel wire. Most surprising, the amplitude of the observed voltage V2 of Fig. 2, was many times that which would be expected if a con- ventional pickup loop were used. After determining experimentally that the observed voltage was generated solely in the nickel wire and was not a result of air flux coupling the sensing loop (nickel wire plus unavoidable copper return wire), it was concluded that the flux in the nickel wire must follow a helical path. This suggested that torsion was the cause of the observed effect, a con- clusion verified experimentally. The direction of the applied twist de- APPLY I, TWIST OBSERVE V2 Fig. 1 — Observation of an internally induced voltage V2 generated by a mag- netic wire under torsion. TWIST Fig. 2 — Comparison of the internally induced voltage v-i to the voltage Vt induced in the oickup loop. THE TWISTOR 1321 termined the polarity and the amount of the twist determined the mag- nitude of the observed voltage. As a consequence of these results, it is possible to build mechanical- to-electrical transducers,^ transformers with unity turns ratio but possess- ing a substantial transforming action, and a variety of basic memory cells. This paper will be concerned with a discussion of the memory cells from both a practical and theoretical viewpoint. It will be shown how these cells can be fabricated into memory arrays. One such configuration consists solely of vertical copper wires and horizontal magnetic wires. Experimental results of the switching behavior of many magnetic ma- terials when operated in the "twisted" manner will be given. II. A COINCIDENT-CUERENT MEMORY CELL — THE TWISTOR Consider a wire rigidly held at the far end and subjected to a clockwise torsion applied to the near end. This will result in a stress component of maximum compression^ at an angle of 45° with respect to the axis of the wire in the right-hand screw sense, and a component of maximum tension following a left-hand screw sense. All magnetic materials are strain sensitive to some degree. This will depend upon both the chemical com- position and the mechanical working of the material. For example, if unannealed nickel wire is subjected to a torsion, the preferred direction of magnetization will follow the direction of greatest compression, as would be predicted from the negative magnetostrictive coefficient of nickel. Unannealed nickel wire, then, will have a preferred remanent flux path as shown in Fig. 3. If the ease of magnetization as measured along the helix is sufficientl}^ lower than that along the axis or circumference, it is possible to insert information into the wire in a manner somewhat analogous to the usual FLUX PATH CLOCKWISE TWIST TENSION -COMPRESSION Fig. 3 — Relationship of the mechanical stresses resulting from applied torsion to the preferred magnetic flux path in nickel. lo22 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 coincident-current method. Consider a current pulse /i applied through the nickel wire in such a direction as to enhance the spiraling flux, and a second current pulse h applied by means of an external solenoid (see Fig. 4). Coincidentally, the proper amplitude current pulses will switch the flux state of the wire; either alone will not be sufficient. To sense the state of the stored information it is necessary either to reverse both cur- rents, or to overdrive Ii in the reverse direction. In an array, the output, in the form of a voltage pulse, would be sensed across the ends of the nickel wire. The solenoid may be replaced by a single copper conductor passing at right angles to the nickel wire. For obvious reasons the mem- ory cell has been named the "twistor". The above method of operation will be referred to as mode A. Mode B is the use of the magnetic wire as a direct replacement for the conventional coincident-current toroid. Its use here differs only in that the wire itself is used as a sensing winding (refer to Fig. 5). The pulses /i and 1-2 are eciual in value and each alone is chosen to be insufficient to switch the magnetization state of the wire. The coincidence of /i and Ii will, however, result in the writing of a bit of information into the wire. To read, /i and I-i are reversed in polarity and applied coincidently. The output appears as a voltage pulse across the ends of the nickel wire. Fig. 4 — Coincident currents for the "write" operation in a twistor operated mode A. Wire under torsion. •SIGNAL ^i'^" ^ 77 ^°^ mode B the coincidence of 7i and Ii is required to exceed the knee ot the <(>~NI characteristic. Wire under torsion. THE TWISTOR 1323 The third method of operating the twistor, mode C, is similar in nature to a method proposed by J. A. Baldwin/ In this scheme the wire is not twisted, so that neither screw sense is favorable. By the proper ap- plication of external current pulses, information will be stored in the wire in the form of a flux path of a right-hand screw sense for a "1", and a left-hand screw sense for a "0". The operation of the cell is indi- cated in Figure 6. Note that the writing procedure requires a coinci- dence of currents; the reading procedure does not. The sign of the output voltage indicates the stored information. Modes A and C are best suited for moderate sized memory arrays since the readmg procedure is not a coincident type selection. Thus to gain access to ri storage points, an access switch capable of selecting one of n points is recjuired. For large arrays the use of mode B is mdi- cated. It then becomes possible to select one of n points with a 2n posi- tion access switch. The crossover point (about 10^ bits) is determined by access circuitry considerations. WRITEx^ I I I I ^ 2 WRITE, ^=C>' ~L OR ^ ^^ c^ ^ ) I I ^ SIGNAL OUT READ 0=Z] rT^ I I c ■ ) < > 1 I I OR Fig. 6 — Read-write cycle for a twistor operated mode C. The wire is not under torsion. 1324 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 III. ANALYSIS OF THE SWITCHING PROPERTIES OF THE TWISTOR Section 3.1 will deal with the basic properties of magnetic wire as they pertain to the twistor memory cell. Section 3.2 will be concerned with a composite magnetic wire. The theoretical conclusions will be supported by expermiental results wherever possible. 3.1 Solid Magnetic Wire It has been stated above that there is a voltage gain inherent in the operation of the twistor. This voltage gain makes it possible to obtain millivolt signals from wires several mils in diameter. An expression will now be derived relating the axial flux of an untwisted wire to the circular flux component of that wire when twisted. Assume that the magnetic wire has been twisted so that the flux spirals at an angle 6 (normally 6 = 45°) with respect to the axis of the wire. If d and I are the diameter and length of the magnetized region respectively, then, for a com- plete flux reversal the change in the circular flux component is ^circ = l(d/2){2Bs sin 6). Here, ^circ is the flux change that would be observed on a hypothetical pickup wire which passed down the axis of the magnetic wire. The flux change which would be observed by a single pickup loop around the wire, if the magnetic wire were not twisted, is ^longituudinai = tt d~Bs/2. Therefore, ^circ/v'iong = 2 Z sin d/rd, and for 6 = 45°, this expression reduces to ^ciro l/d 9 99- ^^^ Thus, for example, if the storage length on a 3-mil wire is 100 mils, then a 15:1 gain in flux change (or voltage) is obtained. V, OBS R(r) (a) (b) v(r)- V(0) Fig. 7 — (a) Calculation of the observable voltage Fobs for a solid magnetic wire, (b) Diagram of induced voltage V{r) and resistance RO'). THE TWISTOR 1325 The above derivation assumed that the entire circular flux change could be observed externally. Since the magnetic wire must, of necessity, serve as the source of the generated voltage the resultant eddy current flow reduces the observable flux change by a factor of three. Consider Fig. 7; assume that the flux reversal takes place in the classical manner and consider the circular component of this flux since it alone contributes to the observable signal. The induced voltage V(r) at any point r is V{r) = F(0)/(/-o — r/ro), where ro is the radius of the wire and F(0) the voltage at r = 0. But V{r), the induced or open-circuit voltage per length of wire I, could only exist if the wire were composed of many con- centric tubes of wall thickness dr, each insulated from one another. In a long wire no radial eddy currents can exist. Therefore the wire of length I can be assumed to be faced by a perfect conductor at both of its ends. It remains to calculate the potential between these ends. The resistance of the tube is R{r) = pl/'Ivr dr, where p is the resistivity in ohm-cm. The resistance of the wire is given by Ro = pl/irvo . These resistances form a voltage divider on the induced voltage in the tube and the total contribution of all tubes is obtained by integration; Fohserved - [ V h^ [-J^d \pl/2Trrdr J *" dr (2) ro — r\ 2r ro / To- F(0) Thus, (1) must be modified by (2) with the voltage step-up per memory cell becoming, Fobs _ l/d /„v long 6.66 3.11 Bulk Flux Reversal — - Classical Case The switching performance of a magnetic wire under transient condi- tions will now be considered. The speed of magnetization reversal of magnetic materials vmder pulse conditions is best characterized by Su, , the switching coefficient, usually expressed in oersted-microseconds. It is defined as the reciprocal of the slope of the 1/Ts versus H curve where Ts is the time required to reverse the magnetization state and // is the applied magnetic field intensit3^ Onl}'^ eddy current losses will be con- sidered. 1320 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 First, consider the case in which the magnetization is entirely circular. Reversal from one flux remanent state to the other is assumed to occur uniformly in time Ts . Axial eddy currents will flow down the center of the wire and return along the surface. The switching coefficient, Sw , will be obtained by equating the input energy to the dissipated energy . The total energy dissipated per unit length is, 8 = n f " 27rrP(r) dr, (4) Jo and pw=Mr)l\ (5) P where P(r) the power density is given by E{r) the voltage gradient squared divided by the resistivity. The average energy per unit volume is therefore Sav/cm3 — 5 / ^^ 27rr (//' Trro ^0 P^' " ■ (6) ^ T^ /my 18pV I J Now F(0) = [{dB/dt)rd]\^~\ so F(0)// = (25,ro/n)10^l Putting this expression into (6) yields 2 2 _ 2Bs Vq 16 ,-,s Oaver/cm^ — —x — jf^ — i.\J . \l ) The input energy per unit volume is . 3 (25,i/cos0i) 10"' .„. S/cm = , (8) 47r since ABH = 2BsH cos 9i where di is the angle betw^een the applied field H and the switching flux. The factor 10~ /47r is a constant relating the energy in joules to the BH product in gauss-oersteds. By equating (7) and (8), and replacing H hy {H — Ho), the desired s,„ expression is obtained ; s^ = T.{H - Ho) = (^TnB.ro^) 10 ' ^^^_^^^^^^ (9) \)p cos ^1 The substitution oi H — Ho for H requires some explanation. The switching curve of \/Ts versus H is not a straight line as would be pre- THE TWISTOR 1327 dieted from (9) but generally possesses considerable curvature at low- drives. Equation (9) satisfactorily predicts the slope of the switching curve in the high drive region, but Ho must be determined experimen- tally. In Section 3.12, flux reversal by wall motion is treated as it is a possible switching mechanism at low drives. The switching coefficient s^, for the case in which the magnetization is purely axial will now be treated. As above, the flux density will change from —Bs to -{-Bs uniformly in time Ts . The eddy currents, which are circular, result from an induced voltage V{r) where V(r) = [V{ro){r/rof], and 7(^o) is given by F(ro) = [(25./r,)W]10"'. Thus, E{r) = V{r)/2Tr, and E{r) = {Bsr/Ts)lO~ . Following the procedure used above, the in- ternally dissipated energy density is Sav/cm3 = — . / zirr dr, Ecjuating this expression to (8) yields s. = (H - H,m = "^^fl^ , (11) p cos 02 where 6-2 is defined as the angle between the applied field and the switch- ing flux now assumed axial. The helical flux vector in a twist or can be resolved into a circular and an axial component. Fortunately, since the dissipated energy is pro- portional to the eddy current density squared, and the axial and cir- cular current density vectors are perpendicular to each other, it is possible to write £av/cm 3 (helical) = 8av/cm3(axial) + Sav/cm 3 (circular). (12) It follows, for a 45 degree pitch angle, that ^.(helical) = ^-(axial) + ..(circular) ^^^^ where the factor "2" is a consequence of the flux density components being smaller by l/\/2 than their resultant. Substitution of (9) and (11) into (13) gives the desired switching coefficient ..(helical) = {H - Horn = ^ ^.^0^10' ^4) 18 p cos d 1328 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 The term cos d requires further explanation. The magnetization vector is constrained by energy considerations to ahgn with the easy direction of magnetization. The angle between the applied field and the easy direction of magnetization is called 6. Equation (14) is valid for any direction of applied field. The angles ^i and di used in deriving (9) and (11) respectively are each 45 degrees for the helical pitch angle assumed above. Equation (14) indicates that for maximum switching speed a material with low saturation flux density and high resistivity is required. The lower limit on s^ will be determined by internal loss mechanisms not treated here. Experimentally, this lower bound is found to be approxi- mately 0.2 oe-/isec. 3.12 Reversal by Single Wall The switching time of a twistor when operating in a memory array under coincident current conditions will depend upon the low^-drive switching coefficient. Experimentally, it is observed that the low drive Sy, is several times the high-drive value. In this section, following the method of Williams, Shockley, and Kittel,^ flux reversal by the move- ment of a single wall will be treated. Only the circular flux case will be considered. The technique used to obtain Sw is identical to that used in Section 3.1.1 except it is postulated that a single wall concentric to the wire moves either from the wire surface inward, or from the wire axis outward. The result is independent of the direction in which the wall moves. As- sume the wall moves from r = 0 to r = ro , as indicated in Fig. 8. In- V{0) Fig. 8 — Flux reversal by expanding wall instantaneously located at radial position aro moving with velocity v. THE TWISTOK 1329 stantaneously, the wall is located at aro and is traveling with a velocity v. The induced voltage Voc{r) is, Vocir) = (2Bslv)10-'' 0 1 mil) the switching coefficient Sw is unreasonably high. The typical ferrite memory toroid, for example, when used as a memory element has an s», of 0.6 oersted-microseconds. The only possi- bility for high speed coincident-current operation for solid magnetic wires is that the material have a high coercive force He , a conclusion not con- sistent with the trend toward transistor driven memory systems. By the use of a composite wire it should be possible to reduce the eddy current losses and still preserve a reasonable wire diameter. A composite wire, by definition, will consist of a non-magnetic inner wire clad with a magnetic skin. It may be fabricated by a plating or an extruding process. The solid wire analysis of Section 3.1 is a special case of composite 5 - O LU CO z - 2 1 4-79 PERMALLOY;! MIL UNANNEALED o 2 83 NL,17Fe, 0.5Mn;2MIL UNANNEALED | 3 nickel;3mil annealed ^ .X^ "^ / X ^ -^ ^ ^ 1 1 1 1 3 - 1 - 10 15 20 25 Haxial in OERSTEDS 30 35 40 Fig. 9 — Reciprocal of flux reversal time T s as a function of applied axial drive, H , for solid and composite magnetic wires. Sufficient torsion applied to reach saturation. THE TWISTOR 1331 wire analysis which is given in Appendix I. Only the results of the com- posite wire case will be given here. As indicated in Fig.* 10, pi and p2 AT, v(r)- V(0) (a) (b) Fig. 10 — (a) Composite wire is composed of non-magnetic core covered by a magnetic skin, (b) A voltage V{r) is induced in the wire during flux reversal. are the resistivities of the inner (non-magnetic) and outer (magnetic) materials. The inner material is contained within a radius ri . The over- all wire radius is Ti . Defining a = n/r-i , if Fobs is the voltage obser\'ed across the ends of the composite wire twistor memory cell, and T^(0) is the induced voltage at ?• = 0 for a solid magnetic wire of radius r-z , T^obs = bV{0), and + 0" a (19) Pi P2 (1 - a2) -j- a" The parameter "6" reduces to \ for a = 0 in agreement with (2) which was derived for the solid wire case. Table I gives "b" for various material and geometry combinations. Table I — The Parameter ''6" 1 Pl/P2 0.9 0.8 0.7 0.0 (Solid Wire) 0 0.100 0.200 0.300 1.000 t'(J 0.0988 0.194 0.285 .333 \ 0.0963 0.184 0.259 .333 1 0.0903 0.163 0.219 .333 3 0.0790 0.135 0.180 .333 10 0.0643 0.112 0.155 .333 00 0.0491 0.0963 0.141 .333 1332 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 Table II • — The Parameter "Ccirc" Pl/P2 0.9 0.8 0.7 0.0 (Solid Wire) 0 0.0858 0.353 0.820 1.396 1 0.0847 0.339 0.763 1.396 1 3 0.0842 0.311 0.657 1.396 1 0.0737 0.256 0.498 1.396 3 0.0595 0.159 0.341 1.396 10 0.0286 0.124 0.243 1.396 00 0.0209 0.0833 0.186 1.396 The switching coefficient, s„ , for circular flux reversal, is derived as -3 OlB (87rB.r2')10 P2(l — a^) cos 6 4a (1 ,a (1 - a - bY^ - (1 - hY Pi + h) a 2 + (1 - bV 4(1 - 6) l\ 3 ■^21' (20) or = Co (g.r2-)10"' P2 cos 6 (oe-fisec). (21) Table II gives Ccirc as a function of a and pi/p2 . The switching coefficient s^ for axial flux reversal is derived as "7B V5,r2'lO~' 1 - 4a' + a'(3 - 4 In aY P2 cos 6 1 - a^ ii I — \P2 (22) (23) cos d I Table III gives Caxiai as a function of "a". Since, as explained for the solid wire case, the eddy current density- vectors for circular and axial flux reversal are in quadrature, s„ (axial) + s„, (circular) s^, (helical) = 2 (24) Substitution of (21) and (23) into (24) gives the required expression; ^.(helical) = iC-^r.^C.^,.\{B,ri)\Q-\ ^^5) A number of composite wire samples have been prepared and evalu- ated. These include nickel on nichrome and nickel on copper. The switch- THE TWISTOR 1333 Table III — The Parameter "Caxiai" a 0.9 0.8 0.7 0.0 (Solid Wire) '^ax ial 0.0795 0.300 0.633 3.142 ing curves for these samples as well as for a number of solid magnetic wires are shown in Fig. 9. The agreement between the measured values of s,„ and the calculated values [(14) and (25)] is ciuite good. Improved composite wire samples are under development. IV. EXPERIMENTAL MEMORY CELLS AND ARRAYS The initial experiments were performed using commerciall}^ a\'ailable nickel wire of 3-mil diameter. The ^p-'Nl characteristic of this wire in the helical direction is extremely square. This is a feature of all the magnetic materials tested whether annealed or unannealed. As a typical example, APPLIED TWIST IN RADIANS PER CM 1.5 1.0 0.5 -0.5 -1.0 PULSE RESPONSE 9S-NI, 60 CYCLE AXIAL CIRCULAR ■aniSBBBBBV mmmmmmmm ■■■■■■rfi ^■■■■■■■■B ■■■■■■!■■ ■■■■■■■■ ■■■■■■■■■■ aiiaBBBB! BtaBfiH^Ba BBBBBBBBBS ibbbbbbb ■■■■■■■■ ■■■■■■■■■■ BBBBBBB^ BBBBBBBB SSBBBBBBBS ■■■■■■■■ ■■■■■■■■ BBBSSBB9BB BBBHBBHI ■■■■■BBB ■■■■■■■■■■ BBBBBBBI BBBBBBBB ■itomm Bsaus; bibb:: BBUBBliBB lESSSai ■■e--=:: ■^^■■■■■■B ■■■■■ Fig. 11 — Sixty cycle and switching waveforms for 83 Ni, 17 Fe wire (see Fig. 9) as a function of applied torsion. 1334 THE BELL SYSTEM TECHNICAL JOUliXAL, XOVEMBEU 1957 the 60-cycle characteristics of the axial and circular flux versus axial drive and the switching voltage waveforms under pulse conditions are given in Fig. 11 for 2-mil wire of composition 83 Ni, 17 Fe. Note the negative prespike on the switching waveforms. By simultane- ous observation of both the axial and circular switching voltage wave- forms on many different magnetic wires it has been concluded that the negative prespike is due to an initial coherent rotation of the magnetiza- tion vector which results in an initial increase in the circular flux com- ponent. It is during this coherent rotation that the normal positive pre- spike on the axial switching voltage waveform is observed. Because of the mechanically introduced strain anisotropy, however, the magnetiza- tion A'ector is constrained to remain nearly parallel to the easy direction of magnetization. Thus, the coherent rotation soon ceases and the re- ABRUPT INCREASE N NOISE to Q UJ I- 10 a. LU o 0. o o I 20 40 60 80 100 ImaGNETiC 'N MILLIAMPERES 120 140 Fig. 12 — Range of writing currents for 83 Ni, 17 Fe wire operated mode. A Read drive held constant at 9 oersteds. Tjpical signal-to-noise ratio for a read is indicated. THE TWISTOR 1335 Fig. 13 driven. A 320-bit experimental twistor memory array. The arraj- is transi.stor mainder of the flux reversal process is by an incoherent rotational process. During this latter time the circular and axial voltage waveforms are virtually identical. Fig. 12 gives the range of operation of 2-mil 83 Ni, 17 Fe wire as a twistor operated by mode A. As a result of the extreme squareness of the ^-NI characteristic in helical direction the range of operation en- closes an area nearly the theoretical maximum. The switching times of other memory cells tested ranged from 0.2 /xsec for a 1 mil 4-79 moly- permalloy wire to 20 )usec for a 5 mil perminvar wire. Thus it is seen that the switching speeds of the twistor compare quite favorably ^\ith those of conventional ferrite toroids and sheets. It is, of course, possible to store many ])its of information along a single magnetic wire. The allowable number of bits per inch is related to the coercive force, the saturation flux density, and the diameter of the wire. For the nickel wire, about 10 bits per inch are possible. Predictions as to the storage density for a given material can be made bj' referring to 1336 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 suitable demagnetization data. There are, however, interference effects between cells which are not completely understood at the present time. A memory array (16 X 20) has been constructed as a test vehicle. An illustration of this array is shown in Fig. 13. The drive wires have been woven over glass tubes which house the removable magnetic wires. Provision is made for varying the torsion and the tension of the in- dividual magnetic wires. As an indication of the performance of the twistor, Fig. 14 is a com- posite photograph showing the minimum and maximum signal over the 16 bits of a given column for 3-mil nickel wire. Also included are the noise pulses for these cells, the so-called disturbed zero signals. The write currents were 2.3 ampere-turns on the solenoid and 130 ma through the magnetic wire. The read current was 6.0 ampere-turns. The array Fig. 14 — Composite photograph of the 16 output signals from a column of the array of Fig. 13. Average output signal al)out 3.5 millivolts; sweep speed equals 2 /isec/cm. was transistor driven. A read-write cycle time of 10 microseconds ap- peared to be possible. V. DISCUSSION The twistor is presented as a logical companion to the coincident- current ferrite core and sheet. ' In many applications it should compete directly with its ferrite equivalents. Perhaps its greatest use will be found in very large ( > 10^) memory arrays. From a cost per bit viewpoint the future of the twistor appears quite promising. Fabricating and testing the wire should present no special problems as it is especially suited for rapid, automatic handling. The possibility of applying weaving techniques to the construction of a twistor matrix looks promising. It is possible that, for l)oth mode A and C operation of the twistor, an array can be built which consists simply of horizontal copper wires and THE TWISTOR 1337 vertical magnetic wires — - much like a window screen. Preliminary ex- periments have shown that single cross wires do operate successfully. The operation of this array would be analogous to a core memory ar- ray. Physically it could look just like a core array — but without the cores. ACKNOWLEDGEMENTS The author wishes to acknowledge the help of R. S. Title in obtaining the memory array data, R. A. Jensen in constructing the test jigs, and D. H. Wenny, Jr. in supplying the wire samples. The discussions with my associates, in particular D. H. Looney, R. S. Title, and J. A. Baldwin, have been very helpful. The writer would like to acknowledge the in- terest and encouragement shown bj^ R. C. Fletcher. APPENDIX I From Fig. 10, for bulk circular flux reversal in a composite wire, the induced voltage V(r) for a wire length / is nr) ^lir.-nnC^-p) lir2 - n)lC 10 , 0 < r < n, (26) ?'i < r < r-i. For a solid magnetic wire of radius r- F(0) = C^) 10-^ (27) Therefore, V(r) = l-^^) V(0), 0 < r < ri , (28) In general, the resistance of a tube of wall thickness dr is /?(/•) = pi/ 1338 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 2Trrdr. The resistance of the wire in R t = p,P2l/T-[pi{r2~ — Vi") -\- po/'i']- The observable voltage for a length of wire, /, is Fobs = / [Vir)] (Volt-Divider) Pl/32^ f'-2 - >'i\ y/Q) 7r[pi(r2- - ri^) + p^rj^] 2Trr dr P1P2I + / ' (^''^ " ') 7(0) ' ^^P^'^^^' ~ ''1') + P''^'^^ r-i ) \ P2I 27rr dr This reduces to (1 - a^)pi/p2 + a- = 6F(0), (30) where a = ri/r-i and b is given by reference to (29). The ratio b/^ = 36 is the relative efficiency of the composite as compared to the solid magnetic wire from an available signal viewpoint. An expression for s„, will now be derived. The total energy dissipated per unit length I is ^r/l = Ts r pij{r)2wr dr, (31) Jo ''•2 where idir) is the current density. Now, ij{r) = Y{r) — T''obs/p/, therefore i,{r) = (1 - a - b)^, 0 < r < r^ pit = 11 — — — 0 1 — — /'i < /■ < ro \ r2 / p2i The substitution of (32) into (31) yields, after manipulations. (32) ?av/« _ TT^r/ (Vm\ / 2 P. y^lTl 4a(l - 5) a (1 -a-6)^'^-?-(l -6)^ Pi + 3 2 + a-«=-W^ + ^] (33) THE TWISTOR 1339 From (8), the applied energy per wiie length / is '[B.,(// - //o) cose] 10^' m = 27r 7r(r2 - /-r), (34) where only that part of the applied energy associated with th(^ high drive dynamic losses is included. Ecjuating (33) and (34) and replacing V(0)/l by (27) results in - (1 - hy + SirBsr^'lO'' po(l — a'-) cos d 4a(l — b) a I a (1 - a - bf 2 P2 Pi + (1 - by - 4(1 - b) , ]| (35) + 2/- This can be expressed as s. = {H - m)T. = C.,,J-?^ri}}^ (oe-/.sec). P2 COS 6 (36) Bulk axial flux reversal in a composite magnetic wire can be treated in a manner analogous to that used in Section 3.1.1 for the solid wire. The uniform reversal of the axial flux induces a voltage T^(r) in the wire where 0" - & V{r) = V(r.;) = 0, and FCro) = [(2B./7\)7r/-.>'] 10^'. Since £"(/■) = T^(/-)/27r/-, E^r) = I (r - ^Jl)iO-1 Following the procedure of Section 3.1.1., TsiQ-" r By ( nX- .^ , (37) _ J2BsWlO -16 \ P2T, L I - a'- In a) (38) where a = ri/r-2 as before. Equating this expression to (8) yields tBsiVIO^' Vl - 4a'-' + a'(3 - 4 In a) pi cos 6 ^^ v.' axial (BsrjlQ-' \ p2 COS 6 1 - a" j (oe-Msec). (39) (40) 1340 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 REFERENCES 1. R. M. Bozorth, Ferromagnetism, D. Van Nostrand Companj% Inc., New York, N. y., 1951, p. 628. 2. U. F. Gianola, Use of Wiedemann Effect for Magnetostrictive Coupling of Crossed Coils, T. Appl. Phys., 26, Sept. 1955, pp. 1152-1157. 3. H. F. Girvin, Strength of Materials, International Textbook Co., Scranton, Pa., 1944, p. 233. 4. J. A. Baldwin, unpublished report. 5. H. J. Williams, W. Shocklev, and C. Kittel, Velocity of a Ferromagnetic Do- main Boundary, Phys. Rev., 80, Dec. 1950, pp. 1090-1094. 6. J. A. Rajchman, Ferrite Apertured Plate for Random Access Memory, Proc. I.R.E., 45, (March, 1957), pp. 325-334. 7. R. H. Meinken, A Memory Array in a Sheet of Ferrite, presented at Conference on Magnetism and Magnetic Materials, Boston, Mass., Oct. 16-18, 1956. Non-Binary Error Correction Codes* By WERNER ULRICH (Manuscript received April 19, 1957) If a noisy channel is used to transmit more than two distinct signals, information may have to be specially coded to permit occasional errors to be corrected. If pulse amplitude modulation is used, the jnost probable error is a small one, e.g., 6 is changed to 7 or 5. Codes for correcting single small errors, and for correcting single small errors and detecting double small errors, in a message of arbitrary length, for an arbitrary number of differ- ent signals in the channel, are derived in this paper. For more specialized situations, the error is not necessarily restricted to a small value. Codes are derived for correcting any single unrestricted error in a message of arbitrary length for an arbitrary number of different sig- nals. Finally, a set of codes based partially upon the Reed-Muller codes is described for correcting a number of errors in a more restricted class of message lengths for an arbitrary number of different signals. The described codes are readily implemented. Many techniques are used which have an analog in a binary system. Other techniques are broadly analogous to binary coding techniques or are special adaptations of a binary code. I. INTRODUCTION 1.1 Use of Error Correction Codes One function of an error correction code is to aid in the correct trans- mission of digital information over a noisy channel. This process is illustrated in Fig. 1. An information source gives information to an encoder; the encoder converts the information into a message containing sufficient redundancy to permit the message to be slightly mutilated by the noisy channel and still be correctly interpreted at the destination. The message is then sent ^'ia the noisy channel to a decoder which will * This paper was submitted to Columbia University in partial fulfillment of the requirements for the degree of Doctor of Engineering Science in the Faculty of Engineering. 13-11 1342 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 reconstruct the original information if the mutilation has not been ex- cessive. Finally, the information is sent to an information receptor. One scheme for correcting errors in a binary system is to send each binary digit of information three times and to accept at the receiver that value which is represented by two or three of the received digits. Then, the encoder is simply an instrument for causing each digit to be sent three times, and the decoder consists of a majority organ. However, many methods are available which are considerably more elegant, and which will permit more information to be passed through a noisy channel in a given unit of time. This paper will deal with such methods for channels capable of sending h different symbols instead of the usual 1 and 0 of a binary channel. The most convenient explanation of an error correction code has been made with respect to the transmission of correct digital information over a noisy channel. This does not imply the restriction of such codes INFORMATION SOURCE ENCODER CHANNEL DECODER (CORRECTOR) INFORMATION RECEPTOR — * 1 NOISE Fig. 1 — Transmission over a noisy channel. to the noisy channel problem exclusively. Actually, the first application considered for such a code was with respect to computers.^ Many large high speed computers stop whenever an error is detected in some calcu- lation and must be restarted; with the use of an error correction code this could be avoided by permitting the computer to correct its own random errors directly. To the best knowledge of the author, error correction codes have not yet been used in any major computer. But the storage system of a computer may, in the future, lend itself to the use of error correction codes. Frequently, very elaborate precautions must be taken in present storage systems to insure that they are free from errors. Magnetic tapes must be specially made and handled to guarantee the absence of defects, magnetic cores must be carefully tested to make sure that no defective cores get into an array, cathode I'ay tubes used in Williams Tube or Barrier Grid Tube storage systems must be perfect. Probably, there are other storage methods whose development is hampered because of a common requirement for error-free performance in all storage locations. With the use of error correction codes, such storage systems could be used, if they are sufficiently close to perfection, even though not perfect. XO\-BIXAHY EKHOR COHUEC'TIOX CODES ]'.]4'.] It is not unlikely that the near futin-e will see the development of storage systems which will be able to store more than twcj states at every basic storage location.- If such systems are developed, it seems likely that they will be more erratic or noisy than binary storage systems, since each location must store one of h signals instead of one of two. If a cathode ray tube storage system were used, for example, different quan- tities of charge would have to be distinguished; in a binary storage system, only the presence or absence of charge must be detected. This suggests that error correction codes may become essential with certain types of non-binary storage systems. One object of this paper is to develop codes for this purpose and to discover which number systems are most easily correctable. Some investigations have been made on the use of computer sj^stems using multi-state elements.* A switching algebra has been developed similar to Boolean algebra for handling switching problems in terms of multi-state elements. Single de\'ice ring counters (the cold cathode gas stepping tube for example) alread}^ exist and might be useful in such systems. But currently, only limited steps in this direction have been made. Another object of this paper is to show the advantages and problems of error correction codes in multi-state systems; it is not un- reasonable to predict that error correction codes may be more necessary in multi-state systems than in binary sj'stems. 1.2 Geometric Concept of Error Correction Codes A geometric model of a code was suggested by R. W. Hamming' which can be altered slightly to fit the non-binary case. For an n digit message, a particular message is a point in n dimensional space. A single error, however defined, will change the message, and will cor- respond to another point in n dimensional space. The distance between the original point and the new point is considered to be unity. Thus, the distance d between the points corresponding to any two messages is defined as the minimum number of errors which can convert the first message into the second. With an error detection and/or correction code, the set of transmitted messages is limited so that those which are correctly recei^•ed are recog- nizable; those messages which are received with fewer than a given number of errors are either corrected or the fact that they are wrong is recognized and some other appropriate action (such as stopping a com- puter) is taken. In the ease of binary codes, an error changes a 1 to 0 or a 0 to 1 . In the non-binary case, two definitions of an error are possible and Mill he 1344 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 used in this paper. A small error changes a digit to an adjacent value. In a decimal system, a change from 1 to 2 or 1 to 0 is a small error. An unrestricted error changes a digit to any other value. In a decimal sys- tem, a change from 1 to 5 is an unrestricted error. 1..3 Material To Be Presented The various types of codes described in this paper and the sections in which they are to be found are summarized in Table 1. The tech- niques which are described are summarized below. The geometric model suggests the simplest approach to error correction codes. A transmitter has a "codebook" containing all members of the set of transmitted messages. If the message source gives to the encoder the signal that the information to be sent is k (that is to say, the A'th Table I — Types of Codes Type of Code Distance Type of Error Described in Section Single Error Detection Single Error Correction Single Error Correction Prime Number Base Composite Number Base Single Error Correction and Double Error Detection Multiple Error Correction 2 3 3 4 Small and Unrestricted Small Unrestricted Unrestricted Small Small II III and 6.1 4.1 4.2 V and 6.1 6.2 output of all the outputs associated with the message source), the en- coder chooses the kth member of the set. The decoder will then look up the message it receives in its own codebook which contains all possible received messages, and corresponding to the entry of the received mes- sage will find the symbols corresponding to k. Or the receiver may compare the received message with every member of the set of trans- mitted messages, calculate the distance between the two, and correct the received message to whichever of the transmitted messages is sep- arated from the received message by the smallest distance. (It has been shown by Slepian* that this is the message most likely to be correct in a symmetrical binary channel having the property that changes from 1 to 0 and from 0 to 1 as a result of noise in the channel are equally likely.) The practical difficult}' with such a code is the large size of the re- quired codebooks. Most coding schemes try to eliminate such codebooks and substitute a set of rules for encoding, decoding and correcting messages. NON-BINARY ERROR CORRECTION CODES 1345 One approach toward creating a simple association between the infor- mation and the message is to use some of the digits of the message for conveying information directly. The Hamming Code' uses this tech- nique. An information digit is a digit of a message that is produced directly by the information source; in a base b code, an information digit may have b different values, the choice between these values representing the information that is to be sent. A check digit is a digit of a message that is calculated as a function of the information digits by the encoder. It is sometimes convenient to represent or calculate a check digit in terms of a recursive formula using previously calculated check digits as well as information digits. In a base b code, a check digit may have b check states. When more than one check digit is used, each different combination of check digits corre- sponds to a different check state for the message; a message with tn check digits will have 6" message check states. A systematic^ code encoder generates messages containing only infor- mation digits and check digits. The information source generates only base 6 information digits. The Hamming Code is a systematic code. Section II offers a general method for obtaining single error detection codes for both small and unrestricted errors. The idea of mixed digits (digits which are, in a sense, neither information nor check digits, but a combination of both) is introduced, and it is shown how mixed digits may lead to more efficient coding systems. This idea is believed to be novel. Code systems which use mixed digits are called semi-systematic codes. Semi-systematic codes are used extensively throughout this paper. Section III offers a general method for obtaining single small error correction codes, including both systematic and semi-systematic codes. Section IV offers a general method for obtaining the more complicated single unrestricted error correction codes. The problem is diAided into two parts. Section 4.1 describes codes for correcting single unrestricted errors in case b, the base of the channel, is a prime number.* Section 4.2 describes a special technique for obtaining the more complex codes for correcting single unrestricted errors in the event 6 is a composite num- ber. Section V offers a general method for obtaining semi-systematic codes for correcting single small errors and detecting double small errors. No general solution has been found for obtaining single error correction or double error detection codes for the case of unrestricted errors. Xo gen- * This class of codes was previously described in u brief summary liy Golay.® 1341) THE BELL SYSTEM TECHNICAL JOUKXAL, NOVEMBER 1957 eral solution has been found for multiple error correction codes for the unrestricted error case. In Section VI, a number of techniques are presented for using binary error correction coding schemes for non-binary error correction codes. Section 6.1 shows how such techniques may be used to obtain non-binary single error correction codes, and single error correction double error detection codes, for the small error case. Section 6.2 presents a special technique, involving the use of an adaptation of the Reed-Muller binary code, to obtain a class of non-binary multiple error correction codes, for the small error case. Section VII shows that an iterative technique of binary coding can be directly applied to non-binary codes. It also shows how an adapted Reed-Muller code can be profitably used in such a system. Section VIII summarizes the results obtained in Sections II-VII and shows the advantages and shortcomings of many of these codes. Section IX presents general conclusions which may be drawn from this paper. II. SINGLE ERROR DETECTION CODES Single error detection codes rec^uire message points separated in n dimensional space by a distance of two. For the binary case, the only two possible types of errors are the change from a 1 to a 0 and from a 0 to a 1. A simple technique that is used frequently for binary error detection codes is to encode all messages in such a manner that every message contains an even number of I's. This is accomplished by adding a 'parity check digit to the information digits of a message; this digit is a 1 if an odd number of I's exist in the information digits of a message and is a 0 if an even number of I's exist in the information digits. At least two errors must occur before a message containing an even number of I's can be converted into another message containing an even number of I's, since the first error will always cause an odd number of I's to appear. A message with an odd number of I's is known to be incorrect.* An analogous technique may be used for the unrestricted error case in non-binary codes. We can obtain a satisfactory code by adding a com- plementing digit to a series of information digits to form a message. A complementing digit, base b, is defined as a digit which when added to some other digit will yield a multiple of 6. * Parity check digits may be selected to make the number of I's in a message always odd, but the principle is the same; in this case, an error is recognized if a received message contains an even number of I's. NON-BINARY ERROR CORRECTION CODES 1347 For a single unrestricted error detection code, the complementing digit complements the sum of the information digits. A complementing digit is a check digit. In the binary case, it is a parity check digit. As an example, consider a decimal code of this type. A message 823 would require a complementing digit 7, making the total message 8237 (8 + 2 + 3 + 7 = 20, a multiple of 10). An error in any one digit will mean that the sum of the message digits will not be a nuiltiple of 10. For the small error case, it is sufficient to make certain that the sum of all digits is even since any error of ±1 would destroy this property. For the binary case, all errors are small since the only possible error on any digit is a change by ±1; a simple parity check is adequate. For a non-binary code, it would be wasteful to add a digit just to make sure that the sum of all digits is even. In a decimal code for example, if the sum of the message digits is even, the values 0, 2, 4, 6, 8 for the check digit will satisfy a check, or if the sum of the message digits is odd, the values 1, 3, 5, 7, 9 will satisfy the check. More information could l)e sent if a choice among these A'alues could be associated with informa- tion generated by the information source. This introduces the concept of a mixed digit ; i.e., a digit which conveys both check information and message information A mixed digit is defined as follows: a mixed digit x, base h, is composed of two components (y, z) where y represents an information component and z represents a check component. The number of information states of a mixed digit is jS, wdth y taking the values 0, 1, ■ ■ ■ , 0 — 1 ; the number of check states of a mixed digit is a, the number base of z. In a message containing m check digits and h mixed digits, the number of check states for the message is b"'-ai-a-y ■ . . -au , where a, is the number of check states of the t'th mixed digit. If mixed digits are used as part of a code, information must be avail- able in at least two number bases; 5, the number base of the channel, and (3, the number base of the mixed digit. A situation where this aris(»s naturally is in the case of the algebraic sign of a number; this is a digit of information, base 2, which may be associated with other digits of any base. Similarly, any identification which must be associated with numerical information can be conveniently coded in a number base different from the number base of the numerical information. Thus, a mixed digit can sometimes be used conveniently in an information trans- mission system without complicating the infoi'mation sonrco and re- ceptor. An error detection code for single small errors suggests tlic use of a mixed digit. In the decimal code for example, the quibinary" representa- 1348 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 Table II — Quibinary Code Quinary Component Binary Component Decimal Digit 0 0 0 0 1 1 1 0 2 1 1 3 2 0 4 2 1 5 3 0 6 3 1 7 4 0 8 4 1 9 tion of the mixed digit might be used, letting the quinary component of the mixed digit convey information and the binary component a check. (Table II.) The information source generates blocks of decimal digits followed by one quinary digit. The messages are then generated in the following way : record all decimal information digits as information message digits and take their sum; if the sum is even, the binary component, z, of the mixed digit is 0, otherwise it is 1. The quinary component, |/, of the mixed digit is taken directly from the information source and combined with the calculated binary part by the rules of the quibinary code to form the mixed decimal digit. Thus, a;, the value of the mixed digit, is given by the formula : X = 2\j -\- z. (1) For example, if the decimal digits of a message are 289 and the quinary digit of the message is 3, the mixed digit is 7, and the message is 2897. The sum of the decimal information digits is 19, which is odd, so that the binary component of the mixed digit is 1 ; this is combined with the quinary component, 3, bj^ the rules of the quibinary code table, to form decimal digit 7. The requirement that the sum of all digits be even is satisfied by the binary component of the mixed digit, and the informa- tion associated with the mixed digit is contained in the quinary com- ponent. This method is easily extensible to any other number base and is also extensible to the case of slightly larger but still restricted errors (such as ±1 or ±2), provided that the maximum single error is less than (& - l)/2. From the preceding example, it is apparent that mixed digits can be usefully employed in error detection codes. The use of mixed, check and NON-BINARY ERROR CORRECTION CODES 1349 information digits simplified the encoder and decoder. To differentiate among the classes of codes which will be described in this paper, the following terms will be used, in addition to those previously defined. A semi-sijsiematic code encoder produces messages containing only- information, mixed and check digits. The information source generates information digits in base h for information digits, and in base /3 for mixed digits. (The example given above is a semi-systematic code.) Of two coding schemes in the same channel base 6, each working with messages of the same length, and each satisfying a given error detection or correction criterion, the more efficient scheme is defined as the one which produces the larger number of different possible messages. III. SINGLE ERROR CORRECTION CODES, SMALL ERRORS (±1) The problems of error correction codes in nonbinary systems are ex- tensive and must be treated in several distinct sections. The basic differ- ence between the error correction problem in binary and non-binary codes is the fact that the sign of the error is important. In a binary code, if the message 11 is received and it is known that the second digit is incorrect, only one correction can be made, to 10. But in a decimal code with errors limited to ±1, if the message 12 is received and it is known that the second digit is wrong, it can be changed to either 11 or 13. Consider the following simple code for correcting single small errors. A decimal channel is used, and a message is composed of three informa- tion digits and one check digit. Let Xi represent the check digit and .T2 , .Ts, Xi the information digits. Here, .ri is chosen to satisfy* Xi -f 2.r, -f- 3.r3 + 4.r4 = 0 mod 10. (2) The encoder calculates Xi , and transmits the message a:iX2a:3.i"4 . This is received as XiXo'xzXi. The decoder then calculates c given by c = {xi' + 2x2' + 3.r3' + 4a-4') mod 10. (3) If the assumption is made that at most a single small error exists, then this error can be corrected by using the following rules, which may be verified by inspection. If c = 0, no correction is necessary; 5 > c > 0, decrease the cth. digit by one ; * B3' definition a = r mod h is eciuivalent to a = c + nb, where a. b, c and n are integers. Tlie eciuality notation is used in j)refeience to the congruenee nota- tion throughout this paper, since an addition performed without carry occurs naturally in many circuits; in terms of such a circuit, the mod b signifies only the base of the addition, and a true equality exists between the state of two circuits, with the same output even though one has been cycled more often. 1350 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 5 < c, increase the (10 — c)th digit by one; c = 5 implies a multiple error or a larger error. Since the value of c is used for correcting a received message, it is called the corrector.* For the general case, a corrector is defined as follows. In a message encoded to satisfy m separate checks, the result of cal- culating the checks for the received message at the decoder is an m digit word called the corrector. There are as many possible values of the cor- rector as there are check states of the message, although all of the values of the corrector need not correspond to a correctable error. It is important that, for a given transmitted message, every different error will lead to a different value of the corrector; otherwise there will be no way of knowing which correction corresponds to a particular value of the corrector. The number of correctable errors may be far less than the number of possible values of the corrector, so that not all of these values may be useful for a code to correct a particular class of errors. However, the number of corrector states sets an upper limit to the num- ber of possible corrections. For many codes, it is convenient to associate a particular value of a corrector for the condition that a particular digit has been received too high by a single increment, for example, a 7 received as an 8. The characteristic of a digit for a particular code is defined as the value of the corrector if that digit is incorrectly received, the error having increased the value of the digit by + 1 , and all other digits are correctly received. Obviously, this definition only applies to those codes having the property that the value of the corrector is independent of the value of the incorrect digit and of the other digits. A simple characteristic code encoder produces messages in which each digit has a distinct characteristic as defined above. The Hamming code is an example of a simple characteristic code as is the code previously described. In that example, the characteristic of Xi is i. The advantage of a simple characteristic code for single small error correction is obvious: the association between the calculated checks and the correction to be performed is simple and does not depend on the values of the digits of the message. The following example of a simple characteristic code will illustrate this principle more fully. Consider a single small error correction code, working with a quinary * The terms corrector and characteristic were first used in a more restricted sense in an article on binary coding by Gola3^* NON-BINARY ERROR CORRECTION CODES 1351 (base 5) channel. Each message will consist of ten information digits and two check digits. Let .ri and xo represent the check digits, and x^ , Xt , ■ ■ • , Xn represent the information digits. The equations for calculating .ri and X2 are: I.T1 + Oa-2 + 0.r3 + 1.1-4 + l.r5 + l.re + Ixj + 2xs + 2x9 + 2xw + 2xu + 2x-i2 = 0 mod 5, Oxi + U-2 + 2.r3 + 1x4 + 2.1-5 + 3.1-6 + 4x7 + 0.r8 + I.T9 + 2.rio + 3.TU + 4.ri.- = 0 mod 5. (4) (5) At the decoder, the corrector terms, Ci and d , are calculated using x/, the received value of Xi , in the following formulas: Ixi' + 0.1-2' + 0x3' + 1x4' + 1.1-5' + Ixe' + Ixt' + 2x8' + 2x9' + 2xio' + 2xn' + 2xio' = ci mod 5, Ox/ + 1x2' + 2x3' + 1.1-4' + 2.1-5' + 3x6' + 4x7' + Oxg' + Lrg' + 2.rio' + 3xu' + 4x12' = c^ mod 5. (6) (7) The values of C1C2 corresponding to the condition that one and only- one digit is too high by 1, x/ = Xi -\- 1, can be read by reading the coeffi- cients of the ith digit in the corrector formulas. This quantit}^ is therefore the characteristic of the ith. digit. If x/ = Xj — 1, then the fiv^es com- plements of these coefficients will be the value of the corrector. Table III lists the characteristics and characteristic complements associated with each digit. Table III — Characteristics and Characteristic Complements Systematic Quinary Code Digit Characteristic Complement of Characteristic Xl 10 40 X2 01 04 X3 0-2 03 X4 11 44 X5 12 43 Xs i;-i 42 X7 14 41 Xs 20 30 X9 21 34 Xio 22 33 Xii 23 32 X12 24 31 1352 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 In this code all the possible values of C1C2 correspond to the charac- teristic of a digit or the complement of this characteristic, except 00 which corresponds to the correct message. (An inspection of equations (4) through (7) reveals that if Xi = Xi for all values of t, the values of Ci and Ci are 0). Thus, we can assign a unique correction to each value of C1C2 . The above techniques are extensible to other number bases and dif- ferent length words provided 6, the number base of the channel, is greater than 2. (The equivalent binary channel problem has been treated by Hamming. ) The following set of rules and conventions may be used for deriving a satisfactory set of characteristics for a simple charac- teristic systematic code used to correct single small errors for any length message, and any base, 6^3. The rules must be followed, and the con^'entions (which represent one pair of conventions out of the set of pairs of conventions, which together with Rules 1 and 2 can be used for deriving a code of this class) if followed, will lead to a reasonably simple method for encoding and decoding messages.* Since the rules, not the conventions, limit the efficiency of the code, no set of conventions can be found which will lead to a more efficient code of this class. Rule 1. For an n digit message (including check digits), m check dig- its are required and m must satisfy the following ineciualities : if 6 is odd, — - — ^ n, (8a) if b is even, ^ n. (8b) Rule 2. No characteristic may be repeated; i.e., each digit must have a characteristic different from that associated with any other digit. Convention 1. The various digits of a characteristic are arranged in a set order; i.e., Cn , Co, , • • • , Cmi • The first digit which is neither zero, nor (in case h is even) 6/2, must be less than 6/2. There must be at least one such digit. Convention 2. The characteristic of the 7th check digit has a 1 in the jih. position and O's elsewhere. Rule 1 is required since, for a code of this type, we must be prepared to correct any digit in one of two ways (±1). This implies a mininuun of 2 n + 1 values of the corrector, one for each possible correction, and one for the case of no corrections. This means that 6"', the number of possible I * The above distinction between rules and conventions will be observed tliroughoiit tills paper. NON-BINARY ERROR CORRECTION CODES 1353 values of the corrector, must be at least 2 n + 1, equation (8a). For even bases, we must reject all values of the corrector containing only the digits 0 and b/2 for representing error conditions for the following reasons: a positive error leads to a corrector that is the characteristic of the hicorrectly received digit, and a negative error leads to the ?j-com- plement of such a characteristic. In order to have uniciue error correc- tion, we must be able to distinguish between these two conditions. If a characteristic were to contain only the digits 0 and 6/2, it would be equal to its own 6-complement ; such combinations of digits are therefore not useable as characteristics or characteristic complements. Rule 2 is reciuired to permit a unique identification of an incorrect digit in case of a single error. Convention 1 allows us to distinguish between positive and negative errors. By observing this convention, a characteristic (corresponding to a positive error) can be distinguished from its complement (corresponding to a negative error) by inspecting the first digit of a corrector which is neither 0 nor 6/2. A characteristic will have this digit less than 6/2, a characteristic complement will have this digit greater than b/2. If the corrector is a characteristic, the correction is minus one; if it is a characteristic complement, it is plus one. Once the characteristics have been chosen, the corresponding encoding procedure may be performed in the following manner: Let aij represent the Jth digit of the characteristic of information digit .r, . Let Zj represent the check digit which has a characteristic containing a 1 in the jth. position. If convention 2 has been observed, (9) can be used to cal- culate Zj : n — m J2 (liji'i = —Zj mod 6. (9) i=l An encoder calculates each Zj and inserts it into the message in those digit positions which have the characteristic of the 7th check digit as- signed to them. In more general terms, we use implicit relations that are equivalent to the explicit equations given by (9). Letting x, represent an informa- tion or a check digit, and letting dj represent the jth digit of the charac- teristic of the tth information or check digit, these formulas may be re- written as J2 CijXi = 0 mod 6. (10) t=i At the receiver, the decoder calculates m different check sums. Let Cj 1354 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 represent the check sum corresponding to the jth corrector term, and Xi represent the received vahie of Xi : Then, n ^ CijX/ = Cj mod b. (11) t=i The difference between equations (10) and (11) is the result of any mutilations caused by the channel. If no error has occurred, all the c/s are 0; if an error of ±1 has occurred, the m c/s will form the characteristic or the characteristic complement, respectively, of the incorrectly re- ceived digit. One disadvantage of a systematic code is the discontinuity in the number of check states as a function of w, the number of check digits. For example, in decimal code one check digit is required for a message of up to four digits, and two check digits for up to forty-eight digits. Obviously, for a message of intermediate length, for example, twelve digits, many of the corrector states cannot be used for single error cor- rection smce they will not correspond to any single error. A more effi- cient code would be obtained if the check states were limited to a smaller number. One method of reducing the number of check states is to perform the check in a different modulus than the modulus of the channel. In the single error detection code using a mixed digit, binary check informa- tion and quinary message information was conveyed by this digit. This | code was more efficient than a systematic code because each message contained the minimum number of check states which is 2. If a mixed digit, x, is composed of the two components (y, z) where y is the information state of the digit and z the check state, it is conven- ient to combine these two components to form x by means of the formula , x = ay -\- z. (12) We calculate z by using a linear congruence equation modulo a. The use of this formula permits a decoder to act on x', the received value of x, directly, without first resolving x' into y' and z', because (12) insures that x' = y' mod a. This permits x' to be corrected directly and then resolved into its components. As an example, consider a semi-systematic code for correcting a single small error in a decimal system, using a twelve digit message; ten of the digits are information digits and two are mixed digits, each conveying binary message information and quinary check information. (One of these binary digits might represent the sign of the number.) With two quinary checks, twenty-five different check states are pos- sible ; for correcting single small errors in a twelve digit message, twenty- NON-BINARY ERROR CORRECTION CODES 1355 Table IV — Characteristics and Characteristic Complements, Semi-Systematic Decimal Code Digit Characteristics Cliaracteristic Complements Xi (mixed digit) 1 0 4 0 Xo (mixed digit 0 1 0 4 X3 0 2 0 3 X4 1 1 4 4 Xs 1 2 4 3 Xe 1 3 4 2 X7 1 4 4 1 Xs 2 0 3 0 X9 2 1 3 4 Xio 2 2 3 3 Xii 2 3 3 2 X12 2 4 3 1 five corrector states are required, one for each of the two possible cor- rections (±1) for each digit, and one for the case of a correctly received message. Characteristics may be chosen for the various digits in accord- ance with the rules and conventions outlined above in this case, since the check modulus is the same for both check digits. Consequently, it is no accident that these characteristics, shown in Table IV, are the same as those shown in Table III. Let Ca and Ci2 represent the characteristic of the ith digit, and let l/i and 2/2 represent the two binary information digits. Then: 12 £ CaXi ^ —zi mod 5, Xi = 21 + 5y, i=3 12 ^ Ci2Xi = —Z2 mod 5, 0^2 = 22 + 5yo . (13) (14) 4 = 3 Because Xi = Zi mod 5 and X2 == 22 mod 5, these relations can be re- written implicity to resemble equation (10): 12 23 CnXi = 0 mod 5, i=l 12 ^ Ci2Xi = 0 mod 5. 1=1 At the decoder, the corrector C1C2 is calculated by: 12 S C'tl•^•^•' = Ci mod 5, 1=1 12 ^ Ci2Xi' = C2 mod 5. (15) (16) (17) (18) t=i 1356 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 If the corrector is 00, the message has been correctly received; other- wise, the corrector is either the characteristic or characteristic comple- ment of the incorrect digit, from which plus one or minus one respec- tively must be subtracted as a correction. Consider the general case. Let Xi , x-i , • • • , Xk represent the /.• informa- tion digits; yi , 1/2 , • • • , Vm represent the information state of the m mixed digits, and Zi , 2-2 , • - • , Zm represent the check state of the m mixed digits. In addition, let ai , a2 , ■ • • , am represent the number base of ^1 , 2-2 , • • • , z,„ respectively; I3i , ^2 , • ■ ■ , /3,„ represent the number of possible states of yi , 2/2 , • • • , y,,, respectively, and 0:^+1 , Xk-+2 , ■ • • , Xk+m represent the values of the mixed digits after the message has been encoded. (Note that for simplicity, a check digit is considered as a special case of a mixed digit; its information state is permanently 0.) The follow- ing encoding procedure may be used in which Xi , 2:2 , • • • , Xk are used directly as part of the transmitted message. This is a semi-systematic code, which means that information digits are not changed in coding. To derive the mixed digits, the following formulas are used : anXi + • • • + auXk = —zi mod ai (19-1) x^k+i) = yioci + zi (20-1) ai2Xi + • • • + a2kXk + a2ik+i)X(k+i) = —22 mod 0:2 (19-2) X(k+2) = y2a2 + Z2 (20-2) ttjiXi + • • • + ajkXk + • • • + aj(k+j-i)X(k+j-i) = —Zj mod aj (19-j) Z(k+j) = yjaj + Zj (20-j) ttmiXi + • • • + a,nkXk + • • • + am(k+m-i)Xa-+m-i) = — z ,n uiod «,„ (19-m) X(^k + m) = ymOim + Z^ . (20-m) In each case, the value of the check component Zj , of a mixed digit X(k+j) is determined by a formula involving the information digits and previously calculated mixed digits. Immediately after Zj has been de- termined, X(k+j) is calculated for possible use in calculating z^j+d . After the message has been completely encoded the following equations, analogous to (10), will be satisfied. NON-BINARY ERROR CORRECTION CODES 1357 Let Cij represent aji in equation (19-j). Then, k-\-w, X CijXi = 0 mod a,. (21) 1=1 (Since Xqc+j) = ^j rood ay, substitution of X(k+j) ioY Zj inequation (19-j) will continue to satisfy the equation.) At the decoder, equation (21) is changed to k-\-m ^ CijXi = Cj mod aj (22) i=l In (22), Xi represents the received value of Xi , and Cj represents the jth digit of the corrector. If all the digits have been correctly received, i.e., x/ = Xi for all values of i, then Ci = C2 = • • • = c,„ = 0; [see equation (21)]. If Xh. had been received incorrectly so that xi/ = xi, + 1, but all other digits had been correctly received, then the value of Cj (the ^th digit of the corrector) would be calculated in the following manner: k+m Cj mod aj = ^ CijXi' k-^m Cj mod aj = Yl CijXi + Chj = Chj (23) 1=1 Equation (23) proves that Chj is actually the Jth digit of the charac- teristic of Xh , because by definition, the characteristic of Xh is the value of the corrector when Xh = Xh -{- 1 , and all other digits have been cor- rectly received. This means that the general term. C,> of (21), is actually the jih digit of the characteristic of the ith. digit and that this is a simple characteristic code. For the case that Xh = Xh — 1, the value of the corrector is such that if it were incremented, digit by digit, by the characteristic of Xh , the corrector would be composed only of zeros. Incrementing the corrector by the characteristic of Xh is equivalent to recalculating the corrector with .T;,' increased by one, which in this case would amount to calculat- ing the corrector for the case of a correctly received message. The latter is composed of all zeros [see (21)]. Thus, for the case of a single error of —1, the corrector is the characteristic complement of the digit which is incorrectly received. For a semi-systematic or systematic code, the characteristic complement is an m digit word whose Jth digit is the complement modulo aj of the jth digit of the characteristic. E(iuation (20-j) shows that generally aj^j cannot exceed b. (An ex- ception is given below.) The maximum \'alue of i/j is /3> — 1 since y is a, 1358 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 digit in the number base 0j . The maximum vahie of Zj is usually «_, — 1, since Zj is a digit in the number base ay. Thus, Xk+i = y,a, + ^, ^ 6 - 1, (24) (^, - l)a, + a; - 1 ^ 5 - 1, (25) ocj^, ^ h. (26) Equation (24) restates (19-j), and also states that the maximum value of any digit x, is 6 — 1, where b is the number base of the channel. In (25), the maximum values of tjj and Zj are substituted to yield the result shown in (26). It was stated above that the maximum value of Zj is usually aj — 1. An exception occurs only in case Zj checks only itself and other mixed digits, the latter being restricted to fewer than 6—1 states. Under such circumstances, the value of z is sometimes restricted, so that even though z is calculated to satisfy a check, modulo aj [see equation (19-j)], it can- not assume a> — 1 values. For example, a code for transmitting a single digit message over a decimal channel and permitting the correc- tion of small errors, might use as the set of transmitted messages the digits, 0, 3, 6, 9. In this case, a = 3 (any correct message satisfies the check X = 0 mod 3) and (5 — 4 since four different messages may be transmitted. In this case, z is restricted to the value 0 because the mixed digit checks only itself. In order to correct single errors of ±1, using a simple characteristic code, it is necessary and sufficient that every characteristic be different from every other characteristic, and that it also be different from the complement of every other characteristic. The following rules and conventions may be used to derive a set of characteristics which meet the requirements for a simple characteristic semi-systematic or systematic code for correcting small errors for any base 6^3 and an arbitrary length message. No set of conventions can be found which will lead to a more efficient code of this class, since the rules, not the conventions limit the efficiency of the code. Rule 1 . For an n digit message, including mixed digits, containing ?/? mixed or check digits of which mi are associated with an even modulus, a, the inequality (ara-y ... -a,,. - 2"'i)/2 ^ n (27) must be satisfied. Rule 2. No characteristic may be repeated, i.e., each digit must have a characteristic different from that associated with any other digit. Rule 3. Since the mth check is the last one to be calculated, and the NON-BINARY EIIKOR COKKECTION CODES 1359 characteristic of the mth mixed digit must therefore contain only a single digit which is not 0, a,„ must be greater than 2. Convention 1 . The various digits of a characteristic are arranged in a set order, i.e., Ca , Ca, • • • , dm • The first digit which is neither 0 nor (Xj/2 must be less than olj/2. There must be at least one such digit. Convention 2. The characteristic of the jth mixed digit has a 1 in the jth position and O's elsewhere, provided that ay 9^ 2. If a^ = 2, the char- acteristic of this mixed digit has a 1 in the jth and mth positions, and O's elsewhere. Rule 1 is required because the number of possible corrector states is ai-ar ... •oim , of which only those containing at least one digit which is neither 0 nor a/2 can be associated with the 2n possible errors. The same reasons used for Rule 1 for the systematic code case are equally applicable here; a characteristic containing only the digits 0 or a:y/2 in the jth position is not distinguishable from its complement. Rule 2 is required to permit a unique identification of an incorrect digit. Rule 3 is necessary to derive the sign of an error on the mth mixed digit. The reasons for using Conventions 1 and 2 in the case of the sys- tematic code are equally applicable in this case. For the case a = 2, however, a special convention must be used to avoid a conflict with Convention 1. The procedure for converting a set of characteristics into an error correcting code system is the same for a semi-systematic code as for a systematic code except that the following additional functions must be performed: the encoder must combine check states with information states to derive mixed digits, and the decoder must resolve mixed digits into information and check digits offer it has performed its corrections. By using these rules and conventions, the most efficient simple charac- teristic code can be determined. For messages of length n (including mixed or check digits), the following relations must be satisfied: Let P = avoi-r ... •«,„ , Q = ^v^-r ... ■^,n, mi = number of even as. Then: (P - 2"'0/2 ^ n, (28) a^^i ^ b. (29)* For exceptions, see above. 13()0 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 Table V — Decimal Error Correction Codes lO™ n P Q ai , 02 , ... 01, /32, ... 2 « + 1 1 3 2.5 3 4 3* 2 5 5 5 2 5 3 10 10 10 1 7 4 10 10 10 1 9 5 15 16.7 5, 3 2,3 11 6 15 16.7 5, 3 2,3 13 7 15 16.7 5, 3 2,3 15 8 20 20 10, 2 1, 5 17 9 25 25 5,5 2, 2 19 10 25 25 5, 5 2,2 21 11 25 25 5, 5 2,2 23 12 25 25 5, 5 2, 2 25 13 30 33.3 10, 3 1, 3 27 14 30 33.3 10, 3 1,3 29 15 40 40 10, 2, 2 1, 5,5 31 16 40 40 10, 2, 2 1,5, 5 33 17 50 50 10, 5 1, 2 35 18 50 50 10, 5 1, 2 37 19 50 50 10, 5 1, 2 39 20 50 50 10, 5 1,2 41 * The single digit me.s.sage containing the points 0, 3, 6, 9 is an exception to the inequality a/3 ^ h, because the mixed digit checks only itself. For the most efficient code b"7Q should be minimized. This term repre- sents the ratio of the number of possible messages for an n digit message with and without error correction. This is normally at least as great as 2n + 1, the number of possible corrections on such a message. Table V shows the most efficient decimal codes of this type for an n digit message, for values of n from 1 to 20. Where two or more different codes are eciually efficient, the code with the fewest mixed digits is shown. It is easy to convert from a code using two mixed digits with ai = 5, a-i = 2, to one using a check digit with a = 10, or to make the inverse conversion, and to show that both codes are equally efficient. IV. SINGLE ERROR CORRECTION CODES, UNRESTRICTED ERROR The problem of correcting an unrestricted error on one digit of a message must be divided into two categories, depending on whether h is a prime number or a composite number. As will be seen, the error correction problem for prime bases is considerably simpler than that for composite bases. The method for correcting errors in prime number systems was discovered by Golay,^ although this did not come to the author's attention until after he had worked out the same method. The N'OX-BIXARY ERROR CORRECTION CODES 1361 adaptation to non-prime channel bases is believed to be novel. Since the adaptation makes use of the code for prime bases, both will be described. 4.1 Prime Number Base, Single Unrestricted Error Correction Code This code depends upon a fundamental property of prime numbers, well known in number theory.^ Let p represent a prime number and d, c, and w represent non-negative integers less than p, related by the expression : dw = c mod p. (30) If d 9^ 0, then d and c uniquely determine w. In order to have a simple characteristic systematic code for correcting unrestricted errors, it is necessary and sufficient that the set of charac- teristics shall have the property that all multiples of all characteristics are distinct. Equation (30) implies a unique correspondence between mul- tiples of a characteristic and the characteristic itself, if we consider c to be the multiple, d the multiplying factor and w a digit of the charac- teristic. An error, d, is simply identifiable if a known digit of a charac- teristic is always 1. If each characteristic is distmct from everj' other and if a sufficient number of check digits are available, a simple characteristic code can be obtained. In the following set of rules and con^•entions which may be used for deriving a set of characteristics for a simple charac- teristic systematic code for correcting single unrestricted errors, p repre- sents the prime number base of the channel. The number base of the channel must be prime, and the length of the message is arbitrary. Since the rules and not the conventions limit the efficiency of the code, no other set of conventions may be found which will lead to a more efficient code of this class. Rule 1. For an n digit message, m check digits are required and m must satisfj^ the inequalitj- n ^ ^-^. (31) Rule 2. Each digit must have a difi"erent characteristic. Convention 1. The digits of a characteristic are arranged in a set order, i.e., CuCa • • • dm • The first digit which is not 0 must be 1. Convention 2. The characteristic of the jih check digit has a 1 in the jth position and O's elsewhere. Rule 1 is required for a code for correcting single unrestricted errors since any digit must be correctable in one of p — 1 ways. This implies a minimum of n(p — 1) + 1 states for the corrector, one for each cor- 1362 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 rection and one for the correct message. When m check digits are used, p™ corrector states are obtained. Rule 2 and Convention 2 are the same for the single small error cor- rection systematic codes. The same reasons apply for both cases. Convention 1 is changed from the equivalent convention for the small error correction code, because the magnitude of the error, not only its sign, must be derivable for a code for correcting single unrestricted errors. An encoder first encodes the message according to (32), where dj represents the jth digit of the characteristic of Xi , J2 CijXi = 0 mod h. (32) The decoder calculates the corrector using the following formula where Xi represents the received value of Xi ; XI Cij^i = Cj mod h. (33) The decoder then examines the digits of the corrector in order. The first digit which is not 0 shows the magnitude, d, of the error. All digits are then divided by d (provided d 7^ 0). (That division is unique, as shown by (30).) The result of this division is the characteristic of the incorrect digit, which is then corrected by subtracting d. Consider a code for correcting a single unrestricted error in a six digit message for a base 5 channel: 6 ^ ''—^. (34) A value of 2 for m will satisfy equation (34). The characteristics are 14, 13, 12, 11, 10 and 01, the last two being check digit characteristics, for Xi , X2 , X3 , Xi , X5 , and X6 respectively. Here, Xi , X2 , Xs , and Xi are in- formation digits. The encoding formulas are: xi + .T2 + X3 + .T4 = —Xi mod 5, (35) Axi -f 'Sx'i -f 2x3 + Xi = — .Te mod 5. (36) The decoding and correcting formulas are: {x/ is the received value of Xi) Xi + x-/ + X3 + Xi + Xr/ = ci mod 5, (37) 4.t/ -\- 3x2' + 2x/ + Xi' + .Te' = C2 mod 5. (38) The corrector is C1C2 . NON-BINARY ERROR CORRECTION CODES 1363 Suppose that a message 221321 is received as 224321. Then : ci = 13 = 3 mod 5, (39) C2 = 26 = 1 mod 5. (40) To find the characteristic of the digit, Xh , that was incorrectl}^ received from the value of the corrector, (41) and (42) must be solved: d C,a = Ci = 3 mod 5, (41) d Ca2 = C2 = 1 mod 5. (42) Because the first non-zero digit of any characteristic is 1, (41) can be solved for d since Chi = 1- This yields the result, d = 3. Using this result, (42) is solved for Ch-i ; by inspection, Ch2 = 2, since 3-2 = 6= 1 mod 5. Thus the characteristic of the incorrect digit, Cm Chi , is 12, and the error d, is 3 ; Xz must therefore be reduced by 3 to get the correct value. Since the message was received with .1-3' too high by an amount 3, this result confirms our expected correction. Any correction that is applied must be applied on a modulo b basis. For example, if a correction of —2 is indicated on a digit whose re- ceived value is 1, 1 — 2 = 4 mod 5, which means that the digit is cor- rected to 4. Codes of this type are restricted in their construction. Xo mLxed digits may be used, and the number base must be prime. For the case of n — [{p" — l)/(p — I)] -\- I, g -\- I check digits are recjuired [see (31)]. This means that the number of information digits for a message of this length is the same as for a message one digit shorter, which requires only g check digits. A comparable binary case is the Hamming Code example of an eight binary digit mes.sage (four information digits) compared with a se^'en digit message (also four information digits). In the binary case, the extra digit is useful for double error detection, but unfortvniately, this is not the case for non-binary codes. 4.2 Composite A^miibcr Base, Single Unrestricted Error Correcting Code The problem of correcting an unrestricted error on a single digit, working with a number base h, that is not a prime is much more difficult. Many relatively inefficient techniques exist. For example, characteristics containing only binary lumibers (0 and 1) might be used; (this would amount to using the Hamming Code directly). This is obviously ineffi- cient since the corrector associated with any single digit error of amount 136-i THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 d, would contain only the digits 0 and d, thus wasting most of the pos- sible corrector values.* It is possible to encode and decode using the prime factors of the number base, performing separate and independent corrections on each factor. This is also inefficient, since for many cases, information as to which digit is in error is found independently in two or more ways, while for certain values of the error, it can be found in only one way. Working with mixed digits and check bases, a lower than 6, is not satisfactory since certain values of the error {a in particular) will never show up in a particular check. The technique used for primes will not work since multiples of two different characteristics may be identical; for example, base 10, characteristics 11 and 13, error 5, will both yield correctors of 55. Another technique that is relatively efficient is, however, available. It involves performing all check, encoding and decoding operations in a number base p, where p is some prime number (usually, the lowest) that is equal to or greater than 6. (In case 6 is a prime, we use the pro- cedure outlined above, which is a special case of the procedure to be described below.) The obvious difficulty in such a procedure is that while the informa- tion channel can only handle h levels, the check digits may assume p levels, corresponding to the required p check states. This dilemma can be resolved by adding an adjustment digit. The object of this digit is to permit check hiformation to be transmitted in a base greater than h, the channel base. The idea of an adjustment digit can best be illus- trated by an example. Suppose for a decimal channel, checks are performed in a unodecimal (base 11) code. Let 7 represent the value corresponding to ten. (The consecutive integers in a unodecimal system are then 0, 1, 2, 3, • • • , 9, 7, 10, 11, • • • , 19, I7, 20, etc.) Suppose in a particular mes- sage, four check digits, Zi , Zo , zs , Zi , calculated modulo 1 1 from decimal information digits are used, whose values are 1, 0, 7, 8. A fifth digit, Zo is added such that the sums modulo 11 of 21 + 20 , 22 + zo , Zs + ^o , 24 + Zq are kept constant at 1, 0, 7, 8 respectively. There are eleven dif- ferent words satisfying the condition: [1, 0, 7, 8] = [(^i + Zo), (zo + Zo), (23 + Zo), (24 + Zo)]. These are shown in Table VI. Of these words, six do not contain the digit 7, and so may be transmitted over a decimal chan- nel. Thus, an adjustment digit permits check digits which are calculated in a number system of a higher base than h, to be transmitted over a base h channel. When an adjustment digit is used in base p for adjusting m digits so that transmission over a channel in base h is possible, a mini- * A waste of corrector values is equivalent to an excessive number of check states for a message, which in turn implies an excessive number of check digits. NON-BINARY ERROR CORRECTION CODES 13G5 mum of 6 — 7n{p — h) states are allowed for the adjustment digit. (For certain values of the check digits, more states could be allowed, but a code for utilizing these extra states becomes unwieldy.) For the case b = 10, p = 11, this turns out to be 10 — m. At least one state must be available for each adjustment digit, to have a workable code. The characteristic of an adjustment digit is determined in the follow- ing way: if an adjustment digit adjusts the Jth check digit, then the^th digit of the characteristic of the adjustment digit is 1 ; otherwise, it is 0. The characteristic of all other digits may be derived using the rules de- scribed above for the prime number base channel, except that p, the prime number base of the code must be used instead of b, the number Table VI — Illustration of Adjustment Digit =0 Zl Z2 Z3 Z4 0 1 0 7 8 1 0 7 9 7 2 T 9 8 6 3 9 8 7 5 4 8 7 6 4 5 7 6 5 3 6 6 5 4 2 7 5 4 3 1 8 4 3 2 0 9 3 2 1 7 7 2 1 0 9 base of the channel, for generating characteristics. A message is initially encoded using a value of 0 for an adjustment digit. Subsec^uently, if the adjustment digit always has at least q allowable states, it may be u.sed to transmit one additional information digit, base q, of information. If the value of this information digit is y, the (y + l)st lowest possible value of the adjustment digit (making the lowest value equivalent to // = 0) meeting the requirement that all adjusted check digits are no greater than b — 1 is transmitted. The adjustment digit in conjunction with its associated check digits conveys a digit, base q, of information. In the example given above, q = (S and if y is 4, the fifth lowest value of ^0 , 7, is transmitted. The lowest ^'alue must be associated with y = 0. The values of ZoZiZ2Z32i that are sent over the decimal chamiel are 75431. An example of such a code is one using a decimal channel working in a unodecimal base for the purposes of encoding and error correction. The word length, n, is twelve, nhie decimal information digits, one octal (base 1306 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 8) information digit a.ssociated with the adjustment digit, and two check digits. The characteristics are the following: Xi I7 X5I6 X, 12 X2 19 .Te 15 .rio 11 (adjustment digit) X318 Xi U Xn 10 (check digit) Xi 17 XslS Xn 01 (check digit) Let 2ii and 212 represent the vahies of the check digits .Th and Xio , originally derived from .Ti , X2 , • • • , Xs , x^ : Xi + X2 + Xz + 7.ri + 9.r.2 + 8.r3 + • • + Xg = —Zn mod 11, + 2.r9 = —Zn mod 11. (43) (44) From Zn and 212 , the ten different words (0, Zn , 212), (1, ^n — 1, 212 — 1), (2, Zn — 2, Z12 — 2), • • • , (9, Zn — 9, Zn — 9) are formed. If y is the value of the octal information digit, the {y + l)stsuch word, that does not contain the digit 7, is selected and transmitted as the last three digits of the message. For example, if ^u = 2, Zvi = 1 and y = Q, the ten words are (0, 2, 1), (1, 1, 0), (2, 0, 7), (3, 7, 9), (4, 9, 8), (5, 8,7), (6, 7, 6), (7, 6, 5), (8, 5, 4), (9, 4, 3); the word (8, 5, 4) is selected since it is the seventh in the secjuence that does not contain any 7's. Table VII shows the choice of the three last digits as a function of y, given 2:11 = 2, 212 = 1. Formula (45) is used for calculating the corrector. Let C> represent the jth digit of the characteristic of Xi , Cy the jth digit of the cor- rector, and Xi the received value of Xi . Then, 12 Cj = ^ Cijx/ mod 11. (45) The translation from corrector to correction is the same as if the original Table VII Relation Between Adjusted Digit and Associated Information y ATlO Xn Xl2 0 0 2 1 1 1 1 0 2 4 9 8 3 5 8 7 4 6 7 . 6 5 7 6 5 6 8 5 4 7 9 4 3 il NON-BINARY ERROR CORRECTION CODES 1367 message had been in a unodecimal code. (This has been illustrated in Section 4.1.) The first step of the encoding procedure is to calculate the unadjusted check digits. Next, the adjusted check digits and adjustment digit are selected according to the value of y, the information digit associated with the adjustment. The message is then ready for transmission. At the decoder, the message is first corrected as if it had been re- ceived as a unodecimal message. The information digits are then hi their corrected states. Next, the adjustment digit and the check digits are examined and the inverse of the encoding process used to select a particular set of check and adjustment digits is used to reconstruct the value of y which originally controlled the selection. In the example given above, the values of Xw , Xn , Xn are 8, 5, 4 respectively; the decoder recog- nizes that this is the seventh lowest value of Xio , which means that the value of y, used in selecting .Tio and the adjusted values of .ru and Xn , was 6. The code described above is fairly efficient; about 90 per cent of the corrector values can be associated with corrections; the product of the information states and the check states is about 97 per cent of the total number of states of a twelve decimal digit word. Each of the above factors reduces the efficiency of the code below a possibly unattainable maximum. It will be noted, however, that this reduction is relatively small in both cases, and is very much lower than would be the case for any of the rejected schemes. The scheme is not difficult to instrument; relatively little additional ec^uipment is required in addition to the basic equipment for instrumenting a simple prime number base chan- nel, unrestricted single error correcting code system. The method of adjustment digits is general and can be used for de- riving a single error correction code for correcting unrestricted errors for any channel base. Any convenient prime check base, p, at least as great as h may be used, although the lowest will generally be the most efficient. The only requirements which must be fulfilled are that the number of states of the adjustment digit must be at least 1, and that at least two check digits must be associated with each adjustment digit. An adjustment digit associated with m check digits, working with a channel base 6 and a check base p, may have b — m{p — h) different states. V. SINGLE ERROR CORRECTION, DOUBLE ERROR DETECTION CODES FOR CORRECTING SMALL ERRORS Single error correction, double error detection codes are ver}^ useful in situations where a message may occasionally be repeated. In order 1368 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 for a correction code to be reasonably useful in a system with random noise or errors, the errors must be relatively infrequent, which makes double errors still more infrequent. If means are available for an occa- sional but very infrequent repetition of a message, a single error correc- tion, double error detection code will increase the reliability of a digital system, since a message may be repeated if a double error is recognized. This section will show how the ideas of the single error correction, double error detection Hamming Code may be combined with the ideas of semi-systematic single small error correction codes (described in Sec- tion III) to derive simple and efficient codes for correcting single small errors and detecting double small errors. In order to derive a simple characteristic code for correcting single small errors, and detecting double small errors, a set of characteristics must be found having the property that the sum or difference of two characteristics or their complements or double the value of one charac- teristic or its complement be distinguishable from the value of any single characteristic or its complement. The sum of two characteristics represents the value of the corrector for a message with two errors of + 1, -fl, the difference represents two errors of -f-l, —1, the sum of their complements represents two errors of —1, —1; double a charac- teristic represents an error of +2, and double a complement represents an error of —2. To have a true single error correction, double error de- tection code for small errors, all these cases must be distinguished from the case of a single error or no error by making certain that the value of the corrector for any of these cases is different than the value of the corrector corresponding to any single error and no error. Table VIII gives the characteristics used in the single error correction Hamming Code and the single error correction, double error detection Hamming Code for conveying four digits of information in a message containing seven or eight binary digits respectively. An inspection ot Table VIII shows that the sum (performed without carries from column to column) of any two characteristics in the right part of the table is distinguished by having at least one 1 in the first three places and a 0 in the last place. This distinguishes it from any single characteristic since all characteristics have a 1 in their last place. Some difficulties arise in trying to adopt such a scheme directly in a non-binary system. For the code to be efficient, an over-all check would have to be performed using a mixed digit; only two check states are required for an over-all parity check, and if b > 3, (5 representing the number base of the channel) at least two information states are pos- sible. But the over-all check digit, which performs a binary check, is not checked by any other digit. This means that although errors might be NON-BINARY ERROR CORRECTION CODES 1369 detected in an over-all check digit, difficulties would be encountered in determining the direction of the correction, so that the information conveyed by the mixed digit could be used. Actually, means are avail- able, for accomplishing an adaptation of binary techniciues. These meth- ods are described in Section \ll but they are less straightforward than the ones described below. For channels with base b, greater than 3, at least one check may be made using a check base, am , that is 4 or greater. If characteristics are used whose last digit (the digit associated with the a,„ check) is always 1, and whose only other limitation is that each characteristic is different from every other characteristic, a satisfactory code is obtained. Single errors are corrected in the normal way. If the last digit of the corrector is 1 or a,n — 1, the error is ±1 respectively on the digit whose charac- Table VIII — Characteristics for Hamming Codes Single Error Correction Single Error Correction Double Error Detection 001 010 oil 100 101 110 111 Check Digit Check Digit Information Digit Check Digit Information Digit Information Digit Information Digit Over-all Check Digit Xi X2 Xs. Xi Xs X6 X7 Xs 0011 0101 0111 1001 1011 1101 nil 0001 teristic or whose characteristic complement is indicated by the cor- rector. If the last digit of the corrector is 2 or a^ — 2, or the last digit is 0 and other digits are not all 0, a double error is indicated. If the entire corrector is made up of O's, the message is correct as received. An example is a code for a ten digit message, decimal base channel; eight decimal information digits, one mixed digit conveying binary message information (such as the sign of the decimal number) and cjua- ternary (base 4) check information, and one check digit are transmitted in each message. Let Xi and .r^ represent the mixed and check digit re- spectively, Xs through Xio the information digits, yi the binary informa- tion conveyed by Xi , and Zi the quaternary check information conveyed by Xi . The encoding formulas are : 2.1-3 + 3.^4 + 4i-5 + 5.r6 + 6.^7 -\- 7xs + 8.1-9 + 9.rio = -x-. mod 10, (46) x-2 + X3 -f .T4 + .Ts + .Te + .Ty + .^'s + -n + .rio = —zi mod 4, (47) xi = z,-{- 42/1 . (48) 1370 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 Note that (46), (47) and (48) must be applied consecutively, in that order, since (47) cannot be applied without knowing Xi obtained from (46), and (48) requires Z\ , obtained from (47). The characteristics are 01, 11, 21, 31, 41, 51, 61, 71, 81, 91 respec- tively; the complements of the characteristics are 03, 93, 83, 73, 63, 53, 43, 33, 23, 13 respectively. The corrector, C1C2 , is calculated at the decoder by the following formulas (x/ is the received value of Xi): 10 ci = E (x^') a - 1) mod 10 (49) 10 C2 = S ^i mod 4 (50) Consider the example of a message with decimal information digits 37520652 and binary information digit 1. Then X'i = 3, Zi = 3, and 7ji = 1, yielding a value of 7 for .I'l . The message is sent as 7 3 3 7 5 2 0 6 5 2. Suppose that the sixth digit is changed to 1 in transmis- sion. Then the corrector has a value 53; this is the complement of the characteristic of the sixth digit and indicates that the sixth digit should be incremented by 1 according to the rules previously stated. If the sixth digit had been received as 1 and the seventh digit also received as 1 (an error of +1), then the corrector value would be 10, indicating a double error (see rules stated above) . If a multiple of 4 is used as am , the last digit of a characteristic may assume all odd values below am/2. The rule then is that an even value of the last digit of the corrector, or a 0 for the last digit and other digits of the corrector not all 0, indicates a double error. The following set of rules and conventions may be used with any base & ^ 4, and anj^ length of message, for deriving a set of charac- teristics for a semi-systematic code for correcting single small errors and detecting double small errors. Since the conventions restrict the effi- ciency of the code, it is conceivable that a different set of conventions will yield a more efficient code in some cases; (51) may be modified through the use of an alternate set of conventions. Rule 1. No two digits may have identical characteristics. Convention 1 . Choose for a^ a multiple of 4. Let am/4 = g. Convention 2. The characteristic of the mixed digit associated with am contains a single 1 in the last position; the rest of its digits are 0. Convention 3. The characteristics of the jih mixed or check digit con- tains a 1 in the last position, a 1 in the jth position and O's elsewhere. Convention 4- The characteristic of an information digit has an odd NON-BINARY ERROR CORRECTION CODES 1371 number less than a,„/2 in its last position. The rest of its digits are arbitrary. Convention 5. The above conventions restrict the choice of charac- teristics. In order to have n distinct characteristics, m mixed or check digits, using check bases ai , a-, , •■-,««, are required, and inec{uality (51) must be satisfied: n ^ aia2- ... -am-i-g. (51) Codes may be derived using the above conventions only if b ^ 4. For the ternary case, a relatively efficient code may be obtained by using one ternary digit as an over-all parity check digit. The rest of the message is in a single small error correction code, derived using the rules and conventions of Section III. Any single small error will lead to a failure of the parity check, and a double small error will lead to a failure of other checks but not the parity check. No general solution has been found for deriving an efficient single error correction double error detection code for the unrestricted error case. Also, no general solution has been found for deriving an efficient multiple error correction code for the unrestricted error case. A reason- ably efficient method has been found for correcting multiple errors in the more important small error case; this is discussed in Section 6.2. VI. THE USE OF BINARY ERROR CORRECTION TECHNIQUES IN NON-BINARY SYSTEMS In this section, methods for using binary codes for the correction of errors in a non-binary system are described. Although the single small error correction codes obtained in this manner are generally less flexible than the codes obtained in Section III, the class of multiple error correc- tion codes described in Section 6.2 is the only reasonably satisfactory class of such codes that has been found. The codes described in this section are semi-systematic but are not simple characteristic codes. 6.1 Single Small Error Correction Codes Binary codes are most conveniently used for correcting small errors (±1). Suppose any digit, base h, has an associated pair of binary digits, arranged in such a way that a change of ±1 in the base b digit will change only one of the two binary digits. For b = 10, an association such as the one shown in Table IX might be used. For example, if a 6 is received as a 7, the associated binary message would indicate that the second of the binary digits is incorrect; a 7 can be corrected 1372 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 Table IX — Assocl«lted Binary Digits for Correction OF Small Errors Decimal Digit Associated Binary Digits 0 00 1 01 2 11 3 10 4 00 5 01 6 11 7 10 8 00 9 01 Table X — Reflected Quibinary Code Decimal Digit Quinary Component Binary Component Associated Binary Digits 0 0 0 00 1 0 1 01 2 1 1 11 3 1 0 10 4 2 0 00 5 2 1 01 6 3 1 11 7 3 0 10 8 4 0 00 9 4 1 01 to an 8 or a 6, but only the correction to 6 would correspond to a change in the second binary digit of the associated binary message. If the first of the associated binary digits is the odd or even indication of a quinary component of a decimal digit, a decimal digit can convey ten states rather than the four states of the associated binary digits. The combination of binary and quinary digits shown in Table X may be called a reflected quibinary code because of its analogy with the re- flected binary code.* If a method were available for transmitting without error (e.g., by using an error correcting code) a message composed of the associated binary digits in a base b code, small errors could be corrected in the base h digits. An examination of Table X for resolving a decimal digit into binary and quinary components, reveals that a change of ±1 on any decimal * The reflected binary code lias the property that each increment changes only one binary digit; for example, the eight successive words of a three binary digit reflected l)inary code are 000, 001, Oil, 010, 110, 111, 101, 100. NON-BINARY ERROR CORRECTION CODES 1373 digit will change only one of these two components. Further, an error corresponding to a change in the quinary component can be unic^uely corrected if the error in the decimal digit is assumed to be ±1. For example, if a received 6 is discovered to have an incorrect quinary com- ponent, only a decrease in the quinary component making the decimal digit 5 is a possible correction, since an increase in the c^uinary com- ponent would correspond to the decimal digit 9, a change of more than ±1 from 6. A system is shown in Fig. 2 for taking advantage of these properties. INFORMATION SOURCE QUIN NFORM DIGl ARY ATION TS n n-m BINARY INFORMATION DIGITS ' ODD OR EVEN RECOGNITION CIRCUIT BINARY DIGITS ' ; ' n-m SYSTEMATIC BINARY ERROR CORRECTION CODE ENCODER 1 m n 1 ] yJ ^ BINARY MESSAGE INFORMATION DIGITS (NOT USED) BINARY PARITY CHECK DIGITS INFORMATION RECEPTOR BINARY INFORMATION DIGITS n-m QUINARY INFORMATION DIGITS DECIMAL MESSAGE 4 QUINARY DIGITS QUINARY CORRECTION CIRCUIT BINARY DIGITS 20 ODD OR EVEN RECOGNITION CIRCUIT 2n BINARY DECODER AND CORRECTOR BINARY DIGITS ^ Fig. 2 — Use of binary codes with a decimal channel. 1374 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 In this example, an information source generates n quinary and n — m binary information digits for each message. All quinary digits go through an odd or even recognition circuit to be converted into binary digits for the purpose of generating a binary error correction code message. These binary digits and the binary digits generated by the information source are fed into a systematic binary error correction code encoder whose output is a binary message containing 2n. digits, of which m are parit}^ check digits. This output is divided into two parts, 2n — m original inputs to the encoder unchanged by the encoding process (this is a sys- tematic encoder which does not change information digits in encoding), and m parity check digits. The m parity check digits are then combined with m of the quinary information digits through the use of the reflected quibinary combiner to form m of the decimal digits of the decimal message that is trans- mitted; the other decimal digits are formed by combining the n — m binary information digits with the rest of the quinary information digits. The decimal message is transmitted over the noisy channel and arrives with one or more (a number limited by the choice of the binary code) errors of ±1 on decimal digits. It is fed into a reflected quibinary resolver which resolves decimal digits into binary and quinary components in accordance with the reflected quibinary code (Table X). The quinary digits are then fed into an odd or even recognition circuit to form binary digits; these and the binary outputs of the resolver are fed into a binary decoder and corrector, working with the same code as the binary en- coder. The output of this corrector should correspond to the output of the original binary encoder. In the decoder, the binary digits are corrected. When the binary digit derived from a quinary digit is corrected, however, the quinary digit is not yet correct. The correction of the quinarj^ digit is performed by examining both the corrected binary digit derived from the quinary digit and the corrected binary digit which was deri^'ed from the same decimal digit as the quinary digit in ([uestion. The rules for correcting the quinary digit are given in Table XI. As an example, consider the application of a Hamming Code for transmitting ten binary digits in a fourteen binary digit message. Using a code of this type, single errors of ±1 may be corrected in a seven digit decimal message, transmitting seven ciuinary digits of in- formation and three binary digits of information. The characteristics required for a fourteen binary digit Hamming Code message are shown in the first column of Table XII. NON-BINARY ERROR CORRECTION CODES 1375 Table XI — Correcting Quinary Digits Q Bi B, Correction of Quinary Digit Even 0 0 None Even 0 1 None Even 1 0 -1 Even 1 1 + 1 Odd 0 0 + 1 Odd 0 1 -1 Odd 1 0 None Odd 1 1 None Table XII Binary Code used for Correcting Decimal Message Binary Charac tenstics 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 I 0 0 1 1 0 1 ] 1 1 0 Parity Check Digt Parity Check Digit Parity Check Digit Parity Check Digit a b (0) (0) 1 (0) (0) 1 (1) 0 (1) 0 0 0 1 3 (1) 1 (1) 3 0 2 0 4 1 1 1 3 0 0 Position in Decimal Message inary comp. inary comp. inary comp. inary comp. inary comp. inary comp. uinary comp inary comp. uinary comp uinary comp uinary comp uinary comp uinary comp uinary comp of Lst digit of 2nd digit of 3rd digit of 4th digit of 5th digit of 6th digit . of 7th digit of 7th digit . of 6th digit . of 5th digit . of 4th digit . of 3rd digit . of 2nd digit . of Lst digit To illustrate the method completely, a strictly binary example will first be illustrated, then a related decimal example. In column a of Table XII, the digits of a binary message are indicated and in column b, the binary and quinary information digits. The values of the parity check digits, which are shown in parentheses, are calculated by the usual for- mula. Let Cij represent the jth digit of the characteristic of the fth digit (including parity check digits) : 14 X) XiC.j = 0 mod 2. (52) i=l This formula applies for all values of j and in this case will yield four implicit eciuations each with one unknown term, the value of the parity check digit. Using the given values of the binar}^ information digits, the values of the parit}^ check digits are calculated. These are shown in parentheses in Table XII. 1376 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 The binary message is 00110011100110. For this example, the quinary components (quinary information digits) of decimal digits are chosen odd if the corresponding digit of the binary example is 1, even if that digit is 0. The binary and c{uinary components are then combmed by the rules of the reflected ciuibinary code to form the decimal digits 0 7 2 9 4 7 6. For example, the cjuinary and binary components of the fifth digit are 2 and 0, respectively; the decimal digit which has these components is 4, the fifth decimal digit of the message. Consider the binary case. Suppose that the message is mutilated in transmission so that the tenth digit is received incorrectly. The message is mutilated from 001100111001 10 to 00110011110110. The decoder and corrector calculates the corrector by 14 Cj = ^ Xidj mod 2. (53) !=1 In this formula, Cj is the jth digit of the corrector and .r/ the received value of Xi . In this example the corrector is 1 0 1 0, which means that the tenth digit, which has this characteristic, is wrong and should be changed to 0. The corresponding error in the decimal example is a change in the fifth digit from 4 to 3. If the message 0 7 2 9 3 7 6 is received, the resolver and quinary to binary converter delivers the message 00110011110110 to the decoder instead of 00110011100110 corresponding to the correct message. The corrected binary message is produced at the output of the decoder and corrector. When the quinar}^ and binary components of the fifth digit are examined by the quinary correction circuit, the following inputs exist: Received quinary digit 1 (Odd) (quinary component of Corrected binary digit derived from quinary 0 (Bi) Corrected binary digit from same decimal number 0 {B-i). received decimal 3) NON-BINARY ERROR CORRECTION CODES 1377 Table XI shows that the quinary digit must be increased by 1 to 2, which combined with the binary 0 conveyed by the same decimal digit yields a decimal value of 4, the original transmitted value. The best semi-systematic simple characteristic code for correcting single small errors in a seven digit message allows 6 X 10 possible mes- sages in a seven digit message (see Table V), whereas this code allows 6.25 X 10''. This code is therefore slightly more efficient. In addition, this code has the special advantage that any error of ±2 on one digit is recognizable since the corrector will have a value of 1111 for the asso- ciated binary message. (An inspection of the choice of characteristics and assignment of characteristics to the two components of any decimal digit will confirm this.) This general technique can be applied to any base h channel, provided T 'able XIII - — Components of Quinary Digits Mixed Digit Information Digit Quinar>' Digit Info. Comp. Check Comp. Quinary Digit Binary Comp. Ternary Comp. 0 1 2 3 4 0 0 1 1 not used 0 1 1 0 not used 0 1 2 3 4 0 1 1 0 0 0 0 1 1 2* * If quinary information is initially generated, the combination (1, 2) will not occur. that h is greater than 3. For odd bases, the digits which convey a parity check component and an information component cannot be utilized effi- ciently since one state of the base h digit is not available. For example, using a base 5, (see Table XIII), only two information and two parity check states may be conveyed by one digit, since the use of a third infor- mation state would require at least six states for the mixed digit. In the case of information digits, however, all states can be used. In the ciuinary example, the resolution of a digit into two components and the subseciuent recombination is subject to the restraint that one of the com- binations (1, 2) will not occur, which can be assured if the information source generates quinary digits. For the case of high redundancy codes having the property that the associated binary code contains more than 50 per cent parity check digits (corresponding to a negative value of n — 7n in Fig. 2), at least some of the base h digits must convey two or more parity check digits. This can be easily accomplished: a decimal digit can convey three 1378 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 Table XIV — Decimal Digit Conveying Three Binary Digits Decimal Digit Binary Components 0 0 0 0 1 0 0 1 2 0 1 1 3 n 1 0 4 1 1 0 5 1 1 1 6 1 0 1 7 1 0 0 8 not used 9 not used parity check digits if a simple reflected binary code correspondence be- tween binary and decimal digits is maintained as shown in Table XIV. An extension of this idea is the encoding of the original information (i.e., the information that is shown coming out of the information source in Fig. 2) in some error detection or correction code. For example, the decimal to reflected quibinary code resolver will cause both components to be incorrect if an error of ±2 in a decimal digit occurs. In this case, the system shown in Fig. 2 will automatically make a correction on the decimal digit of either +2 or —2 dependuig upon the value of the re- ceived decimal digit, and provided a double error correction binary code is used. Such a correction wall be incorrect about half the time. If the received binary digit is compared to the corrected binary digit and the received quinary digit is compared to its corrected odd or even digit, an error of ±2 can be detected without changing the code. If one extra binary check digit, treated as an information digit by the encoder and decoder, is transmitted in the message, this binary digit can convey the information necessary for determining the sign for a correction of dz2, provided that only one such correction is required for any one message. A rule for determining the value of this digit is: Be = 0 if X) Qi = (0 or 1) mod 4, i=l n 5e = 1 if 53 Qi = (2 or 3) mod 4, (54) where g, represents the zth quinary information digit, and Be represents the special check digit. If the received message contains one error of ±2 on a digit, two possible corrections may be made on the quinary compo- nent of this digit; ±1. Obviously, only one of these corrections will satisfy the equation for determining Be since the two possible corrected values of q are two units apart. NON-BINARY ERROR CORRECTION CODES 1379 Note that the associated binary codes for performing such a correc- tion must have the property that two binary digits may be corrected since an error of ±2 corresponds to incorrect values for two associated binary digits. If the noise is such that errors of ±2 are not very unhkely, it may be desirable to place the binary and the quinary components of any one decimal digit in a different binary error correction code word so as to make the errors independent. In a seven decimal digit message, as an example, the quinary components of the first four decimal digits can be used to generate parity check digits which are conveyed by the binary components of the last three decimal digits. The binary component of the fourth decimal digit (this might be Be) and the ciuinary com- ponents of the last three decimal digits generate parity check digits conveyed by the binary components of the first three decimal digits. Two separate binary error correction code messages are then conveyed by a single seven digit decimal code message. Each message is in a four information digit, three parity check digit Hamming Code. Through the use of this code, one error in the binary component of any decimal digit, and one error in the quinary component of any decimal digit may be corrected. In certain cases, the quinary digits themselves might be encoded in an error correction code for single unrestricted errors before the binary process is carried out. This is helpful chiefly for occasional large errors, leading to initial miscorrections. The variations based upon the principles described, which can be applied to any channel, provided 6^4, including the pyramiding of one code scheme upon another, are almost endless. Generally, the last encoding and first decodhig step should be able to correct many more errors than the first encoding step. For example, if quinary components are encoded in single unrestricted error correction quinary code, the bi- nary code should probably be a triple or quadruple error correction code; otherwise a correction may not correspond to the most probable error condition, and the correction scheme loses its effectiveness. These techniques cannot be conveniently applied to the ternarj^ chan- nel, since a ternary digit cannot be resolved into two components effi- ciently. 6.2 Multiple Small Error Correction Codes One limitation of the above techniques is the requirement for a sys- tematic binary code; i.e., a code in which some of the binary information digits are transmitted directly, and others are determined by paritj'' checks on information and previously calculated check digits. These 1380 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 Table XV - — Reed-Muller Codes — 256 Digit Message Number of Digits of Information per Message Number of Errors Correctable per Message 255 0 247 1 219 3 163 7 93 15 37 31 9 63 1 127 systematic codes are conveniently applicable only to the correction of single errors and a few special cases of multiple errors. The Reed-Muller^*' codes are not systematic codes, ("systematic" being used in the narrow sense indicated above, not in the sense of Ham- ming"), but offer the advantage that multiple error correction is rela- tively straightforward. For this reason, it is desirable to find some way of adapting the binary Reed-Muller codes for correcting a number of small errors in non-binary codes. To explain the nature of the Reed-Muller codes completely is beyond the scope of this paper; a list of their important features is sufficient. This is: 1. The length of a message is 2 binary digits for the simpler versions of the code. 2. If Cc represents the number of combinations of d items taken c at a time, and Cf = dl/[cl(d — c)!], then 2^ — ^T=o Ck-i information digits may be transmitted correctly in a message containing 2 digits, if no more than 2'" — 1 errors occur in the messages; 2'" errors are de- tected but they are not always correctable. The Reed-Muller codes for correcting a large number of errors will frequently correct more than 2" — 1 errors, and will always correct 2'" — 1 or fewer errors. These values are given for a 256 digit message in Table XV. 3. Each digit of the transmitted message is a parity check of a group of digits from the information source ; the message cannot be broken down into information digits and check digits. 4. The decoding is accomplished by a number of majority decisions among different groups of message digits. A technique will be described for using a Reed-Muller code efficiently to correct a number of small (±1) errors for any code base h that is a multiple of 2, and also, at a small sacrifice of efficiency, a number of larger errors. A theorem, stating that any code which is generated by a set of parity NON-BINARY ERROR CORRECTION CODES 1381 checks will contain the same set of allowable messages as some systematic code, was proved by Hamming. ^ In particular, such a theorem indicates that a Reed-Muller code will contain the same set of allowable messages as some systematic code. This was also proved by Slepian, who has given a simple method of deriving a systematic code generating the same set of messages as a Reed-Muller code. For convenience, such a code will be called an SERM code (Systematic Equivalent Reed-Muller code). A Reed-Muller decoder serves to derive the information digits from a message in Reed-Muller code which may have been mutilated by noise. If a Reed-Muller decoder is followed by a Reed-Muller encoder, the com- bination serves as a noise eliminator (provided the noise is within the correction bounds of the code), since the output of the encoder is the noiseless Reed-Muller code message that is equivalent to the noisy message that entered the decoder. This property is useful since it means that any message, drawn from the set of Reed-Muller code messages, which has not been mutilated outside the bounds set up by a particular Reed-Muller code, will be restored to its original form, by a Reed-Muller decoder followed by a Reed-Muller encoder. Since an SERM code will produce only messages included in the set of messages of the correspond- ing Reed-Muller code, the SERM code can be used in conjunction with a Reed-]\Iuller decoder and encoder to permit transmission over a noisy channel in a systematic code. The two systems shown in Fig. 3 are therefore equivalent in their error correction properties. In both cases, messages from the set of Reed- Muller code messages are sent, and since the same decoder is used ini- tially, both systems will correct errors in the received message in the same manner. The Reed-Muller encoder in the second system is re- (luired because a Reed-Muller decoder does not correct a message but derives information digits from the received message directly. The derived information digits, however, necessarily correspond to some corrected form of the received message and, in effect, the decoder performs the same correction as it would perform by deriving the corrected form of the message first. INFORMATION REED MULLER NOISY CHANNEL REED MULLER INFORMATION — *► ENCODER DECODER . > INFORMATION SERM ENCODER NOISY RM DECODER RM — DIGIT SELECTOR INFORMATION Ch ANNEL ENCODE :R — * Fig. 3 — Equivalent systems using SERJM and Reed-Muller codes. 1382 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 Table XVI — Multiple Small Error Correction Code Using SERM Codes with Decimal Channel Message Length Information Digits (Equivalent Decimal Digits) Check Digits (Equivalent Decimal Digits) No. of Small Errors Correctable per mes. 128 128 128 128 127.7 125.3 116.9 100.0 .3 2.7 11.1 28.0 0 1 3 7 This means that a Reed-Muller code can be adapted to the system shown m Fig. 2. The Systematic Binary Error Correction Code Encoder is simply an SERM encoder; this is permissible since the SERM codes are .systematic. The Binary Decoder and Corrector is simply a Reed- Muller decoder followed b}^ a Reed-Muller encoder. Everything else remains unchanged. This scheme offers flexibility for the correction of large numbers of small errors. Proper initial error correction encoding of the original in- formation digits will permit correction of a small number of large errors. Table X^T shows some tj^pical cases of the correction of many small errors in a decimal message as a function of the number of information and check digits in a message of constant length. For convenience, every- thing is sho^^^l in equivalent decimal digits, even though in the actual code, binary and quinary information digits are used. Only the first few entries are considered, since the message composed exclusively of the digits 0, 3, 6, 9 in which any number of small errors in a decimal channel may be corrected (this code is described by the first entry of Table Y) is more efficient than the codes corresponding to subsequent entries on Table XXl. This code, which is very easy to instrument, will transmit the equivalent of 77 decimal digits in a 128 decimal digit message. One problem not efficiently solved by these techniques is the multiple- error correction ternary channel problem. A technique which can be used is a code identical to the regular binary Reed-Muller Code, except that all equations will be modulo 3 instead of modulo 2. In decoding, this will sometimes require subtraction instead of addition; in modulo 2 ecjuations there is no difference between these operations, but in modulo 3 equations, the two operations are distinct. The same procedure can be used for correcting multiple unrestricted errors in any base. VII. iterative codes All the codes described above have one disadvantage; occasional ex- cessive noise will jdeld a non-correctable message. In order to approach NON-BINARY ERROR CORRECTION CODES 1383 error free transmission, some iterative coding procedure may be used. This problem has been solved by Elias.'^ His methods are directly appli- cable to non-binary codes, since nothing restricts the digits to binary values. L I In order to minimize the complexity of an iterative coding procedure, systematic codes are desirable. The advantages of the Reed-Muller code are significant however, especially for the case of a relatively noisy channel. A sound procedure for a binary channel would therefore be to use SERM codes, (see Fig. 3) ; such codes are more efficient than iterated Hamming Codes in a relatively noisy channel. VIII. SUMMARY AND ANALYSIS : . Many codes have been presented in this paper, all constructed by some combination of procedures involving linear congruence or modulo equations. In most cases, more efficient codes exist. Exhaustive procedures exist for deriving maximum efficiency codes, although the codes derived in this manner usually require an extensive codebook, both at the encoder and at the decoder. Even for simple single error correction binary codes, the most efficient code is not always a systematic code. For example, the best systematic single error correction binary code working with an eight digit message has only 16 different allowable messages; it is known'* that a non-systematic code with at least 19 allowable messages exists. In the case of non-binary codes, the situation is somewhat worse. Very few of the codes given in this paper take advantage of the fact that, for most situations, a digit that is incorrectly received as 0 or 6 — 1 is usually corrected only in one direction and no need exists to specif \'^ whether the correction is ±1. Most of the codes are arranged so that any received digit may be corrected either positively or negativel}'. Xo codes have been found which take full advantage of such a property, other than codebook codes, except for isolated instances of short message codes having symmetrical properties. For example, the single digit, single small error correction decimal code having 0, 3, G, 9 as the allow- able messages takes full advantage of this property, and is, at the same time, a true semi-systematic code. It is extremely difficult to find the ultimate limits of efficiency of code- book codes. The exhaustive procedures are totally impractical except for very short messages. If an analysis is restricted to codes which do not take advantage of the property that certain values of digits may be corrected in only one direction, and it is assumed that each possible message is mutilated to the same number of incorrect messages, one 138-4 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 limit to the efficiency of codes may be found. This Umit can be derived from the fact that an error correction code decoder and correction cir- cuit must be able to convert any message which contains errors within the bounds of the correction performed by the code, into the value of the message as originally transmitted, or must be able to derive the original information which was fed into the encoder. Thus, if each mes- sage may be mutilated in w ways, and still be corrected, then at least w messages must be associated with each allowed message. This is indi- cated diagrammatically in Fig. 4. The messages produced by the encoder are shown at the left; each one fans out to w — 1 mutilated messages plus the original message. The decoder converts any of these w messages into the original message. The value of w can be determined by taking all possible combinations of errors that can be corrected by a coding system. For example, for a code system which can correct up to {d — l)/2 small errors in different digits in an n digit message, w is given by w (d-l)/2 (55) i=0 where d is the minimum distance between messages, and n! (n — i)li\ This equation merely signifies that w is the sum of all combinations of positive and negative (accounting for the 2 term) errors in up to {d — l)/2 different digits out of n digits. For single errors, iv = 2n -f 1. INFORMATION SOURCE ENCODER CHANNEL DECODER INFORMATION RECEPTOR W DIFFERENT ^7 MESSAGES Fig. 4 — Graphicjil representation of an error correction code. NON-BINARY ERROR CORRECTION CODES 1385 The number of different messages that can be produced by the en- coder must be no greater than b"/w, subject to the above restriction, 6" representing the maximum numbei- of messages that the decoder may receive as an input. If only systematic and semi-systematic codes are considered, the number of messages is Umited to multiples of powers of b and of the information component base /3 of mixed digits. The number of check states must be at least as large as w, so that w different correc- tors may be calculated and associated with w different corrections. Subject to the above restrictions, the following statements may be made. 1. The systematic single small error correction codes derived using the rules of Section III are the most efficient systematic single small error correction codes possible. For those codes in which the two sides of inecjuality (8a) are equal, no code, not even a non-systematic code, is more efficient. 2. The systematic single unrestricted error correction codes deri\'ed using the rules of Section 4.1 are the most efficient systematic single unrestricted error correction codes. For those codes in which the two sides of inequality (31) are equal, no code is more efficient. 3. No codes are more efficient than those semi-systematic codes, derived using the rules of Section III, for which the two sides of in- equalities (28) and (29) are equal and mi = 0. It is difficult to make more general statements about semi-systematic codes, because spe- cial techniques (such as those of Section VI), not all of which are known, may be used with these codes. For multiple error correction codes, other techni(|ues are both simpler and more efficient than the straight systematic and semi-systematic techniques described in Sections III, lY and Y. One such scheme has been described in detail in Section VL No codes have been found which approach the limit set by iv, but the codes described in Section 6.2 are moderately efficient. Throughout this paper, all techniques which in\-olve vast complica- tions at the expense of slight additional efficiency have been avoided. Codebook methods are always possible. If a technique is almost as com- plicated as a codebook technique with only slightly greater efficiency than a simple technique, the simple technique would always be used in practice, and the codebook satisfies the mathematical and theoretical requirements. In a sense, a really complicated technique is only useful for deriving a better lower limit for the maximum efficiency of a code- book code. In the non-binary case, howe^'er, a codebook system is con- siderably more efficient than any code system which does not take ad- 138G THE BELL SYSTEM TECHNICAL JOUKXAL, NOVEMBER 1957 vantage of the fact that all transmitted messages are not mutilatable to an equal number of correctable received messages. From the point of view of deriving lower limits to the maximum effi- ciency of a codebook technique, such a consideration is vital. Except for a few relati^'ely trivial cases, no codes have been found which take sig- nificant advantage of the above consideration, for deriving such a limit.* IX. CONCLUSION In this paper, techniques have been presented for deriving error cor- rection codes for non-binary systems. None of the methods presented are overly complicated, nor do they recjuire excessive storage capacity for either the encoding or decoding and correction system. The codes are sufficiently simple so that their use with a non-binary storage system may be considered, and the development of such a storage system should not be stopped because a system without flaws or not subject to noise cannot be realized. An important disadvantage of using error correction codes with such a system is the time recjuirement. Correction usually requires a signifi- cant amount of time. This is probably one reason why the Hamming Code is not used more extensively. The more advanced and complicated codes, such as the Reed-Muller Codes, suffer particularly from the amount of time required for a correction. The codes described in this paper are therefore probably best suited to medium or low speed stor- ages, which are not read too frecjuently. A study of this type may be of some interest to those who have been considering the use of multi-state devices for building switching systems and computers, since this paper represents a stvidy of a typical problem. Certain lessons may be derived from this study: 1. Restriction to a single number base for all operations is a severe handicap. The more advanced codes presented in this paper, require extensive use of different number base operations. The abiUty, inside the computer, to change number bases for different operations, may well be useful. 2. Different problems are best solved using different number bases. For example, the use of an even number base is desirable for multiple small error correction codes, while the use of a prime number base is desirable for correcting single large errors. It is the author's opinion that * Note that this restriction has less significance in the case of binary codes. In a symmetrical channel with only two available signals, each value of a digit ma\' be changed in as many ways, namely, one, as every other. NON-BIXARY ERROR CORRECTION CODES 1387 number bases which are the product of several small factors are best. Suggested values are six, ten and twelve. Number bases with two differ- ent prime factors, may offer an advantage, since they permit simple translation and change of number base among at least three different numbers. In the comparison between binary and non-binary error correction codes, the following observations may be made: 1. Keeping the amount of information per message fixed, a binary single error correction code is less efficient than a non-binary single small error correction code, provided b, the channel base, is greater than three, but is more efficient than a non-binary single unrestricted error correction code. 2. Non-binary codes are slightly more complicated to implement than binary codes; this applies to multiple error correction codes as well as to single error correction codes. The amount of added complication is in no case really extensive. It was initially hoped that this study might also produce some addi- tional binary error correction techniciues. One such technique was dis- covered: the use of a systematic ecjuivalent Reed-]\Iuller code to ap- proach error free coding (see Section VII) . Finally, the author wishes to express the hope that further work on non-binary systems will be encouraged by this study. ACKNOWLEDGEMENTS This work was performed under the part-time Graduate Study Plan of Bell Telephone Laboratories at the Columbia University School of Engineering under the guidance of Prof. L. A. Zadeh. The author wishes to acknowledge the help of Prof. Zadeh, both in the selection of a dis- sertation topic and in the subsequent guidance of the study. In addition, a number of helpful discussions with C. Y. Lee and A. C. Rose helped to guide the research into a study of the most significant problems in the field. REFERENCES 1. R. W. Hamming, Error Detecting and Error Correcting Codes, B.S.T.J., 29, p. 147-160, April, 1950. 2. Of Current Interest, Elec. Engg., p. 871, Sept., 1956. 3. C.Y.Lee and W.H.Clien, Several-Vahiod Combinational Switching Circnit.s, Trans. A.I.E.E., 75, Part I, p. 278-28:3, Jiilv, 1956. 4. D. Slepian, A Class of Binary Signaling Alphabets, B. S.T.J. , 35, p. 203-234, Jan., 1956. 1388 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 5. Hamming, op. cit., Section 1. 6. M. J. E. Golajs Notes on Digital Coding, Proc. I.R.E., 37, p. 657, June, 1949. 7. W. Keister, A. E. Ritchie, and S. H. Washburn, The Design of SivUching Cir- cuits, D. Van Nostrand Co., Inc., New York, 1951, p. 316. 8. M. J. E. Golav, Binary Coding, 1954 Svmi)osium on Information Theory, Trans. I.R.E., PGIT-4, p. 23-28, Sept.,'l954. 9. G. H. Hard}- and E. AI. Wright, An Introduction to the Theory oj Numbers, Oxford University Press, O.xford, 1954, p. 51, Theorem 57. 10. I. S. Reed, A Class of Multiple-Error-Correcting Codes and the Decoding Scheme, 1954 Symposium on Information Theory, Tran.s. I.R.E., PGIT-4, p. 38-49, Sept., "1954. 11. Hamming, op. cit., Section 7. 12. D. Slepian, A Note on Two Binary Signaling Alphabets, Trans. I.R.E., IT-2, p. 84-86, June, 1956. 13. P. Elias, Error Free Coding, 1954 Symposium on Information Theory, Trans. I.R.E., PGIT.4, p. 29-38, Sept., 1954. 14. V. I. Siforov, On Noise Stability of a System with Error-Correcting Codes, Trans. I.R.E., IT-2, p. 109-115, Dec, 1956. See Table II, Column 8. Shortest Connection Networks And Some Generalizations By R. C. PRIM (Manuscript received May 8, 1957) The basic problem considered is that of interconnecting a given set of terminals with a shortest possible network of direct links. Simple and prac- tical procedures are given for solving this problem both graphically and computationally. It develops that these procedures also provide solutions for a much broader class of problems, containing other examples of practical interest. I. INTRODUCTION A problem of inherent interest in the planning of large-scale communi- cation, distribution and transportation networks also arises in connec- tion with the current rate structure for Bell System leased-line services. It is the following: Basic Problem — Given a set of (point) terminals, connect them by a network of direct terminal-to-terminal links having the smallest possible total length (sum of the link lengths). (A set of terminals is "connected," of course, if and only if there is an unbroken chain of links between every two terminals in the set.) An example of such a Shortest Connection Net- work is shown in Fig. 1. The prescribed terminal set here consists of Washington and the forty-eight state capitals. The distances on the par- ticular map used are accepted as true. Two simple construction principles will be established below which provide simple, straight-forward and flexible procedures for solving the basic problem. Among the several alternative algorithms whose validity follows from the basic construction principles, one is particularly^ well adapted for automatic computation. The nature of the construction principles and of the demonstration of their validity leads quite naturally to the consideration, and solution, of a broad class of minimization prob- lems comprising a non-trivial abstraction and generalization of the basic problem. This extended class of problems contains examples of practical 1389 1390 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 -a ti o a o '-2 w "length" (or "weight") of edge connection network <-^ spanning subgraph (without closed loops) <-^ (spanning subtree) (a) Fig. 4 — Example of a shortest spanning subtree of a complete labelled graph. (D ® 6.7 % / \\^^>^ \ fo/ '^.o ^X^^ '^\o- V iri S \ck diagram 1411 V. Transmission loss 1413 VI. A simple example 1414 VII. Numerical examples 1416 VIII. The successive approximation scheme 1417 8.1 Preliminary steps 1418 8.2 Matrix description of the successive approximations 1420 8.3 Convergence proof 1421 IX. Modification of the block diagram to improve the zeroth approxima- tion 1422 X. Conclusions 1423 Appendices I. Analysis of the resonant circuit 1423 II. Study of the limiting case T -* 0 1425 III. Zeroth approximation in the case where A'^i is not identical to N2 1425 IV. Derivation of equation (24) 1426 1403 1404 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 I. INTRODUCTION One main contributor to the cost of transmission circuits is the trans- mission medium itself. Thus it is important to share the transmission medium among as many messages as possible. One possible method is the frequency multiplex where each message vitilizes a different frequency band of the whole band available in the medium. An alternate method is the time multiplex where each message is assigned a time slot of dura- tion T and has access to that time slot once every T seconds. It is obvious that the economics of the situation requires that r be as small as possible and T as large as possible so that the largest possible number of messages are transmitted over the medium. For this very reason the analysis of periodically switched networks is of special interest in the case where t/T is small. W. R. Bennett'' has published an exact analysis of this problem without any restrictions either on the network or on the ratio r/T. It is believed, however, that the analysis presented in this paper will, in most practical cases, give the desired answer with a considerable reduction in the amount of calculations. The simplification of the analysis is mainly a result of the assumption that t/T is small. First the successive approximation method of solution will be discussed in general terms. Next it will be shown that the zeroth approximation to the transmission through the network can be obtained from the gain of a block diagram analogous to those used in the analysis of sampled servomechanisms. The nature of the zeroth approximation is further clarified by some general discussion and some examples. Next it is shown that the successive approximations converge. The convergence proof then suggests some slight modifications of the block diagram to obtain a more accurate solution. II. DESCRIPTION OF THE SYSTEM The system under consideration is shown on Fig. 1. It consists of two reactive networks Ni and A''2 connected through a switch S which is it- self in series with an inductance /. A^i is driven at its terminal pair (1) Fig. 1 — System under consideration. I SWITCHED NETWORK FOR TIME MULTIPLEX SYSTEMS 1405 ;C fr = Fig. 2 277- r = 2f. 77 CJq 7r\ri Resonant circuit. by a current source h which is shunted by a one ohm resistor. N2 is also terminated at its terminal pair (1) by a one ohm resistor R^ which is the load resistor of the system. The switch S is periodically closed for a dura- tion T. The switching period is T. Thus if the switch is closed during the interval (0, r) it will be closed during the intervals (nT, nT + r) for n = 1, 2, 3, • • • . The inductance t is selected so that the series circuit sho^vn on Fig. 2 has a resonant frequency fr = 1/2t; i.e., the time r during which the s^\-itch is closed is exactly one-half period of the circuit of Fig. 2. The switch S acts as a sampler and, as a result of the well-known modu- lating properties of sampled systems, the sampling period T must be chosen such that the frequency l/2r is larger than any of the frequencies present in the signals generated by /o . Furthermore, in order to eliminate all the sidebands generated by the switching, N2 must have a high in- sertion loss for all frequencies above 1/2 T cps. In the analysis that follows networks Ni and A^2 will be assumed to be identical: it should, however, be stressed that this assumption is not necessar}?- for the proposed method of analysis.* This assumption is made because in the practical situation which motivated this analj'sis Ni and A'^2 were identical since transmission in l^oth directions was re- cjuired. In order for the system under consideration to achieve the maximum degree of multiplexing, the closure time r of the switch will be taken as small as practically possible and the switching period T as large as pos- sible (consistent with the bandwidth of the signals to be transmitted). As a result the ratio t/T is very small, of the order of 10~" or less in prac- tical cases. Consequently the resonant frequency /r of the series resonant circuit sho^^^l on Fig. 2, is many times larger than any of the natural frequencies of Ni and A^2 • * The modifications required for the case where -Vi is not identical to N2 are given in Appendix IV. 1406 THE BELL SYSTEM TECHNICAL JOURXAL, NOVEMBER 1957 ■ ^ W S o 6+ oi7 I 4) T3 m m <» CO m O C o ;-• o -1-2 02 ;Z2 SWITCHED NETWORK FOR TIME MULTIPLEX SYSTEMS 1407 The problem i.s to determine the relation between K4 , the voltage across R^ , and /o . III. METHOD OF SOLUTION Let us first write the equations of the system. Obviously the equations will depend on the exact configuration of the networks A'': and No . For simplicity we shall write them for the case where .Vi and N2 are dissipa- tionless low-pass ladder networks. As will become apparent later this assumption is not essential to the argument. What is essential, however, is the fact that both A^i and N-> should start (looking in from the switch) with a shunt capacitor C and a series inductance L„ , the element value of Ln being much larger than (. Using a method of analysis advocated by T. R. Bashkow,'^ we obtain, for the network of Fig. 3, the equations: J dii Rii — i'2 + Rio Ci dv2 dt t\ - l2 > L ^ dVn _ . _ . dt di dt (l.a) C^^ = in - iA{t) (Lb) ] dt t ^ = k - e,]A(t) (Lc) } R dt c^' = iMt) -i,: (Ld) dt r din t Ln -jr = es — Vn at CdVn . / . / n J, 'n In —1 dt > h Ci -7- = li — i\ dt T dii , j3 . / Lx -^ = V2 — RlIi dt (1) 1408 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 where A(0 = E Ht - kT) - u{t - kT - t)], (2) +00 z fc= — 00 with u{t) = 1 for ^ > 0, and u{t) = 0 for t < 0 This system of linear time varying equations may be broken up into three sub-systems /« , R and h . It is this subdivision that suggests a successive approximation scheme that will be shown to converge to the exact solution. The zeroth approximation is obtained as follows: when the switch is closed, i.e., A(^) = 1, the resonant current ir is much larger than the cur- rents in and i,/. Thus, during the switch closure time, in and in' are neg- lected with respect to ir in (l.b) and (l.d). Hence when A(0 = 1 the system R may be solved for ir{t), €2(1) and es(t) in terms of the initial conditions. The resulting function €2(1) and given function io{t) are then the forcing functions of the system /a. The other function es{t) is the forcing function of the system /b. Under these assumptions, the periodic steady-state solution corresponding to an applied current io{t) = /oc'" is easily obtained. The zeroth approximation will be distinguished by a subscript "0". Thus iro{t) is the (steady state) zeroth approximation to the exact solu- tion ir{t). The first approximation will be the solution of the system (1), pro- vided that during the switch closure time the functions in{t) and in'{t) in (l.b) and (l.d) are respectively replaced by the known functions ino{t) andino'it). And, more generall}^, the {k + l)th approximation will be the solution of (1) provided that during the switch closure time, the functions in{t) and in(t), in (l.b) and (l.d), are respectively replaced by the known solutions for ^„(0, and in'it) given by the Ath approximation It will be shown later that this successive approximation scheme con- verges. Let us first describe a simple method for obtaining the zeroth approximation. IV. THE ZEROTH APPROXIMATION 4.1 Introduction The problem is to obtain the steady-state solution of (1) under the excitation io{t) = /oe'"'. Using the approximations indicated above, during the switch closure time (that is when A(^) = 1) the system R becomes SWITCHED NETWORK FOR TIME MULTIPLEX SYSTEMS 1409 C f de2 ~dt dir dt -ir(t)A(t), [e. - c-Mt), c^« = aoA(o. (3) (4) (5) Differentiating the middle equation and eliminating de^/dt and dez/dt we get f or 0 ^ / < r : d ir ^zVA(o + -J h(/) - c,mm (0) in which we used the notation bit) for the Dirac function and the knowl- edge that dA{t) di = 5(0 - bit - r). (7) Equation (6) represents the behavior of the resonant circuit of Fig. 2 for the following initial conditions: i(0+) = 0, (/tV(0 + ) cM - e^m dt I (8) (9) In Appendix I it is shown that the resulting current ir{t) is, for the in- terval 0 ^ / < T, where m = ch(o) - cM]si{t), IT . TTl 1 . , r r\ ^ , — - sm — = - 0)0 Sill coof tor 0 < / < r Si( ) =\'^r r 2 0 elsewhere (10) (11) with ■K Wo (C (12) Thus the zeroth approximation to the exact ir{t) is given for the interval 0 ^ / ^ r by iM = C[em - f3(0)]si(/). (13) 1410 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 We shall now show that the zeroth approximation may be conveniently ol)tained from the block diagram of Fig. 4. 4.2 Description of the Block Diagram All the blocks of the block diagram are unilateral and their correspond- ing transfer functions are defined in the following. Capital symbols repre- sent ^-transform of the corresponding time functions, thus /o(p) is the £-transform of in(/). Referring to Fig. 1, Z,,{v) = E,{v) hip) lr=0 Thus Znip) represents the transfer impedance of A^i when its output is open-circuited (i.e., Ir = 0). Since A''! and N2 are identical we also have, from /?i = 1 and reciprocity, Znip) = Ei/Ir, where Ir is the cur- rent entering A? . The impulse modulator is periodically operated every T seconds, and has the property that if its input is a continuous function f{t) its output is a sequence of impulses: x;/(0 5(/ - i-T). The transfer function Sx{p) is defined by >Si(p) = £[si(0] = - Wo p" + coo cosh -? e-'"\ (14) Let Z{p) be the driving point impedance at the terminal pair (2) of A^ . It is also that of Nt since Ai and A'2 are assumed to l)e identical. Let V{p) be the output of the first block, then, by definition, V{p) = Zn{p)h ■ Let v{f} be the corresponding time function. The voltage v{t) Z,2 v(p) IMPULSE MODULATOR <^ -fO CS,(p) 2Z(p) -12 note: all blocks are unilateral Fig. 4 — Zeroth-approximation block diagram. SWITCHED XETWORK FOR TIME MULTIPLEX SYSTEMS 1411 is the output voltage of Ni , when A''! is excited by the current source /o and the switch S remains open at all times. 4.3 Analysis of the Block Diagram For simplicity, vsuppose that the system starts from a relaxed condi- tion (i.e., no energy stored) at i = 0. Let z{t) = £~\Z{p)]. Considering the network A'': as driven by io and zVo , it follows that the voltage ^2(0 shown on Fig. 3 is given by 620(0 = v(t) - [ iM)z{t - t') dt'. (15) Similarly Thus ez,{t) = f iM)z{t - t') dt'. (16) eM - eUt) = v(t) - 2 [ ir,{t')z{i - t') dt' . (17) ''0 These equations have been derived by considering Fig. 1. They could have been also derived from the block diagram of Fig. 4 as follows: let /ro(p) be the output of CSi{p). x\s a result, the output of the block 2Z(p) is 2Z(p)Iro{p). When this latter quantity is subtracted from V(p) one gets V(p) — 2Z{p)Iro(p), which is the Jt^-transform of the right-hand side of (17). Referring to the block diagram it is also seen that this quantity is the input to the impulse modulator. Thus we see that if Iroip) is the output of CSi{p), then the input of the impulse modulator is e^oit) — 630(0 by virtue of (17). If this is the case the output of CSi(p) is given by Cho(O) - e^o{0)]si{t) , iorO ^tco,). It should be stressed that (21) and (22) are not vaHd when r is made identical to zero. When r = 0, Siip) = 1 for all p's and since Zip) '^ 1/Cp as p — > 3c the time function whose transform is Zip)Siip) is differ- ent from zero at / = 0. In such a case (20) does not hold. From a physi- cal point of view, the feedback loop of Fig. 4 is unstable when r is identi- cally zero since an impulse generated by the impulse modulator produces instantaneously^ a step at the input of the impulse modulator. This step causes an instantaneous jump in the measure of the impulse at the output of the impulse modulator and so on. In short the feedback loop is unstable. It should be pointed out that if the power density spectrum of h is zero for frequencies higher than cos/2, (21) reduces to h 1 CSiip)Ziiip) for \p\ < COs (23) T\ + 2C[Siip)Zip)]* '"- '" ' ^ 2 For certain applications it is convenient to rewrite (21) in a slightly by * When/(0), as defined above, is different from zero, (20) should be replaced £ 23 /(/) i{t - nT) n=0 = F*ip) +-/(0+). SWITCHED NETWORK FOR TIME MULTIPLEX SYSTEMS 1413 different form. Advancing the time function Si{t) by t/2 seconds, one gets the function So{t) which is even in t. As a result its transform So{p) is purely real, that is, Soip) = ^ ^° g cosh ^. p -\-coo ^ From an analysis carried out in detail in Appendix IV we finally obtain ^^°^^^= 2[Z(p)So(p)]* • ^'^^ It should be pointed out that (23) is still valid when r = 0. Equations (20) and (23) give the zeroth approximation to the gain of the system for any driving current nit). In many cases it is sufficient to know only the steady-state response Eioip) to an input io{t) = /oe^"^' . The response Eio(p), as given by (23) [or (20)] includes both transient and steady-state terms. Since hip) = ^-r— equation (24) gives P - J^o (^ E Zuip + jnco.) ^ /" r-) So{p)Zn{p) ^"^^^ 2[Z{p)So(p)]* • ^^"^ Since neither So(p) nor Ziiip) have poles on the imaginary axis, the steady state includes only the terms corresponding to the imaginary axis poles of the summation terms. Thus the steady-state response is of the form where, from (25), 2 X) Zijuo + j(k - ti)cos]So[j(jOQ + j{k - n)a).v] . _ IoZi2(,j^(i)So(juo — jnuis)Zr2U^o — Jnc*}s) .. ^« - ■ +^ ■ . (26) V. TRANSMISSION LOSS A practically important question is to find out a priori whether a switched filter necessarily introduces some transmission loss. The following considerations apply exclusively to the zeroth order approximation. It will be shown that assuming ideal elements, the trans- mission at dc may have as small a loss as desired. 1414 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 By transmission at dc we mean the ratio of the dc component of the steady state output voltage to the intensity of the applied direct current. Thus we refer to (26) and set coo = 0 and n = 0. Suppose the lossless networks Ni and A^2 are designed so that their transfer impedance Zu is of the Butter worth type, that is I Zuiju) p = 1 + C02^' where for our purposes AI is a large integer. In the following sum, which is the denominator of (26) when coo = n = 0 2 E Z{jkc,.)So{jko::), k=— 2 since the cutoff of the networks N occurs at w = 1), the terms corresponding to values of /c f^ 0 will make a contribution that vanishes as M -^ x . This is a consequence of the following facts : (a) Re[Z(jA-coJ] = | Zuijkuis) \ , since the networks A^i and A^2 are dissipationless. Hence for k ^ 0 and as M ^ ^o Re[Z(yAws)] -^ 0, (b) lm[Z{jko:S\ = -Im[Z(-iA-a;.)], (c) So{jo}) is real. Thus the imaginary part of the products Z{jkus)So(jkws) cancel out and the real part (for k 7^ 0) decreases exponentially to zero as ilf -^ oc . Hence for sufficiently large M the denominator of (26) may be made as close to two as desired. It is easy to check that the numerator of (26) reduces to 7o , the in- tensity of the applied direct current. Therefore the ratio of A^ , the dc component of the output voltage to /o may be made as close to one-half as desired. VI. A SIMPLE EXAMPLE Since the approximate formulae derived in Section IV are somewhat unfamiliar it seems proper to consider in a rather detailed manner a simple example.* Consider the system of Fig. 5. Assume that the current source applies a constant current to the system and assume that the steady state is reached. For simplicity let hR = E. The steady-state behavior of the voltages ^^2(0 and e:i{t) = €4(1) is * In addition, the limiting case of the sampling rate — > <», i.e., T" — > 0, is treated in Appendi.x II. SWITCHED XETWORK FOK TIME MULTIPLEX SYSTEMS 1415 C <'R e. Fig. 5 — A simple example. V, +A Fig. 6 ■ — Waveforms of the network of Fig. 5. shown on Fig. 6. It is further assumed that the duration r during which the switch is closed is negUgible compared to T, the interval between two successive closures. Let 64 be the average value of the steady-state voltage ei{t). Thus Ci is equal to Ao as given by (26) with wo = n = 0, namely, _ ^ ^12^(0) So(0) 64 — -to +00 2 2 ^(J/^'^s) Soijkcos) In this particular case Zip) = Zviip) = R c- 1 ^pRC ,1 Since we assume r to be infinitesimal Soip) and Si{p) ma}' be con- sidered equal to unity over the band of interest. Using the expansion 1416 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 1 °° coth 2 = - + ^ 2z z 1 2^ + nV^ ' we obtain 1 +°° C"^ 1 ^•W4g 1 ^2^"°"' (p + jnojs) + " + m)1 Hence i —00 , = .= ^™*'>(2Sc) Thus finally -^ ^ '''^^ = £ ^ 1 (27) This last result obtained from the theory developed above is now going to be checked directly. Referring to Fig. 6, where the notation is defined, and noting the periodicity of the boundary conditions, we get {E - Vr)e-''"''' = E - {V, + A). Noting that ei{t) = (Vi + A)e''"''^, and solving for T'l and A we fin- ally get — t/RC By definition 64 E RCl - r'"^'' T 1 + e-^/«^ ' or RC 1 e, = E coth I - \2RC/ This last equation checks with (27). VII. NUMERICAL EXAMPLES Consider the network of Fig. 7. The cutoff of both Ni and A''2 occurs at w = 1. In view of the sampling theorem good transmission recjuires SWITCHED NETWORK FOR TIME MULTIPLEX SYSTEMS 1417 2.0 Fig. 7 — Computed transmission loss. that the signal be sampled at a rate at least tmce as large as its highest frequency component. Since the cutoff occurs at w = 1, the sampling angular freciuency should at least be ec^ual to 2. For illustration purposes we have taken cos = 2.67 and co., = 5 for the angular sampling frequency The value cos = 2.67 corresponds to a cutoff at 3 kc and a sampling rate, of 8 kc. The ratio r/T was taken to be 1/125. The transmission through the switched network as given by the zeroth approximation is shown for both cases on Fig. 7. As expected the transmittance of the switched filter gets closer to that of an ordinary filter as the switching frequency increases. VIII. THE SUCCESSIVE APPROXIMATION SCHEME The ideas involved in the successi^'e approximation scheme are simple and straightforward. One point remains to be settled, namely the con- vergence of the procedure. We shall assign a subscript 1 to the correction to be applied to the 1418 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 zeroth approximation in order to obtain the first approximation. Thus adding init) to iroit) we get the first approximation iro{t) + iriit). More generally the A-th approximation is ^„=otrn(0- The procedure will con- verge if, in particular, the infinite series 22*=o^Vn(0 converges. 8.1 Preliminary Steps (a) Let us normalize the frequency (and consequently the time) so that the switching period T is unity. Since the networks A''! and N2 must have high insertion loss for co > h{2Tr/T) = tt, the pass band of A'^i and N2 must be the order of 1 radian/sec. As a result the element values of the capacitor C and the inductance L„ (see Fig, 3) are also 0(1). (b) For the excitation io = e'" , the zeroth approximation derived above may be written in terms of Fourier components: ■ /.\ iwt V~* 7- iiirkl Uo{t) = e 2^ lro,ke , k=-K, +00 tnoW = e 2^ ino.ke Let Iro denote the complex conjugate of iVo , then +00 iroit)lro(t) = XI IrO,kIrO,(e^''' " ^\ k,(=-ao Since the functions e'"' \k — • • • — 1, 0, 1, • • • ] are orthonormal over the interval (0, 1) and form a complete set, we have from Bessel's equal- ity: f I iM \'dt = E I ho,k I'- = A^(/.o), Jo A=-oo where N{Iro} denotes the norm of the vector Iro which is defined by its components /,o,/t(/v = • ■ • — 1, 0, +1 • • • )• Similarly, /.I +00 / I ino(t) f dt = ^ \ InO,k 1' = .V(/„o). Jo k=-ac (c) Since the switch is periodically closed we shall be interested in the Fourier series expansion of A(/) : A(0 = u(t) - u(t - r) = i: A,c'''''\ —00 where Ao = r and +00 SWITCHED NETWORK FOR TIME MULTIPLEX SYSTEMS 1419 Since r/T < \a=— 00 / If we introduce the infinite matrix G defined by Gik = A,_,. ii,k= - X, ... , -1, 0, +1, • • • x), the convolution may be represented by the product, GIno , where /„o is the vector whose components are /„o, a(A" = • • ■ — 1, 0, 1, • • •). (d) Considering the network shown on Fig. 3, let E{p) be the ratio of In'iv) to Iriv)- Taking into account the assumed identity between A'^i and A^2 it follows that + In{v) Iriv) = ^ = E(V). 70=0 Iriv) Using the system of (1) and, for example, by Neumann series expan- sion of the inverse matrix, Ave get (e) Considering now the effect of init) and in it) on irit), (42) of Appendix I gives Iriv) ^s a function of Iniv) ^^nd In'iv)- I^^ ^he present discussion where we are interested in the steady state of irit) it is es- sential to keep in mind that since the switch opens at i = r, the memory of the resonant circuit extends only over an interval 0 < / ^ r. To take this into account we must modify the factor (coo /2)/(p" + wo") of (40), because the impulse response (which represents this memory) must be identically zero for t > t. The resulting new expression is 2 Fiv) =^.r^.e-'"^'~W-" + e--"'], or V + coo- 2 Since the time function whose transform is F(p) is non-negative for all fs and since F(0) = 1, it follows that IF(ico) I ^ 1. (28) 1420 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 8.2 Matrix description of the successive approximations From the developments of Section IV, we know i,o{t), i„o(t) and ino'it) or what is equivalent, the vectors Iro , Ino and I„o'. The first approxi- mation takes into account the effect of i„o{t) and t„u'(0 on ir{t). [See eciuation (l.c) and (l.d)]. The time functions i„o(0 and z„o'(0 affect the system R only during the interval (0, r) . Therefore we must consider the vector G(I„o + /„o') which corresponds to the excitation of the resonant circuit. Since the opening of the switch after a closure time r forcibly brings ir{t) to zero we have In = GFG{InO + Ino'), (29) where the matrix G has been defined above and the matrix F is a diago- nal matrix whose diagonal elements Fa (/.' = ••• — 1, 0, +1 •••) are defined by Fk = F(jco, + /27rA-). Note that (28) implies that | F^ | ^ 1 for all A-'s. It should be kept in mind that Iro + In is the first approxima- tion to the exact Ir{p)- The next iteration is obtained by first taking into account the effect of In on the rest of the network: /„i = E In , (30) Inl = E In , where E is a diagonal matrix whose elements Ek {k = • • ■ , — 1, 0, +1, • • •) are defined by Ek = E{jus + 27rAy), and then the effects of /„2 and In2 on /, , that is, 1,2 = GFG{I,a + /„i'), (31) combining (30) and (31), hi = 2G F G E In ■ A repetition of the same procedure would lead to la — 2 G F G E Ir2 , and in general Im + i = 2GFGE Irn. Since the nth. approximation to Ir(p) is given by the sum ^ILoIrk , the successive approximation scheme will be conA'ergent only if the series converges. This will be the case if and only if the series [\ -\-2GFGE -^ ■■■ + (2 G F G F)" + • • •]/,! (32) converges. SWITCHED NETWORK FOR TIME MULTIPLEX SYSTEMS 1421 8.3 Convergence Proof Consider a vector X of bounded norm corresponding to a time func- tion x{0 having the property that x(t) = 0 for r ^ f ^ T and x(t) 9^ 0 for 0 < ^ < T. In the above scheme, the vector .Y would be /r„ . Let us define the vectors F, Z, IJ and F by the relations Y = EX, (33) Z ^ GY, (34) U = FZ, (35) V = 2GU, (36) hence V = 2GFGEX. (37) We wish to show that N{V) ^ aN(X) with a < 1, since these inequali- ties imply that the infinite series (32) converges. Since (a) A^i and A^ are low-pass filters with cutoff ^ x radians/sec, (b) E{p) = 1 for p = 0, (c) E{p) ex l/LnCp' for p » 1, only a few of the Ek's will be of the order of unity In most cases E-i , Eq , Ei will be smaller than unity, thus, N(Y) ^ NiX). (38) In view" of the pulsating character of x{t) the power spectrum of x{t) is almost constant up to frequencies of the order of tt/t radians/sec. Because of the low-pass characteristic of E{p), the function y(t) associ- ated with the vector Y is smooth in comparison to x{t), thus from (34), N{Z) = f 1 z{t) {' dt= f \ y{t) I' dt = arNiY), Jo Jo where a = 0(1). Since | F, ] ^ 1 for all k% from (33), NiU) ^ N{Z), hence N{U) = hTN{Y) with h = 0(1). N{U) = brNiY) with 6 = 0(1). From (36) we have N{V) = 2 [ \ u{t) I' f// ^ 2 f I u{t) \- dt = 2N{U). Jo Jo Thus we finally get N{V) = 2bTN{Y) where 6 = 0(1), (39) 1422 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 and since r « 1 we get from (38) and (39) N(V) = aN{X) with a < 1. Hence the convergence is estabhshed. IX. A MODIFICATION OF THE BLOCK DIAGRAM TO IMPROVE THE ZEROTH APPROXIMATION In principle it is possible to obtain a block diagram whose transmission characteristic is equal to the first approximation. In many cases it is not necessary to go that far. The first approximation takes into account the effect of the currents ino{t) and z„o'(0 on the resonant circuit of Fig. 2. Since during the switch closure time the currents t„o and t,,n' cannot vary much, let us assume that they remain constant for the duration of the switch closure. Referring to the analysis of Appendix I and to (42) in particular, we see that the current ir is increased by 8in{p) = C^O^ 4(0 — ) + in\0 — ) p2 + 0)0^ 2p or 3i(0 = C ^^(Q-) - ^3(0-) (1 _ ,^, ^^^) o^t)/o(p)]*-^i(?>) + C[pZr,(p)Io(p)]*SM '^^' 1 + 2C{[Z{v)S,{p)]* + [pZ{j>)SM]*\ ' X. CONCLUSION Let us compare the method of solution presented above with the more formal approach proposed by Bennett. The latter method leads to the exact steady-state transmission through a network containing periodi- cally operated switches. This method is perfectly general in that it does not require any assumption relative to the properties of the network nor to the ratio of t/T. As expected this generality implies a lot of de- tailed computations. In particular it rec^uires, for each reactance of the network, the computation of the voltage across it due to any initial con- dition. The method presented in this paper is not so general because it assumes first that the ratio t/T is small; second the value of the induct- ance ( is very much smaller than that of L„ (see Fig. 3). The result of these assumptions is that the system of time varying equations may be solved by successive approximations with the further advantage that the convergence proof guarantees that, for very small r T, the zeroth approximation will be a close estimate of the exact solution. The zeroth approximation may conveniently be obtained by consider- ing a block-diagram analogous to those used in the analysis of sampled servomechanisms. Further the proposed method leads directly to some interesting results, for example, as far as the zeroth approximation is concerned, the dc transmission may be achieved with as small a loss as desired provided the lossless networks Ni and N-i are suitably designed. Another advantage of the proposed method is that the simplicity of the analj'sis permits the designer to investigate at a small cost a large num- ber of possible designs. Finally it should be pointed out that this approach to the solution of a system of time-varying linear differential equations may find applica- tions in many other physical problems. Appendix I ANALYSIS OF THE RESONANT CIRCUIT Consider the re.sonant circuit of Fig. 2. Suppose that at t = 0, the left- hand capacitor has a potential ro(0) and the right-hand capacitor has 1424 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 a potential 63(0) and that at ^ = 0 the current v through the inductance ( is zero. The network equation is dt ir-\-lf ir dt = 0. Now tV(0) = 0 and di,{0)/dt = [e.,(0) - c,{0)]/(. Let 2/(C = wo', then diM/dt = coo'C[e2(0) - e8(0)]/2. Using Laplace transforms, (p^ + Uo^)Ir{p) = piriO) + '■c dirjO) dt ' (40) Irip) = "^ [^2(0) - eM] -^ ■p- + wo- hence • (,^ r ^2(0) - ^3(0) . ^ %r\t) = (jOqC sni COol (41) and q{t) - f irif) dt = C- Jo eM - cM [1 — cos wnt]. If 27r/wn = 2r, i.e., r = Tr\/(C/2, which means that the duration of the switch closure is a half -period of the resonance of the tuned circuit, then ..,. tCIsM- eM] . ^t ir{t) = sni — , T Z T ( q{t) Ch(0) - ^3(0)] 1 — cos — T It is clear then that, during the period r, the charge transferred onto the 1 Ir(P) " ? ? coi In(P) + In(P) Fig. 9 — Resonant circuit excited b.y current sources 7„ and /,/ SWITCHED NETWORK FOR TIME MULTIPLEX SYSTEMS 1425 right-hand capacitor is ^(t) = C'[(?2(0) — f:i(0)] and as a result at time I = T the right-hand capacitor has a voltage CoCO) and the left-hand capacitor has a voltage fsCO). Considering now the network of Fig. 9, the ecjuation is dr C C Assuming all initial conditions* to be zero we get, /Xp)=^^^=M+A:W. (42) p2 -f coo- 2 Appendix II STUDY OF THE LIMITING CASE T -^ 0 We expect that if the sampling period T — > 0, which is equivalent to stating that the sampling freciuency w^ ^ ^ , then the inductance ^ -^ 0 and as a result the voltage e-i{t) will be infinitely close, at all times, to the voltage e-2{t). Thus, in the limit, everything happens as if the termi- nal pairs (2) of A^i and A^o were directly connected. In that case the gain of the system is 2Z(^) ^"^P'- as is easily seen by referring to the Thevenin equivalent circuit of A^i . Let us show that as T — > 0, (21) leads to the same result. First note that both Z12/0 and Z»Si go to zero at least as fast as l/p" for p -^ x . Hence the summations in (21) reduce to the term corresponding to 71 = 0. Therefore, „ / V C IZ12/0J *J1 rj C Ziolo^n^^l ^12 T 1 + 2C[ZSi]* T + 2CZS1 2Z "■ Appendix III ZEROTH approximation IN THE CASE WHERE A^i IS NOT IDENTICAL TO A^2 Let, for k = 1,2; Ck be the shunt capacitor at the terminal pair 2 of Nk , Zk{p) be the driving point impedance of Nk , and Zu''\p) be the transfer impedance of N'k • In the present case the capacitors Ci and C-i are in series in the resonant circuit of Fig. 2. It can be shown that the * Their contribution has been found in (40). 142G THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 charge exchanged during one-half period of the resonance is ,^^ k(0) - eMl ^1 -+- ^2 For the present case, (16) and (17) become 62(0 = lit) - / ^Vo(r)^l(^ - r) dr, J — 00 ^3(0 = f uMz.it - t) dr. J — GO Following the same procedure as before we are finally led to the block diagram of Fig. 10 whose output is given by E,{p) = [Zn''\p)h(p)]* ^^p^ S^(p)Z,S-\p) ^1 + C2 Appendix IV THE DERIVATION OF EQUATION (24) Considering the method used in Section IV to derive the zeroth ap- proximation, it is clear that during the switch closure the voltages e^it) and €^{1) vary sinusoidally, that is. lo 62(0 = 62(0) e^{t) = eM + 62(0) - 63(0) 62(0) - 63(0) 1 — cos — 1 — cos irt IMPULSE MODULATOR -12 «H 2C,C2 Si(p) Zi(p) + Z2(p) ,(2) -12 Fig. 10 — Zeroth approximation: modified bloclv diagram for the case where A^'i and A^2 are not identical. SWITCHED NETWORK FOR TIME MULTIPLEX SYSTEMS 1427 Thus, it always happens that for t = r/2, i.e., at the middle of switch closure time, 62(0 — es(t) = 0. Therefore if we consider the time function 62(0 ~ ^3(0 we have for all A:'s (-a>, ... 0, ••• + ^), 62 (kT + l)-es (jcT + ^) = 0. If, for simplicity of analysis, we assume that the switch is closed during the intervals -(r/2) + kT ^ t ^ +r/2 + kl\ then for all A-'s, 62(^7^) - e.ikT) = 0. Using (17), this condition implies that [V{p)]* - 2[Iro{p)Z{p)]* = 0. Now, remembering that irn{t) couvsists of a sequence of half sine waves whose shape is defined by So{t) (which is by definition identical to Si{t) except for an advance in time of t/2) it follows that 7ro(p) = B{p)So{p), where B{p) is the .^^-transform of the seciuence of impulses whose measure is eciual to the charge interchanged between A''i and A^2 at each switch closure. Since [B(p)Soip)Z(p)]* = Bip)[Soip)Z{p)]*, then j.(. ^ [Zn{p)h{p)\* ^^^ 2[So{p)Z{p)\*- From which it immediately follows that [Zr,ip)Up)]*So{p) Iroip) = 2[So{p)Z{p)y and ,,./!_ [Za(p)Up)]*Up)Zn(p) ^'° / V / 60 62 64 66 68 70 72 74 76 78 FREQUENCY IN MEGACYCLES PER SECOND 80 Fig. 1 — Over-all delaj^ distortion of a typical microwave repeater, TD-2 system. EXPERIMENTAL TRAXSVERSAL EQUALIZER FOR TD-2 1431 tioiis of delay slope equalizers. The characteristics of the 319A, B and C equalizers provided for this purpose are shown in Fig. 2. Each equalizer consists of two bridged-T all-pass sections. There is also some variation in bandwidth of the TD-2 repeaters, resulting in part from the fact that the waveguide filters used in the higher frequency radio channels are somewhat broader than those in the lower frequency channels. This ^'ariation in bandwidth results in delay distortion which has a parabolic shape with frequency. Use of a larger or smaller number of the basic 315A ec^ualizers corrects this. Over long circuits, small distortions in the gain shape of the TD-2 a 16 14 12 10 O o UJ I/) O tr u z 5 o r- UJ > 1- < _J UJ tr $ UJ a 6 4 2 0 -2 -4 -6 -8 -10 -12 -14 -16 -18 / ^ / ■ ^ \ / f s. N \ 3t9A / \ \, \ 319B Ik / \ \, \ i / 319C N \ / > \ / / V y / \ IN \^ / \ \ \, / r > V \ \ / \ N / f > \ > / \ / k \ 60 62 64 66 68 70 72 74 76 78 80 FREQUENCY IN MEGACYCLES PER SECOND Fig. 2 — Delaj- characteristics of 319 type equalizers. Combinations of these are used at main stations to equalize delay slope of the system. 1432 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 equipment produce a cumulative gain-frequency distortion which is noticeable in television circuits. Present practice is to correct for this by standard video equalizers after the FM signal has been demodulated to baseband. In connection with the experimental eciualizing program to be described, parabolic gain equalizers operating on the FM signal before demodulation were used. III. RESIDUAL DISTORTION After correction of the known shapes discussed above, there remains a certain residual gain and delay distortion which results from a random summation of many minor sources. The shape of this distortion is not predictable, but its statistics are known. Examination of typical delay versus frequency characteristics have shown that these may be reason- ably well approximated by six cosine terms: a 40-mc fundamental and the next five harmonics. Similar gain terms are needed. However, the gain and delay distortion, when examined within the 20-mc band of interest, do not have a minimum phase relationship. This is to be ex- pected because of the presence in the system of the delay eciualizers, which are non-minimum-phase networks, and of amplifiers with com- pression. The magnitude of the residual distortion is small enough so that trans- continental TD-2 circuits provide television and telephone transmission of commercial quality. Some effects, such as cross modulation, are sufficiently marginal so that improvement would be desirable. To deter- mine whether this could be achieved by improved gain and delay eciuali- zation, the development of an experimental adjustable equalizer was undertaken. The considerations outlined show that such an equalizer should approximate the desired characteristics with independent gain and delay terms of the harmonically related cosine type. Equalization to reduce cross modulation in telephone channels and differential phase in color television must be performed before demodulation of the FM signal to base band. The equalizer was, therefore, built to operate in the 60- to 80-mc IF band. IV. TRANSVERSAL EQUALIZER One method of obtaining independent control of the loss and delay characteristics of a network has been achieved in the transversal filter." Equalizers have been designed on this principle for the equalization of television circuits. ' This type of equalizer, referred to here as a trans- versal equalizer, provides a flexible means of synthesizing any loss char- EXPERIMENTAL TRANSVERSAL EQUALIZER FOR TI)-2 1433 at'teristic and aii}^ delay characteristic limited 011I3' by the number of harmonics that are provided and the range of each. Basically, the transversal eciualizer consists of a delay line with eciually spaced taps, with a means for independentl}^ controlling the amount of signal fed through each of the taps to a summing circuit, as shown schematically on Fig. 3. The input signal is fed into one end of the delay line which is terminated at the other end. The center tap is fed to the output and forms the main transmission path. The operation of the equalizer can best be described using the "time domain" analysis based on the theory of paired echos.^ Portions of the signal tapped off the "leading" or first half of the delay line will not be delayed as much as the main signal and will introduce leading "echos". Similarly, lagging echos can be obtained from the taps on the lagging or second half of the delay line. Combinations of both types of echos, either positive or negative as required, can be added to cancel out, to a first approximation, distortion present in the input signal. This analysis can also be carried out in the frequency domain. To obtain a family of cosine loss versus freciuency characteristics without any appreciable delay characteristic, equal leading and lagging echos of the same polarity are added to the main signal in the summing circuit. To obtain a corresponding family of cosine delay versus frequency characteristics without loss distortion, leading and lagging echos equal INPUT P L_^J OUTPUT Fig. 3 — Block schematic of transversal equalizer. 1434 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 in magnitude but of opposite polarity are added in the summing circuit to the main signal. To achieve a practical eciualizer for operation over the GO- to 80-mc band recjuires the following components: delay line or delay networks, means for tapping off small portions of the signal controlled both in amount and polarity, and a suitable summing circuit. V. DERIVATION OF THE EQUALIZER CIRCUIT A brief analysis of the operation of the equalizer will be given at this point as a basis for discussion of the method of tapping the signal and controlling the amplitude and polarity of the tapped portion. Fig. 3 shows the basic delay line PQ as well as the means used for producing the main signal and a single pair of leading and lagging echos. The tap labeled "o" in the center of the line produces the main signal. The tap "a", being closer to the input, produces a signal which leads the main signal by time t. The tap "5" produces a signal which lags the main signal by the same amount. The boxes "/va" and "/vb" control the ampli- tude and polarity of the leading and lagging signals which are to be com- bined with the main signal to produce one term of the desired equaliza- tion characteristic. It will be shown that these three signals will provide one cosine gain term and one cosine delay term, both having the same period, but being independently controllable as to amplitude and polarity. We will choose as our reference point for phase the main output sig- nal, eo = -E'c^"'. The output from tap "a" is then After passing through box "Ka", this becomes Similarly, Here the terms Ka and Kh are of the form K = is"" where a is the attentuation in nepers of the box K. Note that \K\ is less than unity, assuming the box represents a passive network. Combin- ing these two signals with the main signal, we have er = Co + e„ + e, = Ee''"[l + A^a^"'"^ + /Uf^^l- (1) EXPERIMENTAL TRANSVERSAL EQUALIZER FOR TD-2 1435 Now it will be shown that, by the adjustment of the two parameters Ka and A'fc , it is possible to realize independent control of a cosine gain term and a cosine delay term. Since, in general, Ka 9^ Kb , let us define Ka = Kg -\- Kp and Then Kr Substituting the trigonometric form: Bt = Ee'"''\\ + 2Kg cos ix>t + j 2Kp sin oif]. (2) (3) (4) Note that for Ka equal to Kb , the sine phase term is zero and that for Ka eciual to —Kb the cosine gain term is zero. Similarly, by proper pro- portioning of Ka and Kb , Kg and Kp may be assigned any desired values. If we normalize (3) by setting Co = Ee^"^' = 1, the expression in brackets can yield two vector diagrams which are useful in explaining the functioning of the eciualizer. To obtain the diagram shown in Fig. 4(a), we have set Kp = 0. We then have a unit vector, representing the main signal, a leading echo K„e~^"^, and a lagging echo KgE^"^. The en = i Knf er= 1 + 2KnCOSaJ7' (a) Kpf-J'^^ eo=i (b) Fig. 4 — Vector diagrams of paired echos. (a) Kqual eclios of same polarity produce magnitude change without phase change, (b) Equal echos of opposite pohirity produce a change in phase shift with a minor change in magnitude. 1436 THE BI<:LL system technical journal, NOVEMBER 1957 v^ector representing the leading echo rotates clockwise with respect to the main signal when the frecinency increases, whereas the vector repre- senting the lagging echo rotates counterclockwise by the same amount, and the resultant thus varies in magnitude but not in phase. The magni- tude of the resultant is given, for this case, by the first two terms in parentheses in (4). If, on the other hand, if we set Kg — 0, we have the three vectors shown in Fig. 4(b), identical with those in Fig. 4(a) except that the polarity of the lagging echo has been reversed. In this case, the two echos produce a resultant, Cp , which is in ciuadrature with the main signal. For small echos, Cr is thus shifted in phase from the main signal, with substantially no change in magnitude. The resultant in this case is given by the first and third terms in parentheses in (4). This gives a sinusoidal variation in the phase of the resultant. Since envelope delay is defined as rf/3/rfco, where (8 is the phase shift through the circuit in question, the sinusoidal phase ripple will be seen to yield, after differenti- ation, a cosine delay ripple. The period of the ripple can be seen from the above expressions to depend on r, the delay between the leading and the main tap, and be- tween the main tap and the lagging tap. Other pairs of echos, each pair symmetrically disposed about the main tap, but with different values for T, will give transmission ripples of different periods. To provide a series of orthogonal terms, the values of r must be integral multiples of a common value, normally that required to produce 180° phase shift across the band of interest. A complete ecjualizer must, of course, sum up the various echos and the main signal, taking care that the delay between the tap and the summing point is the same for each echo and the main signal, that parasitic losses such as losses in cabling are the same for each path through the equalizer, and that any frequency characteristic in the tap- ping device or other parts of the ec^ualizer is properly eciualized out so that the over-all equalizer introduces a minimum of distortion of its own. VI. directional coupler To reduce incidental distortion, it is desirable that the device used to tap the delay line for the main signal and the echos introduce substan- tially no discontinuity in the main line. The device chosen for this pur- pose is a directional coupler. It is shown symbolically in Fig. 5. The di- rectional coupler is a four port device having properties similar to a jij EXPERIMEXTAL TKAXSVERSAL EQUALIZER FOR TD-2 1437 hybrid coil. Power entering one port divides (not necessarily equally) between two other ports, but none of it reaches the fourth, or conjugate port. In Fig. 5, the power entering at 1 divides between 2 and 4, that entering at 2 divides between 1 and 3, that entering at 3 divides between 2 and 4, and that entering at 4 divides between 1 and 3. Directional couplers inherently provide an impedance match at all four ports. Thus, such a coupler sets up no reflections in the main line. Its insertion loss in this line may be kept small by having nearly all the power enter- ing at 1 come out at 2; then only a small fraction is diverted to 4. Co- axial directional couplers have been discussed in the literature ' ' and will not be dealt with in detail here. INPUT DIRECTIONAL COUPLER /9Ef-i COit-K^) E€ ja>(t+JJ Q -o- > Fig. 5 — Diagram of directional coupler. Input .signal divides between Ports 2 and 4 with no output at Port 3. Termination Z at Port 4 reflects some signal to Port 3, proportional to the reflection coefficient, p. The coupler used here (J68333C) is one originally developed to measure reflections on IF transmission lines in the TD-2 system. The directivity of a coupler is defined as the coupling loss between main line and branch line in the undesired direction less the loss in the desired direction (loss from 1 to 3 less the loss from 1 to 4, for example). In the J68333C coupler, the directivity can be adjusted to exceed 45 db over the band of interest. This can be done by adjusting two screws, shown on model in Fig. 6, to obtaiit the optimimi spacing between the coupling elements. The loss between the main line and the branch line in the desired direction is about 23 db at mid-band (70 mc), and decreases 6 db per octave with increasing freciuency. The loss along one of the coupled lines (1 to 2 or 3 to 4) is very small. Use has been made of the directional properties of the coupler in pro- viding a simple means of controlling the amplitude and polarity of the tapped signal. Referring to Fig. 5, and keeping in mind the properties of the coupler, it will be noted that a small portion of the input signal appears at Port 4 of the coupler, but none at Port 3. If the impedance Z 1438 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 Fig. 6 — J-6S333C directional coupler with cover plate removed to show cou- pling elements. Optimum spacing for maximum directivitj'can be obtained b}' ad- justing screws. matches the impedance seen looking into Port 4, all of the small signal will be absorbed in Z. If Z is an adjustable resistance, then a controllable portion of the small signal can be reflected back into Port 4, whence most of it will come out Port 3. A small portion of the reflected signal will emerge at Port 1, headed toward the input. This portion will be attenu- ated b}' twice the coupling loss between the main and the branch line plus the return loss of the reflection at Z, and can be made negligible. The interactions caused by the reflected signal on the main delay line entering previous couplers are also reduced by twice the coupler loss. ii EXPERIMENTAL TRANSVERSAL EQUALIZER FOR TD-2 1439 The coupler in Fig. 5 represents any one of the taps on the line PQ in Fig. 3. The signal emerging from Port 4 can be written as E£^"''^^^\ where 5 is a time delay dependent on the location of the tap on the line PQ. The signal emerging from Port 3 is then p£'f:"'"""'^*\ where p is the voltage reflection coefficient at Z, and is given by _ R — Ra ^ ~ R + R,- Here R is the value of resistance used to provide the impedance Z, and Rq is the impedance seen looking into Port 4. An examination of the signal from Port 3 shows that it is the same as the signals Ca or Cb in Fig. 3, with the reflection coefficient p substituted for variable Ka or Kh in Fig. 3. Thus, it is seen that we may use the reflection at Z, variable by controlling the value of /?, to perform the function of the box K in Fig. 3. Neglecting parasitic losses we may then write: jjr R — Ro K = p = R -\- Ro and ^ = ^0 ^-^. (5) This gives us the value of R to use for any desired value of K for any of the taps which derive echos, assuming the summing circuit has equal attenuation in all paths. In the case of the main central tap, the signal from Port 4 of the coupler is seen to be the same as the main signal eo in Fig. 3, and is used as such directly. VII. METHOD OF ADJUSTMENT The detailed design of a manually adjustable eciualizer is materially influenced by the method to be used in the field for determining the setting of its controls. The present equalizer with 14 independent con- trols would present a complex problem of field adjustment unless special procedures were developed to simplify the adjustment. To adjust the equalizer, the radio circuit being equalized must be taken out of com- mercial service, so any reasonable measures to simplify the adjustment or reduce the time reciuired are justified. Two methods appeared to be feasible at the time the de\elupment was started. One would be to use existing gain and delay sweep test circuits. These present a visual display of the circuit gain or delay dis- 1440 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 tortion versus frequency. These displays are not available simultane- ously with present equipment. To adjust the equalizer controls using this equipment, it must be possible to adjust either gain or delay without affecting the other. Thus, all the gain terms can be adjusted in suc- cession using the gain display. Then the procedure is repeated with the delaj^ display, adjusting the delay terms. Since a combination of leading and lagging echos in equal amounts is reciuired for this procedure, an arrangement of the controls to facilitate this is required. One way to achieve this is to use stepped rheostats with the steps proportioned to introduce ecjual amplitude changes in the echo voltage. With this ar- rangement, gain changes can be introduced by rotating the two switches corresponding to a pair of echos in the same direction an equal number of steps. Delay changes can be obtained by similar rotation in opposite directions. A further refinement consisting of mechanically ganging the controls is possible but this was not done on these experimental models. The second method of adjustment would be to develop a special test set similar to the one developed for the L3 system.^ This could produce a meter reading proportional to the amount of gain and delay distortion present in the circuit. Successive controls could then be adjusted for min- imum meter readings. Experience with the L3 system cosine ecjualizers has shown the desirability of continuously adjustable controls for such a method. To test both methods under field-trial conditions, two versions of the eciualizer were built — one with stepped rheostats and one with con- tinuously adjustable rheostats. VIII. COAXIAL RHEOSTAT Since there were no available continuously adjustable rheostats sat- isfactory for operation at 70 mc, a special rheostat was developed for FRAME r// '/////////////////////////////// : '/////////////////A TX SLEEVE I' ' ■////'/////////////////. '/7/////////////////////.'. '///A Fig. 7 — Schematic of coaxial rheostat. Moveable sleeve changes position of inner contacts touching ceramic rod, changing resistance. Fixed outer contacts maintain constant path length to frame. EXPERIMENTAL TRANSVERSAL EQUALIZER FOR TD-2 1441 Jiiiii iiiiiJwiiPiWiWWWillllilllWiili Pi*^ Fig. 8 — Model of coaxial rheostat with cover removed. this purpose. It employ's a ceramic rod, | inch in diameter, coated with a pyrolytic carbon film, asa centermember of a coaxial structure. A metal sleeve which is moved longitudinally by a lead screw carries sliding con- tacts along the rod. These parts are supported inside a rectangular hous- ing which forms the outer conductor. A second set of fixed contacts at- tached to the rectangular housing makes contact with the sleeve. This arrangement maintains a substantially constant length of path from the input end of the rod to the housing, which forms the ground, inde- pendent of the position of the sleeve. The schematic of the rheostat is shown in Fig. 7. A model of the rheostat is shown in Fig. 8. To obtain uniform adjustment of amplitude in decibels, a resistance that varies exponentially with length or with rotation of the lead screw is required. Such a resistance characteristic is realized by varying the thickness of the carbon film along the rod. This produced a total re- sistance which varied from 20 ohms at the low setting to about 350 ohms at the high resistance setting. .After an initial wearing-in period of 1,000 cycles of moving the contacts over their full travel, the resist- ance was changed less than 1 per cent by another 9,000 cycles. This amount of wear is estimated to be greater than that encountered in twenty years of normal operation. The housing and rod were dimensioned to form a 7o-ohm transmission line. Measurements of the impedance at the input connector, made at frequencies from (iO to 80 mc, showed that this impedance can be approx- imated by a resistor terminating 6.7 cm of 7o-ohm coaxial cable. For the 7o-ohm setting, the reflection coefficient of the rheostat is less than 2 per cent across this frequency band. 1442 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 One model of the equalizer was completely equipped with these rheo- stats. By allowing for the equivalent length of cable within the rheostat, an essentially pure resistive termination was obtained. IX. OTHER COMPONENTS Other components reciuired for the equalizer included stepped rheo- stats, delay line or delay networks, a suitable summing network, and a loss equalizer. The stepped-switch rheostats were made from standard switch parts with eleven positions. Deposited carbon resistors, 205D, were used for the steps. The mid-position corresponded to the circuit impedance level, 75 ohms. The other steps were arranged to provide equal increments of echo amplitude measured in decibels. With careful control of lead lengths, special shielding and a coaxial cable connector, satisfactory control of the return loss of this rheostat was obtained. Resistance pads were added to the switch assemblies associated with each of the echo terms. The loss of each pad was determined so that the corresponding term would have the desired maximum amplitude. In addition, the losses of the pads associated with the leading echo terms were increased to compensate for the midband loss of the delay line be- tween the leading coupler and the corresponding lagging coupler. This insured that the two echos would have equal amplitudes. The delay required between taps in the delay line is 0.025 microsecond, corresponding to a change in phase shift of 180° from 60 to 80 mc. In order for the equalizer cosine characteristics to have maxima at the band edges, the total phase shift at 60 and 80 mc must be successive integral multiples of 180°. Since the phase shift of coaxial patch cable is closely linear and proportional to length, it could be used for the delay line. Lumped-element delay networks consisting of two or more all-pass sec- tions are a feasible alternative and would reduce the over-all size and weight. In view of the additional development effort involved to produce these and the experimental nature of this equalizer, it was decided to use coaxial patch cord. The type selected, 728A cable, has a polyethylene dielectric and is tested during production for return loss in the 50- to 95- mc band. The length reciuired for each section is about 15.6 feet. This much cable has a loss of about 0.3 db at 70 mc. It was originally proposed to use a series of directional couplers for summing the echo voltages with the main signal. This would provide additional isolation between terms. However, tests on a preliminary model indicated this isolation was not required in this application. In- EXPERIMENTAL TRANSVERSAL EQUALIZER FOR TD-2 1443 yjumuunii uiM Fig. 9. — Summing network with cover removed. Main signal input is at right, echo signal inputs on top, and output is at left.. stead, a resistance summing network was developed using deposited carbon resistors. An L-pad is used in each echo path and a series resistor is added to the main path to preserve the 75-ohin impedance level, intro- ducing a main path loss of about 0.4 db per tap. A model with cover removed is shown on Fig. 9. The main signal is introduced at one end of the structure, the echo voltages are connected along the side and the sum is taken off the other end. The return loss measured at any of the connectors with the others terminated was of the order of 40 db over the 60- to 80-mc band. An attentuation equalizer is required to make the transmission through the main path constant. This path consists of about 108 feet of 728 cable, the straight -through loss of six couplers, and the coupling loss of the main coupler. The net distortion over the band is a slope of about 1.5 db and is corrected for by a constant resistance ec^ualizer. Return losses exceeding 34 db were obtained over the frequency band. X. ASSEMBLY All the components were mounted on the rear of a standard i-elay rack panel. The rheostat controls are arranged on the front of the panel as shown on Fig. 10. This is a front view of the completed eciualizer. The controls for the leading echo terms are on the left and for the lagging echo terms on the right. They are arranged vertically in numerical order with the first terms (shortest time separation from the main signal) at the top. The rear of the panel is shown on Fig. 11. The directional couplers are mounted horizontally in two vertical columns. The cables forming the delay line sections are terminated in a plug and a jack and these are inserted in successive couplers, from the second port of one to the first port of the next. The third port of each coupler is connected through a short cable to its corresponding rheostat assembly. The fourth port of each coupler is connected to the summing network. An exception is 1444 THE BELL SYSTEM TECHXICAL JOURNAL, NOVEMBER 1957 Fig. 10 — Front view of equalizer, showing rheostat controls. Leading echo controls are on left, lagging ones on right. First harmonic controls are at top. EXPERIMENTAL TRANSVERSAL EQUALIZER FOR TD-2 1445 the middle coupler, the fourth port of which is terminated in 75 ohms and the third port connected to the summing network. The envelope delay in the cables connecting each coupler to the rheo- stat and to the summing network appears as delay for the particular echo path. Since these delays are not negligible compared to the 25 milli- microsecond delay between echos, the cable lengths were controlled so that the same amount of additional delay was introduced into each path including the main path. XI. ADJUSTMENT AND PERFORMANCE After the eciualizer was assembled, the length of each of the cables connecting the couplers to the summing network was adjusted so that Fig. 11 — Equalizer with cover removed. Calile.s wound out.-^ide frame are the delay line sections. Summing network and directional couplers are in center. Rheo- stat cases are mounted on panel with coaxial connection in rear. 1446 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 the zeros of the cosine shape occurred at the proper freciuencies, as ob- served when the associated rheostat was set at maximum and minimum positions, with all other rheostats set at midrange, or no-echo, setting. Some reflections were present in the main signal path as evidenced by ripples in the gain characteristic when all rheostats were set at midrange, corresponding to the "flat" loss condition. These reflections were reduced to some extent by minor readjustments of the balancing screws on the directional couplers. The over-all flat gain characteristic obtained after these adjustments is shown on Fig. 12. This figure also shows the seven gain characteristics obtained when each pair of rheostats is set for maximum gain. The markers on the refer- ence trace correspond to the band edges. A sharp gain bump resulting M 1.0 DB _1 P 1 60 MC 80MC FLAT GAIN jams. /I ._m FIRST TERM f, = 40 MC IF /nnnm mm SECOND TERM f^ = 20 MC THIRD TERM f,= 13.33MC ^■■k ^IBk ^BHk ^Hflk flffiiiin mmxm iBmiiBi pnRii mmmw wskkiw mmim mmism "^mKF HHV ^^ 375 ^ 5 < / \ / \ 475 725 1125 1875 FREQUENCY IM CYCLES PER SECOND Fig. 2 — Double sideband signal with auxiliary start channel. Marking consists of maximum carrier amplitude and spacing is zero carrier amplitude. The pulses are shaped both at the transmitting end and at the receiver before sampling. The earlier prototype system as described by Horton and Vaughan was tested over a variety of telephone facilities (not including Nl carrier) running up to over 12,000 miles in length and found to be quite rugged. For reasons which are to be discussed later, the use of these systems over compandored circuits presents certain extra transmission problems regarding noise and level changes. 2.4 Voice Frequency (VF) Carrier Telegraph The opposite extreme to the use of the telephone facility as a single band, to carry short duration pulses, is to subdivide the band into a large number of subchannels, each using longer duration pulses. As already noted, this has advantages against impulse noise, and also delay distortion. There is available for this use the VF telegraph system.^ In an AIM form (40C1) this subdivides the space into 18 telegraph channels, which can each carry 100 words per minute (or 74 bits per second). A fre- (luency shift form (48A1) is available, to give 17 channels, each to carr}^ 74 bits per second. The 18 channels use a band of 200 to 3,200 cycles in the telephone facility, and the lowest channel permits only a lower word speed. The 17 channels occupy the band from 350 to 3,200 cycles. It has been mentioned that the telephone channels which provide the most serious problem for data transmission are those using compan- dors. The untreated Nl carrier is a principal example of such. Further, the type of circuits which use compandors are apt to be placed in plant which is relatively exposed to impulsive noise. The principal interest in the telegraph channels, therefore, is to exam- 14G4 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 ine how they fare in appHcation over untreated Nl carrier. There have been some studies of this point. The general conclusion, to be elaborated below, is that although the frequency subdivision (and also the fre- quency shift) helps against impulsive noise, fewer telegraph channels may be used than over good non-compandored facilities; and at best, the transmission is accompanied by more distortion than expected in a telegraph link of the highest grade. However, a serious possibility for data transmission is indicated. 2.4.1 Telegraph Tests on Nl Carrier Tests on this subject have been carried out by S. I. Cory, J. M. Fraser and others and reported in unpublished memoranda. Before presenting the results of the tests, some background is necessary on the terms in which the results are reported. The performance is usually evaluated in tests of this kind in terms of a "maximum checkable" telegraph distortion over a short time (about 5 minutes). The "telegraph distortion" represents the displacement from correct timing, of received signal transitions, after the initial mark-to-space transition in the "start" element. These displacements are measured in percentages of the signal element duration. By "maxi- mum checkable" distortion is meant the maximum such displacement that is consistently reproduced in repetitions of the short testing period. This is somewhat larger than the root-mean -square distortion. A larger displacement is, of course, obtainable over a longer testing period. Although this measure of performance has had long use in the telegraph art, other measures are perhaps more readily grasped by and probably of more value to the data transmission engineer. Such a measure, for example, is the error rate. The error rate may be estimated through the use of the telegraph transmission coefficient.^ This is a figure which has been designed by telegraph engineers to indicate the performance of a telegraph circuit, particularly when it is made up of several sections. It is more or less proportional to the square of the distortion, and has the property that, when carefully chosen, it can be added for circuits connected in tandem. A small coefficient thus characterizes good transmission, and correspond- ingly, a large coefficient characterizes poor transmission. The correlation between peak distortion over 5-minute intervals and error rate, through the telegraph transmission coefficient, is indicated in Reference 8 and Table II. It is to be understood that the correlation is only a rough one. Particularly at the two extreme ends of the scale, the entries in the table can serve only as a general guide to the perform- ance, and the specific numbers are not to be taken too literally. PRIVATE LINE DATA TRANSMISSION 1465 Table II — Characterization of Telegraph Distortion and AND Error Rates by Telegraph Transmission Coefficient Distortion Errors Transmission Coefficient RMS 5 min. peak 1 in « characters 1 in >n bits in) («») 13.9 30 30 40 2.9 X 102 12.6 27 25 87 6.2 X 102 11.2 24 20 2.5 X 102 1.8 X 10^ 9.8 21 15 1.5 X 10^ 1.1 X 10^ 8.0 17 10 4.4 X 10^ 3.2 X 10^ 5.6 12 5 10^ 7.4 X 109 4.3 9 3 10'2 7.4 X 10'2 2.5 5 1 — — A very brief summary of some of the experiments in the use of VF telegraph over untreated N carrier is given in Table III. This portion of the results covers Nl circuits with compandors which have slightly more noise than the objective which is set for the telephone use of such circuits. The noise was 28 dba at the zero transmission level point, as against an objective of 26 dba at that point. It is noted in Section 3.3.2 that the measurement of noise in these terms is not altogether reliable in the evaluation of its effects on transmission systems that use pulses. Thus, these experiments must be considered as giving only a general indication of the situation. Table III — Summary of Telegraph Peformance over Noisy N-I Carrier Link 1. Number of channels. . 2. Frequency space used . 3. Words per minute .... 4. Total bits per second. 40C1 (AM) 6 1020 75 342 43 Al (FS) 75 684 12 2040 cycles 100 888 Average Channel 5. Peak distortion 6. Estimated Transmission coeff . . 7. Estimated errors, 1 in 16 9 10« 8 2.5 10'^ 18 per cent 11.5 10^ bits Worst Channel 8. Peak distortion 25 21 1.5 X 103 17 10 4 X 105 22 per cent 17 5 X 103 bits 9. Estimated transmission coeff.. . 10. Estimated errors, 1 in 14()6 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 The tabulation is first given for an average channel. The performance of the worst channel has, however, also been included to give an indica- tion of its contribution to over-all operation. Many of the Nl carrier telephone circuits in the plant show lower noise than the objective, and to this extent Table III is somewhat pessimistic. Also some of the tests have shown, particularly for AM, that the performance is somewhat improved by removing the com- pandors. Thus, allowing for both points, better performance can be expected from the average Nl circuit (less than 200 miles) in the plant. The transmission coefficient of 11.5 listed for Item 6 at 100 words per minute might go down to say 9. At 75 words per minute with FS or AM, it might not be over 4.5. It is clear, of course, that with further modifications of the Nl channels, such as to reduce noise exposures, better performance could be obtained. The broad conclusions that can be derived from these considerations are: 1. The subdivision of the frec}uency band into telegraph channels, and the use of FS, permit a workable system to be operated over a compandored facility like the Nl carrier without modification. This occurs even when the latter has noise up to and a little over the tele- phone objective. 2. This workable system under such noisy conditions transmits up to some 350 bits per second with AM, and some 800 bits per second with FS. It is accomplished with an error rate of the order that has been implied for data transmission, even in the worst channel. 3. There is a relatively wide range of performance of the system over different Nl circuits, and the average performance is sensibly better than that under the limiting conditions which have been considered. 2.4.2 Distribution of Signal in Allocated Bandwidth A more extensive discussion of the use of bandwidth is given in Sec- tion 3.1, below. However, a few specific points are appropriate here on the band use in telegraph channels. The spectrum of the original voice frequency telegraph system, based Table IV — Use of Frequency Spectrum in Telegraph Channel AM FS 1. Channel spacing 2. Nominal effective bands 3. Roll -off band (both sides) 4. FM swing 5. Guard band (both sides) 170 74 37 0 59 170 cycles 74 26 70 0 PRIVATE LIXE DATA TKAXSMISSIOX 14G7 ^- 170 'Xy 2 X NOMINAL EFFECTIVE BAND 74 -Aj ROLL- OFF 18.5 '~0 \ 170'\' ■*\ NOMINAL EFFECTIVE BAND X 37 '\j FM SWING _ ♦ 70Oj ROLL- I OFF 130) FREQUENCY ^-*> (a) AM (b)Fs Fig. 3 — Utilization of telegraph channels. on 170 cycles between carriers, was conservatively developed for the 60 word per minute speed of the time. The 100 word per minute speed has used up some of this conservatism. The use of frequency shift in the same channels has, however, used up the spectrum space even more. An outline of the band allowances is given in Table IV, and illustrated in Fig. 3. Item 2 of the table is based on the 100 word per minute speed, using double sideband. On this basis, the number is equal to the num- ber of bits per second. This is the minimum double sideband over which that number of bits can be transmitted, according to the Xycjuist theory. Each such sideband is sometimes called a "nominal effective band." In practice various allowances are necessary over this minimum. In the first place a roll-off is necessary because filters are not infinitely sharp, and in addition the nature of the modulation itself forms a roll- off. Roll-off also leads to a signal which is more free of overshoots and generally "cleaner" than when a sharp cutoff is used. Item 3 and Fig. 3(a) and (b) show an allowance for roll-off. For the AM case this amounts to half the nominal effective band. For the FS case there is not quite that much space available. For the FS signal it is necessar}' to allow for the frecjuency swing as Item 4. For the 43A1 system this amounts to 70 cycles. In Fig. 3(b) the spectrum includes the region comprised by the FM swing, and up- per and lower sidebands. The upper and lower sidebands as formed by the modulation of a random signal are shown extending respectively above and below the extremities of the swing (instead of only above and below a central carrier, as they would with AM). A final allowance in Item 5 is a "guard band." This is taken to mean a region in which the signal energy is negligible, but at the same time 1468 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 a region in which no appreciable interference is tolerated from the ad- jacent band. The allowance for this is generous in the AM case. In the FS case the roll-off band of Item 3 tends to use up all the space not employed by the nominal effective band and the swing, and nothing is indicated as left for guard band. This is illustrated in Fig. 3(b) by the extremities of the roll-off band reaching the extremities of the 170-cycle spacing. It is to be recognized that the illustrations are diagrammatic. However, the extremities mentioned measure the bands occupied by power from random signal transitions between marking and spacing (as distinguished from mere mark-space reversals), analogous to the bands occupied by power from AM signal transitions. Comparison of Figs. 3(a) and 3(b) suggests how modulated signal components of signifi- cant intensity are displaced farther from the edges of the channel with FS than with AM. 36 32 28 K 24 z UJ U UJ 20 z 1,6 cc o I- ° 12 / / / If 1 / / / 1 II ' 11 FS, DIODE 1 MODULATOR ' /J ' 1 1 1 1 j / / / / , 1 1 1 1 /b) ^FS, RELAY / 1 / 1 1 r / 7 .^r^ / ^ /^ (A) , RELAY . — ^ 60 80 100 120 140 160 SPEED IN WORDS PER MINUTE 180 Fig. 4 — Experimental relation between telegraph distortion and speed, with fixed channel filters (after Jones and Pfleger'). PRIVATE LINE DATA TRANSMISSION 1469 The conclusion is reached that there is hardly any excess conservatism in the 43A1 system. Some confirmation of this is indicated in a paper by Jones and Pfleger.^ Fig. 4 reproduces some curves presented in that paper. The curve at (B) (from Fig. 5 of that paper) shows that the FS telegraph rises rapidly in distortion above the 100 word/min speed. The curve at (A) (taken from the same Fig. 5) for level-compensated AM shows a substantially broader and somewhat lower curve in this region. From curve (C) (taken from Fig. 3 of the paper) for diode modulated signals, it is seen that the sharp rise in distortion for FS is even more accentuated than for the relay modulator. This indicates how much more characteristic distortion FS exhibits than AM because of the sharper roll-off of its signal bands within the confines of the same 170- cycle channel spacings. Of course, as the word speed is raised beyond the practically usable values, either type of modulation leads to so much power in the filter cutoff regions that the characteristic distortions be- come more or less indistinguishable. 2.5 "Polytonic" System This is a frequency discrimination system experimentally proposed for toll and local signaling.^ It works on 5 channels at speeds of 100 and 300 decimal digits per second (or the equivalent of some 330 to slightly under 1,000 bits per second). It has some similarities to an earlier multi- frequency system,'" but is faster. The distinguishing characteristic of the polytonic system lies in the mathematical theory which has been followed to reduce interchannel interference. This analysis makes use of the theory of orthogonal func- tions, and is similar to that used in the computation of Fourier com- ponents. The mathematical analysis leads to an ideal receiver design for minimum interchannel interference. The ideal detector in this receiver closely resembles the conventional homodyne detector. The detector actually UvSed, however, represents a practical simplification of the latter. A complete description cannot be given here, but it may be noted that the theory leads to a need for synchronization of the signal elements in the five channels, and to the setting of an exact timing instant for the sampling of the received wave to obtain minimum inter- channel interference. The indication for this instant is obtained from the use of a sharp wave-front pulse in the marking channels. Tests with the 100 decimal digit per second system (100 decimal digits normally correspond to 332 binary digits) indicated that it gave 1470 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 good operation'' over toll circuits of comparatively limited length (350 miles for four-wire voice frequency, 1,900 miles for K carrier). The higher speed system was designed only for local plant. It is clear that this system has too low a bit rate for the application contemplated, even in the faster form. It is also not generally adaptable to the variety of circuit lengths which are expected to be encountered. III. UTILIZATION OF THE TELEPHONE CHANNEL The discussion herewith covers a broad examination of some major characteristics of telephone communications facilities, to evaluate their bearing on the choice of a system for the data transmission service outlined before. It is of course clear that different conclusions might be reached for other types of service. The first item is an outline review of the different types of message telephone facilities in the plant. This is followed by an analysis of the different possibilities in the use of the frequency spectrum, of noise, and of delay distortion, in the application of the data signals. 3.1 Telephone Facilities There is a rather wide variety of facilities to be found in the tele- phone plant, to be examined with respect to the factors that are ger- mane to the present question. The first of these factors is the frequency bandwidth capability of the facility. For message-type voice circuits, this is generally character- ized as being three kilocycles (with the exception of "emergency banks," which are substantially narrower, and are not to be considered as useable for data transmission).^^ However, some of the telephone circuits in the plant, aside from the emergency banks, are also somewhat nar- rower than 3-kc, and in any case, not all the band is effectively usable for data transmission. As will be seen, the net a^^aiIable band is, in practice, about half of the 3kc. Part of the reason that not all of the frequency band is effectively usable is that the circuit shows delay distortion. This tends to become large at both the lower and the upper edges of the band. Some details of the delay correction are discussed further below. Another impairing factor in telephone facilities is the nonlinear dis- tortion encountered. In voice frequency facilities this comes from ampli- fiers and loading coils, and increases progressively with circuit length. In carrier facilities the nonlinear distortion arises almost exclusivelv at PRIVATE LINE DATA TRANSMISSION 1471 carrier terminals, in the part of the circuit where the signal is at voice frecjuency. In such a case, the distortion increases with the number of times in the telephone facility that the signal is modulated down to voice frequency. Second order nonlinear distortion tends to develop modulation products in the lower portion of the transmission band which are a source of potential interference wdth the signal. Another impairment encountered in carrier telephone channels is a slight frequency shift; that is, a 1,000 cycle input may appear at the output, say at 998 cycles. This occurs because modulator and demodula- tor frequencies are not identical. With independent oscillators on recent systems this shift may amount to some two cycles. With older systems it can run from 5 to 10 times as much. The effects of this shift are dis- cussed below. The frequency shift may be avoided by working double or vestigial sideband and using an envelope detector, or in some carrier systems by locking the oscillators in a constant frequency network. This locking may or may not result in close phase synchronization of the carriers, depending on the method used to lock and the particular carrier system involved. Still another factor is the use, or not, of "compandors." A compandor compresses the range of speech volume in the impressed line signal and correspondingly expands this range at the receiver. This raises the line signal level during periods of low speech power, and lowers it during periods of high speech power without, in principle, affecting the final received level. The effect is to reduce the final noise in periods of low speech power, and increase it during periods of high speech power. A listener is less perceptive to the noise during high speech power levels than low. By this means, it has been found that the telephone circuit can be engineered to some 23 db more noise (and also crosstalk and simi- lar forms of interference) than it can without the use of a compandor. In the case of data signals, however, the influence of noise in causing error is not very much different whether the signal is marking or spac- ing. Thus, there is no "compandor advantage"* (indeed there is a cer- tain disadvantage as pointed out earlier), and facilities that have been engineered to be entirely satisfactory for voice transmission are effec- tively some 23 db more noisy for data transmission. As a practical mat- ter it appears desirable to remove compandors from circuits used ex- clusively for data. A short listing is presented here of the various types of message facili- * Perhaps a simpler way to think of it is that all possible "compandor advan- tage" has already been obtained in a data system by using the best combination of amplitudes for mark, space, start, etc. 1472 THE BELL SYSTEM TECHXIC'AL JOUK.VAL, XOVEMBER 1957 ties most frequently found in the telephone plant, and some comments are made on each. 3.1.1 Voice Frequency Circuits There is a variety of open-wire facilities of this type. They are mostly short, and two-wire. Thus, repeaters can to advantage be turned one-way for data service. Delay correction is discussed later. Voice frequency cable facilities over more than a very short distance are loaded. This gives appreciable delay distortion. The loading used is indicated by a letter denoting the spacing, followed by a number denoting the loading coil inductance. Thus "H-44" means G,000-foot spacing, of 44-millihenry coils, and "B-88", 3,000-foot spacing of 88- millihenry coils. Conductor capacities range from 0.62 microfarads per mile for toll circuits, to 0.82 microfarads per mile or sometimes even higher for local circuits. This affects the delay distortion. 3.1.2 Type-C Carrier Circuits^^ This is an open-wire three-channel system operating at different frequencies in opposite directions, over the same pair. Historically there has been a variety of C systems developed, but only the C-5 system exists in any extensive quantity. The upper frequency cutoff in the voice channel is well under 3 kc. The delay distortion varies widely with the specific channel and direction of transmission. There is a variety of channel frequency allocations, and the distortion varies with this also. The delay distortion over some channels increases rapidly above 2,400 cycles. The frequency shift discussed before may be as much as ±20 cycles. 3.1.3 Type-N Carrier Circuits^ This is a short-haul twelve-channel system for use over cables. Be- cause of its economy it has been extensively introduced. Its principal characteristic, in the application of data circuits, is that it uses com- pandors. It therefore presents a noise problem. The delay distortion, introduced almost exclusively by the terminals is not excessive, and depends very little upon circuit length between the terminals. The N system uses double sideband transmission, and therefore exhibits no frequency shift between input and output signals. , 3.1.4 Broadband Carrier Systems Using A Channel Banks^'" There is a variety of carrier systems designed for paired cable, coaxial cable, open wire, and radio, that use a standard grouping of twelve channels with associated filters, known as an "A channel bank." The delay distortion in these associated filters constitutes nearly all of the distortion measurable over the complete system. These are single side- band systems, and unless the local modulator and demodulator carrier PRIVATE LINE DATA TKANSMISSION 1473 supplies are locked in a constant frequency network, frequency shifts of some ±2 cycles may be expected between input and output. For paired cables, these are known as Kl andK2 systems. For coaxial, they are LI and L3, for open-wire, J, and for microwave radio, TD-2. 3.1.5 Other Broadband Carrier Systems An 0 carrier system has been developed for open wire, and combina- tions of it are used with N for open-wire and carrier. These are com- pandored systems. 3.2 Use of Bandwidth This section examines the more important factors which affect the choice of how the available bandwidth of a facility is to be used, either in one band or a subdivided band. 3.2.1 Baseband Transmission This is the simplest type of transmission. It is used in telegraph loops and other short distance telegraph transmission. A mark is indicated by placing marking voltage across the wire line, and a space by placing spacing voltage. In the simplest systems the latter is zero. In "polar" systems it is the negative of marking voltage. The frequency spectrum of the signal runs down to and includes dc, as illustrated by the solid lines in (a) of Fig. 5. With many transmission facilities it is difficult or impossible to trans- mit the dc; i.e., the circuit cuts off as is illustrated by the dotted lines. In such cases it is impossible to distinguish between a permanent mark and a permanent space. Extra pulses can, however, be added to the signal to insure that marks or spaces are not permanent, but are relieved by the opposite signal in some maximum interval of time. In such cases the received signals can be clamped on mark or space signals and the opposite condition can be readily distinguished. This is sometimes called "dc restoration," and strictly speaking the system ceases to use baseband transmission. It may be designated as "modified baseband transmission." Methods other than clamping have been suggested for dc restoration. Reverse pulses can be systematically inserted after each mark or space pulse, according to various patterns.'^ Two suggested are "dipulse" and "dicode" pulses. Such signals approach carrier signals, which are dis- cussed below. The principal weakness of baseband transmission appears when it is sent over C carrier or other single sideband telephone facilities, where the recovered signal may vary in frequency from that sent. This causes a distortion of the received pulse which makes it difficult to recognize. 1474 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 An analysis of this point is given in Appendix I. It is concluded that while there may be long range possibilities in baseband transmission, it requires more study, and it will not be considered further in this paper. 3.2.2 AM Carrier Transmission The simplest of this type is double sideband transmission, as illus- trated by the full line of Fig. 5(b). A comparison of the susceptibility to noise of this arrangement, with that of baseband transmission, is considered in the next section. A further consideration required is susceptibility to nonlinearity in the facility. Second order modulation leads among other things to a recti- fication of the signal back to baseband. This is indicated by the dotted lines in Fig. 5(b). After such rectification of the signal by the facility, it is impossible to separate any overlapping portions of the signal between the baseband and lower sideband. Some o^'erlap is shown. This inter- ference was first considered in telephotography^' and is known as "Ken- dall effect." The possibility of Kendall effect may be eliminated insofar as second order modulation is concerned by mo^'ing the carrier frequency high LJJ a D _l Q- 5 < (b) A ■-/--. \ i (c) y I \ \ / 1 X NOMINAL EFFECTIVE BAND (d) GUARD BAND -^ SWING l«— FREQUENCY — ROLL-OFF Fig. 5 — Spectra of signals with various modulations. PRIVATE LINE DATA TKANSMISSIOX 1475 enough to prevent such an overlap. This is indicated in Fig. 5(c). It does not prevent third order modulation effects. It has been found necessary to allocate frecjuency bands thus to avoid the overlap discussed in the transmission of high grade telephotography over telephone type facilities. It has also been noted that allocation ^vith such overlap was undesirable in some data transmission experience. However, the question has not been resolved in complete detail. For the data service under consideration, which is expected to show a very low error rate, it is deemed conservative to allocate bands without the over- lap. This conclusion then leads to wasting a certain part of the lower fre- quency range. It is still possible, however, to use this range for an auxil- iary signal, as in the system illustrated in Fig. 2, if the auxiliary signal occurs only during word starts. The double sideband frequency range, as indicated in Fig. 5(b) or 5(c), is about twice the baseband range of Fig. 5(a). It is possible to re- duce this extension by cutting down one of the sidebands to a "vestige" of itself and sending carrier at a reduced level, as indicated by the diag- onal dotted line about the carrier in Fig. 5(c). This was proposed by Nyquist.'^ It is done at the expense of an increased vulnerability to noise, which in total amounts to some 5 or 6 db in certain typical cases."' ^' In Section 2.1.3 discussion was given to account for 3 db of this. In the references cited herewith it is noted that vestigial sideband transmission is accompanied by an interfering component (called a "quadrature com- ponent") which accounts for the other 2 or 3 db. 3.2.3 FM Carrie?- Transmission Certain additional immunity to noise is gained by the use of frec{uency modulation (or "frequency shift") of the carrier. The immunity which can be obtained against impulse noise can be even greater than that against random noise, provided that the receiver is precisely tuned. This was noted in Section 2.4 in connection with voice frequency telegraph. The noise immunity obtained from FS is in part due to the use of a higher average power and is at the expense of a wider frequency band as illustrated in Fig. 5(d). In addition to all the band that is used for a double sideband system, a space must be allowed for the swing. FS is also much less vulnerable to sudden level changes than DSB and thus may well be preferable to DSB for medium bit -rate service. As shown in Table I, these advantages can be obtained with only a small sacrifice of bit rate compared to DSB for equal bandwidths. So far the single channel broadband FS system has not been generally 1476 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 used over wire circuits. Hence its exact performance, particularly with impulse noise, is only estimated. On occasion not all of the band illustrated in Fig. 5(d) is allowed for. This leads to an increase in distortion of the signal, which has some simi- larity to a very close-in echo. It uses up some of the additional noise immunity provided by the FM, as an engineering compromise. Another direction along which the FM system may be practically extended is to use four instead of two (marking and spacing) frequencies. This would double the bit capacity at the expense of only a moderate widening of the frecjuency band and somewhat tighter requirements on noise and delay distortion (but not of level regulation, which would be required for a similar extension of the AM signal) . 3.2.4 Multichannel Systems It is possible to divide up the entire frequency band available into a number of separate channels and use any one of the various carrier sys- tems which have been described, in each individual channel. This may be done because the nature of the information transmitted may be better adapted to the narrow channel, as in conventional telegraph. It permits certain elements of flexibility in layout, and offers certain noise advan- tages (and also disadvantages) as discussed in the next section. In an idealized way one can proportion the various allowances for nominal effective band, roll-off, guard band, and swing (FS) in the same proportion in which they would occur in a single broad channel over the whole facility. Thus no frecjuency space would be lost by the subdivision. In practice, however, subdivision usually does lead to some actual loss in the frequency space. A significant limitation to frequency subdivision lies in nonlinearity of the facility. This leads to modulation products between the various channels, which interfere with other channels. In the case of voice frequency telegraph and other multiple channel systems the modulation effects are mitigated by allocating the carriers at odd multiples of a basic frequency. That is, any given carrier / is set at / = n/v, where n is odd and A; is a basic figure. Then the three second order modulation products are 2/ = 2nk, /i + f- = {fh + n-i) k, /i - fi = (wi - no) k. PRIVATE LINE DATA TRANSMISSION 1477 Table V — Use of Telephone Band by Various Data Systems System 1. Proposed. . . 2. Exploratory 3. Exploratory 4. Polytonic ■ / / • 85 1 / / f f A 5 / f y / 80 / / / / v\ 75 SUMMARY BUSY CHANNELS/ 7- / / r, 1 1 P) ( P / / / / 70 ^ / / / / / 1/ f 1 ^ • / 1 ^-* i f 5^^ 66 k ^ r- '^ i '^^ ^if J ^J^ i/ "•• *u / / • 60 / f \J // \/ 1 1 / 1 55 •■ 1 1 1 A /* -4 /• SUGGESTED REQUIREMENT \ ( / , r 1 / / 50 TH RU CHANNEL \ < /I 1 1 -^ A- m / / 1 1 1 t y i / r T •ij / 45 COMPANDOR CHANNEL / / SUMMARY IDLE CHANNELS 40 5 10 15 20 25 30 35 2B SET- FIA WTG- DBA (ZERO TRANSMISSION LEVEL) Fig. 6 — Noise measurements in Nl carrier facilities. 40 dots refer to an estimate (computed from the known properties of the compandor) of what the noise peak levels would have been, had the channel tested been busy with an operating data transmission signal (of the general type illustrated in Fig. 1). Under this condition the com- pandor setting would of course be different from that of an idle channel. 1480 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 In such cases the 2B meter reading is also adjusted to the effective mes- sage circuit noise which would have existed in the presence of speech on the tested channel. Open triangles connected by fine dotted lines indicate summary plots for the idle channels, and for the busy channels. Examination of the plot shows that there is only a general correlation between the 2B set and level distribution recorder readings, as sum- marized by the dotted lines. Thus the 2B meter is not a reliable instru- ment to denote how noisy a circuit is for data transmission of the speed used in the proposed project. The telephone objective for Nl circuits, as read on the 2B meter, is indicated by the vertical dotted line. This show^s that most of the cir- cuits (actually 55 out of 62) met the objective. The suggested requirements for data are shown by the horizontal dotted lines. The "through" or noncompandored channel has a 3 db more lenient requirement (as indicated during some of the tests) than the compandored one. This results from the penalty mentioned earlier which compandors impose on in a data circuit, as compared with the 23 db or so advantage that it introduces for voice transmission. Only a few" of the circuits measured (actually 10 out of 62) met the suggested require- ments. The principal conclusion reached from these measurements is that where used for a data service of the type considered, with vestigial sideband transmission, most of the hitherto installed Nl circuits (and probably other compandored circuits) will require modification to reduce noise exposure. Also noise measurement will be more complicated for such a service than for telephony. 3.4 Envelope Delay Distortion Some simple theoretical considerations'' have shown that the envelope delay distortion limits for a telephotograph circuit generally also hold for a data transmission circuit of the same speed. The principal difference is that less emphasis need be placed for data circuits upon fine structure deviations of the envelope delay as plotted on a frequency scale. In general, distortion of ±0.4 signal element in the important part of the band has been found to give a signal-to-noise impairment of some 3 db in signal reception. This has been assumed here as a tentative engineer- ing objective. In accordance with this, the envelope delay requirements for service with the vestigial sideband signal consideration have been set at not to exceed 500 microseconds (±250 microseconds) between 1,000 and 2,500 PRIVATE LINE DATA TRANSMISSION 1481 cycles. This contains an element of conservatism inasmuch as the strict requirement is really fully implied only on the nominal effective band (1,200-2,000 cycles). The signal power is reduced in the roll-off and vestigial bands, respectively 1,000-1,200 and 2,000-2,500 cycles, and some corresponding liberality may be expected there. The delay distortion constitutes a more serious problem with a faster system as compared with a slower one, in part because of the wider frequency band occupied by it, and in part because 0.4 signal element represents a more severe tolerance in microseconds for a shorter element than for a longer one. Consequently, the limits given represent about as severe tolerances as may be expected to be needed with the use of a telephone channel. The distortions of various circuits have been considered to estimate the order of the problem involved in meeting the proposed requirements over Unks of 100 to 500 miles. The following conclusions are reached first for the vestigial sideband signal, and after this for the slower systems. 3.4.1 Facilities Requiring No Treatment As already noted, K2, LI, and L3 carrier, and TD-2 microwave, use "A" channel banks to separate the individual channels, and these give the dominant delay distortion. This amounts to a maximum of about 200, and a minimum of 150 microseconds, according to the exact com- bination of filters used. This figure is for one link of transmitter and receiver. A single section delay equilizer can cut the maximum residual to about 80 microseconds. It is concluded that these facilities present no important delay distortion problems. An Nl carrier link gi^'es a maxi- mum delay distortion of 220 microseconds, which can be reduced to 50 microseconds by one section of equalizer. This, then, also presents no serious problem. 3.4.2 Facilities Treated by Simple Prescription The delay distortion of H-44 voice frequency cable in the 1,000- to 2,400-cycle range runs to slightly under 900 microseconds for 300 miles, if the cable is of standard toll capacitance (0.062 mf per mile), and to slightly under 2,000 microseconds if of higher local plant capacitance (0.084 mf per mile). The use of about one section of ecjualization per 100 miles reduces the residual to less than 330 microseconds for the low capacitance cable. For the higher capacitance cable, about three sections are needed per 110 miles. The J-2 carrier uses A channel banks, but has, in addition, directional separation filters at each repeater. This gives maximum and minimum distortions, respecti^'ely, for 100 miles, of slightl}'' under 300 and slightly under 160 microseconds. The precise 1482 THE BELL SYSTEM TECHNICAL JOURNAL, XOVEMBER 1957 distortion in any given channel depends upon its proximity to the cut- off of the directional filter. For 500 miles the figures are slightly over 500 and slightly under 50 microseconds. With the same single section of equalization the maximum figures are reduced to about 100 microseconds for 100 miles, and about 300 microseconds for 500 miles. To carry out this equalization requires onl}' rudimentary information on the general nature and correction of delay distortion. If moderate care is used in the prescription of equalization on a packaged basis no delay measurement of the circuit would in general be needed, though it is recognized that some difficult cases may arise. 3.4.3 Facilities Requiring More Involved Prescription The delay distortion in C-5 carrier^^ is influenced to a dominating ex- tent both by channel and directional separation filters. It varies in a complex fashion from channel to channel, and according to the direction of transmission. Its correction thus requires more involved prescription than is required for the other types of circuit. In some few cases measure- ment may be necessary. The distortion of H-88 voice-frequency cable runs from some 1,400 to over 3,000 microseconds per 100 miles accord- ing to capacitance. For 20 miles of H-174 toll cable the distortion is slightl}^ under 1,400 microseconds, and its use is not contemplated. 3.4.4 Data Systems Requiring No Corrections The delay distortion problem is practically non-existent for the slower systems. For the double sideband .systems some delay correction may be needed if long heavily loaded circuits are used or perhaps for some other rare unfavorable situations, but otherwise no correction is necessary. No correction is needed for the telegraph systems. APPENDIX I — BASEBAND SIGNAL DISTORTION CAUSED BY CARRIER FREQUENCY SHIFT A simple analysis of the phenomenon may be considered. Let the voltage input, as in Fig. 7(a), be a raised cosine pulse between the angular arguments of — tt and -\-ir. That is Vi = 1 + cos m, (1) where O/tt is the envelope frequency. When this is transmitted on the carrier, cos ut, the carrier signal voltage is Vo = (1 + cos m) cos o:t, (2) = cos wt -\- \ COS (o) — 0)/ + I cos (o) + ^)t. (3) When the carrier and one sideband are removed (say the lower side- PRIVATE LINE DATA TRANSMISSION 1483 band),Fc becomes (neglecting the factor §) Vc = cos (oj + ^)t. (4) At the receiving end, Vc is modulated with a carrier which may mo- mentarily differ in phase from the signal carrier by angle tp, giving Vo = cos (w + 12)^ cos {ut + (f), (5) = ^ cos [(w + U)t - (oot + -p)] + I cos [(co + n)t + {cot + vtcv . (9) Substituting the \'alues of 1,.^ and 0;, from (6) and (7) and neglecting all higher order Fourier components of 0, one obtains Eo ^ — wAi cos de . (10) Similarl}'- one obtains for the amplitude E^ of the sine voltage : Es = wAi sin de . (11) As required, the two induced secondary voltages are proportional to the cosine and sine of the electrical rotor angle. As shown in the appendix, an analysis which takes into account the higher order Fourier components of the pole-shoe flux shows that a sinusoidally distributed Avinding is sensitive solely to the so-called slot- harmonics. The order "m" of these harmonics is given by the expression m = A-g ± 1 (12) where "/c" is any integral positive nvnnber and q is the number of pole- shoes divided b}^ the largest integral factor common to the number of pole-shoes and the number of rotor teeth. For instance, in the case of a 1494 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 to Q z o u to z a. o a. tr 5 0 c -5 10 y^ r /^ > L /^ ---^ /— r \/ 1 ^"""^ ^v^ u 25' 50' SHAFT ANGLE, ©rn I'lS' Fig. 5 — Error of a 27th order vernier resolver over | vernier interval. 27th order vernier resolver this common factor is 1 and consequently the slot harmonics are of order: 9, 11, 19, 21, etc. The effect of the slot harmonics can be reduced by the following means : a) Selecting the dimensions as well as the number of rotor and stator teeth such as to keep the higher order flux components low. b) Using a ''skewed" rotor or stator, in which successive laminations are progressively displaced with respect to their angular orientation. III. PERFORMANCE Clifton Precision Products Co. built experimental resolver models of order 26, 27, 32 and 33 using the laminations shown in Figs. 3 and 4. The best results were obtained with 27th order resolvers. Their per- formance is described in the following sections. 3.1 Repeatability and Accuracy The repeatability is better than d=3 seconds of shaft angle. Figs. 5, 6 and 7 show the error curves taken on a 27th order vernier resolver after compensating with trimming resistors for the fundamental and second harmonic error with respect to the vernier interval. (In es- sence, the effect of these trinnning resistors is either to add or to sub- tract a small voltage to one or both of the resolver signals.) Fig. 8 shows an error curve before trimming.* 3.2 Temperature Sensitivity The error introduced by a temperature change of 70°C is less than 25 seconds of shaft rotation. * The error curves really represent the combined error of the tested resolver itself plus that of the testing apparatus. VERNIER RESOLVER 1495 10 Q z o o LU m z -10 o 3° 20' 6° 40' SHAFT ANGLE, ©rn 10°0' 13°20 Fig. 6 — Error of a 27th order vernier resolver over one vernier interval. It may be pointed out that the housing of the tested unit was of aluminum. A unit with a non-magnetic steel housing should be of lower temperature drift, because stator stack and housing would then have the same temperature coefficient of expansion. 3. .3 Transformation Ratio, Input and Output Impedances At maximum coupling the induced output voltage is 0.123 times the exciting voltage and is leading in phase by 6°. The impedance of the input winding with the output windings open is 117 + J 781 ohms. The impedance of the output windings with the primary winding shorted is 235 + j 920 ohms. The effect of the rotor position on this impedance is hardly noticeable. 3.4 Output Signal Distortions The harmonic content of the output signal at maximum coupling is: fundamental 1.7 volts 2nd harmonic 0.2 mv 3rd harmonic 13.5 mv 5th harmonic 5.4 mv The harmonic content of the output signal at minimum coupling (null voltage) is: fundamental 1.6 mv 2nd harmonic 0.05 mv 3rd harmonic 2.0 mv 1496 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 90 180° SHAFT ANGLE, (9^ 270° 360° Fig. 7 — Error of a 27th order vernier resolver over one shaft revohition. 180° SHAFT ANGLE, ©rn 360° Fig. 8 — Error of a 27th order vernier resolver before trimming. 3.5 Moment of Inertia and Friction Torque The moment of inertia of the rotor of a 27th order harmonic resolver is 63 gram em sq. The maximum break-away friction torque among five units was 0.027 in. oz. No change in this torque due to excitation of the unit could be detected. VERNIER RESOLVER 1497 IV. APPLICATION In its application, the vernier resolver is usually directly coupled to a standard resolver or some other coarse angle transducer. Such a system which represents a ^'ariable, in this case the shaft angle, in two scales, coarse and fine, will be called a vernier system. The following sections describe applications using the vernier resolver in an encoder, a follow-up system and an angle-reading system. 4.1 Vernier Angle Encoder A vernier angle encoder converts a shaft angle into a pair of digital numbers, one being the coarse and the other being the vernier number. This type of encoder can be built by mechanically coupling a standard resolver directly to a vernier resolver. The outputs of the two resolvers, after encoding, represent the coarse and the vernier number. The output of a resolver may be encoded, for instance, by the following method. The primary winding of the resolver is excited from an a-c source of, say, 400 cycles per second. The two induced secondary volt- ages are in phase with each other. Their amplitudes are proportional to the cosine and sine of the electrical rotor angle, de . These two amplitude modulated voltages are combined by means of two phase-shifting networks into two phase-modulated voltages. One net- work first advances the sine voltage by 90° and then adds it to the cosine voltage. The other network performs the same addition after retarding the sine voltage by 90°. The result is two constant amplitude voltages with relative phase shift of twice the electrical rotor angle. The time in- terval between the respective zero crossings of these two voltages is con- _Y/. PHASE MOTOR Fig. 9 — Resolver servo system. 1498 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 verted into digital representation by means of an electronic stop-watch (time encoder). 4.2 Vernier Follow-up System A vernier follow-up system can be built much like the present two speed synchro control-transformer system, except that the geared up synchros are replaced by vernier resolvers. Fig. 9 illustrates the vernier portion of this system. Since the output impedance of the vernier re- solver is fairly large, it may be desirable to use amplifiers, as shown in Fig. 9, to energize that vernier resolver which plays the part of the con- trol-transformer. 4.3 Vernier Angle-Reading System A visual vernier angle-reading system as reciuired to read the position of a rotary table can be built by using the output of a vernier resolver to position a standard resolver. The coarse angle can be read as usual from calibration lines marked directly on the rotary table. The vernier angle reading is obtained by coupling a vernier resolver directly to the rotary table. The output of this resolver is used to position a standard control transformer. This control transformer will go through "w" revolutions for each revolution of the rotary table, where "w" is the order of the vernier resolver. The reading of a dial coupled either directly or through gears to the control transformer provides the vernier reading. V. SUMMARY Vernier resolvers of order 26, 27, 32 and 33 have been designed, built and tested. The construction of the unit is very simple because all windings are located on the stator. The absence of brushes and slip rings makes the unit inexpensive in production and reliable in performance. The performance of present experimental models is characterized by a repeatability of better than ±3 seconds of arc and by a standard de- viation error over one revolution of less than 10 seconds of arc. Production units should be of even higher accuracy because better tooling fixtures would be used and minor design improvements would be incorporated. The principal forseeable application of the resolver lies in vernier sys- tems. Vernier encoder, vernier servo and vernier angle-reading systems VERNIER RESOLVER 1499 are readily obtained by applying existing techniques to the vernier re- solver. ACKNOWLEDGEMENT The development of the vernier resolver was undertaken under the sponsorship of the Wright Air Development Center. The work was en- couraged and furthered by J. C. Lozier of Bell Telephone Laboratories. Valuable design contributions were made by J. Glass of Clifton Precision Products Co. All testing and evaluating of test results was done by T. W. Wakai of Bell Telephone Laboratories. APPENDIX Sy7nbols E Amplitude of induced voltage p Number of pole-shoes n Number of rotor teeth de Electrical rotor angle, equal to its geometrical angular position mul- tiplied by ri q p divided by largest integral factor common to n and p n' n divided by the same factor V Pole-shoe number running from 0 to (p — 1) m Order of Fourier component representing the pole-shoe flux as a function of the electrical rotor angle, de ae Electrical angle between adjoining pole-shoes, equal to the geometri- cal angle multiplied by n k A number equal to zero or to any positive integer. In accordance with eciuations (7) and (8) the voltage induced in the sine-winding coil on the i^th pole-shoe by the mth flux harmonic is: Esm, = Co[Am COS m (de — Vae) t siu (uCX,)]. (13) After trigonometric transformation: Esm,> = hAmtco [sin {mde — (ni —I) vae) (14) + sin (-171 6 e -\- (m ^ I) vae)] . The voltage, Esm , induced in the sine winding is obtained by summing the expression of (14) over all values of v. Since (pa^) is a multiple of 27r the summing of all sine terms from 1^ = 0 to 1/= {p — 1) results in zero unless the angle (m ± 1) a? is an integral multiple, k, of 2ir. This condi- tion is spelled out in the following equation: 1500 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 (w ± 1) ae = k2Tr . (15) The electrical angle ae being the mechanical angle between successive pole-shoes divided by the number of rotor teeth is: 27rn , . Oie = . (16) p Dividing p and 7i by the largest common integral factor, one can write «. = '^'. (17) Substituthig this expression into (15) and solving for m, one obtains m = ^ ± 1 (18) n where m and k are integers or zero. Consequently, (18) is satisfied for the following values of m: m=l; g±l; 2q zL 1; ■ ■ • . (19) The amplitude of the voltage, Esm , induced in the sine winding by flux harmonics of order m, where m is specified by (19), is 7) Esm = ~ Amtu sin {7nde). (20) Similarly one obtains for the voltages, Ecm , induced in the cosine winding Ecm = ^ Ajw cos (mde). (21) Bell System Technical Papers Not Published in this Journal Anderson, 0. L.,^ Christensen, H./ and Andreatch, P., Jr.^ A Technique for Connecting Electrical Leads to Semiconductors, J. Appl. Phys., Letter to the Editor, 28, p. 923, August, 1957. Andreatch, P., Jr., see Anderson, O. L. Benson, K. E., see Pfann, W. G. Benson, K. E., see Wernick, J. H. BiRDSALL, H. A.^ Insulating Films, in "Digest of Literature on Dielectrics", Publica- tion 503, National Academy of Sciences, National Research Council, 19, pp. 209-220, June, 1957. Bogert, B. P.^ Response of an Electrical Model of the Cochlear Partition with Dif- ferent Potentials of Excitation, J. Acous. Soc. Am., 29, pp. 789-792, July, 1957. BoHM, D., see Huang, K. BoYET, H., see Weisbaum, S. BOZORTH, R. M} The Physics of Magnetic Materials, in "The Science of Engineering Materials", John Wiley & Sons, New York, pp. 302-335, 1957. Brady, G. W.^ Structure of Tellurium Oxide Glass, J. Chem. Phys., 27, pp. 300-303, July, 1957. ^ Bell Telephone Laboratories, Inc. 1501 1502 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 Brady, G. W.,' and Krause, J. T} Structure in Ionic Solutions. I, J. Chem. Phys., 27, pp. 304-308, July, 1957. Breidt, p., Jr., see Greiner, E. S. Chynoweth, a. G.,1 and McK\y, K. G.^ Internal Field Emission in Silicon p-n Junctions, Phys. Rev., 106, pp. 418-426, May 1, 1957. Chrlstensen, H., see Anderson, 0. L. Dacey, G. C.,1 and Thurmond, C. D.' p-n Junctions in Silicon and Germanium: Principles, Metallurgy, and Applications, Metallurgical Reviews, 2, pp. 157-193, July, 1957. Ellis, W. C., see Greiner, E. S. Frisch, H. L.' The Time Lag in Nucleation, J. Chem. Phys., 27, pp. 90-94, July, 1957. Fuller, C. S.,^ and Reiss, H.^ Solubility of Lithium in Silicon, J. Chem. Phys., Letter to the Editor, 27, pp. 318-319, July, 1957. Gibbons, D. F.' Acoustic Relaxations in Ferrite Single Crystals, J. Appl. Phys., 28, pp. 810 814, July, 1957. Gianola, U. F} Damage in Silicon Produced by Low Energy Ion Bombardment, J. Appl. Phys., 28, pp. 868-873, Aug., 1957. Githens, J. A.^ The TRADIC LEPRECHAUN Computer, Proc. Eastern Joint Com- puter Issue, A.I.E.E. Special Pubhcation, T-92, pp. 29-33, Dec. 10-12, 1956. Glass, M. S.i Straight Field Permanent Magnets of Minimum Weight for TWT — Design and Graphic Aids in Design, Proc. I.R.E., 45, pp. 1100-1105, Aug., 1957. Bell Telephone Laboratories, Inc. technical papers 1503 Green, E. I.^ Evaluating Scientific Personnel, Elec. Engg., 76, pp. 578-584, July, 1957. Greiner, E. S.,^ Breidt, P., Jr.,^ Hobstetter, J. N.,' and Ellis, W. C.i Effects of Compression and Annealing on the Structure and Electrical Properties of Germanium, J. Metals, 9, pp. 818-818, July, 1957. FIamming, R. W., see Hopkins, I. L. Barker, K. J.' Nonlaminar Flow of Cylindrical Electron Beams, J. Appl. Phys., 28, pp. 645-650, June, 1957. Herman, H. C.^ Jumbo Case Considerations, J. Patent Office Society, 39, pp. 515-523, July, 1957. Hobstetter, J. N., see Greiner, E. S. Hopkins, I. L.,^ and Hamming, R. W.^ On Creep and Relaxation, J. Appl. Phys., 28, pp. 900-909, Aug. 1957- Huang, K.,^ Bohm, D.,^ and Pines, D.^ Role of Subsidiary Conditions in the Collective Description of Elec- tron Interactions, Phys. Rev., 107, pp. 71-80, July 1, 1957. Ingram, S. B.^ Graduate Study in Industry — The Communications Development Training Program of the Bell Telephone Laboratories, Eng. J., 40, pp. 993-996, July, 1957. Jaccarino, V.,1 Shulman, R. G.,' and Stout, R. W. 10 Nuclear Magnetic Resonance in Paramagnetic Iron Group Fluorides, Phys. Rev., Letter to the Editor, 106, pp. 602-603, May 1, 1957. Jones, W. D., see Turrell, G. C. ' Bell Telephone Laboratories, Inc. * Technion, Haifa, Israel. ^ Princeton University, Princeton, N.J. '" University of Chicago, Chicago, 111. 1504 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 KlERNAN, W. J.^ Appearance Specifications and Control Methods, Elec. Manufacturing, 60, pp. 126-129, 294, 296, 298, July, 1957. Krause, J. T., see Brady, G. W. Lander, J. J., see Morrison, J. Legg, V. E.i Survey of Square Loop Magnetic Materials, Proc. Conference on Magnetic Amplifiers, A.LE.E. Special Publication, T-98, pp. 69-77, Sept. 4, 1957. Logan, R. A.,^ and Peters, A. J.^ Diffusion of Oxygen in Silicon, J. Appl. Phys., 28, pp. 819-820, July. 1957, Letter to the Editor. Luke, C. L.^ Determination of Sulfur in Nickel by the Evolution Method, Anal. Chem., 29, pp. 1227-1228, Aug. 1957. Maki, a., see Turrell, G. C. Marcatili, E. A.i Heat Loss in Grooved Metallic Surface, Proc. I.R.E., 45, pp. 1134- 1139, Aug., 1957. Mertz, F} Information Theory Impact on Modern Communications, Elec. Engg., 76, pp. 659-664, Aug., 1957. McCall, D. W.i Dielectric Properties of Polythene, in "Polythene, The Technology and Uses of Ethylene Polymers", edited by A. Renfrew and P. Mor- gan, published for "British Plastics" by Iliffe and Sons Limited, London, 1957. McCall, D. W., see Slichter, W. P. McKay, K. G., see Chynoweth, A. G. > Bell Telephone Laboratories, Inc. technical papers 1505 Meitzler, a. H.* A Procedure for Determining the Equivalent Circuit Elements Repre- senting Ceramic Transducers Used in Delay Lines, Proc. 1957 Elec- tronic Components Symposium, pp. 210-219, May, 1957. Miller, R. C.,^ and Smits, F. M.' Diffusion of Antimony Out of Germanium and Some Properties of the Antimony-Germanium System, Phys. Rev., 107, pp. 65-70, July 1, 1957. Montgomery, H. C.^ Field Effect in Germanium at High Frequencies, Phys. Rev., 106, pp. 441-445, May 1, 1957. Morrison, J.,^ and Lander, J. J.^ The Solution of Hydrogen in Nickel Under Hydrogen Ion Bombard- ment, Conference Notes M.LT. Physical Electronics Conference, pp. 102-108, June, 1957. Nielsen, E. G.^ Behavior of Noise Figure in Junction Transistors, Proc. LR.E., 45, pp. 957-963, July, 1957. Payne, R. M.^ Clemson Conducts School for Bell, Telephony, 152, pp. 20-21, 50-51, June 15, 1957. Perry, A. D., Jr.^ Pulse-Forming Networks Approximating Equal-Ripple Flat-Top Step Response, LR.E. Convention Record, 2, pp. 148-153, July, 1957. Peters, A. J., see Logan, R. A. Pfann, W. G.,^ and Vogel, F. L., Jr.^ Observations on the Dislocation Structure of Germanium Crystals, Acta Met., 5, pp. 377-384, July, 1957. Pfann, W. G.,^ Benson, K. E.,^ and Wernick, J. H.' Some Aspects of Peltier Heating at Liquid-Solid Interferences in Germanium, J. Electronics, 2, pp. 597-608, May, 1957. ^ Bell Telephone Laboratories, Inc. « Southern Bell Tel. & Tel. Co., Atlanta, Georgia. 1506 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 Pfann, W. G.i Zone Melting, Metallurgical Reviews, 2, pp. 29-76, May, 1957. Pines, D., see Huang, K. Reiss, H., see Fuller, C. S. RUGGLES, D. M.l A Miniaturized Quartz Crystal Unit for the Frequency Range 2-kc to 16-kc, Proe. 1957 Electronic Components Symposium, pp. 59-61, 1957. SCAFF, J. H.i Impurities in Semiconductors, Effect of Residual Elements on the Properties of Metals, A.S.M. Special Vol., pp. 88-132, 1957. Shulman, R. G., see Jaccarino, V. Slighter, W. P.,' and McCall, D. W.^ Note on the Degree of Crystallinity in Polymers as Found by Nuclear Magnetic Resonance, J. Poly. Sci., Letter to the Editor, 25, pp. 230- 324, July, 1957. Smits, F. M., see Miller, R. C. Steele, A. L.^ The 2-5 Numbering Plan and Selection of Exchange Names, Tele- phony, 153, pp. 24-25, 48, July 20, 1957. Stone, H. A., Jr.^ Component Development for Microminiaturization, I.R.E. 1957 Convention Record, 6, pp. 13-20, 1957. Stout, J. W., see Jaccarino, V. Thurmond, C. D., see Dacey, G. C. TuRRELL, G. C.,1 Jones, W. D.," and Maki, A." Infrared Spectra and Force Constants of Cyanoacetylene, J. Chem. Phys., 26, pp. 1544-1548, June, 1957. 1 Bell Telephone Laboratories, Inc. ■• Oregon State College, Corvallis. ' Indiana Bell Telephone Company, Indianapolis. TECHNICAL PAPERS 1507 Van Bergeijk, W. A.' The Lung Volume of Amphibian Tadpoles, Science, 126, p. 120, July 19, 1957. VoGEL, F. L., Jr., see Pfann, W. G. Weinreich, G.' Ultrasonic Attenuation by Free Carriers in Germanium. Phys. Rev.. Letter to the Editor, 107, pp. 317-318, July 1957. Weinreich, G.,' and White, H. G.^ Observation of the Acoustoelectric Effect, Phys. Rev., Letter to the Editor, 106, pp. 1104-1106, June 1, 1957. Weisbaum, S.,' and Boyet, H.^ Field Displacement Isolators at 4-, 6-, 11- and 24-Kmc, Trans. LR.E- PGMTT, MTT-5, pp. 194-198, July, 1957. Weiss, M. T.^ Quantum Derivation of Energy Relations Analogous to Those for NonUnear Reactances, Proc. LR.E., Letter to the Editor, 45, pp. 1012-1013, July, 1957. Weiss, M. T.^ A Solid State Microwave Amphfier and Oscillator Using Ferrites, Phys. Rev., Letter to the Editor, 107, pg. 317, July 1, 1957. Wernick, J. H.,^ and Benson, K. E.' Zone Refining of Bismuth, J. Metals, 9, p. 996, July, 1957. Wernick, J. H., see Pfann, W. G. White, H. G., see Weinreich, G. 1 Bell Telephone Laboratories, Inc. Recent Monographs of Bell System Technica] Papers Not Published in This Journal* Aaron, M. R. Use of Least Squares in System Design, Monograph 2828. Andreatch, p., Jr. and Thurston, R. N. Disk-Loaded Torsional Wave Delay Line, Monograph 2827. Bond, W. L., see McSkimin, H. J. BooTHBY, 0. L., vsee Williams, H. J. BoYET, H, see Seidel, H. BoYET, H. and Seidel, H. Analysis of Nonreciprocal Effects in N-wire, Ferrite -Loaded Trans- mission Line, Monograph 2829. Buck, T. M. and McKim, F. S. Depth of Surface Damage Due to Abrasion on Germanium, Mono- graph 2805. Burke, P. J. Output of a Queuing System, Monograph 2766. Burns, F. P. Piezoresistive Semiconductor Microphone, Monograph 2830. ClOFFI, P. P. Rectilinearity of Electron-Beam Focusing Fields from Transverse Determinations, Monograph 2844. David, E. E., Jr. Signal Theory in Speech Transmission, Monograph 2831. * Copies of these monographs may be obtained on request to the Publication Department, Bell Telephone Laboratories, Inc., 463 West Street, New York 14, N. Y. The numbers of the monographs should be given in all requests. 1508 MONOGRAPHS 1509 Dewald, J. F. Transient Effects in Ionic Conductance of Anodic-Oxide Films, Monograph 2767. Easley, J. W. Effect of Collector Capacity on Transient Response of Junction Trans- istors, Monograph 2832. Green, E. I. Evaluating Scientific Personnel, Monograph 2846. Herrmann, G. F. Transverse Scaling of Electron Beams, Monograph 2839. Karp, a. Backward -Wave Oscillator Experiments at 100 to 200 Kilomegacycles, Monograph 2833. Law, J. T. and Meigs, P. S. Rates of Oxidation of Germanium, Monograph 2834. LUMSDEN, G. Q. Wood Poles for Communication Lines, JMonograph 2818. Marrison, W. a. A Wind-Operated Electric Power Supply, IVlonograph 2837. McKiM, F. S., see Buck, T. M. McSkimin, H. J. and Bond, W. L. Elastic Moduli of Diamond, Monograph 2793. Meigs, P. S., see Law, J. T. Read, M. H., see Van Uitert, L. G. Schnettler, F. J., see Van Uitert, L. G. Seidel, H. Ferrite Slabs in Transverse Electric Mode Waveguide, Monograph 2798. Seidel, H., see Boyet, H. 1510 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 Seidel, H. and Boyet, H. Polder Tensor for Single -Crystal Ferrite with Small Cubic Sym- metry Anisotropy, Monograph 2843. Sherwood, R. C, see Williams, H. J. Shockley, W. Transistor Physics, Monograph 2836. Slighter, W. P. Nuclear Magnetic Resonance in Some Fluorine Derivatives of Poly- ethylene, Monograph 2819. SwANEKAMP, F. W., see Van Uitert, L. G. Thurston, R. N., see Andreatch, P., JR. Van Uitert, L. G. Magnesium-Copper-Manganese-Aluminum Ferrites for Microwave Uses, Monograph 2799. Van Uitert, L. G. Magnetic Induction and Coercive Force Data on Members of Series BaAlxFei2-xOi9 , Monograph 2801. Van Uitert, L. G. Effects of Annealing on Saturation Induction of Ferrites With Nickel or Copper, Monograph 2845. Van Uitert, L. G., Read, M. H., Schnettler, F. J., and Swane- KAMP, F. W. Permanent Magnet Oxides Containing Divalent Metal Ions, Mono- graph 2841. Walker, L. R. Magnetostatic Modes in Ferromagnetic Resonance, ]\Ionograph 2800, Wertheim, G. K. Energy Levels in Electron-Bombarded Silicon, Monograph 2840. Williams, H. J., Sherwood, R. C., and Boothby, O. L. Magnetostriction and Magnetic Anisotropy of MnBi, Monograph 2838. Willis, F. H. Some Results with Frequency Diversity in a Microwave Radio Sys- tem, Monograph 2842. Contributors to This Issue Andrew H. Bobeck, B.S.E.E., 1948; M.S.E.E., 1949, Purdue Uni- versity; Bell Telephone Laboratories, 1949-. Since completing the Lab- oratories' Communications Development Training Program in 1952 Mr. Bobeck has been engaged in the design of both communications and pulse transformers and more recently in the design of solid state memory devices. Member LR.E., Eta Kappa Nu and Tau Beta Pi. B. C. Bellows, Jr., B.S., Cornell LTniversity, 1936; General Electric Co., 1936-39; Bell Telephone Laboratories, 1939-. From 1939 to 1941 Mr. Bellows was engaged in engineering trial installations of telephone equipment, particularly multi-channel coaxial cable equipment. During World War II he specialized in the mechanical design and engineering of airborne radars. From 1945 to 1957 he was engaged in the design of circuits and equipment for point-to-point microwave radio relay systems for telephone and television transmission. On May 1, 1957 he was named Transmission Measurement Engineer. Member Eta Kappa Nu and Phi Kappa Phi. Charles A. Desoer, Dipl. Ing., University of Liege (Belgium), 1949; Sc.D. Massachusetts Institute of Technology, 1953; Bell Telephone Laboratories, 1953-. Since joining the Laboratories Mr. Desoer has specialized in linear and transistor network development in the Trans- mission Networks Development Department. Senior Member LR.E. R. Shiels Graham, B.S., LTniversity of Pennsylvania, 1937; Bell Telephone Laboratories, 1937-. His work has been with the design of equalizers, electrical wave filters and similar apparatus for use on long- distance coaxial cable circuits, microwave systems and both telephone and television transmission. During World War 11, Mr. Graham de- signed circuits for electronic fire control computers for military use. He also developed methods for computing network and similar problems on a digital relay computer. He presently supervises the video and inter- mediate frecjuency network group. He is a senior member of the LR.E., and a member of Tau Beta Pi, and Pi Mu Epsilon. 1511 1512 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 Gerald Kronacher, Dipl. Eng., Federal Institute of Technology, Zurich, Switzerland, 1937; Assistant Professor, Federal Institute of Technology, 1938; mining engineer, Bolivia, 1939-1946; General Electric Company, 1946-1948; Air Associates, Inc., 1948-1951; Arma Corpora- tion, 1951-1953; Bell Telephone Laboratories, 19513-. Since joining the Laboratories Mr. Kronacher has been associated with the Military Sys- tems Engineering Department studying input and output problems for digital computers. He is the author of many published technical articles. Pierre Mertz, A. B., 1918; Ph.D., 1926, Cornell University; Ameri- can Telephone and Telegraph Company, 1919-1921, 1926-1934; Bell Telephone Laboratories, 1935-. Mr. Mertz 's work with the Bell Sys- tem has been concerned primarily with transmission problems relating to telephotography and television. Since 1950 Mr. Mertz has acted as a consultant in the Systems Engineering Department on such projects as micro-image readers and commercial and military data transmission problems. Fellow of the I.R.E. and the Society of Motion Picture and Television Engineers; member, American Physical Society, Optical Society of America and the Inter-Society Color Council. DoREN Mitchell, B.S., Princeton University, 1925; American Tele- phone and Telegraph Company, 1925-1934; Bell Telephone Labora- tories, 1934-. Mr. Mitchell's early work with the Bell System was con- cerned with field studies of transmission on long telephone circuits and radio circuits, including supervision of the initial operation of the New York to Buenos Aires radio-telephone circuit. Until 1942 Mr. Mitchell worked on voice operated devices of various kinds including compandors, echo suppressors and automatic switching devices. During World War II he participated in military projects involving transmission systems and problems of laying wire from airplanes. Since the war Mr. Mitchell has been primarily concerned with radio systems. In 1955 he was ap- pointed a Special Systems Engineer supervising a data transmission system for the SAGE project, and planning other special services in- volving radio. Mr. Mitchell has been granted over seventy patents. Mem- ber I.R.E. R. C. Prim, B.S. in E.E., University of Texas, 1941; A.M., Ph.D., Princeton LTni versify, 1949; General Electric Company, 1941-1944; Naval Ordnance Laboratory, 1944-1948; Bell Telephone Laboratories, 1949-. Since joining the Laboratories Mr. Prim has been a member of the Mathematical Research Department engaged in research and con- CONTRIBUTORS TO THIS ISSUE 1513 sultation in the fields of theoretical mechanics, solid state electronics, aerial warfare and activities analysis. In 1955 he was placed in charge of a sub-department concerned with Computing and Theoretical Me- chanics, and is presently in charge of the Communications Fundamentals sub-department. Member American Mathematical Society, American Physical Society, Tau Beta Pi and Sigma Xi. Werner Ulrich, B.S., 1952; M.S., 1953; Eng. Sc.D., 1957, Columbia School of Engineering; Bell Telephone Laboratories, 1953-. Mr. Ul- rich's first assignment was on the design of an input circuit for an elec- tronic memory and control device. Subsequently he was engaged in the design of logical circuits for electronic controls. Since 1954, he has been working on automatic testing and maintenance facilities for electronic switching systems. Mr. Ulrich is a member of the I.R.E. and Tau Beta Pi. Index to Volume XXXVI AF See United States Air Force Activation of Electrical Contacts by Or- ganic Vapors (L. H. Germer, J. L. Smith) 769-812 Agatneninon (cable ship) 303 Air Force .See United States Air Force Alaskan Telephone Cable 168 Alignment See Misalignment Allentown Plant (Western Elec- tric) 107, 123-25 Alternator Set two-motor carrier, L-type 140 American Telephone and Telegraph Company 3, 14-15 Amplitude Modulation data transmission systems 1451-86 Amsterdam, Holland 9 Analysis combinatorial, error correcting coding 517-35 Angell, Miss D. T. 1033 Angle(s) measurement vernier resolver 1487-1500 Anglo-Irish Cable 179 Anson, H. W. 1093 Antenna radio transmission beyond the horizon 639-40 diagrams 599 height 597; transmission loss 593-97 Armor, repeaters, transatlantic tele- phone cable 58 Array See Memory Arrays Atlantic Cable 1-2, 4, 303 Atlantic Ocean Mid-Atlantic Ridge 1066-68 North Atlantic, see North Atlantic Ocean physiographic diagram inside rear cover Sept. Atmosphere, dielectric constant 603, 627 Attenuation Newfoundland-Nova Scotia link 221- 23 nonlinear, FM signal 879-89 waveguide coupling 392 Aulock, Wilhelm von biographical material 591 Measurement of Dielectric and Magnetic Properties of Ferromagnetic Materials at Microivave Frequencies 427^8 Azores map 8. 294, 296 B BOD Test See Test : biochemical oxy- gen demand BSTJ See Bell System Technical Jour- nal Bacteria 1097-1127 Baldwin, J. A. 1337 Bampton, J. F. biographical material 338 System Design for the N ewfoundland- Nora Scotia Link 217-44 Bandwidth transatlantic telephone cable North Atlantic link 34-35 Battery See Storage Battery Beam See Electron Beam Bechofer, R. E. 576 Bell System Technical Journal advisory board, see inside front covers Bulloch, W. D., editor 710 editorial committee, see inside front covers editorial staff, see inside front covers Bell Telephone Laboratories 4, 57- 58, 163 Bellows, B. C, Jr. biographical material 1511 Experimental Transversal Equalizer for TD-2 Radio Relay System 1429-50 THE BELL SYSTEM TECHNICAL JOURXAL, 1957 Benes, Vaclav E. biographical material 1045 Fluctuations of Telephone Traffic 965- 73 Sufficient Set of Statistics for a Tele- phone Exchange Model 939-64 Berne, Switzerland 9 Binary Block Coding (S. P. Lloyd) 517-35 Binary Digit See Bit Binomial Processes 537-76 Biochemical Oxygen Demand Test See Test Biskeborn, M. C. biographical material 338 Cable Design and Manufacture for the Transatlantic Submarine Cable Sys- tem 189-216, 496 BIT (Binary Digit) AM leased-line transmission 1451-86 twistor devices 1336 Bleicher, E. 576 Block Coding See Code Bobeck, Andrew H. biographical material 1511 New Storage Element Suitable for Large Sized Memory Arryas — the Twistor 1319-40 Bobis, S. 1449 Borer (s), marine 194 Boston map 8 Boyd, Richard C. biographical material 588 New Carrier Systein for Rural Service 349-90 Boyet, H. 426 Braga, F. J. biographical material 338 Repeater Design for the North Atlantic Link 69-101 Bridgers, H. E. 1004 British Post Office, submarine cables, 3-5, 14-15, 57-58, 245 Brockbank, R. A. biographical material 339 Repeater Design for the Newfoundland- Nova Scotia Link 245-76 Brussels 9 Buckley, O. E. 67 Buildings, radio transmission and 613-14 Bullington, Kenneth biographical material 828 Radio Propagation Fundamentals 593- 626 Bulloch, W. D., B. S.T.J, editor 710 Burke, P. J. 964 C.C.I.F. See International Consulta- tive Committee on Telephony Cable (s) Alaska telephone, see Alaskan Tele- phone Cable Anglo-Irish, see Anglo-Irish Cable Hawaii telephone, see Hawaiian Tele- phone Cable short-circuits, Poisson patterns 1005- 33 submarine, see Submarine Cable transatlantic telegraph (1866), see Atlantic Cable transatlantic telephone, see Transat- i lantic Telephone Cable trunks, see Trunk Cable Design and Manufacture for the Transatlantic Submarine Cable Sys- i tem (M. C. Biskeborn, H. C. Fischer, - A. W. Lebert) 189-216, 496 Cable Laying 13 dynamics 1129-1207 kinematics 1129-1207 laying effect 43-44 methods, early 303 oceanography* 1049 , strains 13-14 transatlantic telephone cable 29.3-326 Cabot Strait 3 Canadian Comstock Co., Ltd. 244 Canadian Overseas Telecommunica- tion Corporation 3, 7, 244 Capacitance geometries, pressure coefficients 485- 95 submarine cables 485 Capacitor carrier, PI 367-68 mica, repeater, flexible. North Atlantic link 125-26 parallel plate capacitance, pressure coefficients 485-95 INDEX Carbon activating contacts, electrical 769-812 Carrier(s) history 350 L-type alternator set 140 PI 349-90 capacitors 367-68 channels 357-59 compandors 357 dialing 361-62 equipment arrangements 369-76 filters 365-66 inductors 366-67 installation 380-90 maintenance 375 miniaturization 370 networks 369 parameters 351-65 power supply 376-80 printed circuitry 371 repeaters 362-65, 373-75 ringing 359-61 signaling 359 terminals block diagram 354 mounting 373-75 testing 375 transformers 368-69 transistors 349-90 transmission plan 351-55 trunks 350 Casting Resins BOD test 1099 marine conditions 1095-1127 Catalina Island 13 Central Office, service range 350 Chaffee, J. G. 1449 Channel(s) carrier, PI 357-59 human, information rate, reading rates and 497-516 noisy, error correction codes 1341-88 North Atlantic link 38 Character of Waveguide Modes in Gyro- magnetic Media (H. Seidel) 409-26 Circular Electric Wave Transmission in a Dielectric-Coated Waveguide (H.-G. Unger) 1253-78 Circular Electric Wave Transmission throuch Serpentine Bends (H.-G. Unger) 1279-92 Circular Waveguide See Waveguide Circuit See subhead circuit under names of specific equipment and apparatus, e.g. Repeater: flexible: North Atlantic link: circuit; Also see Printed Circuitry; Short Circuit Clapp, William F., Laboratories 1115-21 Clarenville, New^foundland 2, 9, 29, 49, 57, 140, 145, 147, 150, 164-65, 217, 219, 221 , 246, 248, 293, 301 , 317-18, 323; map 8, 218, 300 Clarenville-ObaxN Link See North Atlantic Link Clarenville-Sydney Mines Link See Newfoundland-Nova Scotia Link Clifton Precision Products Com- pany 1494, 1499 Code(s), Coding block, binary 517-35 error correcting 517-35 binary, non 1341-88 geometric concept 1343-44 non-binary 1341-88 purpose 1341-43 Reed-Muller 1341 Coincidences in Poisson Patterns (E. N. Gilbert, H. O. Pollak) 1005-33 Cold Cathode Gas Tubes for Telephone Switching Systems (M. A. Townsend) 755-68 Combinatorial Analysis error correcting coding 517-35 Communication channel, see Channel Connection, shortest, network 1389-1401 Companding improvement 671, 688-90 instantaneous signals, quantized 653-709 carrier, PI 357 Company, Telephone See Operating Companies Conduit metal, testing 737-54 round, strength requirements 737-54 6 THE BELL SYSTEM TECHNICAT JOURNAL, 1957 Conduit (Cont.) underground clay, vitrified 737 loads 737 metal, testing 737-54 round strength requirements 742-54 CoNSOL (navigation system) 1050 Contact(s) relay arcing 769-812 erosion, by vapors 769-812 Continental Shelf, North Atlantic Ocean 1063-64 Cook, Madeline L. 1126 Cooperation See International Co- operation Copenhagen 9 Copper Tubing repeater, flexible, North Atlantic link 114-15 Corona power supply, transatlantic telephone cable 159 Coupled-Wave Transducer See Trans- ducer Coupler, waveguide attenuation 392 design 394-401 Crawford, Arthur B. biographical material 828 Reflection Theory for Propagation be- yond the Horizon 627-44 Crosstalk, transatlantic telephone ca- ble 161, 230, 243 Crystal ferrites, see Ferrite quartz repeater, flexible. North Atlantic link 120-23 Cuba 13 Curtis, Harold E. 889 biographical material 828 Interchannel Interference clue to Kly- stron Pulling 645-52 D DC See Direct Current Dagnall, C. H. 1449 Data Transmission AM systems 1451-86 error correcting codes, non-binary 1341-88 leased-line services, transmission as- pects 1451-86 mutilation 1342 Dawson, Robert W. biographical material 588 Experimental Dual Polarization An- tenna Feed for Three Radio Relay Bands 391-408 Daytona Beach, Florida, test site 1115-21 Decca Navigator 1050 Decoder, error correcting codes, non- binary 1341-88 DeCoste, J. B. 1126 Defense Work See Military Commu- nications De Hoff, Barbara 448 Depew, C. 768 Design, Performance and Application oj the Vernier Resolver (G. Kronacher) 1487-1500 Desoer, Charles A. 156-58 biographical material 1511 Network Containing a Periodically Operated Switch Solved by Successive Approxi)nations 1403-28 Determination of Pressure Coefficients of Capacitance for Certain Geometries (D. W. McCall) 485-95 Dial Telephone, Dialing cable, see Cable carrier, see Carrier channels, see Channel circuit data transmission services 1451-86 companies, see Operating Companies exchange, see Telephone Exchange leased-lines, see Leased-Line Services repeaters, see Repeater rural, see Rural Telephone Service telephone exchange, see Telephone Exchange traffic, see Traffic transmission, see Transmission trunks, see Trunk INDEX Dielectric, inhomogeneous, waveguide, circular, curved 1209-51 Dielectric-Coated Waveguide See Waveguide Dielectric Constant capacitance, pressure coefficients 485 Digit, binary See Bit Direct Current transatlantic telephone cable 139-62 Distortion FM signal, noise modulated 879-89 TD-2 radio relay system 1429-50 Distortion Produced in a Noise Modulated FM Signal by Non-Linear Attenua- tion and Phase Shift (S. O. Rice) 879-98 Doba, S. 889 Dynamics and Kinematics of the Laying and Recovery of Submarine Cable (E. E. Zajac) 1129-1207 E.P.I, (electronic position indicator) 1050 Earthquakes, ocean bottom 1086-88 Easter.x Telephone and Telegraph Company 7, 244 Ebbe Grace L. 1449 Echo, transatlantic telephone cable 21 Echo Sounding 1051-52, 1055 Efficiency electron tubes, transatlantic telephone cable 3 Elastomer(s) BOD test 1099 marine conditions 1905-1127 Electric Wave See Wave Electrical Attenuation See Attenua- tion Electrical Capacitance See Capaci- tance Electrical Capacitor See Capacitor Electrical Contacts See Contact Electrical Distortion See Distortion Electrical Filters See Filter Electrical Inductor See Inductor Electrical Interference See Inter- ference Electrical Loading See Loading Electrical Loss See Net Loss; Trans- mission Loss Electrical Network See Network Electrical Noise See Noise Electrical Transformer See Trans- former Electrically Operated Hydraulic Control Valve (J. W. Schaefer) 711-36 Electron Beam (in) magnetic field, longitudinal noise spectrum 831-78 growing noise 831-53 UHF 855-78 noise, electron beam, relation 832 Pierce-type, noise 833 Electron Tube 6P10 179-80; ilhis 165 6P12 180-88 electrical characteristics 184-86 lifetime 185-86 tests 186-88 175HQ 163-79 cathode assembly illus 169 electrical characteristics 171-77 fabrication 177-78 heater illus 169 mechanical features 168-78 reliability 178 selection 177-78 SP61 179-80 gas diode by-pass 88-90; illus 89 gas discharge characteristics 755-65 switching sj'stems 755-68 submarine cables, performance re- quirements 163-88 traveling-wave, noise 831 See also Klystron Pulling Electron Tubes for the Transatlantic Ca- ble System (M. F. Holmes, J. O. McNally, G. H. Metson, E. A. Veazie) 163-88 Electronic Position Indicator 1050 Elmendorf, C. H. biographical material 1317 Oceanographic Information for En- gineering Submarine Cable Systems 1047-93 8 THE BELL SYSTEM TECHNICAL JOURNAL, 1957 Emling, J. W. biographical material 339 Translantic Telephone Cable System — Planning and Over- All Performance 7-27 Encoder, error correcting codes, non- binary 1341-88 Engineering, traffic 940 England map 294, 296 Equalizer(s) repeater, flexible North Atlantic link 99-100 shore transatlantic telephone cable 46-49 transverse TD-2 radio relay system 1429-50 Equipment Miniaturization See Mini- aturization Error Correcting Codes See Code Ewing, Maurice 1093 Experimental Dual Polarization Antenna Feed for Three Radio Relay Bands (R. W. Dawson) 391-408 Experimental Transversal Equalizer for TD-2 Radio Relay System (B. C. Bellows, Jr., R. S. Graham) 1429-50 Fischer, H. C. biographical material 339 Cable Design and Manufacture for the Transatlantic Submarine Cable Sys- tem 189-216, 496 Fletcher, R. C. 426, 483, 1337 Fluctuations of Telephone Traffic (V. E. Benes) 965-73 Fog, and radio transmission 602 Foster, H. 1093 France map 294, 296 Frankfurt, Germany 9 Eraser, John M. biographical material 340 Systerii Design for the North Atlantic Link 29-68 Frequency, transatlantic telephone cable 18, 24-26 Frequency Modulation interference, interchannel klystron pulling 645-52 Fresnel Zones 597-99 Friis, Harald T. biographical material 828 Reflection Theory for Propagation be- yond the Horizon 627-44 4B Transistor See Transistor 5B Transistor See Transistor FM See Frequency Modulation Fading, radio transmission 600-01 Fedukowicz, W. 1093 Feher, George biographical material 588 Sensitivity Considerations in Micro- wave Paramagnetic Resonance Ab- sorption Techniques 449-84 Ferrite microwave region, dielectric proper- ties, measurement 427-48 parameters 428-30 Ferrite Loaded Waveguide See Wave- guide Ferromagnetic Materials See Ferrite Field, Cyrus 293 Field See Magnetic Field Filter(s), carrier, PI 365-66 Gas Diode Tube See Electron Tube Gas Discharge Tube See Electron Tube Geiger Counters, Poisson patterns 1005-33 Generalized Telegraphist's Equa- tions waveguide, circular, curved dielectric, inhomogeneous 1209-51 Gere, E. 483 Germer, Lester H. Activation of Electrical Contacts by Organic Vapors 769-812 biographical material 829 Geschwind, S. 483 Gibson, W. C. 1126 Gilbert, E. N. 964 biographical material 1045 Coincidences in Poisson Patterns 1005-33 Gilbert, J. J. 67 INDEX Glaser, J. L. 698 Glasgow, Scotland 9 Gleichmann, T. F. biographical material 340 Repeater Design for the North Atlantic Link 69-101 Graham, R. Shells biographical material 1511 Experimental Transversal Equalizer for TD-2 Radio Relay System 1429-50 Great Eastern (cable ship) 293, 303 Greenland map 8 Griffith, R. G. biographical material 340 Transatlantic Telephone Cable System — Planning and Over-All Performance 7-27 Grismore, O. D. 495 Guide See Waveguide Guided Missiles See Nike Gumley, R. H. 812 Gun See Electron Gun Gupta, S. S. 576 H H.M.T.S. Monarch See Monarch Hagelbarger, D. W. 1033 Hale, A. L. 1093 Halsey, R. J. biographical material 341 System Design for the Newfoundland- Nova Scotia Link 217-44 Transatlantic Telephone Cable System — • Planning and Over-All Performance 7-27 Hamming, R. W. 535 Hawaiian Telephone Cable 168 Hawthorne Works (Western Elec- tric) 107 Heezen, Bruce C biographical material 1317 Oceanographic Information for En- gineering Submarine Cable Systems 1047-93 HefTner, William W. biographical material 341 Repeater Production for the North Atlantic Link 103-38 Heskett, H. E. 405 High-Voltage Conductivity-Modulated Silicon Rectifier (M. B. Prince, H. S. Veloric) 975-1004 Hillside Plant (Western Electric) 103-38 Hipkins, Renee 512 Hogg, David C. biographical material 829 Reflection Theory for Propagation be- yond the Horizon 627^4 Holdaway, V. L. 768 Holmes, M. F. biographical material 341 Electron Tubes for the Transatlantic Cable System 163-88 Hoth, D. F. 698 Howard, John D. biographical material 588 New Carrier System for Rural Service 349-90 Huyett, Marilyn J. biographical material 589 Selecting the Best One of Several Bi- nomial Populations 537-76 Human Channel See Channel Iceland map 8 Inductor carrier, PI 366-67 repeater, flexible North Atlantic link 127-29 Information Rate channel, human 497-516 prose 501-04 reading rates 497-516 word length 500 vocabulary size 409 vocoder 497 Information Storage twistor 1319-40 Inhomogeneous Dielectric See Di- electric Inspection repeater, flexible, transatlantic tele- phone cable 131-38 Installation carrier, PI 380-90 10 THE BELL SYSTEM TECHNICAL JOURNAL, 1957 Instantaneous Companding of Quantized Signals (B. Smith) 653-709 Integrity (components) 31, 33 Interchannel Interference due to Klystron Pulling (H. E. Curtis, S. O. Rice) 645-52 interchannel, frequency modulation klystron pulling 645-52 power spectrum 647—48 transatlantic telephone cable power supply 161 Intjcrnational Consultative Com- mittee ON Telephony standards 17 International Cooperation 7-8, 14-15, 27, 246, 326 Ionosphere, radio transmission 618-23 Iowa Engineering Experiment Sta- tion conduit, underground 737-54 Ireland map 294, 296 J-7 Transducer See Transducer: elec- trohydraulic Jack, John S. biographical material 341 Route Selection and Cable Laying for the Transatlantic Cable System 293-326 Jacobs, O. B. 67 Jensen, R. A. 1337 Jervey, W. T. 754 Jute, in BOD test 1099 K Kankowski, Edward 448 Kaplan, E. L. 576 Karlin, John E. biographical material 589 Reading Rates and the Information Rate of a Human Channel 497-516 Kearney Works (W. E. Co.) 103-38 Kegelman, T. D. 1126 Kelly, J. L. 512 Kelly, Mervin J. biographical material 342 Transatlantic Communications — .4 n Historical Resume 1-5 Kelly, R. biographical material 342 Power-Feed System for the Newfound- land-Nova Scotia Link 277-92 Kelvin, Lord 11, 293 Kip, A. F. 483 Klystron Pulling interference, interchannel 645-52 Kohman, G. T. 495 Kronacher, Gerald biographical material 1512 Design, Performance and Application of the Vernier Resolver 1487-1500 L-Type Carrier See Carrier Laboratories See Bell Telephone Lab- oratories Lamb, Harold A. biographical material 342 Repeater Production for the North Atlantic Link 103-38 Lawton, C. S. 1126 Laying See Cable Laying Leach, Priscilla 1126 Leased-Line Services data transmission transmission aspects 1451-86 network, shortest connection 1389-1401 Lebert, Andrew W. 495 biographical material 343 Cable Design and Manufacture for the Transatlantic Submarine Cable Sys- tem 189-216, 496 Lee, C. Y. 1387 Leech, W. H. biographical material 343 Route Selection arid Cable Laying for the Transatlantic Cable Systoii 293-326 Letham, D. L. 512 Levenbach, G. J. 1004 Lewis, Herbert A. biographical material 343 Route Selection and Cable Laying for the Transatlantic Cable System 293-326 System Design for the North Atlantic Link 29-68 INDEX 11 Lewis, J. A. 495 Life Expectancy electron tube 175HQ 166, 171-77 6P12 185-86 transatlantic telephone cable North Atlantic link 66-67 LiMNORiA 1096-1127 Lince, Arthur H. biographical material 344 Repeater Design for the North Atlantic Link 69-101 Linear Programming binomial processes 537-76 Lloyd, Stuart P. 964 Binary Block Coding 517-35 biographical material 589 Loading repeaters, submarine cable 20 London 7-9; map 8 Looney, D. H. 1337 Lorac (naviagtion system) 1050 LoRAN (navigation system) 1050 Loss See Net Loss; Transmission Loss Lovell, G. H. biographical material 344 System Design for the North Atlantic Link 29-68 Lozier, J. C. 1499 Lutchko, F. R. 1004 Lutz, Mary 512 Lynch, A. C. 495 M McC'all, D. W. biographical material 589 Determination of Pressure Coefficients of Capacitance for Certain Geometries 485-95 McClure, B. T. 768 McMillan, B. 698 McNally, J. O. biographical material 344 Electron Tubes for the Transatlantic Cable System 163-88 Magdalena River turbidity currents 1089-90 M.AGNETic Wire See Wire Maintenance carrier, PI 375 Newfoundland-Nova Scotia link 235-41 North Atlantic link 55-57 transatlantic telephone cable 21-23, 55-57, 235-41 Marine Borer (s) test sites 1115-21 transatlantic telephone cable 194 Marine Navigation See Navigation Maritime Provinces of Canada 9 Measurement of Dielectric and Magnetic Properties of Ferromagnetic Materials at Microwave Frequencies (W. von Aulock, J. H. Rowen) 427-48 Memory Arrays twistor 1319-40 Mertz, Pierre biographical material 1512 Transmission Aspects of Data Trans- mission Service Using Private Line Voice Telephone Channels 1451-86 Meszaros, George W. biographical material 345 Power Feed Equipment for the North Atlantic Link 139-62 Metering current, transatlantic telephone cable 151-58 Methyl-Methacrylate See Plexiglass Metson, G. H. biographical material 345 Electron Tubes for the Transatlantic Cable System 163-88 Mica Capacitors See Capacitor Michaels, S. E. 512 Microwave (s) feed, polarization, dual 391-408 paramagnetic resonance techniques 449-84 Microwave Relay Systems See Radio Relay Systems Mid-Atlantic Ridge 1066-68 Military Commixications Nike, electrohydraulic transducer 711-36 servomechanisms, hydraulic 736 Miller, S. E. 405 12 THE BELL SYSTEM TECHNICAL JOURNAL, 1957 Miniaturization, carrier, PI 370 Misalignment, transatlantic cable. North Atlantic link 42-46 Mitchel, Duncan M. 754 Mitchell, Doren biographical material 1512 Transmission Aspects of Data Trans- mission Service Using Private Line Voice Telephone Channels 1451-86 Mode(s), normal, electric waves, circu- lar 1292-1307 Modulation amplitude, see Amplitude Modulation frequency, see Frequencj' Modulation Modulation transatlantic telephone cable North Atlantic link 63 pulse amplitude (PAM) 655-57 code (PCM) 655-57 quantizing impairment 656-57 duration (PDM) 655-57 position (PPM) 655-57 Monarch (cable ship) 162, 244, 250, 303-26; illus 305 cable gear line schematic 310 Monographs, recent, of Bell System technical papers not published in this Journal 335-37, 583-87; 823-27; 1043-44; 1313-17; 1508-10 Monro, S. 576 Montreal 7-9; map 8 Morgan, Samuel P. biographical material 1318 Theory of Curved Circular Waveguide Containing an Inhomogeneous Di- electric 1209-51 Mottram, Elliott T. biographical material 345 Transatlantic Telephone Cable System — Planning and Over- All Performance 7-27 Murphy, R. B. 576 Mutilation (data transmission) 1342 N No. 4B Transistor See Transistor No. 5B Transistor See Transistor No. 6P10 Electron Tube See Electron Tube No. 6P12 Tube See Electron Tube No. 7F Test Set See Test Set No. 175HQ Tube -See Electron Tube No. SP61 Tube See Electron Tube Nantucket 13 Navigation marine, systems table 1050 Net Loss transatlantic telephone cable 18 Network carrier, PI .369 shortest connection 1389-1401 construction principles 1.391-94 U. S. state capitals illus 1390 switching, periodic 1403-28 Network Containing a Periodically Oper- ated Switch Solved by Successive Approximations (C. A. Desoer) 1403-28 New Carrier System for Rural Service (R. C. Boyd, J. D. Howard, L. Pedersen) 349-90 New Storage Element Suitable for Large Sized Memory Arrays — the Twistor (A. H. Bobeck) 1319-40 New York City map 7-9, 11; 8 Newfoundland map 294, 296, 300 Newfoundland-Nova Scotia Link attenuation 221-23 circuits 223 crosstalk 230, 243 design 217-44 electron tubes 163-88, 179-88 maintenance 235-41 noise 229, 241-42 power supply 225-27, 277-92 repeaters 163-88, 245-76 route selection 317-20 terminals 227-29 transmission loss 229, 241 transmission objectives 217 Niagara (cable ship) 303 Nike roll servo purpose 711 simplified schematic 712 transducer, elect rohydraulic, J-7 711-36 INDEX 13 Noise electron beam 831-78 electron tube, traveling-wave 831 error correction codes 1341-88 Newfoundland-Nova Scotia Link 229, 241-42 transatlantic telephone cable North Atlantic link 39-42, 62-63 radio transmission 623-25 Noise Spectrum of Electron Beam in Longitudinal Magnetic Field: The Groicing Noise Phenomenon; The UHF Noise Spectrum (W. W. Rigrod) 831-78 Non-Binary Error Correction Codes (W. Ulrich) 1341-88 Nonlinear Attenuation See Attenua- tion Normal Mode Bends for Circular Electric Waves (H.-G. Unger) 1292-1307 North America map 294, 296 North Atlantic Link bandwidth 34-35 cable current regulation 143-45; simplified sche- matic 143-45 channels 38 description 29-31 design 29-68 electron tubes 163-78 equalization shore 46-49; block schematics inaccessibility 34 integrity 33 maintenance 55-57 misalignment 42—46 modulation 63 noise 39-42, 62-63 performance 59-65 power feed, see Power Supply repeaters, see Repeater schematic diagram 30 signal-to-noise design 35 spares 65-66 terminals 52-55 testing 55-59 North Atlantic Ocean basins 1064-65 bottom 1072-74 temperature 1077-86 continental shelf 1063-64 earthquake epicenters map 1087 telegraph cables map 294 topography 1061-70; illus North Sea 3 Northern Electric Company, Ltd. 57, 244 Norton, E. L. 736 Nova Scotia map 294, 296 Noyce, R. N. 1004 Number 4B Transistor See Transistor Number 5B Transistor See Transistor Number 6P10 Electron Gube See Electron Tube Number 6P12 Tube See Electron Tube Number 7F Test Set See Test Set Number 175HQ Tube See Electron Tube Number SP61 Tube See Electron Tube 175HQ Tube See Electron Tube Oban, Scotland 2, 9, 29, 49, 57, 140, 145, 147, 150, 164-65, 217, 219, 221, 246, 248, 293, 301, 317-18, 323; 7nap 8, 218, 300 Ocean Bottom catastrophic changes 1086-93 knowledge, present 1070-74 sediment 1071 study 1048 evaluation 1056-1057 methods 1065-70; illus presentation 1057-61 topography 1049-65 turbidity currents 1089-93 Ocean Cable See Submarine Cable Oceanographic Information for Engineer- ing Submarine Cable Systems (C. H. Elmendorf, B. C. Heezen) 1047-93 Oceanography, defined 1047-48 Office See Central office O'Neil, H. T. 1033 Operating Companies carrier, PI 350 Ordnance Survey of Great Britain 244 14 THE BELL SYSTEM TECHNICAL JOURNAL, 1957 PI Carrier See Carrier PAM See Modulation : pulse; amplitude PCM See Modulation: pulse: code PDM See Modulation: pulse: duration PPM See Modulation: pulse: position Parallel Plate Capacitors See Capacitor Paramagnetic Resonance absorption 450 Parameter(s) carrier, PI 351-65 ferrites 428-30 Paris 9 Pauer, J. J. 754 Pedersen, Ludwig biographical material 589 New Carrier System for Rural Service 349-90 Periodic Switching See Switching Perkins, E. H. 390 Phase Shift FM signal, noise modulated distortion 879-89 Pholadidae 1096-1127 Pierce, John R. biographical material 590 Reading Rates and the Information Rate of a Human Channel 497-516 PiERCE-TypE Electron Gun See Elec- tron Gun Plastics marine conditions 1095-1127 Plexiglass properties 115 repeaters, flexible. North Atlantic link 115-16 PoissoN Patterns, coincidences 1005-33 Pollak, H. O. biographical material 1045 Coincidences in Poisson Patterns 1005-33 Polyethylene BOD test 1099 submarine cable 189-93, 197, 199, 205 Polyvinyl Chloride, BOD test 1099 Populations, binomial See Binomial Processes Port is, A. M. 483 Portland, Maine map 8 Post Office See British Post Office Power, dc, reliability 140 Power-Feed See Power Supply Power Feed Equipment for the North Atlantic Link (G. W. Meszaros, H. H. Spencer) 139-62 Power-Feed System for the Newfoundland- Nova Scotia Link (R. Kelly, J. F. P. Thomas) 277-92 Power Supply carrier, Pl 376-80 Newfoundland-Nova Scotia link 225-27, 277, 292 transatlantic telephone cable crosstalk 161 North Atlantic link 49-52, 139-62; schematic diagram 51 equipment design 158-62 standby sources 145-51 Prim, R. C. biographical material 1512 Shortest Connection N^etworks and Some Generalizations 1389-1401 Prince, M. B. biographical material 1045 High-Voltage Conductivity -Modulated Silicon Rectifier 975-1004 Printed Circuitry carrier, PI 371 Private Line Services See Leased- Line Services Probabilities, binomial processes 537-76 Processes See Binomial Processes Programming See Linear Programming Propagation See Transmission Prose, information rate 501-04 Pulse Modulation, quantized 655-57 Quality Bell System 103 Western Electric 103 Quantized Signal See Signal Quartz Crystal See Crystal Quebec (city) map 8 INDEX 15 Radio Propagation Fundamentals (K. BuUington) 593-626 Radio Relay Systems TD-2 distortion 1429-50 equalizer, transversal 1429-50 repeaters, equalizer, transversal 1429-50 Radio Telephone, transatlantic 5 Radio Transmission Loss See Trans- mission Loss Rain, and radio transmission 602 Radley, Sir Gordon biographical material 345 Transatlantic Communications — An Historical Resume 1-5 Rayleigh Distribution 600-01, 624 Reading Rates and the Information Rate of a Human Channel (J. E. Karlin, J. R. Pierce) 497-516 Rectangular Waveguide See Wave- guide Rectifier silicon, conductivity-modulated high-voltage 975-1004 solid state voltage 975 Reed-Muller Codes 1341 Reflection Theory for Propagation beyond the Horizon (A. B. Crawford, H. T. Friis, D. C. Hogg) 627^4 Regenerative Repeater See Repeater Regulator current, transatlantic telephone cable 143-45 Relay Systems See Radio Relay Sys- tems Reliability electron tube, 175HQ 178 Repeater carrier, PI 362 65, 373-75 flexible North Atlantic link 69-138 capacitors 125-26 circuit 71 components 81-88 container 90-94 coupling networks 73-76 design 69-101 equalization 99-100 feedback loop 78-79 gain formula 72-73 gas diode tube 88-90; illus 89 inspection 131-38 manufacture 103-38 assembly 116-20 brazing 116-20 clothing, special 109 dust count 110 quartz crystals 120-23 mechanical design 79-81 packing 130 performance 96-98 power feed 139-62 production 110-14 raw materials 114-16 schematic diagram 70 seals 90-94, 123-25; illus 118 shipping 130 subcontracted operations 107-08 testing 77-78, 94-96 Newfoundland-Nova Scotia link 245-76 regenerative, self-timing 891-937 reliability 245 submarine cable British Post Office 12 loading 20 TD-2 radio relay system equalizer, transversal 1429-50 transatlantic telephone cable armoring 58 efficiency 2-3 electron tubes 2-4 specifications 2 Repeater Design for the Xewfoundland- Nova Scotia Link (R. A. Brockbank, D. C. Walker, V. G. Welsby) 245-76 Repeater Design for the North Atlantic Link (F. J. Braga, T. F. Gleichmann, A. H. Lince, M. C. Wooley) 69-101 Repeater Production for the North Atlantic Link (W. W. Heffner, H. A. Lamb) 103-38 Resin (s) casting 1095-1127 BOD test 1099 marine conditions 1095-1127 16 THE BELL SYSTEM TECHNICAL JOURNAL, 1957 Resistance of Organic Materials and Ca- ble Structures to Marine Biological Attack (L. R. Snoke) 1095-1127 Resistor repeater, flexible North Atlantic link 126-27 Resolver See Synchro Resolver; Ver- nier Resolver Resonance 450 See also Paramagnetic Resonance Rice, Stephen O. 698 biographical material 829, 1046 Distortion Produced in a Noise Modu- lated FM Signal by Non-Linear At- tenuation and Phase Shift 879-89 Interchannel Interference due to Klys- tron Pulling 645-52 Richards, A. P. 1126 Rigrod, W. W. biographical material 1046 Noise Spectrum of Electron Beam in Longitudinal Magnetic Field: The Growing Noise Phenomenon; The UHF Noise Spectrum 831-78 Riordan, J. 964-65 Ringing carrier, PI 359-61 Rose, A. C. 1387 Round Waveguide See Waveguide: circular Route Selection and Cable Laying for the Transatlantic Cable System (J. S. Jack, W. H. Leech, H. A. Lewis) 293-326 Rowen, John H. biographical material 590 Measurement of Dielectric and Magnetic Properties of Ferromagnetic Materials at Microwave Frequencies 427-48 Rural Telephone Serivce carrier, PI 349-90 S Tube Tube See Electron 6P10 Electron Tube 6P12 Electron Tube 6P12 Tube See Electron Tube 7F Test Set See Test Set SP61 Tube See Electron Tube See Electron Schaefer, J. W. biographical material 830 Electrically Operated Hydraulic Control Valve 711-36 Scotland map 294, 296 Sea See Ocean Bottom Seal(s), repeater, flexible. North Atlan- tic link 90-94, 123-25; illus 118 < Seasons, transmission, radio, bej'ond the horizon 640-43 Sediment, ocean bottom 1071 Seidel, Harold biographical material 590 Character of Waveguide Modes in Gyro- magnetic Media 409-26 Selecting the Best One of Several Binomial Populations (Marilyn J. Huyett, M. Sobel) 537-76 Self -Timing Regenerative Repeaters (E. D. Sunde) 891-937 Semiconductor(s), Semiconducting Ma- terials See Ferrite Sensitivity Considerations in Microwave Paramagnetic Resonance Absorption Techniques (G. Feher) 449-84 Serpentine Waveguide See Wave- guide: circular Service See Maintenance Servo Systems electrohydraulic, Nike 711-36 hydraulic, military communications 736 power supply, transatlantic telephone cable 155-58 vernier resolver illus 1497 Shoran (navigation system) 1050 Short Circuit cables, Poisson patterns 1005-33 Shortest Connection Networks and Some 1 Generalizations (R. C. Prim) 1389-1401 Signal(s), Signaling binarj', data transmission 1451-86 1 carrier, PI 359 j companding, instantaneous 653-709 FM, noise modulated distortion 879-89 quantized, companding, error 665-76 instantaneous 653-709 spectrum 663 transatlantic telephone cable 20-21 INDEX 17 Si.\u'i>Ex Wire and Cable Company 196-97 Silsbee, R. H. 483 Silverman, S. J. 1004 Simonick, V. F. 736 Slepian D. 512 Slichter, C. P. 483 Smith, Bernard biographical material 830 Instantaneous Companding of Quantized Signals 653-709 Smith, D. H. 390 Smith, James L. Activation of Electrical Contacts hy Organic Vapors 769-812 biographical material 830 Snoke, Lloyd R. biographical material 1318 Resistance of Organic Materials and Cable Striictures to Marine Biological Attack 1095-1127 Snow and radio transmission 602 Sobel, Milton biographical material 590 Selecting the Best One of Several Bi- nomial Populations 537-76 SoFAR (naviagtion sj-stem) 1050 Solenoid electrohydraulic, J-7 711-36 Sounding, echo 1051-52, 1055 Southern United Telephone Co., Ltd. 244 Spare Parts, North Atlantic link 65-66 Spencer, H. H. biographical material 346 Power Feed Equipment for the North Atlantic Link 139-62 Spruce Lake, New Brunswick 11 St. John, New Brunswick map 8 Standard Telephones and Cables, Ltd. 244, 274, 292 States (United States), capitals, net- work, shortest connection 1389- 1401; ill us 1390 Statistical Methods telephone exchange model 939-64 traffic fluctuations 965-73 Storage Battery, as power source 140 Storage See Information Storage Strength Requirements for Round Conduit (G. F. Weissmann) 737-54 Submarine Cable(s) background experience 11-15 British Post Office systems 12-13 capacitance 485 electron tubes 3 marine organism attack 1095-1127 North Atlantic link 33 oceanographic information 1047-93 recovery dynamics 1129-1207 kinematics 1129-1207 research 5 stresses 1 transatlantic telephone, see Trans- atlantic Telephone Cable transistors 3-^ United States 13-14 Submarine Cables, Ltd. 196-97, 274 Sufficient Set of Statistics for a Telephone Exchange Model (V. E. Benes) 939-64 Sunde, Erling D. 889 biographical material 1046 Self-Timing Regenerative Repeaters 891-937 Switching periodic, network 1403-28 Switching Systems electron tubes, gas discharge 755-68 Switching Time twistor 1328 Synchro Resolver accuracy 1487-88 See also Vernier Resolver Sydney Mines, Nova Scotia 11, 29, 164-65, 219, 221, 232, 246, 248, 318, 321,323; map 8,218,300 Syste77i Design for the Newfoundland-Nova Scotia Link (J. F. Bampton, R. J. Halsey) 217-44 System Design for the North Atlantic Link (J. M. Fraser, H. A. Lewis, G. H. Lovell, R. S. Tucker) 29-68 TD-2 Radio Relay System See Radio Relay Systems Tacan (navigation system) 1050 Technical Papers, Bell System, not published in this Journal 327-34, 577-82, 813-22, 1035-42, 1308-13, 1501-07 18 THE BELL SYSTEM TECHNICAL JOURNAL, 1957 Telegraph North Atlantic routes viap 294 transatlantic cable 2, 20, 26-27 Telegraph Construction and Main- tenance Co., Ltd. 308 Telegraphist's Equations See Gen- eralized Telegraphist's Equations Telephone Exchange model, statistics 939-64 Temperature North Atlantic Ocean 1077-86 ocean bottom 1075-86 Terminal(s) carrier, PI 354, 373-75 network, shortest connection 1389-1401 Newfoundland-Nova Scotia link 227-29 transatlantic telephone cable North Atlantic link 52-55 Terrenceville, Newfoundland 11, 219, 232, 246, 248, 293, 295, 318-19, 322, 324; mav 218, 300 Test(s), Testing biochemical oxygen demand 1098-1 1 14 carrier, PI 375 electron tube, 6P12 186-88 conduit, thin-walled 737-54 repeater, flexible North Atlantic link 77-78, 94-96 Test Set 7F 389-90; illus 390 conduit, thin-walled illus 739 Tharp, Marie 1093 Theory of Curved Circular Waveguide Con- taining an Inhomogeneous Dielectric (S. P. Morgan) 1209-51 Thomas, J. F. P. biographical material 346 Power-Feed System for the Newfound- land-Nova Scotia Link 277-92 Time of Day, and radio transmission noise 624 Title, R. S. 1337 Tonawanda Plant (W. E. Co.) 107 Townsend, Mark A. 88-90 biographical material 830 Cold Cathode Gas Tubes for Telephone Switching Systems 755-68 Traffic demand 941 engineering 940 fluctuations 965-73 measurement 939-64 Transatlantic Communications — An His- torical Resume (M. J. Kelly, Sir G. Radley) 1-5 Transatlantic Radio Telephone 5 Transatlantic Telephone Cable cable, see Submarine Cable crosstalk 19-20 echo 21 facilities block diagram 10 frequency characteristics 18, 24-26 maintenance 21-23, 55-57, 235-41 map 8, 302 net loss 18 noise 19-20 operating services 21-23 performance 24-27 profile 304 repeaters, see Repeater route selection 293-326 service objectives 16 signaling objectives 20-21 submarine cable, see Submarine Cable system planning 15-24 telegraph facilities 2, 20, 26-27 telephone circuits 9 temperature profile 1083 transmission objectives 16-18 Transatlantic Telephone Cable System - Planning and Over-All Performance (J. W. Emling, R. G. Griffith, R. J. Halsey, E. T. Mottram) 7-27 Transducer coupled-wave, problems 391 electrohydraulic, J-7 711-36 illus 717, 718 actuating mechanism 719-24 cutaway section 716 description 715-19 exploded view 717 hydraulic characteristics 724-34 internal view 720 ports illus 714 See also Vernier Resolver Transformer, carrier, PI 368-69 INDEX 19 Transistor 4B, carrier, PI 355-56 4C, carrier, PI 355-56 carrier, PI 349-90 submarine cable prospects 3-4 twistor memory arrays 1333-36 Transmission carrier, PI 351-55 information, see Information Rate radio beyond the horizon antenna size 639-40 experimental data 608-11 reflection theory 627-44 seasons 640-43 buildings 613-14 fog 602 fundamentals 593-626 ground wave 614-18 ionospheric 618-23 noise levels 623-24 rain 602 snow 602 trees 613-14 transatlantic telephone cable 16-18 Transmission Aspects of Data Transmis- sion Service Using Private Line Voice Telephone Channels (P. iSIertz, D. iMitchell) 1451-86 Transmission Loss Newfoundland-Nova Scotia Link 220, 241 radio 593-97 earth, plane diagrams 598 line of sight 596-602 Transoceanic Cable See Submarine Cable Transverse Equalizer See Equalizer Traveling-Wave Tibe See Electron Tul)e Trees, and radio transmission 613-14 Tretola, A.R. 1004 Trunk(s), Trunking carriers 350 defined 941-42 TiBE See Electron Tube Ttbing »See Copper Tubing Tucker, Rexford S. biograi)hical material 346 System Design for ike North Atlantic Link 29-68 Tukey, J. W. 576, 964 Turbidity Currents 1089-93 Twistor 1319-40 bits (binary digits) 1330 switching time 1328 transistor powering 1333-36 USAF See United States Air Force Ulrich, Werner biographical material 1513 Non-Binary Error Correction Codes 1341-88 Unger, Hans-Georg biographical material 131S Circular Electric Wave Transmission in a Dielectric-Coated Waveguide 1253-78 Circular Electric Wave Transmission through Serpentine fiends 1279-92 Normal Mode Bends for Circular Elec- tric Waves 1292-1307 United States submarine cable systems 13-14 United States Air Force Missile Test Center, submarine cable 190-92, 214 Van Uitert, L. G. 448 Vapor, organic, contacts, electrical activation 769-812 erosion 769-812 Vasko, T. J. 1004 Veazie, Edmund A. l)iographical material 347 Electron Tubes for the Transatlantic Cable System 163-88 Veloric, Harold S. l)iographical material 1046 High-Voltage Conductivity-Modulated Silicon Rectifier 975-1004 Vernier Resolver applications 1487- 1500 design 1487-1500 output 1489 performance 1487-1500 20 THE BELL SYSTEM TECHNICAL JOURNAL, 1957 Vernier Resolver (Cont.) rotor lamination ill us 1492 schematic diagram 1490 servo system illiis 1497 stator lamination illus 1491 Vocabulary Size information rate 499 Vocoder channel capacity 497 Voltage rectifier, solid state 975 Volz, A. H. 1449 W Wakai, T. W. 1499 Walker, D. C. biographical material 347 Repeater Design for the A'ewfoundlat^d- Nova Scotia Link 245-76 War Work See Military Commun. Watling, R. G. 754 Washington, D. C. state capitals, shortest connection network 1389-1401; illas 1390 Wave circular bends, serpentine transmission 1279-92 modes, normal, l)ends 1292-1307 waveguide, dielectric-coated transmission 1253-78 radio, path 600 See also Microwave Waveguide circular bends, modes, normal 1292-1307 birefringence, effect 409-26 curved, dielectric, inhomogeneous 1209-51 modes, in gj^romagnetic media 409-26 propagation characteristics 409-26 serpentine wave, circular, transmission 1279-92 coupler, see Coupler coupling attenuation 392 coupler, see Coupler dielectric-coated, wave, circular, trans- mission 1253-78 ferrite loaded, propagation character- istics 409 rectangular birefringence, effect 409-26 modes, in gj-romagnetic media 409-26 propagation characteristics 409-26 round, see Waveguide: circular Weatherington, C. A. 495 Weissmann, Gerd F. biographical material 830 Strength Requirements for Round Con- duit 737-54 Welber, I. 1449 Welsby, V. G. biographical material 347 Repeater Design for the Newfoundland- Nova Scotia Link 245-76 Weniw, D. H., Jr. 1337 Werner, J. K. 1449 West Haven, Connecticut map S White, A. D. 768 White Plains, New York map 8 Williams, I. V. 754 Winnicky, A. P. 512 Wire(s) magnetic, twistor 1319-40 Wiring, printed, see Printed Circuitry Wittenberg, A. M. 768 Wooley, M. C. biograjihical material 347 Repeater Design for the North Atlantic Link 69-101 Words familiarity, and information rate 500 length, information rate 500 Wright Air Development Center 1487, 1499 Wrightsville Beach, North Caro- lina, test site 1115-21 Zadeh, L. A. 1387 Zajac, E. E. biographical material 1318 Dynamics and Kinematics of the Laying and Recovery of Submarine Cable '1129-1207 ZoBell, Claude E. 1126 Printed in U. S. A.