IlKfl'Jt.'ilil*;:;:: .' Q--;')2ft5 publir Htbrary This Volume is for REFERENCE USE ONLY Eifsai^imiaTifniirT^^irTriirTriiiyTiB^iini&sii^^^ From the collection of the n m o irrefinger t ibrary San Francisco, California 2008 1>>>')^ J33 THE BELL SYST'Ej TECHNICAL JOURNAL A JOURNAL DEVOTED TO THE SCIENTIFIC AND ENGINEERING ASPECTS OF ELECTRICAL COMMUNICATION EDITORIAL BOARD Bancroft Gherardi H. P. Charlesworth F. B. Jewett A. F. Dixon O. E. Buckley O. B. Blackwell D. Levinger M. J. Kelly H. S. Osborne W. Wilson R. W. King, Editor J. O. Perrine, Associate Editor TABLE OF CONTENTS AND INDEX VOLUME XVI 1937 AMERICAN TELEPHONE AND TELEGRAPH COMPANY NEW YORK Bound PtriodictI PRINTED IN U. S. A. ^^o9^^^ THE BELL SYSTEM" TECHNICAL JOURNAL VOLUME XVI, 1937 Table of Contents January, 1937 A Million-Cycle Telephone System — AI. E. Strieby 1 A Power Amplifier for Ultra-High Frequencies — A. L. Samuel and N. E. Sowers 10 The Physical Reality of Zenneck's Surface Wave — W. Howard Wise 35 Radio Propagation Over Plane Earth — Field Strength Curves — - Charles R. Burrows 45 The Inductive Coordination of Common-Neutral Power Distri- bution Systems and Telephone Circuits — J. O'R. Coleman and R. F. Davis 76 Series for the Wave Function of a Radiating Dipole at the Earth's Surface— 5. O. Rice 101 Technical Digest — Currents and Potentials along Leaky Ground-Return Con- ductors— E. D. Sunde 110 April, 1937 Recent Trends in Toll Transmission in the United States — Edwin H. Colpitis 119 Crosstalk Between Coaxial Transmission Lines — 6'. A . Schelkunoff and T. M. Odarenko 144 Sound Recording on Magnetic Tape — C. N. Hickman 165 Constant Resistance Networks with Applications to Filter Groups — E. L. Norton 178 A Laboratory Evaluation of Wood Preservatives — R. E. Waterman, John Leutritz and Caleb M. Hill 194 Study of Magnetic Losses at Low Flux Densities in Permalloy Sheet— W^. B. Ellwood and V. E. Legg 212 Moisture in Textiles — Albert C. Walker 228 3 ^<'*.i !: ': : ;-; ,'^,£;L>;/JirXyir4f technical journal {"r^ri July, 1937 Scientific Research Applied to the Telephone Transmitter and Receiver — Edwin H. Colpitis 251 The Use of Coaxial and Balanced Transmission Lines in Filters and Wide-Band Transformers for High Radio Frequencies — W. P. Mason and R. A. Sykes 275 A Ladder Network Theorem — John Riordan 303 Contemporary Advances in Physics, XXXI — Spinning Atoms and Spinning Electrons — Karl K. Darrow 319 A Multiple Unit Steerable Antenna for Short-Wave Reception — H. T. Friis and C. B. Feldman 337 October, 1937 Resistance Compensated Band-Pass Crystal Filters for Use in Unbalanced Circuits— PT. P. Mason 423 Magnetic Generation of a Group of Harmonics — E. Peterson, J. M. Manley and L. R. Wrathall 437 The Vodas— 5. B. Wright 456 Radio Telephone Noise Reduction by \'oice Control at Receiver — C. C. Taylor 475 Transmitted Frequency Range for Circuits in Broad-Band Systems—^. A. Affel 487 The Dielectric Properties of Insulating Materials — E. J. Murphy and S. 0. Morgan 493 Variable Frequency Electric Circuit Theory with Application to the Theory of Frequency-Modulation — John R. Carson and Thornton C. Fry 513 Irregularities in Broad-Band Wire Transmission Circuits — Pierre Mertz and K. W. Pfleger 541 Technical Digests — Transoceanic Radio Telephone Development — Ralph Bown. 560 A Negative Grid Triode Oscillator and Amplifier for Ultra- High Frequencies — A. L. Samuel 568 Addendum — Radio Propagation over Plane Earth — Field Strength Curves — C. R. Burrows 574 I Index to Volume XVI Affel, H. A., Transmitted Frequency Range for Circuits in Broad-Band Systems, page 487. Amplifier for Ultra-High Frequencies, A Power, A. L. Samuel and N. E. Sowers, page 10. Amplifier for Ultra-High Frequencies, A Negative Grid Triode Oscillator and (a Digest), A. L. Samuel, page 568. Antenna for Short- Wave Reception, A Multiple Unit Steerable, H. T. Frits and C. B. Feldman, page 337. B Bown, Ralph, Transoceanic Radio Telephone Development (a Digest), page 560 Burrows, Charles R., Radio Propagation Over Plane Earth — Field Strength Curves, page 45. Addendum to "Radio Propagation Over Plane Earth — Field Strength Curves," page 574. Broad-Band Systems, Transmitted Frequency Range for Circuits in, H. A. Affel, page 487. Broad-Band Wire Transmission Circuits, Irregularities in, P. Mertz and K. W. Pfleger, page 541. C Carson, John R. and Thornton C. Fry, Variable Frequency Electric Circuit Theory with Application to the Theory of Frequency Modulation, page 513. Circuit Theory, Variable Frequency Electric, with Application to the Theory of Frequency Modulation, John R. Carson and Thornton C. Fry, page 513. Circuits in Broad-Band Systems, Transmitted Frequency Range for, H. A. Affel, page 487. Coaxial: Irregularities in Broad-Band Wire Transmission Circuits, P. Mertz and K. W. Pfleger, page 541. Coaxial: A Million-Cycle Telephone System, M. E. Strieby, page 1. Coaxial Transmission Lines, Crosstalk Between, 5'. A. Schelkunoff and T. M. Odarenko, page 144. Coaxial and Balanced Transmission Lines in Filters and Wide-Band Transformers for High Radio Frequencies, The Use of, IT. P. Mason and R. A. Sykes, page 275. Coleman, /. O'R. and R. F. Davis, The Inductive Coordination of Common-Neutral Power Distribution Systems and Telephone Circuits, page 76. Colpitis, Edwin H., Recent Trends in Toll Transmission in the United States, page 119. Scientific Research Applied to the Telephone Transmitter and Receiver, page 251. Contemporary Advances in Physics, XXXI — Spinning Atoms and Spinning Elec- trons, Karl K. Darrow, page 319. Crosstalk Between Coaxial Transmission Lines, 5. A. Schelkunoff and T. M. Odarenko, page 144. Crystal Filters for Use in Unbalanced Circuits, Resistance Compensated Band-Pass, W. P. Mason, page 423. Cycle, A Million-, Telephone System, M. E. Strieby, page 1. Davis, R. F. and J. O'R. Coleman, The Inductive Coordination of Common-Neutral Power Distribution Systems and Telephone Circuits, page 76. 5 •': •'•BEjX:''6i^f^'M TECHNICAL JOURNAL Darrow, Kar}.K.^ (Contemporary Advances in Ph\sics, XXXI — Spinning Atoms and Spinr{inj< '.Electrons, page 319. Dielectric Properties of Insulating Materials, The, E. J. Mnrphy and S. 0. Morgan, page 493. Electric Circuit Theory, Variable Frequency-, with Application to the Theory of Frequency Modulation, JoJm R. Carson and Thornton C. Fry, page 513. Ellwood, W. B. and V. E. Legg, Study of Magnetic Losses at Low Flux Densities in Permalloy Sheet, page 212. Feldman, C. B. and H. T. Friis, A Multiple Unit Steerable Antenna for Short-Wave Reception, page 337. Filter Groups, Constant Resistance Networks with Applications to, E. L. Norton, page 178. Filters, Resistance Compensated Band-Pass Crystal, for L^se in Unbalanced Circuits, W. P. Mason, page 423. Filters and Wide-Band Transformers for High Radio Frequencies, The Use of Coaxial and Balanced Transmission Lines in, W. P. Mason and R. A. Sykes, page 275. Frequencies, Ultra-High, A power Amplifier for, A. L. Samuel and N. E. Sowers, page 10. Frequency Modulation, Variable Frequency Electric Circuit Theory with Applica- tion to the Theor}- of, John R. Carson and Thornton C. Fry, page 513. Frequencies, Ultra-High, A Negative Grid Triode Oscillator and Amplifier for (a Digest), A. L. Samuel, page 568. Friis, H. T. and C. B. Feldman, A Multiple Unit Steerable Antenna for Short-Wave Reception, page 337. Fry, T. C. and J. R. Carson, Variable Frequency Electric Circuit Theory with Appli- cation to the Theory of Frequency' Modulation, page 513. Ground-Return Conductors, Leaky, Currents and Potentials along (a Digest), E. D. Sunde, page 110. H Hickman, C. N., Sound Recording on Magnetic Tape, page 165. Hill, Caleb M., R. E. Waterman and John Leutritz, A Laboratory- Evaluation of W'ood Preservatives, page 194. Insulating Materials, The Dielectric Properties of, E. J. Murphy and S. 0. Morgan, page 493. Legg, V. E. and W. B. Elhvood, Study of Magnetic Losses at Low Flux Densities in Permalloy Sheet, page 212. Leutritz, John, R. E. Waterman and Caleb M. Hill, A Laboratory Evaluation of Wood Preservatives, page 194. M Magnetic Generation of a Group of Harmonics, E. Peterson, J. M. Manley and L. R. Wrathall, page 437. Magnetic Losses at Low Flux Densities in Permalloy Sheet, Study of, W. B. Ellwood and V. E. Legg, page 212. Magnetic Tape, Sound Recording on, C. N. Hickman, page 165. Manley, J. M.. E. Peterson a^id L. R. Wrathall, Magnetic Generation of a Group of Harmonics, page 437. BELL SYSTEM TECHNICAL m]f^AL,\ .-. Mason, W. P., Resistance Compensated Band-Pass Crystal Fill^ers^ for Use in Un- balanced Circuits, page 423. j' .'j ,' ', Mason, W. P. and R. A. Sykes, The Use of Coaxial and Balanced J^iV4ii^n\ission Lines in Filters and Wide-Band Transformers for High Radio Frequencies, page 275. Mertz, P. and K. W. Pfleger, Irregularities in Broad-Band Wire Transmission Circuits page 541. Moisture in Textiles, Albert C. Walker, page 228. Morgan, S. O. and E. J. Murphy, The Dielectric Properties of Insulating Materials, page 493. Murphy, E. J. and S. 0. Morgan, The Dielectric Properties of Insulating Materials, page 493. N Network Theorem, A Ladder, John Riordan, page 303. Networks, Constant Resistance, with Applications to Filter Groups, E. L. Norton, page 178. Noise Reduction, Radio Telephone, by Voice Control at Receiver, C. C. Taylor, page 475. Norton, E. L., Constant Resistance Networks with Applications to Filter Groups, page 178. O Odarenko, T. M. and S. A. Schelkiinoff, Crosstalk between Coaxial Transmission Lines, page 144. Oscillator and Amplifier, A Negative Grid Triode, for Ultra-High Frequencies (a Digest), A. L. Samuel, page 568. P Permalloy Sheet, Study of Magnetic Losses at Low Flux Densities in, W. B. Elhvood and V. E. Legg, page 212. Peterson, E., J. M. Manley and L. R. Wrathall, Magnetic Generation of a Group of Harmonics, page 437. Pfleger, K. W. and P. Mertz, Irregularities in Broad-Band Wire Transmission Circuits, page 541. Physics, XXXI, Contemporary Advances in — Spinning Atoms and Spinning Elec- trons, Karl K. Darroiv, page 319. Power Distribution Systems, Common-Neutral, and Telephone Circuits, The In- ductive Coordination of, /. O' R. Coleman and R. F. Davis, page 76. R Radio Frequencies, High, The Use of Coaxial and Balanced Transmission Lines in Filters and Wide-Band Transformers for, W. P. Mason and R. A. Sykes, page 275. Radio Telephone Development, Transoceanic (a Digest), Ralph Bown, page 560. Radio Telephone Noise Reduction by Voice Control at Receiver, C. C. Taylor, page 475. Radio Propagation over Plane Earth — Field Strength Curves, Charles R. Burrows, page 45; Addendum to, page 574. Radio: A Power Amplifier for Ultra-High Frequencies, ,4. L. Samuel and N. E. Sowers, page 10. Radio: A Negative Grid Triode Oscillator and Amplifier for Ultra-High Frequencies (a Digest), A. L. Samuel, page 568. Radio: A Multiple Unit Steerable Antenna for Short-Wave Reception, //. T. Frits and C. B. Feldman, page 337. Radio: Series for the Wave Function of a Radiating Dipole at the Earth's Surface, 5'. 0. Rice, page 101. Radio: The Vodas, 5'. B. Wright, page 456. Radio: The Physical Reality of Zenneck's Surface Wave, W. Howard Wise, page 35. Receiver, Scientific Research Applied to the Telephone Transmitter and, Edwin H. Colpitis, page 251. Research, Scientific, Applied to the Telephone Transmitter and Receiver, Edwin H. Colpitis, page 251. . . . ,',B ELl^, JS \'B T^I TE CHNICA L JO UR NA L Rice, S. 0., Series for the Wave Function of a Radiating Dipole at the Earth's Surface, page Atri ••..•; Riordan, Jo/bj/'j^'J^adder Network Theorem, page 303. Samuel, A. L., A Negative Grid Triode Oscillator and Amplifier for Ultra-High Frequencies (a Digest), page 568. Samuel, A. L. and N. E. Sowers, A Power Amplifier for Ultra-High Frequencies, page 10. Schelkunoff, S. A. and T. M. Odarenko, Crosstalk between Coaxial Transmission Lines, page 144. Short-Wave Reception, A Multiple Unit Steerable Antenna for, H. T. Friis and C. B. Feldman, page 337. Sound Recording on Magnetic Tape, C. N. Hickman, page 165. Sowers, N. E. and A. L. Samuel, A Power Amplifier for Ultra-High Frequencies, page 10. Strieby, M. E., A Million-Cycle Telephone System, page 1. Sunde, E. D., Currents and Potentials along Leaky Ground-Return Conductors (a Digest), page 110. Sykes, R. A. and W. P. Mason, The Use of Coaxial and Balanced Transmission Lines in Filters and Wide-Band Transformers for High Radio Frequencies, page 275. Taylor C. C, Radio Telephone Noise Reduction by Voice Control at Receiver, page 475. Telephone Circuits, The Inductive Coordination of Common-Neutral Power Distri- bution Systems and, J. O'R. Coleman and R. F. Davis, page 76. Textiles, Moisture in, Albert C. Walker, page 228. Toll Transmission in the United States, Recent Trends in, Edwin H. Colpitis, page 119. Transmission, Toll, in the United States, Recent Trends in, Edwin H. Colpitis, page 119. Transmitter and Receiver, Telephone, Scientific Research Applied to the, Edwin H. Colpitis, page 251. Transoceanic Radio Telephone Development (a Digest), Ralph Bown, page 560. Vodas, The, 5. B. Wright, page 456. W Walker, Albert C, Moisture in Textiles, page 228. Waterman, R. E., John Leutritz and Caleb M. Hill, A Laboratory Evaluation of Wood Preservatives, page 194. Wave Function of a Radiating Dipole at the Earth's Surface, Series for the, 5. 0. Rice, page 101. Wide-Band Transformers for High Radio Frequencies, The Use of Coaxial and Balanced Transmission Lines in Filters and, W. P. Mason and R. A. Sykes, page 275. Wise, W. Howard, The Physical Reality of Zenneck's Surface Wave, page 35. Wood Preservatives, A Laboratory Evaluation of, R. E. Waterman, John Leutritz and Caleb M. Hill, page 194. Wrathall, L. R., E. Peterson and J. M. Manley, Magnetic Generation of a Group of Harmonics, page 437. Wright, S. B., The Vodas, page 456. Z Zenneck's Surface Wave, The Physical Reality of, W. Hmuard Wise, page 35. VOLUME XVI JANUARY, i9^Z ^^^^^ ^ THE BELL SYSTEM TECHNICAL JOURNAL DEVOTED TO THE SCIENTinC AND ENGINEERING ASPECTS OF ELECTRICAL COMMUNICATION A Million-Cycle Telephone System — M. E. Strieby .... 1 A Power Amplifier for Ultra-High Frequencies — A. L. Samuel and N. E. Sowers 10 The Physical Reality of Zenneck's Surface Wave — W, Howard Wise 35 Radio Propagation Over Plane Earth — ^Field Strength Curves — Charles R. Burrows 45 The Inductive Coordination of Common-Neutral Power Distri- bution Systems and Telephone Circuits — J. O'R. Coleman and R. F. Davis 76 Series for the Wave Ftmction of a Radiating Dipole at the Earth's Surface— S. O. Rice 101 Technical Digest — Currents and Potentials along Leaky Ground-Return Conductors— E.D.SuTide 110 Abstracts of Technical Papers 113 Contributors to this Issue 116 AMERICAN TELEPHONE AND TELEGRAPH COMPANY NEW YORK 50c per Copy $1.50 per Year THE BELL SYSTEM TECHNICAL JOURNAL Published quarterly by the American Telephone and Telegraph Company 195 Broadway, New York, N. Y. iiiiiiiimiiiiiiiiiiiiiiiiiiiiiniiiiii EDITORIAL BOARD Bancroft Gherardi H. P. Charlesworth F. B. Jewett A. F. Dixon E. H. Colpitis O. B. Blackwell D. Levinger O. E. Buckley H. S. Osborne R. W. King, Editor J. O. Perrine, Associate Editor ■iiiiiiiiinininiiiiiiiiiiiiiminiii SUBSCRIPTIONS Subscriptions are accepted at $1.50 per year. Single copies are fifty cents each. The foreign postage is 3S cents per year or 9 cents per copy. iiiiiiiiiiiiiiiiiiniiiiiiiiiiiiiiiiiiii Copyright, 1937 American Telephone and Telegraph Company PRINTED IN U. S. A. The Bell System Technical Journal Vol. XVI January, 1937 No. 1 A Million-Cycle Telephone System * By M. E. STRIEBY ABOUT two years ago a new wide-band system for multi-channel telephone transmission over coaxial cables was described.^ An experimental system has now been installed between New York and Philadelphia. The various tests and trials which are planned for this system have not been carried far enough to justify a formal technical paper. Meanwhile, the considerable interest that has been aroused in the system has led to this brief statement of its principal features and its general technical performance as so far measured. The coaxial cable itself has been installed between the long distance telephone buildings in New York and Philadelphia, a distance of 94.5 miles. It has been equipped with repeaters, at intervals of about 10 miles, capable of handling a frequency band of about 1,000,000 cycles. This million-cycle system is designed to handle 240 simultaneous two-way telephone conversations. Only a part of the terminal apparatus has been installed, sufficient in this case to enable adequate tests to be made of the performance of the entire system. A general view of the New York terminal is shown in Fig. 2. Some preliminary test conversations have been held over the system, both in its normal arrangement for providing New York- Philadelphia circuits, and with certain special arrangements whereby the circuit is looped back and forth many times to provide an approximate equivalent of a very long cable circuit. The performance has been up to expectations, and no important technical difficulties have arisen to cast doubt upon the future usefulness of such systems. Much work remains to be done, however, before coaxial systems suitable for general commercial service can be produced. The Coaxial Cable Figure 1 shows a photograph of the particular cable used in this installation. It contains two coaxial units, each having a 0.265-inch inside diameter, together with four pairs of 19-gauge paper insulated wires, the whole enclosed in a lead sheath of 7/8-inch outside diameter. * Published in Electrical Engineering for January, 1937. ^ "Systems for Wide-Band Transmission Over Coaxial Lines" by L. Espenschied and M. E. Strieby, Bell Sys. Tech. Jour., October, 1934; Elec. Engg. {A. I. E. E. Transactions), Vol. 53, 1934, pages 1371-80. 1 BELL SYSTEM TECHNICAL JOURNAL Fig. 1 — View showing structure of coaxial cable. Fig. 2 — The New York terminal of the coaxial system. A MILLION-CYCLE TELEPHONE SYSTEM The central conductor of the coaxial units is a 13-gauge copper wire insulated with hard rubber discs at intervals of 3/4 inch. The outer conductor is made up of nine overlapping copper tapes which form a tube 0.02-inch thick; this is held together with a double wrapping of iron tape. The transmission losses of this coaxial conductor at various fre- quencies are shown in Fig. 3. This attenuation is about 4 per cent higher than is calculated for a solid tube of the same dimensions and material. Another matter of importance is the shielding obtained from one conductor to the other or to outside interference. Inasmuch as the most severe requirement is that of crosstalk from one coaxial unit to another, this has been usad as a criterion of design. Figure 4 lb 10 ^ ^ _i ^6 DC UJ c Q. = _] 4 UJ 111 □ 1 ^ y^ X y ,^ ^ X ^^ ^ ^ ^ ^ ^ ^ y ^ 30 50 100 200 500 1000 2000 5000 FREQUENCY IN KILOCYCLES PER SECOND Fig. 3 — Attenuation of the coaxial conductor. shows the average measured high-frequency crosstalk in this particular cable on a 10-mile length without repeaters, both near-end and far-end. Repeaters The amplifiers used in this system were designed for a 10.5-mile spacing and a frequency range of 60 to 1024 kc. A total of 10 complete two-way repeaters has been provided including those at the terminals. Two of the intermediate repeaters are at existing repeater stations along the route, the other six being at unattended locations along the line. Four of these are in existing manholes, while the other two are placed above ground for a test of such operation. Figure 5 shows a manhole repeater with the cover removed for routine replacement of vacuum tubes. Figure 6 shows one of the installations above ground. The measured gain of a typical repeater is shown by the points on the curve of Fig. 7. The curve itself is the line loss that the repeater fe 140 \ \ s \ \ \ S \^ > \ s. X N "N N \, \ FAR-END \ CROSSTALK s NEAR-END CROSSTALK ^ 20 30 40 50 100 200 300 400 500 FREQUENCY IN KILOCYCLES PER SECOND Fig. 4 — Crosstalk between the two coaxial conductors in the new cable. Fig. 5 — Million-cycle repeater mounted in a manhole. Fig. 6— Installation of coaxial repeater above ground. 60 ^ ^ 50 ^ . ^^ in _i iij (D 40 U UJ Q i ^ ^ Z ;3o < y^ /^ Y 20 J / / 10 0 100 2 00 300 400 500 600 700 600 900 1000 FREQUENCY IN KILOCYCLES PER SECOND Fig. 7 — Gain-frequency characteristic of coaxial repeater. BELL SYSTEM TECHNICAL JOURNAL PHILADELPHIA Fig. 8 — Frequency characteristic allocation assignments of a typical speech channel. Broad-band system over coaxial cables (240 telephone circuits). — Con- tinued on page 7. A MILLION-CYCLE TELEPHONE SYSTEM NEW YORK PRIMARY POWER SUPPLY Fig. 8 — Continued from page 6. 8 BELL SYSTEM TECHNICAL JOURNAL is designed to compensate. Three stages of pentodes are used with negative feedback ^ around the last two stages. Attenuation changes due to temperature of the line are compensated automatically by a pilot channel device which has been installed at every second or third repeater. The regulating mechanism uses four small tubes and is added to the normal repeater when desired. The amplifiers shown in Figs. 5 and 6 are regulating. As the cable is underground, the temper- ature changes are very slow and but meagre data on the accuracy of compensation are yet available. Terminals A schematic diagram of the terminal arrangements for a 240-channel million-cycle system is shown on Fig. 8. In this installation the New York and Philadelphia terminals have each been equipped to handle only 36 two-way telephone conversations. As has been pointed out, the scheme employed involves two steps of modulation, the first of which is used to set up a 12-channel group in the frequency range from 60 to 108 kc. Three such groups have been provided in this installation. In order to transmit at the higher frequencies, a second step of modulation is used in which an entire 12-channel group is moved to the desired frequency location by a "group" modulator. Six such group modulators have been provided at various frequencies throughout the range, including both the top and bottom. Patching facilities have been provided so that any 12-channel group may be transmitted over any one of the high-frequency paths. A typical frequency characteristic of one of the channels is shown in Fig. 9. It may be observed that relatively high quality has been obtained, due largely to the use of quartz crystal electric wave filters, even though the channels are spaced throughout the frequency range at 4000-cycle intervals. "^ Preliminary Tests As already noted, various long circuits have been built up by looping back and forth through the coaxial system. One setup over which conversations were successfully carried out consisted of five voice-frequency links in tandem, each link being 760 miles long, giving a total circuit length of 3800 miles. This setup included, in each direction, seventy stages of modulation and the equivalent of 400 line amplifiers, the transmission passing twenty times through each one of the twenty one-way line amplifiers constituting the ten two-way repeaters. 2 "Stabilized Feedback Amplifiers" by H. S. Black, Bell Sys. Tech. Jour., January, 1934. A MILLION-CYCLE TELEPHONE SYSTEM 20 lb V ^ U 0 500 1000 1500 2000 FREQUENCY IN CYCLES PER SECOND 2500 Fig. 9 — Schematic diagram of a coaxial million-cycle system showing frequencies assigned to the different channels. This demonstrated that the complete assemblage of parts, including filters which divide the frequency range into the required bands, modulators which produce the necessary frequency transformations, and amplifiers which counteract the line attenuation, introduced very little distortion. Many problems require further consideration, however, before these systems will be ready for design and production for general use. The final systems must have such refinement that they are suitable for transcontinental distances; the tremendous amplifications needed for such distances must have very precisely designed regulation systems, particularly where aerial construction is involved; noise and crosstalk must not accumulate over the long distances; the repeaters must have such stability and reliability that continuity of service will be assured with hundreds of repeaters operat- ing in series and each repeater handling several hundred different communications simultaneously. A Power Amplifier for Ultra-High Frequencies * By A. L. SAMUEL and N. E. SOWERS A consideration of the special problems encountered at ultra- high frequencies has led to the design of a push-pull power pentode, useful as an amplifier, frequency multiplier, and modulator at fre- quencies of 300 megacycles per second and below. Unusual con- struction features include the mounting of two pentodes in the same envelope with interconnected screen and suppressor grids, complete shielding between the input and output circuits with no common leads, and provision for cooling all grids while maintaining extremely small inter-electrode spacings. The electrical char- acteristics depart from the conventional mainly in the low value of lead inductances and the high value of the grid input resistance at ultra-high frequencies. The second part of the paper describes a single stage amplifier unit built for testing the tube at frequencies between eighty and 300 megacycles, and the associated apparatus for measuring input impedance, gain, and harmonic distortion. The results given indicate that by using this new tube it is possible to construct stable amplifiers at ultra-high frequencies up to 300 megacycles, having gains of twelve to twenty-five decibels per stage and delivering several watts of useful power. Stability and distortion compare favorably with those obtained from conventional tubes at much lower frequencies. PART I— THE VACUUM TUBE By A. L. SAMUEL WE ARE witnessing a rapid expansion and extension in the use of radio communication. A corresponding extension in the usable portion of the radio-frequency spectrum is highly desirable. With this in mind, special forms of vacuum tubes have already been developed for use as oscillators at frequencies above 100 megacycles.^- ^ Except at low power levels,^ amplifier tubes have not been available. * Presented at Institute of Radio Engineers meeting, New York City, October 7, 1936. Published in Proceedings I.R.E., November, 1936. 1 M. J. Kelly and A. L. Samuel, " Vacuum Tubes as High-Frequency Oscillators," Elec. Eng., vol. 53, pp. 1504-1517, November, 1934; Bell Sys. Tech. Jour., vol. 14, pp. 97-134, January, 1935. 2 C. E. Fay and A. L. Samuel, "Vacuum Tubes for Generating Frequencies Above One Hundred Megacycles," Proc. I.R.E., vol. 23, pp. 199-212, March, 1935. ' B. J. Thompson and G. M. Rose, "Vacuum Tubes of Small Dimensions for Use at Extremely High Frequencies," Proc. I.R.E., vol. 21, pp. 1707-1721, December, 1933. 10 ULTIL4.-HIGH-FREQUENCY POWER AMPLIFIER 11 It is the purpose of this paper to discuss the problem of amplification at ultra-high frequencies and to describe one form of amplifier tube designed for moderate power in that frequency range. The Triode as an Amplifier at Ultra-High Frequencies A simple triode amplifier as used at low frequencies becomes un- stable as the operating frequency is increased, exhibiting a tendency to oscillate or "sing" because of the interaction between the input and output circuits. This interaction or "feedback" is, in the main, pro- duced by the grid-plate capacitance of the tube. It may be overcome either by the introduction of a compensating capacitance somewhere in the circuit or by the introduction of an electrostatic shield or screen within the tube envelope. The first expedient, known as neutraliza- tion, is employed in the case of a triode. The second expedient results in the screen-grid tetrode. At moderately high frequencies either arrangement may be used. The conventional triode is unsatisfactory at very high frequencies. The usual capacitance neutralization scheme fails, partly because of the inductance of the tube leads which makes difficult the correct loca- tion of the neutralizing capacitance. The appreciable time required for the electrons to traverse the interelectrode spaces within the tube structure makes neutralization more difficult by introducing a shift in the phase of the necessary compensation. A more serious effect of electron transit time is the marked increase at high frequencies in the input conductance of a tube over the value observed at low frequencies. This effect has been the subject of con- siderable study .^•^' *• '' Theory and experiment both agree in relating the input conductance loss to the tube geometry and the applied electrode potentials. The conductance depends upon the electron transit time and increases rapidly with increasing frequency. The transit time may be reduced either by decreasing the electron paths or by increasing the electron velocities. Decreasing the path calls for smaller interelectrode spacings, and increasing the velocity calls for higher electrode potentials. On the other hand, practical considera- tions limit both the dimensions and the potentials. An optimum de- sign may utilize special mechanical arrangements to combine both expedients. * J. G. Chaffee, "The Determination of Dielectric Properties at Very High Fre- quencies," Proc. I.R.E., vol. 22, pp. 1009-1020, August, 1934. ^ F. B. Llewellyn, "Operation of Ultra-High-Frequency Vacuum Tubes," BellSys. Tech. Jour., vol. 14, pp. 632-665, October, 1935. ^ W. R. Ferris, "Input Resistance of Vacuum Tubes as Ultra-High-Frequency Amplifiers," Proc. I.R.E., vol. 24, pp. 82-104, January, 1936. ' D. O. North, "Analysis of the Effects of Space Charge on Grid Impedance," Proc. I.R.E., vol. 24, pp. 108-136, January, 1936. 12 BELL SYSTEM TECHNICAL JOURNAL The electron transit time limitation becomes of particular importance at frequencies above one hundred megacycles and sets an upper fre- quency limit on the useful operation of the usual triode as an amplifier just as it sets the limit at which the tube will operate as an oscillator. Because of the similarity in the special high-frequency requirements, negative grid tubes designed for use primarily as ultra-high-frequency oscillators are good amplifiers at somewhat lower frequencies. The necessity for very careful circuit design and for critical adjustment of the neutralization becomes particularly pronounced when triodes are used as ultra-high-frequency amplifiers. The Multi-element Tube as an Amplifier at Ultra- High Frequencies Conventional screen-grid tetrodes and pentodes are also unsatis- factory at very high frequencies. Two factors are again primarily re- sponsible, the one set by the circuit requirements, the other set by the electron transit time. These limitations will be considered in detail. In the usual radio-frequency amplifiers using tetrodes or pentodes the input and output circuits are tuned to the desired frequency. For most practical purposes the upper limit to the frequency for which these circuits may be tuned is set by the natural period of the circuits formed by the corresponding lead inductances and interelectrode ca- pacitances. Even before this limit is reached the major portions of the tuned circuits are within the tube envelope. Their inaccessibility makes it difficult to obtain efi'ective coupling between amplifier stages. Interaction between the input and output circuits if excessive may cause "singing." Such interaction is usually due to the residual value of the grid-plate capacitance. Not only must this capacitance be made very low by the proper design of the screen and suppressor grids, but its effective value must remain low at the operating frequency. This latter is realizable only if the screen and suppressor grids can be coupled to the cathode by leads having extremely small inductances. A further desirable feature is that there be no appreciable circuit im- pedance in the form of lead inductance common to both input and out- put circuits. The use of short leads is thus seen to be just as important in the design and use of the multi-element tube as it is in the design of the triode. As in the case of the triode, the electron transit time is effective in limiting the useful frequency range of the multi-element tube. The increase in the input conductance which it introduces is again primarily responsible. In considering the design of an amplifier tube for ultra-high fre- quencies, it appeared desirable to select frequency and power levels ULTRA-HIGH-FREQUENCY POWER AMPLIFIER 13 such that a break from conventional design was inevitable, leaving for future work the satisfactory coverage of the transition region. Since triodes had already been studied as oscillators it was decided to design and construct a pentode. A tentative rating of fifteen watts anode dissipation (per tube) with an operating range up to 300 megacycles was chosen. It was further thought desirable to limit the sum of the grid-to-ground and plate-to-ground capacitances to a value less than eight micromicrofarads in order to facilitate the design of the accom- panying circuits. Preliminary considerations led to the conclusion that the desired results could be best obtained by push-pull operation. In view of the required shortness of leads it seemed logical, if not essential, to inclose both sets of tube elements within one envelope and to provide an internal by-pass condenser between the screen and suppressor grids. It also appeared desirable to design the structure so that a simple ex- tension of the screen-grid element would form a partition separating the input portion of the tube from the output portion. By mounting the tube so that the internal partition forms a continuation of the external partition separating the input and output circuits, quite adequate shielding should be possible. From previous experience, it was con- cluded that the special frequency requirements for a 300-megacycle amplifying tube would be satisfied by a design patterned after a 600- megacycle oscillator tube.^ To summarize, the following construction features were considered desirable : (1) The mounting of two sets of elements in the same envelope. (2) A method of interconnecting the two screen grids by a low im- pedance conductor. (3) A method of grounding the screen and suppressor grids inside the tube envelope. (4) Complete shielding between input and output sides of the tube. (5) The use of extremely short leads. (6) Means for maintaining very small spacings between the elements. (7) Provision for adequate cooling of all grids. (8) Adequate insulation paths to permit a high anode potential. (9) The absence of any leads common to both input and output circuits. The first of the experimental tubes designed to have a fifteen-watt dissipation per anode is shown in Fig. 1. It will be noted that a parti- tion divides the envelope into two parts. This partition is in reality double, being made up of two sheets, one being connected to the sup- 14 BELL SYSTEM TECHNICAL JOURNAL pressor grids and the mid-point of the filament circuit and the other being connected to the screen grids. Slots in these sheets provide space to mount the tube elements. The capacitance between the two closely Fig. 1 — An early experimental type tube. spaced sheets forms an effective radio-frequency by-pass condenser between the screen grids and the filaments. Fig. 2 is a section view Fig. 2 — Section view of the tube shown in Fig. 1. through the middle of the tube showing the disposition of the elements. While entirely satisfactory from an operating viewpoint, this design proved to be rather difficult to fabricate. ULTRA-HIGH-FREQUENCY POWER AMPLIFIER 15 The Ultra-High-Frequency Double Pentode Tube The successful operation of the experimental models described above indicated the desirability of continuing this line of attack. A complete mechanical redesign to facilitate the fabrication and pumping was undertaken. Fig. 3 is a photograph of this design. Section views are shown in Fig. 4. The large capacitance between the screen and suppressor which characterized previous models was retained in the form of concentric cylinders instead of parallel plates. These cylinders and the flange at one end effectively shield the input and output sides of the tube. The low impedance connection between the two screens provided by these cylinders is an important feature of the design. Adequate cooling of the screen grid is provided by mounting it directly Fig. 3 — The ultra-high-frequency double pentode vacuum tube. in a slot in one of the cylinders. The control grids are of the so-called fin type of construction already employed with considerable success in triode oscillators. They consist of a series of tungsten loops attached to a common cooling fin. This construction makes feasible the use of extremely small dimensions, so that the grid-filament spacing is com- parable with the filament diameter. One of these grids is illustrated in Fig. 5. The length of leads has been kept as small as is consistent with mechanical requirements. The longest lead, measured from the mid-point of its attached element to the outside of the envelope, is about three centimeters. Other details of the design are evident from the photograph and the diagram. Operating characteristics and constants are listed in Table I. Special attention is directed to the values of interelectrode capaci- tances and lead inductances. It will be observed that while the inter- Fig. 4 — Section view of the double pentode tube. Fig. 5 — One of the control grids used in the double pentode tube. ULTRA-HIGH-FREQUENCY POWER AMPLIFIER 17 TABLE I Operating Characteristics and Constants of the Double Pentode Tube Filament current (each side) 5.0 amperes Filament potential (each side) 1.5 volts Rated anode dissipation (each anode) 15 watts Rated screen dissipation (each side) 5 watts At anode and screen potentials of 500 volts and anode current of 0.030 ampere — characteristics of each side Transconductance 1250 micromhos Anode resistance 200,000 ohms Normal control grid potential —45 volts Inlerelectrode capacitances {when properly mounted) Direct control grid to control grid 0.02 micromicrofarad Direct plate to plate 0.06 micromicrofarad Total control grid to ground (each side) 3.8 micromicrofarads Total plate to ground (each side) 3.0 micromicrofarads Control grid to plate (each side) 0.01 micromicrofarad Lead inductances Total grid to grid 0.07 microhenry Total plate to plate 0.08 microhenry Rating as class A amplifier Maximum direct plate potential 500 volts Maximum direct screen potential 500 volts Maximum continuous plate dissipation (each) 15 watts Maximum continuous screen dissipation (total) 10 watts Maximum output at 150 megacycles with distortion down 40 decibels 1 watt Nominal stage gain at 150 megacycles 20 decibels Nominal control grid potential —45 volts Rating as class B amplifier Maximum direct plate potential 500 volts Maximum direct screen potential 500 volts Maximum space current (total) 150 milliamperes Maximum continuous plate dissipation (each) 15 watts Maximum continuous screen dissipation (total) 10 watts Maximum output at 150 megacycles 10 watts electrode capacitances are low they have not been reduced in propor- tion to the reduction in operating wave length. The more important feature is the reduction of the lead inductances. Tabulation of the value of these inductances represents a departure from the conven- tional practice and is made desirable by their relative importance. A feature of the design not directly measurable under actual operat- ing conditions but nevertheless responsible for some of the improve- ment over the more conventional designs is the reduction of an auxil- iary dielectric material and the attending dielectric losses that occur at ultra-high frequencies. The usual static characteristics given in Figs. 6 and 7 are seen to resemble those of the conventional pentode. For a tube which is to be used at ultra-high frequencies, certain other characteristics have a much greater significance. One of the most important of these is the 18 BELL SYSTEM TECHNICAL JOURNAL active grid loss which as already mentioned comes about because of the appreciable electron transit time. Fig. 8 gives a plot of the push-pull input shunting resistance of this tube as a function of frequency. The / f J / / FILAMENT CURRENT, 5 AMPERES / / / / / / / Ep=Es=600 y / / / > / "y / A / / / / 400 / / / / / / 300 / / / ^^ ^ ';^ ^ ^ ^ 200/ / 80 70 60 50 40? I- Z UJ a. 30 § o 20 10 FILAMENT CURRENT, 5 AMPERES f ' ' Ep=Es=600 y 500/ 400 / ^ / /.. •/ 200/ -:: ^ ^ ^'^^ -^ < 100 90 80 70 60 50 40 30 20 CONTROL GRID POTENTIAL IN VOLTS 10 Fig. 6 — Mutual characteristics of the double pentode tube. 40 30 20 10 value of 30,000 ohms at 150 megacycles is to be compared with 2000 ohms, a typical value for two conventional tubes in push-pull. At 300 megacycles the input resistance of the twin pentode is still above 5000 ohms while for conventional tubes it is so low as to make them com- ULTRA-HIGH-FREQUENCY POWER AMPLIFIER 19 pletely inoperative. The variation in the input resistance with the operating conditions of the tube for a constant frequency of 150 megacycles is shown in Fig. 9. It is evident that if a high value of input resistance is to be realized, high anode potentials with low space cur- 60 50 40 30 < ^ Eg=-30 FILAMENT CURRENT, 5 AMPE SCREEN POTENTIAL, 500 VO RES LTS -^ -40 -— 20 -50 10 -60 n -70 a^o 30 20 10 s FILAMENT CURRENT, 5 AMPERES SCREEN POTENTIAL, 500 VOLTS Eg= -30 ^ -40 -50 ~~— -60 -70 300 400 500 600 PLATE POTENTIAL IN VOLTS 90(7 Fig. 7 — Anode characteristics of the double pentode tube. rents must be used. The reduction in the filament grid spacing made possible by the unusual construction is in a large measure responsible for the improvement in the input resistance just noted. A characteristic measurable only at the operating frequency is the interaction between the input and output circuits which results from 20 BELL SYSTEM TECHNICAL JOURNAL the residual value of the grid-plate capacitance. This reaction differs from that predicted from the low-frequency capacitance measured on a cold tube because of the inductance of the screen-grid lead and be- cause of the electron space charge. The reaction can be measured by' observing the variation in the input impedance resulting from a varia- tion in the tuning and loading of the output circuit. Experimentally determined values are given in Fig. 10. 100 80 60 40 20 10 \ "^ \ V 1- TYPICAL CONVt.NI lONAU TYPE TUBE 2-MIDGET RECEIVING TUBE ^ 3-ultra-high frequency \ double pentode \ (grid to grid) V \ \ \ \ L \ \ \ N \ \ \ 3 \ 1 > \" \ V > ^ \ \ \ \ \ \ \ \ k \ \ \ \ 40 60 80 100 200 400 FREQUENCY IN MEGACYCLES PER SECOND Fig. 8 — The input resistance as a function of frequency. The double pentode tube has been found useful as a high quality class A amplifier, a class B amplifier, a frequency multiplier, and as a modulator at frequencies of 300 megacycles per second and below. Its performance in these various modes of operation is quite comparable to the performance of conventional pentodes of similar ratings at much lower frequencies. Stable operation with some gain has been obtained at frequencies as high as 500 megacycles. Because of the increased im- ULTRA-HIGH-FREQUENCY POWER AMPLIFIER 21 portance at ultra-high frequencies of circuit design in the over-all performance of an amplifier or modulator, such tests cannot be con- sidered as a definite measure of the capabilities and limitations of the tube but they indicate what has already been accomplished. When operating as a class A amplifier at 150 megacycles an output of one watt is obtained with the distortion forty decibels below the fun- 28 2 O 24 20 16 12 TYPICAL VALUES AT 150 MC: ^ 500 V ^^ ~^ "^ 400 V. ^~^ ^~^ ^ ^~- 320 V. ^ ^ 60 70 80 90 TOTAL SPACE CURRENT IN MILLIAMPERES Fig. 9 — The variation in input resistance with operating conditions at 150 megacycles. 100 damental. Under these conditions the stage gain is twenty decibels. Outputs of ten watts with a plate efficiency of sixty to seventy per cent and a gain of ten decibels are secured with class B operation. Ex- perimental results confirming these statements together with a dis- cussion of the principles of circuit design and the technique of measure- ments are given in the accompanying paper by N. E. Sowers. 22 BELL SYSTEM TECHNICAL JOURNAL 40 UJ u ^^ '£1 z UJ H IX I I o •-1- z z — UJ UJ o 36 32 28 24 20 TYPICAL VALUES ^^ ■\ AT 150 MC : ^ ^ 1 Eb=Es= 600 V. ^- ^^ ^~^ --. .^ ^ ^ 400 V. --- — - -^ 32 D V ^ ^ 60 70 80 90 100 TOTAL SPACE CURRENT IN MILLIAMPERES Fig. 10 — The input-output reaction at 150 megacycles. Conclusion The development of this ultra-high-frequency pentode demonstrates that amplifier tubes of the negative grid type are usable at higher power levels and frequencies than have been reported previously. The extension of the principles underlying the design of this tube to the design of a tube with approximately ten times the output is now being considered. This type of development removes a practical barrier which has, up to the present, prevented the successful utiliza- tion of this frequency range. PART II— THE CIRCUIT By N. E. SOWERS Introduction In the first section of this paper A. L. Samuel has described the development of a push-pull pentode designed to function as a stable i ULTRA-HIGH-FREQUENCY POWER AMPLIFIER 23 amplifier at frequencies up to at least 300 megacycles. It is the pur- pose of the present section to describe the methods and apparatus used in testing this tube and to set forth the results of some of the tests. An attempt to study the operating characteristics of an amplifier tube at ultra-high frequencies brings up many new problems. Such fundamental properties of the tube as amplification factor, transcon- ductance, and plate impedance do not convey as much information about the behavior of the tube at these frequencies as they do at lower frequencies. The presence of unavoidable stray inductances and capacities makes it much more difficult to separate tube problems from circuit problems. Consequently, at ultra-high frequencies we are vir- tually forced to consider the tube and its associated circuits as com- prising a single piece of apparatus. If the circuit design is carefully made the stray inductances and capacitances can be greatly reduced in magnitude and so localized that their effects upon the over-all perform- ance of such a piece of apparatus can, to a certain extent, be computed. Circuit Design Some idea of the extreme attention to detail required in designing amplifier circuits for use at ultra-high frequencies may be gained from the following considerations. Computations indicate that even with the tuned plate and grid circuits placed as close as physically possible to one of these push-pull pentodes, at 300 megacycles, the radio-fre- quency voltage actually applied to the grids of the tube may be as much as twenty-five per cent greater than the voltage developed across the tuned grid circuit. At the same time the load presented to the tube plates may be as much as twice the load actually present across the tuned plate circuit. These discrepancies are a direct result of the in- ductance of grid and plate leads which, in the case of this new tube, have already been reduced well nigh to the minimum possible. In studying the performance of these tubes we wished to be able to check experimental results against theory at every possible point. Consequently the simplest auxiliary circuits were chosen, namely, shunt-tuned antiresonant circuits from grid to grid and from plate to plate, with screens and filaments by-passed as directly as possible to ground. In their mechanical design these circuits embody a number of features intended to reduce and localize stray inductances and capacities, into the details of which it is not possible to go at present. A simple arrangement was evolved to provide a maximum of conven- ience and flexibility for experimental work. The single stage amplifier unit consists of three sections, an input circuit section, a tube housing section, and an output circuit section. This arrangement permits 24 BELL SYSTEM TECHNICAL JOURNAL tubes to be changed with a minimum of disturbance to the circuits. During experimental work it is almost inevitable that circumstances will arise calling for major changes in the nature of the circuits, or the size, shape, and lead arrangement of the tubes. This sectional construction provides the necessary flexibility to take care of such needs, as the construction and substitution of appropriate new sec- tions would permit the experimental work to proceed with a minimum of delay. To facilitate the operation of several units in tandem for tests on a multistage amplifier, each section is provided with its own power supply jacks so that the only longitudinal connections required BLOCKING CONDENSERS TUNING CONDENSERS TUNING COILS BYPASS CONDENSERS CAPACITY BETWEEN SCREEN 2. SUPPRESSOR CYLINDERS INSIDE TUBE LOAD RESISTANCE RADIO FREQUENCY CHOKES PEAK VOLTMETER CIRCUITS Fig. 1 1 — Circuit diagram of single stage test amplifier. within the sections are those between tube leads and the circuits. These connections are so arranged as to be very easily broken when sections are to be separated. Each circuit section has built into it a pair of peak voltmeters for indicating the radio-frequency voltage de- veloped across the tuned circuit. These voltmeters consist of RCA type 955 tubes used as diode rectifiers in the familiar self-biased peak voltmeter circuit. Fig. 11 shows the circuit in schematic form. Fig. 12 shows an experimental two-stage amplifier constructed in substan- tially the same fashion as the test circuit, but without the sectionaliz- ing feature. ULTRA-HIGH-FREQUENCY POWER AMPLIFIER 25 The desire to reduce the length of all leads to a minimum has naturally resulted in bringing the tuned circuits rather close to the sides of the circuit housings. Nevertheless care and attention to Fig. 12 — An experimental two-stage one-meter amplifier using two of the earlier type push-pull pentode tubes. detail in the circuit design have enabled the stray capacities to be kept down to satisfactory values. Fig. 13 shows in'schematic form one of 0.025 MH 150 MMF 50MMF 0.025 MH 3.8 --l- MMF-J-- I -7- I I I 3.8 _!.. MMF-r- I I I ^75M^ 0.025 MH .0.02 'MMF Fig. 13 — Diagram of interstage circuit. these circuits employed as the interstage circuit between two of these push-pull pentodes, all of the important inductances and capacities being included. 26 BELL SYSTEM TECHNICAL JOURNAL Input Impedance Measurement One of the factors which effectually limits the performance of a vacuum tube at ultra-high frequencies is the internal grid resistance or active grid loss. Consequently, this factor is of extreme interest in the development of amplifier tubes for use in the ultra-high-frequency range and much of this work has centered around the development of apparatus and technique for rapidly and accurately measuring these input resistances. The method employed has been the simple resist- ance substitution method used by Crawford.* An adjustable quarter- wave Lecher frame is provided with suitable means for inducing a radio-frequency voltage across it and a suitable detector for indicating the current flowing at the short-circuited end. A calibration is made by noting the detector indication corresponding to various known resistances connected across the open end of the frame, with the input voltage held constant. The input circuit of the tube under test is then connected to the end of the Lecher frame in place of the calibrating resistors and the detector indications corre- sponding to various voltages and loads applied to the tube are noted. Since the Lecher frame is initially tuned to the operating frequency, and when the tube input circuit is attached the circuit itself is retuned for resonance, it follows that the quantity actually measured is the efi'ective resistance across the tuned circuit, including both the circuit losses and the active grid loss of the tube. It is of course possible to determine the circuit losses separately and to compute the contribution to the total resistance offered by the tube losses, and also to compute the active grid loss existing directly at the grids of the tube, taking into account the impedance transformation existing between the tube grids and the tuned circuit, brought about by the lead inductances. Practi- cally, however, the total effective shunt resistance across the tuned circuit as actually measured is a more significant quantity, as this quantity determines more or less directly the gain which can be ob- tained from a multistage amplifier. It frequently happens that changes in the voltages applied to the tube produce small changes in the reactive component of the input impedance. These may be taken into account by noting the changes in grid circuit tuning required to maintain resonance. These changes are usually so small as to be of only minor interest. The Lecher frame used in these measurements is shown in Fig. 14. The plate bridging the frame nearest the open end carries the detector, an RCA type 955 tube set into the plate. The grid of this tube is * A. B. Crawford, "Input Impedance of Vacuum Tube Detectors at Ultra-Short Waves" (Abstract), Proc. I.R.E., vol. 22, pp. 684-685, June, 1934. ULTRA-HIGH-FREQUENCY POWER AMPLIFIER 27 coupled to the frame by means of a small rectangular single turn loop mounted just beneath and quite close to the bars at the short-circuited end. The second plate bridging the bars, in conjunction with the elec- trostatic screen between the bars and the input coupling coil, aids in ' 1 Fig. 14 — Photograph of impedance measuring Lecher frame. 1. Short-circuiting bridge carrying detector tube and detector coupling coil. 2. Auxiliary bridge for breaking up unbalance currents flowing on the frame. 3. Input circuit. Note electrostatic screen between frame and input coil mounted on end of flexible transmission line leading to driving oscillator. 4. Clips carrying calibrating resistors. 5. Jacks into which plugs on amplifier input circuit fit. eliminating any unbalance of the currents flowing in the two sides of the frame. The aluminum trough surrounding the frame provides sufficient shielding to render the apparatus virtually immune to the operator's body capacity effects. The whole resistance measuring 28 BELL SYSTEM TECHNICAL JOURNAL setup is remarkably stable and satisfactory to operate. Resistance measurements on a given tube at specified operating points can be repeated with a precision of two or three per cent even when weeks elapse between measurements. In addition to being a function of frequency, the input resistance of one of these tubes is also a function of all of the operating conditions, that is, applied voltages, plate circuit tuning, and load. In Table II are shown values of this input resistance for a typical tube at several frequencies and over a considerable range of operating conditions. Because of the large number of variables which affect this input resist- ance it is difficult to devise any way of plotting up these data so as to give a comprehensive picture of tube performance. The variation of input resistance with plate circuit tuning has, for this design, consistently been of the form illustrated in Fig. 15. How- 1.4 ^1.3 D h- Zl.2 liJ 1'- ^ 1.0 O 0.9 (£ 0.8 A — \ ^ ^ V ^ ^ 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00 1.01 TUNING VARIATION 1.02 1.03 1.04 1.05 1.06 1.07 1.08 Fig. 15 — Reaction curve. ever, the relations between maximum, minimum, and "in-tune" values vary somewhat with frequency, operating conditions, and plate load. Also, as may be expected, they vary somewhat in different tubes which have been made up with various grid and screen spacing, etc. A con- venient numerical measure of the magnitude of this reaction is ob- tained by taking the difference between the maximum and minimum values at any specified operating point and dividing this difference by the "in-tune" value. This reaction ratio will also be found listed in Table II for various operating conditions. Gain Measurements The measurement of the voltage gain of an amplifier stage con- taining one of these tubes is a relatively simple matter. As stated in the description of the circuit, provision is made for connecting a peak voltmeter directly to each tuning condenser plate in both plate and ULTRA-HIGH-FREQUENCY POWER AMPLIFIER 29 < D < &§ wo §§ ^J P' ^ u < w < <; ^ ►J H z o Oi, oot-~ o (n oo o vo t^ O VO lO 0\ ^00 ^ \o -^ O— ' _4; ^d -^d ^d "o >. CJ O OOO O'* o»^ a; 00 O CN lO t^ lo o E o (V> ^ Tl< -H t^ CN '^'d "^d ^d o fO II ■<*0 ro O lO o^ vO O (T) Ot^ O'l 0,-( O ^ •^ CN -^d ^d ^d o o ■* O r. n! OOJ^ O-H Ot^ OOO ■* IT) ^ lO lO E o 00 •rH ro CN <-^ CN •^d *^d ^d II 'i'OO Ot^ o o "*-. \0 O lO "0 CN Ot- vO'-i •^ (M O CN ^d °°d 2d OOrt* O-^ O PC o lo t^ lO ^ lO t^ ■^ r^ r-< ro CS CN CN _a; *-d ^d> :^d >. rt o o lo O-H OOO M ooio 00 lO "0 O ON E o VO-H OS CN \0 CN °°d 2d :2d o CN II •^ Ol^ Ot^ O'* **-» OOCN lOsO lO CN Ov -^ ■^ tM Ov CO ^d ::jd ^d OOt^ o-^ o^ OOO U-) t^ O -H ^ irjCN CN CN pom :2d 2d ;^o >t o rt OOO OOs oo ^d ?Jo So _o _o _o C3 (ti rt 01 u 0) u (U l- o _ o _ CJ _ c S c c c S 5-2 2-2 1-2 .<£ tj ^ u ^ u ' b^ > bl > 11 o >. o 11 o ■* ID a. "^ „ a. ft. „ ►-ife; II kl 11 ttl II Pi ^ 30 BELL SYSTEM TECHNICAL JOURNAL grid circuits so that the applied grid drive and developed plate voltages may be read directly. Of course, the gain figure arrived at in this man- ner is an over-all factor, a function both of tube conditions and circuit construction and loading. Nevertheless, it is a satisfactory figure of merit for the stage. In Table III are shown these gain figures for a typical tube under various conditions. Fig. 16^ — Distortion measuring equipment. Nos. 1 and 2 — Signal oscillators. 3 — Capacitance bridge. 4 — Auxiliary amplifier. 5- — Power supply unit for auxiliary amplifier. 6 — Transmission lines to tube under test. 7 — Transmission line from tube under test to radio receiver. 8— Beating oscillator, first detector and attenuator. 9 — Intermediate amplifier and second detector of receiver. ULTRA-HIGH-FREQUENCY POWER AMPLIFIER 31 u D H :z; u erf erf D U 0 ro 0 OS 10 ^_ 0 ■-H t^ so 0 '*d'* rOCN '^ roodrfj 1 CN tN ^ CM ^ ■r-l CM -H ^ >1 be 0 0 >o iq -*OOs sq CM p i 00 Tt* 0^ ^ ro Os fC ri 06 rri CN T^ .-c CM T^ -H CM -^ -- O o 11 11 "* -H t^ \0 10 —_ 0 °9 ■* fO 0 . o 0 OsOn^_ CCCO 00 IT) liO OS 00 f^ 06 IT) rr> 00' cm' cm' t-^ •rH CN •^ -H CM ^ •rt CM -H •^ o m '^i' II s; 0 oiq '*!'*'^ t^ 1^ CM 0 re 00' t^' CN t--^ -^ ^o'-h' CN •r-< ^ CM -H ^H CM -H .^ 0 OvOO^ 0 '"IP sq 1-- sq 0 •** Os r^j ■^' 0C3 cm' po t-^ ^ ■Si ■5 CN •^ •rt C-1 rt -r-^ CN >-i —1 >. 0 c4 0 IT) VO 10 On p 0\ '^. '^. P E 00 Tt< odr-i . 0 to 0 ■r-H •.— 1 t^ 10 10 --H t-- t^ CM 0 E 00 vd Ov csi iri 00 CM ■5t' t^ -H CSJ •rt ^ CM ^H .rt CM -H -^ p 7 ^ CM CM 00 vq sq CM OS Os uo 0 irj 00 ■^ Tt't^ -^ fOso'o cs ^ ^ CM ■^ •.-1 CM -H T-H en 0 1^ 0 4* T3 * -a U v 0) -a-<— TD-t— "O-*— Q^ S — 0 0 ^O-t- rtO-4- ir> i! ooo qOO rz d — 00 — 00 *5 ?r 0 Cirjo Cir50 CioO ^D- hJ 3 ^10 3— .irj 3 -H uo tn tn tn tO-Q to 0 to 0 H^ > b^ > [t^ > II g II g 118 + , "^ . "* 10 c t. ft. „ c. *-, [:ti II bj II tj II in u 4) 4) F s 0 > 0 ^ > (U ^ a 11) 0 a *^ 5.0 *^ c 32 BELL SYSTEM TECHNICAL JOURNAL Distortion Measurements One of the quantities of fundamental interest in studying class A amplifiers is the amount of distortion to the applied signal generated in the tube. The technique of making distortion measurements at audio and carrier frequencies is well understood and presents no outstanding problems. However we would not expect distortion measurements made at low frequencies to have any significant application to ultra- high-frequency operation. Since the input resistance of a tube at these frequencies is obviously a function of the various voltages and currents we should expect this input resistance to vary throughout the radio- frequency cycle, that is, to be essentially nonlinear. The question of whether or not this nonlinearity is of sufficient magnitude to cause trouble can best be answered by making direct distortion measure- ments at the ultra-high frequencies. After some consideration of the various methods of measuring distortion we have chosen the two- tone method as being the most promising. In this method two inde- pendent frequencies suitably chosen in the transmission band of the amplifier are fed into the amplifier and the amplitudes of these two tones and such of their modulation products as are of interest are measured in the output of the amplifier by means of a suitable voltage analyzer. In the present case the "tones" are actually a pair of ultra- high-frequency signals. The principal precaution which must be taken in this method is to prevent the oscillators which supply the driving frequencies from reacting on each other and producing distortion prod- ucts ahead of the amplifier under test. In the present case we have taken care of this requirement by using relatively high powered driving oscillators, very well shielded, from which only very small amounts of power are taken by means of very loosely coupled and electrostatically screened coupling coils. The outputs of the two oscillators are still further isolated from each other by connecting each across opposite diagonals of a balanced capacity bridge and taking off the voltage to drive the circuit under test across one arm of the bridge. A small amount of the voltage developed in the output circuit of the amplifier under test is picked up by a small coupling coil and fed into a voltage analyzer by means of which the relative amplitudes of the testing fre- quencies and their modulation products may be measured. This voltage analyzer consists of a high gain superheterodyne receiver having a rather sharply tuned, intermediate-frequency amplifier and an extremely precise tuning arrangement on the beating oscillator. The intermediate-frequency amplifier contains an attenuator which, in conjunction with the second detector current meter, permits the rel- ative amplitude of signals to be measured. ULTRA-HIGH-FREQUENCY POWER AMPLIFIER 33 The oscillators are push-pull tuned-plate — tuned-grid oscillators employing Western Electric type 304-A tubes with about 900 volts on their plates. These oscillators each deliver about twenty-five watts of radio-frequency power, nearly all of which is dissipated in a resist- ance load inside the shielding compartments. The receiver (voltage analyzer) has approximately one hundred decibels gain and a ninety- three-decibel attenuator adjustable in one-decibel steps so that measurements over a very wide range of amplitudes are possible. It was found desirable to interpose an additional amplifier (also using these push-pull pentodes) between the output of the bridge and the tube and circuits under test. Of course this amplifier introduces a possible source of distortion ahead of the circuit under test and care must be taken to operate it under such conditions that an adequate margin exists between distortion level measured at its output and distortion level existing at the output of the tube under test. In Table IV are shown the results of distortion measurements made under several typical sets of operating conditions. TABLE IV Ratio of Amplitude of Third Order Modulation Products to Amplitude OF One of Two Equal Test Frequencies Frequency = 80 megacycles Ep.Es Eg ip Is Distortion ratio, decibels Distortion ratio, decibels Volts Volts Mils Mils at 0.33 watt * output at 0.75 watt * output 320 -27.4 43.5 19.5 -52 -44 320 -23.8 54.0 26.0 -54 -46 320 -19.0 66.5 33.5 -56 -48 400 -38.3 44.0 22.0 -53 -44 400 -34.5 55.0 25.0 -54 -45 400 -29.5 68.5 31.5 -57 -49 500 -53.5 45.5 19.5 -57 -50 500 -49.0 56.0 24.0 -58 -50 500 -44.2 70.0 30.0 -56 -48 * For single frequency whose amplitude is the sum of the amplitudes of the two test frequencies. Other Applications A study of the performance of these tubes as class B amplifiers, as narmonic generators, and as modulators apparently presents no serious additional problems and requires very little in the way of additional new technique. Tests indicate that in the neighborhood of 150 mega- cycles the performance of these tubes in such modes of operation is comparable to that of conventional pentodes in the ordinary short- wave range. In a two-stage amplifier using these tubes, with the first 34 BELL SYSTEM TECHNICAL JOURNAL tube working as a class A amplifier and the second tube under class B conditions an output of over ten watts has been obtained with a second stage plate efficiency of around seventy per cent and with an over-all voltage gain for the two stages of twenty-four decibels. Using the first tube as a harmonic generator, driven at fifty megacycles, and the second tube as a class B amplifier, over six watts of 150-megacycle power have been obtained with an over-all voltage gain from fifty- megacycle input to 150-megacycle output of about four decibels. Conclusions It is often little realized how completely our present highly de- veloped technique of making communications measurements depends upon our ability to set up stable and reliable amplifiers at the frequen- cies we wish to use. We are now in a position to set up such amplifiers in the ultra-short-wave range; amplifiers of sufficient gain, stability, and most important, of sufficient power handling capacity to enable us to make many of the measurements we may wish, at low enough im- pedance levels to minimize some of the effects of unavoidable stray in- ductances and capacitances in our circuits and at high enough power levels to make practicable the use of simple and reliable, and almost necessarily rather insensitive measuring apparatus. Furthermore, our experience in this work indicates that it is not necessary to modify drastically our experimental procedures when we move into the ultra- short wave field. Much more care in circuit design is required, but with more attention to details formerly unimportant, much of the background of electrical measuring technique becomes, with the advent of this new tool, available in the ultra-short-wave range. The Physical Reality of Zenneck's Surface Wave By W. HOWARD WISE The first part of the paper shows that a vertical dipole does not generate a surface wave which at great distances behaves like Zenneck's plane surface wave. In Parts Two and Three it is shown that it is not necessary to call upon the Zenneck wave to explain the success of the wave antennas. IN 1907 ^ Zenneck showed that a plane interface between two semi- infinite media could support, or guide, an electromagnetic wave which is exponentially attenuated in the direction of propagation along the interface and vertically upwards and downwards from the interface. Zenneck did not show that an antenna could generate such a wave but, because this "surface wave" seemed to be a plausible explanation of the propagation of radio waves to great distances, it was commonly accepted as one of the components of the radiation from an antenna. After Sommerfeld ^ formulated the wave function for a vertical infinitesimal dipole as an infinite integral and noted that the integral around the pole of the integrand is the wave function for a surface wave, which at great distances is identical with the Zenneck wave, no one questioned the reality of Zenneck's surface wave. There has been recently pointed out by C. R. Burrows ^^ the lack of agreement between various formulas and curves of radio attenuation over land when the dielectric constant of the ground must be taken into account. The values of Sommerfeld ^ and Rolf ^ are stated to differ from those of Weyl ^ and Norton ^ by an amount just equal to the surface wave of Zenneck. Burrows ^^ presents experimental data supporting the correctness of the Weyl-Norton values and raises a question as to whether a surface wave really is set up by a radio antenna. A vertical current dipole does not generate a surface wave which at great distances behaves like Zenneck's plane surface wave. Theoretical and numerical evidence leading to this conclusion is presented in Part One of this paper. A contemporary theoretical investigation by S. O. Rice * leads to the same conclusion. The reader familiar with wave antennas will at once ask why the wave antennas seem to justify the Zenneck surface wave theory by means of which they were conceived and designed if there is no surface * "Series for the Wave Function of a Radiating Dipole at the Earth's Surface," this issue of the Bell Sys. Tech. Jour. 35 36 BELL SYSTEM TECHNICAL JOURNAL wave. In Part Two of this paper it is shown that a plane electro- magnetic wave, polarized with the electric vector in the plane of incidence and in the wave front, impinging on a plane solid at nearly grazing incidence produces a total field in which the horizontal elec- tric field near the solid has very nearly the same ratio to the vertical electric field as in the Zenneck surface wave. In Part Three of this paper it is shown that the wave tilt near the ground at a great distance from a vertical dipole is almost the same as that found for the plane wave at nearly grazing incidence. Part One — The Evidence Against the Surface Wave The following discussion centers around the surface wave wave- function P and the series (5), (6), (8) and (9) of paper 3 in the bibliography.* These series and P follow P = - j!^^H,^'Ksr)e"^',] (12) (2i + P/2 = -„T-^ i: ^n(- xY, (5) r\ - t'- n=0 1 t2/,X2 00 Q, + P/2 = -^Y^ ^ ^"(- ^2)"' (6) ^1 ''■ n=0 1 1 _ ^1 n=l Q, = Q, + P ~ - j-^ry2 T. CnX~\ (8) (2i~^r^'^^"^2-", (9) where r = horizontal distance, x = — ik\r, x^ = — ik2.r, r = kilk^, S = ^i/Vl + T^, k^ = €//aj2 — 4:Tr(TfJLia}, ki^ = kr (e — ilcXcr), ki « 2x/X in air, a = 7^(1 + r^), a^ = 1/(1 + t^), Ao = I, Ai = y[a tanh""'Va, A2 = Ai — a, Ar, = {{In - 3)^„_i - o^„_2]/(w - \)\ 5o = 1, -Si = Va2 tanh"^Va2, Bi = Bx — ai, Br, = l{2n - 3)5„_x - 025„_2]/(w - 1)2, Ci = - l/a, C2 = - 3/^2 + l/a, C„ = l(2n - l)C„_i - (« - iyCn-2']la, Di = — 1/^2, Di = — 3/a2^ + l/<22, D„ = l(2n - l)Z)„_i - (n- lyD^-il/a^. * Sommerfeld's time factor e"*"' which was used in paper 3 has been replaced by t z, the height above ground, is zero in paper 3. PHYSICAL REALITY OF ZENNECK'S SURFACE WAVE 37 The left hand side of (8) has been altered to correspond with the facts as now known. P is the wave-function for a surface wave which at great distances behaves like Zenneck's plane surface wave. The series (5) and (6) constitute the complete wave-function for a unit vertical dipole centered on the interface between air and ground. The series (8) and (9) are the asymptotic expansions of (5) + P/2 and (6) - P/2. The series (5), (6), (8) and (9) are exact and it is from them that the attenuation charts in a paper by C. R. Burrows in this issue of the Bell System Technical Journal were computed. Since interchanging k\ and k^ in (5) gives (6) and interchanging ki and ^2 in (8) gives (9) but interchanging ki and k^ in P changes its sign it follows that if (6) ~ (9) + P/2 then (5) ~ (8) - P/2. Hence the complete wave-function H, = (5) + (6) ~ [(8) - P/2] + [(9) -\- P/2] = (8) -f- (9) and P does not appear in the asymptotic expan- sion of the wave-function. The series (5) and (6) have been computed and found to be respec- tively equal to (8) — P/2 and (9) -f P/2.* These computations show again that Hz = (5) -+- (6) ~ (8) + (9) or putting it in words, that there is no surface wave wave-function P in the asymptotic expansion of the complete wave-function. As a further check S. O. Rice has derived the series (5) and (6) in an entirely different manner and verified that their asymptotic expan- sions are indeed ^o — P/2 and Q^ + P/2. In order to get a direct numerical check on the series the wave- function integral was computed by mechanical quadrature for two cases. Van der Pol's transformation of the wave-function integral with the path of integration deformed upward along the lines Im{ihru) constant was used.^ 1. With r/X = l/47r and e — i2c\r]:^T2^Mi ri I ife/'2T2(l - r2) J The wave tilt near the surface of the ground is then E, rvr Ez 1 + tVI — rHkz This is the wave tilt in the asymptotic field of a quarter wave antenna or flat top antenna. If a is not zero but c is small the final field expressions are . e-'*^2 r 2 + rV'l - rHk{_w + (2a - w)e^^-'' ''''-'] CLo = — too ^2 I ikr^T-^l 3 T— ;; [(w — 2a)g'*2°^/'--' — w] ^^2 6 - 6t'' - 3t* + 6tV1 - r^i'y^T^ + 2x^1 - T'-)(ikwy- {ikr2yT'{l - t2)3/2 "^ 44 BELL SYSTEM TECHNICAL JOURNAL . e-'*'^[/t, , .^/^ , 1 \ , 2(1 + T^ll - THkw) + (iyfera)^ 2 - 6/t2 - (6 - Sr'^ + ST*)ikwlTyl\ - r^ - 2{ikwY If klazjri -C 1 the leading terms give g-ikn 2(1 + tVI - T^iM Ed = — ioi ^2 ikr^T^l _ _ . e-^*^2 2(1 + tVI - T'^^y^2)(l + tVi - r^'iy^a) and EJEz is the same as obtained above with a = 0. Bibliography 1. J. Zenneck: Ann. der Physik, Bd. 23, page 846, 1907. 2. A. Sommerfeld: Ann. der Physik, Bd. 28, page 705, 1909. Jahrb. d. drahtl. Tel, Bd. 4, page 157, 1911. 3. W. H. Wise: Proc. I. R. E., Vol. 19, page 1684, 1931. 4. W. H. Wise: Bulletin Amer. Math. Soc, Vol. XLI, pp. 700-706, October, 1935. 5. Bruno Rolf: Ingeniors Vetenskaps Akademien, Handlingar, Nr 96, 1929. 6. Balth. van der Pol: Zeitschrift fiir Hochfrequenztechnik, Bd. 37, page 152, 1931. 7. H. Weyl: Ann. der Physik, Bd. 60, page 481, 1919. 8. W. H. Wise: Physics, Vol. 4, page 354, 1933. 9. K. A. Norton: Proc. I. R. E., Vol. 24, page 1367, 1936. 10. C. R. Burrows, Nature, Aug. 15, 1936. A more complete description will appear in the February issue of the Proc. I. R. E. Radio Propagation Over Plane Earth— Field Strength Curves By CHARLES R. BURROWS Curves are presented to facilitate the calculation of radio propa- gation over plane earth. The magnitude and phase of the reflection coefificient for all conductivities of interest and for four values of the dielectric constant are presented in the form of curves from which the significant quantities may be read with the same degree of accuracy for all conditions. Simple equations, from which the effect of raising the antennas above the earth's surface may be readily calculated, are presented. Introduction npHIS paper is intended to facilitate the calculation of radio propa- -^ gation over plane earth. In Part I curves are presented that show the decrease of field strength with distance for antennas on the surface of the earth. In these curves the results obtained by Sommer- feld ^ and Rolf ^ are corrected and certain approximations ' introduced by Rolf to reduce the number of variables to a workable number are eliminated. For a discussion of the Sommerfeld-Rolf curves, the reader is referred to a companion paper.* Part II is concerned with the more general case of antennas above the surface of the earth. The complete equation that gives the field strength for antennas at any height above the earth is reduced to a simple equation which allows the calculation of the field under con- ditions of practical interest. To facilitate field strength calculations, the values of the reflection coefilicient are presented in the form of curves from which the significant quantities may be read with the required degree of accuracy for ail angles of incidence. Preliminary Remarks A rectilinear antenna in free space generates an electric field whose effective value in the equatorial plane of the antenna at a distance large compared with the wave-length and the antenna length is where HI is equal to the line integral of the current taken over the ^ Numbers refer to bibliography at end. 45 46 BELL SYSTEM TECHNICAL JOURNAL antenna.* If the antenna is placed above and perpendicular to a perfectly conducting plane and the antenna current is maintained the same, the electric field will be twice as great f or £ = 2£. = H^. (2) To maintain the current constant, however, it is now necessary to deliver more power to the antenna. For a short doublet antenna in free space the radiation resistance is i?o = SOTr^H^IX"^ and hence the effective value of the received field strength is given as a function of the radiated power by J If this antenna is placed perpendicular to and very near a perfectly conducting plane the field strength pattern will be unchanged in the upper hemisphere but there will be no field below the perfectly con- ducting plane. The power that was required to produce the field in the lower hemisphere, which because of symmetry is half the total, is no longer radiated so that the same field strength will be produced by half the power, ff or E=l^. (4) a If the transmitting antenna is removed so far from the ground that the reaction of the currents in the ground on the antenna current is negligible its radiation resistance is the same as if the ground were not present. The receiving antenna, however, still "sees" the image of the transmitting antenna in the ground. At a distance large compared with the height above ground, the transmitting antenna and * The units are volts, amperes, meters and watts. H is the effective height of the antenna as defined in the most recent "Report of the Standards Committee" of the I.R.E. (1933). t Under the hypothetical conditions taken by Sommerfeld, namely the antenna half in the ground and half in the air, the field is the same above a perfectly con- ducting plane as in free space. When the antenna is entirely above a perfectly conducting plane the field is the same as it would be if the plane were replaced by the image of the antenna in it. That is, the field is the sum of two equal components, one due to the antenna itself and the other due to its image. At distances large compared with the height of the antenna above the plane these two components are in phase and their sum is equal to twice either of them. J For half- wave antennas the numerical factors in equations (3), (4) and (5) are respectively 7.0, 9.9 and 14.0. tt Let El be the received field strength in free space produced by a power Pi and let £2 be the field strength for an antenna perpendicular to and very near a perfectly conducting plane produced by a power P2. Then £2 = -Ei when Pj = Pi/2, and by equation (3), £2 = £1 = 3V5V-Pi/^ N -^ ~^ "^ 1 Ro < ^ / —" ^ ^ / / / / J < < a. 0.8 ^0.6 < ^0.4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 I.I 1.2 1.3 1.4 1.5 1.6 ANTENNA HEIGHT IN WAVELENGTHS (^/j^ Fig. 1 — Ratio of the radiation resistance of a short doublet antenna above perfectly conducting ground to that of the same antenna in free space. short vertical and horizontal doublets above perfectly conducting earth respectively, and Ra is the radiation resistance of the same antenna in free space. For the same input power the received field is inversely proportional to the square root of these ratios which are plotted in Fig. 1. It is sometimes convenient to express the results in terms of the ratio of transmitted power to useful received power. The useful re- 48 BELL SYSTEM TECHNICAL JOURNAL ceived power is the maximum power that can be transferred from the receiving antenna to the first circuit of the receiver. This is for a short doublet. From equation (3) it follows that the ratio of transmitted to useful received powers for antennas in free space is * For short vertical doublets above the surface of a perfectly con- ducting plane this becomes, at distances that are large compared with the antenna heights. Here RvJRo and RvJRo are the ratios given by equation (6) and Fig. 1 for the transmitting and the receiving antenna respectively. When the antennas are more than a wave-length above the ground these ratios are substantially unity, and only one-fourth as much transmitted power is required as would be if the antennas were in free space. When both antennas are very near the surface of the earth, Rv/Ro — 2 and the same transmitted power is required as in free space. Part I — Vertical Antennas on the Surface of the Earth In this section transmission between two short vertical antennas above and very near to the surface of plane earth will be considered. The attenuation factor will be taken as the ratio of the received field strength to that which would result if this plane surface had perfect conductivity. In evaluating the electromagnetic field generated by a short vertical antenna on the surface of an imperfectly conducting plane it is con- venient to first determine the auxiliary function 11, called the Hertzian potential, from which the vertical component of the electric field may be obtained by means of the relationship.f 240^x2/ , , X^ 32 \ £= -^^(^l+^,^jn volts per meter. (11) * For half-wave antennas the right-hand side of equation (9) must be multiplied by r73.2/80)2 = 0.837. t Bold face type is used to indicate a complex quantity. The same character in light face type represents its magnitude with which the radio engineer is concerned. The imaginary unit, V— 1, is represented by i. RADIO PROPAGATION 49 For an antenna on the surface of a perfectly conducting plane this function may be written * /7"/g-2irifli/X n = 2no = 2 — -i-^ amperes, (12) 47r/&g _ 2irdA l/(£-0g+(2Cf/f)^ ^ 21TdA \j,*i,-ycfo^ ' i+ki2 " Ve'H2tf/f)2 V ^^H^o/fy ' vq '+0= Fig. 2. • pl.i. earth. The number on each curve gives the value of the Q ( = efl2a) to which it applies; a is the conductivity and « the dielectric constant in electrostatic nits; / is the frequency in cycles per second; d/X is the ratio of the distance to the wave-length. Fig. 3 — Attenuation factor for radio propagation over a dielectric plane. The number on each curve gives the value of the dielectric constant to which it applies. 50 BELL SYSTEM TECHNICAL JOURNAL by using equation (15) to calculate the field strength. This is for- tunate since series D requires laborious calculations. The attenuation factor may be obtained from W by means of the relation,* /here E ^ W 1_ 2£:o ~ 1 + T-^ 1 - 1 ' +74yKp]- (") lirid/X {lirifj e - Half = e{\ - i/Q). (18) In this equation 2Eo is the inverse distance, or radiation, component of the field that would result from transmission over a perfectly con- ducting plane, and Q is the ratio of the imaginary component to the real component of the admittance of the ground. In other words, Q is the ratio of the dielectric current to the conduction current.f The parameter e occurring in equation (18) is the relative dielectric constant (with respect to vacuum), a pure numeric that is numerically equal to the dielectric constant measured in electrostatic units. If the value of W f rom equation (16) is substituted in equation (17) and terms which involve (l/d) to powers higher than the first are neglected as may be done at the greater distances, we have 1 - r' lirrHd/X J [ 1 ... (-5) 2Trld f , 1\ -, X 2E^. (19) (1 + r^) The magnitude of the second factor on the right differs from unity * This expression may be obtained as follows. II satisfies the wave equation which in cylindrical coordinates (z, Q, d) is (I d d I d^ d^ iir^ \ ddd'^dd'^d'^dd^'^di^'^1^)^^^- Because of symmetry the second term is zero. Solving for the value of the last two terms and substituting it in equation (11) yields The differential equation given by Wise " for II becomes _ xi/a^ , i3n\ _ n 2 r 1 ^ In in'' \ dd'^ ^ d dd J 1 + t2 "^ 1 - T* L 2Tridl\ ^ (iTid/xyj " when the value of y = (1 + t2)II/2 is substituted in his equation (7), and the result multiplied by 2/(1 + t^). Substitution of this relation in the preceding equation and division hy Eo = ~ liOiir^UoIX gives equation (17) of the text. Since Eo is the inverse distance component of the free space field, this relation follows from equa- tion (11). t In practical units Q = Iwfe'jg, where «' is the dielectric constant in farads per meter and g is the conductivity in mhos per meter. On frequent occasions, the constants of the dielectric are expressed in electrostatic units; then Q = fe/2<7. RADIO PROPAGATION 51 by less than 2| per cent for values of e greater than 4. Accordingly the magnitude of the first factor (which is equal to the first term of C) gives the attenuation factor at great distances with a degree of accuracy sufficient for all practical purposes. If we choose our unit of distance such that X = \2tt^(1 - t2)^/X1 I " e/Q 1 + Q' e 1 + 1/(2^ ^ all of the attenuation curves will tend to coincide at the greater distances. This is done in Figs. 2 and 3. Figure 2 shows the varia- tion of received field strength with distance for seven values of Q for the case where the impedance of the ground is very different from that of the air.* These curves give the correct attenuation factor for arbi- trary ground constants at the greater distances. At any distance the above assumption introduces a significant error only when Q is large. Accordingly the curves of Fig. 3 have been calculated for various values of the relative dielectric constant when Q is large. f The short vertical line on each curve indicates the abscissa corresponding to a distance of one wave-length. The curves do not depart appreciably from that for an infinite dielectric constant except for distances less than this.f Since the error introduced in applying the curves of Fig. 2 to the general case is greatest for the conditions represented in Fig. 3, the curves of Fig. 2 may be used with confidence. It should be emphasized that the curves of Fig. 2 give the ratio of the received field strength to that which would result from the same current in the same antenna on the surface of a plane earth of perfect conductivity. The antenna is assumed at the earth's surface so that the curves are strictly true only for short antennas. The error for half-wave doublets whose mid-points are not more than a half wave- length above the surface of the earth is negligible except in the im- mediate vicinity of the transmitter. The effect of height above the surface of the earth is taken up more fully in the next section. * Since the writing of this paper, Part I of a paper by K. A. Norton on "The Propagation of Radio Waves Over the Surface of the Earth and in the Upper Atmosphere" has appeared in Proc. I.R.E., 24, 1367-1387, October, 1936. The curves of Fig. 2 in this paper are similar to those of Norton's Fig. 1, but by presenting the curves as a function of x their validity is extended to include a wider range of ground constants. t The writer is indebted to Miss Clara L. Froelich for making these calculations. i The ratio E/2Eo is greater than unity at the shorter distances because Eo is the inverse distance or radiation component of the free space field while E is the total field. At distances that are small compared with a wave-length, £/2£o is given by the second and third terms on the right of equation (17) and the effect of the ground is to increase the field by the factor 2/(1 — t*). 52 BELL SYSTEM TECHNICAL JOURNAL The calculation of the field strength as a function of the radiated power requires a knowledge of the effect of imperfect conductivity on the resistance of the antenna. The reader is referred to papers by Barrow ® and Niessen ^ on this subject. In the wave-length range where these curves are of greatest applicability, the practice is to minimize the ground losses by a ground system consisting of a counter- poise or a network of buried wires. When this is done the ground losses are properly part of the antenna losses and the radiated power may rightfully be taken as the rate of flow of energy past a hemisphere large enough to include the antenna and ground system. If this is done, the field strength is given by E^'J^n.). (20a) where F(x) is the ratio plotted in Fig. 2* Part II — Antennas Above the Surface of the Earth It is well known *• ^ that calculations based on the physical optics of plane waves give the first approximation to the received field for radio propagation over plane earth. This approximation is accurate enough for all practical purposes if the antennas are sufficiently removed from the surface of the earth.f Under these conditions, the ratio of the received field strength to that which would be received in free space is given by f E/Eo = V(l - Kf + 4K sin2 (7/2), (21) * In estimating the fraction of the total power input that is radiated the following papers may be helpful: George H. Brown, "The phase and magnitude of earth currents near radio transmitting antennas," Proc. LR.E., 23, 168-182, February, 1935 ; and H. E. Gihring and G. H. Brown, " General considerations of tower antennas for broadcast use," Proc. I.R.E., 23, 311-356, April, 1935. t This height depends upon the distance, wave-length and ground constants. The range of validity of this approximation is discussed more fully in connection with equation (27). J Equation (21) gives the received field strength for either polarization for trans- mission along the ground. In this case the direct and reflected components are oriented in the same direction in space. It may also be used to calculate the effect of the ground for signals arriving at large angles by taking into consideration the space orientation of the components. For horizontal antennas the orientation of the electric vector is horizontal for all angles of incidence so that equation (21) applies directly. For vertical antennas the electric vector makes the angle ?2 with the vertical, both in the direct and reflected wave. Hence if the ratio given in equation (21) is taken as the ratio of the vertical component of the received field to the total incident field it must be multiplied by cos ^2. Even if the ground were not present, however, the vertical component would be reduced by this factor so that the effect of the presence of the ground on the field received by a vertical antenna is given by equation (21) as written without the cos ^2 factor. RADIO PROPAGATION S3 where K is the ratio of the amplitude of the reflected wave to that of the direct wave and 7 + tt is their phase difference. 7 = 'A - A, (22) where A is 2ir times the path difference in wave-lengths and

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V S s s V Vi ^s \ S \ V '^1\ s. s s N \ ^ ^" \^ S'' \ ' \ o \ ^'■^^ \ s \ ^ s, V O "1 ^ ^ X v^J o o. O- ^- \ \ \ ^s ^ ^ \. K S \ sJ \ > s 5 s s N, s > s \ V S \ s s s V \ \ V N, s \ \ V \ \ ^ ^ \ s ^ \ fs \ V s. ^ s N •■ V >, s ' s s s \ \, \ \ \ \ \ S s — \ \ \ S s S \ \ I ■ s \, \, \ \ \ s V s \ S s s V s ■^ _^ s s s, \, s, \ 0 u 1 LI CM 1 s s \ s \ - f\j < \ \ s s i^ \ N, c A \ ^ N ^. \ \, ^ \ \ \ s "> s \ \ k, ^'■ \ V V \ s S 1 c "> V \ V. N N N -T ^ J: N \, s s \ \ \ \, \ \ s N tH S 6-" \ N 's. s, s \ s ^ 1 'v \ \ vO_II N \, s^ ir A'-^^ s V s s \ 1 N \ A V 's _S. s S, \, . v^ \ \ s \, «Ss o" ^ N s s ^v S^ N N, s V s s. ^. ^ \ \, \ s 1- ^ >^ \, s V \ \ oV , s \ V S ~ ""v.T s. s \ s s s \ \ \ \, \ \ "?>< N ^ ^ k s s \ s ^ s s ^ 1 s s -^^ rr \L 1 1 >_ '-^ V ^.0^, N, \ s. 1 c 2" s Q^ k 1 1 r ^ — s. ■< S 3 C P a 0) c > o 1- N o - c 1- U3 S >> (A 11.1 o 00 0> 0> Oi o d o d ' V'^J T-T— T— r- ry F" ■T- Y 1^ i—r- 1— 1 — [7v T— n? F" r^ r 1— 1 -TO— 1 y / / s / r^ .-s ^- (/ i :^ V / ' » y ' Is / ^ o / / \ * y. y >^J / \ ro // / / ^ , N / \ , / 's'.A / /t / / ^, ' "'Oy ^, W" 7 ' / \ i/ > y X V > '' 12 '^- ,// / / \> / r^^ \ / ■\ LU '/ / ^ / '\ '\, / V z. o> / < T ^ i) iS / ^ \/ / r-^ f / / <^v y \ / ' ^ \ / ^^ A 1 / / •\ / ^ > / \^vi / z A 1 / / / y < \ / '/\ •,/ V / L / / XI ^ ^ / (M >0- IV / / \ y V 1 y vf \ / / / ^o •s . / ^^ N, / -:/ .v^C^l. ' ., / V / / / i'o >' / f ^ / / / ( / \ ^ / \ y •f\i / / T \i \ / \ % / / -> )/ > f O — IT)- O o. si X \ / / / 's / \ \ / \ / / / / / \ / 'v \ / / / N ^ / \ .' / . y \ ^ / s / ^ / / / ^^J / y s ^ k / / / V i \ ^ K ' ■^ , / / / ^ J s >« > / ^ \ \ / s ^. / / ' \s ■, \ ' / \ V / / / ^j ' y K V \ ^ / / \v \ / \ / ' \ •^ / \n / \ / / / :>, ') i )( V s / ^ f \ A S, / "*( / / \ / 1 \ / / \ \ V in- to o II (1> ^ 1 V A 1 % V > \, / s \ > \ •^ - s y \ / \ / \ '^ U '^- y \ \/ \t / ■s \ ^ _ lt ^ \ /< \ V / s \ '"1 ^ / s / \, / \ \ "^wO 5 / \ ' \ / \ \ IK z 1 y. /^ ,< s. K ^J^ *s \ / \ / \ / ' \ s S i" c\ N V w< ' \ / s / V v S > ^ ( V s > s \ n / \ / S, \ Co,^ s k, s "^ \ / N / ^ ^ \ V s \ s ««(, ^ . S v"u N X V i V s !^ / s \ \ s ^, / /' V N ^^ V s N "^ J / \ N. s^ \ s \ *^ I \ N .c 4v -^ N '"^ s S, \ , s s, ^ \ N s N s ^ -^ s ^ s \ \ a o\ k \ s s \ s \ s s V \ .\^ . V \ \ _ 1 V o's. S \ \ ©■I I s \ \ \ s ^ \ \l^ \ \ \ \ \ *oV > s s \ s ^oX V r s \ \ S \ \ v^ Iv N. s V 1 3 u 1 1 \ \ \ \ o z o (o ifi 'J - d d d d — CD U5 lO ^^ fO o o o o o d d d d d d — CO n P o o o o o o o d d d M fc RADIO PROPAGATION 59 ^ IN DEGREES (H.P.) 00 •OiO O 00 1 1 1 1 t 1 (\J - O 1 1 do 1 1 1~ — """ — c^ IN M ■ - T ^ -^ o II pSS N ^^ U 'P iD' v^ S . N -. \ 'v\ s o > o ■.V ^ \ 1 fO- -^.L o- '^< K.I < A^ . iN r - A> o V i" , H> ^ ^l . s [^ « S' 1 o n1 s V *• M^ ^ _ __ _ _ _ _ ^ _ ^ _ ^ ^ _ Q ~ - ~ ■s — ^ — ' - - — ~ == = — — — ^ - E^ z i N «,, ■>\ ^ \ ■s s N V -lo A s N> s ' ,^N Is in- : S - - s s K* ->N N •>,, -i< s. s S \ s \ s s ^ N N \ s N .N - ^^ < z o o a. a. LU o > I 1 1 1 V CM- \ \ S \ sl s c k N ' s. s s \ 1 \ s s s \ s 's s s I s s. \ s ,-0- N V s N \ i \ V V s" s - v S s S, > s . s, fl- ^ s s, s S y s, s s o. s s s ^j s s s. s s \ 1 N s '\ ^d s V \ \ 's \ s, \ S \, -" \. 's s \ \ \ \ S s V s, V s ^ \ s \, s. s ' s. lO- S V S 1 s \ \ s s s, s •- V k V s V ^ s 'S o ■< ^ \ s s \ s d ^s a> A \^ N s y 'v S ^ v^^ 1 1 V ^ s \ o CO c 3 3 c 3 t c c > IJ c c 5 5 c a c 3 U 5 C 1 \ > t c 3 c c 3 c ) a 3 (C > 1/ •) \ f ■) 0 J - c ) c d > f) z (flO b CN .—4 II c v^^ ^ w o «* « XI o >^ (U XI 3 a CTl o > •i~t (1> ?^. J= u tn a 01 n > a M — ; U Ji en HI c c o u •n X n h tn 3 C Xi o ui^tro 0 1 0 n'^\[ \ ■i^4- .2 - N J o > T «s -^^ i> *> ""• ^^^^v ^, ^v -a .^ QV L ^SnjOsT (0 o_ in- i c X^-1 \ 1 ' "■ \ ~ P^c t ^\l ' \ '^^TT ^\ H: ^ \.III>J tu ^ ^ ^-v-- \\ s s\ _ ^bk a \^ « = — - — — — o3ffi>^ — - — - — = - -^ =;- «=: ni'O - 1 *■ ** "^ _^ ^ "^ ..^ ■uj> hV- s, 1 ^ ~^ ■^ ~^ m- \ "^ V ^Vv, \ \, ^^ N \ s, \ S N^ 1 V S V S ^ \ ^, ^ s \ N \ ^ \ .^ \ \ \ > \ °N \ V ^; ' — \ \ S, s^ s ^O- ^ t ^ ^i N+n^ s 1 1 S \ \ '^ Mill "s - N, N ^, ^^ ""^^ si"~ 3 ro" \ s. \ <\j k - s I s, S s c i \ \ s •^ "^ ^ (\J \ s \, \ 1 \ \ \ \^ N \ 1 V \ \ ^v; ^ \ ^ \ ^ \ - v, N \ '\ \ I S \ s \ ^. \ ^ s s \ /> ''^- \ N ^ \ s \ s N \ "s V . ^ \ •^ K ^- s. s '^ \ ^" s s s IS" i 1 s, s N ^ \ s s \ \ s \, ^ \ s,. ujl 1 \ V \ ^; S 1 \ s i \ 'S^^ ^ N \ \ \ s, N \ S ^___q. 1 V, \ \ \^ y^^^u. " \ \ ^ s ° \i " \ \ N \ "" \ ^, N , j_ \ ■^ s. \^ \ N, s ^ A-, "'^ ^ ^ "> V s s. ^ X \ \ Sj \ N \" \ \ s, s, ^N \ " S s N, ^v -- \ __^ N \ \ \ N V V \ ^, ^No^ V — \ N N ^-3i \ s d s, N \ \ ^__ _ s \ \ ^ \^ ^ _ "s > s ,^ ' . ^ ^ v s t \ - ^v ■v ^ . 1 ^. " ^ N oS s ?^ V >'-!- \ N \ o N,. l~ ^s:^._ _ ^ \ ._:^ >o -5 4) o taO— X 2 u j: tn ^ CI rn V c c o -o B s a >. u Xi Oh <~> oooo o ocoiDin-rt-co 00(0>0';f(OtM — \lr IN DEGREES FOR VERTICAL POLARIZATION 62 BELL SYSTEM TECHNICAL JOURNAL of the curves in this cycle may be used to obtain the values oi 1 — K and i/' for any value of ^2 for which the curves go below the edge of the charts, as follows. Multiply ^2 by the smallest power of ten that will give a value on the chart, read the value oi I — K or ip corresponding to this new ^2 and divide this value of 1 — -K" or 1/' by this power of ten to obtain the desired value of 1 — iiC or ^. To obtain values oi I — K and 1/' for larger values oi q = 2(r// than shown on Figs. 5-12 use is made of the fact that both of these quantities may be expressed as functions of the parameter V5 sin ^2 for large values of q, (Q « 1). That is, the shape of all the curves for values of Q that are small compared with unity is the same. Hence to obtain values oi 1 — K and ^ for values of q greater than those for which curves are shown, divide the given q by some power of one hundred that gives a value of q for which a curve is drawn, and read the desired value of I — K or xj/ opposite the value of sin ^2 that is the same power of ten times the given sin ^2 as the power of one hundred by which q was divided. If the following characteristics of the curves are taken into con- sideration, interpolation is simplified. The similarity of the i^T-curves suggests relabelling the abscissa so that the value of K for some intermediate value of q may be read from one of the curves that is drawn. Any curve for a large value of q, {Q is replaced by {R + \yd'^l2{h\-\-h2Y to which it is equal to the required order of approximation. Another form of equation (27) that may be preferred in some cases is given as equation (35) in the conclusions. This form results from substituting for — gi its value (a — iby/2. RADIO PROPAGATION 65 II to + + CN °cy CN 1 CN % ~E" CN ^ 3^ CN 1 CN II 2i + 1 "=»^ c 1 CN •> CN 1 to > > CN CN -> o 1 V «, CN t3 1 1 — 1 1 + CN CN c + CN 5 CN 1 CN CN CN CN 1 CN 5 ~E" CN 1 CN CN a 3i + 'a + so W CN i CN to CN -5 ~E" CM 1 2 CN a 1 1 — 1 >~ 1 <^ "> 1 + 1 — 1 > CN 1 &< ^ •^ CM 1 c 1 CN 5 1 1 C o Q C u > r > c y c n 5 3 c D 3 6 c r u d -5 c , ■J/ / — — — ,rV / — __ nV / / 0.1 0.2 0.3 0.5 1.0 2 3 4 5 10 RELATIVE ANTENNA HEIGHT (Kh) Fig. 13 — Variation of received field strength with antenna height. The variations of the received field strength with antenna height for the four cases of especial interest given by equations (32) and {33) are plotted in Fig. 13. The ordinate gives the ratio of the field strength at the height corresponding to the abscissa to that for zero height. If both antennas are off the ground the product of the ratios corre- sponding to the antenna heights gives the ratio of the field strength to * As the antennas are removed from the earth's surface the error introduced because of this deviation is less. 68 BELL SYSTEM TECHNICAL JOURNAL that for both antennas on the ground. The distances between the curves and the straight line labelled " asymptote " give the magnitudes of the factors in equations (32) and {33) by which {4:Trhih2/\d)Eo must be multiplied to give the field strength. For transmission over a ground of good conductivity (Q y ^ ^ ^ ~ 1.0 ■^ X _.^' S 0.8 ^ s. « ' X y^ ^0"^ ^ 0.6 iOA 0.3 0.2 0.1 > ,, y y , '\ z' ^ y ^ '^ y^ / y / y^ / / / y -^ CURVE 1 / / / / / / / / / / y / / / / / / / / jT /■ WAVELENGTH =14 METERS CURVE 1 e=80 a' = 3.6XI0'° CURVE 2 6 = 30 0'=3.4Xlo5 CURVE 3 e= 10 0^ = 1.075 XI08 CURVE 4 e= 4 0^= 1.075X107 0,08 / / / / / / 0.06 0.05 0.04 0.03 0.02 0.01 / y / / / / / / / .' < / / / / Y / / / / / / / _ 0.001 0.002 0.02 0.05 SIN t,2 Fig. 14 — Relative advantage of different types of ground for low-angle reception on 14 meters with vertical polarization. locating an antenna above sea water instead of above the following grounds on a wave-length of 14 meters is given in Table II. TABLE II Ground Constants Dielectric Constant — e Conductivity — a Gain in db for reception at Electro- static Units Electro- static Units Small Angles 1° 2° 5° 1. Sea Water . . . 2. Salt Marsh . . . 3. Dry Ground . . \. Rocky Ground. 80 30 10 4 3.6 X 101" 3.4 X 103 1.075 X 108 1.075 X 10' 0 10 24 28 0 7 19 23 0 5 15 20 0 3 11 14 Acknowledgment The value of a paper of this type depends to a large degree upon its freedom from errors. With this thought in mind the equations and tables have been checked by my associate, Mr. Loyd E. Hunt, whose cooperation is hereby acknowledged. 70 BELL SYSTEM TECHNICAL JOURNAL Conclusions For transmission over plane earth with antennas on the ground the received field strength in volts per meter is given by the formula, £=i2^f(,)=3V|V?^(^)_ (34) where HI is the transmitting ampere-meters, P is the radiated power in watts exclusive of ground losses, d the distance in meters, X the wave-length in meters and F(x) is the factor plotted in Fig. 2. When the Q of the ground is large compared with unity, the factor plotted in Fig. 3 is to be preferred to that plotted in Fig. 2. When the antennas are not on the ground the received field strength may be calculated by means of equation (27) or its equivalent, I- + ^ + ^"^ aJ^^'^ L-4.iA,A,/x„, 71 ZTTHa/X I Z) = - _^-_e(2--L ( ^V/l )"[l-3-5---(2»-l)]/,„ (41) 1 — 7-^ „=i \ — livialKT / 2ialf (42) where ~2= ^ and r is in the first quadrant. The positive square root of i is to be taken in equation (38). These expressions follow from those given by Wise '^ when the sign of i is changed so that the impHed time factor is e'"' in accordance with engineering practice instead of the e~^'^' employed by Sommerfeld and Wise. Their expressions were derived for an antenna half in air and half in the earth. To obtain the above expressions which apply to antennas on the surface of the earth, Wise's expressions have been multiplied by 2/(1 + t^), A corresponds to his expression (5), B to his (12), C to his (8) and D to his (6). The quantities, a^ and Cn are substantially unity except when r is not small. tanh-^V^ * yfe"-i oi = 7= — = L. k n=i(2w - 1) ' {2n — 1)(2« — 3)(a„_i — an-2 02 3(ai - 1) Ci = 1, C2 Cn — Cn—l (n - l)~k 3' (43) (2w - l){2n - 3) Cn-2, (44) ti{2n - 1)' (2« - 3)Dn-l - IDn-i where Do =1, Di = V/tanh-i V7 = ^ D2^ Di- I, D„ = k = ^ " rr^ ~ e+ 1 - Half /« 'n — {n - \Y r2 1 1 + t' e + 1 - Half 1 e - Half (45) (46) (47) 72 BELL SYSTEM TECHNICAL JOURNAL The /„'s are the same functions of / that the c„'s are of k. Appendix II The phase angle introduced by the path difference is: A = Y [ a/c sin ^2 and yp —^ -k — hjc sin ^2 are useful. These coefficients are given in Table III. IT 1 • -^ • ^ 1 V2V7+"e , ^ , V2VF^ i^or normal mcidence, sm ^2= 1, « = — ; — and tan \p = — z • s-\-\ 1—5 At Brewster's angle, cot ^2 = Ve and i^ = 0 when g = 0 for vertical polarization. For vertical polarization the minimum value of K is i m and occurs when x = 1 and sin ^2 V? For hori- 2 + w ^^"'^ '^ ^ "' \e2 + g2 zontal polarization the maximum value of b occurs when q = 4S r and is equal to — 1/V2?'. Under these conditions s = 2r and n = — \. ,n " 1 a = mVc J = jjVc (J m V2 V2 Ve' + S= ^ [Ws + r + gV5 - r] ^[aV7T7-.V7^] , Vertical Polarization ■/'^^ . /•"' " pr_ f^: r in General [<^-{\y v-arJ [<'*{{)• v-(d . V. P., ()<1 V2 V2 1 V5 VI^ V2^ * VI -Vl .V.P.,o»i 2 Ir - , ^' = Vr\ Ve-1 (. - 1)'" 7« - S + 8 s (. - 1 + sir 2V«- 1 +sin=fi in' { V. - 1 + sin -^3 . Horizontal Polarization in General V2^ll+^ -viv'i-; V] V2Vj + r V2V5 - r . H. P., 0■ b^2- On vertical polarization near normal incidence for e^ -]- q^ ^ l, x ^ 1 and the approximations 1— K —^ a/c sin ^2 and 1/' — > x — &/c sin ^2 are useful. These coefficients are given in Table III. 17 1 • -^ • ^ 1 V2V^+"e , , , V2VF^ i^or normal mcidence, sm ^2= 1, a = —. — and tan ^f/ = — ;; • At Brewster's angle, cot ^2 = Ve and K = 0 when g = 0 for vertical polarization. For vertical polarization the minimum value of K is j2 — ffi .Is ■\ h: — ; and occurs when x — I and sin ^2 = \ hr-, — 5- For hori- \2+w "Xe^ + g^ zontal polarization the maximum value of b occurs when q = -^3 r and is equal to — l/-'j2r. Under these conditions s = 2r and n = — I. — \ a m b n Vertical Polarization in General ~] V. P., g«:i * 4 -4 * .. V. P.,Q»1 2Vf - 1 + sin2 t2 7e - 8 + 8 sin2 ? Ve - 1 + sin^ ^2 (e - 1 + sin^ ^) 4£2 Horizontal Polarization in General H. P., g 1 and the ground tends to resemble a dielectric; at lower frequencies it tends to resemble a conductor. Columns 7, 8, 9 and 10 give the values of the parameter x of Fig. 2 for a distance of 1 km. and the indicated frequency. For any other distance, x is equal to these values times the distance in kilometers. When Q<^1, .r is proportional to the distance and to the square of the frequency. When the frequency is small compared with that * The first equation was obtained from the values given for sodium chloride in the International Critical Tables. The second equation is given in the same source for pure water. s o . t^ 360 0.36 1.8 0.036 VO 00 -^ !>■ c/5 d -H d 1,560 2.4 8.8 CS 00 d-; d 8 . IT) a II -« IN CO vO 00 ■^ t^ rcO_'-i 0 00 0 ^ CO 0 CN 00 vo" to -^'" 0000 OO^CN vO_00_'*l>. r^Td'-H d" cn'oo" vo 00 0\ r; d d es ooo — to 1 0 X So d to do d « OJ O Ov' d to to to vO^ 0 10 > o 3 •a c o U O V- K lO T ^2x2 10 c c „ T T 7 Y 000 2xxx la T T „ „ 00 1 1 — ' — 00 CN CO X X J^ JI^CN ro 1 T 00 XX ■rt CN 3 •* 2 .- f- » 0000 xxxx Ov On lO 0\ d d ■*■ d 00 00 r^ t- 0000 XXXX Ov t^ vO 00 d CN PO — ' 2 o2 X vX 00 f- „ t, 0 0 0 0 xxxx ,1, r-< — <* CN 0 oX ■^ CN 1 3 a t«5 -. .» T "» T T 2'i' 22x2 to ~ T T T V 000 2xxx en •«* cs 1 V 1 2 o2 X xX fO . •^ T T 3 s 00 1 1 — -HOO X X s^ w CN <0 ^ -^ 1 1 CN CO T T 22 XX ■^ CN _• 1 Rela- tive Dielec- tric Con- stant ts OOO'* 0000 ^ too CN --I to CN to 10 0 COO (O c § O "o &> p. - +j .-a rs >< 3 S . • to 1 — 1 D C g u a; le 0 - _ "u •- 03 to -a . . c ^^ ^ p R = o- _'o c s »-iCNfO -* to vo r- 00 OvO —1 Cv) ro «* to VOI- RADIO PROPAGATION 75 given in Column 6 these conditions are fulfilled and the proportionality- factor is given in Columns 7, 8 and 9 for three frequencies. When the frequency is large compared with that given in Column 6, (2 » 1 and the parameter x of Fig. 2 is proportional to the distance and the first power of the frequency. This proportionality factor is given in Column 10 for a frequency of 50 mc. The parameter q = 2cr/f of Figs. 5-12 is given in Columns 10, 11 and 12 for three frequencies. Bibliography 1. Arnold Sommerfeld, "Ausbreitung der Wellen in der drahtlosen Telegraphic. Einfluss der Bodenbeschaffenheit auf gerichtete und ungerichtete Wellenzuge," Jahrb. d. drahtl. T. u. T. 4, 157-176, December, 1910. 2. Bruno Rolf, "Numerical Discussion of Prof. Sommerfeld 's Attenuation Formula for Radio Waves," Ingeniors Vetenskaps Akademien, Stockholm, 1929 and "Graphs to Prof. Sommerfeld's Attenuation Formula for Radio Waves," Proc. I.R.E., 18, 391-402, March, 1930. 3. W. Howard Wise, "Note on the Accuracy of Rolf's Graphs of Sommerfeld's Attenuation Formula," Proc. I.R.E., 18, 1971-1972, November, 1930. 4. Chas. R. Burrows, "The Surface Wave in Radio Propagation over Plane Earth," Proc. I.R.E., 25, February, 1937. 5. E. J. Sterba, "Theoretical and Practical Aspects of Directional Transmitting Systems," Proc. I.R.E., 19, 1184-1215, July, 1931. 6. W. L. Barrow, "On the Impedance of a Vertical Half- Wave Antenna above an Earth of Finite Conductivity," Proc. I.R.E., 22, 150-167, February, 1935. 7. K. F. Niessen, " Erdabsorption bei verlikalen Dipolantennen in grosser Hoeh Uber ebener Erde," Aftn. d. Phys. 5, 25, 673-687, March, 1936. 8. M. J. O. Strutt, "Strahlung von Antenen unter dem Einfluss der Erdboden- eigenschaften; (a) elektrische Antennen, (b) magnetische Antennen, (c) Rechnung in zweiter Naherung, (d) Strahlungsmessungen mit Antennen," Ann. d. Phys., 5, 1, 721-772; 4, 1-16; 9, 67-91, 1929-1931. 9. W. Howard Wise, "Asymptotic Dipole Radiation Formulas," Bell. Sys. Tech. Jour., 8, 662-671, October, 1929. 10. W. Howard Wise, "Note on Dipole Radiation Theory," Physics, 4, 354-358, October, 1933. 11. W. Howard Wise, "The Grounded Condenser Antenna Radiation Formula," Proc. I. R. E., 19, 1684-1689, September, 1931. 12. Glenn D. Gillett and Marcy Eager, "Some Engineering and Economic Aspects of Radio Broadcast Coverage," Proc. I.R.E., 24, 190-206, February, 1936. 13. C. B. Feldman, "The Optical Behavior of the Ground for Short Radio Waves," Proc. I.R.E., 21, 764-801, June, 1933. 14. R. L. Smith-Rose, "Electrical Measurements on Soil with Alternating Currents," I.E.E. Jour. (London) 75, 221-237, August, 1934. The Inductive Coordination of Common- Neutral Power Distribution Systems and Telephone Circuits * By J. O'R. COLEMANt and R. F. DAVIS Early installations of three-phase, four-wire power distribution systems of the multi-grounded or common-neutral type in some cases created noise problems involving neighboring telephone cir- cuits. Operating experience, studies of specific situations and comprehensive cooperative research over a period of years have developed means of largely avoiding difficulties of this character. The relative importance of various features of the power and telephone systems which have been found to affect the noise induc- tion problems involved is discussed and the general cooperative procedures, most helpful in conversions to or extensions of these types of power distribution systems, are outlined. Introduction PRIOR to about 1915, delta-connected 2300-volt, three-phase, pri- mary circuits were used extensively for the distribution of electric current. While some distribution networks throughout the country still operate in this manner, the marked increase in load densities, starting about 1915, often made the retention of the 2300-volt delta system impracticable. In a few instances the development of the particular network was at a point where it was feasible to change from the 2300-volt delta to a 4600-volt delta arrangement but in other cases the existing equipment represented too great an investment for a complete change of this character. From studies of various methods of caring for the augmented load densities it was found that the existing equipment could largely be saved and the capacity of the distributing networks substantially increased by converting them to a 2300/4000-volt, star-connected, four-wire primary system. By about 1925 this system had extended to most of the larger cities and most power companies had found it economical for use in at least some parts of their territories. In using the 2300-volt equipment on the 4000-volt, four-wire system it was necessary to stabilize the neutral conductor in some way. Most of the four-wire systems had the neutral conductor grounded at the * Published in Electrical Engineering, January, 1937. t Mr. J. O'R. Coleman, joint author of this paper, is an engineer on the staff of the Edison Electric Institute, New York City. 76 INDUCTIVE COORDINATION 77 substation only although sometimes low-voltage lightning arresters were placed on it at various points in the distribution network to aid in its stabilization in case of a break in it. In some instances, at the time of the installation of the four-wire system, the primary neutral was connected at various points in the network to driven ground rods thus resulting in a multi-grounded neutral system. In at least one instance the neutral conductor was not solidly grounded even at the substation, it being connected to ground through lightning arresters. The experiences of the power companies with the multi-grounded neutral were generally favorable. It was found to be more reliable and to embrace some simplifications over other distribution methods. While the early multi -grounded neutral arrangements were obtained by making connections to ground along the primary neutral conductor and interconnecting it, at service transformers, to well-grounded secondary neutrals a further simplification in the arrangement was readily apparent. It will be noted in Fig. 1 that this interconnection of the primary and secondary neutrals resulted in two grounded neutrals on the pole line in all sections where the secondary neutral existed. In extending the multi-grounded neutral arrangement or in reconstructing existing portions of the network, these two neutrals were combined into a single well-grounded conductor continuous in all portions of a feeder area and often continuous in all parts of a substation area or of several contiguous substation areas. This arrangement, called the "common- neutral," which was first extensively applied in Minneapolis* by Mr. S. B. Hood, resulted in certain savings in equipment and relief of congested pole heads and in a neutral network most effectively grounded since all secondary neutral grounds were thus made avail- able, in addition to any driven grounds along the pole line. The operation of this system in Minneapolis showed many advan- tages in the protection of secondary networks from the effects of voltage rises under abnormal conditions. In addition a paper presented in 1925 by Mr. Hood ^ pointed out that over a period of three years the rate of transformer failure was reduced to 8/10 of 1 per cent per annum. This excellent performance in transformers arose undoubtedly from the fact that with the "common-neutral" or interconnected neutral arrangements the lightning arresters are connected directly around the transformers. Later studies showed that the connection of the light- ning arresters directly between the primary conductors and secondary neutral provides a degree of protection which cannot readily be ob- tained in any other way.^- '• *• ^' ^' '' * Prior to applying this system in Minneapolis, Mr. Hood introduced it at Toronto, Canada. 78 BELL SYSTEM TECHNICAL JOURNAL In urban areas, the multi-grounded or common-neutral method of distribution introduced, in some instances, noise induction in nearby telephone circuits. In view of this fact an extensive cooperative investigation was undertaken by Project Committee No. 6 of the •PRIMARY CIRCUIT SERVICE TRANSFORMER SECONDARY- O O — t 110-120 VOLTS TO LOADS O jo - ^f 1 _. ^ ^ NEW SINGLE-PHASE BRANCH OPERATING ^ ON "common-neutral" BASIS (B) Fig. 1 — A. Simplified feeder operating with primary neutral grounded at source only. B. Simplified feeder operating with multiple grounds on primary neutral- older part of feeder having ties between primary and secondary and new extensions being of common-neutral arrangement. Joint Subcommittee on Development and Research of the National Electric Light Association and Bell Telephone System to determine the factors involved in the coordination of local power distribution systems and telephone systems. A study was carried out in Minneapolis during the years 1924 to 1926 having as its primary objective the determination of the factors involved where the telephone distribution INDUCTIVE COORDINATION 79 was largely in aerial cable. The investigation was continued in Elmira, New York in 1926 to 1929 to embrace the factors introduced when the exchange telephone plant was of open-wire construction.^ Sup- plementing these detailed technical studies, an investigation of certain economic features of various arrangements of power and telephone distributing methods and of their practical application under varying conditions was carried out in California in 1928 and 1929. As a result of these investigations the various factors involved in the co- ordination of multi-grounded or common-neutral power systems and telephone distribution systems were determined and certain practices developed for the coordination of these systems under various condi- tions in urban areas. ^ The purpose of this paper is that of briefly outlining a few of the more important features of power and telephone circuits affecting noise coordination. Following such a review there is presented a list of measures which extended experience has shown will, where given proper consideration by both parties, enable multi-grounded or common- neutral power circuits and telephone circuits to live harmoniously. No attempt is made, however, to reiterate the extensive technical information obtained from the investigations outlined above as these are adequately covered in the references cited. Recent Trends During the past few years there has been extensive conversion from other types of urban power distribution to the multi-grounded or common-neutral system of primary distribution. Where there exists a three-phase, three-wire delta circuit the system is converted by making the secondary neutral network continuous, reinforcing it where necessary, and making the required changes in transformer connections. Where there is a three-phase, four-wire uni-grounded primary system the conversion is, as previously mentioned, made by interconnecting the primary and the secondary neutral at each load transformer generally removing the primary neutral only at the time of major rebuilding. In either case extensions are usually made using a single neutral in the secondary position. In the urban areas most of the multi-grounded or common-neutral systems are of the 2 300/4000- volt class, although there are a few instances where 4600-volt systems have been converted. At the present time there is being constructed a 6900/1 2, 000-volt common- neutral distribution system at Wichita, Kansas. The distinct trend in power distribution practice has been, in no small measure, influenced by the improved overall protection features 80 BELL SYSTEM TECHNICAL JOURNAL readily obtained by the multi-grounded neutral arrangement as well as by certain equipment savings. The recent emphasis placed on the electrification of rural areas and the distinct need for maximum service continuity on rural power circuits has increased the interest in the use of the multi-grounded or common-neutral method of distribution in rural areas. The rural systems are generally of the 7600/13, 200-volt class, although 4600/8000-volt circuits have been used to some extent. The factors affecting inductive coordination involved in the use of the common-neutral method of distribution in rural areas, are some- what different from those encountered in urban areas. This is largely due to the lower load densities, the greater lengths of circuits, higher operating voltages and to the somewhat different types of equipment employed in rural telephone distribution. These factors were in- vestigated by the Joint Subcommittee on Development and Research during the summers of 1935 and 1936 and the more important con- siderations determined.^" Factors Influencing Inductive Coordination In any problem of inductive coordination it is convenient to sub- divide the factors influencing coordination into those relating to the inductive influence of the power circuit, the inductive susceptiveness of the telephone circuit and the inductive coupling between the two types of circuits. As far as urban distribution circuits are concerned the load current unbalance of the power circuit is usually the controlling influence factor. For rural distribution circuits the unbalanced charging currents are generally more important than the unbalanced load currents. Likewise, in an exchange telephone circuit the admit- tance and impedance unbalances of the two sides of the circuit are usually the controlling factors in its inductive susceptiveness. As far as coupling between the power and telephone circuits is concerned this is largely controlled by their relative positions and the lengths of the exposure. For urban areas their relative positions are largely fixed by the normal arrangement of conductors and cables on jointly- used poles. In rural areas power and telephone circuits are generally at roadwa\' separation although some joint use exists. In urban areas considerable control can often be exercised over the coupling by planning the routes of the main feeds of the two services so as to avoid long sections of close exposure. In rural areas where there are no paralleling routes close together it is generally necessary for both services to use the same roads and therefore the opportunity to control the coupling by the cooperative planning of routes is much reduced. INDUCTIVE COORDINATION 81 Certain quantitative indications of the extent to which this measure of coordination is applicable in the two types of areas are shown in the illustrative examples in the Appendix. Power Circuits Power systems operate, for the most part, at frequencies of 60 cycles and below. Telephone circuits, on the other hand depend mainly upon frequencies above about 200 cycles for the transmission of speech. Ordinarily, therefore, the effects of induction from the fundamental frequency currents and voltages in neighboring power lines are negli- gible as far as telephone circuit noise is concerned. It is quite generally recognized, however, that it is impracticable commercially to build rotating machinery and transformers which are entirely free from harmonics. There are, therefore, harmonics present on all operating power systems and it is the harmonic-frequency components induced into telephone circuits from these power system harmonics that are of major importance from the noise standpoint. ^^ In any distribution circuit the harmonic currents present will fall within the following classes: — load currents, transformer-exciting currents and line-charging currents. With a uni-grounded neutral the load currents and the transformer-exciting currents are practically entirely confined to the wires of the circuit. Where the neutral is multi-grounded, the vector sum of the currents in the phase conductors (residual current) will divide between the neutral conductor and the paralleling earth path as determined by the relative impedances of these two paths. W^hile there is some variation in the division of the return current between the neutral and ground paths, for most practical purposes this division may be assumed to be about half in each path at all the frequencies of interest. As pointed out above, in the case of a line operating with uni- grounded neutral, the earth-return components of the load and transformer-exciting currents are ordinarily negligibly small. How- ever, this is not true of the line-charging current which is chiefly a function of the magnitude and frequency of the impressed voltage, the circuit length, and, at non-triple harmonic frequencies, of the balance of the admittances to ground of the various phase conductors. While multi-grounding the neutral ordinarily increases the earth- return components of the load and transformer-exciting currents, it has been found, due to the parallel path provided by the neutral wire, on an average to decrease slightly the amount of charging current in the earth. In an urban distribution system where the load density is relatively 82 BELL SYSTEM TECHNICAL JOURNAL high, the load currents and transformer-exciting currents are relatively large and the line-charging currents are usually negligible. In such a system multi-grounding the neutral results in an increase in the current returning through the earth and a consequent increase in the inductive influence of the power distribution system. In rural areas, however, where the load density is low and the load currents and transformer-exciting currents are relatively small, the line-charging currents become significant. In general, under such conditions the multi-grounding of the neutral does not increase the magnitude of the ground-return current at frequencies of interest from the noise induction viewpoint. Under certain conditions the mag- nitude of this ground-return current may actually be substantially decreased by the multi-grounding of the neutral. This effect is more marked for the higher voltage circuits. The harmonics present in a distribution circuit may be divided into (1) triple harmonics, that is, the third harmonic and odd multiples of it, and (2) non-triple harmonics, that is, the odd harmonics, starting with and including the fifth, which are not multiples of three. The triple harmonics in a three-phase system are in phase in the three line conductors so that their residual value (vector sum) is the arithmetic sum of their magnitudes in the three-phase wires. The non-triple harmonics are spaced, in time phase, the same as the 60-cycle funda- mental and the magnitude of the residual current (vector sum) for these harmonics is usually much less than their arithmetic sum. If these harmonics were perfectly balanced the residual current for these frequencies would be zero. In exposures involving three-phase sec- tions of line the balance of the non-triple harmonics between phases is influenced by the degree of balance of the loads and single-phase branches and therefore has an important effect in reducing the overall influence of the power system. In exposures involving single-phase extensions, or extensions consisting only of two-phase wires and a neutral wire this advantage of the balancing of the non-triple har- monics is, of course, not obtainable. The extent to which induction from the non-triple harmonic voltages and currents in power distribution circuits can be controlled by power circuit transpositions is ordinarily very limited. Usually, due to the large number of exposure discontinuities arising from changes in the power or telephone circuits, the power circuit transpositions are quite ineffective. This is particularly true in cases where the induction from the ground-return current is controlling. In specific cases where considerable wave shape distortion exists and the induction from the balanced voltages and currents may therefore be relatively important, transpositions in power distribution circuits may be found helpful. IND UCTI VE COORDINA TION 83 Table A shows the average harmonics present on three-phase, four- wire industrial and residential feeders under light and heavy load conditions. The reduced magnitudes of the non-triple frequencies in the residual current (neutral and ground-return) are evident. The importance of this as regards noise induction is further indicated in the illustrative examples of the Appendix. TABLE A * Average Current and Voltage Wave Shapes of 2300/4000-Volt, 3-Phase, 4-Wire Distribution Circuits Current in Industrial Feeder Current in Residential Feeder Order Phase-to- (In Amperes) (In Amperes) Fre- quency of Har- Neutral Voltage Light Load Heav ' Load Light Load Heavy Load monic at Bus. Phase Re- sidual Phase Re- sidual Phase Re- sidual Phase Re- sidual 60 2380 65. 130 53 99 180 3 16 1.1 2.6 1.1 2.9 1.8 5.2 1.9 6.0 300 5 21 1.0 .15 1.3 .16 .43 .21 .75 .29 420 7 6.4 .3 .03 .3 .05 .13 .06 .17 .08 540 Q 1.7 .04 .08 .04 .13 .04 .09 .04 .09 660 11 1.9 .07 .01 .09 .01 .04 .01 .06 .02 780 13 1.8 .08 .01 .05 .01 .02 .01 .04 .01 900 15 .42 .01 .01 .01 .03 .01 .01 .01 .01 1020 17 .90 .03 .01 .07 .01 .02 .01 .03 .01 1140 19 .87 .02 ■ — .04 — .01 .01 .02 .01 1260 21 .16 — — — .01 — — .01 .01 1380 23 1.4 .05 — .06 — .01 — .03 .01 1500 25 2.1 .06 .01 .09 .01 .01 .01 .03 .01 1620 27 .79 — .01 .01 .02 — — .01 .01 1740 29 1.5 .02 — .03 .01 .01 — .02 .01 1860 31 1.4 .01 — .02 — — — .01 — TIFt 9.7 11.2 — 8.9 — 6.6 — 5.8 — Kv. T 23.2 733 193 1160 330 346 238 571 283 or I.T. Note: Triple harmonics are italicized. * Tables 31 &32 — pp. 235 & 236 of Vol. II of Eng'g Reportsof Joint Subcommittee. t New weighting — see Engineering Report No. ii of Joint Subcommittee. The triple-harmonic currents present on a feeder supplied from a delta-wye substation transformer bank are generally due to the exciting currents of the single-phase load transformers. Under this condition no excessive triples are impressed on the feeder at its source as is some- times the case where the source is a wye-connected, grounded-neutral generator directly connected to the feeder. The exciting currents flow from the individual single-phase transformers toward the delta- wye transformer in the substation. The presence on the feeder of a large three-phase wye-delta load transformer with its neutral con- nected to the system neutral, provides a parallel path for supplying 84 BELL SYSTEM TECHNICAL JOURNAL part of these triple-harmonic exciting currents as well as part of the unbalanced non-triple and fundamental currents and under certain conditions may substantially decrease the overall inductive influence of a feeder by reducing the ground-return current flowing through an exposure. The effect of such a connection in reducing the noise is dependent upon the location of the bank with respect to the exposure and its relative impedance to the various harmonics as compared to that of the path back to the substation. From the power operating standpoint such a bank tends to supply part of the unbalanced load and also, in case of the interruption of one phase between it and the substation, tends to supply the power to that portion of the phase still connected to it. Under certain conditions, the action of such a bank may prove detrimental to the operation of the power feeder due to its action in attempting to balance the voltages at the point of its connec- tion to the feeder. Under other conditions the neutral of an existing bank can readily be connected to the feeder neutral with distinctly beneficial effects on the inductive influence and with little or no adverse effects on the power-system operation. The tendency of such banks toward noise reduction and towards unbalanced load supply is shown in two of the illustrative examples in the Appendix. Telephone Circuits The voltages induced into a telephone circuit may be divided into (1) metallic-circuit induction, that is, a voltage induced between the two sides of the circuit with a resultant current flowing around the circuit, and (2) longitudinal-circuit induction, that is, a voltage in- duced along the conductors such that the resultant current flows in a circuit having the telephone conductors as one side and the earth as the other. This latter voltage may also result in noise, due to its action upon telephone circuit unbalances, setting up currents in the voice channel (metallic-circuit). For either type of voltage, the induction may be "electric," that is, from the voltage on the power circuit, or "magnetic" from the current in the power circuit. The local telephone circuit may be divided into three parts: (a) the central office equipment, {h) the line conductors and (c) the subscriber equipment. Inter-office circuits include only the first two items. {a) Central Offices Equipment The central office equipment associated with a subscriber circuit consists essentially of two elements: (1) line signaling equipment connected to the circuit for indicating to the operator, or to the dial equipment, the desire of a subscriber to start a call and (2) a linking or switching circuit or circuits for interconnecting two subscriber cir- INDUCTIVE COORDINATION 85 cuits either directly or through intervening trunk circuits and pro- viding supervision during the call. The line signaling equipment with its associated relay is either bridged across the line or arranged so that, when two subscriber cir- cuits are interconnected, any ground connections on the line relays are automatically opened. The line signaling equipment is not, therefore, ordinarily a factor in noise considerations. Occasionally, however, the effect on noise of the ground connection on the line signaling equip- ment requires specific treatment when the longitudinal-circuit induc- tion is sufficiently high. The noise in such instances occurs either dur- ing the pre-answering period before the line relay is "cut-off" or, in certain types of switchboards, on conversations between two persons on the same line (party-line) where the use of a switching circuit in the office is unnecessary. The linking or switching equipment in the central office may consist of a pair of wires with bridged supervisory relays as in the case of a magneto office or may be a complicated arrangement of relays, re- peating coils, condensers, etc., as in the case of common-battery offices of the manual or dial type. The necessary ground connections of the latter type of apparatus introduce the possibility of the unbalances in the equipment contributing to the overall noise when the longitudinal- circuit induction on the outside conductors is impressed on the switch- ing circuits. Ordinarily in urban areas, due either to the frequency make-up of the longitudinal-circuit induction or to the relationships of the various impedances-to-ground, the amount of noise contributed by the central office equipment is relatively low. This is readily evident from Table B which shows, at 500 and 1000 cycles, the relative proportions of overall noise due to the action of induced voltages on station, cable and central office unbalances: TABLE B * Relative Importance of Circuit Unbalances 500 Cycles 1000 Cycles Type of Service Contribution from: Contribution from: Station Cable Office Station Cable Office Individual (bridged ringers) Party-line (grounded 8-A ringers) Negligible 100 3 3 3 3 Negligible 100 20 20 20 20 See p. 72 of Vol. I of Eng'g Reports. 86 BELL SYSTEM TECHNICAL JOURNAL Cases arise, however, quite frequently where the relative circuit impedances or the frequency make-up of the induction or both are such that the noise contribution from the unbalances in the central office equipment becomes important. Such cases usually involve long subscriber or inter-office trunk circuits and particularly where sections of open-wire construction are present. Values of the unbalances in certain types of central office equipment are given on page 91 of Volume I of the Engineering Reports of the Joint Subcommittee on Development and Research. {b) Line Conductors Where the telephone line conductors are in open-wire, the induced voltage between conductors (metallic-circuit) as well as along these conductors (longitudinal-circuit) must be considered. The direct metallic-circuit induction can be greatly reduced by systematic transpositions in the telephone circuit. Due to the physical limita- tions in a practical layout of telephone transpositions, the reduction in metallic-circuit induction is, on the average, from 60 to 80 per cent on non-pole pairs and about 90 per cent on pole-pairs. Transpositions also tend to lessen the capacitance and inductance unbalances of the two sides to ground and to other circuits, thereby reducing the effect of the longitudinal-circuit induction on such unbalances. The im- proved balance of the mutual impedances between the various tele- phone conductors is, of course, distinctly beneficial in reducing cross- talk and transpositions are generally used for limiting the crosstalk where open-wire telephone circuits extend for substantial distances. The construction of telephone cables is such that there is inherently very close spacing between the conductors and they are frequently transposed due to the continuous twisting of the pairs in manufacture. Due to this close spacing and frequent transposing there is practically no voltage induced between the wires of a cable pair or quad (group of four conductors). The unbalance to ground of the conductors of the present type of cable is so small that it is not ordinarily a contributing factor to noise induction. It may be noted, however, from Table B that in cases where the central office unbalances are of importance, the effect of shunt or series unbalances in the cables also needs consideration. The lead sheath of a telephone cable provides practically perfect shielding against induction from power system voltages when it is grounded at one or more points. The sheath likewise provides sub- stantial magnetic shielding when it is grounded more or less continu- ously as in underground construction or is grounded at both ends of the aerial section or near both ends of an exposure. The degree of magnetic shielding effected varies, depending on the size of the cable IND UCTI VE COORDINA TION 87 CQ < g w ^; Dg So Pi « 9 > ^ fa ffl s 3 a w o S ? rt •a 4) •0 ^-^ C bn 3 C 0 -0 I-. 10 (M r^ -H re 10 -H On 00 t-~ 0 10 •>* 0 ^ "1 — < t— Tt 1^ -H r^i t^ 10 ■^ PO fO CN * i 0 0\ 0 On 00 t^ 65 On On 00 t^ t^ to 0 ^ 1^ •>*' r- -^ tN r— U-) ■<* fO (^ fN Rio _^ I' 0 * t 0 6? irj On ^ ro NO -^ On 00 00 t~- NO U-) » On t^ "0 10 t-^ U1 00 t^ NO "-) •* ^ 10 NO ■r}< ro tN CN -H * t 0 On NO ir> 00 •>* Cn) On On On 00 00 t— 10 65 10 On -- re NO ^ On 00 00 t^ NO 10 0 65 iO G r^ T-f IT} ,-1 irj nO •^ (^ CN CN ■rt N 3 * 0 65 ■^ tN 0 tN t^ 00 J^ 10 Tf rr> CN •-^ » 65 0 rO >* On NO -H in (^ c<\ T^ —< ^ 0 65"^ rt> 00' NO 10 ■* ro * -1- k 0 65 "^ Tt "^ NO -^ Tf Tt On 00 t^ t^ NO '* 65 '^ "1 fN 10 C^ fi t^ uS 00 NO UT* f^fN •1- 0 65 "1 Tt 00 NO 10 •^ ro «3 _4; "u; ; : :: ; >. U 000000 000 fN Tj u ■- be be c S _Ot3 4> U C 0 be m tn TS ■M 0 0 •4-* t« rn V. u V 4> 4) 4> aioi 88 BELL SYSTEM TECHNICAL JOURNAL and the resistance of the ground connections, reaching optimum values of over 90 oer cent. Table C gives the magnitude of this shielding for various selected sizes and lengths of cable. Table C brings out distinctly the variation in the magnetic shielding due to the factors mentioned above. The effect of cable sheath shielding in several typical cases is further indicated in the Appendix. TABLE D Relative Susceptiveness of Several Types of Station Sets Noise in Receiver Branch for 100 Noise Units to Ground — Average Power Wave Shape {One Station on Line-Effect of Set Only) General Description of Station Set 350 Noise Units Approximately 120 Noise Units Approximately 120 Noise Units Approximately Class 1 — Types of sets in most common use today a. Sidetone type of party-line set using 8A ringers or equivalents (one end of ringer grounded). (Common- battery talking and signaling) b. Same type — -local-battery talking c. Magneto party-line set (52A Ringer or equivalent) d. Individual-line set — any type Class 2 — Types of sets frequently encountered a. Sidetone type of 4-party full-selective or 8-party semi-selective set (using relay or cathode tube to connect ringer to circuit during ringing period) b. Four-party selective or 8-party semi- selective sets employing high im- pedance ringers or relays con- nected to ground c. Eight-party selective (harmonic ring- ing) sets employing ringers con- nected to ground and tuned to 4 different ringing frequencies d. Ground-return rural circuits (usually of magneto type and having code ringing) Class 3 — Special types of sets a. Sidetone type of party-line set using split-condenser and higher im- pedance ringer (one end of ringer grounded) b. Type of party-line set using split con- denser arrangement with 8A ringer or equivalents (one end of ringer grounded). (c) Station Apparatus Individual-line stations employ a "bridged" ringer connection, i.e., the ringer is, in effect, connected between the two line conductors. Negligible Negligible About 30 Limited data indicate that, de- pending on frequency for which ringer is tuned, noise will range from about 100 to about 400 units 3500 or more noise units About 20 noise units About 90 noise units IND UCTI VE COORDINA TION ^9 However, for selective signaling purposes party-line stations frequently have the ringer connected, in effect, between one of the line conductors and ground. The unbalance of the party-line station equipment is therefore affected by the impedance of the ringer and its point of connection in the station equipment. The relative susceptiveness of several types of station sets to noise-frequency induction is shown in Table D. Table D shows that, with advance planning in areas where noise induction is or may likely become a matter of importance, much can be accomplished by the use of station sets of decreased inductive sus- ceptiveness. Where such types of apparatus are substituted in existing plant, except in gradual replacements or in connection with general rearrangement programs, the expense is, naturally, increased. Inductive Coupling As stated above, the inductive coupling between exchange telephone plant and power distribution circuits in urban areas is largely con- trolled by such factors as the street layouts and the joint use of poles. (See following page) 90 BELL SYSTEM TECHNICAL JOURNAL Direct Metallic Circuit Induction in Untransposed Telephone Circuits Magnetic Induction, 1000 Cycles Volts Metallic per Ampere of Power Circuit Current per 1000 Feet of Exposure Type Power Circuit Induction Com- ponent Power Conductors* Pair 1-2 Pair 5-6 Pair 9-10 Avg. Single Phase Residual A&N C&N E&N .021 .0044 .0002 .043 .018 .023 .0044 .0053 .0013 .022 .0092 .0082 Two Phase Wires & Neut. Residual A, C, & N A, D, & N .013 .008 .031 .018 .005 .009 .016 .012 Three Phase Residual A, B, C, & N A, C, D, &N .012 .007 .033 .01 .005 .004 .017 .007 Two Phase Wires & Neut. Balanced A, C, & N A, D, & N .017 .026 .026 .13 .0009 .026 .015 .061 Three Phase Balanced A, B, C, &N A, C, D, & N .015 .023 .023 .123 .012 .026 .017 .057 * In each case, conductor "N" is a multi-grounded neutral, the other wires being phase conductors. Assumed 50% of the residual current in the neutral and 50% in the ground. Electric Induction Volts per Kilovolt Vm/Kv Type Power Circuit Induction Com- ponent Power Conductorst Pair 1-2 Pair 5-6 Pair 9-10 Avg. Single Phase Residual A&N C&N E&N 7 2 .4 19 7.3 9 3 2.3 .2 9.7 3.9 3.2 Two Phase Wires & Neut. Residual A, C, & N A, D, & N 5 2 13 7 2.6 2 6.9 3.7 Three Phase Residual A, B, C, &N A, C, D, & N 2.8 1.4 10 2.2 2 .7 5.0 1.4 Two Phase Wires & Neut. Balanced A, C, & N A, D, & N 3 6 7 30 .4 5 3.5 13.7 Three Phase Balanced A, B, C, & N A, C, D.&N 2.7 5.6 5.8 27 .4 5.4 3.0 12.7 t Wires S & S assumed continuous through exposure and grounded. Fig. 2 — Effect of relative positions on joint-use pole of power and telephone con- ductors on coefficients of induction for voltages and currents. However, by cooperative planning of routes it is frequently practicable to secure lower coupling by avoiding long e.xposures between the main feeds of the two plants. As shown by the illustrative examples this procedure is, where applicable, very beneficial. INDUCTIVE COORDINATION 91 In rural areas where both distribution services must ordinarily be carried along the highways the opportunity for controlling the coupling between the two classes of circuits by cooperative planning of routes is much reduced. Some benefit may be gained, however, in the case of open-wire construction particularly at joint-use separations, by arrangements of the conductors on the pole so as to avoid excessive spacings. As shown on Fig. 2 certain arrangements tend to minimize the amount of noise induction arising from the power circuit voltages and currents. This beneficial effect is, however, much less noticeable at roadway separations. Summary and Conclusions Since about 1915 there has been a continued increase in the use of the multi-grounded or common-neutral arrangement of power distri- bution in this country. At the present time, approximately half of the distribution is by 4000-volt multi-grounded or common-neutral cir- cuits. A large part of the higher-voltage rural distribution is also operating with this arrangement. In general it may be said that for the lower-voltage 2300/4000-volt distribution circuits, the use of the multi-grounded or common-neutral arrangement may be expected to increase the inductive influence of the power circuits. Unless attention is given to cooperative planning to secure features beneficial from the inductive coordination stand- point, noise problems may result either in restricted or extensive areas. With proper attention to the coordination features ^ such noise situa- tions as develop are largely in the nature of isolated cases and can usually be cared for by relatively minor changes or adjustments in either or both plants. For the higher voltage (11-13 kv.) rural distribution circuits, there seems to be little difference, from the noise induction standpoint, between the uni-grounded four-wire system and the multi-grounded or common-neutral arrangement. ^° Under many conditions the placing of multiple grounds on the neutral will result in noise reductions due to the effect, previously mentioned, of the multi-grounded neutral on the line charging currents. It is interesting to note that experience to date with the multi-grounded or common-neutral in rural areas has shown that many of the measures of coordination applicable in urban areas will prove similarly helpful in rural communities. The measures of coordination which investigations and operating experience have shown to be practicable and effective include: 1. Cooperative planning by both parties to avoid not only severe exposure conditions but also types of equipment likely to aggravate the possible noise induction situation. 92 BELL SYSTEM TECHNICAL JOURNAL 2. A reasonable degree of balance of the loads between the three phases of the power circuit. In the higher- voltage rural circuits this also includes the lengths of branches consisting of one or two phase wires and neutral. 3. The avoidance of unnecessarily heavily loaded branches consist- ing of one or two phase wires and neutral. 4. The prevention of excessive over-excitation of transformers. 5. The grounding, where necessary, of aerial telephone cables at or near both ends of an exposure to obtain the benefits of magnetic shielding. 6. The use of adequately coordinated telephone transpositions on open-wire extensions and the avoidance of severe unbalances in the open-wire conductors. 7. The correction of badly distorted voltage or current wave shape on the power system. 8. The connection of the neutral point of three-phase wye-delta load banks to the system neutral conductor. 9. The use of telephone station apparatus, on party-line service, of lower susceptiveness. 10. Occasionally the use of arrangements or apparatus to minimize the effects from unbalances in central office equipment. It is, of course, essential in successfully coordinating the power distribution and telephone circuits that, as in other coordination situations, the power and telephone people view the matter as a mutual responsibility and fully cooperate in the application of the tools available. Experience over a period of years has now shown that where this is done adequate overall coordination can be readily secured. ^^ The authors wish to acknowledge their indebtedness to their many coworkers who aided in carrying on the various investigations on which this paper is based. Bibliography 1. "Improvement in Distribution Methods," S. B. Hood — p. 1038 of 1925 Trans. A.I.E.E. 2. "Interconnection of Primary Lightning Arrester Ground and the Grounded Neutral of the Secondary Main," C. F. Harding and C. S. Sprague — p. 234 of 1932 Trans. A.I.E.E. 3. "Lightning Protection for Distribution Transformers," K. B. McEachron and L. Saxon— p. 239 of 1932 Trans. A.I.E.E. 4. "Lightning Protection for Distribution Transformers," A. M. Opsahl, A. S. Brooks and R. N. Southgate— p. 245 of 1932 Trans. A.I.E.E. 5. "Studies of Lightning Protection on 4000-volt Circuits — III," D. W. Roper — p. 252 of 1932 Trans. A.I.E.E. 6. "Lightning Protection for Distribution Transformers," T. H. Haines & C. A. Corney— p. 259 of 1932 Trans. A.I.E.E. INDUCTIVE COORDINATION 93 7. "Distribution System Lightning Studies by Philadelphia Electric Company," H. A. Dambly, H. N. Ekvall, and H. S. Phelps— p. 265 of 1932 Trans. A.I.E.E. 8. Engineering Reports 6, 9, 13 and 15 — Vols. I and II of Engineering Reports of Joint Subcommittee on Development and Research of National Electric Light Association and Bell Telephone System. 9. Common-Neutral Practice Confirmed in California — p. 980 — ^June 4, 1932 issue of Electrical World — (See also May 15, 1932 issue of Electrical West.) 10. Provisional Report No. 18 of Joint Subcommittee on Development and Research of Edison Electrical Institute and Bell Telephone System. 11. "Measurement of Telephone Noise and Power Wave Shape," J. M. Barstow, P. W. Blye and H. E. Kent— p. 1307 of 1935 Trans. A.I.E.E. 12. Reports of Joint General Committee of National Electric Light Association and Bell Telephone Systems on Physical Relations between Electrical Supply and Signal Systems — Edition of Dec. 9, 1922. Appendix For the sake of brevity, the detailed calculations and some of the minor assumptions for the following examples have been omitted. Illustrative Example 1 The purpose of this example is to show, for average power system wave shapes: 1. The noise induction problem that might be created by the exposure of a reasonably long aerial telephone cable in an urban area with a heavily loaded single-phase feeder. It features: a. The relative importance of triple and non-triple har- monic induction, and b. The extent to which planning of routes, grounding of cable sheaths, etc. might improve the situation. 2. The changes in the noise magnitudes for the same situation with the various single-phase loads well distributed among all three phases. Under this condition, attention is directed to: a. The change in the relative importance of the triple and non-triple harmonic induction. b. The amount of reduction obtained by the same remedial measures tried in \-b above. Figure 3 shows a possible method of supplying the single-phase loads •n a rather extensive part of an urban area. The general layout shown on Fig. 3 is such that all of the current for the feeder area traverses a considerable part of the exposure. Under this quite extreme condition — essentially single-phase supply for a relatively large area — the noise at location C under heavy load conditions would be about as shown on Table I. 94 BELL SYSTEM TECHNICAL JOURNAL CENTRAL OFFICE — B- APPROXIMATE SCALE IN FEET TYPICAL POLE-HEAD CONFIGURATION 15 15 LOCATION B X LOCATION A AERIAL TO UNDERGROUND POLE TO SUBSTATION 15 4 15 • 10 I5u SECTIONS A-B — LEGEND — E 3- PHASE PORTIONS OF FEEDERS : 2 -PHASE PORTIONS OF FEEDERS - I -PHASE PORTIONS UNDERGROUND TELE PHONE CABLE AERIAL TELEPHONE CABLE •J\f\« "drop" WIRE TO SUB- SCRIBER'S STATION — • SERVICE TRANSFORM- ER—KVA AS INDICATED ALL SECTIONS ASSUMED AT JOINT-USE SEPARATIONS — SEE TYPICAL POLE-HEAD CONFIGURATION ABOVE ^ 3-100 KVA f4PER , .CENT)YA • 10 rx LOCATION C Fig. 3 — Example of possible arrangement of feeder layout in an urban area where long aerial telephone cable is exposed to a heavily loaded one-phase feeder. INDUCTIVE COORDINATION 95 --e — e — B CENTRAL OFFICE -e — D D — B — e a I0 10 f 10 10 LOCATION A 15 15 15 10 AERIAL TO UNDERGROUND POLE TO SUBSTATION ■5500'- SECTION A-B B-C D-E E-F C| F-G 3 i»l5 3-100 KVA (4 PER cent)ya 10 A2 G-H C? X LOCATION C Fig. 4 — Example of possible rearrangement of feeder layout shown in Fig. 3 to reduce magnitudes of "ground-return" currents. 96 BELL SYSTEM TECHNICAL JOURNAL TABLE I Noise Contributions (Fig. 3) of Various Harmonics and Sections of Exposure Section RMS Magnitude of Residual Current Approximate Total Noise Contribution * Approximate Noise Contribution From: of Exposure 180 Cycles 300 Cycles and Higher Frequencies A-B 210 amperes 157 30-107 " Total 1240 noise units 1130 " 500 " 2870 " 270 noise units 250 " 100 " 620 " 1215 noise units B-E 1100 " E-I 490 " 2800 " * Location C — For party-line service using 8A ringers, during heavy power loads. It is evident from Table I that most of the party-Hne stations fed by the aerial telephone cable would need treatment. It will be noted from Table II that completely replacing the existing party-line stations with special station apparatus will, to a large extent, care for the situation since, in this case, the amount of noise contributed by the cable and central office unbalances would aggregate less than 150 units. Other measures either singly or in combination, probably more economical in their application, would provide substantial reductions in noise but would not be adequate for the more severely exposed stations. TABLE II Comparison of Effectiveness of Various Remedial Measures (Fig. 3 Conditions) Approximate Noise on Party-Line Stations (Heavy Power Loads) Type of Remedial Measure Location A or B Location C 1. Before applying remedial meas- ures 1800 noise units 2870 noise units 2. Using special telephone station sets _ 75 " " 125 " 3. Avoiding exposure in section A-B by cooperative planning of routes 560 " " 1630 " 4. Cable sheath shielding by tying aerial and underground tele- phone cables at junction pole and connecting aerial sheath to 1 ohm ground at point X. 1160 " " 1700 " " 5. Interconnecting 300 leva wye- delta bank with system neutral 1430 " " 1600 " " (170 leva of unbal- anced load) 6. Combination of measures 3, 4, and 5 365 " " 420 " IND UCTIVE COORDINA TION 97 Assume, however, that instead of supplying the single-phase loads in the area shown on Fig. 3 from one phase only, the single-phase loads were distributed reasonably uniformly among the phases. This would be advantageous not only by the noise reduction possibilities, which will be more fully discussed but also by the improved regulation attainable on the feeder. Figure 4 shows a possible rearrangement of Fig. 3 along these lines and Table III shows the noise conditions with the feeder arrangements of Fig. 4. TABLE III Noise Contributions (Fig. 4) of Various Harmonics and Sections OF Exposure Section of Exposure RMS Magnitude of Residual Current Total Noise Contribution * Noise Contribution From: 180 Cycles 300 Cycles and Higher A- B- E- -B -E -/ 6 amperes 45 5-45 Total 280 noise units 370 " 150 " 735 " 270 noise units 250 " 100 " 620 " 75 noise units 275 " 115 " 375 " * Location C — For party-line service using 8A ringers, during heavy power loads. A comparison of Tables I and III shows that the noise from the non- triple harmonics has been very materially reduced by the balancing of loads made possible by the more favorable feeder arrangement of Fig. TABLE IV Comparison of Effectiveness of Various Remedial Measures (Fig. 4) Approximate Noise on Party-Line Stations (Heavy Power Loads) Type of Remedial Measure Location A or B Location C 1. Before applying remedial meas- ures 480 noise units 735 noise units 2. Using special telephone station sets 25-30 " " 40-50 " 3. Avoiding exposure in section a-5 by cooperative planning of routes. 190 " " 460 " 4. Interconnecting 300 kva wye- delta bank with system neutral 330 " " 535 " " (26 kv. of unbal- anced load) 5. Cable sheath shielding — ground- ing at jet. pole and to 1 ohm ground at X 325 " " 420 " 6. Combinations of measure 3, 4, and 5 85 " " 245 " 98 BELL SYSTEM TECHNICAL JOURNAL 4, although that from the triple harmonics has been inappreciably changed. The net efifect has been a reduction of nearly 75 per cent in the noise on the party line stations served by the telephone cable. The reductions afforded by various remedial measures are shown in Table IV. It is evident from Table IV that, by the application of various of the measures of coordination, the need for an extensive rearrangement of either plant is avoided. Illustrative Example 2 The purpose of this example is to show the extent to which remedial measures of the type generally applicable in urban areas (see Example 1), may be applied in a less thickly settled area where exposures to 2.3/4 kv. multi-grounded neutral arrangements are encountered under average conditions of power system wave shape. In detail the example covers: a. The extent to which such measures as cooperative planning of routes and use of wye-delta load banks may be in- effective. TABLE V Noise at Various Locations (Fig. 5) and for Various Types OF Telephone Service Contribut ion From: Loca- Type of Telephone Service Total Noise tion Remarks Cable Open Wire Exposures Exposures A L Common-Battery Party-line stations 225-345 220-270 45-215 Open-wire noise de- (Class 1-a Table D) pendent on effec- tiveness of tele- 2. Magneto party-lines 85-225 75 app 40-215 phone transposi- (Class 1-c Table D) tions. 3. Individual Line 40-210 25-35* About Lower values of (Class \-d Table D) 10-210 noise on circuits controlled by ef- B 1. 170-1200 10-100 170-1190 fects of station 2. 75-1175 20-35 70-1175 sets — higher val- 3. 60-1175 About 20* 55-1175 ues by effective- ness of telephone C I. 400-975 285-325 275-925 transpositions. 2. 150-870 110-125 110-860 3. 100-860 60* 75-860 *Noise in cable sec- tion due to office and cable unbal- ances. IND UCTI VE COORDINA TION 99 b. The importance, particularly under joint-use conditions, of noise directly induced into the metallic circuit of open- wire telephone pairs and the importance, therefore, of suitable telephone circuit transpositions. Figure 5 shows exposure conditions such as may be encountered in a small community serving a nearby rural area and Table V shows the noise conditions at several locations during heavy power loads. TO LOADS 75KVA- PHASE A 90 KVA- PHASE 60 KVA- PHASE 45 KVA -3 PHASE A PHASE WIRE — LEGEND — 3- PHASE PORTION OF FEEDER 2-PHASE PORTION OF FEEDER I -PHASE PORTION OF FEEDER UNDERGROUND TELEPHONE CABLE AERIAL TELEPHONE CABLE •\Ar« "DROP"WIRE TO SUBSCRIBER'S STATION — ^^ PROTECTED TERMINAL FEEDING OPEN-WIRE TELEPHONE PLANT SERVICE TRANSFORMER— KVA AS INDICATED ALL SECTIONS NOT SPECIFICALLY INDI- CATED ARE AT JOINT-USE SEPARATIONS WITH POLE-HEAD CONFtGURATIONS AS SHOWN IN TYPICAL LAYOUTS APPROXIMATE SCALE IN FEET Fig. 5 — Example of exposure conditions between 2300/4000-volt distribution feeder and exchange telephone plant in suburban and rural area. 100 BELL SYSTEM TECHNICAL JOURNAL The extent to which various measures of coordination could be applied to reduce the noise induction or to restrict the extent of special arrangements is shown in Table VI. TABLE VI Comparison of Effectiveness of Various Remedial Measures Approximate Noise at: Type of Remedial Measure Location A Location B Location C \* 2 3 1 2 3 1 2 3 1. Before applying 225- 85- 40- 170- 75- 60- 400- 150- 100- measures 345 225 210 1200 1175 1175 975 870 860 2. Using special tel. sets 40- 40- Neg. 60- 60- Neg. 100- 100- Neg. 210 210 Change 1175 1175 Change 860 860 Change 3. Avoiding exposure 130- 65- Neg. Neg. Change 350- 115- Neg. section B-C by 250 220 Change 950 860 Change cooperating plan- ning 4. Interconnecting neu- 180- Neg. Change 150- Neg. Change 370- Neg. Change tral of 150 kva 310 1175 950 wye-delta bank 5. Average degree of 250 80 50 200 175 175 340 175 130 coordinated tel. transpositions 6. Tel. transpositions 210 70 50 180 175 175 320 165 130 -j- cable sheath shielding f 7. Combination of 4, 5 185 65 50 160 155 155 310 160 125 and 6 * Type of station apparatus shown on Table V. t Cable was assumed to be grounded at junction pole at end of Section F-G to 2.5 ohm ground; at other junction poles to grounds exceeding 10 ohms. It is evident from this table that, for the conditions assumed, the use of reasonably coordinated telephone circuit transpositions will be necessary to care for the stations served by open-wire. Ordinarily the use of such transpositions in combination with such other measures as are reasonably effective would serve to take care of the stations served by telephone cable and would limit the extent to which special telephone station apparatus might be needed for the stations served by the longer open-wire extensions. Series for the Wave Function of a Radiating Dipole at the Earth's Surface By S. O. RICE In this paper three series expansions are derived for the wave function of a vertical dipole placed at the surface of a plane earth. Two convergent series and one asymptotic series are obtained. A remainder term for the latter series is given which enables one to set an upper limit to the amount of error obtained by stopping at any particular stage in the series. Introduction THE wave function above the earth of a vertical dipole placed at the surface of a plane earth is ^ ni(r, Z) = [ki- + k2-) I TO,., , A , , , /T^r^^T^ ' ^^^ Jo ^2-V^^ - ki^ + ^i2V^2 _ ^^2 where r and s are the horizontal and vertical distances from the dipole. ki and k2 are constants depending upon the electrical properties of the air and ground, respectively.^ We shall be concerned with the value of this function at the surface of the earth. Setting 2 = 0 gives us an integral for Tli{r, 0) which is the function of r to be investigated here. Although the electric and magnetic intensities are the properties of an electromagnetic field which have the greatest physical significance, writers on this subject often deal with the wave function because of its simpler form and because in many cases of practical interest it is nearly proportional to the electric intensity. However, the electro- magnetic field may be obtained from the wave function by differ- entiation. If the real parts of iJe~*"* and £e"'"' represent the electric and magnetic intensities the field above the earth produced by the dipole is dUi(r, z) Hr = Hz = 0, H^ = — dr ic' dm^jr, z) ic^^l d / dU,(r,z) drdz ' IP ' 0} r dr\ dr 1 A. Sommerfeld, Ann. der Physik, vol. 28, pp. 665-736, No. 4 (1909). 2 The symbols used here are defined in a list at the end of the paper. 101 102 BELL SYSTEM TECHNICAL JOURNAL From these expressions it will be observed that if we obtain ex- pressions for li\{r, 0) we shall be able to compute the field at the earth's surface except for the radial component Er, which is small compared to Ez. Statement of Results The asymptotic expression for Tli{r, 0) is ni(r, 0) = - 1 (1 - r'~)r g/t,r ^ n\Pn{k2/s) „=i (irsr)'^ where Riy and R20 satisfy the inequalities \Rin\ < {N + l)\e^^^'-ylcscd lr(k, - s) sin 6^+' Ri + i?i < 'Ro (9) MiK^r rki — rs 6 = 7r/2 — arg (^1 — s) being an angle slightly greater than t/2. The convergent series for IIi(r, 0) are ^ Mr, 0) = 1 (1 - T')r '( g'^'^E {- isrryPHy^ikr/s) n=0 \*T sr Pl!iT2''(k2 and ni(r, 0) /5)j (14) (1 - r')r[} (ikir) » (ikir)'' -T^E F(l, - n/2; 1/2 ; ^V/fer) (19) The quantities r and 5 are defined by r = ki/ki and I/5- — l/ki^ + l/^2^ and the numbers on the right are the equation numbers in the text. W. H. Wise ■* has obtained series which are equivalent to those ap- pearing in (9) and (14). Procedure The results given here depend upon a transformation of the integral obtained by setting z = 0 in equation (1). This integral can be expressed in the following way as has been shown by B. van der Pol : ^ ni(r, 0) ^2/^ pisrw diw"" - \)-'i\ (2) 2 The Legendre functions are discussed by E. W. Hobson, "Th. of Spherical and Ellipsoidal Harmonics." Hypergeometric functions are discussed in Chap. XIV, "Modern Analysis," by Whittaker and Watson. " W. H. Wise, Proc. I.R.E., vol. 19, pp. 1684-1689, September 1931. ^ Jahrbuch der drahtlosen Telegraphie Zeilschr. f. Hochfrequenz Tech?!., 37 (1931), p. 152. SERIES FOR WAVE FUNCTION OF RADIATING DIPOLE 103 which becomes, after integration by parts, = -r^{ — e' ^\'w^ — 1 A-2/s + is Mils gisrw^^ -. (3) The path of integration is the straight Hne in the complex w plane joining the points ^1/5 and k2/s. Arg (w — 1) and arg (w + 1) are taken to be zero at the point this contour crosses the real axis. The Argand diagram for a typical case is shown in Fig. 1. From the definitions of ki, k^, and 5 it follows that \s\ < \ki\ < |^2|, and 0 = arg ^1 < arg 5 < arg ^2 < 7r/4. W^-l-l IS F - ki/5 IS A = ka/s IS B Fig. 1 — Paths of integration in the w plane. Asymptotic Expansion To obtain an asymptotic expansion for ni(r, 0) we deform the linear path joining A and B into the path ACDB as is shown in Fig. 1. The lines AC and BD are both inclined to the real axis at the angle arg (is*) where 5* is the conjugate of s. This is the direction in which the exponential term e"''"" decreases most rapidly since along it the variable part of the exponent is real and negative.*"' The section CD may be displaced to infinity where its contribution to the value of the integral becomes zero because of this exponential decrease. ^ To show this for the line A C we set w = ^1/5 + is*u. As w goes from A to C u is real and increases from zero. The exponent then becomes isrw = ikir — j^prM since j.?* = \s\^. 104 BELL SYSTEM TECHNICAL JOURNAL The integral ni(r, 0) is then composed of two components consisting of the integrals along AC and DB, respectively, and we may write ni(r, 0) = - (Y^^^ [^(^0 - ^(-^2)], (4) where •00 is* lik) = r '* e'^^-'diw'' - \)-^i\ (5) Jkis We integrate (5) by parts N times and find I{k) N ( \n rln loois* fxis* pisrw flN+l The derivatives may be expressed in terms of Legendre polynomials by means of the relation (_)n^(^2 _ l)-l/2 = „!(^2 _ l)-»/2-l/2p / "^ \ . When the limits in the integrated portion are inserted and the definition of 5 used we see that m)^''-^g[^)'n^.P.(k.ls)+Rjf, (6) where HN+ 1)! Utsr) .„.^^^ + 1)! C^''* \ w '\ e'"'^ , ,., An inequality for i^iAr may be obtained by using ^ |P,v+i(/)| ^ |/ + V^^^^K+^ which holds for all values of / in the / plane cut from — 1 to +1, if arg ^t^ — 1 = 0 when t is real and greater than + 1. For then the absolute value of the Legendre polynomial in the integrand is seen to be less than | (w + l)/(w — 1) | (^+i>/2 when R{w) > 0, and Rm may be compared with an integral having [e"''"'| and powers of the factors I w + 1 1 and \w — 1 j in the integrand. On the path yl C we ^ E. W. Hobson, loc. cit., p. 60. SERIES FOR WAVE FUNCTION OF RADIATING DIPOLE 105 have \w — 1| — \(ki/s — 1) sin d\ where d = arg is* - arg ( Y - 1 j = ^ - arg (ki — s) > ^ • Similarly we have [w + 1| — \kils + 1|- These inequalities enable us to deal with the integral of |e"''"'| which may be integrated to show that (N + i)!givVcsc d i?i < lr{ki - s) sin 0]^+i (8) By interchanging k] and ^2 in (6) and (7) we obtain expressions for 7(^2) and RiN- An inequality for |i?2iv| is obtained from (8) by setting 9 — -kII and interchanging kx and ki. By combining these expressions in accordance with equation (4) we obtain an asymptotic expansion for Ilifr, 0). In general, I{ki) is negligible in comparison with /(^i) because ^2 has a positive imaginary part which causes e'^s"" to decrease rapidly. Since lijki) — R20, R20 being the remainder after zero terms, w^e may obtain an inequality for 7(^2) by setting N = 0, 6 = t/2, and inter- changing ki and ki in (8). Then from (4) we have the result ni(r, 0) = 1 n=l (iTsr)'^ ^ T^ia (1 - T'-)r where Rm satisfies the inequality (8) and |i?2o| < \ e'''^'' / (rki — rs) Series for ni(r, 0) in Ascending Powers of r , (9) Put ^2 Ji 4 w^ (10) and define K{ki) as being obtained from (10) by interchanging ki and ki. By referring to equation (3) we see that 7 may be written in the form 1 ni(r, 0) = We write K{kx) = e'^i^ 1 - 1 - (1 - r')r ikisr ikisr IKiki) - r'Kikin (11) Ji 4w' - 1 J (12) the infinite series being uniformly convergent. 106 BELL SYSTEM TECHNICAL JOURNAL From Hobson's contour integral definition ^ of PiJ^iO it can be shown that if R(m) < 1/2 i^i;2W - Vx r(l/2 - m)~" J, V.^^^^^ ' where arg (w — 1) = ip, arg (w — /) = — tt + (^, where

I- 'Jkils Jkii's Jk^ls ^ ' r{w- — \y'- (1+) gixrw^d^ with the understanding that arg w — 1 and arg w -\- \ have their principal values at the beginning of each integration. Upon referring to (2) we see that the middle integral is — ni(r, 0) and hence TIi(r, 0) = - iLih) - Lihn where L{kO 2r{\ - r') •(1+) e'^'''''wdw ^ (isr)" r^^+'> w"+^dw {w- - ly'-' (15) (16) and L{k2) is obtained from L(ki) by interchanging ki and ki. Let w- — 1 = T-(l — t), or sw — kl^J]. — ts~jk-f, then .(1+) ^n^idw h / kiY f^'+'[(l - (5-///^2-)]"'- tJkils (7t'2 - 1)3/2 2^1 \ 5 Jo (1 - ty^'^ dt = 2^(-^\ F{\, -n/2;\/2;syk,'), (17) where it is understood that at the initial point of the contour 108 BELL SYSTEM TECHNICAL JOURNAL arg (1 — /) = 0, arg (1 — {s^lkr)t) = 0. This may be verified by expanding the numerator of the integrand and using I. "+' /. ■, J. ,. ON rC"! + i)r(i' + 1) where w is a positive integer or zero, with v = — 3/2. Expression (16) now becomes Uh) = 2 1? E ^^" F{\, - n/2 ; 1/2 ; s^h') (18) and the series converges for all finite values of r since the series inte- grated termwise in Equation (16) is uniformly convergent. We obtain the series for Tli{r, 0) given in statement of results as equation (19) by putting (18) and the corresponding expression for L{k2) in equation (15). Notation The following symbols are used. C.G.S. electromagnetic units are used throughout the paper. c = velocity of light, 3 X 10'° cm. /sec. F{a, h;c',x) = The hypergeometric function «& a(a + 1)6(6+1) ^ \\c ^ 2!c(c + 1) ^ -A)(^0 = Bessel function of the first kind, zero order. k\ = co/c. ki = Veco^ + i^Tvaca. The real and imaginary parts are positive. Pn{t), Pli\~2'{t) = Legendre's polynomial, and associated Legendre's function of the first kind. RiN, R20 = Remainder terms in asymptotic series. r = horizontal distance of representative point from dipole. 5 = kik2Hki' + ki" or 1/52 = l/kr^ + l/y^a^. The real and imaginary parts of 5 are positive. 5* = The complex conjugate of s. t = time in the introduction, otherwise a complex variable. w = complex variable. SERIES FOR WAVE FUNCTION OF RADIATING DIPOLE 109 s = height of representative point above ground. € = dielectric constant of the ground in e.m.u. The dielectric constant of air in e.m.u. is l/c^. If the dielectric constant in e.s.u. is e', then e = e'/c^. The dielectric constant of air in e.s.u. is 1. Ui{r, z) = Wave function for s ^ 0 for a vertical unit dipole centered at the interface between air and ground. The wave function for a unit dipole wholly in air is obtained by multiplying the wave function given here by 2/(1 + r^). By a unit dipole is meant the system obtained by letting the length / of a conductor approach zero while the current in the conductor ap- proaches infinity in such a way that // = unity, where the current equals the real part of Ie~'"' and does not vary with position along the conductor. ni(r, 0) = Value of wave function at earth's surface. 0 and : GiT) (3) (4) r = vz(r)G(r). „, s tcov 1.85- Z(T) = 2 + -— log, ZTT aa G(T) = , . p . 1.12- g 1 + - log, —-—- T or a = {iwvp-^ + T'^y-. CO = 2irf. f = frequency in cycles per second. X — distance from origin, in meters. a — conductor radius, in meters. 2 = internal impedance in ohms per meter. g = leakage conductance in ohms per meter. p — earth resistivity in meter- ohms. V = 47r-10~'^ henries per meter. 112 BELL SYSTEM TECHNICAL JOURNAL The transcendental equation defining the propagation constant F may be solved by successive approximations; a convenient first approximation is T = Ti = 4gZ{G), Z(0) being the earth-return self- impedance of the conductor. Equations (3) and (4) are of the same form as the solution for conductors of small leakance, except that the propagation constant for the latter is taken equal to Fi above. The effect of the earth potential appears in a first approximation as the second term in the expression for G{T). For earth resistivities within the usual range and for electric railway tracks or underground cables the two terms in the expression for G{V) are frequently of the same order of magnitude. Appreciable errors may therefore be obtained by neglecting the second term, and in correlating the results of measurements this must be kept in mind. The second terms in the expansions are given below, but may be neglected in the range of most practical applications. /2i(x) = /2i(- x) = - /(O)^^^ 1(1 + Vx)e^^Ei{Vx) 47r - (1 - Fx)e-r^[£i(- Fx) + ^V]}, (5) F2i(x) = - F2i(- x) = I{{i)^ [Txe^-Ei{Vx) - Vxe-^^'lEii- Vx) -f iV] - 2}, (6) I u where Ei{u) — | — du is the exponential integral. For sufficiently large values of Fx the bracket terms of expressions (5) and (6) vanish as — 8/(Fx)=' and 4/(Fx)2, respectively, so that in this case the second terms in the expansions predominate. Abstracts of Technical Articles from Bell System Sources Electricity in Gases} Karl K. D arrow. The material in this paper was presented as the Joseph W. Richards Memorial Lecture delivered before the Electrochemical Society at Cincinnati, April 23, 1936. This lecture presents in a vividly descriptive manner some of the material published in past issues of the Bell System Technical Journal. Electron Diffraction Experiments Upon Crystals of Galena} L. H. Germer. Cleaved surfaces of galena crystals yield electron diffraction patterns made up of Kikuchi lines, and spots which are drawn out into streaks by refraction. After etching, the spot pattern predominates and the individual spots are sharp. The lines are then rather diffuse and ill-defined. Rocking curves upon various Bragg reflections from the surface plane prove that the imperfection of a certain crystal does not exceed about 15 minutes, and that the projections through which the electrons pass are relatively thick. Estimates of imperfection and thickness made from rocking curves are in approximate agreement with those obtained from widths of Kikuchi lines. A galena crystal which has been filed or ground parallel to a cube face exhibits two dilTerent sorts of surfaces. There are smooth "mirror" surfaces from which large blocks of the crystal have been mechanically torn, and there are very deeply scratched portions of the surface. The "mirror" surfaces give diffraction patterns which are qualitatively similar to patterns from cleaved surfaces, although there are notable differences. From mirror surfaces produced by filing, Kikuchi lines are very diffuse or are entirely missing, and diffraction spots form an extended array. The diffuseness of the lines and the extent of the array of spots correspond to great crystal imperfection, or to exceedingly thin projections. Reasons are advanced for believing in imperfection rather than extreme thinness. The deeply scratched portions of the surface of a galena crystal give diffraction patterns which are entirely unlike patterns from cleaved surfaces. Before etching, Debye-Scherrer rings are produced. After a light or moderate etch a complex pattern appears, the nature of which is related to the angle between primary beam and direction of filing. 1 Transactions Electrochemical Society, Vol. LXIX, 1936. ^Phys. Rev., October 1, 1936. 113 114 BELL SYSTEM TECHNICAL JOURNAL The pattern is that of a mass of minute crystallites which have been rotated about an axis in the surface normal to the direction of filing, and in the sense determined by imaginary rollers which would be turned by slipping on the (0 1 0) plane. The magnitude of the rotation varies for different crystallites over a range from 5 to about 35 degrees. By alternate etching and examination by electron diffraction it is found that this layer of rotated crystallites extends beneath the surface to a depth of 0.003 mm. Rotation of crystallites accompanying slip along slip planes is the mechanism reported to account for strain hardening in metals. This same rotation is observed in the present experiments on galena. It seems altogether possible that the simple technique of these experi- ments can be applied directly to study the disturbance in surface layers of metal crystals produced by abrasion. It may thus be a useful way of studying strain hardening in metals. The Photoelectric Cell and Its Method of Operation} M. F. Jamieson, T. E. Shea, and P. H. Pierce. This paper gives a simple description of the laws governing the release of electrons from photoelectric surfaces, their collection at anodes, and the creation of ions in photo- electric cell gases by the "ionization" process, and discusses questions of spectral selectivity of various photoelectric surfaces, the influence of spectral characteristics of illumination, and the dynamic characteristics of vacuum and gas-filled cells. Modified Sommerf eld's Integral and Its Applications} S. A. Schel- KUNOFF. The purpose of this paper is to obtain a certain integral expressing the fundamental wave function and with the aid of this integral to calculate the radiation resistances of small doublets and small loops placed inside an infinite hollow cylinder. Some applica- tions of this integral to calculation of radiation from parallel wires in free space are also discussed. Diffusio?i of Water Through Insulating Materials} R. L. Taylor, D. B. Herrmann, and A. R. Kemp. Data are presented on the rate of water diffusion through various organic materials. A diffusion con- stant based on Kick's linear diffusion law is calculated for each material. Several equations are derived from Pick's law to show how valuable information can be obtained in connection with practical problems. 3 Jour. S. M. P. E., October, 1936. ^Proc. L R. E., October, 1936. ^ Indus, and Engg. Chem., November, 1936. ABSTRACTS OF TECHNICAL ARTICLES 115 The effect of variations in methods and conditions of test is studied. The rate of diffusion through a water-sorbing material such as rubber does not obey Pick's law when under diffusion conditions favoring high water sorption. V^arious concepts involving sorption and diffusion processes are dis- cussed as bearing upon the mechanism of the diffusion of water through organic substances. k Contributors to this Issue Charles R. Burrows, B.S. in Electrical Engineering, University of Michigan, 1924; A.M., Columbia University, 1927; E.E., Univer- sity of Michigan, 1935. Research Assistant, University of Michigan, 1922-23. Western Electric Company, Engineering Department, 1924- 25; Bell Telephone Laboratories, Research Department, 1925-. Mr. Burrows has been associated continuously with radio research and is now in charge of a group investigating the propagation of ultra-short waves. R. F. Davis, B.E.E., Cornell University, 1921. American Tele- phone and Telegraph Company, Department of Operation and En- gineering, 192 1-. Mr. Davis' work has been largely concerned with the electrical protection of communications circuits and with the electrical coordination of such circuits with power transmission and distribution circuits. S. O. Rice, B.S. in Electrical Engineering, Oregon State College, 1929; California Institute of Technology, 1929-30, 1934-35; Bell Telephone Laboratories, 1930-. Mr. Rice has been concerned with various theoretical investigations relating to telephone transmission theory. A. L. Samuel, A.B., College of Emporia (Kansas), 1923; S.B. and S.M. in Electrical Engineering, Massachusetts Institute of Tech- nology, 1926. Instructor in Electrical Engineering, Massachusetts Institute of Technology, 1926-28. Bell Telephone Laboratories, 1928-. Mr. Samuel has been engaged in research and development work on vacuum tubes. Nelson E. Sowers, B.S. in Engineering Physics, 1924, University of Illinois; M.A., Columbia University, 1927; Engineer-Physicist (Professional), University of Illinois, 1936. Engineering Department, Western Electric Company, 1924-25. Bell Telephone Laboratories, Inc., 1925- Since 1931, Mr. Sowers has been engaged in studies per- taining to amplifiers for ultra-high radio frequencies. M. E. Strieby, A.B., Colorado College, 1914; B.S., Harvard, 1916; B.S. in E.E., Massachusetts Institute of Technology, 1916; New York 116 CONTRIBUTORS TO THIS ISSUE 117 Telephone Company, Engineering Department, 1916-17; Captain, Signal Corps, U. S. Army, A. E. F., 1917-19. American Telephone and Telegraph Company, Department of Development and Research, 1919-29; Bell Telephone Laboratories, 1929-. Mr. Strieby has been associated with various phases of transmission work, more particularly with the development of long toll circuits. At the present time, in his capacity as Carrier Transmission Research Engineer, he directs studies of new and improved methods of carrier frequency transmission over existing or new facilities. Erling D. Sunde, E. E., Technische Hochschule Darmstadt, 1926. American Telephone and Telegraph Company, Department of De- velopment and Research, 1927-34; Bell Telephone Laboratories, 1934-. Mr. Sunde's work has been mainly concerned with inductive effects of electric railways. W. Howard Wise, B.S., Montana State College, 1921; M.A., Uni- versity of Oregon, 1923; Ph.D., California Institute of Technology, 1926. American Telephone and Telegraph Company, Department of Development and Research, 1926-34; Bell Telephone Laboratories, 1934-. Dr. Wise has been engaged in various theoretical investiga- tions relating to transmission theory and telegraphy. VOLUME XVI APRIL, 1937 ^aJMBER2 THE BELL SYSTEM TECHNICAL JOURNAL DEVCEED TO THE SCIENTIFIC AND ENGINEERING ASPECTS OF ELECTRICAL COMMUNICATION Recent Trends in Toll Transmission in the United States — Edwin H. Colpitis 119 Crosstalk Between Coaxial Transmission Lines — S. A. Schelkunoff and T. M, Odarenko 144 Sound Recording on Magnetic Tape — C. N. Hickman . . . 165 Constant Resistance Networks with Applications to Filter Groups — E, L. Norton 178 A Laboratory Evaluation of Wood Preservatives — R, E, Waterman, John Leutritz and Caleb M, Hill 194 Study of Magnetic Losses at Low Flux Densities in Permalloy Sheet— PF. B. Ellwood and V. E, Legg 212 Moisture in Textiles — Albert C. Walker 228 Abstracts of Technical Papers 247 Contributors to this Issue 249 AMERICAN TELEPHONE AND TELEGRAPH COMPANY NEW YORK 50c per Copy $1.50 per Year THE BELL SYSTEM TECHNICAL JOURNAL Published quarterly by the American Telephone and Telegraph Company 195 Broadway, New York, N. Y. iiimiiiiiiiiiiiiiiiiiiiiiiiiiiininii Bancroft Gherardi A. F. Dixon D. Levinger R. W. King, Editor EDITORIAL BOARD H. P. Charlesworth O. E. Buckley M. J. Kelly W. Wilson F. B. Jewett O. B. Black well H. S. Osborne J. O. Perrine, Associate Editor luiiiiiiiniiiiiiiiiiiiiiiniiiiiiiiiii SUBSCRIPTIONS Subscriptions are accepted at $1.50 per year. Single copies are fifty cents each. The foreign postage is 35 cents per year or 9 cents per copy. iiiiiiiiiniiiiniiiiiiiiiiniiiiiiiiiii Copyright, 1937 American Telephone and Telegraph Company PRINTED IN U. S, A. The Bell System Technical Journal Vol. XVI April, 1937 No. 2 Recent Trends in Toll Transmission in the United States * By EDWIN H. COLPITTS YOUR country is advancing industrially and commercially with tremendous strides. Adequate telephone communication is of such great importance under these conditions that I felt a general statement as to methods in process of being applied to the plant of the Bell System would be interesting and possibly helpful. I am fully aware that, in some or even many respects, your problems will differ from ours. Much of what I have presented may, therefore, serve only to suggest research and development to meet your own requirements. Perhaps also, in some small way, this statement of progress in communication may stimulate research and development in other industries and services. In the year 1885, only nine years after the telephone was invented, a Telephone Company was chartered in the United States for the following purpose: "to connect one or more points in each and every city, town, or place in the State of New York with one or more points in each and every other city, town or place in said State and in each and every other of the United States and in Canada and Mexico; and each and every of said cities, towns, and places is to be connected with each and every other city, town, and place in said states and countries, and also by cable and other appropriate means with the rest of the known world." This was an ambitious program, and thirty years passed before the results of research and development could be embodied in apparatus and equipment to make it possible to talk between cities on the Atlantic and Pacific coasts of the United States, and about forty years passed before the establishment of telephone service between America and Europe. Telephone service was later extended to other parts of the world including your country, and it is now possible for a telephone subscriber in the United States to converse with a person at any one of thirty-four odd million subscriber stations in a large number of countries of the world. Further, it is possible to talk with persons on suitably equipped ships at sea. Expanding still further beyond the goal set in 1885, and departing from the idea of two-way conversation, * One of three Iwadare Foundation lectures delivered during the past month in Japan by Dr. Colpitts. 119 120 BELL SYSTEM TECHNICAL JOURNAL this same company provides a portion of the faciHties which make it possible for a person speaking at one place almost anywhere in the civilized world to have his voice heard at almost any other. I refer to broadcasting. Figure 1 shows a wire map of a few of the principal toll lines in the United States. This toll plant affords facilities that, in connection with the local plant, enable any telephone subscriber at any point to communicate promptly with a subscriber at any other point in the United States, Canada, or Mexico. With the growth of radio broadcasting, a service with which you are all familiar, it became necessary to provide circuits to interconnect radio broadcasting stations. Figure 2 shows a wire map of such interconnecting circuits commonly spoken of as "program circuits." Figure 3 shows schematically the radio-telephone circuits that connect the United States to foreign countries. Another extension of the service rendered by the Bell System is indicated by Fig. 4, which shows a wire map of circuits devoted to the telephotograph service. It is not my purpose to take your time to discuss these past develop- ments, since they have already been described quite fully in technical literature, which I know is available to you. I propose rather to discuss some of the more recent trends in toll circuit development in the United States, but the subject is so large that I can touch only upon the more salient factors, indicating to you the direction in which the art is moving. This new art, or perhaps more accurately this extension of an older art, utilizes the results of continuing researches on vacuum tubes and their uses as amplifiers, modulators, and oscillators, on filters as a means of splitting up broad bands of frequencies into the relatively narrow bands required for telephony or the still narrower bands required for telegraphy, and on methods of electrically isolating a particular circuit so as to avoid crosstalk and noise. These are not all the factors requiring research, but are merely some of the more important ones. In this connection, it should be emphasized that these new systems or methods are still under development, and that their development for commercial application will require continued effort over a con- siderable period. We have come to group these new systems or methods under the term "high-frequency broad-band wire trans- mission." Instead of confining ourselves to a frequency range ex- tending to about 30,000 cycles, as used for our present carrier systems, we are setting for our objective the transmission and utilization of bands of frequencies a million or more cycles wide in the case of TOLL TRANSMISSION IN THE UNITED STATES 121 / i Y^ i "rr- / ^ 122 BELL SYSTEM TECHNICAL JOURNAL TOLL TRANSMISSION IN THE UNITED STATES 123 124 BELL SYSTEM TECHNICAL JOURNAL TOLL TRANSMISSION IN THE UNITED STATES 125 certain line structures. For other structures, the frequency range is narrower, but for all these systems the frequency range is transmitted as a single band, and split into communication channels for telephone or telegraph only at the terminals. If the transmission of television signals should become necessary, a very broad band — one or more million cycles — would, of course, be required. Although I have referred to television, our primary interest in broad-band wire trans- mission is for telephone transmission purposes, where the wide trans- mission band can be used to give a large number of talking channels. You will recall that the idea of deriving more than one communica- tion channel from a single pair of conductors, by what we now call carrier methods, is old — in fact, as old as the telephone itself. Until quite recently, however, physical devices and methods have not been available to make the carrier method utilizable in practice. Beginning about fifteen years ago, the Bell System began to install carrier systems, and since that time this method has had continued growth on open-wire lines, with the result that a substantial amount of toll traffic is now carried over carrier systems on open-wire lines. A relatively simple form of carrier equipment provides one two-way telephone circuit in addition to the usual voice frequency circuit, while more elaborate and refined equipment adds three two-way telephone circuits. In addition to the economic urge to obtain the largest possible number of telephone channels over a given pair of wires, there is an additional factor that has influenced the development of broad-band systems, and that is, the speed of transmission. Even in the lowest- speed telephone circuits, the speed of transmission of voice waves, as judged by ordinary standards, is high, being from ten to twenty thousand miles per second (32,000 km. per sec.) in the loaded cable circuits that are now used for many of the long toll lines. For ordinary distances, moreover, the speed of transmission is not of any particular moment, but when the voice must be transmitted over distances of thousands of miles, it becomes important. Echo effects become exaggerated, and in a long connection, the actual time for speech to reach from the first subscriber to the second subscriber, added to the time required for the second subscriber to answer the first subscriber, may become an annoying factor. The broad-band transmission method furnishes circuits, however, in which the speed of transmission is raised from about 20,000 miles per second, as on loaded cable circuits, to a speed approaching that of light. In developing a new toll system, there are many other factors, of course, that must be considered. In our case, just as in yours, there 126 BELL SYSTEM TECHNICAL JOURNAL is first, an existiiiii toll telepluMio jilant, which imist be utilized to the maxitmnn ad\;uita.s;e. Also, distances between toll offices or toll centers \ar\-, and particularh- the number of circuits required between given [oW centers varies ovcv a wide range. It follows, therefore, that there is no one type of construction or method which can be economically utilized in all situations. Figure 5. for example, showing a poW line carrying open-wire circuits ami circuits in cable, illustrates some oi our present methods. The high-freiiuency broad-band tiansmission dexelopment is being proposed foi three uses: (H for applicatiiMi on telephone toll cables alreadx' in cxistcme. or on future toll cables of \er>- similar t>'pe of Fig. 5 — A t\ pii-.il polo lino carr\ ins; both opon wire and cablo. consnuciion: {2^ tor an extension to higher frequencies on open-wire telephone circuits, sit as to secure more telephone channels on a given pair; (^v^'i for applicatii>n to new t\-pes of conductors capable of transmitting a \-er>' wide frequency band, such as the "coaxial" ciMiductor. nmv being tried experimentally. 1 need hardly point out to you that as the frequency of transmission is raised, the attenuation or line loss is greatly increased. This is due more particulaiK- to two factors: an increase in series resistance due to skin ettect. and an increase in shunt conductance due to increased dielectric losses. As the frequenc>- increases, the currents transmitted tend moie and nune to a\oid tlie inner paits of the conductor and lo TOLL TRANSMLSSION IN TIIK UNITED STATES 127 concentrate on ihe surface, so increasing the effective series resistance. Dielectric losses in the insulalion between the conduclors also increase with the frequency, and so increase the effective shunt conductance. Figure 6 shows graphically the increase in attenuation with frequency, 100 200 BOO 1000 300 400 500 600 700 FREQUENCY IN KILOCYCLES PER SECOND Vi^. 6- At I ciuiat ion-frequency characteristics of various types of tclcijlione circuits. and also shows the relative attenuations of various types of con- struction. Until ihe vaciuim tube ami)lifier became available, the only practical method of overcoming high attenuation in a given type oi line con- 128 BELL SYSTEM TECHNICAL JOURNAL struction was to provide larger conductors. With the development of the vacuum tube, high amplification became available as an alternative method. Since increasing the size of the conductor in order to decrease attentuation involves large expense, we are naturally led to consider the use of as much amplification as possible. Before referring further to the utilization of high amplification, I wish to point out that at the present time for distances greater than about 150 miles (240 km.) in cable, we utilize the so-called 4-wire method to obtain two-way telephone transmission ; that is, transmission in one direction is carried by one pair of wires, and transmission in the other direction is carried by a second pair of wires. What is in effect the same method is employed in our present carrier systems, transmission in one direction being superposed on one frequency, and transmission in the other direction being superposed on a different frequency. l-WAY REPEATER STATION A Mm X 2 NET- WORK NET- WORK X X X mw Fig. 7 — Block schematic of a four-wire circuit showing two two-wire circuits with one-way repeaters. Figure 7 shows diagrammatically a 4-wire telephone circuit in cable. You will note that one-way amplifiers are introduced in each pair of wires at points which in present practice are about fifty miles (80 km.) apart. The question naturally arises: Why not increase the distance between amplifiers and at the same time increase their amplification, and so reduce the cost? The answer is that two sources of noise disturbance have to be considered: first, induction from neighboring circuits; second, the noise of thermal agitation. The line circuit, depending in degree upon the type of construction, receives unwanted interference from the outside, such as induced currents from power lines, lightning, and crosstalk from adjacent circuits, and it is not possible, as a result, to allow the transmitted speech signals to be attenuated below a certain level with respect to such noise interference. As a consequence, the amount which we can allow a speech signal to be attenuated before it reaches an amplifier, TOLL TRANSMISSION IN THE UNITED STATES 129 depends on how completely the transmission system is free from external interference. Two methods are commonly employed to minimize external inter- ference: shielding, and a geometrical arrangement of the conductors of the circuit so as to balance out certain forms of interference. The open-wire line, which has no shielding, depends wholly on the symmetry of its conductors and the transpositions to balance out interference. Conductors surrounded by metal sheath, such as cable pairs, are less subject to interference than open-wire lines. The conductors of a pair are close together, are well transposed by twisting, and are shielded to a certain extent by the outside lead covering. As a result of this, the noise due to outside sources has a low level, and the telephone speech currents can be permitted to become attenuated to a relatively low value before reaching an amplifier where they are stepped up to their original value. It is evident, of course, that such cable pairs, being made up of small conductors close together and having paper dielectric, have correspondingly high attenuations. Fig. 8 — Diagrammatic representation of the coaxial structure. The ideal conductor would be one for which the attenuation over the whole operative frequency range was not too great, and at the same time one completely shielded from the influence of external electric or magnetic fields. The so-called coaxial conductor approximates to these requirements. This conductor transmits efficiently over a wide frequency band, and at the same time is well shielded from external influences, the degree of shielding being higher at the higher fre- quencies where greater amplification is needed to overcome the greater attenuation. The coaxial conductor upon which we are experimenting consists of an inner wire and outer tube separated by spacing insulators. It is desirable to separate the two conductors by a minimum amount of solid insulation to the end that the dielectric will be largely air, and the losses at high frequencies be at a minimum. Figure 8 shows diagrammatically a coaxial structure. At high frequencies the current travels chiefly on the outside of the inner conductor, and on the inside of the outer conductor. It will be obvious to you that there is a wide latitude of choice in the dimensions of coaxial structures- 130 BELL SYSTEM TECHNICAL JOURNAL Although we are experimenting with a structure capable of trans- mitting a band of one or two million cycles in width, a coaxial structure capable of transmitting a band twenty million cycles in width is apparently not wholly unfeasible. The question naturally arises whether, with interference from outside sources almost wholly or entirely eliminated, it is possible to allow speech currents to be attenuated to an unlimited degree before the introduction of amplification to bring them back to their original value. With all outside interference eliminated, however, noise arising within the conductor itself sets the limit. This interference is termed resistance noise or sometimes thermal-agitation noise because it is a function of the temperature of the conductor. It is apparently due to the continual moving around of the free electrons which exist in all conductors. Our Laboratories have investigated this phe- nomenon and determined its characteristics. This resistance noise varies in amount with the resistance of the conductor and with the temperature. It is uniformly distributed over the whole frequency range from lower voice frequencies up to the highest frequency which we have considered using. One ready means of observing this phe- nomenon is to provide an amplifier covering the voice range, with its input connected across the resistance, and to listen on the output of the amplifier with a telephone receiver. If the amplifier has an amplification of about 140 db, the noise heard in the telephone receiver is about as loud as would be heard in the receiver were it connected directly ^across the output from a telephone substation. To prevent this thermal or resistance noise from being noticeable in a telephone conversation, we must limit the amount of amplification used at any one point in a long system, even though it were perfectly shielded, to an amount considerably less than 140 db. These con- siderations have led us to conclude that for a long circuit with many amplifiers distributed along the route, the amount of amplification at any one point should not exceed about 70 db. The amount of amplification involved in present-day telephone circuits is illustrated by the 4-wire cable circuit, in which amplifiers are located in each pair at intervals of about 50 miles (80 kilometers) and each amplifier is set to give an amplification of about 25 db, or a power amplification of 300 times. For such a circuit between, say. New York and Chicago, a distance of about 900 miles (1450 km.), the total amplification is about 500 db, or a power amplification of 10^". It is obviously necessary that these amplifiers must be made very stable so that the cumulative variations in the many amplifiers may not make it impossible to obtain the required degree of overall stability TOLL TRANSMISSION IN THE UNITED STATES 131 of transmission. The total amplification is affected by the require- ment that the New York-Chicago circuit is expected to have a net attenuation of not over 9 db, and to be stable within about ± 2 db. These figures may seem large and the requirements difficult to meet, but with the systems under development, the magnitude of the high-amplification problem is even greater. In the carrier on cable development, the circuits will consist of non-loaded pairs, and it will be necessary to so space the amplifiers and adjust their amplification that the total amplification on, for example, a New York-Chicago circuit will be about 3000 db at the center of the frequency band, or a power ratio of 10^"". Obviously, the stability requirement has been made much more rigid. With a typical coaxial circuit, the overall amplification at a million cycles for a thousand-mile circuit (1600 km.) may well be 6500 db or a power ratio of 10^^''. Fig. 9 — Simplified schematic diagram of a feedback amplifier. Furthermore, with the relatively simple circuit shown in Fig. 7, the amplifiers are called upon to handle merely the currents corresponding to one telephone conversation, while in ,the broad-band system an amplifier is required to handle simultaneously a large number of carrier telephone channels. To avoid the generation of extraneous frequencies or intermodulation products which would cause inter- ference between the channels, an amplifier must be adopted which is more nearly perfect in this respect than any heretofore standard. This problem of amplifier stability and perfection was solved some little time ago by an invention of one of our engineers. This engineer devised a new amplifier circuit which has been termed the "stabilized feedback amplifier." Some older types of amplifiers took some of their output and fed it back to the input for the purpose of increasing the amplification. This new feedback circuit controls the phases of the currents in the amplifier and feedback circuits so that the amplifi- cation is decreased. As a result, we have available an amplifier which is remarkably stable and closely linear in its performance. Figure 9 132 BELL SYSTEM TECHNICAL JOURNAL shows schematically the circuit of such an amplifier, but the actual detailed design is not simple and involves great technical skill. Since the high amplifications just discussed are employed to offset the equally high attenuation of the line structures, careful consideration must be given to the stability or constancy of the attenuation caused by the line structure. The fact is that as the temperature changes, the attenuation of any line structure varies correspondingly. If the line structure is underground in cable, the temperature changes are slow in rate and the variations in line attenuation correspondingly slow, but if the structure is in aerial cable or consists of open wire, not only do we have variations in temperature with the season of the year, but large daily variations as well. With an aerial cable, for example, the change in loss of 19-gauge B & S non-loaded pairs through- out the year for a circuit 1,000 miles (1600 km.) in length amounts to approximately 500 db in the frequency band we propose to use. For our long cable circuits operated on voice frequencies, we have developed automatic regulating means, so that amplification is varied to com- pensate for changes in attenuation. With the much higher attenua- tions and equally higher amplifications involved in broad-band systems, more refined methods of compensating for temperature changes are under development. This is a very serious problem and sets one limit to the use of such systems. I spoke of the new type of amplifier, employing negative feedback, which became available at a most fortunate time. It is almost equally fortunate that, due to continued research and development, new and simpler forms of electric wave filters became available. Time does not permit me to go into details, but in these newer types of electric filters suitably cut quartz crystals are utilized. Develop- ments have also made it possible to use inductance coils with iron cores. As a result of these two changes the filter structure is simplified and its size reduced. Fundamental to the whole broad-band transmission development, there are many other elements which have required much research and development effort such, for example, as modulators and de- modulators, but I shall be able to discuss only the more striking problems underlying all broad-band systems as they pertain to certain specific applications. Cable Carrier Systems We plan as a first step to apply the cable carrier system to pairs in existing cables. These cables were designed and manufactured with the expectation that they would be required to transmit frequencies TOLL TRANSMISSION IN THE UNITED STATES 133 only up to a few thousand cycles, that is, these cables were not designed to meet crosstalk requirements at high frequencies. Crosstalk between pairs in a cable arises from a lack of geometrical symmetry between each pair and every other. As a result of very careful research, we have developed a method of connecting small mutual inductance coils, or condensers, or both, between all the pairs concerned, and in this way reducing crosstalk to a satisfactory degree. At present coils alone are being used. Figure 10 shows schematically the balancing method. I REPEAT-I I ERS INTERMEDIATE LINE SHOWING PATHS OF CROSSTALK BALANCING COILS -1 r 1 ' J u -J L^ REPEAT- ERS Fig. 10 — Diagrammatic representation of method of balancing out cross-talk. It is obvious that in this process of balancing out the crosstalk, the value given to the adjusting coil or condenser must be determined for each particular unit involved. When the balancing units have been installed and once adjusted, however, we feel that they will remain permanent. Present indications are that by adopting this procedure, we can employ frequency ranges up to 60,000 cycles upon our toll cables, and this will permit us to secure 12 one-way channels on each pair of conductors. With at least our present type of cables, we anticipate that it will be necessary to use separate cables in opposite directions to avoid the additional crosstalk that arises when adjacent pairs are used to transmit in opposite directions. Referring to our present cables, if the pairs which it is desired to utilize are loaded, it is necessary first to remove the loading coils. Repeaters will be spaced about 17 miles (27 km.) apart. Since the present repeater points on cables are about 50 miles (80 km.) apart, it will be necessary to add on the average two new repeater points between existing repeaters. The total amount of apparatus at these new repeater points, however, does not bulk very large, because a repeater handling 12 channels will be no larger than the older type voice repeaters 134 BELL SYSTEM TECHNICAL JOURNAL TOLL TRANSMISSION IN THE UNITED STATES 135 handling only one channel. The present plans call for these inter- mediate repeater stations to be substantially non-attended. The electrical units employed in a cable carrier system are shown sche- matically in Fig. 11. Some idea of the possibilities of this carrier cable system may be formed from the results of a trial installation made on a laboratory- scale. In one case, we had circuits as long as 7,500 miles (12,000 km.) set up, over which we carried on satisfactory conversations. The total attenuation over some of these circuits was such as to require power amplifications of 12,000 db, which corresponds to a power ratio of 10^^"° to 1. This amplification was applied at nearly 400 points. Broad-Band System for Open- Wire Lines In the Bell System, as you know, along many toll routes, there is still much open-wire construction, aggregating tens of thousands of miles. At the present time, many thousands of miles of open-wire lines are equipped with 3-channel two-way carrier systems. These systems employ frequencies up to about 30,000 cycles, and with the regular voice frequency circuit provide facilities for four simultaneous conversations over one pair of wires. This might appear to be an efficient use of the wire plant, but the proposed system employs an additional frequency range from about 30,000 cycles to perhaps 150,000 cycles, adding 12 channels in each direction to a pair of wires. This will furnish a total of sixteen simultaneous conversations over a pair of wires. Extending the frequency range accentuates the problem of crosstalk and some of the other problems of interference, but it is our present feeling that a substantial number of the pairs on a suitably constructed pole line can be rearranged for operation by this broad-band method. Figure 12 shows schematically the arrangement of apparatus at a terminal to provide these sixteen talking circuits, and Fig. 13 shows diagrammatically the arrangement of apparatus at a repeater station. Since increased frequency means higher line attenuations with corresponding higher amplification, the use of higher frequencies means additional repeaters on the line, so that the line currents will not at any point be attenuated below a certain level. The present proposal is to provide repeater spacing of approximately 75 miles, instead of the 150 miles used on the present open-wire carrier systems. Coaxial Cable System This is the most radical of the broad-band developments that we have attempted to develop practically. Instead of several pairs 136 BELL SYSTEM TECHNICAL JOURNAL 2- Q.UJ ■510 0 0 • J z Z 2: u. if) c/1 1 if) CO I/O a: id 0 li- , _l < 2 tr h- UJ 0 1- UJ -1 a. u. 01 UJ u. CL 5 X < Ul cc < 0 CL ^;- UJ (0 , , ' ' - ' UJ Q- 2 i 1 < dx. (4) ZZ1Z2 The contribution dVn to the potential across the left end of line (2) due to crosstalk in the section dx, x cm. away from the left end of the line, is dVn= {Hl)nZ2 = ^ Zi2 B'^y^+y^^^dx. (5) Hence the total induced voltage at the near end is Vn= CdVn= C ^^Zi^e-^y^+y^Hx. Integrating, we obtain (6) 2Zi Ti + 72 The near-end crosstalk is thus given by the expression \ E J 12 2Zi 7i + 72 If we reversed the procedure and considered the crosstalk from circuit (2) into circuit (1), we would similarly obtain ;V. = (§) =§'--"-"'". (9) \ E /21 2Z2 7i + 72 By the reciprocity theorem, Z21 — Z^- Incidentally, if instead of adopting as the definition of crosstalk the ratio of two voltages we regarded it as the ratio of the induced voltage to the current through the disturbing generator, we should have obtained N21 = N12. Finally, if the circuits are alike Zi = Z2 = Zo, 7i = 72 = 7 and the near-end crosstalk is given by the expression We observe that the near-end crosstalk depends on length /. Two limiting cases are of importance here. For a length / so small, that for CROSSTALK BETWEEN COAXIAL TRANSMISSION LINES 149 a given frequency lyH"^ is negligible when compared with 2yl, we have g-2yi = I _ 2yl + 272/2 = 1 - 2t/, (11) and the expression (10) becomes The near-end crosstalk is therefore proportional to /. For very large values of yl, that is, a very high frequency or extreme length or both, where the exponential expression is negligible as com- pared to unity, the expression (10) becomes which is independent of length. The variation of the near-end crosstalk with length for intermediate values of 7/ can be best followed if instead of the expression (10) we use its absolute value |iVi2| = Here Vn IZ12I Vl - 2g-2°' cos (2/3/) -f e-'"' 2 1 Zi I V^M^ (14) 7 = a + i^, (15) a is the attenuation constant in nepers per unit length and (3 is the phase constant in radians per unit length. We observe that for a given value of / one of the factors in (14) is oscillating with frequency. Thus, if we plot the crosstalk against frequency, the resulting curve is a wavy line superimposed upon a smooth curve, with the successive minimum points corresponding to the frequencies for which the given line is practically a multiple of half wave-lengths. The smooth curve is of course given by the magnitude of the expression (13). The curves on Fig. 2 illustrate the change of the near-end crosstalk with frequency for different lengths of a triple coaxial line made of copper conductors. Direct Far-End Crosstalk In order to determine the far-end crosstalk, we have to compute the induced voltage arriving at the far end of the system. Proceeding in a way similar to the derivation of the near-end crosstalk, we obtain the contribution dVf to the potential across the right end of circuit (2), due 150 BELL SYSTEM TECHNICAL JOURNAL O 160 < 200 L^oo^"-- L = l.76 / 0.128 X ^--- "7- ^ s., k).527^g ; %;^;625%X L=d.22 N MILES 7 ^ »« ■5 ^ ^ % 1- 2.37"— J 2.50" \ V \, > y \ 1 ) % V \ 5 10 20 30 50 100 200 300 500 1000 2000 FREQUENCY IN KILOCYCLES PER SECOND Fig. 2 — Direct near-end crosstalk in a system of three coaxial conductors. to the electromotive force in the section kl, to be given by the expression E dVf = ■;^Zi2e-^2ie^^2-y0^dx. (16) Integrating this over the total length / we obtain the total voltage induced at the far end Vt = E Zii e-T2' - g-Ti 2Zi 7i - 72 and the far-end crosstalk from circuit (1) into circuit (2) is Vf Zi2 1 - e(^i-T2)^ Fl2 = £e-Ti^ 2Zi 72 7i (17) (18) If two similar lines are considered, with equal propagation constants and the characteristic impedances, equation (18) becomes F = Vf _ Z,2 Ee-y^ 2Zo (19) The far-end crosstalk is proportional to the length of the line at all frequencies. Inasmuch as we have ignored the reaction of the induced currents upon the disturbing line, the foregoing equations must be regarded as approximations. Under practical conditions these approximations are CROSSTALK BETWEEN COAXIAL TRANSMISSION LINES 151 very good. Only equation (19) must not be pushed to its absurd implication, that for long enough transmission lines most energy will eventually travel via the disturbed line. The true limiting condition is that the energy will ultimately be divided equally between the two lines. Crosstalk Via an Intermediate Circuit The simplest case of the coaxial conductor system where the only crosstalk present is of the direct crosstalk type, as considered in the previous section, is the triple coaxial conductor. The mutual coupling in this case is due only to the transfer impedance between two circuits, as there are no other physical circuits involved. The case of two single coaxial conductors, the outer shells of which are in continuous electrical contact or strapped at frequent intervals, approximates the condition for the direct crosstalk if the system is sufficiently removed from any conducting matter. When two single parallel conductors in free space do not touch, an extra transmission line, an "intermediate circuit," is present consisting of the two outer shells of the coaxial conductors. Even two conductors, the shells of which are electrically connected, will form an intermediate circuit consisting of the outer shells and the other parallel conductors. The voltage impressed on the disturbing coaxial circuit induces currents' and voltages in the intermediate circuit, which now acts as a disturbing qi^rcuit for the second coaxial circuit, thus causing crosstalk. We shall rrow consider the near-end and far-end components of this indirect type of crosstalk. Indirect Near-End Crosstalk Let us consider a system shown in Fig. 3. The circuit (3) is the Z\ Z3 T k I P-(z,3dx) ■ X »-| dx (1) Ee" C3J p q ^^Usgdyf (2) -J dyk- Fig. 3 — Indirect crosstalk between two coaxial pairs. Yf Z| •Z3 152 BELL SYSTEM TECHNICAL JOURNAL intermediate circuit with an impedance Z3 and propagation constant per unit lengtli 73. Let the disturbing voltage E be appHed at the A end of circuit (1). Then the current in the section kl is given by the expression similar to (3) iki=^^e-yi^dx. (20) ZZ1Z.3 The current in the section pq is ipg = ikte-''', (21) where s = \y - x\. (22) The total current in the generic element of the intermediate trans- mission line due to coupling with circuit (1) is, then, ly = Cip, = ^^ r e-y^^e-yi^dx. (23) In carrying out the process of integration, we must keep in mind that from 0 to y, s = y — X and from y to I, s = x — y. Hence, we have e~yz^e~y^Hx = e'^^y \ e^-y^-yO^dx + ey^^ | e~'-y3+yi'>''dx, , „ Jo Jv and ^ _ EZ 13 ^~2ZiZ3 73 - Ti 73 + Ti (24) The elementary electromotive force induced in the second coaxial conductor by the current ly is f Ey = Znlydy. (25) The contribution of this electromotive force to the voltage across the near-end of the second coaxial pair will be then dVn=\ Eye-y^y = ^ Iye~y^ydy. (26) The total induced near-end voltage will be given by the expression F„=^ r Zs.Iye-y^ydy. (27) CROSSTALK BETWEEN COAXIAL TRANSMISSION LINES 153 Using the expressions (23) and (24), we obtain Vn — E „ „ Sn, (28) w here Jo S„ = e-y^y g-JlV — g— )'32/ g-TlJ/ — e'>'3yg-('>'3+Tl> ' 73 - Ti 73 + 7i Integrating (29) we have 273 1 — e-(T2+Tl)' 1 _ g-(73+T2)i dy. (29) 5: 7i + 72 73^ - 7i^ (73 - 7i)(73 + 72) 1 _ g(73-72)' (73 + 7i)(73 - 72) Thus, the near-end crosstalk from circuit (I) into circuit (2) via the intermediate circuit (3) is given by the expression In a similar manner we can derive the following expression for the near-end crosstalk from circuit (2) into circuit (1) via the intermediate circuit (3) : iV,/=|^^5„. (31b) '±/S2Z,3 The factor 5„ present in (31&) is the same as in (31a), being symmetrical with respect to the subscripts 1 and 2 as a close inspection of the formula (30) would prove. Zu — Z31 and Z23 = Z32 by the reciprocity theorem. For the case of two similar coaxial pairs with equal characteristic impedances Zq and propagation constants 7, and symmetrically placed with respect to the intermediate line, so that Z13 = Z32, we have ^, ^ (Zi3)^ r 73 1 - e~'y' _ 1 - 2g-(^3+T)^ 4- g-27^ 4Z0Z3 [7 73^- 7^ 73^ - 7^ (32) Now for short lengths we may use again the approximation e-a = 1 - a + ^a\ (33) The expression in the brackets of (32) then becomes equal to P and the 154 BELL SYSTEM TECHNICAL JOURNAL near-end crosstalk is given by the expression which is proportional to the second power of length. For 7/ very large we can rewrite expression (32) as follows: 4ZoZ3t(73 + 7) ^ ^^ Thus, for a system sufficiently long the near-end crosstalk via an intermediate line is independent of length. If the intermediate transmission line is short-circuited a large number of times per wave-length, its propagation constant 73 becomes very large on the average and we have approximately 2[1 - ^-(1^2+.!)^] On = 7 J- X ' (36) (Ti + 72)73 ^^^ - £ - 2Z.Z373 7X + 72 ^^^^ and But Z373 = Z, the distributed series impedance of the intermediate transmission line. Hence the "indirect" cross-talk becomes direct with the mutual impedance given by Y Z13Z23 ^12 — 79 • Indirect Far-End Crosstalk Using the method outlined in the previous section we arrive at the following expression for the far-end crosstalk from circuit (1) into circuit (2) via the intermediate circuit (3) ; see Fig. 3. The crosstalk from circuit (2) into circuit (1) will be given by a similar expression with Z2 replacing Zi in the denominator, namely F.^'^j^Sf. (386) CROSSTALK BETWEEN COAXIAL TRANSMISSION LINES 155 The factor 5/ used in the above formulae is given by the expression 273 1 — e-(Tl-T2)i 1 — e-(T3-72)i Sf -(72— 7i)' Tl 72 73^ - 7l^ (73 - 7i)(73 \ — g(73+72>' (73 + 7i)(73 + 72) -72) g-(73+7l)^ (39) When both coaxial pairs are similar and placed symmetrically with respect to the intermediate conductors we obtain the following expres- sion for the far-end crosstalk between two coaxial conductors via an intermediate circuit: F' = 273/ 1 _ g-(73-7)i 1 _ e-(y 3+1)1 73 (73 - 7)' (73 + 7)' For small / the expression for the far-end crosstalk becomes ^Z,Z,' (40) (41) which is the same as (34) for the near-end crosstalk. For large / and provided the attenuation of the intermediate circuit is greater than that of the coaxial circuit we have F' = 4Z0Z3 273/ 2(73^^ + 7^) ,^ - 7^ (73^ - I'Y (42) Finally, letting 73 approach 7 and considering a limiting case when attenuation of the intermediate circuit is equal to attenuation of either of the coaxial conductors we obtain F' = (ZnY 4Z,Z, 11 1 — e-27 _ 4- 1/2 _ ^ 27^2 47' -J (43) If the intermediate transmission line is short-circuited a large number of times per wave-length its propagation constant 73 becomes very large on the average. The equation (37) becomes, then, and Sf- Fm' = 2[1 - e-(-y2-7i)^] (72 - 7i)73 Z13Z32 1 - g^n-72)^ 2Z1Z373 72 — 7i (44) (45) The indirect crosstalk becomes direct with the mutual impedance given by the expression Z13Z23 Z13Z23 Z12 ^373 (46) 156 BELL SYSTEM TECHNICAL JOURNAL where Z — Z373 is the distributed series impedance of the intermediate transmission line. Comparison between Direct Crosstalk and Crosstalk via Intermediate Circuit for Two Parallel Coaxial Conductors We have already seen that two parallel coaxial conductors in free space form actually three transmission circuits, the third circuit being formed by two outer shells of the coaxial conductors. When this third line is shorted by direct electrical contact or by frequent straps only direct crosstalk is present. When the third circuit is terminated in its characteristic impedance we have crosstalk via the third circuit. In this last case, however, the crosstalk via the third circuit is also the total crosstalk, since the only available path for the transfer of inter- fering energy is via the third circuit. Thus, we can directly compare the values of crosstalk for the system for both conditions. We have shown that for sufficiently short lengths of the crosstalk exposure the direct type of crosstalk is given by (12) or (19), namely, F=N = ^l. . (47) We have also found that the crosstalk via an intermediate circuit is given by (34) or (41) provided that the length of conductors is small enough. Thus F' = N' =-^^P. (48) 4Z0Z3 Consequently In seeking an experimental verification of equation (49) a series of measurements were taken on a pair of coaxial conductors of varying lengths, separations, and different terminating conditions of the third circuit. The results agreed fully with the theory. Mutual Impedance Like the other constants of transmission lines the distributed mutual impedance can be measured. In certain cases, however, it is possible to obtain simple formulae for this impedance. For details of such calculations the reader is referred to a paper by one of the authors.^ In this paper the mutual impedance is expressed in terms of surface CROSSTALK BETWEEN COAXIAL TRANSMISSION LINES 157 transfer impedances. Consider a coaxial pair whose outer conductor is either a homogeneous cylindrical shell or a shell consisting of coaxial homogeneous cylindrical layers of different conducting substances. The transfer impedance from the inner to the outer surface of the outer conductor is then defined as the voltage gradient on the outer surface per unit current in the conductor. In a triple coaxial conductor system this transfer impedance is evidently the mutual impedance between two transmission lines, one comprised of the two inner conductors and the other of the two outer conductors. On the other hand the mutual impedance has a quite different value if one line consists of the two inner conductors while the other is comprised of the innermost and the outermost conductors. The surface transfer impedance of a homogeneous cylindrical shell is given by the following expression, good to a fraction of a per cent for all frequencies up to the optical range if the thickness / is smaller than 20 per cent of the average radius Zab =,r-^csch(c7/). (50) ^^^^|ab In this equation: a is the inner radius of the middle shell in cm. b is the outer radius of the middle shell in cm. / is the thickness of the middle shell in cm. 0- = -^lirgiJifi nepers per cm. lirufi . ^— ohms g is the conductivity in mhos per cm.* fjL is the permeability in henries per cm.* / is the frequency in cycles per second. If the ratio of the diameters of the shell is not greater than 4/3 the following formula correct to 1 per cent at any frequency will hold for the absolute value of the transfer impedance \Zab\ — Rdc I , (51) Vcosh u — cos M where Rdc — the dc resistance of the shell, u = tyf^Tfigf. * As in the previous paper by Schelkunofif we adhere throughout this article to the practical system of units based on the c.g.s. system. For copper of 100 per cent conductivity g = 5.8005X10^ mhos/cm. and n = iirlO~^ henries/cm. 158 BELL SYSTEM TECHNICAL JOURNAL The expression (51) is plotted in Fig. 3, p. 559 of Schelkunoff's paper. ^ As it has been already mentioned, (50) and (51) represent the mutual impedance in a triple conductor coaxial system. One might anticipate that if the arrangement is not coaxial the mutual impedance has a different value. This is indeed the case if all three conductors have different axes. But if one transmission line is a strictly coaxial pair, then its own current remains substantially uniform around its axis and from equation (81) of Schelkunoff's paper we immediately conclude that the mutual impedance will be the same as if all three conductors were coaxial. Both transmission lines must be eccentric before their mutual impedance becomes affected by their eccentricities. Thus the mutual impedance Zn between a coaxial circuit and the circuit consisting of its outer shell and a cylindrical shell parallel to it is given very accurately by (50) and (51). The surface transfer impedance across a shell consisting of two coaxial homogeneous layers is given by 7 {Zah)l{Zah)2 , rn,s ^12—— 7^ , \0^) where Z„6 is the transfer impedance for each layer and Z is the series impedance per unit length of the circuit consisting of the two layers insulated from each other by an infinitely thin film, when one layer is used as the return conductor for the other. The mutual impedance between two coaxial pairs the outer con- ductors of which are short-circuited at frequent intervals is also given by (52) provided Z is interpreted as the distributed series impedance of the intermediate transmission line comprised of the outer shells of the given coaxial pairs. This Z is the sum of the internal impedances of the two shells {Zhb)i and {Zbb)i and of the external inductive reactance coLe due to the magnetic fiux between the shells. If the proximity effect is disregarded, the internal impedance of a single cylindrical shell is the same as that with a coaxial return and various expressions for it are given in equations (75) and (82) in the previous paper. ^ The inclusion of the proximity effect does not complicate the formulae if the separation between the shells is fairly large by comparison with their radii, but in this case the proximity effect is not very large either. The more accurate determination of Z leads to complicated formulae; for these the reader is referred to a paper by Mrs. S. P. Mead.^ How- ever, at high frequencies the important factors in the mutual impedance are the transfer impedances in the numerator of (52). CROSSTALK BETWEEN COAXIAL TRANSMISSION LINES 159 Under certain conditions it is easy to obtain approximate values of the denominator of (52) and use them for gauging the limits between which the mutual impedance must lie. If the frequency is so high that the proximity effect has almost reached its ultimate value the external inductance and the internal impedance of the intermediate line are approximately Le — ^z^ cosh 2bib2 (Zbb)l + (Zbb)2 lujj. bi bi + ^^1^ r- 62' / 1_ b, 1 (bi + b^r I 1 - (bi - 62)- / (53) where bi and &2 are the external radii and / is the interaxial separation. Usually b2 = b\ — b and consequently Le = -r- cosh~^ ZTT {Zbb)i + (Zw)2 =;^\/v^ /2 (54) If the proximity effect is disregarded then the external inductance is simply Le =- log. / /6165 (55) For this case, then, the mutual impedance is given by the expression {Zah)\{Zah)2 Z\2 — {Zbh)\ + {Zbh)2 +-^l0ge , ^ V6162 (56) For two identical coaxial conductors the expression is further simplified to Z12 = ^^ -, • (57) lAbh + lOge 7 TT 0 Measuring Method As defined above, crosstalk between two transmission lines termi- nated in their characteristic impedances is given by the ratios of the induced and disturbing voltages. Consequently, if the input voltage into the disturbing circuit is known and the induced voltage at one of 160 BELL SYSTEM TECHNICAL JOURNAL the ends of the disturbed pair is measured, the far-end or near-end crosstalk values are obtained readily. In fact, the magnitude of the near-end crosstalk is given by the expression N\ = Vn E (58) and the magnitude of the far-end crosstalk is given by the expression F\ = Vr E e- (59) Taking 20 logm j^ and 20 logio-j-pr, we obtain an equivalent loss in db between the disturbing and disturbed levels of the two crosstalking circuits. This consideration determined the method of measurements used in our experimental studies. Fig. 4 — Crosstalk measuring circuit arranged for far-end measurements. The circuit used is given in Fig. 4. The two branches of the meas- uring set are the comparison circuits, the upper containing the cross- talking system and the lower including adjustable attenuators. The input and output impedances of both branches are kept alike by adjusting the resistances Ri and i?2- Thus, when the lower branch of the circuit is adjusted to produce the same input into the detector as through the crosstalking branch the loss in the calibrating branch gives an equivalent crosstalk loss in db. These values of crosstalk in db below the input level in the disturbing circuit are plotted on all our sketches. CROSSTALK BETWEEN COAXIAL TFLiNSMISSION LINES 161 Both coaxial circuits were terminated in resistances closely equal to the absolute values of their characteristic impedances. The termi- nations were carefully shielded to prevent any crosstalk at these points. Careful shielding and grounding were found necessary to reduce errors due to longitudinal currents, unbalances, and interference between different parts of the measuring circuit. The overall accuracy of the measuring circuit attained was better than .5 db when the difference in input to output levels amounted to 150 db. Agreement between Theory and Experiments The general agreement between the theory and the experiments is indicated by the curves in Fig. 5 and Fig. 6, which give the crosstalk values for cases of two small coaxial pairs with solid outer shells in Q 120 \ "X - * EASURED DMPUTED o- o-o C N .^ •***, '^^^^ *^ ■**-^. "^^^ '^^ -^ ss:^ 20 25 30 35 40 45 50 FREQUENCY IN KILOCYCLES PER SECOND Fig- 5 — Crosstalk between two coaxial pairs 20 ft. long using refrigerator pipe .032 inch thick for outer conductors. Both coaxial pairs terminated in 70 ohms. Outer conductors in contact. u no \ E - MEASURED - COMPUTED \ «^ -^ .^ ^ ■~H«. ^^, *"* "■ — 60 80 100 120 FREQUENCY IN KILOCYCLES PER SECOND Fig. 6 — Crosstalk between two coaxial pairs 25 ft. long. Outer conductor made of copper .008 inch thick, .232 inch inner diameter. Both coaxial pairs terminated in 40 ohms. Outer conductors in contact. 162 BELL SYSTEM TECHNICAL JOURNAL ^ 1 k 1 ^ N ^ URED JTED "^ \ COMP \ \/ ^ 0 10 20 30 40 50 60 70 80 90 100 110 120 FREQUENCY IN KILOCYCLES PER SECOND Fig. 7 — Near-end crosstalk on a triple coaxial system of conductors at Phoenixville, Pa. Outer to inner circuits. Length .088 mi. continuous contact. The curves in Fig. 7 show a comparison between measured and computed values of near-end crosstalk for a system of three coaxial conductors .88 mile long as installed at Phoenixville, Pennsylvania. Also, as was already stated above, full agreement between theory and experiments was established as to validity of equation (49). Crosstalk in Long Lines Employing Coaxial Conductors In a system consisting of two coaxial pairs, where two outer con- ductors are in contact, essentially only one kind of crosstalk is present depending on the direction of transmission on both pairs. It is near- end crosstalk when transmitting in opposite directions and far-end crosstalk for transmission in the same direction. Where more than two coaxial conductors are grouped together and transmission is in both directions both types of crosstalk are present. Although for a sufficiently short length of crosstalk exposure near-end and far-end crosstalk are identical, in a sufficiently long system the transmission characteristics of the line and associated repeaters will make a marked difference between them. It has been a common experience that in a long system using unshielded balanced structures near-end crosstalk imposes more severe requirements on balance between crosstalking circuits than far-end crosstalk. We shall now consider a coaxial pair. Here, the magnitude of the far-end crosstalk was found to be given by expres.sion (19). The CROSSTALK BETWEEN COAXIAL TRANSMISSION LINES 163 magnitude of the near-end crosstalk is given by expression (14), which for equal level points becomes N\ Z\i 2Zn e«Wl - 2g-2«' cos (2,3/) + e"""' (60) 2Va' + ^'' Thus, the ratio of the corrected near-end to the far-end crosstalk is obtained by combining equations (60) and (19): g"Wl - 2g-^"' cos (2/3/) + g-^"' U{a.iy + w (61) The curve in Fig. 8 gives the db difference between near-end and far-end crosstalk for different frequencies on a 10-mile length of two 20 16 12 8 4 0 -4 -A ^-N. r^ ^ -- "^^^ ^, '^^ J N \ \ s. S \ \ \ \ V \ 50 100 200 300 500 FREQUENCY IN KILOCYCLES PER SECOND Fig. 8 — Values of 20 logio \FIN\ for a 10 mi. repeater section of two parallel coaxial pairs in continuous contact. Coaxial pairs consist of No. 13 AWG solid copper wire, .267 in. inner diameter copper outer conductor .020 in. thick, and rubber disc insulation. parallel coaxial pairs with hard rubber disc insulation. Each pair consists of a copper outer conductor of .267" inner diameter and .020" thick, and a .072" solid copper inner conductor. It is evident that in a single repeater section far-end crosstalk is higher than near-end cross- talk up to about 900 kc. When a number of repeater sections are connected in tandem the near-end crosstalk contribution from a single repeater section will reach the terminal of the system modified both in magnitude and in phase due to transmission through intervening sections of crosstalking circuits. At the terminal the phase changes will distribute the crosstalk from all sections in a random manner, which, in accord with both the theory and 164 BELL SYSTEM TECHNICAL JOURNAL experimental evidences, will result in a root-mean-square law of addi- tion. Thus, the overall near-end crosstalk from m sections will be equal to the crosstalk from a single section multiplied by the square root of m. On the contrary, in a system using similar coaxial pairs transmitting in the same direction and employing repeaters at the same points, the far-end crosstalk is affected mostly by the phase differences of the repeaters. If these do not vary from the average by more than a few degrees, the far-end crosstalk in a system involving even a compara- tively large number of repeaters will change proportionally to the first power of the number of repeater sections m. Only with a very large number of repeater sections (perhaps 500 or more) and random phase differences of repeaters and line of perhaps 5°-10° will the far-end crosstalk from single sections tend to approach random distribution. In this case the root-mean-square law will hold reasonably well. Thus, far-end crosstalk will grow faster than near-end crosstalk as the number of repeater sections increases. This, combined with the relationship between the far-end and the near-end crosstalk in a single repeater section as given by equation (61) and Fig. 8, leads us to conclude that in long systems with both near- and far-end crosstalk present the limiting factor will be the far-end crosstalk. This is contrary to the experience with balanced structures stated above. References 1. A. G. Chapman, "Open-Wire Crosstalk," Bell System Technical Journal, Vol, XIII, January 1934, pp. 19-58, and April 1934, pp. 195-236. 2. S. A. Schelkunoff, "The Electromagnetic Theory of Coaxial Transmission Lines and Cylindrical Shields," Bell System Technical Journal, Vol. XIII, October 1934, pp. 532-579. 3. L. Espenschied and M. E. Strieby, "Systems for Wide-Band Transmission Over Coaxial Lines," Bell System Technical Journal, Vol. XIII, October 1934, pp. 654-769. 4. E. J. Sterba and C. B. Feldman, "Transmission Lines for Short-Wave Radio Systems," Bell System Technical Journal, Vol. II, July 1932, pp. 411-450. 5. H.F. Mayer and E.Fisher, "Breitband Kabel mit Neuartige Isolation," E.T.Z. No. 46, Nov. 14, 1935. 6. S. P. Mead, "Wave Propagation Over Parallel Tubular Conductors: The Alter- nating Current Resistance," Bell System Technical Journal, pp. 327-338, April 1925. 7. John R. Carson and J. J.Gilbert, "Transmission Characteristics of the Submarine Cable," Journal Franklin Institute, December 1921. 8. John R. Carson and Ray S. Hoyt, "Propagation of Periodic Currents over a System of Parallel Wires," Bell System Technical Journal, July 1927. 9. H. Kaden, "Das Nebensprechen Zwischen Parallelen Koaxialen Leitungen," Electrische Nachrichten Technik, Band 13, Heft 11 (1936), pp. 389-397. 10. M. E. Strieby, "A Million-Cycle Telephone System," Electrical Engineering, January 1937; Bell System Technical Journal, January 1937. Sound Recording on Magnetic Tape By C. N. HICKMAN This paper describes an improved method of recording sound magnetically on a steel tape, similar in principle to that of the Poulsen telegraphone. In the latter a longitudinal magnetic pat- tern of the voice current is imprinted on a steel wire by drawing it rapidly past recording pole pieces. The high speed used by Poulsen and subsequent investigators has been directly and indirectly a lim- iting factor in the application of magnetic recording to commercial uses. The system here described makes use of perpendicular magnetization. This method makes it possible, with suitable equalization, to obtain a substantially uniform frequency-response characteristic up to 8000 cycles per second with a tape speed of only 16 inches per second. In many cases a speed of 8 inches per second is adequate for recording speech. At the same time the ratio of signal to background noise has been substantially increased. The decrease in efficiency resulting from the use of perpendicular instead of longitudinal magnetization is offset to a great extent by the use of a better design and construction of the pole-pieces and a more suitable recording medium. The recording medium is a steel tape having a thickness of about 1.0 to 2.0 mils (0.025 to 0.051 mm.) and a width of about 50 mils (1.3 mm.). Introduction A SYSTEM of recording speech magnetically on a steel wire was invented by Poulsen almost forty years ago. The wire was drawn past a pair of pole-pieces surrounded by coils carrying a speech current. A magnetic pattern corresponding to the current was thus impressed on the wire. When the wire thus magnetically treated was again drawn past the pole-pieces a current corresponding to the recording current was induced in the surrounding coils. It was common practice to place the pole-pieces on opposite sides of the wire and offset with respect to each other. The magnetic pattern in the wire thus con- sisted mainly of a variation in the intensity of magnetization, the direction of the magnetization being substantially parallel to the axis of the wire. This method of putting the record on the wire is known as longitudinal magnetization. With such a system the wire must travel at a very high speed if high frequencies are to be recorded and reproduced. It was customary to use speeds of from six to ten feet per second. By using tape instead of wire, the recording and re- 165 166 BELi SYSTEM TECHNICAL JOURNAL producing pole-pieces may be placed directly opposite each other so that the magnetic pattern consists of variations in the intensity of magnetization, the direction of the magnetization being substantially perpendicular to the surface of the tape. This type of magnetization will be called perpendicular magnetization. There is another method of recording in which the magnetization is in a direction perpendicular to an edge and parallel to the surface of the tape which has been called cross or transverse magnetization. In spite of the fact that the principle of magnetic recording has been known for a long time, there has been very little literature on the sub- ject until recently. Several papers ^ which deal almost entirely with the longitudinal method of magnetization have been published abroad during the past two years. Cross magnetization is discussed briefly in one of the papers. Apparently, perpendicular magnetization has not been seriously considered. This paper will treat mainly the perpendicular method of magnetization with which a good frequency- response characteristic may be obtained with a tape speed of only 16 inches per second. Forms of Recording Media Steel wire has been used as a recording medium in most of the telegraphones. This was probably because it was easier to obtain. When wire is used it is necessary to make the longitudinal separation of the pole-pieces rather large. This is done in order to minimize the distortion caused by the continual rotation of the wire about its axis. Such rotations change the relation of the magnetic patterns in the wire with respect to the reproducing pole-pieces from that which existed at the time the record was made. «. When the pole-pieces have a wide separation, high linear speed must be used in order to record and reproduce high frequencies. The high speed required in this method of recording gives rise to a number of mechanical difficulties. The contacting pole-pieces wear away rapidly and it is difficult if not impossible to construct and hold them so that they will ride smoothly against the wire. These variations in contact with the wire change the magnetic reluctance of the flux path so that the signal strength varies and an excessive amount of noise is introduced. Recording on steel discs has been investigated from time to time but no practical results have yet been reported. ^ See list at end of this article of recently published papers dealing with magnetic recording. SOUND RECORDING ON MAGNETIC TAPE 167 Steel tape as a recording medium was suggested by V. Poulsen in his U. S. patent No. 661,619-1900. Its use eliminates many of the objectionable features of the wire recording system. The magnetic patterns in the tape pass the pole-pieces during reproducing in the same relative positions as at the time they were made. It is practical to wind the tape on reels of pancake shape. Snarling difftculties en- countered when using wire are thereby avoided. Thin tape permits the use of smaller pulleys without exceeding the bending fatigue limit of the metal. The use of tape permits the perpendicular method of magnetization to be employed. High frequencies may therefore be recorded and reproduced with a relatively low linear tape speed. Methods of Magnetization There are two methods of longitudinal magnetization in use, one and two pole-piece recording. A detailed description of these methods is given in two of the papers which have been mentioned. It will be sufficient here to consider them only briefly. LENGTH OF TAPE Fig. 1 — Longitudinal magnetization of a recording medium by a single pole piece. SIG = Signal coil; DP = Depolarizing coil. Figure 1 shows the action taking place in recording with one pole- piece. M is the recording medium and P is the recording pole-piece. 168 BELL SYSTEM TECHNICAL JOURNAL It will be assumed that the recording medium has been previously magnetized by drawing it past a pole-piece so that the residual mag- netization in it has a direction as indicated by the upper arrow at the left.^ In this method of recording the magnetization is principally parallel to the axis of the medium but in order to simplify the drawing, the direction of magnetization in Fig. 1 is shown at a considerable angle. If the pole-piece P carries a steady flux in the direction indi- cated by the heavy lines, this flux will spread in the medium. At the point 2 in the middle of the pole-face, the flux will be substantially perpendicular to the axis of the medium. On either side it will be approximately parallel to the axis of the medium but of opposite directions. As the elements of the recording medium approach the pole-piece P, they will first be subjected to the flux 1 which is in ap- proximately the same direction as the residual magnetization in the medium so that no appreciable change will take place. When the elements are directly opposite the face of the pole-piece they will be acted on by a flux 2 which is nearly perpendicular to the residual magnetization of the medium. When the elements reach the position 3, the flux will be in opposition to the original magnetization within the medium. If it were not for these changes in the direction of the flux while the elements are passing from the position 1 to the position 3 a signal record without appreciable distortion could be left on the medium at the point 3 by superimposing a signal flux on the steady flux in the pole-piece P. It will be realized that the positions 1, 2 and 3 are not discrete points but that they cover an appreciable distance. The spreading of the flux at 3 will be considerable so that it will be necessary for the medium to travel at high speed in order to get the recorded signals away from the recording flux before the record is distorted by subsequent signals. Figure 2 shows a similar diagram for two pole-piece recording. Where two pole-pieces are relatively close to each other, the flux will not spread so much in the medium and the direction of magnetiza- tion will be approximately the same as that of the recording flux. It is again assumed that the residual magnetization within the medium is mainly in the opposite direction to the motion of the medium as indicated by the upper arrow at the left. The flux 1 will have no appreciable effect on the residual magnetization. The flux 3 is in the opposite direction to the residual magnetization and were it not for 2 In Figs. 1, 2, 3, 4 and 6, the heavy lines passing through the pole-pieces represent the instantaneous recording flux. The density of the fine lines in the recording medium represents the intensity of magnetization. The arrows above and below the medium show the direction of this magnetization. The curve below represents the nature of the signal that has been recorded on the tape. SOUND RECORDING ON MAGNETIC TAPE 169 these changes in the direction of the flux while passing from 1 to 3, a modulation of the flux 3 might be expected to leave an undistorted record on the medium as was the case with one pole piece recording. However, in the case of two pole-pieces, the elements still must pass the pole-piece P2 where the flux 4 is approximately perpendicular to the medium. After passing the pole-piece Pi the record is subjected to the flux 5 which is in the opposite direction to the recorded flux. The record which was made by the flux 3 is therefore distorted by fluxes 4 and 5. This distortion is greater than it is for one pole-piece ^2 7 0 - K- ^^***««s^ ^^ 1 "^^^ < ^\ ^^ N X \ \- / \ Z X d N. / < N. ^ 2 v^ LENGTH OF TAPE Fig. 2 — Longitudinal magnetization of a recording medium by two pole pieces. recording. In practice the stray fluxes 4 and 5 are sufficiently small so that the distortion introduced may be tolerated in exchange for the improved frequency response which is obtained with two pole-piece recording. Figure 3 shows the action taking place where cross-magnetization is used. It is here assumed that the recording medium has been pre- viously magnetized so that the residual magnetization is in the di- rection indicated by the upper arrows at the left. W represents the width of the recording medium which in this case is a steel tape. It will readily be seen that if Wi's, very large there will be considerable spread- 170 BELL SYSTEM TECHNICAL JOURNAL LENGTH OF TAPE Fig. 3 — Transverse magnetization of a steel tape. LENGTH OF TAPE Fig. 4 — Perpendicular magnetization of a steel tape. SOUND RECORDING ON MAGNETIC TAPE 171 ing of the recording flux within the tape. The recording flux is always at substantially right angles to the axis of the tape and parallel to its surface and is in the opposite direction to the residual magnetization. If W is made quite small or in other words if the pole-pieces Pi and P2 are directly opposite each other with the thin dimension of the tape between them, we have the conditions shown in Fig. 4. The tape is so thin that there is very little spreading of the flux so that the width of the flux path is not appreciably dependent on the strength of the signal. This type of recording is called perpendicular magnetiza- tion in order to distinguish it from cross-magnetization, where the width of the tape instead of the thickness determines the pole-piece separation. The perpendicular method of magnetization permits a relatively low tape speed. The thickness of the pole-piece tips determines the frequency response for a given tape speed. Method of Recording with Perpendicular Magnetization If the tape is first subjected to a saturation flux which is at right angles to the surface of the tape, it will be left with one side of north and the other of south polarity. If the tape in this condition is passed between recording pole-pieces carrying only AC flux, it is obvious that only half cycles will be recorded. The record is therefore much distorted. The current reproduced from such a record is similar to the alternating current which may be obtained from a single wave rectifier. If on the other hand the tape is passed through an alternating high- frequency field which is strong enough to erase the record, it is left in a substantially neutral condition. If it is then passed between the recording pole-pieces, both half cycles will be recorded but there will be amplitude distortion. Figure 5 shows a magnetization curve for iron which has previously been demagnetized with alternating current. The slope of the first part of the curve is small in either direction of magnetization and then increases with increase in the flux and finally becomes smaller again. Small signals will therefore be recorded weakly and strong signals will be recorded relatively higher. Both will have wave form distortion. The same effects would be obtained with longitudinal or cross magnetization. In the past, investigators have often utilized only one side of the magnetization curve, A direct current was used as a bias to bring the recording flux to the most suitable part of the curve such as at n, Fig. 5. The method employed here will be made clear from Figs. 6 and 7. As the tape elements enter the field of the polarizing pole-pieces Pi, P2 (Fig. 6) they are subjected to an increasing magnetizing force. The 172 BELL SYSTEM TECHNICAL JOURNAL Fig. 5 — Typical magnetization curve for steel. POLARIZING POLES RECORDING POLES LENGTH OF TAPE Fig. 6 — Perpendicular magnetization method of recording on steel tape. SIG = Signal coil; P = Polarizing coil; DP = Depolarizing coil. SOUND RECORDING ON MAGNETIC TAPE 173 elements are magnetized to the saturation point P as shown by curve a, Fig. 7. As the elements leave the polarizing field they are subjected to a field of decreasing strength so that the magnetic induction drops along the curve b to R, this point being reached when the applied field is zero. In Fig. 7, the magnetizing force // refers to the externally applied field. The tape elements then pass between the recording pole-pieces which carry a flux in opposite direction to that of the polarizing pole-pieces. If there is no signal current present, the magnetic induction will be brought down to the point N by the biasing field. As the elements pass out from between the pole-pieces, the field will decrease to zero and the magnetic induction will change from Fig. 7 — Diagram showing the cycles of magnetization through which the elements of a steel tape may pass during the process of recording. N to 0, which is a substantially neutral condition. However, if there is a signal current present at the time the tape elements are passing between the recording pole-pieces, the magnetization will be reduced to a point A higher than N if the cycle is in opposition to the bias flux or to the point B lower than N if the signal flux is in the same direction as the bias flux. In either case the elements will retain a magnetiza- tion value corresponding to ^' or B' respectively. This system makes it possible to record over a longer portion of the magnetization curve without appreciable distortion. Unless the proper value of biasing field is used to bring the magneti- zation approximately to the point N when no voice current is present, the maximum recording range cannot be obtained without excessive amplitude distortion. For example if no bias is used, it has been found 174 BELL SYSTEM TECHNICAL JOURNAL that the output plotted against input will be too steep as shown in the curve 1, Fig. 8. If the bias is too great, the output input curve will be inclined too much as shown in curve 2 of the same figure. When the o 30 3 20 10 ^ - V /- 3^ ^— / / / / 2. / / / ^ X / / ^ y / / y A / ^ y ^ / / y 20 30 40 50 INPUT IN DECIBELS 60 70 80 Fig. 8 — The effect of the biasing current on the slope of the output-input level curves. proper value of bias is used the curve 3 is obtained which is inclined at 45 degrees. Measurements of output versus input may therefore be used to determine the proper bias current. Another method of determining the proper amount of bias is to plot the output obtained from records of very weak signals as a function of 0 12 3 4 BIAS CURRENT IN MILLIAMPERES Fig. 9 — Effect of the biasing current on the intensity of weak signals. the bias current used during recording. Figure 9 shows such a curve for a 1000-cycle record. In selecting the proper bias current from the curve, the point at the crest gives the most efficient value but it is SOUND RECORDING ON MAGNETIC TAPE 175 better to favor some point slightly to the right of the crest in order to avoid the danger of very strong signals operating too far down on the left side of the curve. The recording current for the 1000 cycles had a value 30 db below the overload so that only a small amplitude was used in obtaining the data for this curve. If the same set of pole-pieces is used both for recording and repro- ducing, there is no question of getting the reproducing pole-pieces in the same alignment as the recording pole-pieces. If different sets are used care must be taken to get the same alignment. In order to keep the signal high above the tape noise, it is desirable to record so that the flux or current amplitude is independent of the frequency. Since the impedance of the recording coils rises rather sharply with frequency, it is necessary either to place a high resistance in series with the recording coils or to connect them to a high impedance. The later method is of course the more efficient. Since the energy present in the higher frequencies of voice and music is usually less than in the 1000-cycle region, an amplifier having a rising character- istic may be used in order to record these frequencies at a higher level. A corrective network may be used in reproducing to obtain the de- sired frequency response. Such a procedure increases the apparent ratio of signal to the tape noise. Reproducing If the thickness of the pole-piece tips is small with respect to the wave length of the signal on the tape, the voltage generated in the reproducing coils is proportional to frequency, so that the coils may be matched to favor the lower frequencies. If a straight line fre- quency characteristic is desired, a corrective network may be used. Z^ N U 30 CQ O / / * t \ V N v 'R=l Fig. 3 an AM — T- 33 ajL -AAAri VW .-i 'R=l Fig. 4 Figs. 3-4 — A pair of constant resistance networks of "constant K" configuration. If X is taken of the form i(f/fo), the structure of Fig. 3 will be made up of series coils and shunt condensers in the form of a low-pass filter. The structure of Fig. 4 will be of the form of a high-pass filter with series condensers and shunt inductances. The loss of the first network IS e2«i = 1 + /o and of the second e2a, = 1 ^ i^j^"' With / < /o the loss of the first network will be small and the loss of the second network large. With / > /o the reverse is true. At/ = /o each of the networks takes half of the available power, illustrating a 184 BELL SYSTEM TECHNICAL JOURNAL necessary property of constant resistance networks of this type, of a three db loss at the cross-over frequency. If X is taken of the form i~-T 7— f t"he networks become band-pass l/™' -t) and band-elimination filters, respectively. By taking other functions for X multiple band structures may be designed, subject always to the limitation that the combined bands of both filters must extend over the whole frequency range, with a three db loss at each cross-over point. The evaluation of the elements is easily done from equations (10). The impedance denoted by aiX, for example, in the low-pass filter would have the value i(f/fo) sin (wjln), which is an inductance of a value (l/27r/o) [sin (7r/2w) J. For a terminating resistance dififerent from unity the value of the first inductance is Li = (i?o/27r/'o)Csin (7r/2«)] or in general any inductance is Lm = dmLo where Zo = Ro/lirfo. Similarly, any capacitance is Cm = OmCo where Co = l/lirfoRo. The corresponding formulas for the second network are C,„ = Co/a„t and Lm = Lo/am- The same formulas hold for n even; in that case the networks of Fig. 3 and Fig. 4 would terminate on the right in a shunt arm with impedances of 1/aiX and X/ai, respectively. This is illus- trated by Fig, 2 for n = 2. Filters with Characteristics Similar to Those of the "M -derived" Type The networks shown in Fig. 3 and Fig. 4 have the same configuration and similar characteristics to constant K filters. They are subject to the same objection of a relatively slow rate of cut-off and an excessive loss at frequencies remote from the cut-off. A type of characteristic similar to that obtained with M-derived filters, with points of infinite loss at finite frequencies, is necessary for an economical design in the majority of cases. The loss characteristic of the network is of course fixed by the function F(\), a ratio of two polynomials in X. It may be written tKK) - A,K ^^ 5iX2 + • • • + ^„X2"-2 • Now the first filter will have infinite loss points when the denominator is zero, and the second filter when the numerator is zero. If these CONSTANT RESISTANCE NETWORKS 185 peaks are to occur at real frequencies, F(\) must have poles at X^ = — 1/5^^ and zeros at X^ = — Pm^- Moreover, since 1/[1 + F{\)'] and l/l^l + (1/F(X)^ must always be positive for real frequencies, the expression for F(\) when all its zeros and poles occur at real frequencies must be a perfect square. It may then be written (1 + Si^x^y •••(! + s\n-i)/2\'y In order to get an idea of the significance of the expression, let X = i(J/fo) and restrict the P's and the S's to values less than unity. The first network will then have zero loss points at/ = 0 and/ = Pmfc and infinite loss points at/ = fo/Sm and/ = oo. The second network will have infinite loss points when the loss of the first is zero, and zero loss points when the loss of the first is infinite. The first network is therefore a low-pass filter and the second a high-pass filter. The following work is considerably simplified if Sm = Pm- This implies that the characteristic of the second filter is the same function of 1/X that the first is of X. If the cross-over point is fixed at X^ = — 1, the value of .<4o is — 1 and in order to write equation (6) or (7), it is necessary to find those zeros with a negative real part of 1 ,, (Pi' + ^'y • • • (P^n-n/2 + X^)^ "^ (1 + P{'\'y •••(!+ P\n-l)/2\'y (Pl2 + X2) . • • 1 +x (1 + Pl'\') J , (P,2 + X2) (1 + Pi'X') Now since the zeros of the second factor on the right are the negatives of the zeros of the first factor, it will be sufficient to find all of the zeros of the first factor and reverse the signs when necessary to secure negativ^e real parts. Consider, then, the equation 1 , . (^l'' + X'') • • • (P^n_l);2 + X^) __ .. ' '^''(1 -f Pi2x2) ... (1 +P2^„ .1)^2X2) ''• One root is X = — 1. It may be shown further that the magnitude of all of the roots is unity. Writing X = pe^^ as a root, the magnitude of the typical product term (P^ -f X2)/(l + P^X') may be written 1 ^„\ / „ 1 P2 -f X2 p ^ J , \ -P' -^-P'Hp'-^^ 1 -f P2X2 /o , 1 \' . . ,. ' I Pp + -p- j - 4 sm2 d 2 p- il-X,) = = 2, = 3, P' - (1 - ^2)P p'- {\-i:,)p'' 186 BELL SYSTEM TECHNICAL JOURNAL Now since the denominator of the expression on the right is always positive, and all of the P's are less than unity, the magnitude of each of the product terms is greater than unity if p is greater than unity and less than unity if p is less than unity. Since, however, the magni- tude of the complete product must be unity, the value of p must be unity. After dividing through by the factor 1 + X, the remaining function is a reciprocal equation in X and may be written as an equation in ^ = X + (1/X). Since the magnitudes of the roots in X are all unity, the roots in p must all be real and be in the region — 2, + 2. The degree of the polynomial in p is {n — l)/2. It may be shown further that if {n — l)/2 is even there are an equal number of positive and negative real roots, if the degree is odd there is one more positive than negative root. The equations in p for various values of {n — l)/2 are -- 0 - (1 - 2i + 22) = 0 2 - (2 - Sx + 23)^ + (1 - 2i + 22 - 23) = 0 = 4, p' - (l - 24)^3 _ (3 _ 2i + 24)^2 + (2 - 2x + 23 - 224)^ + (1 - 2i + 22 - 23 + 24) = 0, where the 2's are the symmetric functions of the P^'s, that is, 2i = Pi2 + P22 + . . . P^„_i)/2, 22 = P^Pi^ + • • • + P^(n--3)/2P^(n-l)/2- The equations in p may also be written in trigonometric form as follows: — - — = 1, cos^^ + 21COS2 = 0 r ^ fl = 2, cos^^ + 22COS2^ + 21COS2 = 0 = 3, COS 2 ^ + 23 COS 2 0 + 2i cos 2 e + 22 cos | = 0 9 7 5 3 = 4, cos ^ ^ + 24 cos - e + 2i cos ^e -\- Xa cos ^ d + 22COs|= 0. CONSTANT RESISTANCE NETWORKS 187 These equations include the root at X = — 1 corresponding to 6 = T. Excluding this they will each have (n — l)/2 roots between 6 = 0 and 6 = tt. The roots in p will then be given hy p = 2 cos 6. Equation (7) becomes (n-l)/2 /3i = tan~^ X -\- J^ tan — 1 ymX 1-^2' (11) where the quantities pm are the roots of the above equations, without regard to sign. We require also the value of d^ijdx, which may be written dSi dx 1 1 + X2 (n-l)/2 1+ L - 1 1 p^ (4 - pj)x' (1 + x^Y J (12) A possible configuration for the first network is shown in Fig. 5 and for the second in Fig. 6. \AAr an-a^ Fig. 5 R=l Fig. 6 Figs. 5-6 — A pair of constant resistance networks of the "M -derived" configuration. To find the elements it would be possible to expand the voltage ratio and solve for the as as was done in the constant K illustration. Another method would be to find the input admittance of the network from the known input conductance, and find the a's from this ex- pression. A simpler method, however, takes advantage of the fact 188 BELL SYSTEM TECHNICAL JOURNAL that each structure is a purely reactive network with the exception of the terminating resistance and finds the network elements in terms of the short circuit reactance as measured from the resistance end of the network. Use may be made of the following theorem : With any four-terminal reactive network the reactance measured at terminals 3-4 with terminals 1-2 short-circuited is equal to the laftgent of the phase shift between a voltage Eq applied to terminals 1-2 and the resultant voltage Ei across a unit resistance connected to terminals 3-4. The open-circuit voltage across 3-4 due to Eo would be ± kEo, where ^ is a real quantity, if the network contains only reactances. By Thevenin's Theorem, then, _ ±kEo ^'~ l-j-iX' where X is the reactance of the network from terminals 3-4. If (3 is the phase shift between Eo and Ei, X = tan /5. Since this phase shift is given by (11) the short-circuit reactance is known. At a value of X = i(l/Pi) or x = 1/Pi, the impedance of the first shunt arm from the right of Fig. 5 is zero, so that the reactance of the filter is simply the reactance of the arm aiX, which gives the value of oi directly as ai = Pi(tan j8i)i, where (tan /3i)i denotes the value of tan ^i when x = 1/Pi. The reactance of the network after subtracting oix is tan j8i — Pi(tan /3i)i.-v;. At values of .v very close to 1/Pi this is the reactance of the first shunt arm, or dx\ X J- (tan j8, - + '-'^')'(f),-'" Similar formulas may be found for the rest of the elements. If Xm denotes the reactance starting with the series arm OmX or with the CONSTANT RESISTANCE NETWORKS 189 shunt arm {Pmn'\^ + l)/amX, then for m odd, that is, for a series element, 1 X = ^^^ am -- — P{m+l)/2Xm and for a shunt arm, m even. 1 1 dXm dm 2Pm/i ' dx (m41)/2 m/2 VVheti m = n, or for the last series arm, a special relation is necessary-, readily obtained by the limiting value of reactance as x approaches zero. This gives (fll + 03 + • • • + an)x = (1 + ^pm)x or 0„ = 1 + l.pm — («! + «3 + • • • + an-2). To use these relations it is necessary to know the expression for Xm, the reactance to the left from the successive points in the network. To determine this in terms of the elements already known use may be made of the following theorem : If the impedance looking to the left into a network is Z, the impedance to the left from A, any point ivithin the network is the negative of the impedance to the right from A when the network is terminated on the right by an impedance — Z. For example, referring to Fig. 5, to determine az it is necessary to know the reactance to the left starting with a^x.- By the theorem this is 1 X3 a^x 1 1 — PiV Oix — tan |3i and when x — I/P2 we have for as 1 _ az _ 1 ^ ~ Pi" - Pi2 ~ ai - P2(tan ^1)2 ' The impedance at that end of the filter terminated by the resistance is of interest. Its value of course depends upon the terminating impedance at the junction of the two filters, but assuming that this impedance and the separate terminating resistances are all Ro, the impedance from the load of the first filter is Ro tanh (02 + ijSi) if terminated in a series arm and Ro coth (a2 + i^i) if terminated in a shunt arm. Note that the impedance of the first filter depends upon 190 BELL SYSTEM TECHNICAL JOURNAL the transfer constant of the second. The impedance from the load of the second filter depends in the same way upon the transfer constant of the first. The proof of these relations is based upon both networks being purely reactive. Applications The use of the constant resistance pairs of filters is indicated wherever the impedance at the junction of two filters is of major importance. Another application which is of some importance is that of separating the energy in a band of frequencies into two or more channels, delivering all of the energy into one or the other of the loads. The method may be extended to more than two networks in parallel or series to give a constant resistance. For example, the combination Gi G.= 1 [l + f.(X)][l+^]' 1 6^3== 1 1 + FM ' will give a constant resistance for the three networks. Designs have been carried through on this basis where the networks are low-pass, high-pass and band-pass, respectively. This is one method of avoiding the Hmit of three db in the loss of the low-pass and the high-pass filters at their cross-over point, since in this case the band-pass filter will take up the power. A second method is to use a pair of low and high-pass filters, each terminated in another pair with different cross- over points. This method requires the use of both a low-pass and a high-pass filter as power absorbing networks but they would be simple structures and together would require no more elements than the single band-pass filter in a three-filter combination. The two methods are illustrated in Fig. 7 and Fig. 8, respectively. The structures for the second type are given by Fig. 9. Note that the filters designated L.P. II, L.P. Ill, H.P. II and H.P. Ill have one series arm missing and are apparently terminated at a shunt point at the load end of the filter. This is a consequence of selecting the two P's in such a way that the coefficient ai becomes zero, a matter of no particular difficulty in the case of a two-section filter. CONSTANT RESISTANCE NETWORKS 191 Fig. 7— A three-filter constant resistance combination. LOW PASS HIGH PASS I LOW PASS n HIGH PASS HI LOW PASS r-J in HIGH PASS rr LOW PASS n HIGH PASS m LOW PASS n HIGH PASS n LOW PASS r HIGH PASS I \, N V '\ . 1 LOOP LOSS ,\ y / "^ ^_ \ -J \J t; ^ /' ^■- ^ 1 / J K 10 15 20 25 30 FREQUENCY IN KILOCYCLES PER SECOND Fig. 8 — Constant resistance networks used as directional filters. 192 BELL SYSTEM TECHNICAL JOURNAL It will be found that a filter of several sections of the type described in this paper will have somewhat less loss in the attenuated band than the usual type of design. On the other hand the loss in the band will, in general, be less unless additional elements are used in the standard type of filter to reduce reflection losses. A design for a pair of constant — vi). LOW PASS I HIGH PASS I ■- vMilrpjmrp 0.172 0.240 0.140 LOW PASS IT AND HI HIGH PASS H AND III Fig. 9 — The configuration of the filters of Fig. 8. 0.181 0.105 0.147 0.152 ih-pHI >0.09l feO.126 )pO.I78 _^I.2I nl^O.aSS =J=0.I78 STANDARD 2.71 0.180 0.172 0.170 o.l49 0.147 0.141 0.0094 >0.264 fc>0.182 "0.416 rilO.232 r:j=O.I34 CONSTANT RESISTANCE Fig. 10 — Comparison of the elements of typical standard and constant resistance filters. resistance filters having a cross-over frequency of 1000 cycles is compared with a design for a pair of standard filters in Fig. 10, No additional elements have been added to the standard type to improve the impedance.^ The loss characteristics for the two low-pass filters '"Impedance Correction of Wave Filters," E. B. Payne, and "A Method of Impedance Correction," H. W. Bode, Bell Sys. Tech. Jour., October 1930. "Extensions to the Theory and Design of Electric Wave Filters," Otto J. Zobel, Bell Sys. Tech. Jour., April l'931. CONSTANT RESISTANCE NETWORKS 193 are compared in Fig. 11, Note that in this case the constant re- sistance filters have only about sixty per cent of the loss of the standard 50 Z 30 O il / ^ \hy V^ STANDARD FILTER M / \ " \J\^ ^ -^ CONSTANT RESISTANCE FILTER 1 •T^ V 2000 5000 FREQUENCY IN CYCLES PER SECOND Fig. 11 — Loss characteristics obtained by the filters of Fig. 10. filters. The dilTerence would not be as great for filters of less sharp discrimination. A Laboratory Evaluation of Wood Preservatives By R. E. WATERMAN, JOHN LEUTRITZ and CALEB M. HILL Evolution of a simple laboratory technique for the assay of materials proposed for use in the preservation of wood is reported in this paper. This test involves a measurement of the actual decay resistance of the treated wood. Included are a resume of the limitations imposed by current test-methods and a discussion of the adaptations of this new technique to the numerous variables inherent in laboratory simulations of outdoor exposure. TTUNDAMENTAL scientific discoveries in the biological sciences -*- during the latter part of the nineteenth century slowly brought organized knowledge out of the chaos of conflicting theories as to the character of many natural phenomena. This was especially true in the field of fermentation where these accumulated findings and observa- tions finally served as the basis for the proof that the filamentous fungi were the causal agents in the decay of wood. This knowledge of the decay mechanism, together with increased demand for wood products due to industrial expansion and the concomitant depletion of our best stands of naturally rot-resistant species of timber, served as a stimulus towards organized studies of the physiology of decay or- ganisms and possible means of prophylaxis. While Nature has been lavish in the supply of fast-growing species, she has also been provident in making such timber more vulnerable to attack by the micro-flora and fauna which act as scavengers for the forests and as conservators for vast quantities of materials which trees take from the soil during their growth period. The necessity of preserving this more easily decayed wood accelerated the search for satisfactory means of protection. This has been especially true in the Bell System where fast-growing but easily rotted southern pine has, to a large extent, been supplanting chestnut and cedar for poles. In the past the use of certain materials for the preservation of wood was based entirely on their availability or the personal prejudice of proponents for them. This method of selection could result only in widespread waste and oftentimes disastrous consequences, but a wood- preserving industry utilizing certain materials such as coal-tar creosote gradually evolved. The controversies as to what properties of creosote make it an effective preservative still rage, and the problem of choosing and specifying the type of creosote best fitted for the preserva- 194 A LABORATORY EVALUATION OF WOOD PRESERVATIVES 195 tion of timber is still urgent. This is particularly vital in that creosote is a loose term covering a congregation of compounds rarely twice the same in quality or proportion. When in 1927, research on the development of a rapid means of evaluating wood preservatives was initiated in the Chemical Depart- ment of these Laboratories, primary consideration was accorded the selection of the best available method for measuring the toxicity of proposed preservatives against wood-destroying fungi. The technique used was one which had been developed and extended to a considerable degree by the workers at the Forest Products Laboratory in Madison, Wisconsin. This petri dish method, described at some length by Richards in 1923,^ was standardized in 1929 ^ at a conference of American workers in St. Louis. Briefly, the method consists in adding various amounts of the toxic agent under test to a nutrient medium in the form of a hot malt-agar solution which is poured into a petri dish, cooled, and the resulting gel inoculated with small sections of the hyphae of a wood-destroying fungus (Fig. 1). The organism usually used is culture no. 517 from the Forest Products Laboratory but others may be chosen. The excellence of the preservative is based on the lowest concentration which is able to kill or totally inhibit growth of the test organism. While the petri dish method can be brought to a high degree of efficiency, accuracy and precision by suitable precautions, it is definitely Hmited in its practical application. It tells nothing of the permanency of the material under test from the standpoint of leaching, evaporation or chemical instability. Nothing is learned of the possible reaction of the preservative with wood, and the dispersion in warm liquid agar which later gels is a far cry from that obtained in wood. There is an axiom of biological assay, that the substratum for in vitro tests be as similar as possible to that encountered in nature. Neglect of this principle in the field of antiseptics and germicides has been responsible for many outstanding failures in vivo of materials which had given brilliant promise in the culture tube. Doubt concerning the validity of the petri dish test was substantiated when several preservatives highly toxic according to this method failed in outdoor exposure tests. In many cases such failures could not be ascribed to obvious conditions such as high volatility or solubility. Instances were also met wherein materials of little value according to the petri dish method were able to prevent decay in the field. There is no dis- position to advise against all use of this method as it is a valuable tool in making initial judgments on a new material; but it should be verified by other means before the expense of a field trial can be justified, and a ^ Numbers refer to bibliography at end. 196 BELL SYSTEM TECHNICAL JOURNAL proper degree of skepticism should be exercised before condemning a preservative on the basis of this test alone. Parallel with the use of nutrient substrata of the malt-agar type in this country, there grew up in Europe a technique which utilized the wood itself as a medium for dispersion of the toxic agent. This kolle flask method (Fig. 2) was standardized and accepted by a conference Fig. 1 — Assay by petri dish method. Test-fungus No. 517 on increasing amounts of coal-tar creosote. of European workers at Berlin in 1930.^ An outline of the method follows: Wood blocks of a convenient size are impregnated with the toxic agent, usually in solution, and after evaporation of the solvent the blocks are placed in kolle flasks and supported on glass rods set in malt-agar covered with the actively growing mycelia of the test fungus. The conference advised the use of ConiophorQ cerehella as the test A LABORATORY EVALUATION OF WOOD PRESERVATIVES 197 fungus, but suggested that at least two species should be used in each test. After three or four months' exposure to the wood-destroying fungi, the blocks are removed from the flasks, freed from adhering mycelium, and the weights taken before and after the test period used as a measure of the amount of decay. The kolle flask method has much to recommend it, overcoming as it does many of the difficulties inherent in the petri dish technique. However, the test as standardized at Berlin presents serious drawbacks. The kolle flasks are expensive, comparatively fragile, difficult to in Fig. 2 — Assay by kolle flask method. Porta incrassata used in comparison of southern pine heartwood versus sapwood. handle, inconvenient to store, and maintenance of proper moisture conditions is particularly difficult. For really satisfactory results the flasks during the tests should be kept at a constant humidity and temperature. Despite all precautions there is the ever-present danger of excess moisture and resultant lack of decay should the test block touch the agar or any condensed moisture on the flasks. Another unusual problem arose when certain over-ambitious fungi rotted the cotton plugs used to stopper the flasks and even continued to grow into other flasks where they did not belong. 198 BELL SYSTEM TECHNICAL JOURNAL A New Assay Method Both the petri dish and kolle flask methods had shown definite limitations, and it became apparent that further experimentation on a laboratory assay-method should be directed along somewhat different lines. By chance a few treated pieces which had been removed unscathed after a routine exposure in the kolle flask, were dropped on a beakerful of moist wood heavily infected with a wood-destroying fungus. The beaker was merely covered with a watch-glass and set aside. Growth progressed over the treated blocks with unexpected rapidity and vigor, and when removed at the end of three months, the specimens were found to be severely decayed. Occasional results of this character were so encouraging that efforts were renewed to Fig. 3 — Apparatus required for modified wood-block method of assay. develop a technique which would incorporate the use of wood as a secondary substrate together with more favorable moisture control. Experimentation had demonstrated that the amount of moisture in the wood block should be slightly above fibre saturation for optimum growth of the fungus. Inoculated wood placed in air at 100 per cent relative humidity will rot but slowly while too much moisture de- celerates and even inactivates the fungal metabolism. The problem therefore was to bring about these optimum decay conditions with low-priced, easily handled equipment. The test in its present state of evolution is inexpensive, easy to manipulate and capable of increased uniformity due to better regulated moisture conditions. The only A LABORATORY EVALUATION OF WOOD PRESERVATIVES 199 equipment necessary consists of a straight-sided screw-capped bottle about 5 inches high and 2 inches in diameter, a smaller bottle 2.5 inches high and 1 inch in diameter, a wad of cotton, a small flat piece of untreated wood and an applicator such as is used by the medical profession for swabs (Fig. 3). The treated blocks, previously brought to moisture equilibrium, are supported by means of a thin slab of untreated wood on the top of the small bottle which is placed inside the larger screw-topped bottle. Fig. 4 — Assembly of apparatus required for modified wood-block method of assay. Through holes bored in the test piece and the thin slab of supporting wood are passed the pieces of wooden applicator, which act as a means of anchorage and as wicks for conduction of water to the wood under test. Although not absolutely necessary, cotton is usually wrapped around the small bottle to reduce shock during handling. Water is placed in both bottles and after sterilization of the complete set-up (Fig. 4) the thin slab of wood is inoculated with a portion of 200 BELL SYSTEM TECHNICAL JOURNAL hyphae of the test-fungus which has been growing on a malt-agar substratum. The bottles are then placed in an incubation room (Fig. 5) at 26-28° C, customarily for a period of 24 weeks. At the end Fig. 5 — Incubator with tests in progress. of the test period the blocks, freed of adhering mycelium, are again brought to equilibrium at a specified humidity, reweighed and the pieces finally dissected to determine the loss of strength occasioned by the attack of the fungus. A LABORATORY EVALUATION OF WOOD PRESERVATIVES 201 Materials to be tested as possible preservatives are injected in serial concentrations into the blocks of sapwood, commonly southern pine, under conditions simulating as nearly as possible those which would Fig. 6 — Constant humidity chamber filled with test blocks. be used in practice. Due to the variance in the moisture pick-up of wood at different relative humidities, it is necessary to bring the blocks to equilibrium under standard conditions both before and after the 202 BELL SYSTEM TECHNICAL JOURNAL test in order to determine actual weight losses. Since oven-drying is obviously a poor reference standard when volatile materials are under consideration and may also bring about serious changes in the wood, a constant humidity chamber is used for this purpose. An ordinary bacteriological incubator kept at 30° C, fitted with slow-moving fans and a shallow pan containing a saturated solution of common table salt (Fig. 6), has proved to be completely satisfactory in this respect, maintaining a relative humidity of 76 per cent with very little devia- tion. The test pieces after treatment are placed on racks (Fig. 7) and only a few days in the chamber are necessary for equilibration. Such a test method allows of three criteria as the basis for judging the degree of attack. First, there is the amount and vigor of the growth of the test-fungus on the wood block, readings of which are made every four weeks. As this is difficult of expression, recourse is had to the classical method of the serologists, wherein plus four denotes the maximum. An attempt is made to evaluate both vigor and extent Fig. 7 — Test blocks and rack. of the fungal growth; the notation "2-4" would mean that the test block was partly covered with a heavy mycelial mat, whereas "3-2" would mean almost covered with relatively weak growth (Figs. 8 and 9). Often no growth occurs on the test piece and sometimes the mycelial inoculum is actually killed. The second measure of extent of decay is based on the loss of weight, with corrections for the effect of leaching and evaporation during the test period, computed from data obtained on treated controls put through the entire cycle without inoculation. These controls are also of value in the empirical strength rating made at the end of the test when the pieces are dissected in an effort to judge the remaining strength — a rating of ten indicates no detectable loss in strength as compared to the control and zero denotes complete disintegration. Long experience with the petri dish method had emphasized the high degree of specificity of the fungi to various toxics. No single A LABORATORY EVALUATION OF WOOD PRESERVATIVES 203 fungus is equally resistant to all preservatives and gross errors are inevitable unless cognizance is taken of this situation. Since it is impossible to use all the organisms which destroy wood, a choice has been made to include genera which are known to be of considerable Fig. 8 — Assay of a polychlor phenol showing effect of increasing concentration. The test organism Lentinus lepideus. The growth ratings from left to right are 4-4, 3-3, 1-2, and V = no growth on specimen. tv^ Fig. 9 — Same range of concentration as in Figure 8 with U-10 as test fungus. The growth ratings from left to right are 4-4, 3-4, 1-3 and 1-2. economic importance in the decay of timber or which have been encountered in the actual decay of telephone poles, being sure to include in any given test the fungi which past experience has shown to be resistant to the type of preservative under consideration. Four 204 BELL SYSTEM TECHNICAL JOURNAL organisms in duplicate are used in each test (Fig. 10). Lentinus lepideus, cited by Buller,^ Snell ^ and Humphrey ^ and isolated several times from posts in the Gulf port, Mississippi, test plot,^ as well as from poles in service, is used in all cases of organic preservatives, but is seldom used against metallic salts, to which it is extremely sensitive. Lenzites trabea, another species of great economic importance, Hubert,* and also isolated several times from rotted southern pine poles, is somewhat parallel in resistance to Lentinus lepideus, but produces a markedly different type of decay. Polyporus vaporarius, Porta in- crassata, and Coniophora cerebella, the common "dry rots," although easily killed by many hydrocarbons, are resistant to most inorganic compounds, and at least one of these organisms is included in each test on such materials. Fomes roseus, another fungus of wide dis- tribution, reacts in a most inconsistent manner, but its occasional specific virulence is sufficient to warrant its inclusion in all assays of Fig. 10.^ — Assay of worthless preservative at maximum concentration. The fungi in dupUcate from left to right are Lenzites trabea, U-10, Fomes roseus aiul Leniinns lepideus. new and unusual preservatives. Unfortunately the fastest and most versatile decay organism used has no name and masquerades under the designation U (unknown)-lO. Isolated several years ago from a decayed pine pole, the identity of U-10 is still a mystery, despite the efforts of many mycological authorities. U-10 is included in every test and is especially valuable when a quick indication of the value of a new preservative is needed, as it is capable of producing an appreci- able weight loss in about three months. In addition to the above fungi occasional use is made of such common wood-destroyers as Trametes serialis, Lenzites sepiaria, Polystictus versicolor, Polyporus sulphureus, and Fomes pinicola. At the present stage of development this wood block method tells nothing directly about the ability of a wood preservative to resist the action of termites. Most materials which inhibit decay also prevent A LABORATORY EVALUATION OF WOOD PRESERVATIVES 205 termite attack. In addition all promising leads are verified by means of the sapling test ^ at Gulfport, Mississippi, and here Nature has provided a bountiful supply of these industrious insects. Fig. 11; — Growth on southern pine sapwood controls. From left to right; Polyporus sulphureus, Polyporus vaporarius, Polystictus hirsutus and U-10. Fig. 12 — Growth on southern pine sapwood controls. Lenzites trabea, Fomes roseus, U-10 and Lentinus lepideus. Experimental Results The above-mentioned fungi have been tested on untreated southern pine sapwood in order to set up standards of comparison (Figs. 11 and 12). Table I shows individual weight and strength losses effected by our most commonly used organisms in the regular 24-week period. Considerable decay with many of these fungi occurs in a somewhat 206 BELL SYSTEM TECHNICAL JOURNAL H o % o u c K O o V u ■ - ^ 03 0) 0 (« OJ "3 "O >^'? Sy S c >. 3 -0 g 0 0 TS"^ 1! ^ ?J 03 P +-" biO-'-' ■M 0 4-1 .4-> 3 33 3 ii 3 3 0 0 0 0 0 0 0 0 J5 U4= 43 -c jr bo ^ bC t* "5 « taO M 3 -^^ 3 3 rt u 3 3 a 2 ^^S 0 - ^ 0 0 u C C u u y ■5 S:S _C .2.9 J3 ji: ra ■M -W Ol a.> Q >> -0 >, >. c .0 o! 03 >N4J >> S 1 -o s 2 1 1 be bO 03 3 0) , u 0 u 1 >>> > 2:> ti 1 1 1 .5000 "^ "5 "5 "5 !5!2 >N-£^ o) c; a> *"• 03 "^ 03 -o Ij-o 'o 4= oj 1 1 1 t-^-o^ -a 03 TJ u 3 JJ 3 3 S ^ CO tn y 3 ^^30 03 0 03 D '-' 4> 0 ^-U J2 cti ji: 0 # -^lO-* ^^^^ 0000 CnI ro CN ■^ rt< so -* ^ C o oJ " "D u 4J 0 1 Zi •0 ? >"•£ — a, 0 -^ 00 f^ fo -^ p "* 10 r^ 00 in •-^_ >n — ; ro '^ '". '^. '^\ ^O aj a; u M 0 0 1-^ -^ 06 On 0 On ■^' -H 0 10 to -^ t^ 00 d r *- 0 vO \o >o vq SO IT) On * m -H ro ^ — iro SO SO ■^ 00 p p OS OS Os On On On P p On On p p 00 00 00 l^ Os On CN csi T^ -rt' ^^^^ CN CS ■^ ■^ cnJ tsi ^ .^' ^ ^ ^ ^" (LI •^ 10 »o 0 int-- CM -H fo m 0 00 CM (r> r~ On CN -H OOSO ■5 " rq fO CN C^_ csj CN OJ rsi ro ro CN >-H CO a 0 s 8 S 0 8 1 0 Kq tt, ^3 *^ a. A LABORATORY EVALUATION OF WOOD PRESERVATIVES 207 shorter time, but experience has shown that more consistent results are obtained with the longer period. This is especially true in the case of materials of moderate toxicity, wherein often little growth is seen for two or three months, after which the fungus may become established and rot the test piece. Using the routine technique, volatile compounds are often found to be practically worthless. This is true of naphthalene, for instance, but when special precautions are taken to insure its presence during the exposure to the fungus, the effective toxicity of this hydrocarbon cannot be questioned. Analysis of control blocks proved that the naphthalene had evaporated quite completely from the test piece even before sterilization. This difficulty can be surmounted satisfactorily in the case of a single compound by injecting a generous quantity and determining the actual amounts of material present from equilibrium weights of the test pieces before treatment and just prior to inoculation. Steam sterilization, of course, would introduce errors under such circumstances, and while the risk of contamination with foreign organisms is high, satisfactory results have been obtained with un- sterilized blocks. In the case of volatile mixtures a similar procedure permits the knowledge of the total evaporation before inoculation, but determination of the loss of the individual constituents is practically impossible. For all relatively volatile preservatives such as creosotes, the regular method including sterilization can in a way be considered a permanency test. Fortunately this evaporative loss is in the same order of magnitude as that encountered in the field after an exposure of several years, and correlation with outdoor tests is unexpectedly good. Closer control of the amount evaporated would be desirable, but experience has shown this to be difficult of consistent attainment. Artificial weathering machines such as that described by Gillander, Rhodes, King and Roche ^° constitute a reasonably successful attempt to reproduce natural conditions. Leaching is more easily controlled and duplicated than evaporation, and preservatives which by their nature might be considered to be water soluble are subjected to a standard leaching cycle if the initial test has shown them to be promising. Again the close correlation of field results with the labora- tory is gratifying. Of necessity, details of technique have been only sketchily reviewed in this paper ; information as to the exact procedure will soon be avail- able in the chemical press together with complete results on several preservatives of interest. Table II contains the results of an assay on a supposedly permanent inorganic preservative before and after 208 BELL SYSTEM TECHNICAL JOURNAL u Q^ Oh ^^ r 1— 1 u >j w CQ _J '►J CQ (-) < t/2 H z 73 Control Weight Loss in Per Cent "tt -^6 ■*o 66 ^o (DO oo 66 ooo 1^6 ts -if ri<6 ao <66 coo 66 oo d<6 22 OOO oo 2"* o — d to tn.S.S °il •2 oo> OOO ©o> OTJ. ON o o ■C5. ^ -OtN 19 tso; Ot-; OOO o r)!-; r^t-^ -n 6>'> 6CS o4 6fO ©2 6>o ■«>, c^ o >7 to >7 >7 >7 >7 >T >7 >T >T ^ i^ •* 4- 22 Ol^ o^ o-o oo C bfl i.S.S °^^ oa o>o 2"* oo oo ^ r^oo 91 O;oo o-* OCN o -•S S Qo6 ri'd 6"i 6f^ 6od 1 .Sf ">o ■o ',-> T).q Ol O; •«j.t^ od d>di ovo ^ '^ lO t •5" >7 >7 >T >? >t ?-B r^ CO 't t >7 >7 >T >T ri-f 1 1 (S fo CO •* -- t 22 o o- 22 OtS OtN C be M.2.S °^i3 22 Ot- 22 ot OvO rfS 9^ -U w r^ CNO •*Q0 OlO o>o ^ :5.sg Tf ^ «-H ^ o<6 --Jco Ovj a (N cs o ro » rot^ ■j: >7 >7 —ICO J. 4. >7 >7 >T >7 >7 r^ ro t ■* 22 O 00 O VO OCS o- C M '-' '-' •-' m.2.S °§5 o 2^ OCN OOO 0\0 Oco a ^ ^0 -i; ■*ir) m ■* TfO OOO a s.sg t~^ *-H CN t-^ •^6 oo 6cN s m CO *** OOO 1 fi ■*1 qvo OOv .a ro-* CS ^ 6"i 6co 6(N '^ ts ^ tifl >T >7 >7 >Y i I ^■B ■>* r<5 ■* ■* — ■ t £ « >7 >7 >7 >7 >t ■* fo ■* •* t c C I- -w 2S.8 ■d"^ d"^ ';3'o -i'o ■z"^ ^»(2 ro OJ 03 !y OJ (y OJ ^ Cu o C^ as: as: C J= s'i :5^ '^^ ii"^ 55^ t- ai k. m I- o; U V 1- o tM -- 6 6 6 c 'a (U C bO = o tn Hr LABORATORY EVALUATION OF WOOD PRESERVATIVES 209 < > 1/1 M 0L, < H •a 1 I' ^ OOroiOOOO O 00 i^ Ov O O CM -^ W.2.S n u 03 mP^ ^ \0 ^O 00 f^ »o S _j_, O (M On t-^ O; t-^ !^ s.sg bfodfo IN d S Mm(J •«i m L-) Ov ^ "^ Ov r^ i ►^ A M < 1 1 1 1 1 11 (N -^ ■<* ■* -^ \ CS CS (N 't ^O ^ «* 0 0^ O fO •^ a M ^^ m.2.S Of^ O^^"^ "^ ^ Tt> •*« O V- ^ C) vO t^ •"* o\ S o ^^^ do^di~ --^ te. 1 --, ^ ro — -«• ■* A M <' 1 1 1 1 1 ^ •* m -t ■* --. rf rf ■* ^ ^ OP^ 1 1 1 1 t 1 O r^ NO NO O' t^ C M '^ m 2.S ■•^11 s On NO »0 lO On '^i* ^ r~-3 j3 M 1 1 1 1 1 ' Tt< Tf •* '^ ^ ■* c (3 Ih -w O JJ O •5 '^.'^ to 't NO ^lO Q looq nOcsno CI §2 So 3 (sdoONO "^(N nfH ^ c(So o O -O O C ^ tn 2 Oi > 210 BELL SYSTEM TECHNICAL JOURNAL ■-J w •T3 Control Weight Loss in Per Cent 1.4 0.8 0.6 0.3 0.3 0.1 0.1 0.0 [3 oooo 4-> .Mm (J 1.3 0.9 0.0 0.0 2.1 0.0 30.8 12.1 .G M II 3-2 2-1 3-2 2-1 4-4 4-4 0 1 C M m.2.S 00 — 0 ■y.c c Mm (J 0.9 0.9 1.0 0.5 38.9 36.1 44.3 32.1 -2 M 6S, 1-1 V 1-1 V 4-4 4-4 4-4 4-4 0 0 e M i.S.S mtlH OOt^O 0 OvO-* Mmcj ^ 0 u 1.3 0.9 3.2 1.5 8.8 6.5 19.4 13.3 J= M 0^ 3-1 2-1 2-2 3-2 4-4 4-4 s .a a ►~1 C M m.2 S oo^ooio OO>00iO 2.7 1.9 2.6 1.8 2.7 2.7 12.6 11.4 2-2 2-2 3-1 3-2 4-2 4-2 4-3 4-3 c 2K8 M mb COhU 0 0 M0v*O» OOCSKNO 4) "- a •S E |a J- in -C C -o o C '-' en 0 ■2 II J Q CO w Q Z Q O o U •a V § a 1 OM-^ odd + -*ooo d>od ++ 0 a >3 C3 M m.2.H 000 000 £.SS Mmu •*-*o ddd ++ -* -*o o<6d ++ OPS 1 1 1 fO fO fO 1 1 1 0 1 ID i.2.S 000 222 ©•*Ov odd + 0*0 ddd + -C (30 'II 1 1 1 1 1 1 a 0 1 0 i.2.S 222 222 :s.sg MmU O-^OO ddd + 00O-* dd'^ 5 M II OPS --■•-Its -H— -M 1 1 1 3 a .a R ►3 i.i.S 222 222 .£f "O ■*•*■* dd-^ + dd-^ + OPS 11^ c c 0 1. c a C c U u 4-t OJ 0 ao m(^ T3 u £5 OO-H Ov CS MO .S.S -o"o o o rt r- U > C bo =•0 •S II A LABORATORY EVALUATION OF WOOD PRESERVATIVES 211 leaching. The losses in weight on the unleached specimens are also present in the controls and are presumably due to an extremely soluble non-toxic salt known to be present. Analysis of the leach waters indicates that the toxic substances were also slowly but definitely soluble. Field results on this same preservative were favorable for a year, but considerable decay was found the second year in all but the two highest concentrations. Table III presents the results obtained with a well-known proprietary preservative of the organic type. The concentrations given are for the preservative as purchased, which consists of a 25 per cent solution of solids in a volatile solvent. This solvent was allowed to evaporate completely before exposure of the test blocks to the fungus. For comparative purposes Table IV illustrates a test of a typical coal-tar creosote. Included as a matter of special interest, Table V outlines the wood-block assay on a material which the petri dish method indicated to be worthless. This adaptation of the kolle flask method has been in constant use more or less in its present form for the past three years. Hundreds of complete assays have been made with results to date in good agree- ment with the slower and more expensive outdoor tests. By the use of a range of concentrations the relative efficacy of various preserva- tives can be judged, but definite expressions of the absolute value of any preservative have been avoided. With conditions controlled for maximum decay, this test is admittedly severe. This very severity, however, is probably an asset in the elimination at the outset of the poor and mediocre materials unworthy of further study. Bibliography 1. Richards, C. A. — "Methods cf Testing Relative Toxicity," Proc. Amer. Wood Pres. Assoc, 19 (1923). 2. Schmitz, H. — "Laboratory Methods of Testing the Toxicity of Wood Preserva- tives," Indus. &■ Engg. Chem., Analytical Ed., 1, 76-79 (1929). 3. Liese, J. et al. — "Toximetrische Bestimmung von Holzkonservierungs Mitteln." Z.f. Angew. Chem., 48, 21 (1935). 4. Buller, A. H. R. — "The Destruction of Paving Blocks by the Fungus Lentinus Lepideus," Jour. Econ. Biol., 1, 101-138 (1905). 5. Snell, W. H. — "Studies of Certain Fungi of Economic Importance in the Decay of Building Timbers," U. S. Dept. Agr. Bull., 1053, 1-47 (1922). 6. Humphrey, C. J. — "Timber Storage Conditions in the Eastern and Southern States with Reference to Decay Problems," U. S. Dept. Agr. Bull., 510, 1-42 (1917). 7. Lumsden, G. Q. — "Proving Grounds for Telephone Poles," Bell Laboratories Record, 2, 9-14 (1932). 8. Hubert, E. E.— "Outline of Forest Pathology," 416 (1931), John Wiley & Sons, Inc., New York. 9. Waterman, R. E. and Williams, R. R. — "Small Sapling Method of Evaluating Wood Preservatives," Indus. & Engg. Chem., Analytical Ed., 6, 413-19 (1934). 10. Gillander, H. E., King, C. G., Rhodes, E. O., and Roche, J. N.— "The Weather- ing of Creosote," Indus. &• Engg. Chem., 26, 175-183 (1934). study of Magnetic Losses at Low Flux Densities in Permalloy Sheet* By W. B. ELLWOOD and V. E. LEGG Energy losses in ferromagnetic materials subject to alternating fields have long been considered as due solely to hysteresis and eddy currents. However, at the low flux densities encountered in certain communication apparatus, a further loss is observed which has been variously termed "residual," "magnetic viscosity," or "square law hysteresis." The search for an explanation of this loss has led to precise measurements of hysteresis loops with a vacuum ballistic galvanometer, and of a.-c. losses with inductance bridges. From these results, it appears that that part of the a.-c. effective resistance of a coil on a ferromagnetic core which is proportional to the coil current is strictly identified with the hysteresis loop area as measured by a ballistic galvanometer, or as indicated by harmonic generation in the coil. The hysteresis loop can now be constructed in detail as to size and skewness on the basis of a.-c. bridge measure- ments. This conclusion was reached previously on a compressed iron powder core, and is now confirmed on an annealed laminated 35 per cent nickel-iron core. Observed eddy current losses for this core exceed those calculated from classical theory by 20 per cent. This excess is ascribed to the presence of low permeability surface layers on the sheet magnetic material. The a.-c. residual loss per cycle (nominally independent of frequency, like hysteresis) is not ob- served by ballistic galvanometer measurements, although it indi- cates an energy loss some eight times the hysteresis loss for the smallest loop measured {Bm = 1.3 gauss). Analysis of the residual loss shows that it increases with frequency up to about 500 cycles, and remains constant at higher frequencies (to 10,000 cycles per second). Concurrently with the increase of residual loss, the per- meability of the alloy is observed to decline with increasing fre- quency about 1 per cent below the value predicted from eddy current shielding. This effect is most noticeable at frequencies below 1000 cycles. THE search for an explanation of the excessive magnetic losses observed at low flux densities by alternating current bridge measurement as compared with theoretical indications based on direct- current measurements has led to a more accurate review of both types of measurement.^' ^' ^ The a.-c. energy loss per cycle which has re- * To be published in May 1937 issue of Jour, of Applied Physics. 1 W. B. Ellwood, Physics, 6, 215 (1935). 2 V. E. Legg, Bell SysL Tech. Jour., 15, 39 (1936). 3 W. B. Ellwood, Rev. Sci. Inst., 5, 301 (1934). 212 MAGNETIC LOSSES AT LOW FLUX DENSITIES 213 ceived most study is the "residual" or "viscosity" loss.^ It appears related to hysteresis loss because it is nominally independent of fre- quency, but it differs in being proportional to Bm^ instead of Bm^ which would be required by Rayleigh's law for hysteresis loops. Any satis- factory investigation of this anomalous loss demands precise determina- tion of its value, and of its variation with frequency. For this purpose, ballistic galvanometer measurements of the hysteresis loop have been made and compared with bridge measurements of a well annealed 35 permalloy laminated core. In a previous paper, the magnetic properties of a ring of compressed powdered iron were studied at low flux densities using a sensitive vacuum galvanometer ^ and a multiple swing ballistic method.^ Hysteresis loops were measured at flux densities Bm ranging from 1.8 to 115 gauss, which showed energy losses proportional to Bm^ in ac- cordance with Rayleigh's law. Alternating-current measurements agreed with the ballistic measurements as to the magnitude of the energy loss and the proportionality to B^^, but in addition showed a residual loss proportional to Bm"^ which was of the same order of magni- tude as the Rayleigh hysteresis at these low flux densities. The analysis of measurements made on the compressed dust core was complicated by the inhomogeneous structure, by the variety of particle shapes and thickness of insulation, and by the mechanical stresses inci- dent to forming the core. To eliminate these objections, the present study was undertaken using a core consisting of well annealed sheet material, for which eddy current losses can be calculated by classical formulae. Selection of Material Considerable a.-c. data were at hand from which to select material for this experiment. The properties of a few representative materials are given in Table I. The constants are defined by the equation = aBm -\- ef -\- c = ^-T- , (1) where R/ is the difference between the resistances measured with a.-c. and with d.-c. on a toroidal coil with inductance of L/ due to core ma- terial of permeability Hm, when the maximum flux density is ± Bm and the frequency is / cycles per second. Here the hysteresis coefficient * H. Jordan, E. N. T., 1, 7 (1924); H. Wittke, Ann. d. Phys. (5) 23, 442 (1935); F. Preisach, Zeit.f. Phys., 94, 277 (1935); R. Goldschmidt, Zeit.f. tech. Phys., 13, 534 (1932). 214 BELL SYSTEM TECHNICAL JOURNAL is a, the eddy current coefficient e, and the residual loss term is c. W is the energy loss per cycle in ergs/cm^ of core material. The permeability coefficient X = (mw — noJlfxoBm. Table I shows that annealed 35 permalloy in sheet form has the most convenient values of Br and c/a for further study of this effect. This alloy is of the face centered cubic lattice type common to a large class of magnetic alloys. The numerals preceding the various permalloys give the nickel or alloy percentages, as classified by G. W. Elmen.^ The measurement of magnetic losses of 35 permalloy involved further refinements in technique. The high initial permeability required the construction of a special air core mutual inductance to simplify the TABLE I Material Initial Permeability X X 10* c X 106 a X 106 da Br* X 10^. Compressed Powder Cores Grade B Iron 35 75 7.0 1.8 no 40 50. 5.5 2.2 7.3 13. 81 Permalloy 3.1 Laminated Cores 35 Permalloy, Annealed 1660 30. 60 5.0 12. 62. 38 Permalloy, Hard 100 7.0 118 9.6 12. 7.2 38 Permalloy, 800° Annealed . 1330 9.0 27 1.5 18. 15. 40 Permalloy, 1000° Annealed 2060 12.0 20 1.4 14. 22. 45 Permalloy, Annealed 2550 5.4 14 .43 33. 8.2 78.5 Permalloy, Annealed. . . . 3900 8.1 0 0.6 0 18. 2.4-78 Cr Permalloy, Annealed 14600 6.4 3 .07 43. 7.6 8-79 Cr Permalloy, Annealed . 3025 31. 14 2.6 5.4 60. 45-25 Perminvar, Annealed . . 450 0.02 0.0 .002 — 0.0 * These values of remanence were computed from Rayleigh's law as 3aiJi.oB,J/l6 for Bm = 2. measuring circuit and increase its stability. The high rate of change of permeability with temperature made it necessary to enclose both the specimen and the air core mutual inductance in a constant tem- perature box (at 37.1 ± 0.01° C.) throughout the tests. The Specimen The material was melted in a high-frequency furnace, cast, and cold-rolled with intermediate annealings, to strip of thickness / = 0.0160 cm. and width 7.62 cm. Analysis showed the following composition; Ni, 35.00 per cent; Fe, 64.25 per cent; Mn, 0.40 per cent; S, 0.030 per cent; Si, 0.02 per cent; C, 0.01 per cent. The resistivity p was 82.2 micro-ohm-cms. at 37.1" C. The strip was wound into a tight ^ Electrical Engineering, 54, 1292 (1935). MAGNETIC LOSSES AT LOW FLUX DENSITIES 215 spiral core with successive turns insulated from each other by painting with a suspension of fine quartz powder in CCI4 immediately prior to winding. The core had an effective magnetic diameter c^ = 11.22 cm., and cross-sectional area of alloy A = 3.96 cm.-. It was annealed in pure hydrogen for one hour at a temperature of 1000° C. In order to protect the annealed core from mechanical stress during subsequent winding, it was placed on felt in an annular bakelite box which held it without constraint. The box was wound with a 20-turn magnetizing coil using a flat tape composed of 28 parallel strands of insulated wires connected together at the ends. This winding prac- tically covered the box with a single layer of wire, and gave a uniform magnetizing force. It was employed as the magnetizing coil in both the ballistic and the a.-c. bridge measurements. For the ballistic SHIELD ^G ^ Sa MUTUAL ^a p f-vw '\mJ jwn ■wv Rs I TO I POTENTIOMETER Fig. 1 — Ballistic galvanometer circuit, showing adjustable air-core mutual inductance in series-opposition with the test coil. tests, a layer of insulation was applied over the primary winding before applying the secondary winding. This insulation consisted of two wrappings of silk tape interspersed with a tinfoil sheath which formed a grounded electrostatic shield between the secondary and the primary winding. The foil was cut to avoid a short-circuited turn. The toroidal secondary winding consisted of 5000 turns No. 19 silk-covered enamelled copper wire. D.-C. Apparatus In the former experiment,^ the specimen was compared with a fixed air core mutual inductance in terms of the galvanometer deflection and the primary currents required to obtain approximate balance. For this experiment, the circuit was modified so that the same current flowed in the primaries of both the specimen and the air core mutual (Fig. 1). Thus variable thermal effects in the primary circuits were 216 BELL SYSTEM TECHNICAL JOURNAL eliminated and the measuring technique simplified. This required that the mutual inductance be adjustable so as to bring the unbalance onto the galvanometer scale. The mutual inductance (approximately 0.260 henrys) was con- structed for convenience in four separate sections. Each section had a hard wood toroidal core, a low resistance toroidal secondary winding, an inter-winding shield, and sectionalized primary windings on the outside. The secondary windings were connected in series with the galvanometer by a twisted shielded pair of wires. The primary wind- ing groups were also connected in series, and adjusted so that the com- bination resulted in a mutual inductance of the right value to obtain balance. To eliminate humidity as a source of error each coil was painted with cellulose acetate, covered with silk tape, painted again, baked 48 hours at 108° C. and finally potted in Superla wax in an earthenware jar with only the tops of the terminals exposed. All con- nections were made by soldering. During the measurements, the maximum primary current corre- sponding to Hm was held constant to 0.01 per cent by comparing the voltage drop across Rs with a battery of Weston standard cells. Switching was automatically performed by a photocell and selector switch mechanism previously described ^' ^ but not shown here. These operated switches 5 and Si at the proper time and in the right order. The difference in flux turns between the air core mutual in- ductance and the specimen was determined in terms of the ultimate galvanometer deflection as before. From this the difference in B between the side of the hysteresis loop and a straight line drawn through its tips could be computed for a given H. A number of values of this difference A5 were thus determined for different values of H, and plotted to give the hysteresis loop. A.-C. Apparatus In order to compare results obtained by the vacuum ballistic gal- vanometer with those obtained with alternating currents, bridge measurements of resistance and inductance were made over the same range of flux densities at a number of frequencies ranging from 35 to 1 0,000 cylces. The secondary winding was removed and the special 20- turn primary winding used for most of the measurements. Later an addi- tional 60-turn winding was used for checking the measurements in the low-frequency range. In either case the inductance was low enough to depress any effect of distributed capacitance far below the precision of the measurements. Measurements were made on a 10-ohm equal ratio arm inductance MAGNETIC LOSSES AT LOW FLUX DENSITIES 217 comparison bridge,^ and were verified at low frequencies using a 1-ohm ratio arm bridge. Calibration of the bridge and standard coils was efifected by making measurements over the entire frequency range on a calibrated high quality air core coil substituted for the test coil. The maximum correction required on this account was approximately 0.1 per cent of the resistance due to the magnetic core. The source of alternating current was an oscillator-amplifier supply- ing approximately 0.4 watt undistorted power, calibrated for these measurements against the Laboratories' standard frequency. The current was adjusted by the insertion of resistance in series with the 5 6 7 8 9 H IN OERSTEADS X 10^ Fig. 2 — Core permeability as measured by the ballistic galvanometer. primary of the bridge input transformer, and was measured by means of a thermocouple between the transformer secondary and the bridge. The bridge unbalance was amplified by means of an impedance coupled amplifier for the 10-ohm bridge, and by means of a resistance coupled amplifier for the 1-ohm bridge. The amplified unbalance was observed by means of head phones at frequencies above 200 cycles, and by means of a vibration galvanometer at lower frequencies. The d.-c. balance required bridge current of about 3 m.a. in the test coil winding, and had the same precision as the a.-c. balance, viz., db 0.0002 ohm. The inductance readings were corrected for the air space within the winding, and had a relative accuracy of about 0.03 per cent, and an absolute accuracy of approximately 0.1 per cent. 218 BELL SYSTEM TECHNICAL JOURNAL D.-C. Results The permeability n = BmjHm of the specimen is shown as a function of Hm in Fig. 2, on a greatly enlarged scale in which the zero of per- meability is not shown. The slope of this line gives X = 21.5 X 10~^. Values of ^B are plotted against // for two different hysteresis loops in Fig. 3, from the area of which the energy loss W is computed. For Z 120 ^^ —•^r^ ^/\ \ / / ' \ >, / / \ \ y \ \ A / RAYLEIGH / / \ ^ \ OBSERVED LOOP / / 1 / \ LOOP 1 \ \ t / \ \ 1 / \ \ 1 / \ \ 1 J \ ^ I 1 1 \ \ 1 1 1 1 \ \ \ 1 \ 1 1 Bm IN GAUSS CURVE 1 CURVE 2 5.35 2.67 \ \ 1 1 1 \ \ 1 Hm IN OERSTEDS 0.00288 0.00145 \ \ 1 W IN ERGS/CC/CYCLE Bm 15X10-6 1.84X10-6 \ \ 1 1 211 423 \ ' 1 1 Br \ ^ 1 1 \ 1 1 \ 1 I J ' 2 \ \ i / ^ y > s\ \\ / / /. \\ \\ / / / V \\ / / ' J \ \\ / / k / / ; \ / n // '\. / / \ < \\ / \ /^ \ { \ -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 H IN OERSTEDS X 10"* Fig. 3 — Two hysteresis (half) loops plotted with reference to a straight line through their tips. comparison, Rayleigh loops are shown as broken lines. By analysis of the interior angles 0+ and _ between the AB vs. H curve and the // axis at points -j- H and — // respectively, it is found that += nokBm, while 0_ is a corresponding amount smaller than for MAGNETIC LOSSES AT LOW FLUX DENSITIES 219 the Rayleigh loop. The hysteresis coefficient a and the permeability coefficient, X are related by the equation a = SX/S/j. for a loop having parabolic shape, in which case the interior angles are equal, and tan 4>-i-= iJ-oXBm. Since the latter equation applies for 0+ only, on the observed skewed loop, it follows that the Rayleigh relation between a and. X is more or less inaccurate. In fact, the ratio of 8X/3;u to a is a measure of the skewness of the loop. For the present material, this ratio is about 1.15. This result is in accord with our previous data, but was evidently not noted by Rayleigh because the free poles in his magnetic circuit tended to mask the asymmetry. The fact that these hysteresis loops are slightly skewed shows that those processes which produce the familiar ^-shaped loop at high flux densities are already present at these low flux densities. Despite a skewed shape, the area of the observed loop approximates closely the area of a parabola drawn through the remanence and the tips. Hence, supplementary values of energy loss W were obtained from remanence observations at several values of Hm, using the formula W = 2BrH„J3ir. The slenderness factor of the loops may be measured by the ratio Bm/Br, which varies from 211 to 890 for the different loops studied. The a.-c. resistance introduced by the hysteresis loss of the core material yields the ratio SttPF/^^^, as noted in Eq. (1). Values of this quantity computed from the areas of the loops of Fig. 3. and from remanence determinations are plotted in Fig. 4, They agree closely with the aB,n term of Eq. (1) obtained by a.-c. measurements, as shown by the solid line in Fig. 4. The sum of c + aBm is shown by the broken line. It is evident that the ballistic galvanometer gives no indication of residual loss. It is interesting to note that the hysteresis loop at low flux densities can now be constructed in detail using the data obtained from a.-c. measurements. The remanence is Br = j^a/jioBrJ and tan 4>+ = ixoXBm. The angle included between the upper and lower branches of the loop at the tips is {4>+ + (/>_) and is given by the equation tan [|(<^+ + 4>-)~\ = s/i oaBm. A.-C. Results Values of R/ and Lf were measured as a function of the current at fixed frequencies. The values of Rf/umfL/ are plotted in Fig. 5 as a function of current with frequency as a parameter. In order to shorten the vertical scale, the appropriate ordinates are indicated in connection with each line. These form a family of straight lines parallel to one another. This shows that the hysteresis coefficient is practically a 220 BELL SYSTEM TECHNICAL JOURNAL constant over the low flux density range for all frequencies. From the slope of these straight lines the hysteresis coefficient a of eq. (1) is calculated to be 2.6 X 10~^ which agrees with the value 2.53 X 10~^ 34 32 28 22 £ CO / / / / / / / / f / / / / / / / / / / 'c + aBm / / / / / / / / /8TTW_ _„ / } r / A / / / t o BALLISTIC LOOPS, INTEGRATED AREA • BALLISTIC LOOPS 8TTW_ 16 Br B^ 3^ Bm / / / / / / 4 5 6 7 8 9 10 FLUX DENSITY IN GAUSS (Bm) Fig. 4 — Comparison of ballistic galvanometer and a.-c. determinations of hysteresis loss. Note absence of residual loss from ballistic observations. computed from the ballistic tests. The divergence of the data from linearity at higher currents is shown by the dotted curves, which indi- cate divergence of the hysteresis loop from the Rayleigh form at higher flux densities. MAGNETIC LOSSES AT LOW FLUX DENSITIES 221 3 4 5 6 7 8 9 COIL CURRENT IN MILLIAMPERES Fig. 5 — A.-c. bridge values of R/li^mfLf vs. coil current of various frequencies. Slope of the straight parallel lines gives the hysteresis coefticient a. 222 BELL SYSTEM TECHNICAL JOURNAL Further information on hysteresis loss is obtained from measure- ments of harmonic voltages generated in the coil winding when there is current /i of frequency /. It has been shown ^ that the third harmonic voltage for materials with Rayleigh hysteresis loops is £3 = 0.6 aB„iiJLmL,„fIi, from which the hysteresis coefficient is a = 25 Es Ad X 10-3 3//i2\ IfiJLJ Measurements of third harmonic voltages have been made on the coil described in this paper by P. A. Reiling and the results are shown in Table II. TABLE II /i £3 a X 106 f /: E, a X 106 1000 2.0 .0168 2.2 100 3.0 .00447 2.6 5.0 .133 2.8 5.0 .0106 2.2 10.0 .55 2.9 10.0 16.8 .0473 .1497 2.5 2.8 400 1.41 .00335 2.2 2.0 .00709 2.3 75 8.0 .0199 2.2 3.0 .0158 2.3 10.0 .0335 2.3 5.0 .0457 2.4 18.2 .112 2.4 10.0 .195 2.5 50 10.0 .0359 3.7 The values of a thus obtained show no consistent variation with current or frequency. They give an average value of 2.5 X 10~^, which is in close agreement with the ballistic and a.-c. bridge results. It therefore appears that that part of the effective resistance which is proportional to current is identifiable with hysteresis loss as obtained by ballistic means, and with that which generates harmonic voltages. The intercepts for / = 0 in Fig. 5 are therefore due to eddy current and any residual losses. They have been plotted against frequency in Fig. 6. The line through these points is generally assumed to be straight, and the eddy current and residual loss coefficients are derived from its slope and intercept. It appears, however, that this line is not strictly straight, but has a somewhat steeper slope at lower frequencies, so that the ordinary graphical method of loss separation fails. An analytical separation of losses can be made for any frequency interval by returning to the values of Rf/nofLf as obtained from Fig. 5, « E. Peterson, Bell Syst. Tech. Jour., 7, 762 (1928). MAGNETIC LOSSES AT LOW FLUX DENSITIES 223 subtracting the value at /i from that at fi and dividing by the frequency interval fi — /i to give the eddy current coefficient e of equation (1).' Figure 6 gives e thus derived, as a function of /, showing a value ap- proximately 20 per cent higher than calculated from the relation e = 4:Tr^t^/3p at frequencies above 500 cycles, and progressively higher as the frequency approaches zero. The fact that e is larger than predictable from classical theory has been ascribed to the presence of a low permeability surface skin on 500 75 25 J Y/ // / J J / ® r 200 400 600 FREQUENCY e,FROM SLOPE OF - — g 154.5 X 10" 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10,000 11,000 FREQUENCY IN CYCLES PER SECOND Fig. 6 — Intercepts of Fig. 5 vs. frequency. Slope of the curve gives eddy current coefficient e. Residual loss coefficient c varies with frequency near/=0. practically all materials which have been reduced to sheet or wire form by mechanical deformation.^ But since the eddy current coefficient depends only on the resistivity and effective thickness of the material, any apparent variation of e with frequency can only be interpreted as an indication that the residual loss is varying with frequency. Taking the value of e = 154.5 X 10~^ characteristic of the higher frequencies, the eddy current loss per cycle has been calculated, and is indicated in Fig. 6. The amount by which the observed loss exceeds ^ Correction terms must be included at higher frequencies to take account of eddy current shielding as noted in ref. 2. 8E. Peterson and L. R. Wrathall, /. R. E. Proc, 24, 275 (1936). 224 BELL SYSTEM TECHNICAL JOURNAL the calculated eddy current loss gives the residual loss coefificient c. Thus, the value of c is found to be a constant 20 X 10~^ at frequencies above 500 cycles, but to decline toward zero as the frequency approaches zero, in evident accord with the ballistic galvanometer result. The inductance due to the core shows a similar frequency effect. The observed inductances for the 20-turn winding are given in Fig. 7. The values at each frequency for the various currents fall on a straight 1.02 3 4 5 6 7 COIL CURRENT IN MILLIAMPERES Fig. 7 — Inductance observed on 20 turn coil, at various frequencies. line, the slope of which gives the permeability coefficient, X = 19.6 X 10~^, for the lower frequencies where eddy current shielding can be neglected. The values of L for / = 0, obtained from Fig. 7, are plotted against frequency in Fig. 8. The most remarkable feature of this curve is the decline of inductance (or apparent permeability) of about 1 per cent at low frequencies, where very little decrease on account of eddy current shielding is to be expected. The characteristic shielding curve has been MAGNETIC LOSSES AT LOW FLUX DENSITIES 225 computed using the value of e obtained from the resistance measure- ments in the relation L _ 1 sinh d + sin 6 Lo 6 cosh 6 -\- cos d ^ 30 "^ 732 where d = V3gMo//7r. Using the values of L/Lo thus computed, the effect of eddy current shielding was eliminated from the observed values, and the results plotted in the upper curve in Fig. 8, showing a rapid J=-0.90 1 ^ ?^ 1 L. X ' EDDY CURRENT SHIELDING ELIMINATED ^ \^ ^v N K^ \, \ ^ CALCULATED, EDDY CURRENT SHIELDING s. FOR e = 154.5 X I0"9 \ ^ OBSERVED , \ INCLUDING EDDY \ CURRENT SHIELDING ^ \ ^ \ \ \ \ \\ \ 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10,000 11,000 FREQUENCY IN CYCLES PER SECOND Fig. 8 — L/Lo from intercepts of F~ig. 7. Observed values about 1 per cent lower than calculated for eddy -current shielding. decline of inductance or apparent permeability with increasing fre- quency at low frequencies, and the flattening off to a fairly constant value at higher frequencies. The initial permeability thus obtained (average of results from the 20-turn and 60-turn windings) is 1780. This is somewhat lower than the value found by the ballistic galvanometer. The difference is due to magnetic aging which was observed to decrease the permeability of * The series is inaccurate at frequencies above 5000 cycles. 226 BELL SYSTEM TECHNICAL JOURNAL the core at the rate of approximately 1 per cent per month. In con- trast, no change of resistivity was detected in an accelerated aging test consisting of a bake at 100° C. for 150 hours. Discussion The ballistic data on both the present annealed 35 permalloy sheet core and the previous compressed powdered iron core show that the area of the hysteresis loop varies as B^^ in agreement with Rayleigh's law. The magnitude of the loss is not given by the fractional slope X of the yi,B line as required by Rayleigh's law because the loops are not parabolic in shape. This discrepancy gives a measure of the skewness of the hysteresis loop. The Bm^ portion of the a.-c. data agrees with the loop areas obtained with the ballistic galvanometer. The threefold agreement between the ballistic data, the harmonic measurements, and the a.-c. resistance measurements indicates that the hysteresis loop is substantially unchanged in shape over a frequency range extending from 0 to 10,000 cycles. Since the hysteresis loop has a size and shape independent of fre- quency, and area strictly proportional to B,n^, it accounts for that part of the effective resistance of a coil on a ferromagnetic core which is proportional to the alternating magnetizing current. The remainder consists of eddy current and residual losses. The ordinary graphical method of separating these losses is excluded by the obviously non-linear relation between Rf/nofL/ and /. Using an analytical method, the eddy current loss is found to be some 20 per cent larger than computed by classical theory, indicating the presence of low permeability surface layers on the sheet material. The residual loss coefficient is found to increase with frequency up to about 500 cycles, and to remain constant at higher frequencies (up to 10,000 cycles). The observed inductance diminishes with increasing frequency about 1 per cent below the value calculated for eddy current shielding, the most noticeable decrease occurring below 1000 cycles where eddy current shielding is practically absent. Various theories have been advanced to account for residual loss, as noted in a previous paper.^ Goldschmidt ^ and Dannatt^" have at- tributed the loss to non-homogeneous alloy structure, or preferred axes in such directions as to give a flux component perpendicular to the sheet surface, with accompanying eddy-currents unconstrained by the sheet thickness. This theory fails to account for residual losses in com- 9 R. Goldschmidt, Helv. Phvs. Act., 9, 33 (1936). 10 C. Dannatt, I. E. E. J., 79, 667 (1936). MAGNETIC LOSSES AT LOW FLUX DENSITIES 227 pressed powder cores, where eddy-currents are confined to single particles and cannot be increased by a modified direction of magnetic flux. The most notable feature of residual loss is its large value for unan- nealed materials, and its extremely small values for well annealed al- loys, particularly 78.5 permalloy and 45-25 Perminvar. (See Table I.) The permeability is increased by annealing while both c and a are decreased. On the other hand Br is slightly increased. The decreases in hysteresis and residual loss are attributed to the decrease in work done against internal strains, which also tend to limit initial per- meability.^^ This suggests that residual loss may be due to elastic hysteresis or even simple mechanical friction, with magneto-striction providing the necessary coupling between the elastic or frictional variables and the magnetizing field, as poi'nted out in our previous paper.^ Thus, in addition to losses from eddy-currents and magnetic hysteresis, mechan- ical work is done by the alternately expanding and contracting core — work expended on itself and its supports and insulation. Since the ballistic galvanometer measures only equilibrium values of B and H, this work is not revealed in the area of the ballistic loop. However, in the a.-c. loop the magnetostriction strains produce stresses too rapidly to be relieved, so that B lags behind //with an absorption of energy into the surroundings. This results in an additional effective resistance beyond that due to magnetic hysteresis and eddy-currents. For a sufficiently slow process in well annealed material supported with minimum constraint, the stresses may relieve themselves by thermal agitation and do very little work. But for sufficiently rapid traversals of the loop, all the magnetostrictive stresses will do the same amount of work on the core and its surroundings every cycle. Unannealed materials, or materials rigidly constrained, should continue to show residual loss at very low frequencies. The magnitude of c and its variation with frequency thus should depend on the magnetostrictive constant for the material, and on the types of dissipative constraints. " R. M. Bozorth, Elec. Eng., 54, 1251 (1935). Moisture in Textiles By ALBERT C. WALKER Evidence is presented that for a cotton hair structure of the specific type described, calculations are in such close agreement with many experimental data as to suggest the following tentative conclusions: 1. The moisture content necessary to form a monomolecular layer on all internal surface of the cotton hair appears to be slightly more than 1 per cent of the hair weight. 2. Less than half the internal surface, that termed fibril surface, appears to be involved in moisture adsorption which causes ap- preciable transverse swelling of the cotton hair. Upon this surface multimolecular chains of water seem to condense, the length of such chains increasing progressively up to saturation with corre- sponding increases in hair diameter throughout the whole of this range, each hydroxyl group in the cellulose surface being the base of a water chain, with separations between these chains along the surface corresponding to the arrangement of the hydroxyl groups on the cellulose surface. 3. Moisture adsorbed on surfaces within the cellulose aggregates composing the fibrils does not appear to be involved in transverse swelling, but may be responsible for the slight longitudinal swelling exhibited by cotton. The capacity of the cotton hair for this tyi:)e of adsorption suggests that its locus is the ends of crystallites and therefore within the body of the fibrils. To account for the slight swelling, it is assumed that only a monomolecular layer can be ad- sorbed on these surfaces. 4. A theory is proposed to ex])lain the dependence of the elec- trical properties of textiles upon their moisture adsorbing proper- ties, and upon the surface distribution of moisture within the submicroscopic structure. 1. Introduction A STUDY of the electrical properties of textiles and their de- pendence on atmospheric conditions and naturally-occurring impurities in the material has resulted in important economies and improvements in the use of textile insulation in the telephone industry. Recently, calculations have been made as to the moisture content and swelling of cotton at various equilibrium conditions, based on assump- tions, first as to the structure of the cotton hair,* then as to the * In keeping with recognized terminology, the individual cotton fiber is called a hair, suggestive of its morphological origin. 228 MOISTURE IN TEXTILES 229 location and distribution of the internal surface upon which moisture might condense, and finally as to the manner in which moisture may be held upon this internal surface. From this rather specific picture of the cotton hair structure it has been possible to calculate moisture contents and swelling properties ^ 8.0 ' 7.5 u. O I 7.0 z UJ -J 6.5 ^ 6.0 -l(\J ir NJ s,s Q- U1 T 5.0 C) o UJ 2 4.5 z HI 4.0 2.0 1.5 1.0 0.5 \ I TEMPERATURE =25 DEGREES CENTIGRADE \ \\ \ \ \ A \ \ B -INSULATION \ RESISTANCE \ \ 1, V 1 \ \ / \ V \ / \ \ \ / \ \ 1 \ \ \ \ / 1 \ J \ \ A -MOISTURE CONTENT^ y \ .^ ^ ^ \ \ /J ^ 1^ \ \\ / A 24 22 20 z UJ O UJ Q. I4z I- I2S O lO"-" 20 30 40 50 60 70 80 90 100 RELATIVE HUMIDITY IN PER CENT Fig. 1 — Moisture sorption and electrical properties of raw cotton. consistent with experimental data. It has been possible, also, to present a more comprehensive explanation of the change in the relations between electrical resistance and moisture content of cotton over the whole range of atmospheric humidity than that given in 230 BELL SYSTEM TECHNICAL JOURNAL previous publications from these Laboratories.* It is therefore con- sidered that such a picture should contribute towards a better under- standing of the moisture-sorbing f properties, not only of cotton, but also of other similar fibrous materials, despite the hypothetical nature of some of the assumptions upon which the calculations are based. o 8 -J 7 -|(\J 6 \ — ■', \ . \ 1 = 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 LOG PER CENT MOISTURE CONTENT Fig. 2 — Effect of previous history on resistance of raw cotton. The electrical insulation resistance of textiles, when dry, is enormous compared with the resistance observed under atmospheric conditions. A change of but 1 per cent in atmospheric relative humidity (R. H.), equivalent to between 0.1 per cent and 0.2 per cent change in moisture content (M. C), causes a change of about 25 per cent in resistance of * See references 1 and 2 of the list with which this article concludes. t "Adsorption" is here defined as the taking up of a gas or vapor by a solid, "desorption" the giving up of a gas or vapor, and "sorption" the general process without special indication of gain or loss. The use of these terms implies no as- sumptions with regard to the mechanism of the processes they denote. MOISTURE IN TEXTILES 231 cotton. With silk the corresponding change in resistance is somewhat greater, and although silk sorbs materially more moisture than cotton at any equivalent atmospheric condition, it is much the better insu- lating material. Small amounts of naturally-occurring, water-soluble salts in cotton, such as NaCl and K2SO4, seriously impair the resistance of this textile. Traces of acids or alkalies left after degumming have a similar effect on silk. By washing these materials in water, their electrical properties are greatly improved. Figure \-A shows the familiar equilibrium relation between relative humidity and moisture content for cotton, including the hysteresis loop. A similar hysteresis characteristic, Fig. 1-B, in the relative humidity-resistance relation has been discussed in previous publica- tions.^- ^ Figure 2 shows more clearly, as suggested by a comparison of the two types of curves in Fig. 1, that the resistance of cotton is critically dependent upon its moisture content. The curves in Fig. 2 show another important fact. The resistance of cotton may have, not one, but a range of resistance values for a single moisture content, depending upon the previous treatment or "history" of the sample. This fact, which is one of great practical importance, is illustrated in Table I. Eleven samples of cotton, taken successively from the same spool, were dried to constant weight at 100° F., in a current of dry air, then equilibrated together under very carefully controlled conditions, first at 87.7 per cent R. H., then re-dried as before and re-equilibrated at 84.3 per cent R. H. several days later. The moisture contents of these samples were as follows: TABLE I. % Moisture Contents Sample No. at 87.5% R. H. at 84.3% R. H. 1 10.95 10.1 2 10.8 10.0 3 10.7 9.9 4 10.8 9.8 5 11.1 10.2 6 11.0 9.9 7 11.8 10.8 8 10.7 10.1 9 10.85 9.8 10 11.0 10.0 11 10.7 9.9 The moisture contents of these samples showed small but definite differences, persisting even between tests several days apart. One of the samples had apparently been treated slightly differently from the others in preparation, since it preserved a marked difference in moisture content in both tests. Since a change of only 0.1 per cent in M. C. 232 BELL SYSTEM TECHNICAL JOURNAL may cause a change of about 10 per cent in resistance, these data are considered significant in such testing methods as are used for electrical textiles. In a previous publication ^ a series of simple equations was formu- lated to show the quantitative relations between moisture content, 3.0 2.5 in O 2.0 lij z o z < ^ 1.0 UJ cr z o H0.5 _i D m z n EQUATION FOR LINEAR PORTION OF CURVE r-\B LOG INSULATION RESISTANCE = -A (PER CENT MOISTURE C0NTENT)+ B SLOPE A=0.7 INTERCEPT B AT INSULATION RESIST- ANCE IS EQUIVALENT TO 0.35 PER CENT MOISTURE CONTENT \ ^ \ o -I -0 5 ' \ ^ -1.5 \ 0 1 2 3 4 6 6 7 MOISTURE CONTENT IN PER CENT (BY WEIGHT) Fig. 3 — Moisture content-resistance relation for rag paper. relative humidity, and the resistance (S2) of cotton: logfi = - A{%M. C.) +5, logfi = - a(log%M. C.) +h, logfi = - a(%R. H.) 4-^. (1) (2) (3) Equation 1 was considered as applying for moisture contents in the vicinity of 3 per cent. Equation 2 between 3 per cent and 10 per cent M. C, and Equation 3 from 10 per cent M. C. to saturation. MOISTURE IN TEXTILES 233 The ranges of application of Equations 2 and 3 are evident from Figs. 2 and \-B, respectively; but since the resistivity of cotton becomes enormously high as the moisture content approaches zero, it has been difficult to verify the application of equation 1 below about 2 per cent. However, a recent study along somewhat different lines has provided us with information on this portion of the moisture content curve down to as low as 0.04 per cent M. C. It will be seen from Fig. 3 that equation 1 holds between 1 per cent and 6 per cent M. C. Below 1 per cent M. C, however, the resistance increases more rapidly with decreasing moisture content than is consistent with equation 1. The data from which Fig. 3 was secured completes a chain of evidence upon which is based a theory of moisture adsorption which appears adequate to explain many properties of cotton. This theory involves, in addition to the data just discussed, a rather specific picture of the cotton hair structure. 2. Structure of the Cotton Fiber According to Balls,^ the cotton hair is formed by the outward extension of a single cell from the epidermis of the seed-coat; this extension, unaccompanied by any cell division may continue until the hair is 2000 times as long as it is broad. Up to about half maturity, the cell wall remains very thin but the hair attains most of its length; during the remaining half of the growth period (about one month) the wall thickens from the outside in until it appears to consist of about 30 to 35 concentric "growth rings" (see Fig. 4). Each growth ring consists, further, of parallel strands of fibrils, which run continuously in spiral form from end to end of the hair making one complete turn around the hair in about three diameters, and with periodic reversals in the direction of this spiral. Balls also suggests that side by side in each growth ring, there are about 100 fibrils, each separated from its neighbor by an air space. These fibrils are described by Balls as "dominoes" laid down one on top of the other in a pile-up of growth rings extending from the wall of the central canal or lumen to the outer wall of the fiber. Thus the front and back of each domino are growth ring boundaries, and each domino is separated from its neighbor by an air space. There are also air spaces between each domino in a growth ring. These air spaces are identified as the so-called pits in the wall structure. They are visible under a microscope, and appear to extend from the outer surface of the cotton hair down to the lumen. These air spaces are far larger in magnitude than those separating the front and back of each domino. Only by swelling the fiber in 234 BELL SYSTEM TECHNICAL JOURNAL (a) CROSS SECTION SLIP SPIRAL PIT SPIRAL (b) SIDE VIEW SHOWING PIT SPIRAL REVERSALS Fig. 4 — The fiber structure of cellulose. (a) An idealized cross-section of the cotton hair. The domino-like blocks shown in cross-section are arranged according to Ball's conception. (b) The spiral arrangement of these domino-like blocks or fibrils is shown, together with the separating pits in the wall, and the slip-spiral effect along the fibrils. Obviously these conventional type figures do not represent the true shape of the cotton of commerce, but they approximate the shape during the growth period, before the boll is opened. As the hair dries out, the central lumen collapses and the hair twists. MOISTURE IN TEXTILES 235 caustic soda can a differentiation be detected in the cross-sectional structure of the fiber to indicate this growth-ring character. Thus the fibrils are considered as being separated by air spaces on all sides, the whole cotton hair is spongy, and the surfaces of cellulose bounding these air spaces are internal surfaces of the fiber. Slip spirals are visible in the hair surface at high magnification. Though decidedly irregular, they appear to cross the pits at approxi- mately right angles, suggesting that there are additional internal surfaces at these points. Cellulose from all sources appears to consist of definitely arranged crystallites or micellae.* Haworth ^ suggested that cellulose is com- posed of an elementary group consisting of two CeHioOs units, called cellobiose (Fig. 5- A). Figure 5-B indicates how these cellobiose units are joined together end to end to provide the fibrous structure of native cellulose. /i CELLOBIOSE ^ B one end of cellulose chain Fig. 5 — Molecular structure of cellulose. Diffraction and chemical evidence indicate that the cellobiose units are arranged parallel to the &-axis of the unit cell, with one cellobiose group at each common edge of adjacent cells and one through the center of each cell. These form long primary valence chains arranged parallel to the fiber axis and are held together laterally by cohesive forces. Figure 6 shows this conception of the unit cell as given by Meyer ar d Mark.^ * Sponsler and Dore,^ Meyer and Mark,^ Freudenberg,^ Herzog,' Polanyi.* 236 BELL SYSTEM TECHNICAL JOURNAL 3. Moisture Adsorption on Fibril Surfaces It appears reasonable to assume that moisture will first adsorb on dry cotton on the outer surface of the hair, and by diffusion in the vapor state will penetrate into the pits and adsorb on the pit walls. Since cotton swells appreciably in a transverse direction, but hardly at all lengthwise, it is further assumed that moisture in the pits will next penetrate between the fibrils which are contiguous to one another in the radial direction. At equilibrium with any humidity below that required to form a monomolecular layer, it is assumed that the water molecules will be distributed at random on active points over all of the internal surface. For humidities above this value, polymolecular chains of uniform thickness are assumed to adsorb at active points on the fibril surfaces only, since moisture on the growth ring surfaces of these fibrils appears to be responsible for the transverse swelling of the cotton. The equilibrium moisture content of cotton is reduced if the hydroxyl groups on the cellulose molecules are acetylated or otherwise esterified. Consequently it seems reasonable to assume that each water molecule adsorbed on the cellulose surface is held by a force originating in the oxygen atom of a surface hydroxyl group. As may be seen from Fig. 5-^, there are six hydroxyl groups per cellobiose unit, and the percentage moisture equivalent to a monomolecular layer covering the surface of the fibril structure with each water molecule satisfying forces of a surface hydroxyl oxygen will now be estimated. The fibril cross-section is estimated to be 1240 X 1300 AU, based on average dimensions of the cotton hair.* Assuming the cellobiose units arranged with the a-axis parallel to the fibril width (Fig. 6), there will be 1240/8.3 = 150 unit cells across the fibril, and 1300/7.9 = 165 unit cells down through the fibril. Therefore the total number of oxygen atoms per unit cell length in the four fibril surfaces is: 6 X 150 X 2 + 6 X 165 X 2 = 3780. From this the moisture content equivalent to a monomolecular layer is: 2 X '/o°x 165 X ^ X '°° = °-^^%-t * The considerations upon which these and subsequent calculations are based are given in detail in separate publications which will appear in the April and May issues of Textile Research. t The Angstrom unit AU is 10~* cm. From Fig. 6 it appears that only the equivalent of one cellobiose unit may be available for surface adsorption per unit cell in the fibril surface. Furthermore, since molecules in solid or liquid surfaces are subject to unbalanced forces (surface tension) it is assumed that all surface cellobiose units are so oriented that all 6 hydroxyl groups have surface forces capable of adsorbing water molecules. MOISTURE IN TEXTILES 237 ANGSTROM UNITS Fig. 6 — The cellulose unit cell or crystallite structure. 4. Hair Swelling due to Fibril Surface Moisture The diameter of the water molecule is reported as 3.8 AU. The surfaces of adjacent fibrils along growth ring boundaries must be separated at least 2 X 3.8 = 7.6 AU when a monomolecular layer of water is present on each contiguous surface. This corresponds to a total increase in hair diameter of 33 X 2 X 7.6 = 500 AU. The percentage diameter increase in the hair is: (500/125000) X 100 = 0.4%. 238 BELL SYSTEM TECHNICAL JOURNAL where 125000 AU is taken as the mean diameter of the dry cotton hair. According to Conins,'" the coefficient of hair diameter increase with humidity is about 0.11 per cent per 1 per^cent R. H. Therefore, an in- crease of 0.4 per cent in hair diameter is found at 0.4/. 11 = 3.6 per cent R. H. From adsorption data (Fig. 7) by Urquhart and WilHams/^ this relative humidity corresponds to between 1.1 per cent and 1.2 per cent moisture content. The difference in this value and that 20 ( O SODA-BOILED COTTON (URQUHART AND WILLIAMS) a= 1.17 PER CENT MOISTURE CONTENT (EQUIVALENT TO MONOMOLECULAR LAYER ON INTERNAL SURFACE) TEMPERATURE = 25 DEGREES CENTIGRADE i \ I I J 1 / / / ^ / .^ ^ ^ 30 40 50 60 70 RELATIVE HUMIDITY IN PER CENT Fig. 7 — Moisture adsorption-lnimidity relation for cotton at 25° C MOISTURE IN TEXTILES 239 calculated under Section 3 is between 0.7 per cent and 0.8 per cent, suggesting that there is additional internal surface within the hair structure upon which moisture may be held without manifesting itself by an increase in diameter. This suggestion appears to be confirmed by quite different considerations. Brunauer and Emmett^^, i3 consider it likely that the linear portion of van der Waals adsorption isotherms for nitrogen on the surface of ammonia catalysts indicates the building up of additional layers of adsorbed molecules. They state that extrapolation of this linear portion to zero pressure indicates the amount of gas needed to form a monomolecular layer upon this surface. Between 3 per cent and 50 per cent relative humidity the adsorption isotherm for cotton in Fig. 7 is very nearly linear. Applying this method to cotton the intercept (o) has values between 1.4 per cent and 0.35 per cent, depending on temperature. The average value is about 1 per cent being of the same order as that estimated from swelling data. Since the estimated moisture content equivalent to a monomolecular layer on the internal surface of the cotton hair is so nearly the same when determined by two independent methods, it seems reasonable to postulate an additional internal surface in the cotton hair, amounting in extent to somewhat more than that corresponding to the fibril surfaces. Slip spirals along the hair, crossing the pits at approximately right angles (see {b) of Fig. 4) suggest that there are discontinuities in the length of the fibril structure, hence further internal surface. Since the additional internal surface suggested by the preceding calculations and estimates does not appear to be involved in the transverse swelling of the cotton hair, it is suggested that this may be held upon the ends of crystallites or micellae which compose the fibril structure. It is considered of much less importance to pursue the detailed calculations of this possibility than it is to point out that some such distribution of surface within the body of the fibril structure may be involved in adsorption of a small amount of moisture, and this picture is of material value in accounting for some of the properties of cotton. 5. MULTIMOLECULAR LAYERS It is further assumed that above 1.5 per cent moisture content, addition of moisture simply increases the thickness of the moisture layer upon the surfaces of the fibrils. The thickness («) of the moisture layer on each fibril, expressed in number of water molecules, and the percentage moisture content at 50 per cent R. H. may readily be obtained. At 50 per cent R. H. the hair diameter increavSe is 5 per cent 240 BELL SYSTEM TECHNICAL JOURNAL (plot of Collins' data). Using the following equation formulated in accordance with the calculations in section 4, n = {^ X 125000^)7.6 X 33 X 2 = 12 molecular layers. (4) Since a layer one molecule thick on the fibril surfaces is equivalent to 0.42 per cent moisture content, 12 such layers are equivalent to 5 per cent M. C. The observed moisture content at 50 per cent R. H. is 5.5 per cent. If to this 5 per cent M. C. thus calculated, is added the 0.7 per cent-0.8 per cent held within the fibril structure, a total of 5.7 per cent to 5.8 per cent is obtained, which checks re- markably well with the observed value (5.5%), considering the method of computation. Collins reported swelling values for cotton exposed to 100 per cent R. H. (some condensation was visible on the cotton), and for cotton immersed in liquid water. Moisture contents calculated from these data as in equation 4 give 21 per cent and 23 per cent respectively, a surprisingly good agreement with observed values at saturation, which, as reported by various observers, lie between 20-25 per cent, depending upon the degree of wetness of the material, as indicated by condensation of moisture on the surface. 6. Moisture Required to Fill Pits and Lumen. From Fig. 4-a, it appears that cotton may hold considerably more moisture than corresponds to the saturation values calculated under Section C. The total moisture calculated to fill the pits and lumen in addition to covering the fibril surfaces is more than 140 per cent. Coward and Spencer^* have shown that wet cotton retains about 50 per cent of its weight of water after centrifuging, and these authors expressed the opinion that the water was not interstitial, but contained in the hairs themselves. The above calculations indicate that not only 50 per cent but much more than 100 per cent may be retained in the cotton hair, and it is possible that the amount retained after centrifuging or pressing may be some function of the treatment and the surface energy relations of the sorbed moisture. 7. Reduction in Moisture Sorption of Cotton by Acetylation New ^^ has shown that the equilibrium moisture content of cotton is progressively reduced as the acetyl (CH3CO) content is increased. Below 21 per cent CH3CO content, acetylation can be carried out in a mild way without appreciable effect upon the strength or physical structure of the hair. Above this value the fiber appears to be MOISTURE IN TEXTILES 241 increasingly attacked by the acetylating mixture. Moisture adsorp- tion isotherms for cotton containing different percentages of CH3CO have been obtained by two investigators, New, and Storks.* Figure 8 shows portions of these adsorption isotherms at two humidities (20 per cent and 40 per cent), sufficient to give on extrapolation, monomolecular layer intercepts similar to that of Fig. 7. With increasing acetyl content, the intercepts indicate progressively lower moisture contents, until at 21 per cent or greater CH3CO content, the extrapolated values are zero. Considering the structure postulated in Fig. 4, it might be expected that a larger proportion of hydroxyls on fibril surfaces would be acetylated than the average throughout the body of the material, at any given acetyl content. The fact that the intercept is zero for acetyl contents in excess of 21 per cent suggests that all surface hydroxyls have been converted to acetate and no longer adsorb moisture. A consequence of this hypothesis is that the slope of the curve should approach zero with increasing acetyl content and reach zero above 21 per cent. Obviously this is not the case. If such partially acetylated cotton has all cellulose molecules in the fibril surfaces converted to the triacetate, and the remaining cellulose structure to the monoacetate, it is conceivable that the cohesive forces originally binding the fibril surface cellulose molecules to those directly beneath them have been so diminished in strength that water molecules can now adsorb upon the available hydroxyls in this second layer. Furthermore, it is assumed that conversion to monoacetate of all cellulose molecules within the fibril structure involves acetylation of all crystallite end hydroxyls, so that adsorption of moisture on cotton having more than 20 per cent acetyl content is upon available hydroxyls in the second layer of the fibril surface only. Based on these considerations, calculations have been made of the moisture content of acetylated cotton containing 21.87 per cent acetyl content at 20 per cent R. H. and 40 per cent R. H. The details of these calculations and discussion are given elsewhere as previously indicated, so that only the essential results are stated below: At 20 per cent R. H. the estimated moisture content held on available second layer hydroxyls on fibril surfaces of the cotton hair is 1.0 per cent. The actual value, show^n on Fig. S-a, is 0.9 per cent. At 40 per cent R. H., the estimated value is 1.85 per cent; the observed value is 1.80 per cent. These agreements are considered as excellent, particularly since the untreated cotton adsorbs 2.83 per cent and 4.50 per cent moisture content, respectively, at these two humidities. * Unpublished data obtained by K. H. Storks, at the Bell Telephone Laboratories. 242 BELL SYSTEM TECHNICAL JOURNAL 5.0 Hi ^.o 00 H 3.5 Z UJ a. Z 2.5 I- m 2.0 h- Z o O 1.5 UJ cc ^ 1.0^ (/I o 5 0.5 0 4- .MZi f ^1> x^ ^ ? ■y ^ >^ ^^ r^ ■^ y • ^ : ^ ;>",- ^^' y^ ^"^ 1 STORKS 2 URQUHART AND WILLIAMS 3 NEW .^>^ i4z ^f fA ^ /^ x^^- /y X ^ y ^^ ZZ y ^ y y y <>:>■. Z ^y'' \y ^ 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 RELATIVE HUMIDITY IN PER CENT Fig. 8 — Moisture adsorption intercepts for acetylated cottons indicating amounts of internal surface. 8. Theory of Conduction of Electricity Through Cotton It now appears possible to provide a more comprehensive theory for the conduction of electrical current through the moisture paths in a textile than has been suggested previously.^- ^ Below 1 per cent moisture content it is likely that equation 1 fails to hold, due to obvious discontinuities in the moisture paths over surfaces containing less than a monomolecular layer of water.* Above 1 per cent, it is not to be concluded, however, that a continuous moisture film exists. It appears that some space is still available between certain water molecules, and the space pattern of water distribution is determined by the type of solid surface and the arrange- ment of active points or zones upon which each water molecule is held. In the case of cotton, such active points are considered to be hydroxyl groups; for silk they may be amino or carboxyl groups or both, and from Astbury's discussion ^^ of the chain structure of these two materials it seems likely that their space patterns for moisture ad- sorption are different. Furthermore, it is assumed that each of these active points may be anchorage not only for a single water molecule, but for a chain of such molecules, the length of the chain being deter- * It is of interest to note that if the linear portion of the curve shown on Fig. 3 is extrapolated to the insulation resistance axis, the insulation resistance correspond- ing to this intercept is found at 0.3 per cent M. C. (see a — Fig. 3), this being of the same order of magnitude as that estimated to cover fibril surfaces with a mono- molecular layer, suggesting that the linear portion of the curve is specifically related to moisture adsorption on the fibril surfaces. MOISTURE IN TEXTILES 243 mined by the relative humidity. This conception is much like the picture of acid or oil molecules standing as a film on a water surface, with the polar end in the water. Some such function as equation 1 may apply since simply increasing the length of the water chains will not cause a proportionate decrease in the resistance. It seems evident from Fig. 5-a that small increments of water might be expected to sufficiently lengthen water chains of minimum separation so as to establish contacts between them along the current path, but that larger increments of water are necessary to accomplish the same result between more widely separated anchorage points. This would explain the gradual change from the relation of equation 1 at low moisture contents to equation 2 at intermediate moisture contents. At some point along the humidity curve it is conceivable that capillary condensation occurs in the pits so that at progressively higher humidities the increasing cross-section of these pits plays a more important part in current conduction than the adsorbed chains of water molecules. This may explain why equation 3 is found to apply at highest humidities. Adsorption, however, appears to continue throughout the whole of the humidity range, consistent with the hair swelling relations. Thus it is shown that adsorption and capillary condensation need not be considered separately but may go along together with a gradual shifting in importance from one to the other in the current conduction process. Evershed ^^ explained the decrease in resistance of a textile with increasing applied potential as being due to elongation of pools of water in the material under electrical stress forming more continuous current paths. This deviation from Ohm's law may be explained also as being due to the influence of increasing electrical stress upon the oscillation of the free ends of moisture chains, bringing more of them into orderly alignment along the line of applied potential, and estab- lishing shorter current paths through the structure. The difference in electrical behavior of different textile fibers may be illustrated by a comparison of the adsorption of moisture on cotton and silk surfaces. From Astbury's pictures of the structure of protein molecules as compared with cellulose molecules it appears that al- though there may be more points per unit surface for moisture to condense upon on protein surface, there are also possibilities of sepa- ration of adjacent moisture chains in a manner similar to that discussed for cellulose, and furthermore, there appear to be side chains of hydrocarbons interspersed in the protein chain which may act as barriers to the ready contact of adsorbed water chains on either side 244 BELL SYSTEM TECHNICAL JOURNAL of these hydrocarbon chains. This may explain why silk has a higher resistance than cotton for a given moisture content. It might be expected that silk, due to these hydrocarbon barriers in the current path might also have a higher dielectric breakdown under potential stress. 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35; MOISTURE CONTENT IN PER CENT OF TOTAL VOLUME Fig. 9 — Relation between power factor components of cable paper and moisture content. Whitehead, ^^ in a study of the effects of moisture on power cable paper insulation, obtained data on the change of power factor with increasing moisture content. Figure 9 shows this relation. It will be noted that the conduction component (tan ypi) of the power factor rises sharply as the moisture content of the paper exceeds 0.2 per cent MOISTURE IN TEXTILES 245 by volume (about 0.3 per cent by weight). This increase occurs in the range consistent with the completion of the monomolecular layer of moisture on the internal surface of the material, particularly since the internal surface of paper and cotton appears to be of the same order of magnitude. 9. General Discussion of Theory Peirce ^^ proposed a two-phase theory for the adsorption of moisture by cotton, based upon the facts that a small quantity of water is adsorbed by dry cotton very much more rapidly than the same amount added to cotton with a moderate water content, that it has much greater effect on the elastic properties, evolves more heat, and is more difficult to remove. He regards the moisture attached to the hydroxyl points as in phase (a) while that in phase (b) consists of an indefinite number of molecules adsorbed in a looser fashion over all available surfaces, limited only by the conditions of space and of equilibrium with the external concentration of aqueous vapor. The differentiation between fibril and other internal surfaces is con- sidered as giving a more definite explanation of such two-phase adsorption than that proposed by Peirce. The (a) phase may be pictured as moisture added to the active hydroxyls which lie on the fibril surfaces where such surfaces are readily available for moisture adsorption, while the (b) phase is associated with a definite number of active hydroxyls but within the body of the fibrils and therefore less accessible than those on the surface. As has been pointed out, it is quantitatively reasonable to suppose these available internal hydroxyls to be located at the ends of the crystallites. According to the cotton hair structure presented in this paper, there is actually more than twice as much internal surface available for moisture adsorption from the dry state as there is in cotton already in equilibrium with a 1 per cent moisture content. The slow diffusion of moisture to those surfaces most deeply buried in the fibrils may ac- count for the fact that while cotton very nearly reaches equilibrium with any given humidity in a relatively few minutes, the final establishment of equilibrium conditions, involving a change of less than 1 per cent in moisture content, may take more than 24 hours. The first water molecule to attach itself to an active hydroxyl might be expected to evolve more heat than subsequent molecules in the chain since the interaction is between water and cellulose hydroxyls, not between water and water. Also, water held within the fibril structure no doubt is the most difficult to remove since it must diffuse out through this fibril structure. 246 BELL SYSTEM TECHNICAL JOURNAL This picture of moisture adsorption seems to provide a reasonable explanation for a variety of practical problems. Thus it is known that if fibrous materials, such as wood, paper or fiber board are dried below a certain critical moisture content, perma- nent changes may be expected in the structure; even serious damage may result from too thorough drying at low temperatures. It seems evident that when the moisture content of such more or less dense structures is reduced to a point where the outer layers have less than 1 per cent of moisture, the internal surfaces of these layers may begin to lose the monomolecular layer of water. The valence forces of surface hy- droxyl groups are now no longer satisfied by water molecules, so that such hydroxyls on contiguous surfaces may stick together. On readsorption of moisture, portions of these surfaces may be so permanently attached to one another that swelling will no longer occur in just the same way as originally, and cracking and warping may result. Bibliography 1. Murphy and Walker, Jour. Phys. Chem. 32, 1761 (1928). 2. Walker, Jour. Text. Inst. 24, T145 (1933) ; also Bell Sys. Tech. Jour. 12, 431 (1933). 3. Balls, "Studies of Quality in Cotton," Macmillan & Co., p. 24 (1928); also Egyptian Cotton Supplement, 14, 10 (1927). 4. Sponsler and Dore, Colloid Symposium Monograph, 4, 174 (1926). 5. Meyer and Mark, Ber. Deut. Chem. Gesell. 61, 593-614 (1928); also " Der Aufbau Der Hochpolymeren Organischen Naturstoffe auf Grund Molekular-Morpho- logischer Betrachtungen," Leipzig (1930). 6. Freudenberg, Ber. 54, 764 (1921). 7. Herzog, Ztschr. Phys. Chem. (A) 139, 235 (1928). 8. Polanyi, Ztschr. Phys. 7, 149 (1921). 9. Haworth, Nature, p. 430, .Sept. 19, 1925; also Jour. .Soc. Dvers and Colourists, Jubilee Issue, 1884 1934, 16-23. 10. Collins, Jour. Text. Inst. 21, T313 (1930). 11. Urquhart and Williams, Jour. Text. Inst. 15, T559 (1924). 12. Brunauer and Emmett, Jour. Anier. Chem. Soc. 57, 1754 (1935). 13. Emmett and Brunauer, ibid. 57, 2732 (1935). 14. Coward and Spencer, Jour. Text. Inst. 14, T30 (1923). 15. New, Electrical Communication, 13, 216-225, 370 (1935). 16. Astbury, "Fundamentals of Fiber Structure," pp. 50 and 96, Oxford Press (1933). 17. Evershed, Jour. Inst. Elec. Engrs. (London), 52, 51 (1914). 18. Whitehead, "Impregnated Paper Insulation," J. Wiley & Sons, p. 31 (1935). 19. Peirce, Jour. Text Inst. 20, Tl 33 (1929). Abstracts of Technical Articles from Bell System Sources Determination of Ferromagnetic Anisotropy in Single Crystals and in Polycrystalline Sheets} R. M. Bozorth. Following the work of Akulov and of Heisenberg on the magnetic anisotropy of cubic crystals, it is shown that by taking account of an additional term in the expres- sion for the energy of magnetization the [110] direction may under certain conditions be the direction for easiest magnetization in a crystal, instead of [100] or [111] as given by previous theory. This is in accord with experiment. Magnetization curves for single crystals are calculated using the additional term and some peculiarities are recorded. The anisotropy constant appropriate for a single crystal (of iron) has been calculated from measurements on hard-rolled sheet in which there is preferred orientation of the crystals. Impact Bend Testing of Wire} W. J. Farmer and D. A. S. Hale. This paper comprises a discussion of a machine designed to make rapid determination of the ability of wire to resist permanent deformation by bending. Two types of machine used in the industry for wire bend testing are described and their features discussed with regard to their suitability for use as standard test methods. A bend tester operated by the impact of a pendulum has been de- veloped by the Bell Telephone Laboratories in collaboration with Subcommittee IV on Mechanical Tests of the Society's Committee B-4 on Electrical-Heating, Electrical-Resistance and Electric-Furnace Alloys. Results of typical tests with this machine are given, together with information gathered from ultra-rapid motion pictures taken of the machine in operation. It is concluded that the impact bending machine described offers a simple, rapid and accurate means of measuring the bending properties of wire and that the information acquired from the test is directly applicable to design problems. Positions of Stimulation in the Cochlea by Pure Tones? John C. Steinberg. The relation between tone frequency and position of ^Phys. Rev., December 1, 1936. "^ Proc. 39th Ann. Mtg. Amer. Soc. for Testing Materials, Vol. 36, 1936 — Part II, Technical Papers. ^ Jour. Acous. Soc. Amer., January, 1937. 247 248 BELL SYSTEM TECHNICAL JOURNAL stimulation on the basilar membrane has been calculated from data on differential pitch sensitivity. The calculations involve assumptions concerning the choice of the upper and lower pitch limits of hearing and the choice of tone levels which should be used in obtaining differential pitch sensitivity data. It is shown that for quite different assumptions the positions of stimulation for tones in the range from 500 to 10,000 cycles are not greatly affected. Outside this range the positions depend on the assumptions. The calculated positions for tones of 1000, 2000 and 4000 cycles fall, respectively, at points on the membrane about \, I and f of its length away from the helicotrema. The calcu- lated positions are compared with positions obtained from post-mortem studies of human cochlea and with positions obtained from electric response measurements on the cochlea of anesthetized guinea pigs. The differences between various methods for the most part are no larger than calculated differences between observers. Some Uses of the Torque Magnetometer.'^ H. J. Williams. The history of torque measurement as an index of ferromagnetic anisotropy is outlined. A simple magnetometer for torque measurement is de- scribed in detail and uses for the instrument are discussed. These include the measurement of anisotropy constants, coercive force, com- plete magnetization curves for single directions, and rotational hys- teresis losses. With auxiliary ballistic measurement residual induc- tions and demagnetizing factors are obtainable. ■• Rev. Scientific Instruments, February, 1937. Contributors to this Issue Edwin H. Colpitts, who has recently retired as Executive Vice Presi- dent of the Bell Telephone Laboratories, scarcely needs an introduction. In 1899 he left Harvard to begin his career of research and development in the Bell System. In 1907, when development work was transferred from Boston to the Engineering Department of the Western Electric Company in New York, he also transferred and headed the Physical Laboratory. Later, with the formation of a Research Department, he became its head. In 1933, preliminary to the consolidation of the Department of Development and Research of the American Telephone and Telegraph Company with the Laboratories, Dr. Colpitts was appointed Executive Vice President. W. B. Ellwood, A.B., University of Missouri, 1924; M. A., Columbia University, 1926; Ph.D., Columbia University, 1933. Bell Telephone Laboratories, 1930-. Dr. Ellwood has been engaged in various in- vestigations relating to magnetic materials and measurements. C. N. Hickman, A.B., Winona College, 1914; M.A., Clark Uni- versity, 1917; Ph.D., Clark University, 1922. Physicist, Bureau of Standards, 1919-22; Physicist, U. S. Navy Yard, 1922-24; Research Physicist, American Piano Company, 1924^30; Bell Telephone Labora- tories, 1930-. Since 1930 Dr. Hickman has been engaged in the development of special acoustical instruments. C. M. Hill, B.S. in Chemistry, Princeton University. American Telephone and Telegraph Company, Long Lines Department, 1929-30; Bell Telephone Laboratories, 1930-. Mr. Hill's work has been on the biometrical problems of wood preservation. Victor E. Legg, B.A., 1920, M.S., 1922, University of Michigan. Research Department, Detroit Edison Company, 1920-21 ; Bell Tele- phone Laboratories, 192 2-. Mr. Legg has been engaged in the develop- ment of magnetic materials and in their applications, particularly for the continuous loading of cables, and for compressed dust cores. John Leutritz, B.S. in Chemistry, Bowdoin College, 1929; A.M. in Botany, Columbia University, 1934. U. S. Navy, Medical Corps, 1921-25. Bell Telephone Laboratories, 1929-. Mr. Leutritz' interest has been along biological lines, primarily in respect to wood preservation. 249 250 BELL SYSTEM TECHNICAL JOURNAL E. L. Norton, S.B. in Electrical Engineering, Massachusetts Insti- tute of Technology, 1922; M.A., Columbia University, 1925. Western Electric Company, Engineering Department, 1922-25; Bell Tele- phone Laboratories, 1925-. Mr. Norton has been engaged in the study of network and transmission problems. His present work is in connection with signaling circuits and apparatus. ToDOs M. Odarenko, University of Technique in Prague, E.E., 1928. New York Telephone Company, 1928-30; Bell Telephone Laboratories, 1930-. Mr. Odarenko has been engaged in the measure- ment and study of transmission characteristics of existing and newly developed types of transmission lines. S. A. ScHELKUNOFF, B.A., M.A. in Mathematics, The State College of Washington, 1923; Ph.D. in Mathematics, Columbia University, 1928. Engineering Department, Western Electric Company, 1923-25 ; Bell Telephone Laboratories, 1925-26. Department of Mathematics, State College of Washington, 1926-29. Bell Telephone Laboratories, 1929-. Dr. Schelkunoff has been engaged in mathematical research, especially in the field of electromagnetic theory. Albert C. Walker, B.S., Massachusetts Institute of Technology, 1918; Ph.D., Yale University, 1923. Bell Telephone Laboratories, 1923-. Dr. Walker has been engaged in developing and applying methods of improving the electrical properties of textile insulation and methods for the inspection control of commercially purified textiles for telephone apparatus. R. E. Waterman, B.S. in Chemical Engineering, Williams College and Massachusetts Institute of Technology. Western Electric Com- pany, 1922-25; Bell Telephone Laboratories, 1925-. Mr. Waterman has been engaged in organic and biochemical investigations and for the past few years has been in charge of a group studying the chemical phases of wood preservation. -J VOLUME XVI JULY, 1937 NUMBERS THE BELL SYSTEM TECHNICAL JOURNAL DEVOTED TO THE SCIENTinC AND ENGINEERING ASPECTS OF ELECTRICAL COMMUNICATION Scientific Research Applied to the Telephone Transmitter and Receiver — Edwin H, Colpitis 251 The Use of Coaxial and Balanced Transmission Lines in Filters and Wide-Band Transformers for High Radio Frequencies — W, P. Mason and R. A. Sykes .... 275 A Ladder Network Theorem — John Riordan 303 Contemporary Advances in Physics, XXXI — Spinning Atoms and Spinning Electrons — Karl K. Darrow 319 A Multiple Unit Steerable Antenna for Short- Wave Reception —H. T. Friis and C. B. Feldman 337 Abstracts of Technical Papers 420 Contributors to this Issue 422 AMERICAN TELEPHONE AND TELEGRAPH COMPANY NEW YORK 50c per Copy $1.50 per Year THE BELL SYSTEM TECHNICAL JOURNAL Published quarterly by the American Telephone and Telegraph Company 19S Broadway, New York, N. Y, mmnmmiiiiiiiiiiiiiHiiiniiHii Bancroft Gherardi A. F. Dixon D. Levinger R. W. King, Editor EDITORIAL BOARD H. P. Charlesworth O. E. Buckley M. J. KeUy W. Wilson F. B. Jewett O. B. Blackwell H. S. Osborne J. O. Perrine, Associate Editor Hmnimiiimitiiininiitnnnm SUBSCRIPTIONS Subscriptions are accepted at SI. 50 per year. Single copies are fifty cents each. The foreign postage is 35 cents per year or 9 cents per copy. nHiimuiiitiimiiiiHiiiiiniiiiiii Copyright, 1937 American Telephone and Telegraph Company PRINTED IN U. 8. At The Bell System Technical Journal Vol. XVI July, 1937 No. 3 Scientific Research Applied to the Telephone Transmitter and Receiver * By EDWIN H. COLPITTS LET us recall a scene at the Centennial Exhibition in Philadelphia in 1876. Across a room had been strung wires connecting crude instruments, at one end of the room a transmitter and at the other end of the room a receiver. Dom Pedro, Emperor of Brazil, takes up the receiver and listens while Alexander Graham Bell speaks into the transmitter. The Emperor, astonished at hearing Mr. Bell's voice in the receiver, exclaims in amazement, "My God, it talks." When at the same place. Sir William Thomson (later Lord Kelvin) took up the receiver and listened to Mr. Bell, the words of this dis- tinguished scientist were, "It does speak," and continuing, "it is the most wonderful thing I have seen in America." Sixty years have passed and, as a result of continued effort, the use of the telephone has become such an everyday matter that even the ability to talk from Tokyo in your country to New York in my country scarcely excites comment or wonder. It is not surprising that, to the layman, the element of distance seems the most striking factor in the technical development of the telephone art. As a matter of fact, while the conquest of distance has involved much scientific effort, and very ingenious and highly developed methods for the transmission of speech currents, the magic of the telephone still resides in the instruments which provide for the conversion of mechanical energy, namely speech sounds of highly complex wave form, into electrical currents of corresponding wave form, and the reverse process of converting these electrical currents into speech sounds. These instru- ments, the transmitter and the receiver, are basic to the whole tele- phone art. As they have been improved by development and design, it has become possible not only to render a higher grade of service but to effect economies in other portions of the plant. For example, the * Another of three Iwadare Foundation lectures deHvered during this past spring in Japan by Dr. Colpitts. One lecture was published in the April 1937 issue of this Journal. 251 252 BELL SYSTEM TECHNICAL JOURNAL very extensive use of fine-gauge cables in the plant of the Bell System was, to a large extent, made possible by the development of more efficient transmitters and receivers. Further perfecting of these instruments promises additional improvements in service and some further economies. Telephony, restricting the term to ordinary two-way talking between individuals, involves an element not present in any other service. It does not greatly concern one customer of an electric light or power company whether another customer chooses to use inadequate or inefficient or poorly located lamps or other equipment. That is, each user of the service is, under any ordinary conditions, independent of all other users. In the case of telephony, however, the problem is entirely different; for one user of the telephone is greatly concerned with not only the apparatus furnished to any one with whom he has occasion to talk but also with other factors afifecting the use of this apparatus, such as the amount of noise in the room where the apparatus is located, the user's habits of speech, and whether his ability to hear is normal. Telephone instrumentalities must therefore be so designed and the plant so engineered as to meet reasonably wide variations from what may be termed normal conditions, and ratings of per- formance should be similarly established. I believe telephony in your country as in ours will find an increasingly wide field of service, and there is no single factor more important to a sound development of this art than the subscriber apparatus. With your permission, therefore, I will broadly outline certain work of the Bell Telephone Laboratories which has had a very direct bearing on these telephone instrumentalities and the form they are likely to assume. I will first discuss the research program which has been carried on in these laboratories, and then indicate to you the general trend which development and design have taken. The research program basic to the development and design of transmission instruments has itself been a matter of development as a better understanding of the problems unfolded and as the need for research in this or that direction became apparent. The research problem basic to the development and design of transmission instru- ments may be described as having the following very broad scope: an understanding of their physical operation viewed as electro- mechanical structures; an understanding of speech mechanism and an accurate physical definition of speech air waves; an understanding of the hearing processes and a determination of how hearing is affected by factors present in telephony. Also, our research program may be said to have included research upon certain materials, the results of SCIENTIFIC RESEARCH APPLIED TO THE TELEPHONE 253 which have an important bearing either upon an understanding of the operation of these instruments or upon their practical design. In addition to the development of many methods of measurement and testing applicable to laboratory research and development, of very great importance has been a development of the testing methods which permit of a better final evaluation of the developments based upon the results of this activity. Instruments as Electromechanical Structures The telephone transmitter itself is a complex mechanical and electrical structure. Its general method of operation can be described qualitatively in relatively simple terms, but the operation of few structures is more difficult to define in definite quantitative terms and relationships. For example, we are concerned with acoustical prob- lems such as those involved in the air connection between the lips of the speaker and the diaphragm of the instrument. This air con- nection may involve a short column of air as in those instruments which have a telephone mouthpiece. Connection between the column of air and the working parts of the transmitter may be partially closed by a perforated section. When we come to consider the operation of the instrument itself, there is involved the mechanical vibration of the diaphragm as it operates on the carbon, and further, the whole question of electric conduction in the small mass of granular carbon itself. In the case of the receiver which converts telephonic currents into speech sounds, we have very similar acoustical, mechanical and electrical problems with the exception, of course, of the mechanical and electrical problems introduced by the carbon of the transmitter. A large amount of research work has been carried on in the Labora- tories relating broadly to the transmitter and the receiver as electro- mechanical physical structures. The theory of these devices as vibrating systems has been developed so that their overall performance can be related to the various structural features. Consequently, our development and design engineers are now enabled to predetermine by calculation how certain modifications in structure will affect the physical performance of the instrument. In other words, the design process has become very much less "cut and try." Research has been undertaken and substantial progress has been made on a study of microphonic action in carbon. In order to develop a complete theory of the operation of the transmitter, it is necessary to understand fully what takes place between each carbon granule in the carbon chamber. 254 BELL SYSTEM TECHNICAL JOURNAL Speech Sounds Let me outline briefly some of the results of these studies on speech. The source of any voiced sound is in the larynx. On both sides of this larynx there are two muscular ledges called the vocal cords. When we breathe, these two ledges are widely separated, but when a voiced sound is produced, they come close together, forming a long narrow slit. As they come close together, the air passing through the resulting slit is set into vibration producing a sound. It has been generally supposed that the pitch of the tone thus produced was determined by the natural frequency of vibration of the two vocal cords, and that by changing the tension of these cords, the pitch of the tone can be raised or lowered at will. As most of you know, their natural frequency of vibration is the rate that they would vibrate to and fro if they were plucked and set into vibration like a banjo string or an elastic band. Our studies revealed that the natural pitch of these cords while a tone is being produced is considerably below that of the pitch of the tone. It is true that the pitch of the tone produced is affected, somewhat, by the elasticity of the vocal cords, but it is principally controlled by the size of the air opening between them. The little plug of air between the two vocal cords vibrates through a very much larger amplitude than the amplitude of the cords themselves and is the real source of the sound. The mass of this small plug is controlled by the size of the opening and by the elastic forces pushing it to and fro — namely, the air pressures on either side of it. It is evident that these oscillating pressures will be influenced by the size and shape of the trachea leading into the lungs on one side and by the size and shape of the tongue, mouth, and nasal cavities on the other. The mechanical action involved is analogous to the electrical action in a vacuum-tube oscillator. The sound which is generated at the vocal cords is modified as it passes through the throat, mouth, and nasal passages. The real character of the sound which enables us to identify words is wholly dependent upon the man- ner in which this cord tone is modified by the changing sizes, shapes, and characters of these passages and the outlet to the outside air. After the various speech sounds leave the mouth, they are trans- mitted to the ear of the listener by means of air vibration. As an example of the type of disturbance created in the air, consider the sentence, "Joe took Father's shoe bench out." This silly sounding sentence is chosen because it is used in our laboratories for making tests on the efficiency of telephone systems. The sentence, together with its mate, "She was waiting at my lawn," contains all the funda- mental sounds in the English language that contribute appreciably SCIENTIFIC RESEARCH APPLIED TO THE TELEPHONE 255 toward the loudness of speech. As the sound wave produced by speaking this sentence travels along, each particle of air over which it passes executes a vibration through its original or undisturbed position. The successive positions occupied by the particle as it moves in the complicated series of vibrations corresponding to a spoken sound can be visualized in laboratory investigations from oscillographic records of the corresponding telephone currents. Each successive particle of air along the line in which the sound is traveling executes a similar complicated series of vibrations but any particular oscillation is performed at a later instant by the particle which is farther away from the source of the sound. The disturbance in the air which represents a spoken sound may then be pictured -2; 2 5 -3.25 A 1 r^ SPO KEN / \ / ■> '1 r VI a / r '~\ u ,/ 0 ^\ y " c VIM^ \ 1 \ \ \ \ 1/ K / / / \ e — J \' JNG 0 / ( \ *-1 ^-n' h UNG \ f\ -^-\ \ Jl V-- a \ \s. >OKE k 1 ^ 7 7 1 1 1 9 \ 5 > ^1 [ V. 1 ^ 5 4 1 1 J 1 7 \J 3 1 1 3 1 \ / f ^i J r 1 iv \^ 2 ^' 1 '< 1 #^ L J r \ 1 -i^^ fe \ k. 1 Nj s J 0 t a k f a th r z sh u b en ch a ' i t O.a 0.3 0.4 0.5 0.6 0.7 0.8 0.9 TIME IN SECONDS I.I 1.2 1.3 1.4 Fig. 2 — Melodic curves showing the variation of pitch with time as the sentence "Joe took Father's shoe bench out" is intoned on the musical intervals do, re, mi, fa, mi, re, do. The pitch changes in regular intervals rather than in irregular intervals as shown in Fig. 1. mately the loudness of any sound. The result of using such a device for recording the variations of loudness in the spoken sentence which we have been discussing is shown in Fig. 3. For comparison, the variations in pitch are also shown in this figure. If the fifteen-hundred-foot wave carrying the sentence above mentioned could all be collected into an energy collector, the question 258 BELL SYSTEM TECHNICAL JOURNAL arises, "How much energy would be involved?" It is not possible here to describe the devices by which we were able to measure accu- rately the energies and frequencies involved in speech, but the results of this research work are interesting. When this sentence is spoken fairly rapidly, it will contain about two hundred ergs of energy. About 500,000,000 ergs of energy pass through the filament of an ordinary incandescent lamp each second. This shows that the acoustic ;!: -3.00 o o ?-3.25 I u t-3.50 Q. -3.75 %. 0 ^. / \ L/ \ "'^ ,w a ': r \/ \ v \' '"^ A / / X\ II \ / \ \ t Fig- ^ — Graph of the loudness of the various sound elements when the sentence "Joe took Father's shoe bench out " is spoken. energy in this sentence is very small. Putting it in another way, it would require five hundred persons speaking this sentence continuously for a year to produce sufficient speech energy to heat a cup of tea. An examination of the wave produced by this sentence shows that the vowels contain considerably more energy than the consonants. Exact measurements have indicated that in ordinary conversation the ratio of the intensity of the faintest speech sound, which is th as in "thin," to the loudest sound, which is aw as in "awl," is about one SCIENTIFIC RESEARCH APPLIED TO THE TELEPHONE 259 to five hundred. The actual power used in producing the various sounds depends, of course, upon the speaker and the emphasis with which he pronounces the sound. The power in an accented syllable is three or four times that in a similar unaccented syllable. Measure- ments upon a number of voices during a conversation have indicated that the average power in the speech produced is ten microwatts (one one-hundred-thousandth watt). Some speak with more and others with less than this power. In Table I is shown how various TABLE I Relative Speech Powers Used by Individuals in Conversation Ratio of power of individual speakers to average power . . Below 1/16 1/16 to 1/8 1/8 to 1/4 1/4 to 1/2 1/2 to 1 1 to 2 2 to 4 4 to 8 Above 8 Per cent of speakers 7 9 14 18 22 17 9 4 0 voices in a sample group vary from the average. It is seen that seven per cent speak with less than one sixteenth the average power, eighteen per cent use powers lying between one quarter and one half the average, and four per cent between four and eight times the average. No speakers were found to use more than eight times the average for conversational purposes. Now let us consider the variations for a typical speaker. As a conversation proceeds, the speech power varies from zero during the silent intervals to peak values which frequently are one hundred times the average power. Extensive measurements of these peak powers upon a number of speakers indicated a distribution about the average as shown in Table II. For example, if we should examine the speech TABLE II Peak Powers in Conversational Speech Power Boundaries In Terms of Average Power Per Cent of Intervals Below 1/8 '. .12 1/8 to 1/4 4.0 1/4 to 1/2 4.5 1/2 to 1 5.5 1 to 2 8.3 2 to 4 12.7 4 to 8 18.6 8 to 16 17.0 16 to 32 10.5 32 to 64 5.1 64 to 128 1.7 Above 128 1 260 BELL SYSTEM TECHNICAL JOURNAL during each one-eighth-second-interval throughout a typical conversa- tion, we should find that for seventeen per cent of them the peak power would lie between eight to sixteen times the average over a long interval. It is seen that the most frequently occurring value of the peak power is about ten times the average. Although a typical voice of a man and a typical voice of a woman are alike in that they use the same average power and variations of power from this average, they are different in other respects which we shall now consider. It is well known that the pitch of the voice of a woman is about one octave higher than that of a man. It was not known, however, until our experiments revealed it, that the intensity of the components having vibration rates above three thousand cycles per second was definitely greater for voices from women than from men. The following investigation shows the extent of this difference. An apparatus has been devised in our laboratory which will receive the speech during a conversation and then sort out the components into groups depending upon their intensity and pitch. Those lying in each half-octave band on the pitch scale are automatically grouped together and the group power measured. Also, by means of another automatic device, a sorting process is accomplished within the group placing together all the components having powers between certain power boundaries so that they operate a particular recording meter. It was by means of an apparatus of this latter type that the results in Table II were obtained. It was found that the powers were dis- tributed in each of these pitch bands in approximately the same manner as indicated in Table II for speech as a whole. The relative values of the average speech power in each of the half- octave bands are shown in Fig. 4. The horizontal positions give the pitch in octaves above or below a tone having a vibration rate of one thousand cycles per second. The vertical positions give the fraction of the total power which comes into each half-octave band. For example, consider the half-octave from — 2.25 to — 1.75, which is the octave with its midpoint at middle "C" on the musical scale. The fraction of the power coming into this half-octave is about one quarter. It will be noted that for both types of voices the maximum power occurs in the second octave below one thousand cycles. This particular octave contains about one half of the total speech power. The octaves on either side of this one containing the maximum power contain slightly less than one quarter of the total power. No other octave contains more than about three per cent of the total power. It is seen that for the band of lowest pitch the voices from men contain SCIENTIFIC RESEARCH APPLIED TO THE TELEPHONE 261 about eight times the power of those from women. Also, as stated above, for pitches above one — that is, for tones having vibration rates above two thousand cycles per second— the voice power for women is greater than for men. For the half-octave in the region of pitch three octaves above one thousand cycles, it is about ten times greater. For some reason which is not very evident, women use higher pitch sounds for producing the fricative consonants, and this results in the greater power shown in the regions of higher pitch. Every one who is familiar with such transmission systems knows well that these high-frequency components are nearly always eliminated. While FREQUENCY IN CYCLES PER SECOND 62 125 250 500 1000 2000 4000 8000 16,000, 1 total/ POWER F= Hl 4 1 —J ' -- 1 1 I 16 1 2 64 a. 1 •-- -- q: 256 1 R_ ^ 1 Q- 1024 1 WOMEN J 1 . i 1 4096 1 PITCH f OF FUNC MEN ^ANGE AMENTAL WOMEN ^ EN |~1 163 84 1 1 1 — " -4 -3-2-1 0 I 2 3 4 PITCH IN OCTAVES Fig. 4 — Distribution of speech power in fractions of the total power for half-octave intervals above and below 1000 cycles. these sounds are not of controlling importance in properly under- standing speech, it is evident that the women's voices are somewhat handicapped as compared with men in systems which eliminate them. Hearing Paralleling our research on speech sounds, an investigation of hearing has been under way in Bell Telephone Laboratories. Broadly speak- ing, the aim has been to arrive at an accurate physical description and a measure of the mechanical operation of human ears in such terms that we may relate them directly to our electrical and acoustical instruments. We have measured the keenness of the sound-discrimi- nating sense, and determined what is the smallest distortion which 262 BELL SYSTEM TECHNICAL JOURNAL the mind can perceive, and how it reacts to somewhat larger distortions. This information is utilized in determining a reasonable basis of design both for separate instruments and for transmission systems as a whole, to give a proper balance between cost and performance. I can only indicate a few of the important results of our investiga- tions. One of the first steps was to determine in a quantitative way the performance of our ears as machines. It was obviously important to know how faint a sound the ear can hear, and also how loud a 1000 5 00 100 50 0.1 0.05 0.01 0.005 0.001 0.0005 0.0001 0.00005 / ^^ \^ \ ^N t / / \ 1 1 I \ \ \ \ < \ \ \ s \ k / \ N, / / ^ ^ J \ / 100 500 1000 5000 10,000 FREQUENCY IN CYCLES PER SECOND Fig. 5 — Auditory sensation area for the typical ear of a young adult. sound the ear can tolerate. With the advent of the vacuum tube, it was possible to develop methods of accurately measuring the intensity of faint sounds and of readily producing such sounds. Figure 5 gives the results of a large number of measurements made to determine the limits of hearing. This graph is called the auditory sensation area. The lower solid curve represents the minimum sound that an average young person can hear. The abscissa gives the frequency of the pure tone, and the ordinate the sound pressure in dynes per square centimeter. The top solid curve represents the SCIENTIFIC RESEARCH APPLIED TO THE TELEPHONE 263 maximum intensity of sound that the ear is capable of handUng. This curve was determined by noting that intensity which produced a feehng sensation. Intensities slightly higher than this result in pain and in some instances serious injury to the ear. The dotted lines on either side complete the enclosure and represent the upper and lower limits of pitch that can be heard. It is obvious from this figure that the upper or lower limit of pitch is greatly dependent upon the intensity at which the sound is produced. It will be seen that near the middle range of frequencies, the pressure range is one million to one. The pitch range of pure tones is from about 16 to 25,000 cycles per second. These results are for young adults, and it may be of interest to note that as one becomes older the hearing acuity, at the higher frequencies particularly, becomes less. In the table below is shown some measure- ments to determine what the effect of age would be upon the hearing acuity: TABLE III Db Loss in Hearing with Age Frequency 60 to 1024 Cycles 2048 Cycles 4096 Cycles 8192 Cycles Ages 20-29 (96 ears) Ages 30-39 (162 ears) Ages 40^9 (84 ears) Ages 50-59 (28 ears) 0 0 0 0 0 0 2 5 6 16 18 30 6 11 16 32 These are average values obtained from measurements on a large number of persons. Another important measurement of average hearing is that con- cerned with minimum perceptible differences in pitch and in intensity. Careful measurements on large groups of people have given us reliable data of this form. In Fig. 6 are shown the results of such measure- ments. They are plotted on the auditory sensation area. The ordinates are decibels above the reference pressure and the abscissas are centi-octaves above or below a pitch of 16.35 cycles per second. A frequency scale is also given for reference purposes. The numbers within the area indicate the minimum changes in the intensity level in db that the average ear is able to detect over that region of the auditory area. It will be seen that near the threshold fairly large changes are necessary to be perceptible, while at fairly high intensities about 1/4 decibel is all that is necessary for the change to be perceived. In Fig. 7 are given similar data for minimum perceptible differences in pitch. The numbers in the figure in this case are given in centi- 264 BELL SYSTEM TECHNICAL JOURNAL octaves; that is, each unit corresponds to 1/100 of an octave. The results of this line of investigation have an important bearing on the physiological theory of hearing which I cannot enter into, and another important result has been the development of methods of determining the degree of impairment of hearing. In telephony we are, of course, not directly concerned with simple sounds, but with the highly complex sounds of speech, and these are 16.35 33 FREQUENCY IN CYCLES PER SECOND 261 522 1044 2089 ^177 8356 16,712 33,424 IJO ^ — -. N 120 ..•^" / /I.5 1.2 0.9 0.7 0.6 0.5 0.45 0.38 0.34 0.30 0.26 0.23 0.20 0.18 \ ^ ."' 0.5 0.7 \ no 100 90 80 70 60 50 ; |4.5 2.1 1.2 0.8 0.6 0.5 0.45 0.36 0.35 0.31 0.26 0.24 0.20 0.19 0.21 0.25 0.32 0.41 0.5 0.7 1 0.9 j 1 \8.0 \ 2.7 1.5 1.0 0.7 0.6 0.48 0.41 0.36 0.33 0.30 0.25 0.21 0.20 0.21 0.26 0.32 0.42 0.5 0.8 1 1.1 r 1 \ \ \ 6.0 3.0 1.5 0.9 0.6 0.5 0.47 0.40 0.37 0.33 0.29 0.24 0.22 0.22 a27 0.33 0.43 0.6 0.8 1 1.3 ( 1 \I0 \ 5.0 2.3 1.2 0.9 0.7 0.6 0.5 0.44 0.38 0.33 0.28 0.26 0.25 0.28 0.34 0.47 0.6 0.9 1 1 \ 10 3.5 1.8 1.2 0.9 0.8 0.6 0.5 0.46 0.38 0.33 0.30 0.29 0.31 0.38 0.5 0.7 1.0 1 1 1 \ 6.5 3.0 2.0 1.4 1.0 0.8 0.6 0.5 0.45 0.42 0.38 0.35 0.36 0.42 0.6 0.8 1.3 1 1 1 \ 6.0 3.5 2.2 1.4 1.0 0.8 0.7 0.6 0.6 0.5 0.45 0.44 0.5 0.7 1.0 1.5 1 ; 30 20 10 \ .6.0 3.5 2.3 1.6 1.2 1.0 0.9 0.8 0.7 0.6 0.5 0.6 0.9 1.4 2.2 / t s s^.O 4.1 2.7 1.9 1.6 1.4 1.2 0.9 0.8 0.7 0.8 1.4 2.3 3.6/ ; V ^ 3.7 2.9 2.2 2.0 1.7 1.2 0.9 1.2 2.5 4.8 J '\ ^ 3.5 3.2 2.4 2.0 1.7 1.8 7 ^ \ 3.5 3.2 y r -10 0 100 200 300 400 500 600 700 800 900 1000 1100 PITCH IN CENTI-OCTAVES Fig. 6 — Minimum changes in intensity level in db that the ear Is able to appreciate at various positions in the auditory area. on actual telephone circuits generally associated with extraneous sounds which we may group under the broad term of noise. Further, telephone instruments are not perfect, and could be made to approach perfection only at a great expense. In order to arrive at a quantitative understanding of the importance of departures from perfection in telephone transmission elements and conditions of use, we have in very general terms proceeded as follows: We set up transmission systems so nearly perfect that even the keenest ear could not find a SCIENTIFIC RESEARCH APPLIED TO THE TELEPHONE 265 flaw in their transmission performance, and then introduce measured imperfections or variations. By this general process, we were able to determine the effect of noise of chosen intensities either as noise present in the telephone receiver or as noise in the room. Similarly, the effect of a line or other characteristic such that voice frequencies above a certain value or below a certain value were not transmitted, was determined. The 16.35 33 FREQUENCY IN CYCLES PER SECOND 261 522 1044 2089 4177 8356 16,712 33.424 130 N, 120 f- — 1 5 7 7 5 3.8 2.9 1.7 1.3 0.88 0.65 0.43 0.32 0.26 X ^^ .-- 0.43 0.52*^ \ 110 / 1 6 6 7 7 5 3.8 2.9 1.7 1.3 0.88 0.65 0.43 0.32 0.26 0.26 0.29 0.33 0.38 0.43 0.52 0. 1 100 V^ 7 7 7 5 3.8 2.9 1.7 1.3 0.88 0.65 0.43 0.32 0.26 0.26 0.29 0.33 0.38 0.43 0.52 0.« ^ 90 \ \ 10 7 7 5 3.8 2.9 1.7 1.3 0.88 0.65 0.43 0.32 0.26 0.26 0.29 0.33 0.38 0.43 0.52 0.- ^'1 SO \ \ V9 9 7 5 3.8 2.9 1.7 1.3 0.88 0.65 0.43 0.32 0.26 0.26 0.29 0.33 0.38 0.43 0.52 1 70 60 \ / > 14 \ 9 6 4.1 2.9 1.7 1.3 0.88 0.65 0.43 0.32 0.26 0.26 0.29 0.33 0.38 0.43 0.52 1 1 \ 13 7 4.5 3.2 1.7 1.3 0.88 0.65 0.43 0.32 0.26 0.26 0.29 0.33 0.38 0.43 0.52 ( 50 s. \ 12 5 3.5 1.9 1.4 0.95 0.67 0.43 0.32 0.26 0.26 0.29 0.33 0.38 0.46 0.58 / 40 s. \ s'° 4.8 2.7 1.6 I.I 0.74 0.51 0.36 0.28 0.26 a29 0.33 a42 0.54 0.62 ' 30 s. s \° 4.6 2.4 1.4 0.94 0.72 0.42 0.32 0.29 0.32 0.36 0.48 0.62 0.91^' _-. 1 X V 2.7 1.6 1.0 0.62 0.39 0.35 0.38 0.43 0.66 0.94 y y "v. ^ 2.2 1.6 0.80 0.58 0.55 0.64 1.0/ ^^ V 1.3 0.98 ^ -10 200 300 400 500 600 700 PITCH IN CENTI-OCTAVES 900 1000 1 100 Fig. 7 — Minimum perceptible differences in pitch in centi-octaves for various posi- tions of the auditory area. effect of introducing a highly resonant element or of a non-linear element was studied. The range in loudness of speech necessary for best reception was likewise measured. As noise became recognized as a very real factor, a standard basis for noise measurements was established. Consequently we are now able to measure noise on a telephone circuit or in a room, and state the result in terms of a standard unit. 266 BELL SYSTEM TECHNICAL JOURNAL Materials In the practical design of modern telephone instruments we owe a large debt to the chemist and the metallurgist. Modern molding materials and processes are utilized in order to secure forms of ap- paratus satisfactory from the standpoint of appearance and of me- chanical strength. The newer types of permanent magnet steel, to the development of which your countrymen have contributed so largely, provide possibilities of light-weight and very efficient magnetic structures. It is a most striking circumstance that commercial telephony is dependent upon the performance of a small mass of carbon granules in the transmitter. No single material entering into the construction of telephone apparatus has therefore greater importance. In America at least, transmitter carbons are largely derived from a certain specially selected anthracite coal. In its natural state, this coal exhibits none of the characteristics required for its use in a transmitter. These characteristics or properties are secured by heat treatment. These heat-treatment processes were for many years the result of empirical development and were not well understood or, as we now recognize, adequately controlled. This resulted in a product of uncertain quality. An important task of the Laboratories was therefore to study each step in the process of producing carbon and to develop a process definitely specified at each step, which would be capable of giving the desired uniform quality. The results so far obtained have had very important reactions upon transmitter performance. The Laboratories have also set themselves the more elementary task of understanding the fundamental properties of carbon contacts. One important element of this research is to determine the causes of resistance changes produced when the compressive force on a mass of carbon granules is changed. It is too early to report results from this research, but it seems clear that granular carbon will be an important element in the design of transmitters for many years to come, and we should seek to obtain complete fundamental knowledge of its operation. Testing Methods Broadly speaking, methods of testing have been developed, first, to enable the development and design engineer to determine quantita- tively the various performance factors of the apparatus under develop- ment, and second, to determine how well the apparatus which has been developed performs under service conditions. In the Labora- tories, we have over the last twenty years developed methods for measuring the physical constants of the apparatus involved so that SCIENTIFIC RESEARCH APPLIED TO THE TELEPHONE 267 we can analyze this apparatus as electromechanical structures. Further, in the design of telephone transmission apparatus we are concerned with a power transmission system in which the design engineer has no control over the power source, the human voice, nor over the receiving agency, the human ear. His control is limited to the conveyance of power from speaker to listener. In the Laboratories, therefore, we have recognized that it is necessary, at least without present knowledge, to supplement physical measurements by measure- ments involving speech sounds and the human ear. Some years ago, these tests consisted of comparisons between different instruments or transmission elements made by the process of talking first over a circuit containing, for example, one instrument, and then over the same circuit containing a different instrument. Dependence was placed wholly upon the listener's skill to detect differences in volume, quality and intelligibility. It was recognized that this method of testing left much to be desired. Owing to the limitations of the human ear, small volume differences could not be detected, but even more important, this simple test furnished no very accurate measure of speech distortion affecting intelligibility, and obviously no definite information as to the relation between volume, various types of distortion, and overall effectiveness. Dr. George A. Campbell, in 1910, proposed a method of testing which has been highly developed in our Laboratories. This method, termed "articulation testing," measures the relation between the reproduced and impressed sounds from the standpoint of effects on intelligibility of different kinds of distortion. This method has been described in a number of publications. Briefly, in this method, lists of syllables chosen at random and usually meaningless monosyllables are called over the circuits to be rated, and the percentage of syllables correctly understood gives a measure of the circuit performance. Further, the method has been extended to give quantitative measures in terms of the recognizability of reproduced speech sounds, of the effects of loudness of these sounds, and of the noise which may be present. While various physical tests and the articulation test method are exceedingly useful tools in the hands of the research and development engineer, they do not give a direct measure of the transmission service performance of a circuit in terms of the ability of the user to carry on a conversation under actual commercial conditions. This ability of the user to carry on what may be termed a successful telephone conversation depends not only upon the performance of the telephone instruments and circuits but also, to a substantial extent, upon the 268 BELL SYSTEM TECHNICAL JOURNAL users' own performances — the subject material of conversation, how they talk into the transmitters, and how they hold the receivers — and upon the room noise conditions. In other words, there are a number of factors random in nature which, while beyond the control of those who design and engineer the telephone plant, must be taken account of in rating the service performance. A large amount of thought and effort has been given to the problem of how best to determine transmission service performance. Very briefly stated, we have been led to the following steps: In order to take suitably weighted account of all the factors involved, service performance ratings should be based on service results, that is, trans- mission service performance should be measured by the success which users of the telephone circuit have in carrying on conversations over the circuit. With the various factors in mind, we have fixed upon what we have termed "effective transmission" ratings for transmission plant design. These ratings are based on a determination of the repetition rate in normal telephone conversations. As the effect of a change in a circuit depends upon its initial char- acteristics, it is necessary in order to be able to compare numerical results to have a basic circuit for reference. By suitable choice of basic circuit, it is possible to express the effects of changes in any one transmission characteristic in terms of the attenuation of the trunk. For example, the effect of changes in sidetone level in the subscriber's set can be expressed as so many decibels change in trunk attenuation. Mr. W. H. Martin's paper, "Rating the Transmission Performance of Telephone Circuits," in the Bell System Technical Journal, January, 1931, discusses the method and general principles. It should be noted that the application of the method requires careful consideration of many factors and the accumulation and analysis of a very substantial amount of data. Based on these data, we have arrived at the fol- lowing relationship: Relative effective loss in db = 50 logio (r) where r is the ratio of the repetition rates for the two conditions compared. Association of Transmitter and Receiver In order to furnish a convenient two-way talking circuit over a single pair of wires, the transmitter and the receiver at each end of the circuit must be continuously associated in the circuit. This has been accomplished by various circuit arrangements since the early days of the telephone, and as every user of the telephone knows, leads SCIENTIFIC RESEARCH APPLIED TO THE TELEPHONE 269 to the condition that when speaking into the transmitter one hears his own voice in the receiver. Local speech so heard is designated as sidetone. The Laboratories have carried on research in order to determine the effect of sidetone on the overall efficiency of the circuit. We find that sidetone above a certain volume decreases the conversa- tional efficiency of the circuit. Parallel with the study of the effects of sidetone, research has been carried on on methods which could be applied to limit sidetone in amount to more nearly its optimum value. This has led to the development of what are known as anti-sidetone circuits, which do not eliminate sidetone but reduce it to an amount which is more nearly that found to be desirable. An important step in the association of the transmitter and the receiver is represented by the handset which provides a rigid mechan- ical connection between the two units. This rigid mechanical con- nection introduces mechanical coupling between the receiver and the transmitter, which had to be given very serious consideration in order to avoid speech distortion. Trends in Instrument Development I have broadly indicated to you fields of research which underlie the development and design of the telephone transmitter and receiver. It will now be of interest for us to note what application is likely to be made of the results of what has amounted to an enormous total of scientific effort. In this connection, it may be well again to emphasize that station apparatus is intimately associated with the user, and has therefore to be designed to fit him, his habits of using the telephone, and the conditions attending such use. The handset has to be designed to fit his head, the holes in the dial to fit the size of his finger, the bell to be loud enough, and so on. Our effective transmission rating system has been set up in an attempt to rate the performance of the telephone when employed by the customer in the way he wants to use it, under the conditions surrounding him. For this reason, this method of rating has been found particularly valuable in the development work on instruments. Because of the wide range of customer usage and conditions, a number of factors have to be taken into account in the design of the apparatus. Also, because this apparatus is located on the customer's premises, where it is relatively inaccessible to the telephone personnel, it must be capable of standing up without undue trouble under this wide range of usage and conditions. To strike a proper balance in meeting all these factors requires an intimate knowledge of the field conditions as well as of the development and manufacturing possi- 270 BELL SYSTEM TECHNICAL JOURNAL bilities. A continuing close contact with field experience is employed to modify the designs towards securing the proper balance to meet these factors. In order to indicate more clearly the present trends in design, I shall refer briefly to the earlier art. In the early development of transmitters and receivers, the matter of getting efficiency was of primary importance since this could be evaluated directly in terms of the amount of copper required in the connecting line. The early transmitters, which were of the same construction as the receiver, depended on the generator action of a diaphragm and coil and de- veloped sufficient power to be heard over only a few miles of heavy- gauge wire. Some amplification was necessary before telephone communication could begin to assume the proportions of a widespread service. This amplification was obtained at a reasonable cost in the carbon contact transmitter. Transmitters of this type are in the order of 60 db more efficient as transducers of acoustic to electric energy than the earlier type. Both the transmitter and the receiver operate by means of dia- phragms which have natural periods of vibration. These resonances and the resonances of the air spaces on each side of the diaphragm were used to obtain as efficient a transfer of energy as possible. In the early design, a great deal of attention was also given to locating these resonances at the portion of the frequency range where they would tend to increase the intelligibility of the reproduced sound. As a result, both instruments were made very efficient in the region of 1000 cycles, which lies within the range where the ear and the sensation of loudness are most sensitive. It was recognized that these resonances caused undesirable distor- tion, but under the conditions the resulting increase in efficiency more than compensated for this disadvantage. As time went on, the diaphragm resonances came to be looked upon as practically inherent in commercial transmitters and receivers, because no way was known of eliminating them without making a very material sacrifice in the efficiency of the instrument. About twenty years ago, the development of the vacuum tube amplifier and the high quality condenser transmitter made it possible to demonstrate and measure quantitatively the advantages of reducing distortion. These high-quality instruments, the improvement in measuring technique and the development of improved methods of designing vibratory systems offered the promise of providing instru- ments in which the resonance effect could be reduced without unduly affecting efficiency. SCIENTIFIC RESEARCH APPLIED TO THE TELEPHONE 271 The first commercial instrument for station use, which demonstrated the possibiHty of carrying out this promise, was the transmitter employed in the handset first supplied by the Bell System in 1927. This transmitter had to meet the requirement of giving the same transmission service as transmitters of the deskstand type, and at the same time meet the very exacting requirements imposed by the handset to make it free from howling and capable of performing over a wide range of positions. The diaphragm resonance was damped to a large extent by the use of paper rings and, by lightening the structure, the point of maximum response was moved up in frequency so that it no longer coincided with the peak of the receiver. The effect of this was not only to broaden the response characteristic and improve intelligibility, but also to reduce the gain in the local howling circuit which is, of course, a maximum when both transmitter and receiver have their greatest efficiency at the same frequency. The same separation of peaks resulted in the received speech being less loud, but in spite of this the overall performance was equivalent to that of the best deskstand type of instrument then available. With this accomplishment, further work was directed toward maintaining the lower distortion and increasing the efficiency. The transmitter introduced in 1934 represented a marked improvement along this line. This instrument still further broadens the transmitted frequency range and is used with about the same efficiency in desk- stands, handsets, wall sets, and coin-collect sets. A new type of handset will be introduced in the Bell System in 1937 which, in addition to having a more pleasing and simplified design, will incorporate the new transmitter mounted in such a way as to make fullest use of its ability to transmit efficiently over a wide- frequency band. During this evolution of the transmitter, the knowledge which had been gained as to the importance of transmitting different widths of frequency band over commercial telephone circuits led to the establish- ment of the range from 250 to 2750 cycles for designs of new circuits. It was not the intention in the establishment of this range that circuits should not do better than this where it is possible without materially increasing cost, but that all circuits should be at least as good as this. The establishment of this frequency range took into account a number of factors of which a very important one is that the overall utilization of this range from the sound entering the transmitter to the sound output of the receiver provides a grade of transmission which is highly satisfactory for the reproduction of conversational material. 272 BELL SYSTEM TECHNICAL JOURNAL The establishment of this frequency range played a part not only in the design of circuits, but also in guiding the evolution of the transmitter and receiver. The transmitter last referred to meets this requirement very well. In fact, its efficiency is fairly uniform for a frequency range extending beyond 4000 cycles. The next step in the process was to improve the performance of the receiver. A pronounced resonance at 1000 cycles was no longer necessary since means had been found to improve the efficiency of instruments in other ways than by concentrating all the resonances at one frequency. The importance of the higher frequencies in trans- mitting and reproducing the transient sounds characteristic of the consonants in speech led to placing more emphasis on these frequencies and attempting to produce more uniformly the band of frequencies which was set as a limit for circuits. This has now been accomplished in a practical fashion in the receiver which is being introduced in 1937. The effect of this evolution in the design of station instruments may be brought out by a comparison of the overall response characteristic — that is, the relation of the sound delivered to the ear to the sound available at the transmitter — for a typical telephone connection having, in one case, both terminal instruments of the 1920 type and, in the other case, the terminal instruments of the coming new 1937 type. In this typical circuit, the trunk has been taken as free from dis- tortion so that its effect will not influence the indicated performance of the instruments, although the circuit does include two 22-gauge loops each three miles long. At the resonance point of the old instruments, just over 1000 cycles, the overall response in going to the new instruments is reduced by almost 30 db while the response in the range from 2000 to 3000 cycles is increased by over 20 db. In the frequency range from 500 to 2000 cycles, the circuit employing the older instruments shows a variation of overall response of over 30 db. For the new type, the variation for this same frequency range is reduced to 15 db, and, furthermore, this variation of 15 db applies approximately for the range of 250 to 2750 cycles which was mentioned as the transmission range requirement for the design of new circuits. In regard to the variation of 15 db in this frequency range, there is good indication that this response is more desirable than one of no variation, from the standpoint of having the telephone performance approach that of direct air transmission. In addition to these improvements in frequency response and efficiency, the intensive development program on these instruments has improved materially the stability of the carbon transmitter under SCIENTIFIC RESEARCH APPLIED TO THE TELEPHONE 273 service conditions. This is an important factor in extending the useful Hfe of these instruments and in reducing the cost of maintaining the desired transmission performance. You will perhaps pardon me if, in concluding, I say a few words which I hope will not seem unduly laudatory of the work of my associates in the Bell Laboratories. The facts seem to be that twenty years ago or thereabouts, there was very little general scientific interest in sound and sound devices. As a result of work begun in 1000 1500 2000 2500 3000 FREQUENCY IN CYCLES PER SECOND Fig. 8 — Comparison of the response-frequency characteristics of telephone instru- . ments since 1927. these Laboratories, and as the possibilities of interesting and important applications became apparent, broad scientific interest was stimulated, and we have seen and welcomed increasing research activity in sound and acoustics in many of the university laboratories and in new industries based upon the results of scientific research in sound initiated by us. A number of my associates have attained world-wide recogni- tion for their scientific and technical accomplishments. Our scientific investigations were undertaken to enable us to develop further the 274 BELL SYSTEM TECHNICAL JOURNAL telephone art, and the results of these investigations are serving to guide us not only in the development of telephone instruments but in all developments of telephone transmission. The Laboratories' scientific and design work has contributed in large measure to the improvement of methods of recording and reproducing sound in the phonograph and sound-picture arts. The art of radio broadcasting owes a large debt to the work of the Laboratories, not only for the fundamental scientific knowledge contributed but also for actual instrumentalities employed. To those with impaired hearing, the Laboratories' investigations have made possible improved means for determining the extent of their impairment, and improved hearing aids. Finally, at least in America, we are becoming what I may term as "noise conscious." In our cities, noise is being recognized as a factor affecting comfort, efficiency, and possibly even health. The development of accurate methods for the measurement of noise is contributing to studies looking towards the reduction of noise. Lecturer's Note: The lecturer wishes to acknowledge assistance given in the preparation of this material, particularly by Dr. Harvey Fletcher and Mr. W. H. Martin of the Bell Telephone Laboratories' staff. The Use of Coaxial and Balanced Transmission Lines in Filters and Wide-Band Transformers for High Radio Frequencies By W. P. MASON and R. A. SYKES At the high radio frequencies, filters and transformers become difficult to construct from conventional electrical coils and con- densers, on account of the small sizes of the elements, the large effects of the interconnecting windings and the low ratios of re- actance to resistance realizable in coils. It is shown in this paper that selective filters and wide-band transformers can be constructed using transmission lines and condensers as elements. The ratio of reactance to resistance in these elements can be made very high; consequently very selective filters and transformers with small losses, can be constructed. The effect of the distributed nature of the ele- ments is taken account of in the design equations and methods are de- scribed for obtaining single-band filters and transformers. Experi- mental measurements of such filters and transformers are shown. The experimental loss curve is shown of a coaxial filter used in the Provincetown-Green Harbor short-wave radio circuit for the pur- pose of connecting a transmitter and receiver to the same antenna. I. Introduction A T the higher radio frequencies, coil and condenser networks become -*- ^ difficult to construct on account of the small sizes of the elements and the large effects of the interconnecting windings. The Q realizable in high-frequency coils is about the same as can be obtained at the lower frequencies but due to the smaller percentage band widths, it is desirable to obtain a higher Q. There has been a tendency to replace coils by small lengths of transmission lines, and these have been used to some extent as tuned circuits, and as single-frequency trans- formers.^'^-^ It is the purpose of this paper to describe work which has been done in constructing selective filters and wide-band transformers from lengths of transmission lines and condensers. Due to the high ratio of reactance to resistance obtainable in both of these types of elements, ^ "Transmission Lines for Short-Wave Radio Systems," E. J. Sterba and C. B. Feldman, B. S. T. J., Vol. XI, No. 3, July 1932, page 411. ^ "Resonant Lines for Radio Circuits," F. E. Terman, Elec. Engg., Vol. 53, pp. 1046-1053, July 1934. ^"A Unicontrol Radio Receiver for Ultra-High Frequencies Using Concentric Lines as Interstage Couplers," F. W. Dunmore, Proc. I. R. E., Vol. 24, No. 6, June 1936. 275 276 BELL SYSTEM TECHNICAL JOURNAL very selective networks can be obtained at the high radio frequencies. The effect of the distributed nature of the elements is considered and methods are described for obtaining single-band filters and transform- ers. Experimental measurements of such filters and transformers are shown, and these results indicate that such structures should be of use in short-wave radio circuits. II. Characteristics of Transmission Lines To facilitate an understanding of the following discussion, the equa- tions of transmission lines as they apply to filter structures will be briefly reviewed first. The equations of propagation for any uniform transmission line can be expressed in the form of equations between the output voltage e^, the output current i^, the input voltage ei, and the input current ii by the relations ^2 = «i cosh PI — iiZo sinh PI, ii = ii cosh PI — -;=- sinh PI, (1) where / is the length of the line, P the propagation constant, and Zo the characteristic impedance of the line. In terms of the distributed resistance R per unit length of line, L the distributed inductance, G the distributed conductance, and C the distributed capacitance, P and Zo can be expressed by the relations P = ^(R-\-jc.L)(G-j-jo:C); Zo = ^^^j^, (2) where co is lir times the frequency. The distributed conductance G is usually very low and can be neglected for coaxial or balanced transmission lines in dry atmospheres. For copper coaxial lines, the values of R, L, and Chave been calculated* to be R = 41.6 X 10~^ ^ff i — |- T ) ohms per centimeter, L — 2 loge- X 1 0~^ henries per centimeter, (3) a ^ 1.11 X 10-^% , ,. , • C = r — farads per centimeter, 2 1oge^ where b is the inside radius of the outer conductor and a the outside radius of the inner conductor. If we define the Q of the conductor as ^ See reference 1, page 415 and page 417. COAXIAL AND BALANCED TRANSMISSION LINES 277 the ratio of the series inductive reactance to the series resistance, the ratio will be (2 = .3026V/(log.^)/(^ + 1), • (4) where k = b/a. It will be noted that this is the value of Q measured for a short-circuited conductor for low frequencies. As an example, a conductor 3 inches in diameter with the optimum ratio of ^ = 3.6 will have a Q oi 3,200 at 100 megacycles. The value of the character- istic impedance Zq of a coaxial line is ^=60 1oge^- (5) For a balanced transmission line the values of R, L, and C are,^ if D is much larger than a, „ 83.2 X 10-^ V7 K = ohms per centimeter, L — 4 loge— X 10~^ henries per centimeter length, (6) „ 1.111 X 10-^% , . ^ C = Y) farads per centimeter, 4 log,- where D is the spacing between wires, and a the radius of one of the pair of wires. With these values, the expressions for Q and Zo become Q = .302 V/a loge- ; Zo = 120 log^- ■ (7) a a Another combination of some interest is obtained by using the inside conductors of two coaxial conductors adjacent to each other. Such a construction results in a balanced and shielded transmission line. All of the constants are double those given by equation (3), except for the capacitance which is halved. III. Filters Employing Transmission Lines as Elements One of the first uses of transmission lines as elements in wave filters is described in a patent of one of the writers.^ In this patent are con- sidered the characteristics obtainable by combining sections of trans- 5 U. S. Patent 1,781,469 issued to W. P. Mason. Application filed June 25, 1927; Patent granted Nov. 11, 1930. Wave filters using transmission lines only are very similar to acoustic wave filters as pointed out in an article, "Acoustic Filters," Bell Laboratories Record, April 1928. Most of the equations and results of a former paper on acoustic filters, B. S. T. J., April 1927, p. 258, are also applicable to transmission line filters. 278 BELL SYSTEM TECHNICAL JOURNAL mission lines in ladder filter structures. The results obtained are briefly reviewed here. One of the simplest filters considered is shown on Fig. 1. The filter consists of a length 2/i of transmission line shunted at its center by a short-circuited transmission line of length U. To determine the trans- mission bands of a filter, it is necessary to neglect the dissipation oc- curring in the elements and hence we assume that R and G are zero. In any case these values are small for transmission lines since they have a high Q. Neglecting R and G, equations (1) become C2 = ei cos — — jtiZo sm — V V t2 ol ei Oil tx COS 7 -7^ sm V Zo V (8) jjjjjjjjjjj?jjjj/jj^jjjf?jj7jjjj?jjj?? V/.ZJ./Z/IZ/.l/ -^- ii ^'I l1 ^'2 — - 4 Zo, ^1 ^'0 \ ? 1 '3 i ^02 l2 Fig. 1 — -Band-pass filter constructed from coaxial conductors. where v, the velocity of propagation , and Zo, the characteristic impedance, have the values V = LC =^/; (9) Using these equations the characteristics of the filter illustrated by Fig. 1 are easily calculated. With reference to Fig. 1 and equations (8) we can write the equations of the network as coil • • rr • ^''1 62 — ei cos niZo, sm — , V V toll . ei . co/i H = 1 1 COS 1 -77- sm - — , V -^ Zoi V Co/l • • rr • l .M -r^^ I FRE- ! OUENCY _z l. - V^ l2 J ^0, m. j_i J_i t?Ft J] "2 I2H J_L i_L l2 - M .'U , FRE- y QUENCY FREQUENCY ^ A i ^ A '1 FRE- QUENCY 1/ FREQUENCY 4 I V j QUENCY 1/ FREQUENCY 4 / /I /l FRE- ^>^^ ! /-V^ I QUENCY I / I / I / FREQUENCY /I /I /U I / FRE- QUENCY FREQUENCY NOTE: DOTTED LINES INDICATE REACTIVE IMPEDANCE. SOLID LINES INDICATE RESISTIVE IMPEDANCE. Fig. 4 — A list of filters constructed from transmission lines. 284 BELL SYSTEM TECHNICAL JOURNAL The filter discussed above shows some of the possibilities and limita- tions of filters constructed from transmission lines. Many other types are also possible. Figure 4 lists a number of these and the types of filter characteristics they give. The design equations for a number of them are considered in detail in the patent referred to above and hence will not be worked out here. IV. Impedance Transforming Band-Pass Filters Employing Transmission Lines as Elements In a good many cases it is desirable to transform from one impedance to another over a wide range of frequencies. Examples of such uses are when antennas are connected to transmission lines, or when trans- mission lines are to be connected to vacuum tubes, etc. Transforming band-pass filters constructed out of transmission lines which will transform over wide frequency ranges are therefore of practical interest. Previously two types of single-frequency transformers, constructed -rrrrj'/j'////7// — -'I ^0, l1 — " 1 "0 A. '2 4 Z02 l2 Fig. 5— A wide-band transformer — constructed from coaxial conductors. from transmission lines, have been suggested ^ but these differ from the types investigated here in that they have a specified ratio of impedances for a single frequency only. One of the simplest types of band transforming filters is shown by Fig. 5. It consists of a series transmission line of characteristic im- pedance Zoi and a shunt line having the characteristic impedance Zog. Since the impedance of the short-circuited line is • ^ . C0/2 JZ02 tan — , the equations for the structure are ei = ei cos-^ 7*/Zoi sm — ; ti — ti cos V CjoIi V tl ei 0)1 1 J 7- sm — Zoi V t2 = — 12 + H ; >0 ei eo; (19) Z02 tan wh ' See reference 1, pages 430 and 431 . COAXIAL AND BALANCED TRANSMISSION LINES 285 Combining these equations we have Co coll ■ ry . ^l\ ei COS Pi^ox sin — , to — ll COS — V Zoi tan 1 + Zo, tan (jil\ co^a Sin J^i Zoi cot Z02 tan oil ioh (20) In order to interpret this equation in terms of transformer theory, it can be shown that equations (20) are identical to the equations for a perfect transformer and a symmetrical filter. To show this, consider the circuit of Fig. 6, which consists of two half-sections of a symmetrical Fig. 6 — Transformer and filter. filter separated by a perfect transformer having an impedance step- down (p^ to 1. The characteristic impedance of the first filter is (p- times that of the second filter. The equations for the first section, the transformer, and the last section are respectively ei = ei cosh -^ — iiKi sinh -z\ ii = ii cosh -^ — -^ sinh — ; L L L Ai / ii = ipii\ ei = ei/ If we consider the special case Z02 = ZoiZoJ^Zq^ + Z03) equation (41) reduces to the simple form tan 2(jili tan 2o)U or for narrow bands 2aji/i 2^1/2 and /i = 4(/i + /a) (42) (43) in agreement with equation (17). At the two cut-off frequencies, it can be shown that 7^ 2 (44) 292 BELL SYSTEM TECHNICAL JOURNAL and throughout the band the value of ip does not differ much from this value for narrow-band filters. Hence the structure of Fig. 8 acts as a narrow-band coupling unit which introduces a transformation from input to output. For narrow bands it is easily shown that the image impedance at the middle of the pass band is given by the expression K,= (fm) ^ (f f\ VZ01Z03 -^r- ^ U2 — Jl) Z03 (45) The design equations for this transforming filter are h = 4/2* l2 = 1-1 /l /2 Zoi — "T ^Riih-h) Zt)i — xi?r(/2-/i) fm

+ Z02C0C2 sin^ — C2 -\- Cs . 2aj/ , ^ sin + C3 V Ci + C2 + C3 . ,'«'/ r^ ^ yr. Sin^ a)Zo]CiC3 !» (50) + Z02WC2 cos^ — ; i^2 i^l COAXIAL AND BALANCED TRANSMISSION LINES 295 These equations give the image parameters for a general transforming band-pass filter. The two uses to which such a structure will ordinarily be put are either to obtain a transformer with as wide a pass band as possible for a given impedance transformation or else to obtain a filter without transformation ratio. For the transformer case it can be shown that the widest pass-band occurs when C3 ^ <» , or in other words the condenser Cs is short-circuited. In order to obtain a simple design, it is assumed that each conductor is an eighth of a wave-length at the mid-band frequency or that — = 7- (51) The mid-band frequency occurs when cosh ^ = 0. Upon substituting the relation Zoy = l/vCo where Co is the total distributed capacity of the input line of the transformer, cosh 6 vanishes when Cp^^'_C2_, (52) Solving for the frequencies for which cosh 0 = ± 1, it is easily shown that the ratio of the band width to the mean frequency is given by the expression _4_ fm J I ^' (53) 2(p^Co The image impedance Ki at the mid-frequency of the band is from equa- tion (50) f. _ TT C2 Kro = Zo, j 'y^. (54) 1+^ ^^ 4:p\ 296 BELL SYSTEM TECHNICAL JOURNAL where Ri is the input impedance from which the transformer must work. When the structure of Fig. 9 is used as a filter without transforma- tion, we have Ci = C3; Zoi = Z02 = Zq. For this case the image parameters become 2 a)/ 2Ci + C2 sm , . Ci + C2 2co/ V cosh Q = 7; cos 1 ^r— L\ V 2 OiZ^Cx' — wL'oZn Ki = K2 = K 1 - (2Ci + C2)cot^ V 2coZoCi(Ci + C2) , Z0C0C1C2 , '^n "^2(Ci + C2)^^"V II + (2Ci + C2)tan^ 2coZoCi(Ci + C2) (56) '^2(c7Tg) V For narrow-band filters it is easily shown that 4 /2 — /l ^ ^ TT ^ (2Cl -f C2)Co _ TT^ C2 /. 1 +^+_^ Ci 2Co Ci^ 16 Co (57) At the mid-band of the filter, since the constants were worked out on the assumption that each conductor was an eighth of a wave-length at the mid-band frequency, the mid-band filter impedance can be obtained from the last part of (56) by setting ccl/v = 7r/4, giving Kn = Zn '1 I ^2 TT C2 "^G 4 Co 1 I C2 ■ TT C2 "^c;^4Co (58) Hence solving for the constants of the filter on the assumption that A is a small quantity, we find Ci = 4Co C2 = I6C0 SR 7r(2 + 7r)A ' / = (TT-f 2)A ' 8/.' 33 31 Co = — ^in /jL/xf, (59) COAXIAL AND BALANCED TRANSMISSION LINES 297 where i? is a resistance equal to K at the mean-frequency of the filter. For narrow bands this gives a very large value for d, the shunt capacity. A more practical arrangement is to replace the two series condensers Ci and the shunt condenser C2 by a tt network consisting of two shunt condensers Ca separated by a series condenser Cb- These have the values C1C2 . ^ Ci" Ca 2Ci + C2 Cn = 2Ci + C2 (60) With this arrangement we find that for narrow bands Ca — Ci and Cb is a very small capacity. This can readily be obtained physically by inserting a partition with a small hole in it at the middle of the section. Then Ca will be the capacity of the inside conductors to the partition, and Cb will be the capacity of one inside conductor to the other looking through the small hole. By adjusting the size of this hole, this capacity can be made as small as desired. -0, Cl C3 -02 Fig. 10— A shunt terminated transformer. The transformer discussed above is suitable for transforming from line impedances down to very low impedances, but cannot be used to transform from line impedances up to very high impedances such as the impedance of a vacuum tube. This generally requires a shunt type of termination rather than the series type discussed above. One such transformer is shown in Fig. 10. It consists of two shunt lines connected together by a T or x network of capacities. The constants of such a transformer are readily calculated, and for the condition of maximum transformation for a given band wndth — which occurs when C3 -^ 00 , and for eighth wave-length conductors on each end — these have been found to be ^^= 1 + C2 7 > -^oi — ■^02 7 ^10 . ^02 - ^3 . r 4Co Cl— — , Co = - Co(^ - 1) ; / = 8/„ (61) 298 BELL SYSTEM TECHNICAL JOURNAL The theoretical band width for this type transformer is given ap- proximately by the expression /2-/1 fm ^(X + 2) (62) Such a transformer is also suitable for connecting together vacuum tubes of high impedance. Another type of transformer of some interest is one which will transform from very high impedances to very low impedances. Such a transformer is shown in Fig. 11. It has a shunt conductor on the high-impedance end and a series conductor on the low-impedance end. Such a transformer does not have a constant transformation ratio over the whole band, but for about 80 per cent of the theoretical band width ^//fffjjj77J-j-77//^Trrr ^0, C| l2 J Fig. 11 — A series shunt type transformer suitable for wide bands. the transformation ratio is approximately constant. The design equa- tions for such a transformer are -^10 _ ^2o -^^-^----<^^--^- 80 90 100 110 120 FREQUENCY IN MEGACYCLES 140 Fig. 13 — Measured insertion loss of a wide-band transformer. shows the measured insertion loss of a wide-band low-impedance trans- former which transforms from 70 ohms down to an impedance of 17.5 ohms. The useful transformation band is from 80 megacycles to 120 megacycles. The measuring circuit is shown in Fig. 14. It consists ;,j/j/;;,wt.w!/t//jiiin;^ 70cj -VvW- YZZ7ZZ2ZZZZZ, I Ml 111^ i-rrr% >>>^>l>> til > I )j . I ijjj jjt -V2 ^l.tim l}}i:iiiii:i inn!}iiiiiii*iiik r" Fig. 14 — Measuring circuit for a transformer. COAXIAL AND BALANCED TRANSMISSION LINES 301 of a source of high-frequency voltage impressed on a divided circuit. In one branch is a series resistance of 70 ohms connected to the 70-ohm side of the transformer. The output of the transformer is connected 80 70 60 u 50 CD (n 40 O _j z o 30 20 10 r jT \ lo 58 59 60 61 62 63 64 65 66 FREQUENCY IN MEGACYCLES 67 68 69 70 Fig. IS^Measured insertion loss of filter used on Green Harbor-Provincetown radio link. to a 17.5 ohm resistance and a high-impedance voltmeter is connected across it. The other branch contains a 52.5-ohm and a 17.5-ohm resistance in series, with a high-impedance voltmeter shunted across the 17.5 ohms. If the transformer were a perfect transformer, the 302 BELL SYSTEM TECHNICAL JOURNAL current from the output of the transformer would be ^° = 140X^17:5 = 70' (^^) where e is the voltage applied to ground at the common point. The voltage across the output should be eo=^Xl7.5=|. . (65) But this is just the voltage that should occur across the voltmeter V\. Hence the difference in reading between F2 and Vi will be a measure of the loss introduced by the transformer. From Fig. 13 we see that this is in the order of 0.1 db, which represents a small loss for a transformer. Several of the narrow-band filters of the type shown in section V, Fig. 9, have also been constructed and tested. One of these has been used on an experimental radio system at Green Harbor, Massachusetts, since 1935, for the purpose of connecting a transmitter and receiver on the same antenna. This filter has been constructed and tested by Messrs. F. A. Polkinghorn and N. J. Pierce using the design data developed here. The filter used consisted of three sections of the type shown in Fig. 9 connected in tandem. The resulting invSertion loss of the filter and associated transformers is shown in Fig. 15. The loss at mid-band is in the order of 1 db and an insertion loss of over 50 db is obtained 2 megacycles on either side of the center of the pass band. A Ladder Network Theorem By JOHN RIORDAN The theorem of this paper gives four-terminal representation of ladder networks satisfying a prescribed condition on the side impedances, in terms of the three parameters specifying the net- work connected as a transducer, the driving-point impedance between short-circuited transducer terminal pairs, and an im- pedance ratio involving the side impedances only. This mode of representation has a special advantage in applications to electric railway networks in that the transducer parameters which alone involve the ladder shunt impedances (under the stated conditions) may be calculated in a relatively simple fashion, and extensive networks reduced to manageable form. The theorem is stated and proved, and its applications are sketched in some detail. 'T^HE theorem of this paper gives a four-terminal representation of -*• ladder networks satisfying a certain condition with respect to the side impedances. Ladder networks appearing in transmission and filter theory generally are connected as transducers, that is, such that the entry and exit terminals on the ladder sides are associated in pairs; the networks are two-terminal pairs. As is well known, passive transducers may be completely specified by three parameters (as is the case for three-terminal networks, with which transducers are similar in some, though not all, respects), the choice of which has been the occasion for much study and ingenuity.^ The present theorem does not assume transducer connection and is thus quite distinct from earlier work; indeed it arose outside the communication field in the problem of the calculation of short-circuit currents and network current distribution of electric railway networks, where at present it seems to have chief application. This paper gives a statement of the theorem, an indication of its applications, and finally its proof. The Theorem A ladder network, composed of any number of arbitrary shunt imped- ances forming sections whose side impedances Zi^^^ Z2^*^ and Z^^''^, k = \, 1 Five types of equivalent networks by which a transducer may be replaced, including T, it, transformer and artificial line networks, and their interrelations are given on Table I of "Cisoidal Oscillations" by G. A. Campbell, Trans. A. I.E. E., 30, pp. 873-909 (1911). The most significant addition to the table would appear to be the image impedance representation due to O. J. Zobel. 303 304 BELL SYSTEM TECHNICAL JOURNAL 2 ■••,are such that [Zi^*) - Zi2(*>][Z2(*> - Zia^*^]-^ is a constant, may be completely specified by its three transducer parameters {with transducer terminal pairs each made up of adjacent terminals on opposite ladder sides'^), the driving-point impedance between short-circuited transducer A . Network Diagram (K) 2^n-0 B. Network Equivalents (V + a)Z|2:34- o3 VZ|2:i2+aZ|2:34 VZ34:34+aZ|2;34 Z-v(l-v)(Z|2:i2 + Z34:34-2Z|2;34) . Ci-v)z,p.|p-az I2;|2-^^I2:34 .Ci-v-a)Z|2:34 (l-V)Z34:34-aZ|2:34 A 4 aZ + v2(Z|2:i2-Z|2:34) (l-a)Z + V^(Z34:34-Z|2:34) 0CZ + (1-V)2(Z|2..|2-Z|2:34) (l-a)Z + Cl-V) (Z34;34-Z|2:34) Notation p = Pk = [Z/*) - Z,2f«][Z,(*) + Zs^*) - 2Zi2('=)]-i »S'l2:i2 = (Zl2:i2Z34:34 — Z^12:34)/Z34:S4 ■534:34 = (Zi2:i2Z34:34 — Z'i2:34)/Zi2; 12 •5'l2:34 = (Zi2:i2Z34:34 — Z-12:34)/Zi2:34 Zi(*) + Z2(*' - 2Z,2<*) a = Arbitrary Constant Fig. 1 — A sample ladder network illustrating notation; and some network equivalents. ^ The theorem also holds when the terminals of each pair are non-adjacent, that is, for terminal pairs 1, 4 and 3, 2 of Fig. \A ; this result is of no importance in the railway applications. A LADDER NETWORK THEOREM 305 terminal pairs, and the constant The current in any branch of the network for any condition of energiza- tion of the network terminals is a linear function of the currents in the same branch for energization at sending and receiving transducer terminals. It should be observed that the result stated is independent of the number or values of the shunt impedances (except as they are included in the transducer parameters); hence in the diagram on Fig. \A illustrating the ladder network in question, any of the shunt imped- ances may be allowed to vanish or become infinite, and their number w + 1 may be increased or decreased at pleasure provided that one shunt remains (this excludes the trivial case in which, the sides being completely insulated from each other, the network degenerates to a pair of single impedances). When the impedances of the sides are linearly extended impedances, as is the case in electric railway applications, the section impedances may be written : Zo^^) = 5,22, Zi2^^^ = SkZi2, where Zi, z^ and 212 are self and mutual impedances of the sides per unit length. The condition, [Zi^ - Zi2(^)][Z2(^-) - Zn^*)]-^ = const., is replaced by the condition that the shunt impedances connect corre- sponding points on the sides. Since a four-terminal network requires six independent quantities for its specification, the conditions (a) that the network be of ladder type and (b) that the given section impedance ratio be constant may be regarded, at least intuitively, as replacing two (or more) of the measur- able impedances at the terminals.^ With the sending and receiving transducer terminal pairs short- circuited, and with the side impedances satisfying the given condition, no current flows in any of the shunt impedances and the driving-point impedance required for the theorem is ^ ^ Zi(^>Z2<^> - Zi2^^^^- _ EZiW^Zz^^) - (i:zi2^^0^ ... C;Zi^*^ + Z2(*> - 2Z12W EZi« + EZ2(« - 2i:zi2(^)' ^ ' 3 It is interesting to observe that, if short circuits between terminals are permitted, there are 64 measurable impedances for a four-terminal network. The network may be specified by any six of these which are independent; hence the number of ways of specifying the network is something less than the number of combinations of 64 things taken 6 at a time, which equals 74,974,368. The number of non-independent sets which make up this large total appears at the moment to be the smaller part, and possibly a very small part indeed. These remarks are inspired by Mr. R. M. Foster. 306 BELL SYSTEM TECHNICAL JOURNAL where the summations in the last expression extend over all the sections; this impedance then is simply the parallel impedance of the sides taken in their entirety. The current in branch k of line 2, designated by Ik on Fig. \A, for any condition of energization is expressed in terms of the currents in the same branch and in the same direction' for unit current supplied between terminals 1 and 2, and 3 and 4 [terminals 3, 4 (1, 2) open, respectively]], designated by 4: 12 and 4:34, respectively, by the following equation : h = V{h + U) - ik:l2lvh - (1 - V)h'] - H-.ulvh - (1 - V)h'], (2) where /i, I2, I3 and li are currents flowing out of the network from the respective terminals, and v is the current in side 2 for unit current between short-circuited transducer terminals, as given on Fig. IB. Thus Ik is a linear function of currents 4:i2 and 4:34, as stated in the second half of the theorem. Three types of networks completely equivalent to any ladder network satisfying the condition of the theorem are shown on Fig. IB. The transducer impedances employed in the representation by these networks are the driving-point impedances between transducer termi- nals 1 and 2, and 3 and 4 [terminals 3, 4 (1, 2) open, respectively]] and the corresponding transfer impedance between the ends of the trans- ducer. These impedances are designated Zn.n, Zzh-.za and Zmisi, following a notation for Neumann integrals used by G. A. Campbell.'* For present purposes the notation has the advantage of putting into evidence the terminals between which current is supplied and the terminals between which voltage is measured; thus Zi2:i2 may be read as the voltage drop from 1 to 2 for unit current from 1 to 2 (terminals 3, 4 open), Zi2:34 the voltage drop from 3 to 4 for unit current from 1 to 2 under the same conditions.^ By the reciprocity theorem Zi2:34 = ^34:12. ^ "Mutual Impedance of Grounded Circuits," Bell System Technical Journal, 2, 1-30 (Oct. 1923). * Further, the subscripts may be handled algebraically to give results following from the superposition theorem. For this purpose the numbers in each part of the two-part subscript are taken as separated by a minus sign and the colon is taken as a sign of multiplication; thus: ■2l2:i2 = ■^(l-2)(l-2) = Zii + Z22 — 2Zi2, the last expression being formed by writing out the indicated product and separating the terms. The equation expresses the fact that the impedance of a circuit may be subdivided into the self-impedances of sides (real or fictional) associated with its terminals minus twice their mutual impedance. Moreover, any additional sub- scripts desired may be intercalated by adding and subtracting the same numeral; the expansion of bracketed terms then gives a relation between circuit impedances; thus: Z(l_2)(l-2) = Z((i_3) + (3_2))((1_3)+C3-2)1 = Z(i3+32)(13+32) = Zir-lS + ^32:32 + 2Z\y.s2- A LADDER NETWORK THEOREM 307 The first two equivalent networks are of the H type; ® as seven impedances are shown on each, whereas only six are required for complete representation, an arbitrary constant a has been introduced so that the mutual impedance of the uprights may be varied at pleasure. Thus in the first H network, the condition a -]- v = 0 puts all the mutual impedance between the uprights below the crossbar; the condition 1 — v — a = 0 puts it all above. The same type of shift may be made in the second H network. The third equivalent is the network of direct impedances ("Cisoidal Oscillations," loc. cit. designation (b)); these are expressed in terms of the transducer parameters with opposite pairs of terminals short- circuited, which following Campbell are denoted by 6"s. Thus 6'i2:i2 is the driving-point impedance between terminals 1 and 2 with terminals 3 and 4 short-circuited; 5i2:34 is the ratio of current from 3 to 4 to voltage from 1 to 2 with 1, 2 energized and 3, 4 short-circuited, or its reciprocity theorem equivalent. These three equivalents correspond respectively to transformer, T and T transducer equivalent networks. For the first H type the transducer condition that currents into terminals 1 and 2, and 3 and 4, shall be equal and opposite entails zero current in the iJ crossbar, which may be removed, leaving a transformer connection. For the second H type the transducer condition allows grouping the impedances of branches 1 and 2 and their mutual impedance, and of 3 and 4 and their mutual impedance, into single branches, say, branches 1 and 3, which gives the T equivalent network. The reduction of the direct imped- ance network is not so immediate. Periodic Ladder Networks When the network is periodic, the transducer impedances and current distribution may be expressed completely in terms of the The justification of the operation Hes in the fact that, as regards the current half of the subscript, a unit current from 1 to 2 is equivalent by the superposition theorem to unit currents 1 to 3 and 3 to 2 and similarly the voltage 1 to 2 for unit current 1 to 2 is the same as the sum of voltages 1 to 3 and 3 to 2. Thus the notation is a shorthand for application of the superposition theorem. Its use is illustrated further in the course of the proof of the theorem. ^ This is a form of equivalent network falling under designation (c) of the list of equivalents for an arbitrary number of terminals given by G. A. Campbell ("Cisoidal Oscillations," p. 889, loc. cit.), which is described as branches radiating from a common concealed point, one to each of the terminals, with mutual impedances between pairs. This is not a unique representation since the number of elements is redundant, and the set of mutual impedances may be given values appropriate for particular purposes pro- vided that the self-impedances are adjusted correspondingly. In the present applica- tion the mutual impedances of branches to terminals 1 and 4, and 2 and 3, have been set at zero and the mutual impedances of branches 1 and 2 and 3 and 4 in the first H diagram, and of branches 1 and 3, 2 and 4 in the second, have been eliminated in forming the cross bar of the H. 308 BELL SYSTEM TECHNICAL JOURNAL section impedances, giving a certain concreteness to the application of the theorem, which may be valuable. Partly on this account, and partly because periodic iterative impedances are in themselves useful in applications, a particular type of periodic network is considered in this section. The network considered is infinite in extent, with section series impedances Zi, z^ and 012 and shunt impedance Z3, as shown on Fig. 2 A. A . Network Diagram Z] Z3 Z|2 Z3 Ik— * B. Network Impedances Zabud \ 06 <;rf\ 12 13 14 24 12 13 14 23 24 34 K AK-T) T+v{K-T) -K+v{K-T) -{,\-v){K-T) T Z+2pHK-T) Z-v(\-2v){K-T) Z-v{\-2v){K-T) Z-2v{\-v)(K-T) Z+K-2p^I-p)(K-T) Z-T-2p(,1-v){K-T) 2 + (l-;,)(l-2W(K-r) (i-v)K+vT Z + (l-^)il-2,){K-T) Z+2{l-y)^K-T) (i-W(x-r) C. Current Distribution Unit Current Between: ik 1 and 2 1 and 3 1 and 4 2 and 3 2 and 4 3 and 4 ^1 ^-ka Ki+Ki- " K1.+ K2 '"' ' "' ' ' K1+/C2''' ^^ '^'- ' Ai + A2 Ai + A2 ^I f-(n+l-k)ni Fig. 2 — Periodic ladder network of infinite extent; network diagram, impedances and current distribution. The infinite network is the simplest to formulate since there are no points of reflection; it is of course symmetrical with respect to the terminal pairs 1, 2 and 3, 4. A LADDER NETWORK THEOREM 309 The impedance across either of these terminal pairs is the parallel impedance of the full-series and full-shunt iterative impedances (or one-half the mid-shunt iterative impedance). The full-series and full- shunt iterative impedances are given by the following formulas: Full-series Ki = ^[V2(2 + 423) + s] = i^2 + 2, Full-shunt K2 = |[V2(2 -f 423) - z] = J^'f' , (3) Ki -\- Z3 where, for brevity, 2 = 2i -}- 22 — 2zi2. Then 7 7 TT ^^^^ \ ^ , 423]-^/^ ... ^12:12 = ^34:34 = A = Z^ _l_ J^ = 23 1 H • (4) The voltage across lines is propagated as exp (— ka) where a is the section propagation constant; hence Zi2:34 = T = Ke-'^\ (5) The propagation factor exp (— a) is defined in terms of the iterative impedances by <^- = 1^ • (6) The currents 4:i2 and 4:34 are given by the following formulas: '"""'jg.+'ji:/''"'""'"'- <^' This completes the formulation, since the remaining quantities, v and Z, are given immediately by 2i — 2i2 2i -f 22 — 2Zi „ 21Z2 — 2i2^ 2i22 — 2i2^ Z = 2^ , ^j — = n k=lZ\ + 22 — 22i2 2i -f 22 — 22i2 Figure 2B shows driving-point and transfer impedances for energiza- tion between terminals, omitting certain impedances equal by symmetry. Figure 2C shows the corresponding ^-section currents in side 2. 310 BELL SYSTEM TECHNICAL JOURNAL Applications to Electric Railroad Networks A.-c. electric railroad networks in one-line diagram are predominantly of the ladder type. The series elements of sides 1 and 2 represent, for two-wire networks, impedances of sections of transmission lines and traction circuits, respectively; the shunt elements represent transformer impedances. For three-wire networks, the series elements may repre- sent trolley-feeder (or feeder-rail) and trolley-rail impedance elements, the shunt elements autotransformer impedances. The theorem may be used for representing portions of a network or a whole network of ladder form,^ when the series impedances satisfy the condition of the theorem. As the circuits are linearly extended this is almost always the case except where the traction circuits change character, from two to four tracks, for example. For approximate purposes the H networks may be used even in these cases provided that the parameter v is properly chosen. In many cases the transfer impedance Zx2:u is negligible and a value of v may be associated with each pair of terminals; the values for the sections immediately ad- joining the terminal pairs 1-2 and 3-4 (sections 1 and n on Fig. 1^) are of dominant importance and serve for rough purposes. If the transfer impedance is not negligible a mean of these values may be sufficiently accurate. In two-wire networks, generator circuits are connected directly to the transmission line (side 1), and the short circuits of chief interest (grounding points on the one-line diagram) are those on the traction circuits (side 2). Thus, for a single generating point the network is energized between points on sides 1 and 2, such as 1 and 4, for example; if the impedance in the generator connection is Zg and the impedance of the short circuit is zero, the short-circuit driving-point impedance and the traction circuit currents are as follows: Z{) ^ Zg -\- Zu:i4 = Zg-^Z -^ p-'Zn-.ii + (1 - J^yZu:u + 2K1 - ^)Zi2..u, (9) h= L^-i- VU:l2 + (1 - V)4:34]-^ , (10) where E is the generator voltage. The impedance may be obtained immediately from either of the H networks — as the sum of the self- ' For multiple transmission-line two-wire networks the ladder form is obtained when aU transmission lines are bussed at all generating stations and substations or when the generators, step-up transformers and substation transformers connected to each line are of similar impedances and are similarly connected. When these condi- tions are not met the network is of multiple-side ladder form, for the representation of which an extension of the theorem would be required. Similar remarks apply to three-wire networks. A LADDER NETWORK THEOREM 311 impedances of legs 1 and 4 and of the crossbar. The current expression follows from equation (2) with I2 = Is = 0; — Ii = I4 = E/Zq. For multiple generating points (or for multiple points of short A . Short Circuit Between Generator Points _[<5>- KS>L j^ Z|'3':i'4' = Z'+v2(Z|'2':i'2.-Z|'2':3'4')-v (l-v)(Z3.4':3.4'-Z,'2':3'4') _cd>j> B. Short Circuit Beyond Generator Points _E7a>-| A4' ^(Z34:34~Z|2:34) El j-a> 1 Z|3:i4 (l-l')Z34:34+l^Z|2:34 yZ,'2':l'2'+0-l')Zi'2':3'4' Zr4':2'4' 4' (l-v)(Z|'2':i'2'-Z|'2':3'4') "1 Z|'4':2'4' = Z'-v(l-v)(z,'2':i'2'-Z|'2':3'4') + ('-v)^ (ZsU': 3'4' -Z,'2': 3'4') Fig. 3 — Equivalent networks for electrified railways; two-wire system, two sources. circuit) the theorem may be used to represent portions of the network. Examples for the case of two generators are shown on Fig. 3 ; on Fig. diA the short circuit is located between generator points, on Fig. SB beyond them. On Fig. ZA the network is supplied with duplicate pairs of terminals at the short-circuit point, separated by an infinitesimal 312 BELL SYSTEM TECHNICAL JOURNAL difference; the parts of the original network thus formed are represented by F-connected impedances which may be derived from the first H network. On Fig. d)B the network is broken at the intermediate generator point and similarly represented. A similar process may be followed for any number of generator points but in some cases it may be expedient to superpose additional generators; the network imped- ances required for superposition may be formulated in the manner followed in the proof of the theorem. The solution of these reduced networks supplies the currents /i, I^, Ii\ //, Iz , li , etc., from which the current in branch k of side 2 of any of the ladder sections may be found from equation (2). Thus, for example the current Ik in the ^th section of the ladder network with terminals 1, 2, 3 and 4 on Figs. 2) A and d>B is formulated as follows: Ik = [l' + 1^4:12 — vik:u']l2, + \iv -\- viic-n + (1 — I')4:34]/4, (H) which follows from equation (2) with I2 — 0; — Ii — I3 -{- li- Similar formulas apply to the other two ladder networks on Fig. 3. In three-wire networks, generators are usually connected to the traction network by three-winding transformers which may be repre- sented on the network diagram by three impedances connected in star. The traction network may be represented on a trolley-feeder, trolley- rail or a feeder-rail, trolley-rail base and it is well known that the three- winding transformer equivalent impedances for the two bases are related. Using the notation shown on Figs. AA and 4^', with primes distinguishing the feeder-rail, trolley-rail base, the relations are as follows: VtfZa = VtfZj + VtrZt', VtfZ, = VfrZb', (12) Vtf'Z. = Vsr^Z: - V,rVs,Z^, where Vtr, Vt/ and V/r are the trolley-rail, trolley-feeder and feeder-rail circuit voltages, respectively. From Figs. 4B and AB' showing the reduced networks for trolley-rail short-circuits on the two bases for a single source feed, it is apparent that the impedances involved in the equivalent networks must be similarly related. The relations are found to be as follows: (13) V^/ Zi2:\2 = Vfr'^Z' 12:12, Vtf ^Z34:34 = Vfr'Z' 34:34, Vtf ^Zi2:34 = Vfr'Z' 12:34, r.(l - ^) = VM - / z = z', 4:12 = i'k:12, 4:34 = i'k-.M- A LADDER NETWORK THEOREM 313 Trolley-Feeder, Trolley-Rail Base A . A dual Network Connections \ 3T-F <)4 T-R B. Equivalent Network for Trolley- Rail Short Circuits 1 ^Z|2;l2 + 0-V)Z,2:34 Zl4:24 Cl-v)(Z|2:i2-Z|2:34) Z|4:24 =Z-V(l-V)(Z|2;|2-Z.i2:34)-*-(^'"'^^ (234:34-^12:34) C. Equivalent Network for Trolley- Feeder Short Circuits ^(Z|2.I2-Z|2:34) Z|3:23 1.^ (l-V)Z|2:12 + ^Z|2;34 Z|3:23 = Z-v(l-V)(Z|2:|2-Zi2:34) + ^^ (234:34-2,2:34) T Fig. 4 — Equivalent networks for electrified railways; three-wire system, single source, trolley-feeder, trolley-rail and feeder-rail, trolley-rail bases. Thus the complete set of short-circuit currents (trolley-rail, trolley- feeder and feeder-rail short circuits) may be made from a single determination of the transducer impedances and current distributions on either of the two bases, whenever the theorem is applicable. For multiple generator three-wire systems, and for three-wire systems with auxiliary transmission lines, the theorem may be used to represent portions of the network, possibly broken as in the two-wire cases illustrated above, four-terminal representation being necessary in general. The application follows the lines indicated above. Proof of Theorem For energization between terminals 1 and 2, the sum of the currents in sides 1 and 2 at any point on the ladder is zero; the current ik-.u may be taken as flowing in a mesh made up of the ^-section sides and its terminating shunt impedances. For unit current supplied, the 314 BELL SYSTEM TECHNICAL JOURNAL Feeder-Rail, Trolley-Rail Base A'. Actual Network Connections i 1 A4T-R B' . Equivalent Network for Trolley-Rail Short Circuits I , /z'ip:ip + 0-v')Z|2:34 Z \a:7>a 0-v')(z;2:i2-z;2:34) T Zl4:24=Z'-v'(l-v')Cz'|2:i2-Z[2:34)+(l-v')^CZ34-.34-Z|2:34) C. Equivalent Netzvork for Feeder-Rail Short Circuits v'(Z|2:i2-Zi2:34) Z|3:23 I-V')Z'|2:I2+^'Z'|2:34 T Z;3:23 = Z'-V'0-V')(ZI2:|2-Z;2:34)+^1^'.>^(Z34:34-Z;2:34) Fig. 4 — Continued from page 34:6. driving-point impedance between terminals 1, 2 and the transfer impedance to terminals 3, 4 for the'network shown on Fig. lA may be formulated immediately as: Zi2:12 = (1 + il:n)Z'^, Zi2:34 = - t„:12Z<"). (14) The positive sense for currents inn and 4;i2 is taken as indicated on Fig. lA, namely, in the direction from terminal 2 to terminal 4 on side 2. From the voltage equation around the loop formed from sides 1 and 2 in their entirety and the terminal shunt impedances, the difiference of these impedances may be expressed by: Zi2:12 - Zi2:34 = - E (^l^^) + Z^^''^ - 2Z n^'^)i,..n. (15) 4=1 A LADDER NETWORK THEOREM 315 The transfer impedances with respect to the side terminals 1, 3 and 2, 4 are formulated as: (16) Zi2:24 = L (^2^ - Zi2(^>)4:12. From the condition [Zi^^^ - Zi2^'=>][Z2('=) - Zi2^*>]-i = const., a con- stant J' may be defined such that: p= p,= [Z/« - Zi2W][Z:(*) + Z2(^-) - 2Zx2(«]-\ 1 - , = [22^ - Zi2(«][ZiW + Z2(^> - 2Zi2<'=>]-\ and equations (16) may be combined with (15) to give: Zi2:13 = J'Zi2:12 ~ »'Zi2:34, Zi2:24 = — (1 — I')Zi2:l2 + (1 " I')Zi2:34. The remaining transfer impedances follow by superposition ; thus Zi2:l4 = Zi2:l3 + Zi2:34 = l'Zi2:i2 + (1 ~ v)Zi2:Zi, Zi2:23 = Zi2:13 — Zi2:12 = — (1 — V)Zii:\2 — vZi^.zi- It may be observed that Zi2:24 = Zi2:13 4" Zi2:34 Zi2:\2- (1") Similarly (17) (18) Zzi:\Z ~ — vZzi-.Zi 4" vZ\2:Zi, Zzi-.U = (1 ~ v)Zzi:Zi + vZ\2:Zi, Zzi:23 = ~ vZzi:Zi "" (1 ~ v)Z\2:Zi, Zzi:2i = (1 — J')Z34:34 — (1 — J')Zi2:34- (20) These impedances, together with Z34:34 and Z34:i2, form a set of 12 impedances of which only five are independent. There are three independent impedances determined by energization at each pair of terminals, including Zi2:34 and Z34:i2, which are equal by the reciprocity theorem; one independent set, for example, is Zi2:i2, Zi2;i3, Znm, Zzi:zi, Zzi-.xz- Consequently the network may be completely specified by the addition of a single impedance; for the set illustrated, the impedance required is Zi3:i3. This impedance may be formulated as: 316 BELL SYSTEM TECHNICAL JOURNAL where the summations extend as above from 1 to n. Writing the equation around the loop used in deriving equation (15) it is found that: Z(Zi(« + Z2W - 2Zi2(*))4:13 = E(Zl(« - Zi2(«) - Zi3a2 + Zi3:34 (22) = i:(Zl(« - Zi2(^>) - KZl2:12 + Z34:34 " 2Zi2:34), the last step being made by use of the reciprocity theorem and the formulas already developed. Thus, finally: Zi3:l3 = Z + J'^(Zi2;i2 + Z34:34 " 2Zi2:34), (23) where r, ^ ^ ZlWZ2^^) - (Zl2(^^)'^ .=iZi(^)+Z2(« -2Zi2^*>* As already mentioned, Z is the impedance between short-circuited terminals 1, 2 and 3, 4; this may be verified in a number of ways. The remaining impedances follow by superposition, which can be carried out formally through the impedance notation in the manner suggested. There are 21 driving-point and transfer impedances between terminals which can be displayed in a triangular array similar to that shown on Fig. 2B. The additional measurable impedances at the terminals arise as follows: 36 from short-circuiting two terminals, 4 from short-circuiting three terminals and 3 from short-circuiting terminals in pairs. Equation (22) may also be written in terms of currents ik-.n and 4:34, since Zi3:i2 and Zi3:34 may be expressed in terms of the latter; this suggests the following relation: 4:13 = V + vik:\2 — vik:5i. (24) The relation is verified by substituting into the mesh equations for currents 4:i3; the typical equation is as follows: - Z(*-1>4-1:13 + [Zi(*) -f Z2<*) - 2Zi2<'=) + Z(^-" + Z<«]4:13 - Z«4+l:13 = Zi(« - Zi2<«. The remaining current relations then follow by superposition, as follows: A LADDER NETWORK THEOREM 317 ik-.li = 4:13 + 4:34 = I' + 1^4:12 + (1 " 1^)4:34, 4:23 = 4:13 — 4:12 = J^ — (1 — 1^)4:12 — I'4:34, (25) 4:24 = 4:14 — 4:12 = I' — (1 — I')4:12 + (1 — J')4;34. It will be observed that only three of the six currents 4.i2, 4:i3, 4:i4, 4:23, 4:24 and 4:34 are independent; one independent set is 4i2, 4:34 and 4:13. Hence any arbitrary set of currents /i, I2, I3 and li flowing out of the network at the terminals may be resolved into three flows, such as those illustrated in the independent set above, which leads to equation (2). The first H network may be obtained in the following manner. The value of Zi2:i3, namely, pZi2:i2 — vZh-.za, in conjunction with the condition Zi + Z2 = Zi2:i2, Zi and Z2 being the impedances of branches to terminals 1 and 2, respectively, suggests the following values of branch self and mutual impedances: Zx = I'Zi2:12, Z2 = (1 — I')Zi2-i2, Zi3 = vZi^.zi. The value of Zu is verified by inspection of Zu-.zi if Z3 = vZ 34:34. Similarly, by inspection of Zi2:i4 and Z34:32, the values of Z24 and Z^ may be tentatively set at Z24 = (1 ~ v)Z\i:Zi, Z4 = (1 — l')Z34:34. The impedance of the crossbar, say Zo, may be found from any of the impedances Zi3:i3, Zu.u, Zi3:iz, Zzi-.n; e.g., Zo = Zi3:i3 — (Zi + Z3 — 2Z13) = Z — v{l — v)(Zi2:i2 + Z34:34 — 2Zi2:34). But the presence of seven elements, as already mentioned, suggests an arbitrariness which may be put into evidence by adding aZi2:34 to Zi, which entails a similar addition to Z3 and Z13, and a similar subtraction from Z2, Z4 and Z24- Similar considerations apply to the derivation of the second H network. The direct impedances may be found, in a well-known manner, by energizing the network between one terminal and the other three 318 BELL SYSTEM TECHNICAL JOURNAL short-circuited terminals or by applying a formula due to G. A, Campbell.^ Acknowledgments I am indebted to Mr. E. D. Sunde for a suggestion which brought this theorem into focus for me; Dr. H. M. Trueblood has aided in eliminating certain weak points in the proof; to Mr. R. M. Foster I owe a number of improvements, aside from that mentioned in the footnote, in the general spirit of the paper. My chief acknowledgment, however, as indicated by the footnotes referring to his work, is to Dr. G. A. Campbell ; I should like the paper to be taken as an instance of the fertility and generality of the methods and results of network analysis he has introduced. * "Direct Capacity Measurement," Bell System Technical Journal, I, 1, pp. 18-38 (July, 1922). The formula, given on page 34, requires modification only to the extent of substituting impedances for capacities; for four terminals the direct impedance, Dij, between terminals i and j is given by: D.i = 2Aij ' where A,j is the co-factor of the element in row i, column _;" of the determinant: A = 0 Zn Zi3 Z,4 1 Z,2 0 Z23 Z24 1 Z,3 2,3 0 Z34 1 Zl4 Zo4 Z34 0 1 1 1 1 1 0 The elements of the determinant are the driving-point impedances between terminals indicated by the subscripts (all other terminals open), namely, Zi2:i2, ^13:13, etc., written for brevity Zn, Z13, etc. Contemporary Advances in Physics, XXXI — Spinning Atoms and Spinning Electrons ^ By KARL K. DARROW NO doubt you are all accustomed to thinking of atoms as objects — very small objects, of course — which are endowed with weight. I can say that with perfect safety to an audience of engineers and physicists; but indeed it can be said with safety to any audience — I mean, of course, any audience literate enough to attach any meaning at all to such a word as "atom." It may be that philosophers of the past have imagined weightless atoms— I am not historian enough to deny that, nor to affirm it; but if such have ever been invented, they have remained quite outside the currents of modern thought. For us, weight is a property which we attribute to the atom. Since this is, after all, a professional audience, I will now change over to that other word which many people have such difficulty in distinguishing from "weight": I will say that mass is a property which we attribute to the atom. In a way, that is a negative statement. It means that we do not hope to explain mass in terms of something more fundamental; it means that we accept mass as being itself so fundamental that even the elementary particles have it. When I say "elementary particles," I am still referring in part to the atoms, though it is a somewhat careless usage to do so; but I am referring also to electrons both positive and negative, to protons, to alpha-particles, to nuclei — to all the particles, in effect, of which the atoms are built up. Also I ought to include the corpuscles of light, but this lecture will be quite long enough if I leave them almost unmentioned. All of these particles, then, are endowed with mass; each of them has a characteristic mass of its own, which we do not attempt to explain, but which we do try to measure as closely as we can. There is another property, familiar to you though not to everyone, which we accept as equally fundamental and equally unexplainable with mass : it is electric charge. We attribute it also to the elementary particles, though not, it is true, to all of them. We assign it to the electrons, of course, and to protons and alpha-particles and all of the hundreds of nuclei which distinguish the elements and the isotopes ' A lecture delivered before the American Physical Society at Chicago on Novem- ber 27, 1936, and before the American Institute of Electrical Engineers at New York on May 6, 1937. 319 320 BELL SYSTEM TECHNICAL JOURNAL thereof from each other. When I say that we "assign" it, I do not for a moment mean that we are doing something arbitrary or un- testable. We know that these elementary particles are charged, and indeed we have measured their charges. Atoms do normally appear to us uncharged, but we know that that is because the elementary particles of which they in their turn are made up are some of them positive, some of them negative, and the balance normally happening to be perfect. Some particles, the neutrons and the corpuscles of light, seem permanently chargeless; but perhaps some day we shall find it expedient to regard them as groups of smaller particles having charges which balance one another. Apart from these two cases, we may say with assurance that whenever we penetrate as far into the fine structure of substance as we are able to go, we find the elementary particles invested with mass and with charge. And now I arrive at the subject of this talk, the third property of the elementary particles: the property which is called "angular momentum," or "spin" for short. Now of course I am speaking as to an audience of physicists, for if this were an audience of laymen it would certainly be frightened by such a term as "angular momentum." This is a misfortune, and perhaps a defect of general education; for angular momentum is about as important as mass or charge, not only on the scale of the elementary particles but also on the scale of the visible world. Think what it would mean if there were no such thing as the conservation of angular momentum! the earth might cease from turning, it might cease from providing us with the regular alternation of day and night, and with our standard of the flow of time; it might even cease from traversing its regular orbit, and fly off into space or fall into the sun. Well, I do not wish to scare you with any such dire imaginings — I only want to remark on the fact that the human race has been acquainted for a very long time indeed with angular momentum as something which is unvarying, imper- turbable, incessant; for of all the unvarying and imperturbable and incessant things in the world, the rotation of the earth is the most obvious and the most striking. So striking it is, that you might reasonably expect that all the philosophers and all the physicists of the past would have conferred the property of spin on all the atoms which they have invented. Well, they did not; the notions of the spinning atom, the spinning electron, the spinning nucleus are among the newest in physics. I think that some of the reasons for the delay will be evident later on in this talk, but it remains partly mysterious, at least to me. Looking back on the situation with the well-known advantages of hindsight, I do feel a good deal of surprise that the CONTEMPORARY ADVANCES IN PHYSICS 321 spinning atom did not make an earlier entry upon the scientific stage. Perhaps some of you will remember hearing the words "vortex atom" and "vortex theory" which used to be so prominent in physics, and will take the spinning atom of today for a lineal descendant of those vortices of old. If this were correct, we could trace back the ancestry of the spinning atom for about three hundred years; but I think that it is not correct. The vortices of which Descartes and Malebranche were dreaming three centuries ago were more like whirlpools of stream- ing particles, and the vortices which were imagined by Helmholtz and Lord Kelvin some fifty years ago were also whirlpools, but they were whirls in an idealized continuous frictionless fluid. Let us pause for a moment to notice how the attitude of physicists has altered in these fifty years! Kelvin and Helmholtz began with the idea of an aethereal fluid pervading the whole of space, and valiantly tried to represent the atoms as whirlpools in that fluid ; but we have long since discarded that aether, and our spinning atoms and other elementary particles are small delimited rotating bodies voyaging in a void. It is nor therefore the vortex which I will introduce to you as the ancestor of the spinning atom, but rather the "Amperian whirl" as it still is sometimes called. You remember, of course, how Ampere in 1820 made a very great achievement which for the purposes of this talk I will divide into three. First, he discovered the fact that an electric current flowing in a circuit is equivalent to a magnet. Next, he worked out the mathematical laws whereby, given a current and the circuit in which that current is flowing, we may calculate the strength or the moment of the equivalent magnet. I will write down the formula for the case of a current i, flowing in a plane loop of area A : the magnetic moment of the equivalent magnet, /x, is given thus: fj. = iAjc. Here c is a factor of transformation which we are now obliged to employ because we habitually use, in atomic physics especially, a unit-system different from Ampere's. The third part of the great achievement was this: Ampere founded what remains to this day the theory of magnetism, by presuming that the individual atoms of any magnetizable substance are themselves little magnets, and that the atoms are magnets because they have little whirls of current in them. This notion — the notion that atoms are magnets, and that they are magnets because they have internal circulating currents — is the true forerunner of our present conception of the spinning atom. It is, however, only a very primitive form of the modern conception, and there is much to be added to it. First of all and above all, there is 322 BELL SYSTEM TECHNICAL JOURNAL the question of angular momentum. Is angular momentum an attribute of these whirling intra-atomic currents, or is it not? You may think that the answer to this question is self-evidently "yes!" but remember that for many generations of our forefathers electricity was an imponderable fluid. Weber, however, did consider the affirma- tive answer, and Maxwell even attempted to ask the question of Nature by experiment — vainly, as it turned out. Not till the electron was discovered did the mass of electricity become a prominent part of experience. A moment ago I divided Ampere's achievement into three parts ; similarly I wish now to divide the discovery of the electron into three. Those who isolated and identified and measured the electron were proving three things: first, that negative electricity consists of corpuscles of a definite charge, e; second, that these cor- puscles have a mass, m; and following from these two, the principle which I have called the third part of the discovery, viz. that an electron revolving in an orbit has an angular momentum. I will designate angular momentum in general by the letter p, and now I will show you a formula for the ratio oi fx to p in an atom in which an electron is running around in an orbit and constituting an Amperian whirl. The formula, like this other one, for ^l, is valid for an orbit of any shape, but to get it quickly I will simplify by postulating a circular orbit. The radius of the circle being r, the area A is irr^; the current around it is equal to the electron-charge e, multiplied by the number of times per second that the electron runs around the orbit; if I denote the velocity of the electron by v, this number is v/lwr; hence the product iA/c is equal to evrjlc. Now the angular momentum p of the electron, as you all know, is mvr; and hence for the ratio I derive: ^llp = e/2mc, ^ which is one of the most important formulae in the whole of atomic physics. You notice that it does not involve in any way the size or shape of the orbit or the frequency with which the electron travels around it. It is the same for any or all of the revolving electrons of any atom of any kind. Now let us see how this formula may be tested. Imagine a rod of some highly magnetizable metal, iron for instance, and imagine it to be unmagnetized at the start. This means, that at the start the little atomic magnets are pointing at random in all directions; that is to say, the vectors which represent their magnetic moments are pointing every way, and so are the vectors which represent their angular momenta, the latter being parallel to the former. Since these atomic vectors of angular momentum are pointing every way at CONTEMPORARY ADVANCES IN PHYSICS 323 random, they add up to zero, and the rod as a whole possesses no resultant angular momentum; it is just standing still. Now let the rod be surrounded with a solenoid, and by means of a current in the solenoid let it be magnetized to saturation. Now all the arrows representing magnetic moments are pointing parallel to the axis of the rod. But so are all the arrows representing atomic angular momenta! their resultant is no longer zero — suddenly there has arisen a resultant angular momentum, belonging to the totality of all the atomic magnets, and quite large enough to be detected, instead of being tiny like the angular momentum of an individual atom. Unless our theory is fundamentally wrong somewhere, we should be able to observe this resultant angular momentum. The experiment is done by hanging the rod vertically from a fine suspension, and sending the magnetizing current through the solenoid. At the instant of the magnetization, the rod turns sharply on its axis, twisting the suspending fibre. Thus it manifests the angular mo- mentum of which I have just been speaking — though I ought to say that what we observe is of the nature of a recoil, or back-kick: when the totality of the little atomic magnets suddenly acquires its resultant angular momentum, the substance of the rod as a whole acquires an equal and opposite amount (so as to keep constant the total amount of angular momentum in the universe) and it is the latter which we detect. The experiment is quite a delicate one, but its technique has been developed to a remarkable degree since it was first attempted twenty years ago by Einstein and de Haas. What we measure is the ratio of the magnetization of the rod-as-a-whole to the angular mo- mentum of the rod-as-a-whole; and this is just the same as the ratio oi fjL to p for the elementary atomic magnets. There are not many properties of matter of which we can say that the value measured on a large piece of matter is the same as the value for the individual atom; but there are a few, and this is one of them. Now in giving you the result, let me first emphasize the general principle that here we have evidence of the spinning of elementary particles, and of the interrelation between spinning and magnetism. Next, I give you the numerical result itself. For iron and nearly all of the other ferromagnetic materials, we find: /jl/P = e/mc or twice the theoretical value which I quoted a moment ago. This cannot be explained by assuming any peculiarity of size or shape or frequency of the electron-orbits in the atoms, for as I just said the theoretical formula is independent of all these things. We 324 BELL SYSTEM TECHNICAL JOURNAL are obliged to make some more drastic assumption. If I had unlimited time before me, I might sketch the history of our assumption; but as I don't, I will come straight to the present situation. We assume first, that in the iron atoms in the rod the electron-orbits are so oriented with respect to each other that their magnetic moments kill one another off completely. We then assume that every electron has a magnetic moment and an angular momentum of its own, intrinsic to it and inherent in it, and altogether independent of whether or not the electron is revolving in an orbit. Just as the earth has a rotation of its own in addition to its elliptical course around the sun, so we imagine that the electron has a rotation of its own; this rotation has an angular momentum, and with it there is connected a magnetic moment. (You will remember doubtless that the earth also has a magnetic moment, but this is one of the analogies which it is better not to force too far.) \A'hen we magnetize the iron rod, it is the electrons which we are turning; the vectors which we cause to point all in the same direction are the magnetic moments and the angular momenta which are inherent in the electrons, and the value of their ratio is the value which is characteristic of the "spinning electron," as we call it. Therefore, amplifying the notation a little, I write: fJ^lP = gie/lmc) U = 1 for electron-orbits, g = 2 for spinning electron, and now I leave the spinning electron for a few minutes, in order to turn again to the theory of electrons revolving in their orbits. You all realized, of course, that when I converted the Amperian whirl of current into an electron running around an orbit, I was adopting the atom-model known by the names of Rutherford and Bohr; for these were the original thinkers who impelled all the rest of us, following in their footsteps, to think of the atom as a positively- charged nucleus around which electrons are revolving like planets around the sun. This is an atom-model in which magnetism is inherent — a Rutherford-Bohr atom is intrinsically a magnet. Anyone who did not know the history of the model might well assume that it was designed expressly to account for magnetism, and any such person might also quite reasonably assume that all the physicists of the early nineteenth century thought of it simultaneously as soon as the electron was discovered. Well, it was not designed expressly to account for magnetism, and most of the physicists of the early nineteenth did not think of it — or if they did, they thought of it only to reject it. At that time, the atom-model with the orbital electrons seemed to be disqualified by a very potent reason; for according to the classical CONTEMPORARY ADVANCES IN PHYSICS 325 electromagnetic theory, an electron revolving in an orbit ought to radiate all of its energy in a very short time and fall into the nucleus. Bohr was the man who overrode this objection. He overrode it, not in order to construct a theory of magnetism in defiance of it, but in order to construct a theory of spectra in defiance of it. This theory has been extraordinarily successful. Our theory of magnetism is hardly more than a by-product of that theory of spectra; and this, in an odd sort of way, enhances its credit. A theory devised expressly for a certain purpose is always less impressive than one which follows incidentally from a successful theory devised for quite another purpose ; and the contemporary theory of magnetism is a wonderful example of this latter and more impressive type. The main element of Bohr's theory of spectra — if one can speak of one element as the main one, which is really not quite proper — is an assumption about the angular momentum of the electron in its orbit or, let me say, the angular momentum p of the electron-orbit. It was assumed that the electron may revolve, without radiating its energy, in any orbit of which the angular momentum is an integer multiple of hjliv, — h now standing, of course, for the famous quantum-constant of Planck which is the emblem of modern physics. I write this down as follows: p = (1,2,3,4, ■■■)(h/2ir). Bohr was thinking at first about the hydrogen atom; but hydrogen is an inconvenient example to use in talking about magnetism, and iron is a very complicated case indeed, so I will talk entirely about the sodium atom. The sodium atom has a nucleus with a charge of -f lie, and eleven electrons circulating in orbits around it. This certainly sounds formidably complex, but it happens — and I shall later remind you of this fact — that the orbits and also the spins of ten of the electrons are so oriented with respect to one another that their angular momenta and their magnetic moments completely neutralize each other. I shall therefore ask you to imagine these ten inner electrons as a sort of cloud. The eleventh electron of the sodium atom — known techni- cally as the "valence" electron — cruises around this system; some- times it is traveling in an orbit completely outside the cloud, sometimes in an orbit which cuts across the cloud, but never in an orbit which is entirely or even mainly inside the cloud. The ten inner electrons which constitute the cloud neutralize a part of the force with which the nucleus acts upon the valence-electron; but they make — I repeat — not the slightest contribution to the angular momentum or to the magnetic moment of the atom. 326 BELL SYSTEM TECHNICAL JOURNAL I have given above, the permitted values of the angular momentum of this orbit of the valence-electron. Now I point out that to each of these permitted values of p corresponds a permitted value of the magnetic moment /i, which I obtain by multiplying the former with ejlmc: n = (1, 2, 3, 4, • • •){eh/47rmc). However, only one (at most) of these values can be appropriate to the normal state of the sodium atom; all the rest must correspond to abnormal, unusual, or "excited" states. We are going to be inter- ested primarily in the normal state, so we must identify the right one. In the early days of the Bohr theory, the right one was supposed to be the first which I have written down. However, the theory has been greatly remodelled and bettered since those days, with the aid of what is known as "quantum mechanics"; and it now seems quite certain that these lists of the permitted values of p and fj, for electron- orbits are both incomplete. I must add to each of them the value zero, so that the two lists become p = (0, 1, 2,3,4, ■■■)hl2ir, /JL = (0, 1, 2, 3, 4, • • •)eh/4:Trmc, Moreover, it is precisely this new value zero which belongs to the normal state of the sodium atom. So the theory, in this stage, quite definitely prescribes that the sodium atom in its normal state should have no magnetic moment and no angular momentum. But now let us look at the data. It would do no good in this connection to make measurements on solid or on liquid sodium, for in those "condensed phases" the atoms are crowded so closely together as to be badly distorted. We can, however, experiment on free atoms of sodium, in their normal state, in the way illustrated by Fig. 1. In the upper portion, A repre- sents an "oven," consisting of a small box heated electrically and containing some liquid sodium which is steadily being vaporized. There is a hole in the wall of the box through which free sodium atoms are steadily shooting in all directions, with the distribution-in-speed which we know from the theory of thermal agitation; and beyond, there is a sequence of diaphragms with slits in them which delimit a straight and narrow beam of these fast-moving atoms . Disregarding what the theory has just said, let us suppose that each of these atoms is a magnet — a bar magnet, with a north pole and a south pole. As they emerge from the oven, these atoms must surely be oriented at random in all directions. CONTEMPORARY ADVANCES IN PHYSICS 327 Continuing to look at the upper part of Fig. 1 , we have two large mag- net-poles, and the beam travels between them, having no trouble with molecules of air as it shoots along, for the whole of this apparatus is en- closed in a highly-evacuated tube. It may seem natural to visualize these magnet-poles as the two broad flat extremities of a horseshoe-mag- net, with a uniform magnetic field pervading all the space between them. Such an arrangement, however, would make the experiment futile. NORTH POLE In S N --^^~--- Fig. 1 — Longitudinal section and cross-section of apparatus for the Gerlach-Stern experiment. Nothing would happen to any of the atoms, for in the uniform field the north pole of each atomic magnet would be pressed downward just as hard as and no harder than the south pole is drawn upward, and the net force would be zero. The beam would go on unbroadened and undeflected, and make a small spot on the screen S, the spot being just opposite the slits in the diaphragms. Something else must be tried; and what we do — or rather, what Gerlach and Stern did in Hamburg some fourteen years ago — is, to shape one of the magnet- poles in the form of a wedge and hollow out the other, so that the field between the two shall no longer be uniform. The lower part of Fig. 1 represents the cross-section of such a pair of pole-pieces. The field- strength is now much greater near the wedge than near the opposite 328 BELL SYSTEM TECHNICAL JOURNAL pole-piece, and there is a vertical gradient of field-strength which may be made fairly constant over most of the interspace. Rabi at Columbia achieves the same result more efficiently by peculiar arrangements of current-carrying wires instead of iron magnets. Now consider (thinking classically!) a few of the atomic magnets as they shoot across this non-uniform field. Think of one which originally is oriented vertically, with north pole down and south pole up — the south pole will be in a stronger part of the field than its mate; it will be drawn upward harder than the north pole is pushed downward; the atom will sweep in a parabolic arc upward. Think of another which originally is oriented vertically with north pole up and south pole down — it will be swept in a parabolic arc downward. Think of another which originally has its axis pointing horizontally — ^it will shoot in a straight line across the field, as though the pole-pieces were not there.^ Now think of all those which are oblique to the vertical ; they will describe parabolic arcs of intermediate curvatures, upward or downward as the case may be. One infers that the beam must be spread out into a continuous fan, making a continuous vertical band upon the photographic plate. Moreover, from the upper edge or from the lower edge of this continuous band, it should be possible to determine the magnetic moment /x of the atoms. For let us consider one of the vertically- oriented atoms, and call its pole-strength M and the length of its magnet r. The upward force on the north pole is MH, — H standing for the field-strength at the point where the north pole is. The downward force on the south pole is M{H + dH/dz • r) . The net force is Mr-dll/dz, which is iJ.(dH/dz), because Mr is the magnetic moment fx of the magnet by definition. The acceleration of the little atom is equal to this force divided by nia, the mass of the sodium atom. The deflection is equal to half the acceleration by the square of the time during which the atom is exposed to the force. This time" is equal to the distance D which the atoms traverse across the field, divided by v the speed which they have when they come out of the furnace. So finally, we have: Deflection = -7:— — - (D v)-. 2 nia We ascertain the deflection by looking at the end of the band on the photographic plate, and we can ascertain all the other things in the ^ When thinking classically, we must not expect the atomic magnets to turn their axes toward the field-direction as they shoot across the field; the gyroscopic quality of these magnets, due to their angular momentum, inhibits this. \ CONTEMPORARY ADVANCES IN PHYSICS 329 equation excepting fx, — v is the hardest to estimate accurately — -and so we can solve the equation for /x. When the experiment is done there appears, however, a very remarkable thing. Instead of there being a long band upon the plate, there are just two spots. Instead of the beam having been broadened out into a continuous fan, it has evidently been split into two separate pencils. It looks as though the field had acted first of all upon the magnets, by setting them all vertical, — half of them with north pole up, and half with north pole down. Not this phenomenon alone, but many others in Nature show us that this is just what happens. You may perhaps feel for the moment that it is intelligible, after all; the compass-needle turns to the north — why should not the little atomic magnets, as soon as they enter the field, turn their south poles toward the north pole of the magnet which attracts them? Well, this would not account for the magnets which constitute the beam which bends away from the w^edge-shaped north pole, instead of toward it; and indeed it does not even account for the beam which bends toward the wedge-shaped pole. Classically the field should have no orienting effect whatsoever upon the atoms, and yet it evidently does.^ This is one of the phenomena of the atomic world which we cannot properly visualize in terms of the behavior of objects large enough to be tangible and visible. All that I can do is to assert it, and to say that it justifies us in using this formula to calculate /z. When we use it, the value which we find for the magnetic moment of the sodium atom in its normal state is eh/4:Tmc, which happens to be one of the values in the sequence which I just wrote down. I repeat that according tp the theory in its present stage, the elec- tron-orbits in the normal sodium atom have a net magnetic moment of zero. This value eh/4:Trmc is, therefore, the magnetic moment due to the spin of the valence-electron — it is the magnetic moment of the spinning electron. I write it in the appropriate place, and then with the aid of the ^- value derived from the gyromagnetic effect I write down the value of angular momentum which we assign to the spinning electron : p = \{hl2T). To this roster of three statements about the spinning electron I now make a final addition. The Gerlach-Stern experiment on sodium shows that a beam of sodium atoms — which for this purpose is the equivalent of a beam of spinning electrons — -is divided into two by a 330 BELL SYSTEM TECHNICAL JOURNAL magnetic field. I write down " 2 " to indicate this number of separated beams; but I will call it by preference the "number of orientations in the field," because that is the fundamental point. The spinning electron always sets itself in one or the other of two orientations, with respect to whatever field it happens to be traversing. We call them the "parallel" and the "anti-parallel" orientations, though according to quantum mechanics these terms are a little too strong. Here then is the list of the properties of the electron-spin: g equal to 2 — angular momentum equal to h(hl2ir) — magnetic moment equal to ehlAirnic — two permitted orientations in any field. It has doubtless struck you as rather odd that I began by talking about the angular momenta and the magnetic moments of electron- orbits, and then carefully picked out a couple of special cases in which these neutralized each other altogether and there was nothing left over except what I ascribed to the electron-spin. Is there no point at all, then, in talking about the electron-orbits? Oh, very much so! Indeed there are cases in which the electron-spins neutralize each other altogether, and we have nothing left over except what is at- tributed to the orbits. To do this I may choose an atom like mag- nesium, which has a nuclear charge of -\- \2e, a cloud of ten inner electrons which neutralize one another completely as to angular momentum and magnetic moment (just as in sodium), and two valence electrons instead of one. In some of the states of the magnesium atom — not in all of its states, but in some of them — the spins of the two valence electrons are oriented opposite to each other in the atom, and cancel each other out. When the atom is in a state of this kind, then nothing is left over except the angular momenta and the magnetic moments of the orbits of the two valence-electrons; and then, all the statements of the orbital theory (page 326) are applicable — g is equal to unity, the angular momentum takes one of the values nh/lir and the magnetic moment takes one of the values n(eh/4:Trmc). Moreover, there is another theorem derived from quantum mechanics which turns out to be valid : the number of orientations of such an atom in a field, the number of separated beams which appear in the Gerlach- Stern experiments, is chosen from among the members of this sequence : 1, 3, 5, 7. . . . (It is a most interesting historical fact, that Gerlach and Stern were moved to undertake their difficult experiment by the wish to test this remarkable assertion of quantal theory.) You notice that the number 2 does not appear in the sequence; were it not for the electron-spin, we never could obtain it; it is distinctive of the spinning electron. CONTEMPORARY ADVANCES IN PHYSICS 331 I must, however, admit that all these cases of which I have been speaking are special, and comparatively rare. Both the cases in which the spins neutralize each other perfectly, and the cases in which the orbital moments neutralize each other perfectly — both types are unusual. Still more unusual, and yet occurring here and there, is the most special of all cases — that in which all of the moments and all the momenta, both those of the spins and those of the orbits, balance one another perfectly so that the sums are zero. An atom in such a state is completely devoid both of magnetism and of spin; such atoms are those of helium, of neon, of argon and the other noble gases, when in their normal states. Usually, however, we find ourselves confronted with some example of the general case, in which neither the spins nor the orbits are completely neutralized. The atom has an angular momentum which is a sort of composite or resultant of the angular momenta of the spins and the orbits, and it has a magnetic moment which also is a sort of composite or resultant. If I were to embark on the description of the general case this lecture might go on interminably, and at its end you would probably not remember anything except what you had already known at its beginning. The laws of the composition of spins and orbits are so foreign to our customary ways of thinking, and the formulae which express them are so curiously built, that to work once only through them is not sufficient: one has to memorize the derivations and the results alike, and go over them incessantly until they are imprinted on the brain. I think you will agree to this readily enough, when I remind you that this theory is none other than the general theory of spectra; for even quite outside the ranks of physicists, the theory of spectra is beginning to be notorious for its complexity. I shall not venture even to give the formulae, much less their derivations; it must suffice to fill out the two lists of ^-values and /^-values on which I have already begun, and the list of w-values or numbers-of-permitted- orientations. The spinning atom is a congeries of electrons, all of them always possessing spin, most of them usually possessing orbital motions; and these motions are compounded with each other in such ways, that: First, the angular momentum of the spinning atom has one of the values, p^ (0, i 1,1,2,1,3 ■■■)hl2ir. Second, the number of beams in the Gerlach-Stern experiment, or the number of permitted orientations of the atom in the field, has one of the values, w = 1, 2,3,4, •••. 332 BELL SYSTEM TECHNICAL JOURNAL Third — -and now comes a surprise, for you will probably expect me to say of the magnetic moment that it is ehjAirm-c multiplied either by an integer or a half-integer; but this is not so. The actual state of affairs is described by a formula which is called the g-formula, because it gives g in terms of the moments, both spin and orbit, of the individual electrons. It was discovered by Lande and interpreted in terms of the spinning electron by Goudsmit. The ^-formula gives unity, as of course it must, in the special cases where the electron-spins cancel each other and only the orbital moments are left over, and it gives 2 in the special cases where the orbital moments are neutralized with only the spins left over. In the other cases it may give any one of a large variety of values: mostly one gets simple-looking fractions such as 9/8 and 4/3 and 5/6. The magnetic moments are then computed by multiplying the appropriate ^^'-values times ejlmc, into the existing values of angular momentum.^ I now turn to that component of the atom of which the spin remains to be discussed — to the nucleus. As I have already intimated, the values of p and n and // for the electron-family of any atom are mostly ascertained by analyzing their spectra and utilizing the great general theory of spectra. Such magnetic experiments as I used for my examples are relatively few, and feasible for relatively few substances. The reason for making this remark at this late moment is, that by analyzing spectra we may also learn something about the spins of nuclei; for nuclei also are invested with these properties of angular momentum and of magnetic moment. I take in particular the case of the proto?i — that lightest of all nuclei, the nucleus of the lightest known kind of atom which is ordinary hydrogen, so called to distinguish it from "heavy" hydrogen. Analysis of the spectrum of hydrogen shows us that the proton is capable of taking two permitted orientations in a field; thus, our first piece of information about the proton-spin is conveyed by writing n = 2. Now that we have this piece of information, we deduce that as the spinning electron has an «-value of 2 and an angular momentum of ^(h/lir), so the proton with its w-value of 2 must have an angular momentum of \{hl2ir). Continuing along this line of thought, we are further tempted to infer that the proton should have a g-value of 2 and a magnetic moment of {ehj^irmc). But what shall we suppose ^ Should any reader intend to proceed from this article to a thorough study ot atomic theory, he should be warned in advance that according to the latest form of quantal theory, the />- values and the /u-values here given are the values of the projec- tions of these vectors upon the field-direction, the magnitudes of the vectors them- selves being somewhat greater: I have given details as to this in "Contemporary Advances in Physics, XXIX, . . ." This Journal, 14, pp. 293 ff.(1935). CONTEMPORARY ADVANCES IN PHYSICS 333 about m? Formerly it represented the mass of the electron; now we are dealing with a different sort of particle, having a mass which (as many other kinds of experiments show us) is about 1835 times as great as the electron-mass. I denote this mass by M. It seems natural, then, to expect for the magnetic moment of the proton the value ehj^irMc, or about 1/1835 of that of the spinning electron. This is a formidably small magnetic moment to hope to measure, nay even to detect! yet Stern and his pupils undertook to measure it, and they succeeded. Of course, modifications had to be made in the technique which worked so well for sodium. Hydrogen being a gas at room-temperature, no heated oven was required; nevertheless they used an "oven," but it was refrigerated instead of being heated — a sort of super-ice-box; this was in order to obtain slow-moving atoms, for the slower the atoms traverse the field, the more accurately the experiment can be made. I just said "atoms"; but as most people know, the particles of gaseous hydrogen are not atoms, but diatomic molecules — systems composed of two protons and two electrons apiece. This is a circumstance which in many desirable tests of modern theoretical physics is a great inconvenience, for usually our simplest theoretical affirmations refer to hydrogen atoms and we should like to be able to experiment on them directly. Here, however, it turns out to be a great convenience, indeed perhaps the only thing that makes the experiment possible. F"or if we had an isolated hydrogen atom, the magnetic moment of its electron would so far exceed that of its proton that the latter would be indetectable. (Perhaps it is not superfluous to mention that bare protons could not be used in the experiment either, as the magnetic field would exert so large a force upon their moving charges that the forces upon their magnetic poles would be insignificant by comparison.) But if in a single hydrogen atom the magnetic moment of the electron swamps that of the proton, how shall this fate be avoided for a system composed of two electrons and two protons? Here enters in, and in a very important and significant way, that law of the permitted orientations. Just as a spinning particle of angular momentum \{hl2ir) can take only two permitted orientations in a field, so it can take only two with respect to another particle of its kind — the parallel and the anti-parallel. It chances — or rather it does not chance, it follows from the underlying laws of Nature — that in the hydrogen molecule the two electrons are oriented anti-parallel to each other. Their magnetic moments cancel each other, and do not trouble the experimenter. 334 BELL SYSTEM TECHNICAL JOURNAL May not, however, the same thing happen in respect to the two protons, so rendering the experiment hopeless? It turns out that for these the spins are anti-parallel in some molecules but parallel in others. Molecules of the former type, which is called para-hydrogen, are indeed useless for the experiment; but molecules of the latter type, which is called ortho-hydrogen, are available, and in them the magnetic moments of the two protons collaborate so that the magnetic moment of the molecule-as-a-whole is twice as great as that of the single proton, a welcome assistance! In ordinary gaseous hydrogen at room temperature, about three-quarters of the molecules are ortho-hydrogen. When the experiment was at last achieved by the school of Stern, it was found that the foregoing inference as to the ^u-value of the proton is roughly but not exactly correct! The latest information is, that the magnetic moment of the proton is close to 2\ times ehjAirMc. Measurements with another method by Rabi and his school have confirmed these results; and we are definitively debarred from believing that for the proton and the electron, the magnetic moments stand in the inverse ratio of the masses. Perhaps this signifies that the proton is itself a composite particle, a notion for which there is some support from other sources. I mention briefly the characteristics of a few other nuclei. After the proton, the next simplest is the deuteron or nucleus of the heavy- hydrogen atom. It is composed of a proton and a neutron, the latter being a neutral particle of about the same mass as the proton. We can observe free neutrons wandering about in space, but we cannot determine their spins nor their magnetic moments. The deuteron, however, has three permitted orientations (this we discern from the spectrum of heavy hydrogen) and consequently an angular momentum of {hjlir). It is inferred that the neutron has |(///27r) for its angular momentum, and that in the deuteron these two constituent particles — proton and neutron — are oriented with their equal spins parallel to one another. The magnetic moment of the deuteron is less than that of the proton, and accordingly the neutron must have its magnetic moment oppositely directed to that of its companion in the system, even though their angular momenta be similarly directed — a strange complication ! After the deuteron, the next simplest among the nuclei (except two which are much too rare for investigation) is the alpha-particle or helium nucleus." It is composed of two neutrons and two protons. We find that its angular momentum and its magnetic moment are zero, a clear indication that the four spins of its components are cancelling each other two by two, and the four magnetic moments CONTEMPORARY ADVANCES IN PHYSICS 335 likewise. Next comes a nucleus composed of three protons and three neutrons, belonging to the element lithium. It is found that in angular momentum as in magnetic moment it is practically a duplicate of the deuteron, its six components having disposed themselves into a nearly normal deuteron attached to a nearly normal alpha-particle. I might proceed some distance farther along the list of the known nuclei after this fashion, were there space; but it is best to close this section with a general rule: nuclei with an eveii number of constituent particles (protons and neutrons) have even spins, nuclei with an odd number of particles have odd spins. "Even " and "odd " in this formu- lation mean that the angular momentum is an even or an odd integer multiple of ^{hjlir), respectively. One sees that if any two spins of magnitude f (/?/27r) are allowed to choose only between parallel and anti-parallel orientations, the rule follows inevitably; reversely, from the rule (which is based on experience with some fifty or sixty kinds of atom), we derive extra strength for that theorem about orientations. Now to come to the conclusion and the climax. Although this property of angular momentum, of being allowed to take only a limited number of permitted orientations — although this strange and wonderful property of angular momentum was introduced in this lecture as though it pertained only to atoms subjected to applied external fields, yet it manifests itself far more broadly. Indeed, it manifests itself universally, and the stability and the character of the world are due to it. I have already mentioned in half-a-dozen places how it manifests itself within the molecule and within the atom: how in the atom, it is responsible for those laws of composition which determine the angular momentum and the magnetic moment of the electron-family — how in the hydrogen molecule, it establishes a difference between ortho-hydrogen and para-hydrogen — how in the nucleus it fixes the angular momenta and the magnetic moments of composite nuclei as sharply as those of their constituents the proton and the neutron. Perhaps these seem to be remote and unimportant qualities; but what has just been ^id of them may be said with equal truth and equal force of all the chemical and physical properties of all the elements, mass alone excepted (and even mass not fully ex- cepted). If this feature of angular momentum did not prevail, there could not be the fixity of properties which characterizes each element by itself and the variety of properties which characterizes the totality of the elements. Gold would not be gold, lead would not be lead, oxygen would not be oxygen, helium would not be helium; for though it is commonly said that each element is distinguished by its nuclear charge and the number of electrons in its electron-family, this is not 336 BELL SYSTEM TECHNICAL JOURNAL adequate. It is the law governing angular momentum which imprints upon these electron-families the characters which we recognize as the properties distinctive of the elements. It seems strange indeed that character should depend upon motion, and fixity upon the laws of whirling things; but however strange it may seem, there is no doubt about it. In the construction of houses the builder requires raw material in the form of brick and stone and wood and steel; but he requires also principles of architecture, whereby the raw materials may be parceled oflf and integrated into the general design. In the construction of the physical world, mass and charge fulfil the role of raw materials, and the laws of angular momentum furnish the principles of the architecture thereof. A Multiple Unit Steerable Antenna for Short- Wave Reception * By H. T. FRIIS and C. B. FELDMAN This paper discusses a recei\ing system employing sharp vertical- plane directivity, capable of being steered to meet the varying angles at which short radio waves arrive at a receiving location. The system is the culmination of some four years effort to determine the degree to which receiving antenna directivity may be carried to increase the reliability of short-wave transatlantic telephone circuits. The system consists of an end-on array of antennas, of fixed directivity, whose outputs are combined in phase for the desired angle. The antenna outputs are conducted over coaxial transmission lines to the receiving building where the phasing is accomplished by means of rotatable phase shifters operating at intermediate frequency. These phase shifters, one for each an- tenna, are geared together, and the favored direction in the vertical plane may be steered by rotating jthe assembly. Several sets of these phase shifters are paralleled, each set constituting a separately steerable branch. One of these branches serves as an exploring or monitoring circuit for determining the angles at which waves are arriving. The remaining branches may then be set to receive at these angles. The several receiving branches have common auto- matic gain control and thus provide a diversity on an angle basis. To obtain the full benefit of the angular resolution afforded by the sharp directivity, the different transmission times, corresponding to the different angles, are equalized by audio delay networks, before combining in the final output. The experimental system, located at the Bell Telephone Labora- tories' field laboratory near Holmdel, New Jersey, is described. This system comprises six rhombic antennas extending three quarters of a mile along the direction to England. Two recei\-ing branches, in addition to a monitoring branch, are provided. Ex- perience obtained with this system since the spring of 1935 is discussed. The benefits ascribable to it are (Da signal-to-noise im- provement of seven to eight decibels, referred to one of the six antennas alone, and (2) a substantial quality improvement due jointly to the diversity action and the reduction of selective fading. While a three-quarter-mile short-wave antenna system is an unusually long one, the steerability feature permits the employment of considerably more directivity, afforded by further increasing the length. A system two miles long is believed to be practicable and desirable. It could be expected to perform more consistently better than the three-quarter-mile trial installation, and should yield a signal-to-noise improvement of twelve to thirteen decibels * Presented before Silver Anniversary Convention of the Institute of Radio Engineers, New York City, May 10, 1937. Published in Proc. I. R. E., July, 1937. 337 338 BELL SYSTEM TECHNICAL JOURNAL referred to one rhombic antenna. With the object of predicting the performance of larger systems, the performance of the experi- mental system is examined in great detail and compared with theory. I. Introduction T?OR more than a decade, point-to-point short-wave radio services -^ have employed directional antennas both in transmitting and receiving. Transmitting antenna directivity results in increased field intensity at the receiving location and receiving antenna directivity discriminates against noise. Both directivities improve the signal-to- noise ratio of a given circuit and permit operation under more adverse transmission conditions. Arrays of simple antennas as well as ex- tensive configurations of long wires have been used to produce these directivities in both the vertical and the horizontal planes. Antennas in present use on the longer circuits, such as the New York-London telephone facilities, represent about the limit of fixed directivity. Further increase or ' ' sharpening ' ' of the directivity would seriously encroach upon the angular range of directions which are effective in the propagation of waves from transmitter to receiver. The vertical angle range useful in transmitting and receiving short waves is considerable. The horizontal range is appreciable although considerably less than the vertical range. To confine the principal antenna response to only a portion of these ranges penalizes the circuit when that portion is inelTective. Much experience and considerable statistical data have been ob- tained which determine this useful range of directions for the New York-London circuits, and antennas have been designed in conformity with these results. However, too much weight must not be given to statistical results which indicate, for instance, that ninety per cent of the time the effective angles are, say, in the range from ten to twenty degrees. For, if the remaining ten per cent includes much of the time that has been lost with existing facilities, an antenna designed for a ten- to twenty-degree response may really be of no value, or even detrimental as a means of extending the usefulness of the circuit. Owing to the great variability in conditions on the north Atlantic path and to the relatively small amount of significant data which has been accumulated during times when gain is most needed it might be detrimental to carry fixed directivity further than present practice has adopted.^ ^ One way of attacking the problem of obtaining increased antenna gain has been proposed by John Stone Stone in U. S. Patent 1,954,898. This patent relates to fixed antennas but has certain features, such as delay equalization, in common with the system to be described in this paper. A MULTIPLE UNIT STEERABLE ANTENNA 339 If, however, the directivity can be varied or "steered" to meet the various conditions imposed by nature, a new field is opened in which a new order of antenna sharpness and gain is possible. In addition to the gain in signal-to-noise ratio afforded by directivity, a reduction in selective fading is possible if the sharpness is increased to the point where a separation of differently delayed waves is achieved. As early as 1927, Edmond Bruce ^-^ found remarkable reductions in short- wave fading by using a receiving antenna having an extremely sharp directional pattern. The successful employment of sharp directivity is, of course, predicated upon considerable stability of wave directions. The experiments reported by R. K. Potter ^ in 1930 suggested that short waves are propagated in a more or less orderly manner and that stable wave directions might exist. Later experiments,^ made in co- operation with the British Post Office, using pulse transmission to resolve angles in time, gave confirming data and demonstrated clearly the physical facts upon which is based the system to be described in the present paper. These fundamental facts, outlined in the paper de- scribing the experiments just mentioned, are recapitulated here because a clear understanding of their nature and significance is an essential introduction to the subject in hand. In the pulse tests it was found that: "1. To the extent that we have been able to resolve the propagation into separate (vertical) angles, the separate angles are found not to be erratic; they vary slowly. " 2. There appears to be at least a qualitative relation between angle and delay; the greater the delay the greater the angle above the hori- zontal. "The existence of the many waves of different delay, which is known to make fading selective with respect to frequency, greatly impairs the quality of a short-wave radio telephone circuit. . . . The experimental facts, tentatively established, that individual wave angles are fairly stable and that waves of different delay invariably possess different vertical angles, make this problem hold considerable promise. "The simple antennas described . . . are suitable for angle determi- nation because of their ability to reject a single wave but they are not ^ E. Bruce, "Developments in Short -Wave Directive Antennas," Proc. I. R. E., vol. 19, pp. 1406-1433, August, 1931; 5e// Sys. Tech. Jour., vol. 10, pp. 656-683, October, 1931. ^ E. Bruce and A. C. Beck, "Experiments with Directivity Steering for Fading Reduction," Proc. I. R. E., vol. 23, pp. 357-371, April, 1935; Bell Sys. Tech. Jour., vol. 14, pp. 195-210, April, 1935. *R. K. Potter, "Transmission Characteristics of a Short-Wave Telephone Circuit," Proc. I. R. E., vol. 18, pp. 581-648, April, 1930. ^ Friis, Feldman, and Sharpless, "The Determination of the Direction of Arrival of Short Radio Waves," Proc. I. R. £., vol. 22, pp. 47-78, January, 1934. 340 BELL SYSTEM TECHNICAL JOURNAL in general suitable for quality improvement. For such studies it would be preferable to construct a more elaborate antenna whose directional pattern has a single major lobe which is steerable in the vertical plane. Such an antenna would aim to select a narrow range of angles in which occur waves of substantially the same delay." The present paper describes a steerable antenna receiving system of the general character suggested by the above quotation, and which has been in experimental operation at the Holmdel, New Jersey, field laboratory of the Bell Telephone Laboratories for the past two years. Certain other important features are incorporated in the system, notably an arrangement whereby individual wave groups arriving at different vertical angles are received separately and, after separate delay equalization, combined, thereby incorporating a unique form of diversity. Another important feature possessed by the system is its frequency range which permits operation on all of the frequencies used in short-wave transatlantic services. II. Principles of Steering Antenna Directivity An old and elemental type of steering of receiving antenna direc- tivity is found in direction finders. The steering of a directional lobe as distinguished from the steering of a null has been accomplished in recent years. .Schelleng •* reported a moderate degree of horizontal plane steering, accomplished by means of phase shifters. Jansky ^ has obtained horizontal steering by bodily rotating an entire broadside array. Bruce and Beck ^ obtained vertical steering by varying the shape of a rhombic antenna by means of ropes, and demonstrated the value of steering in the reduction of selective fading. The present authors ^ have employed rotatable phase shifters to steer the nulls in the directional patterns of two spaced antennas. In that work the value of the rapid adjustments possible with phase shifters was very apparent. In the linear end-on MUSA ^ system to be described rotatable phase shifters are again employed to steer the vertical response.^ In Fig. 1 is shown a schematic representation of a linear end-on array of N equally spaced unit antennas in free space. The antennas are indicated by the numbered points. For simplicity it is assumed, in the following preliminary analysis, that the antennas are spaced far "J. C. Schelleng, "Some Problems in Short-Wave Telephone Transmission," Proc. L R. E., vol. 18, pp. 913-938, June, 1930. ^ K. G. Janskv, "Directional Studies of Atmospherics at High Frequencies," Proc. L R. E., vol. 20, pp. 1920-1932, December, 1932. *The word MUSA is coined from the initial letters of "multiple unit steerable antenna." nj. S. Patent No. 2,041,600. A MULTIPLE UNIT STEERABLE ANTENNA 341 enough to be substantially isolated from each other. Choosing an- tenna No. 1 for reference and considering a plane wave arriving at an angle 8 with the axis of the arra3^ it is clear that the output of No. 2 will add in phase with that of No. 1 if the phase advance cj) is made equal to Iwac/v — lira cos 8, where c = velocity of light and v = the phase velocity of the transmission lines. Similarly, the output of No. 3 will add to that of No. 1 and No. 2 if its phase is advanced 2(f), etc. If the spacing, a\, is sufficient there will be other angles for which the N outputs add in phase; at intermediate angles the outputs interfere with the result that zeros and minor maxima occur. JBy properly designing the unit antenna the undesired maxima may be suppressed. TRANSMISSION LINES Fig. 1 — A steerable antenna array using variable phase shift.-: 4>, 2. The multiple phase shifts of Fig. 1 are obtained by gearing the phase shifters to a common shaft which enables the directional pattern to be steered simply by rotating the shaft. Thus far we have discussed the problem of sharp steerable direc- tivity from the point of view of a single plane wave, whereas it is well 342 BELL SYSTEM TECHNICAL JOURNAL known that multiple Ionosphere reflections usually produce several more or less discrete waves, or bundles of waves, having diff^erent vertical angles and diff^erent transmission delays. To obtain the maximum advantage, however, requires that all of the several wave bundles be separately received and suitably combined after the trans- mission delays have been equalized. The achievement of this objective Fig. 2 — ^Airplane view of the three-quarter-mile experimental MUSA on the re- ceiving laboratory site located near Holmdel, New Jersey. The white line beneath the antennas is the newly filled trench in which coaxial transmission lines are buried. The building appearing in the right-hand foreground houses the receiving apparatus. The ground is flat to within ± 4 feet. not only yields the ultimate gain in signal-to-noise ratio but at the same time reduces the distortion associated with selective fading. The method of obtaining sharp steerable directivity by combining the output of fixed antennas through phase shifters makes it possible to use the same antennas and transmission lines to provide several separately steerable lobes each of which is in effect an independent MUSA.^° In the experimental system, shown schematically in Fig. 3, 1" R. K. Potter, U. S. Patent No. 2,030,181. A MULTIPLE UNIT STEERABLE ANTENNA 343 the antenna outputs are combined at intermediate frequency, and the separately steerable lobes are obtained by branching each of the six first detectors into three phase shifters and combining the outputs of Fig. 3 — Schematic diagram of the experimental MUSA receiver. The five phase shifters 4>2, 4>3, etc., of each branch, are geared to a shaft to provide the phase shifts , 3(t>, etc., of Fig. 1. The inset at the top shows the directional patterns of the two branches when steered at angles of 12 and 23 degrees, at a wave length of 25 meters. the phase shifters to form three steerable branches. One branch is used continuously to explore the angle range to determine at which angles the waves are arriving. The other two branches are set accord- 344 BELL SYSTEM TE.CHNICAL JOURNAL ingly and their outputs are "received" by conventional receivers, with common automatic gain control. The demodulated audio outputs are equalized for difference in transmission time and then combined. A cathode-ray oscilloscope displays the output of the exploring or monitoring branch. It plots amplrtude (provided by a linear rectifier) as the ordinate, against phase shift 02 (corresponding to 0 in Fig. 1). The screen of the oscilloscope is of the retentive type and thus displays several consecutive sweeps at once. A pattern corresponding to two waves is illustrated. The other cathode-ray oscilloscope is used in the adjustment which equalizes the delay of the two waves. Delay is added to the low angle branch until the oscilloscope shows a line (or compact elongated figure) which oscillates between the two axes as the two waves fade differently. This means that all of the audio fre- quencies of one branch are combining in phase with those of the other. The above brief description was introduced to acquaint the reader with the essentially simple features of the MUSA system. Before de- scribing the details and the results obtained with the experimental system, a more comprehensive analysis of steering principles will be given. Returning to Fig. 1, it is assumed, of course, that the transmission lines are terminated in their characteristic impedance at the receiving terminal " (the phase shifters of Fig. 1) so that the phase is distributed linearly along the lines. Neglecting line loss (or equalizing it), the N currents, equal in magnitude and different in phase, are ^2 = /gj{a,<+0-27ra(u-cos 8)) jg = /^j{c>.^+2[0-27ro(u-cos 8)1! j\. = /g?{u<+(A'-l)[0-27ra(<;^cos 8)11 XI) where i = instantaneous current in exponential notation CO = angular frequency N = total number of unit antennas a = spacing in free space wave-lengths V = c/v = the ratio of the velocity of light to that of the trans- mission line. The sum of the N currents is A = /e'"'(l + ^;[0-27ra(i'-cos 8] _|_ ... _|_ ^/(Ar-l) [<^-2ra(i'-eos 8)] 1 ('2') 1' Non-characteristic terminations at the receiving ends of the lines are per- missible if all terminations are identical and if the antennas are matched to the characteristic line impedance. Conversely, characteristic terminations at the re- ceiving ends suffice if the antenna impedances are merely identical. A MULTIPLE UNIT STEER ABLE ANTENNA 345 This exponential series may be evaluated with the aid of the identity ^^ . nd sin-y (n-l)d 1 + e'« + e^-^" + • • • + e'C-i^" = j e^ ^ ^"^ • sin- Using this summation we ha"ve N sin— [0 — Iwaiv — cos 8)j J^ _ J ___Z gy[u«+(iV-l)/2(0-27ra(u-pos «)])_ ^3) sin- \jj) — 27ra(i^ — cos 5)] The amplitude of A in (3) is the array directional pattern or array factor. It is zero when the numerator alone is zero, i.e., when -[ = Z7.5'' / \ / \ /N X \ h V rv f^ |A| /' 1 / 0 = 100° ^- ~x /^ AA m V\ 10 15 20 25 30 EARTH ANGLE 6, IN DEGREES 40 Fig. 4 — Plots of the array factor for a 45-wave-length horizontal end-on array. lengths, i.e., upon Na, while the angular spacing of adjacent principal lobes depends inversely upon the spacing "a." Thus, a single lobed pattern results if the array consists of a large number of closely spaced units. A single lobed pattern is desirable, but to obtain it by using a large number of unit antennas ^^ with separate transmission lines and phase 13 The reader may observe that the reduction of the spacing would, if carried so far as to make "a" a fraction of a wave-length, violate the assumption that there is negligible reaction or coupling between unit antennas. As stated, this assumption is made in the interest of simplicity. It is theoretically possible to compensate for coupling between antennas so that (1), (2), and (3) still hold. A MULTIPLE UNIT STEERABLE ANTENNA 347 shifters would be a rather extensive undertaking. Provided a re- stricted range of steering is permissible, a simpler solution is to employ comparatively few large unit antennas and to let their directional pattern suppress the undesired principal lobes of the array pattern. Useful angles for transatlantic circuits are confined to the range from zero, or some low undetermined limit, to some higher limit. In what follows let 8m represent an angle a little above the useful range so that a a=io •0 = 1 lAl 1 (t)=55° N \\ f\N vW t ^ fm 4 lAl 1 " 0=200° — - ^ AA l\ V m(f m 10 15 20 25 30 EARTH ANGLE 6, IN DEGREES 35 Fig. 5 — Plots of the array factor for a 90-wave-length array; that of Fig. 4 used at twice the frequency. null may be located at 5,„ without imposing an excessive loss. The array may then be designed so that when the first principal lobe is steered at zero angle the second falls at 8,n or beyond. The question of whether the array design permits the construction of a suitable unit antenna in the length a\ allotted to it is considered in the following paragraph. As a matter of fact, this analysis closely follows the actual steps in the development of the MUSA system. 348 BELL SYSTEM TECHNICAL JOURNAL Turning back to the ideal system comprising a very large number of closely spaced unit antennas, which yields the single lobed pattern, let us divide the antennas into N groups with n antennas in each group. Calling the group spacing "a" and the phase shift between adjacent antennas <^ the application of (3) gives, dropping the exponential factor, 0 — ZTT - (f — COS 5) n J sm- . 1 sm- 4> — 2t~ (v — cos b) n J Multiplying numerator .and denominator by results in li'^ - '^''n^' cos 5) (4) A' . n sin 2 sin- l-w-iv — cos 5) n — 2ir— iv — cos 5) n N, sin— [«^ — 2ira(v — cos 5)] X— J -• (5) sin-[w0 — 2Tra{v — cos 5)] Equation (5), which appears as the product of two array factors, is merely another way of writing the array factor for the large number (Nn) of unit antennas. The first factor represents an array of n "sub- unit" antennas of spacing a/n and phase shift 0. The second repre- sents the array of these arrays with a spacing of a\ and a phase shift ncj). We now proceed to treat these two factors independently and assign the values ^/ and „ to replace and n„ = w0/) this system is identical with the array of Nn sub- units. In this case, all principal lobes of the array factor for the N units, excepting the first, coincide exactly with nulls of the array factor for the w subunits, and the familiar tapered distribution of minor maxima associated with the array of Nn subunits results. As 0„ is varied to steer for other angles than 5 = 0, the coincidence of nulls and undesired principal lobes no longer occurs. Since, however, the N 2 O (M — Of 4 2f -4 rO <\l — n fvj _ ? ? ? I I I— I I Of 2v, IN METERS 45 50 55 60 Fig. 7 — Measured upper limits of vertical angles as a function of wave-length, compared with the upper limit of the array depicted in Fig. 6. The measured values represent the highest angles observed; usually stronger waves of lower angles pre- dominate. adopted for the experimental MUSA system to be described. The points denote upper limits of earth angles obtained from measurements made during the years 1933-1936 on signals from Rugby ^ and Daventry, England. The foregoing analysis shows that (1) A MUSA system may be so proportioned that the upper limit of its steering range follows, with fair accuracy, the upper limit of the range of useful angles, as the wave-length is varied. A MULTIPLE UNIT STEERABLE ANTENNA 351 (2) It is theoretically possible to construct a suitable unit antenna in the space provided for it when (1) is satisfied. III. Description of the Experimental MUSA System Antennas and Transmission Lines Any type of unit antenna whose directional pattern suppresses the undesired principal lobes over the required wave-length range is basically suitable for use in a MUSA system. The rhombic antenna ^^ does not fulfill this requirement as well as the linear array of subunits discussed in the preceding section. It was, however, selected on account of its advanced state of development. The manner in which it fits into the MUSA array factor will be discussed later. The coupling or "cross talk" between antennas need not be of neg- ligible magnitude in a MUSA system. For, to a first approximation, ANTENNA TERMINATION RESISTANCE MATCHED OSCILLATOR MATCHED LOAD Fig. 8 — Measurements of cross talk between adjacent antennas in the MUSA as made from the transmitting point of view. the coupling is confined to adjacent antennas and is similar for all pairs so that only the end antennas could be expected to fail to combine properly with the others. At the ends, "dummy" antennas, not con- nected with the receiver but terminated like the others, could be erected to supply the coupling necessary to make all antennas alike. Measurements made on the experimental MUSA (Fig. 2) indicated that the cross talk is small enough to be neglected, however, so that dummy antennas ahead of or behind the six regular ones were con- sidered unnecessary. The performance of the system in subsequent tests corroborates this conclusion. The crosstalk measurements yielded the results indicated on Fig. 8. The small amount of crosstalk current (0.0017) measured at the trans- " Bruce, Beck, and Lowry, "Horizontal Rhombic Antennas," Proc. I. R. E., vol. 23, pp. 24-46, January, 1935; Bell Sys. Tech. Jour., January, 1935. 352 BELL SYSTEM TECHNICAL JOURNAL mission line end of the forward antenna (No. 2) and the larger current (0.167) at the other end reflect the fact that the rhombic antenna is "unidirectional." To a first approximation the current in such an aperiodic antenna accumulates progressively towards the output end. Therefore, the "effective" cross talk current is probably less than (0.16/ + 0.001/)/2 = 0.087; i.e., the effect upon the field radiated in the principal lobe will be altered by less than ten per cent due to the parasitic excitation of the antenna ahead. Antennas farther ahead as well as those behind contribute relatively nothing. Since by the reciprocal theorem the directional pattern of any an- tenna is the same for transmitting and receiving, the crosstalk should likewise result in less than 10 per cent effect in the receiving case. The measurements of Fig. 8 were made at 18 megacycles. At this frequency the rhombic antennas are proportioned to give maximum radiation approximately end-on. At lower frequencies the crosstalk is probably less. The coaxial transmission lines are constructed of 60-foot lengths of one-inch copper plumbing pipe spliced with screw type plumbing unions. The inner conductor is one-fourth inch in diameter and is supported by isolantite insulators. The characteristic impedance of the lines is 78 ohms. The lines extend up the poles where they are con- nected to the antennas through balanced-to-unbalanced matching transformers.^* At the receiving building the lines terminate on a special jack strip. Nitrogen pressure is maintained in all lines to exclude moisture. In order to operate the MUSA system it is iiot essential that the velocity of the transmission lines be known. The velocity must be known accurately, however, in order to determine the angle of the waves as they are selected by the steerable lobe. Accordingly, the velocity was calculated (taking the insulators into account) and also measured. The calculated ratio of the line velocity to the velocity of light is 0.941; measurements yielded 0.933 ± 0.004. Using the value of 0.933, angles less than zero have occasionally been measured. A value of 0.937 would have made the lowest indicated angle just zero. The longest line is about 1000 meters in length. Its impedance measured at one end when the other end is terminated by a resistance of 78 ohms shows some variation as the frequency is varied. In Fig. 9 are shown the results of impedance measurements made by substi- tuting for the line an equivalent parallel combination of resistance and reactance. The two notable variations occurring at approximately 7.7 and 15.4 megacycles are believed to be caused by a slight irregularity at each joint, which adds a shunt capacitance of the order of 1.8 micro- A MULTIPLE UNIT STEER ABLE ANTENNA 353 microfarads. When spaced regularly at 60-foot intervals these capaci- tances have a somewhat cumulative effect at frequencies for which 60 feet (18.3 meters) is a multiple of the half wave-length. Sixty feet, when increased by the line velocity ratio, corresponds to 7.7 and 15.4 megacycles. Clearly, line sections which are not short compared with the shortest wave-length should be made unequal so that joint irregu- larities will not be harmful. The smaller variations of the order of ±10 ohms may be due to random eccentricities produced by slight buckling of the inner conductor between insulators. With the possible O 90 z 50 40 -40 -80 ■120 .J_ 3 . ^T "f 11 1 1 \r\\ \r Vv/ aA iV ^ \f \fk w f/^ Hf J\ Y* \ i ' |V Va \ K>v > ^ ^ Arw k rJ W\ ^ ..A 1 1 9 10 II 12 13 14 15 16 FREQUENCY IN MEGACYCLES PER SECOND Fig. 9 — Impedance measurements made upon the 1000-meter line terminated in a resistance of 78 ohms. The reactance is expressed as shunt capacitance, negative values meaning an inductive reactance numerically equal to the corresponding capacitive reactance. exception of the two large variations this line is sufficiently smooth for use in a MUSA, as both theory and subsequent experience indicate. Input Circuit and First Detectors The MUSA system imposes requirements upon the input circuits and detectors which do not apply to conventional receivers. These requirements are as follows: (1) The circuits must suppress standing waves on the transmission lines. ^* ^''This requirement was more easily met than the alternate requirement men- tioned in footnote (11). 354 BELL SYSTEM TECHNICAL JOURNAL (2) The phase shift from the transmission Hne to the phase shifter stage must be aHke in all six circuits, independent of wave-length. In order to simplify the experimental job it was decided to dispense with the selectivity afforded by high-frequency amplifiers and to use the simple circuits shown in Fig. 10. The capacitive coupling to the transmission line is a convenient means of matching the low-impedance lines to the high-impedance circuits. Plug-in coils (L) are used to cover the range from 4.5 to 22 megacycles. The first detectors are of the two-tube balanced type which sup- presses interference from two signals differing by the intermediate ADJUSTABLE COUPLING CONDENSER INTERMEDIATE FREQUENCY CIRCUITS PARALLEL-BALANCED DETECTOR TUBES TO BRANCH A PHASE SHIFTER TO BRANCH B PHASE SHIFTER TO BRANCH C PHASE SHIFTER Fig. 10 — Input circuit, first detector, and first intermediate-frequency tubes. frequency and isolates the beating oscillator supply from the input circuits. The latter prevents crosstalk between the six inputs, and assures independence in the tuning of the input circuits. The beating oscillator voltage is introduced, at low impedance, between cathodes ^® by means of the distributing system of equal length coaxial lines shown in Fig. 1 1 . This distributing system gives equiphase beating oscillator inputs to all detectors and makes requirement (2) attainable by having nominal similarity in the remaining parts of the six circuits. Requirement (1) is met by feeding a test oscillator of 78 ohms im- pedance into the first circuit jack and adjusting the tuning condenser ^^ W. A. Harris, " Superheterodyne Frequency Conversion Systems," Proc. I. R. E., vol. 22, pp. 279-294, April, 1935. A MULTIPLE UNIT STEERABLE ANTENNA 355 and the coupling condenser (Fig. 10) alternately until the maximum signal voltage appears on an indicating meter in one of the three inter- mediate-frequency branches. The three-terminal coupling condenser is an aid in this procedure since varying the coupling imposes only a slight variation in the capacitance across the coil. When the indicating instrument is a square-law vacuum tube voltmeter with the main Fig. 1 1 — Close-up view of high-frequency panel with cover removed. The beating oscillator supplv line originates in the upper right-hand corner. It supplies the six detectors with 'equiphase and equiamplitude voltages. Plug-in coils fit into the compartments covered by the six circular doors. Micrometer heads which are used to adjust the six tuning condensers appear. The coaxial patch cords appear at the extreme left. 356 BELL SYSTEM TECHNICAL JOURNAL current balanced out and the remainder indicated by a 30-micro- ampere meter, the sensitivity is more than sufficient to tune the circuits correctly. The criterion of correct tune is the degree of suppression of standing waves on the transmission lines. To determine whether or not the maximizing adjustment insures an adequate standing wave sup- pression, a standing wave detector was incorporated in the experi- mental design. This is shown in Fig. 12. It consists of about 16 meters of 78-ohm coaxial line arranged in a coil and terminated by the Fig. 12 — The standing wave detector comprising 50 feet of 3/8-inch coaxial line, which may be used to test the correctness of the input circuit adjustment. first circuit to be tested. It is fed at the other end by a test oscillator. Six capacitively coupled taps are brought to the low-capacitance switch shown in the photograph. The selector arm connects the taps to an auxiliary receiver with a high-input impedance. The absence of standing waves is shown by equal readings at the six positions. It was found that the maximizing adjustment results in a standing wave with less than ten per cent total variation, which represents nearly as much suppression as the smoothness of the line allows. A MULTIPLE UNIT STEERABLE ANTENNA 357 With nominally correct resistance termination standing waves of five per cent usually occur. For standing waves not exceeding ten per cent the accompanying phase distribution along the line does not depart more than a few degrees from the desired linear distribution. The use of the standing wave detector in routine operation was therefore not required. Phase Shifters Of the numerous methods of shifting phase the method ^'' illustrated in Fig. 13 is the one chosen for the 18 circuits (3 branches, 6 antennas) of the experimental MUSA. Here points a, b, d, and c have voltages ^ ROTOR PLATES STATOR PLATES Fig. 13 — Circuit diagram and vector diagram of the phase shifter. The rotor plates are especially designed to give a phase shift proportional to shaft angle. to ground 90 degrees apart. The potential of point b is IR; that of c is — IR; that of a is jI/coC; that of d is — jI/coC. The resistance R and reactance 1/coC are made equal at the mid-band frequency so that four equal voltages, distributed equally over 360 degrees of phase, appear on the four stators of the special condenser. A photograph of this condenser appears in Fig. 14. Two specially shaped eccentric rotors mounted in quadrature to each other on the same shaft com- prise the output terminal. It will be noted that voltages of opposite phase are connected to adjacent stators. Thus, with the rotors in 1' L. A. Meacham, U. S. Patent No. 2,004,613. 358 BELL SYSTEM TECHNICAL JOURNAL the position shown dotted in Fig. 13 the output comes from point a since d is not coupled and b and c cancel each other. By shaping the two rotors so that the difference in exposure to opposite stator plates is proportional, respectively, to the sine and cosine of the angle of shaft rotation, the total current flowing from the two rotors will be constant and of phase proportional to the shaft angle. This is illustrated by the vector diagram in Fig. 13 in which j3 is the shaft angle and vectors a — d and b — c are the quadrature rotor outputs proportional to sin j8 and cos /?. These phase shifters vary in output by less than ± 5 per cent as the shaft is rotated. The departure from linearity of phase shift is corre- spondingly small; i.e., less than ± 5 degrees. Fig. 14 — -The phase shifting condenser. The useful band width of this type of phase shifter is fundamentally limited by the fact that l/coC varies with frequency while R does not. However, this limitation does not appear in the Holmdel MUSA in which the percentage band width is small because the phase shifters operate at the intermediate frequency of 396 kilocycles. The phase shifters are connected to the steering shaft with helical gears of multiple ratios as shown in Fig. 15. The phase shifter shafts may be slipped with respect to the main shaft. After they have been aligned so that locally supplied equiphase inputs to all detectors add in phase at the point where the phase shifter outputs are combined they are locked. This adjustment is independent of signal frequency. Provision is made for adjusting the gain of each of the six phase shifter circuits so that the differences in transmission-line loss may be com- A MULTIPLE UNIT STEERABLE ANTENNA 359 pensated and any other desired amplitude adjustments made. The photograph of Fig. 15 shows the monitoring or exploring branch whose steering shaft is motor driven at one revolution per second. Before leaving the subject of phase shifting it may be well to dis- tinguish between phase shift and delay as here used. All electrical net- Fig. 15 — Phase shifting panel of the monitoring branch. Only five of the six phase shifters are rotated for steering purposes. They are geared to the steering shaft in ratios of 1 : 1, 1 : 2, 1 : 3, 1 : 4, and 1 : 5. works, except for certain highly distortive ones, possess a phase-fre- quency characteristic which is such that higher frequencies have their phases retarded with respect to lower frequencies. The ratio of the ncrement of phase retardation to the increment of frequency, i.e., the 360 BELL SYSTEM TECHNICAL JOURNAL slope of the phase characteristic, is the delay. It is sometimes called the group delay or group transmission time as distinguished from the "phase time." ^^ The delay is the only time which can be measured. It does not determine the phase shift of a particular frequency nor is it determined by the phase shift. A phase shifter applied to the net- work merely moves the phase curve intact up or down on the phase axis. General Description of the System The preceding paragraphs have described features which distinguish the MUSA system from conventional receiving systems. There remain to describe several auxiliary features and to present a unified picture of the whole. The experimental system was designed for double side-band recep- tion and all of the results reported in this paper refer to double side band. There has recently been completed equipment which may be substituted for the double side-band equipment for the reception of reduced carrier single side-band signals. The new equipment may also be used to select, with crystal filters, one side band of double side-band signals. The delay to be inserted in the low-angle branch as indicated in Fig. 3 is obtained electrically from an audio-frequency delay network. The delay could theoretically be provided at the intermediate fre- quency but no advantage would result. The audio-frequency delay network is a special artificial line composed of forty sections and termi- nated by its characteristic impedance. Each section has a delay of 68 microseconds. A special switch is arranged to tap a high impedance output circuit across any desired section, thus providing a delay of 2.7 milliseconds variable in 0.068-millisecond steps. A special equalizing network ^^ which makes the transmission loss the same for all steps and which also equalizes the frequency-loss characteristic so that the re- sponse is flat to 5000 cycles for all steps is automatically controlled by this switch. The forty delay sections appear in Fig. 16 just under the shelf on the right-hand bay. The maximum delay which has been required in actual operation is 2.5 milliseconds. Both linear rectifiers and square-law detectors are provided for final demodulation and either may be switched into service as desired. The 1^ This distinction is brought out by J. C. Schelleng in a "Note on the Determina- tion of the Ionization of the Upper Atmosphere," Proc. L R. E., vol. 16, pp. 1471- 1476, November, 1928. A general discussion of delay distortion (phase distortion) is to be found in three papers appearing in the Bell Sys. Tech. Jour., vol. 9, July, 1930. i"This network and the delay sections were designed by P. H. Richardson of Bell Telephone Laboratories, Inc. A MULTIPLE UNIT STEERABLE ANTENNA 361 automatic gain control for use with either demodulator is obtained from linear rectifiers but a different diversity connection is made for each type of demodulator, in the interest of output volume constancy. A choice of time constants of 0.06, 0.5, and 4 seconds is provided. Keys are provided, the ganged manipulation of which makes it possible, among other things, to compare (1) the MUSA output versus any one of the six antennas connected to one branch receiver, and (2) any pair of antennas in ordinary diversity using both branch receivers, versus one antenna using one receiver. Fig. 16 — Fujiit \ ii w 1)1 ili> AH sA uivi\inu ( (|iiipnh nt . Tlu' hiL;h-frequency bay is at the lett and the audio-trequenc>' bay at the right. The branch receivers are the panels directly above the phase shifting panels. The pulse receivers appear above these. At the top of the bay containing the monitoring branch equipment are the two oscilloscopes referred to in Fig. 3. The large tube with the ruled face is the monitoring oscilloscope. In addition to the regular branch receivers with a 12-kilocycle band width and the monitoring branch receiver with a 2.5-kilocycle band width, two other receivers are provided in the experimental system. These receivers have a 30-kilocycle band width and are used for pulse reception. They are bridged across the inputs of the two regular branch receivers and are connected to a cathode-ray oscilloscope through a commutator.^ Various photographs of the MUSA receiver appear with explanatory captions in Figs. 16, 17, and 18. 362 BELL SYSTEM TECHNICAL JOURNAL Fig. 17— View showing the six transmission lines and coaxial patch cords. The beating oscillator is mounted upon the shelf and is connected to the power amplifier (which is being adjusted by Mr. Edwards) at the top of the bay. A MULTIPLE UNIT STEERABLE ANTENNA 363 Fig. 18 — Rear view of the receiving equipment. The six detector outputs feed the three branches via the square transmission lines. 364 BELL SYSTEM TECHNICAL JOURNAL A family of calculated directional patterns of the experimental MUSA is shown in Figs. 19 and 20. At the top of each column is shown the principal lobe of the vertical directional pattern of the unit rhombic antenna, calculated in the median plane. Beneath are shown six vertical patterns of the MUSA, which are obtained by multiplying the RHOMBUS PATTERNS 1.0 0.5 n ■K = 16M / / \ / \ \ ■h = 24M / /■ N s / / s V MUSA PATTERNS (-0 = 1) 0.5 0 1.0 0.5 Z 0 y 1.0 0.5 5 0 H 1.0 4) = o» , / \ ^^ \r^ w^% 4) = 0° Z' IV^/v/^i_ / \ 4) = 60° y / V Vv (|)= 60°^ y^ V\ r^ vV \- P\ (p = iao° ^ Si ' \^ (l» = 120'' 1 \ ^^ \ rv w-v ./--N \ <|)= 180° ^ V (j) = 180° / \ _ s/' y V \<^ 4) = 240° ^ V L_ 4) = 240° A s^ s/N / Vv 4) = 300° ^_^ '^•^ W v 4> = 300° A ^^ N^ y\ L \ 0.5 0 1.0 0.5 0 5 to 15 20 25 30 35 0 5 10 15 20 25 30 35 EARTH ANGLE 6, IN DEGREES Fig. 19 — Vertical directional patterns of the experimental MUSA. array factor ^^ by the unit antenna pattern. The upper pattern corresponds to phasing for zero angle. The remaining ones are plotted for increments of 60 degrees of phase. These patterns fall short of the "ideal," which the reader may have visualized while reading Section II, in two ways. First, the unit an- ^^ Calculated from (3) putting u = 1. A MULTIPLE UNIT STEERABLE ANTENNA 365 tenna does not suppress the second lobe of the array factor as well as could be desired. By design, it does so for the short waves but in- herently fails to do so for the longer waves. Second, the principal lobe of the unit antenna shifts bodily towards higher angles with increasing wave-length, whereas it is desirable to have only the upper cutoff move 1.0 0.5 n A = 32M RHOMBUS PATTERNS •K - 48M / N \ / /^ N \ / \ ^ / \ V. MUSA PATTERNS (O = l) qMWwyI $ = 0° (t) = 0° / \ ^ ^ V\ A L \ olAjwa. (D= 60° = 120° (t)=l20° A Iv w\ J \ Vv rA h u> START 4 s/^^ y • / ' A/ vu .u WV«*» /W^ J^ v-V^ A^ " y 1 • 1 / / " ^ Af >w/ •v-^ ^^ J^ iA^ A-. " • / y 1 / / - ^ A>A -w/ ^^ vW* ,/w^ i/W W^ " y / ' / / / - Ar A^ A^ >s>. .r^ v»~^ V/^-i^ ■'WV *» y / ' / / / - Ax A^ J\J^ .^v«^ V^ w^ v/s-/" ->v^ " y / y / f 1 ' ^ Ar yw^ JS^J^ V^ ^«w«^ ^--J- .y^^ ^ • / y / « » / A/ ' j\^ yu/» .^ ^^w ^ --.^ ^ y / y / • / 1 • END 1 /^^ END 2 jU END 3 v\.»< END 4 - / / y Fig. 23 — Pictures of the angle monitoring oscilloscope and the delay indicator tube. The right-hand end of the sweep of the monitoring tube represents zero phase. The indicated angles are 8.5 and 20.5 degrees. The MUSA branches were set at these angles (<^a = 240°, 4>b = 30°) using 950 microseconds delay. GSE (11,860 kilocycles) Daventry, February 21, 1936, 11:05 a.m., E.S.T. Musical program. A MULTIPLE UNIT STEERABLE ANTENNA 371 START 1 1 START 2 START 3 /An. START 4 S\r ^w \^ % IK /^ A. hj N / 1 - ^ y - ' ' vu. \-« rv /v W vu M rv / 1 ' • - " / ' VUrf /U 'V '^ vu K, ^ /^ / / 0 / - ' / ' Vv Vw W w lA^ X V K / / X X - - /■ - v^ Va- /vt w vw A^ A^ ^ / / ' ' - - • - \^ ^w r\r v\^ VS/v/ A/ /^ A^ / / * - ' • - •Uj \^ '\ ^ >Aa AV' -/W) Ay / / " / ' ' y - V» END 1 /v END 2 vu END 3 J^ END 4 1 y " ' Fig. 24 — Pictures of the angle monitoring oscilloscope and the delay indicator tube. In films 1 and 2 the indicated angles are 15 and 22 degrees. The MUSA branches were set at these angles (A = 250°). A delay of 1000 microseconds was required. GSB (9510 kilocycles) Daventry, March 10, 1936. 372 BELL SYSTEM TECHNICAL JOURNAL delay used is 400 microseconds. In samples 3 and 4 a third wave of 26 degrees is present. One branch was steered at this wave; the other was steered at the 15-degree wave and a delay of 1000 microseconds was used. It is of interest to compare these samples showing the manner in which the MUSA branch outputs combine, with the samples in Fig. 25 which were obtained with a two-antenna space diversity setup. Six antennas were retained in the monitoring branch but five were cut out of each receiving branch, leaving one antenna to supply each branch. In samples 1 and 2, antennas 1 and 6 (1000 meters apart) were re- tained. In samples 3 and 4, adjacent antennas (Nos. 1 and 2) 200 meters apart were used. These records were obtained about 15 minutes later than those of Fig. 23 and show the same two waves at 8.5 and 20.5 degrees. No delay was used. Note that the outputs combine in phase only when one wave predominates. Inserting delay in either branch is, of course, not effective in improving the audio combination. To do so would impair the addition when one wave is predominant and would not be beneficial when both waves are comparable. Figure 26 shows, in samples 1, 2, 3, and 4, how the delay indicator tube pattern is affected by the delay adjustment. The two branches were steered at the same angle, thus making both branch outputs identical so that perfect delay adjustment occurs with zero delay. This is the condition depicted in sample 1. In samples 2, 3, and 4 the delays are 340, 680, and 2700 microseconds, respectively. A number of tests were carried out with the cooperation of the British Post Office in which twelve tones were transmitted. These tones were nonharmonically related. They were separated at the output of the receiver by means of filters, and commutated to appear successively on an oscilloscope. The reader is referred to a paper * by R. K. Potter describing this technique. Figure 27 shows a sample of motion pictures made of the oscilloscope patterns. Two receiving systems are compared ; the right-hand pattern shows the output of the MUSA while the left shows the output of a conventional receiver con- nected to a horizontal half-wave antenna. The tones trace the hori- zontal lines in sequence from top (425 cycles) to bottom (2125 cycles). After one pattern is executed the commutator switches from one re- ceiver to the other. The twelfth tone is omitted to provide time for the switching. The complete double pattern is traced in about one-sixth of a second and the camera is operated at a speed which exposes each frame a little longer than one-sixth of a second. A MULTIPLE UNIT STEERABLE ANTENNA 373 ./^^ v\^ vw VU vu A^ Att vw vw .A^ .A^ END START 2 A^ A^ Ay^ A^ A-^ A-* END START 3 »Ay WW A^ .Aw END 3 START 4 yw A^ A^ VU Av A^ Aw END 4- Fig. 25 — This plate, made immediately following that of Fig. 23, shows for com- parison the manner in which the audio outputs add in two-station space diversity. The angle monitor shows the 8.5- and 20.5-degree waves as before. Films 1 and 2 taken at 11:15 a.m., E.S.T., were obtained with rhombic antennas 1 and 6 (40 wave- lengths apart). Films 3 and 4 taken at 11:20 were obtained with antennas 1 and 2 (8 wave-lengths apart). Note the second harmonic in film 2 particularly. GSE (11,860 kilocycles) Daventry, February 21, 1936. Musical program. Zero delay. 374 BELL SYSTEM TECHNICAL JOURNAL START 1 A-. / START 2 • START 3 Am* START 4 V 4 A^ /u. As. /^^ A— Am. vy^^ V / / / / / / • I* A^ /u A^ ^^i«> /W- A^ -N*-- % / / / f / / • • A^ /u i^^0» A^ ••«*• Aw yw* - / / / / # / 4 1 A^ /u /U. A-. /\m A^ ^v-«^ * / / / / 1 1 r ' K. A^ /w« -%»# A>^ A,.^ •i^>^ - y / / # / / • « A^ /u A^ - /\i«» A-X^ /s*<» /u f / / / / • t f ^v^ A^ /Vw '%^ ^ ^ /<«-% - / / / ^ • 0 • • ^ END 1 nT^^ END 2 ^^ END 3 A^ END 4 / • • IT Fig. 26 — Film showing tiie effect upon the audio addition of unequalized delay. Both MUSA branches were steered at the same angle, — that of the major wave shown. Film 1 shows no delay added and since each branch receives the same wave the audio outputs add perfectly. Films 2, 3, and 4 show the effect of adding 340, 680, and 2700 microseconds delay, respectively. A MULTIPLE UNIT STEERABLE ANTENNA 375 START i 1 i i I ^ ^ I 1 1 m I 1 i I M A 1 t m I 1 i * I m # ^ In 1 I n 11 f • I * 1 I ♦ II 11 I f I I END Fig. 27 — This is a cathode-ray "multitone" record comparing the MUSA output with that of a horizontal half-wave antenna. The tones on the right-hand side of each frame are the MUSA output; those on the left are the output of the horizontal half-wave antenna. The two MUSA branches were steered at 15 and 22.5 degrees. A delay of 470 microseconds was used to equalize the transmission time. GCS (9020 kilocycles) Rugby, February 24, 1936, at 3:54 p.m., E.S.T. 376 BELL SYSTEM TECHNICAL JOURNAL In Fig. 27 the MUSA branches were steered at 15 and 22.5 degrees and employed an equahzing delay of 470 microseconds. While the MUSA output is not perfect it is vastly superior to that of the doublet. The tone frequencies and filters are such as to suppress harmonic dis- tortion with the result that the patterns show mainly the selective fading of the fundamental audio frequencies. Note that the funda- mental output nearly disappears in the doublet receiver. In practice this would correspond to violent harmonic distortion of speech or music. In addition to the tests and experiments illustrated by the motion picture reproductions in the preceding paragraphs a series of experi- ments were conducted using broadcast transmission on 49 meters from a station at Halifax, Nova Scotia. In these experiments angles and delay differences were measured and compared with the multiple reflec- tion theory. The agreement between measured and predicted values is not only interesting as a study of the ionosphere but constitutes a unique and valuable test of the performance of the MUSA system. Observations on VE9IIX, Halifax During the course of reception experiments with GSL (BBC, Daventry, 6110 kilocycles) performed as a part of the routine operating program for the MUSA system, a broadcast station appeared on GSL's frequency. This station carried the programs of CHNS, Halifax, Nova Scotia, and was subsequently determined to be an experimental station with the call letters VE9HX located hear Halifax and nearly on the great-circle path from New York to London. The trans- mitting antenna is a half-wave horizontal, one-quarter wave above ground and oriented to radiate in the direction of New York. The first experience with this station showed two stable trans- mission paths capable of being separated by the two branches of the MUSA. The delays could be accurately equalized and rather definite correlation was obtained with the multiple "hop" propagation picture. This fact and the additional reason that propagation from England on the same frequency might be compared with the simpler phenomena encountered with Halifax led to the measurements described in the following paragraphs. About eleven hours of observation, distributed over fifteen days, are included. The log aimed to record all changes which occurred during an observation period. The procedure was as follows: The two branches of the receiver were steered at the angles indicated by the monitoring oscilloscope. Delay was added to the lower angle branch until the two audio outputs added. The delay setting was usually A MULTIPLE UNIT STEERABLE ANTENNA 377 critical to one section of the network (67.5 microseconds) and always to two sections. The angles were determined from the calibration curve reproduced in Fig. 28. The phase readings observed on the monitoring oscilloscope were recorded to within ±10 degrees and the earth angles determined by them are liable to be in error by one degree (possibly 1.5 degrees) apart from the ambiguity due to the multiple lobe characteristics of the MUSA. At this wave-length, the major lobe of the unit rhombic antennas is broad, the first null occurring at 58 degrees, so that two angles had to be considered possible. The multiple hop picture is illustrated in Fig. 29. Here the delay *:z:zZ — — -" — 1 ~^ ^^ :::: ^:-*^ d ^'' "" ANGLE CALIBRATION CURVE FOR 6110 KC. '~~~""~~ >> U 1, II ^ II II ^ , ^""^V^ \ / / / / \ V 0 40 80 120 160 200 240 280 320 360 PHASE SHIFTER READING, 02 Fig. 28 — Calibration curves of the Holmdel MUSA for 49.1 meters, giving the angle of the principal lobe as a function of phase advance 4>i (Fig. 3). Note that the sense of the phase shift depends upon the beating oscillator frequency. The curves are calculated for a velocity ratio v = 1/0.933. referred to the ground wave is expressed in terms of earth angles h and «, the number of hops or ionosphere reflections. The height h and angle h are also related through n as shown in Fig. 29. Using the first relation, the curves of Fig. 30 were drawn; using the second relation, points corresponding to various heights were located on the curves. For the Holmdel-Halifax circuit d is 643 miles (1030 kilometers) making ^ = 9° 21'. Corresponding to each measured angle there is a delay (referred arbitrarily to the ground wave which, of course, was not received) and a layer height, for each of the modes or orders. Both angles together yield a delay difference which is to be compared with the measured value. 378 TRANSMITTER BELL SYSTEM TECHNICAL JOURNAL 6 RECEIVER DELAY = 2nRo SIN e C COS (6 + e) COS 6 COS (6 + e) ; 2ne = /9 Fig. 29 — Delay and angle relations for multiple reflection from a uniform reflecting surface. The number of ionosphere reflections is designated by n. 4.5 3.5 2 3. Z Z 2.0 1.5 0.5 °.0 / Ao //o I-ONE REFLECTION I-TWO REFLECTIONS n-THREE REFLECTIONS '/ /T 35 '/j L 3 °y^ / 2; ^°^ 7- )0 2C ^ 250 , 3 300^ ^ C h,fKmJ= 200 ]25.— --^ "^ 15 55 60 65 :0 25 30 35 40 45 50 EARTH ANGLE ,6 IN DEGREES Fig. 30 — Curves giving the delay-angle relations for multiple reflection on the Halifax-to-Holmdel path. A MULTIPLE UNIT STEERABLE ANTENNA 379 TABLE I Observations on VE9HX, Halifax, Nova Scotia 6110 kilocycles 49.1 meters Relative Virtual Delay Height Estimated Field E.S.T. Date ai° «2° milliseconds kilometers decibels above l^v/m. meas. calc. 1st 2nd 3rd 1st 2nd 1935 P.M. 5:00 11-25 18.2 38 1.01 0.77 195 215 P.M. 4:45 11-26 24.5 42 1.01 0.85 260 250 P.M. 4:40 12-17 26.4 44 0.95 0.97 290 270 27 P.M. 4:41 12-17 24.5 43 0.95 0.95 265 255 P.M. 5:01 12-17 24.5 42 0.95 0.85 265 250 P.M. 4:20 12-18 25.5 44 0.95 1.05 275 270 27 P.M. 4:25 12-18 24.0 42.5 0.95 0.90 250 250 A P.M. 4:40 12-18 23.0 42 — . 0.90 245 250 P.M. 4:30 12-23 24.5 44 0.95 1.05 265 270 25 A.M. 10:29 12-26 28.0 44 0.95 0.90 305 270 -14 A.M. 10:46 12-26 28.0 44 0.81 0.90 305 270 A.M. 10:52 12-26 29.5 44 0.78 0.85 330 270 P.M. 4:33 12-26 24.5 44 0.88 1.05 265 270 242 245 18 P.M. 4:49 12-26 24.5 42 0.95 0.85 265 250 P.M. 4:58 12-26 24.0 42.5 0.88 0.90 250 250 A.M. 10:07 12-27 25.5 43 0.95 0.95 275 255 -14 A.M. 10:57 12-27 29.5 42 0.68 0.65 330 250 130 243 A.M. 11:03 12-27 31.0 42 0.88 0.70 250 100 A.M. 11:20 12-27 <8.0 45.5 1.28 1.6+ <120 280 B 1.5 + <120 185 A.M. 11:48 12-27 8.0 47.5 1.28 1.8+ 1.7 <120 <120 300 195 A.M. 11:56 12-27 8.0 45.5 1.28 1.6+ 1.5 + <120 <120 280 185 130 247 P P.M. 4:32 ^ P.M. 4:59 12-27 25.5 44 0.88 1.05 275 270 14 12-27 27.0 43 0.88 0.85 295 255 P, A.M. 10:45 ^ A.M. 11:45 12-31 31.0 42 0.50 0.55 350 250 0 12-31 8.0 35.5 0.71 0.8 + <120 195 1936 A.M. 10:30 1-2 24.5 42 0.88 0.85 265 250 - 2 P.M. 6:05 1-14 20.5 42 1.01 1.00 215 2. SO 8 P.M. 6:35 1-14 18.4 38 1.01 0.77 200 215 E P.M. 6:15 1-15 23.0 42 1.08 0.90 245 250 22 P.M. 6:20 1-15 24.0 42 1.11 0.85 250 250 P.M. 6:40 1-16 25.5 42 1.08 0.85 275 250 14 P.M. 7:21 1-16 24.5 43 1.18 0.95 265 255 P P.M. 8:39 ^ P.M. 9:35 1-16 31.5 37 0.27 0.20 355 205 1-16 26.4 37 0.47 0.42 290 205 27 P.M. 5:50 1-21 24.5 42 0.95 0.85 265 250 267 247 22 G P.M. 6:10 1-21 26.4 44 1.01 0.97 290 270 P.M. 6:16 1-21 22.0 40 0.95 0.80 235 230 232 245 A.M. 10:40 1-22 24.5 43 0.95 0.95 265 255 - 2 A.M. 11:05 1-22 24.5 34 0.41 0.35 0.30 265 265 185 120 H A.M. 11:09 1-22 34.0 43 0.60 0.60 0.65 185 255 255 120 A.M. 11:30 1-22 24.5 43 0.95 0.95 265 255 A.M. 11:35 1-22 24.5 34 0.41 0.35 0.30 265 265 185 120 I P.M. 6:45 1-24 18.4 38 0.74 0.77 200 215 1 2 380 BELL SYSTEM TECHNICAL JOURNAL In Table I the virtual heights are deduced from the curves for the assumed hop orders. The calculated relative delay is the delay differ- ence corresponding to these heights. All angles below 60 degrees were considered and all combinations of hop orders were considered for each angle, subject to the experimental knowledge of the sense of the delay. The values shown in the table are the ones which give the best agree- ment with the measured delay. In most instances there was no question concerning the interpretation; in a few doubtful cases two possibilities are presented (December 27 and January 22). Examination of the table shows that except near noon, the propaga- tion comprises the first and second reflections from the F region of the ionosphere. Groups A, C, E and G illustrate this. In the majority of instances the agreement is excellent; these cases constitute strong evidence that the MUSA performs correctly. The discrepancies in the table between layer heights for the first and second hops and between measured and calculated delay are not entirely experimental error. Assuming errors in measured angles suffi- cient to make the delays agree will, in some cases, increase the dis- crepancy in heights. An interpretation one might make of this is that the ionosphere is not uniform over the circuit and the regular reflection basis of calculating is not strictly in accord with facts. However, there are other theoretical explanations for discrepancies in height. Under usual conditions, the second reflection height should be slightly greater than the first but for certain ionizations in the E region, the first F reflection may be retarded more than the second F reflection in passing through the E region. Thus the heights may differ in either direction without demanding horizontal non-uniformity. The discrepancies be- tween measured and calculated delay may be explained by horizontal non-uniformity in the ionosphere. For an essentially non-dissipative atmosphere of ions having any vertical distribution but no horizontal gradient, and neglecting the earth's magnetic field, the group delay is identical with that calculated from triangular paths coinciding with the initial earth angles. Breit and Tuve showed this in their 1926 paper. With horizontal variations in the ionosphere such as tilting layers, no kind of agreement could be expected; the waves might even travel via other than great circle routes. During three days of our observations W. M. Goodall made measure- ments of virtual height and of critical frequency which enabled him to predict the results we might be expected to observe. His estimates are shown in the next to the last column of the table. The data for December 27 (B) are interesting in that after 11 o'clock the first F reflection apparently disappeared. Instead, a first reflection A MULTIPLE UNIT STEERABLE ANTENNA 381 from the E layer is indicated. This was predicted by Mr. Goodall on the basis that the E region ionization at noon became so great that 24-degree waves should be reflected. For completeness the table shows an alternative interpretation of a first E reflection and a third reflection from a 185- to 195-kilometer height. The first E reflection and second F reflection are perhaps more likely. The 11 :03 record is not explained. Something similar appeared to happen on December 31 (D). On January 22 (H) normal first and second F reflections occurred with angles of 24.5 and 43 degrees. In addition a third wave of 34 degrees appeared. Two interpretations of this are shown but neither seems very plausible. As a general rule propagation from Halifax is simpler than from Daventry on the same wave-length. In particular GSL waves re- ceived by the two MUSA branches are definitely less discrete and include sufficient delay differences in themselves to prevent the nicety of equalization possible with VE9HX. If multiple reflection takes place, which we have no reason to doubt, it is generally so distorted by non-uniformity over the path or by other factors as to be unrecog- nizable. In view of the occasional complexity of the Halifax circuit, only one-sixth as long, this is perhaps to be expected. The absence from these observations on Halifax of any third reflec- tions from the F layer is likely due to the fact that they would fall in the neighborhood of the first null of the rhombic antenna and would have to be much stronger in space in order to appear comparable with the second or first. There have been momentary appearances of waves which might have been third reflections but they did not persist long enough to work with. When single waves were present, which was not unusual in the later evening hours, the angle more often corresponded with the first F reflection rather than the second. Additional Numerical Data on Reception with the MUSA The data shown in Fig. 31 are submitted to supplement the rather meager numerical data on transatlantic reception thus far presented. Here, relative delays and angles taken from the MUSA operating log are shown in plots A, B, and C. Only the end points of the lines are significant; they denote by their abscissas the angles at which the two receiving branches were set. The ordinates of the upper end points denote the equalizing delay. The lines merely connect coexistent points. The data shown were selected from the rather extensive log to present a fair cross section of conditions, omitting, however, all cases 382 BELL SYSTEM TECHNICAL JOURNAL in which both branches were steered at the same wave bundle. They cover winter and summer and were obtained with frequencies appro- priate to the time and season. Most of the observations were made on transmission from Daventry, the remainder on transmission from Rugby. In D are shown the results of pulse measurements made before the MUSA was ia use. Here the angles were measured by the two antenna null method and the delays were observed directly on the oscilloscope time axis.^ Although as many as five points, each de- noting a wave bundle, are shown, generally not more than three were 1.6 1.2 0.8 0.4 I °' O O 2.4 LlJ lO Ij 2.0 _j 2 1.6 Z ~ 1.2 >- < -1 0.8 LiJ Q > K 0 < UJ A 18 MC. ^<^ < ^^ 10 15 20 25 EARTH ANGLE .6 IN DEGREES 35 Fig. 31 — Pairs of measured angles and relative delay denoted by the end points of the line segments. The data in ^, 5, and C were obtained with the MUSA; that of D was obtained by the use of pulses. important at once. These measurements were made on transmission from Rugby. It will be noticed that all four groups of data show that the relative delay per degree of angle difference is small at low angles and increases with the angle, roughly as the multiple reflection theory indicates. (This characteristic is distinctly favorable to the performance of the MUSA since its angle resolving power falls off at very low angles.) The scattering of the data indicates that an equalizing delay deter- mined by the angle settings would not be successful; i.e., the delay A MULTIPLE UNIT STEERABLE ANTENNA 383 must be capable of adjustment to meet the various transmission conditions. Quality Improvement with the MUSA The distortion of speech and musical quality which characterizes short-wave circuits is due entirely to the interference of differently delayed waves each of which individually is fundamentally free from all kinds of distortion except non-selective fading. This conclusion is almost self-evident and is corroborated by the results of several years of pulse investigation ^ made in cooperation with the British Post Office. A MUSA system can be expected to select one out of several multiple reflections. However, these reflections suffer more or less scattering with the result that they appear as bundles of waves of various degrees of compactness. These bundles possess a small spread of both angle and delay. The delay interval included in a bundle of waves is rarely less than 100 microseconds. Double refraction or " magnetoionic splitting" occurring in the ionosphere doubtless accounts for the existence of a small minimum delay. A delay interval of fifty micro- seconds or so may be detected even in the unusually compact bundles represented by the pulses of Fig. 21. Transmission from Halifax appears to include a delay interval of this order, also. With trans- atlantic propagation it is not uncommon to have a bundle containing numerous weaker components extending over several hundred micro- seconds. On rare occasions these have extended over two milli- seconds, masking any multiple reflections which may have been present. The quality associated with one MUSA branch which selects one out of several bundles of waves is thus not perfect. The effect of a delay interval of a few hundred microseconds is scarcely noticeable, however, except during deep carrier fades. Therefore, if diversity action between two branches steered at the low and high angle parts of the same bundle is employed, deep fades are avoided to a large extent, and the quality is almost perfect. When more than one wave bundle is present diversity action between branches steered at the principal bundles accomplishes this escape from deep fades. It is desirable to utilize all of the principal bundles in diversity in order to preserve the discrimination of the MUSA. For, one of the bundles, if not provided with a branch to receive it, would cross talk into the other branches when it momentarily became strong and those provided with branch receivers became weak. Signal-to-noise ratio considerations discussed in Section V constitute an equally important (and related) reason for utilizing all principal bundles. 384 BELL SYSTEM TECHNICAL JOURNAL As distinguished from selective fading, which is greatly reduced by the rejection of all but one wave bundle, general fading is by no means eliminated. The reader may expect, however, that when the MUSA selects one wave bundle from several it restricts the waves accepted to those which have traveled more nearly a common path, and for a given degree of turbulence in the ionosphere, the fading should be slower, since only relative changes among the several waves result in interference fading. Such a tendency no doubt exists and has been noticed occasionally in the operation of the MUSA but rarely has there been a marked effect (excepting certain cases of flutter fading to be described later). This will be understood when it is recalled that even a fifty-microsecond delay interval means that a difference of 500 wave-lengths is involved for a wave-length of thirty meters. In order that the fading rate be sharply reduced it is required that the iono- sphere shall preserve this difference, to within a half wave-length, more effectively than it does if larger differences are involved. Since a hall wave-length is only 0.1 per cent of 500 wave-lengths a rather high degree of balance is thus required. Evidently, the turbulence of the ionosphere usually prevents such a balance. Using broadcast signals (double side band) from Daventry a thousand or more comparisons were made of the MUSA versus a single antenna and receiver, using the switching arrangement mentioned in Section III. Remarkable improvements were sometimes observed and some improvement was almost always noted. The exceptions were the instances when distortion was not detectable using one antenna, and the rare occasions when particularly violent flutter fading occurred. Space diversity reception using two antennas showed a substantial improvement, usually, but failed ever to show the order of improve- ment demonstrated by the two-branch MUSA when two or more wave bundles of comparable amplitude occurred. Figures 23 and 25 sug- gest, by the way in which the audio outputs are seen to combine, that the distortion with MUSA reception is slight compared to that with diversity reception. The increased naturalness which results from reducing the distortion is, of course, pleasing to the ear and has some value in telephone circuits on account of the subscribers' satisfaction. In addition, it increases the intelligibility particularly when considerable noise is present. It is impossible to evaluate the increased intelligibility definitely but, in certain cases at least, it permits the signal-to-noise ratio to be two or three decibels lower. From the point of view of picking up short-wave broadcasts for rebroadcasting, a more sub- stantial value can be attached to the MUSA quality improvement. A MULTIPLE UNIT STEERABLE ANTENNA 385 To a considerable extent, the magnitude of the quality improvement ascribed to the MUSA in the preceding paragraphs depends upon the fact that double side-band signals were employed. For, with double side-band signals the selective fading caused by the interference of the differently delayed waves results not only in selective fading of the audio output, but also produces non-linear distortion when the carrier fades selectively. This non-linear distortion sounds much like over- modulation, and when it occurs in its more violent forms it completely ruins the quality and intelligibility. With single side-band trans- mission it is possible to demodulate with such a strong carrier that non-linear distortion is virtually eliminated. The fading of the audio output is sometimes more selective than with double side-band but the resulting quality is substantially better. Single side-band transatlantic signals were not available during the trial of the MUSA system. However, as mentioned in Section III, receiving equipment was available which rejects one side band and reduces the percentage modulation by a factor of ten or more. It was found that this equipment, applied to the one-antenna system, resulted in substantially reduced non-linear distortion and that the quality could be still further improved by the reduction of selective fading afforded by the MUSA. With MUSA reception there was apparently no quality improvement in going from double to single side band. Summarizing Discussion In this section the general performance of the experimental MUSA has been described in a necessarily qualitative manner. Motion pic- ture oscillograms were shown to illustrate the performance under fairly typical transatlantic conditions. An investigation of propagation from Halifax in which the MUSA was employed to identify ionosphere re- flections was included to supplement the rather fragmentary evidence available in motion picture oscillograms. The improved quality ob- tained with MUSA reception was discussed from several points of view. The evaluation of the MUSA has been general; it serves partly to introduce the following section which deals specifically with the signal-to-noise ratio evaluation. Before closing this section it is appropriate to discuss conditions with which the experimental MUSA could not adequately cope. On numerous occasions the fact that only two branches are provided has definitely handicapped the performance. More often, however, the need for greater angular discrimination or resolving power has been apparent. Except on infrequent occasions a MUSA two to three times the length of the experimental one and equipped with three 386 BELL SYSTEM TECHNICAL JOURNAL branch receivers could be expected to perform as well as the experi- mental one now performs at its best. The occasions when it might not are the infrequent times when violent flutter fading occurs. At least one type of flutter fading appears to be associated with a pronounced scattering which results in a kind of shower of erratic waves arriving over a wide range of directions. Receiving antenna directivity has been found definitely helpful in all except the most violent cases. Apparently when improvements due to directivity occur they occur principally by selecting a more or less normally propagated wave bundle and rejecting the shower of erratic scattered waves. When, in the most violent cases, no reduction of the flutter can be achieved the reason may be that the unit antenna accepts too wide a horizontal range to permit the MUSA to discriminate sufficiently against the shower. (It will be remembered that the MUSA array factor is of the form of a semiconical shell and thus the MUSA will, in general, accept as wide a horizontal range as the unit antenna permits.) V. The Signal-to-Noise Improvement of the MUSA Receiving System Because of the complicated nature of short-wave transmission and also because of the uncertain state of noise measuring technique, it is not a simple matter to give a satisfactory answer to the question: "What is the signal-to-noise improvement of a MUSA system?" In this section an attempt has been made to simplify the problem by separating the various factors involved. The section begins with an analysis of the problem assuming simple types of wave transmission. This is followed by experimental studies and discussions. In discussing the signal-to-noise advantage of a MUSA it is under- stood that a reference receiving system must be adopted, and for this purpose one of the unit antennas connected to an automatic gain con- trolled receiver was chosen. Other types of antennas as, for instance, a simple vertical or horizontal doublet might have been used but other factors not significant to the MUSA would then have been involved. Simple Analysis of the Signal-to-Noise Ratio Improvement The MUSA differs from other directional antennas in that it is an array of antennas between which there is negligible electromagnetic coupling. This allows (but does not require) a different point of view, not explicitly involving directivity, in considering the signal-to-noise advantage of the array. The following analysis is made from this point of view. In Figs. 32 to 34 antennas are represented by signal A MULTIPLE UNIT STEERABLE ANTENNA 387 generators, e^, static generators, e„, and resistances Ra- The input circuits of the receivers are matched to the. antennas. In Fig. 32, A^ spaced antennas are shown connected in parallel. The root-mean-square noise voltage. En, at the input to the receivers represents the thermal noise originating in the receiver input circuits. ANTENNA I R ANTENNA 2 R ---rrri::j::S-I ANTENNA N R input circuit (impedance r) Es.Ea-En WAVE DIRECTION UNIT ^ANTENNA FIRST ASSUMPTION: ALL LINES MATCHED (line IMPEDANCES - R^ PHASE SHIFTER IMP. = Ra INPUT CIRCUIT MATCHED TO IMP. Ra/n) SECOND ASSUMPTION: SINGLE WAVE. SIMILAR ANT (esi=es2 esN=es ®ai~ ©az' 6qn= ©a) SIGNAL CURR. PHASED STATIC CURR. RANDOM r-r 6s K 2Ra' _ N 2Rr i/N 2Ra CONST X /r '^Wa CONST X /R Es ^ es ■r-= Tn -7= CONST. 1 ^r; Fig. 32 — Simple signal-to-noise analysis of a system of N spaced antennas. Signal currents are phased and combined at the incoming frequency. The summa- tion signs include addition on the power basis. For the matched condition this noise is constant and independent of the number of antennas. A single wave is assumed and the signal outputs of the antennas are phased by means of the phase shifters 0. The maximum signal power obtainable from N antennas obviously is N times that obtainable from one antenna. In terms of receiver noise, 388 BELL SYSTEM TECHNICAL JOURNAL Bn, the improvement in signal-to-noise ratio is 10 log N decibels referred to one antenna. If, instead of receiver noise, static is the predomi- nating noise, the signal power received is not significant but the same improvement is realized for the general case in which the static is distributed randomly among the N antennas.^- In that case the TV signals are phased to add on a current basis while the N noise sources ANTENNA 1 ANTENNA 2 R Es.Ea.En SINGE WAVE. SIMILAR ANT ©ai - ®a2-' ^au- ©a AUDIO SIGNALS THEN IN PHASE EjOCNes EgocVFTea E„ ccVNTe Ll = Vn^ En ^"^ e„ En 6n Fig. 33 — Simple signal-to-noise analysis of a system of N spaced antennas. Signal currents are combined at audio frequency. add on a power basis. Analogous arguments apply to a series con- nection of N antennas and result in the same improvement of 10 log N decibels. ^^ If static comes from all directions simultaneously, its distribution is random among the ideal unit antennas discussed in Section II. This is deduced from calcula- tions which show that gain (signal-to-noise ratio) is proportional to the length of the system; i.e., to the number of unit antennas. The assumption of randomness requires that the spacing of unit antennas having a certain angular discrimination must be equal to or greater than the antenna length required to produce that dis- crimination in the simple linear end-on type of unit antenna. That static is, on the average, distributed randomly among the rhombic antennas of the experimental MUSA is shown by measurements described later in this section. A MULTIPLE UNIT STEERABLE ANTENNA 389 The system described above has been shown mainly to introduce the system shown in, Fig. 32). This diagram shows the audio addition of the outputs of N receivers fed by N antennas. Note that this system has no high-frequency phase shifters in the transmission lines. It is in fact similar to the diversity receiving system described by H. H. Beverage and H. O. Peterson. ^^ For a single wave this is seen to be equivalent to the phased addition at carrier frequency shown in Fig. 32. The signal-to-noise improvements shown on Figs. 32 and 2>d> were easily calculated because a single non-fading wave was assumed. In actual practice several fading waves are involved and it is then difficult, if not impossible, to make significant calculations. Later in this section, however, some of the general features of the system shown in Fig. 3?) will be discussed from the point of view of several waves. The MUSA system is characterized by the ability to separate waves and it is therefore possible to analyze it in a simple manner for cases of more than one wave. The arrangement in Fig. 34 corresponds to the Holmdel MUSA. The signals from the equally spaced antennas are here phased at the intermediate frequencies. Since random static and first circuit noise give identical results the analysis is given for static only. As shown in Case I, if only one wave is present and both branches are phased for it the system functions as in Fig. 32 and it yields the same improvement of 10 log A'^ decibels. If as shown in Case II the second branch is not phased for it (i.e., if the wave falls upon a minor lobe or a minimum of the MUSA directional pattern) less than the full improvement occurs. On the basis of linear audio detectors the re- duction of improvement is 20 log x where x lies between 2 and V2. This quantity refers to the manner in which the noise from sources 1,2, • • • A" in Branch A adds with the noise /row the same sources after having been phased differently and perhaps delayed differently in Branch B.^* This involves the audio-frequency band width and method of noise measurement. As will be shown later x is usually not much different from V2. Taking x = V2 the loss in Case II is three decibels. If an audio detector is used which does not demodulate noise when the signal is absent (a square-law detector accomplishes this for practical purposes) this loss disappears, and branches may be phased for temporarily non-existent waves without incurring a penalty. Case III is the important one. It assumes two equal waves. Branch A is ^^ "Diversity Receiving System of RCA Communications, Inc.," Proc. L R. E., vol. 19, pp. 531-561, April, 1931. "The case of .x = 2 (in-phase addition) arises only when the phasing and delay of the two branches are alike. 390 BELL SYSTEM TECHNICAL JOURNAL phased for one ; Branch B for the other. Again taking x = V2, the im- provement referred to e,/e„ is 10 log iV + 3 decibels. Here eje^ denotes the signal-to-noise ratio in each antenna due to one wave" Referring the improvement to the signal-to-noise ratio of one antenna ANTENNA I ANTENNA 2 ANTENNA 3 ®SA ©SB 6c ©SA ©SB 6a I — wv ' Ra ©SA ©SB ©a I VW ' Ra ©SA esB ©a H.F DETECTORS I PHASE r~n SHIFTERS r L_. ANTENNA N ^^^ — 7^ — ;=u I ID N \- I 0 N |- REC A |REC B Es.Ec EsB Eqb -^ EoAo/N'ea'j EaB = ^eaU^-/N-|^ CASE m. SINGLE WAVE A (656= O) BRANCHES A AND B PHASED FOR WAVE A. DELAY ZERO. S/n IN EACH ANT. = esA/ea SINGLE WAVE A (Csb^ o) BRANCH A PHASED FOR WAVE A BRANCH B PHASED AGAINST WAVE A. s/n in EACH ANTENNA TWO EQUAL WAVES A AND B (©SA=esB = es) BRANCH A PHASED FOR WAVE A. BRANCH B PHASED FOR WAVE B. Eja AND EjB DELAY EQUALIZED, s/n IN EACH ANT. = v/2 65/60 Fig. 34— Simple signal-to-noise analysis of the MUSA system. receiving both waves, assumed to add randomly, increases the reference by three decibels and reduces the improvement to 10 log TV decibels. This analysis may be expanded to include K waves in which case K branches would be required to obtain the gain of 10 log N decibels re- ferred to one unit antenna. A MULTIPLE UNIT STEERABLE ANTENNA 391 It has been tacitly assumed in the foregoing analysis of Fig. 34 that the audio outputs of the several branches are delay equalized to add and that there is no diversity action (all of the waves are assumed to remain equal). The influence of fading is difficult to predict and will be discussed later in connection with experimental results. Some readers, not concerned with details, may omit reading the following subsections and find it sufficient to read only the Summarizing Discussion of this section. Test Method From a practical point of view the best way of testing a MUSA system would seem to be to operate it on transatlantic telephone signals and compare its output with that of the reference system. Speech volume and noise could then be measured in the conventional manner. So far as the signal-to-noise improvement is concerned it would be a laborious and lengthy task to get satisfactory data because so often, during the test period, ^^ static and receiver noise is masked by trans- mitted noise, interfering signals, and other man-made noise. To test the experimental MUSA, therefore, a difi"erent method was selected which gave significant data in a shorter time. Since the success of the MUSA is related so fundamentally to the nature of the arriving signal the important thing to be determined by the measurements is how well the MUSA is able to cope with the various conditions of wave arrival. For instance, in the case of a single bundle of arriving waves how close does the actual signal-to-noise improvement come to the 10 log N decibel calculated for Case I (Fig. 34) in which a single non-fading wave was assumed? Likewise, for the case of two-wave bundles do the calculations of Case III agree with measurements? For these purposes the signal-to-noise measurements would have to be free from directional static, interference, and transmitted noise; otherwise the measured improvements would be distorted. To insure uniform and desirable noise conditions it was decided to use thermal noise originating in the receiver input circuits ^^ instead of whatever noise might be present on the radio channel. This was accomplished by inserting resistance pads in the antenna transmission lines to reduce the signal (and external noise) to a level where thermal noise greatly exceeded other noise. Signal-to-noise ratios in the range between fifteen and forty decibels were obtained in this manner, free of inter- ference and directional static, and of transmitted noise. 2* Transmission conditions during 1935 were comparatively undisturbed. ''^ A portion of the noise originates in the plate circuit of the first detector. For the present purposes this is equivalent to first circuit noise. 392 BELL SYSTEM TECHNICAL JOURNAL Substituting thermal noise for external static may at first seem far- fetched. Except for the fact that static is sometimes sufficiently directional to be received with different intensity as the MUSA is steered differently, the substitution is sound. In general, the static output does not vary with steering, as the measurements described later indicate but to avoid the distortion of results which would occur when this is not so, it was desired specifically to substitute non- directional noise. Studies of the characteristics of static and thermal noise have shown that both are alike so far as the effect of band width upon average and effective values is concerned, and have indicated that both consist of extremely short, randomly distributed pulses which overlap when received and detected by receivers of ordinary band widths. In a given band width, the envelope of the currents produced by static sources is highly irregular in comparison with that produced by thermal agitation. It appears, however, that the character of either envelope is not sensibly affected by the number of antennas combined nor by the manner in which the branch outputs are combined, so that both give the same improvement figures using any arbitrary noise measuring method. There were several possibilities with respect to the signal to be employed in these tests. A single tone, a large number of tones dis- tributed throughout the audio band and other special signals were considered. A simple method requiring no modulation was finally adopted. It consisted in alternately connecting the output of the an- tenna to be tested and that of the reference antenna to the same receiver. Assuming that the automatic gain control of this receiver would maintain a constant audio output level the signal-to-noise advantage is the ratio of the noise levels. The automatic gain control of the MUSA receiver did not, of course, hold the output level abso- lutely constant but a correction was easily made for the small varia- tions in level. The circuits of the measuring equipment are shown in Fig. 35. The rectified carrier appearing in the linear speech rectifier is taken to be proportional to signal and is measured simultaneously with the noise demodulated in the rectifier. When the keys are thrown to position 2 (by a gang arrangement) the signal meter shows the sum of the two rectified carriers and the noise meter reads the combined noise in the output of the diversity mixing amplifiers. Using the sum of the two rectifier currents to represent the signal implies that actual audio out- puts from the two branches could be delay equalized to add arith- metically. As applied to a MUSA system this assumption is justified, in general. When the keys are switched to position 1, the rectified A MULTIPLE UNIT STEERABLE ANTENNA 393 carrier of branch B alone appears on the signal meter and noise from branch B appears alone on the noise meter. At the same time the diversity connection is broken and all except one of the six-phase shifter amplifiers in branch B are biased to cutoff; i.e., only one unit antenna is used. The pad "L" is adjusted to give the same audio gain from rectifier B to the noise meter for connection 1 as for con- nection 2. By manipulating the keys which control the cutoff biases on the phase shifter tubes the "1" to "2" switchover may also be used to compare one antenna (one receiver) with two antennas in ordinary space diversity or one antenna with all six in a single branch. The use of receiver noise as a noise source depends upon (1) having the noise equal in all six circuits and (2) upon having it originate ahead of the point where the gain is varied. In well-designed receivers the noise should approach the thermal noise limit of the first circuit. It was found possible to have the signal-to-noise ratio, for a given signal level, of all six high-frequency input circuits equal to within ± 0.5 decibel and within a few decibels of the thermal limit. The first tests were made with a local oscillator supplying the signal. They really constituted tests of the measuring set up. All six input circuits were fed simultaneously through 80-ohm pads giving equiphase and equiamplitude signals on each detector grid. This corresponds to receiving a single steady wave, and one branch was "steered" as if to receive such a wave. When the multiple switch was manipulated as to compare one antenna with the steered branch the indicated signal- to-noise improvement was usually between seven and eight decibels, compared with the theoretical value of 7.8 decibels (10 log 6). Such a local test using the switchover with all associated equipment was made before and after every transatlantic test. Corrections based upon 7.8 decibels were made to the data in cases where the local tests showed a slightly dififerent improvement factor. In all of the work the gains of the phase shifters were adjusted to equalize the difiference in line loss. The effect of this is, however, trivial. In measuring on transatlantic waves with automatic gain control the noise variation, corresponding nearly to the reciprocal of fading, rendered visual noise readings too rough to be suitable. A Weston high-speed db meter (copper-oxide bridge type) having a calibrated range of 16 decibels was used as a noise meter. To this instrument was added a fiuxmeter (Fig. 35) of low restoring torque which automatically averaged the variations of the meter pointer over the 15-second periods of observation used in these tests. The fact that the noise meter recti- fier is linear means that the noise current is averaged arithmetically 394 BELL SYSTEM TECHNICAL JOURNAL -vwv- '^I-vvw^ AW-' .5 I ^ -P uj 0.4 NO. I ANTENNA n VN "T 1\ 0.48_ - y V / U ^A u J yu SIX ANTENNAS S/N IMPROVEMENT = -^^ = 5.6 DB Fig. 36 — Sample of measured noise plotted against time. GAU (18,620 kilocycles) Rugby, September 19, 1935. cannot fall on the apex of the directional pattern. It was encouraging to find that no more loss occurred; i.e., to find that the waves in a single bundle may be phased so effectively. Before leaving these tests, the results for September 18 should be mentioned. On this day the signal-to-noise ratio was so low, even without antenna pads, that measurements could not be made. The noise on this day was first taken to be thermal noise but was found 398 BELL SYSTEM TECHNICAL JOURNAL during the course of experimentation to be external noise ^'' some ten decibels higher than thermal noise, as received on a single rhombus. At the end of the test the operator at Rugby keyed the transmitter with tone, advising us that the schedule was completed and wishing us "good night." With one antenna the signal was hopelessly lost in noise; with the six antennas the code was readable. TABLE III Two Branches GBW 14,440 kilocycles Date Test No. Pads in Ant. db Reference Antenna Number of Readings S/N Improve- ment db Group Average db Number of Wave Bundles 1935 10-2 . . . 21 40 20 2.7 10-2 . . , 23 40 16 5.3 10-2 . . . 24 40 16 4.4 10-8 . . . 29 40 20 6.3 10-10 . . 37 40 20 4.4 4.7 10-2 . . . 20 40 6 19 6.9 10-2 . . . 22 40 6 20 8.4 10-2 . . . 25 40 6 16 9.0 10-8 . . 28 40 6 17 10.9 10-9 . . . 30 40 6 38 8.0 8.5 9-30 . . . 17 40 1 22 3.4 2 9-30 . . 19 40 1 14 4.1 2 10-2 . . . 26 40 1 16 4.6 2 10-10 . . a 40 1 19 2.0 3.5 2 9-30 . . 16 40 6 17 8.0 2 9-30 . . . 18 40 6 17 7.9 2 10-2 . . . 27 40 6 20 6.7 2 10-10 . . . 34 40 6 20 7.3 7.4 2 The apparent line loss is 3.8 and 3.9 db for the one-wave and two-wave groups, respectively. The calculated loss is 3.8 db. The equivalent improvement for one-wave group is 6.8 db to which may be added the later determined correction of 1.2 db for the effect of delay, giving 8.0 db. The equivalent improvement for two-wave groups is 5.7 db to which may be added 0.8 db for the effect of delay, giving 6.5 db. More comprehensive measurements were made on GBW (14,440 kilocycles) and a few on GCW (9790 kilocycles), using the two branches. Since an unmodulated carrier was used, rectified carrier being taken to represent signal, there was no criterion for setting the audio delay. Accordingly, it was kept at zero and a correction intro- duced later. The results are shown in Tables III and IV. ^' This noise, which was directive to the extent that four-decibel variation occurred with steering the MUSA, was doubtless a sample of the "star static." It was encountered also on 31 meters in October. See footnote (32). A MULTIPLE UNIT STEERABLE ANTENNA 399 TABLE IV Two Branches GCW 9790 kilocycles Date Test No. Pads in Ant. db Reference Antenna Number of Readings S/N Improve- ment db Group Average db Number of Wave Bundles 1935 12-13. . . 39 40 1 15 4.8 2 12-13 . . . 40 40 1 14 4.7 4.7 2 12-13 . . . 38 40 6 14 7.9 2 12-13 . . . 41 40 6 13 6.7 7.3 2 The apparent line loss is 2.6 db. The calculated loss is 3.1 db. The equivalent improvement is 6.1 db to which may be added 0.9 db for the effect of delay, giving 7.0 db. The data in the tables are classified roughly according to whether two bundles or one bundle of waves was present. In the latter case the two branches were steered, one on each side of the bundle, a few degrees apart. During these tests slight adjustments in steering were made when indicated by the angle monitoring tube, as in normal operation of the system. The large amount of data taken with GBW makes the results in Table III particularly reliable. This is reflected in the close agreement between measured and calculated line loss. Before discussing the results further the effect of delay needs to be analyzed. Correction Due to Delay The effect upon the noise, of delaying one audio output, is shown in Fig. 37. The curves were obtained with the circuit shown in Fig. 35 1. 0° 40° 1 ftn° ^r:-^ ■~v_ '^ ■> ^ K-^ 160° = ^==^ ^^/ ^/ o z z - 10 100 1000 DELAY IN MICROSECONDS Fig. 37 — The effect of delay and phasing upon noise output of the MUSA receiver. using thermal noise. The equiphase, equiamplitude signal source men- tioned previously was used to supply the inputs. Branch A was kept phased so that the six signals added, and branch B was varied. The 400 BELL SYSTEM TECHNICAL JOURNAL curves show the effect of delay upon noise in a 250- to 2750-cycle audio band, as measured with the Weston db meter, for various differences in steering. The curves are labeled in terms of the difference in the phase settings of the two branches. The 40-degree or 80-degree curves correspond in practice to steering on each side of a single bundle of waves. The 160-degree curve typifies steering at two separate wave bundles. The use of 100 microseconds (or more) delay is generally advantageous for the audio addition when steering at one bundle. Since this amount of delay makes the audio noise addition nearly random and for widely different steering the addition is also random the assumption that the noise from the two branches adds on a power basis, made in reference to Fig. 34 (x = V2), is justified. The effect of delay is to produce an interference pattern in the audio noise spectrum. This accounts for the dip in the noise curve for a delay of 300 microseconds which locates the first interference minimum at about the center of the audio band. The asymptotic approach to 3.5-decibel reduction corresponds more nearly to a reduction ratio of 2 fir than to 1/V2 due to the fact that the Weston db meter is nearer linear than square law in response. In obtaining these curves it was desired to simulate the reception of two waves for which the corresponding branches were phased to add. It was not convenient to set up locally such a two-wave case but the single wave input should give identically the same results provided phases were avoided which resulted in a signal at the second detector too low to demodulate the noise. A signal level so high that further increase did not affect the noise output was used for all points. The real purpose of the signal was to insure that the demodulated noise was not dependent upon the intermediate-frequency bands and that the results would be unaffected by possible differences in intermediate- frequency bands. ^* As mentioned, noise has been measured with an unweighted 250- to 2750-cycle frequency band. Had a weighting network ^^ which em- phasizes frequencies in the vicinity of 1000 cycles been used the dips in the curves marked 0° and 40° would have been deeper and would have occurred in the vicinity of 500 microseconds delay. Returning now to Tables III and IV the measured improvements were corrected to correspond to the effect of the delay which would probably have been used to obtain the best audio addition for the signal. The 1.2-decibel correction for the one-bundle case represents -^This precaution was subsequently found to be unnecessary; i.e., similar results were obtained with no input signal. 2' Barstow, Blye, and Kent, "Measurement of Telephone Noise and Power Wave Shape," Elec. Engg., vol. 54, pp. 1307-1315, December, 1935. Technical Digest published in Bell Sys. Tech. Jour., January, 1936. A MULTIPLE UNIT STEERABLE ANTENNA 401 the reduction of noise obtained with 60-degree phase difference with the addition of 100 or 150 microseconds delay. The 0.8- or 0.9-decibel correction for the two-bundle case corresponds to any large delay and a large phase difference, say 160 degrees. These corrections would not have been much different if a weighting network had been used. The measured difference of 1.5 decibels, shown in Table III, between the one-wave bundle and the two-wave bundle measurements is probably real and due to the fact that when the branches are steered at two separated bundles some loss is incurred when one wave disappears for a few minutes. This loss could have been at least partly recovered by using square-law detectors. Tests showing the advantage of square-law detectors over linear detectors are described later in this section. Employing square-law detectors would justify a correction of about one decibel to be added to the two-bundle improvement measure- ments in Tables III and IV. Applying this correction we summarize the results in Table V. TABLE V Summary of Signal-to-Noise Measurements One Bundle of Waves Two Bundles of Waves One Branch only Two Branches Two Branches 7 db (Table II) 8 db (Table III) 7.5-8 db (Tables III and IV) These improvement figures for two branches as they stand are approximately equal to 10 log 6 = 7.8 decibels as calculated for non- fading waves, and leave nothing to be ascribed to diversity action. Since a loss of perhaps one decibel occurs in the case of one branch (Table II), the recovery of that one decibel with two branches is to be ascribed to diversity action. Originally, considerably more was ex- pected of the angle diversity. It appears however from theoretical and experimental evidence that one decibel is about what should be expected for the case in hand. It seems appropriate to include this study of diversity here. Diversity Action The first attempt to analyze diversity action was made with a graphical approach to the problem. On Fig. 38 is shown a schematic diagram of the system to be analyzed. Two receivers A and B with linear audio detectors may be regarded as fed from two angle branches of a MUSA. The noise generators Bua and enB are assumed to be of 402 BELL SYSTEM TECHNICAL JOURNAL equal power but of random phase. The signal generators e^A and e^s are assumed to fade according to the equations shown beneath the diagram. They represent the carrier amplitude but since fading is assumed to be essentially non-selective in each branch they also repre- TIME.t — — ► 6 "14 U) O 1 / / ',' i / :ii li ^ 1.16 / /J .1- ^$. ^ :._. - ="■ 1.0 1) — POWER - VOLTAGE / r .1- ^■l '^ <.". . ^.97 1 1 1 1 90» teo* = -45° e, = - 90° = + 45° 6,= + 90° ^ '\ V '^ N \ \ j.- i^ k N ^ <;- '>, ^s \ ) >-• SEMI-FADE _J PERIOD "^ 1. 9_ •^ S^i "-- ^.89-1 1 1 1 "> v/ r — ""■"..^ 1 1 ^ ' > \ / y / y - 1. 0 t™ —0^5 1 "1 TIME.t- CIRCUIT USED FOR ANALYSIS OF DIVERSITY ACTION COMMON GAIN CONTROL IMPROVEMENT CURVES POWER VOLTAGE !^ UJ 4 U - > U go 2 1? __AV. 4.9 _ 5^^ PRI.+ SEC. IMP. AV. 2.0 -^ ■ ^^ >^' PRI. IMP. AUTOMATIC GAIN CONTROL LINK 180° ASYNCH. ejA = Vl + 2 X 0.8 COS (2tT t/T + e,) + (0.8)^ esB= Vl + 2 X 0.8 COS (2lTt/T + Bj) + (O.B)* Fig. 38 — Graphical analysis of diversity action as it relates to signal-to-noise ratio. sent the side bands. This type of fading might result from inter- ference between two waves of small relative delay whose amplitude ratio is 0.8, such a pair being received by each branch. The auto- matic gain control is assumed to be perfect; i.e., the audio output, £s, is maintained constant. A MULTIPLE UNIT STEERABLE ANTENNA 403 By definition, diversity in fading occurs when the fading of the two branches is not synchronous. If all degrees of asynchronism are equally probable the diversity is random. This is the case considered. In Fig. 38 five stages in the cycle of variation from synchronous to asynchronous fading are used for calculation. In each of these, fading curves corresponding to the two assumed waves are shown displaced from each other by 0, 30, 60, 90, and 180 degrees. With "ideal" automatic gain control, the two receiver gains, always equal, will be proportional to the reciprocal of the resultant of bsa and csb- For "ideal" linear detectors the noise output of the receivers will be pro- portional only to the gain. The noise curves plot the noise variation on this basis. Two cases of signal addition are considered— voltage and power addition. The corresponding noise curves differ only as the reciprocals of the resultant signal curves dififer. These noise curves are averaged (with a planimeter) and the resulting average signal-to-noise ratios are used to plot the improvement curves shown in the figure. The improvement curve for power addition of signal is located on the improvement axis so that zero improvement is shown for synchronous fading. The curve for voltage addition of signal is located three decibels higher at synchronous fading. These curves are again aver- aged over the cycle from synchronism to asynchronism (by averaging noise voltage). The improvements are 2.0 decibels and 4.9 decibels. Power addition of the two signals corresponds in practice to the case in which the delay is unequalized and sufficient to cause the audio out- puts of each branch to combine on a power basis like noise. The two-decibel improvement might appropriately be called the primary improvement since it is due solely to the diversified fading. The addi- tional improvement of 2.9 decibels found with voltage addition of the signals is due to favorable discrimination in the addition of signal and of noise and might be called the secondary improvement. The secondary improvement occurs in reception with the MUSA; it has already been included in the 10 log iV^ decibel improvement calculation. In practice, it would be undesirable to use the "ideal" automatic gain control assumed in the above analysis; the action must be smoothed out with, for instance, a capacitance-resistance network. The effect of this is to reduce the primary gain since the noise peaks, whose avoidance by diversity action results in the primary improve- ment, are reduced. An analysis of diversity action without automatic gain control was made. In this case the signal was averaged while the noise remained constant. The results are included in the table shown in Fig. 39 which is introduced later. 404 BELL SYSTEM TECHNICAL JOURNAL This treatment of diversity action has been made from the point of view of MUSA reception but is appHcable to ordinary space diversity using two stations or antennas. In the case of a single bundle of waves no modification of the analysis need be made; the signal gen- erators then represent the spaced antenna outputs which are fading randomly. In this case voltage addition of the audio outputs may be NO. OF STATIONS OR BRANCHES 1 ^s= Ve|A+ — efn ^S " GsA "•■ "'GsK ASSUMED DISTRIBUTION CURVES En= VenA+— ©PK , PRIMARY IMPROVEMENT E:n= VenA+— ©m PRI. + SEC. IMPROVEMENT K NO AGC 1 AGC* NO AGC 1 AGC X < 5 O °C 100 X < Ll O 100 X < Ll o s Y ^^ 1 X = y ^ r X QUADRATIC DISTRIBUTION 1 2.5 0 2.5 0 2 2.8 2.2 5.5 4.8 3 2.9 2.5 7.3 6.8 ) 100 Y / /^-ISy^+Sy^ ( X FOUR WAVE DISTRIBUTION 1 3.4 0 3.4 0 2 — — 6.4 5.2 3 — — 8.2 7.5 ) 100 / Z WAVES y 1:0.8 TWO WAVE NEAR-SINUSOIDAL DISTRIBUTION 19 DECIBEL FADE I 2.8 0 2.8 0 2 3.2 2 0 5.8 4.9 3 - — - - ) 100 % OF TIME IG.< ORDINATE AVERAGED RESULTS I 3 0 3 0 2 3 2 6 5 3 3 2.5 8 7 1 * AUTOMATIC GAIN CONTROL Fig. 39 — Summar}' of results of diversity analysis. expected to occur since a single bundle will typically include only a small delay interval. In the general case of two or more wave bundles the signal generators must be interpreted to represent not the carrier but the side-band average, for fading will then be essentially selective and the audio output will not be proportional to carrier as was assumed in the analysis. If this interpretation is made the signal-to-noise ratio in each receiver becomes proportional to the generator amplitudes e^A A MULTIPLE UNIT STEERABLE ANTENNA 405 and BsB, and the analysis of Fig. 38 is applicable. In this case voltage addition does not occur since the audio outputs are essentially different owing to the selective fading.^" They add, in general, to a value inter- mediate between the power and voltage sum, although for the more complicated conditions they combine on a power basis. The above analysis has been based upon simple two-wave inter- ference and the results might not be applicable to the more complicated and changing conditions of actual transmission. Accordingly, R. L. Dietzold has made a statistical analysis for other types of fading and for three stations as well as for two. The results appear in Fig. 39 together with the results of the above graphical analysis for two-wave interference fading. The time sequence of amplitude in the more com- plicated types of fading encountered in practice is not significant; the percentage distribution determines the results. The "four-wave" dis- tribution curve corresponds to four equal waves of random phase. The quadratic distribution curve was deduced experimentally by R. S. Ohl. Except that these different distributions were assumed, the assurnptions were the same as those of Fig. 38. The improvements are expressed in decibels referred to the signal-to-noise ratio for one station or branch with ideal automatic gain control. The small effect upon the results of assuming different time dis- tributions lends significance to these calculations. The averaged round numbers are probably about right. With no automatic gain control (or with one which acts slowly com- pared with the fading) there is little or no primary gain. With in- finitely fast and stiff gain control action there is a 2- and 2.5-decibel primary gain for two and three stations, respectively. A few measurements were made at Holmdel on two-station diversity (antennas 1 and 6 of the MUSA). The thermal noise and rectified carrier technique was used. The results appear in Table VI. The measuring technique was exactly the same as used in obtaining the data for Tables III and IV in which voltage addition of the signal was assumed. A 3-decibel improvement is therefore included in the 3.6-decibel figure. This leaves only 0.6 decibel (possibly one decibel or even 1.5 decibels since the measurements are too meager to be reliable to better than one decibel) for primary gain compared with a possible 2.0 decibels. We are inclined to use about one decibel for primary gain. The time constant on the automatic gain control was of the order of 0.06 second in this and all signal-to-noise comparisons. That this time constant was not fast enough to produce the high noise ^° This refers to speech signals; in the case of telegraph signals the frequency band is so narrow that fading is always essentially non-selective, and voltage addition occurs. 406 BELL SYSTEM TECHNICAL JOURNAL peaks corresponding to the inverse of fading is shown by the transcribed motion picture record of the signal and noise meter variations, shown in Fig. 40. Note the signal fades. A secondary improvement of 3 decibels is too high for two-station space diversity; i.e., the signals do not add on a voltage basis.*" TABLE VI AnTEJJNAS 1 AND 6 IN DIVERSITY GBW 14,440 kilocycles Date Test No. Pads in Antennas db Reference Antenna No. of Readings S/N Improve- ment db Average 1935 10-9 . . . 10-10 . . . 10-9 . . . 10-10. . . 32 35 31 36 40 40 40 40 1 1 6 6 19 20 14 20 1.7 2.2 4.9 5.2 2.0 5.1 The apparent line loss is 3.1 db. The calculated loss is 3.8 db. The equivalent improvement is 3.6 db. Oscilloscope observations of the diversity combinations of the audio outputs of two spaced antennas (No. 1 and No. 6 of the Holmdel MUSA) indicate, however, that on the average the secondary improve- ment is appreciable and probably about 2 decibels for two antennas and 3 decibels for three antennas. This improvement depends upon u -I +10 o -^ io ? -10 UJ (D NO. I ANTENNA 1 & 6 IN DIVERSITY -" y,U ^,^ l^. ■^ ^-' VA "^1 * \{ s^ --r ->-■ .-, /s r>^ ^ / '^ ir ^ -^ (W ^ Vm. . 1^ \ * — 5 SECONDS J^^ 4-1 (, ^Jl 13 ^i_ 0-1.^^' i ^it Ahl I ^ (_ \ h J^r^ — ^\ 7^ Ah^fm^ ^ ' T;r^ VIA HTlf— — " ^^^\ML _ ^h\Jr}y[ Fig. 40 — Sample of signal and noise variations occurring in diversity tests. The arrows indicate noise levels beyond the scale of the meter. GBW (14,440 kilocycles) Rugby, October 10, 1935. 1920 G.M.T. the number of wave bundles, their angular separation, their relative delays, the spacing of the antennas and the frequency band occupied by the signal. For a single compact wave bundle the secondary improvements will be nearly 3 decibels and 4.8 decibels for two- and A MULTIPLE UNIT STEERABLE ANTENNA 407 three-antenna systems, respectively, but for several bundles of large relative delay the secondary improvement may disappear. The results of some recent tests of a three-antenna diversity system on trial at Netcong, N. J., carried out under the direction of F. A. Polkinghorn, showed a signal-to-noise improvement of 3 to 3.5 decibels. Assuming a 3-decibel secondary improvement there remains something of the order of 0.5 decibel for the primary improvement. This is plausible in view of the time constant of one second used on the auto- matic gain controls. Linear audio detectors were used in these tests. As will be discussed later the employment of square-law detectors could be expected to add 0.5 decibel to this figure. Linear detectors are to be preferred, however, on the basis of quality distortion. Table Vn is based upon the theoretical and experimental study of diversity action and gives typical results for space diversity systems. TABLE VII Summary of Space Diversity Improvements Number of Antennas Primary Improvement in db Automatic Gain Control Secondary Improvements in db Number of Wave Bundles 0.06 Sec. 1 Sec. 1 2 3-5 2 3 1 1 0.5 0.5 3 4.5 2 3 1 1.5 Add 0.5 db to primary improvement when square-law detectors are used. Table VII shows that on the average the secondary improvement is larger than the primary improvement. In other words, the advantage which accrues from the similarity of the antenna outputs exceeds that which accrues from their diversification. This result had not been expected. • It should be emphasized here that the improvements summarized in Table VII for space diversity systems and in Table V for a MUSA system refer to signal-to-noise ratios only; i.e., quality improvement is not included. An important advantage of a MUSA system over a space diversity system is its ability to maintain its improvement when more than one wave bundle occur, and since two or more bundles are common, the advantage is distinctly real. A further advantage not discussed thus far relates to interfering signals as distinguished from static. Unless the interfering signals fall upon the principal lobe of the MUSA array pattern when it is steered to receive the desired signal, important directional discrimination against the interference occurs. Little or no 408 BELL SYSTEM TECHNICAL JOURNAL discrimination against interference can occur in a space diversity system since it lacks the phasing which produces directional dis- crimination. The Time Constant of the Automatic Gain Control Thus far no comments have been made on the improvement figures relating to "no automatic gain control" shown in the table of Fig. 39. This table shows that the signal-to-noise ratio for one antenna {K = \) is from 2.5 to 3.5 decibels higher when no automatic gain control is used; i.e., perfect automatic gain control penalizes the signal-to-noise ratio to that extent. ^^ The advantage of automatic gain control is a constant output volume. In practice, a compromise is effected by retarding the action of the control. A time constant of 0.5 or one second is usually used. (This compromise is influenced by quality considerations as well as noise considerations.) In the MUSA system signal-to-noise ratio measurements the time constant of the automatic gain control circuit (0.06 second) was not changed during the switchover from the MUSA to the single antenna. If a time constant of 0.5 second had been used with the MUSA and a one-second time constant with the reference receiver, the measured improvement would probably have been reduced by a little less than one decibel. Method of Averaging Noise In all of the signal-to-noise measurements and in the diversity analysis noise voltage has been averaged arithmetically along the time axis. Owing to a rather marked reduction of noise peaks with the MUSA compared with a unit antenna different improvements would result if different ways of measuring it had been adopted. To investi- gate this, motion pictures were made of the signal meter and noise meter variations for the MUSA and for the single antenna. The transcribed records appear in Fig. 41. Some calculations have been carried out for the noise distributions marked A, B, and C in Fig. 41. If the noise ratio of B/A measured by arithmetically averaging noise voltage is called 0 decibels, it becomes -f 2.4 decibels by averaging power arithmetically. The corresponding figures for BJC are 0 and -|- 2.7 decibels. Thus, if noise power is averaged instead of noise voltage the measured primary diversity improvement is substantially increased. '1 The action of the automatic gain control does not change the instantaneous signal-to-noise ratio. Interpreting signal-to-noise ratio as average signal divided by average noise rather than the average of the signal divided by the noise results in this difference. A MULTIPLE UNIT STEERABLE ANTENNA 409 From the point of view of the interfering effect upon speech it is not clear which method of averaging is more significant. This matter is probably related too closely to the distortion which incidentally accompanies the noise peaks to be considered alone. In the light of the discussion presented in the preceding pages it appears that the signal-to-noise improvement of the experimental MUSA can be expressed as 8 ± 1 decibels. MUSA NO. t ANTENNA m Z Q -5 7, ? -10 '^ >^ .. .- -^r^'- -^ ^"^ - — >^>^:na f ^^^nr '■^^v^^^^ ^r / V ivri 1 f- u +5 2 r, 0 o z z - 1 —\ -5 SECONDS II ,\ ' t, tt^ 1 1.^ rt Bj . t ^C \ 1 \ A M \ 1 y.. n A 1 fl 1 V, 1 k / V V. \ r \J \ \\ U \\J II T" in 1 \ 1 1 \/ \J^ '>' n \. 7 [y '^ \. . / K \ Fig. 41 — Sample of signal and noise variations occurring in MUSA tests. The arrows indicate noise levels beyond the scale of the meter. This record was obtained five minutes before that in Fig. 40. Square-Law Detectors In the discussion of the signal-to-noise measurements it was stated that the measured improvements would have been higher had square- law audio detectors been used instead of linear rectifiers. For the two- bundle MUSA measurements one decibel was allowed for this and for the three-antenna diversity measurements at Netcong 0.5 decibel was allowed. These figures are based upon tests to be described in the following paragraphs. First, however, an analysis will be made of the effect upon the signal-to-noise ratio of various types of detectors in a MUSA system. Figure 42 is a schematic representation of the system to be analyzed, comprising K branches. The K signal generators esA, Csb, • • • esK represent the various wave bundles as received by the steerable branches. The noise generators enA, SnB, • • • CnK are equal in ampli- tude but random in phase. The detectors are generalized to the extent that the audio output is proportional to the u power of the input. Assuming that Bs^^ e„ the audio outputs are proportional to e"sA, B'^sB, • • • e'^sK- The noise outputs are then proportional to e„4esA"~\ enBesB'^~^, • • • «nit^sK"~^ siucc the signal-to-noise ratio in each branch must be independent of u. Assuming the signals to be delay equalized, 410 BELL SYSTEM TECHNICAL JOURNAL DETECTORS iZi^ AMPLIFIERS 1 le":'x( ' tV-'xe -nc @ IV? EoE, ' e.^ X e. Fig. 42 — Circuit employed in the analysis of the effect of detector characteristics upon signai-to-noise ratio. the signal-to-noise ratio of the final output is e"s.4 + e"sB + + e^,K (7) Maximizing this expression with respect to u shows that the maximum occurs for u = 2 (square law) and is {u = 2) (8) That this expression represents the maximum signal-to-noise ratio may also be concluded by observing that it is proportional to the square root of the total energy. For linear detectors u — 1 and the signal-to-noise ratio becomes Es + e,B + + esK en^ K {u= 1) If the branch signals are all equal, i.e., if e^A = e^a (9) = esK, (8) A MULTIPLE UNIT STEERABLE ANTENNA 411 and (9) give the same result, but for unequal amplitudes there is an advantage in using square-law detectors. This analysis shows that square-law detection introduces just the correct amount of emphasis upon the stronger waves and that any additional expansion or contraction of the differences among the waves is detrimental. This means that the gains in all branches should be equal. It also indicates that any arrangement in which the stronger of the several waves is automatically switched in and the remaining ones switched out is inferior. The experimental MUSA receiver is equipped with both linear and square-law detectors, and some signal-to-noise ratio comparisons were made using locally generated signals. Figure 43 shows schematically the essential parts of the test circuit. The noise generators represent the thermal noise originating in the receiver input circuits. The input signal Cs was modulated with a tone. The calculated curves shown in the figure are obtained from (8) and (9) which reduce to (10) u — 2 and to (11) The equation for the square-law detector is sound and was verified by the measurements. The equation for the linear detector should apply only over a certain range of signal and noise levels. The measurements indicate this. Automatic gain control was not used in these tests since the two gain controls could not be relied upon to "track" sufficiently well. To make the measurements significant manual gain control was used to maintain the receiver gains equal and the output normal. It may be pointed out here that in receiving actual radio signals with linear de- tectors accurate equality of gains is not required. Moderate differ- ences in gain (of a few decibels) can be depended upon to be beneficial as often as detrimental. With square-law detectors no departure from equality can be beneficial. The curves of Fig. 43 show that 10- and 20-decibel differences in signal level give the square-law detector an advantage of one and two decibels, respectively. In receiving two bundles of waves the branch outputs commonly fade in and out with the result that their average ratio is of the order of 10 decibels. Such were the conditions, as well Er. oc^l + / esB \esA r u - 2 Es En a — B A MULTIPLE UNIT STEERABLE ANTENNA 415 = 60°). A loss of three decibels is about what one would estimate upon inspecting the directional pattern for 0 = 60 and 120, say, on Fig. 20. The procedure in which two branches are steered at one bundle as in the above is frequently employed and is an important factor in the operation of a MUSA. The case of two wave bundles tabulated in Table V also yields an improvement of 7.5 to 8 decibels. Of this, one decibel and three decibels are due to primary and secondary diversity action, respec- tively, as in the case of one bundle. This leaves 3.5 to 4 decibels for the signal-to-noise improvement in each branch referred to a unit antenna. But the unit antenna has the advantage of two bundles, whereas the MUSA branch excludes one of them, a three-decibel difference. In comparison with a unit antenna receiving only one bundle, the improvement to be ascribed to one branch thus is increased to 6.5 or 7 decibels. This result compares favorably with the seven decibels yielded by one branch steered at one bundle. It is in this case of two bundles that square-law detectors are most important. Their advantage, amounting to an estimated one decibel, has already been included in Table V, it will be remembered. The measurements which have permitted the above analysis of the MUSA signal-to-noise improvement were of course supplemented by aural observations made over the course of a year and a half. The listening tests corroborate the analytical results as well as can be ex- pected of such observations. Not infrequently they showed somewhat less than the full eight-decibel improvement. The indications are, however, that a larger MUSA with three (or possibly four) branches would have yielded more nearly its full gain of 10 log N decibels. For, a MUSA receiving system does not perform its functions properly unless it is sharp enough to separate the waves sufficiently to permit effective delay equalization; also, to obtain the full gain, enough branches must be provided to utilize all of the important wave bundles. The Holmdel experimental MUSA is really a conservative approach to the field of steerable directivity. There is, of course, an upper limit to the size of a MUSA, beyond which (1) technical difficulties in phasing, etc., will occur, (2) the cost of the improvement may be less if introduced at the transmitter, and (3) the directional sharpness becomes too great to permit practical operation with waves of the stability encountered in transatlantic transmission. At present, a system about three times the length of the experimental MUSA com- prising eighteen antennas and equipped with three branches seems practical. It should yield an improvement of 10 log 18 ^ 12.5 416 BELL SYSTEM TECHNICAL JOURNAL decibels more consistently than the present MUSA yields eight decibels. It may be worth while here to point out that as the number of an- tennas in a MUSA system is increased there is no tendency for static to become subordinate to thermal noise (set noise) or vice versa when static, like thermal noise, adds on a power basis. Only to the extent that transmission-line loss increases with the number of antennas will the ratio of thermal noise to static increase. A type of transmission sometimes occurs for which the experimental MUSA gives only small signal-to-noise improvement. We refer to the highly scattered propagation associated with flutter fading, dis- cussed at the close of Section IV. In such cases signal-to-noise im- provement is not highly significant, however, since at least in the worst cases, the distortion renders the circuit worthless. Thus, increasing the transmitting power is likewise ineffective. On the other hand the experimental MUSA can accomplish something by rejecting some of the scattered waves which appear to be responsible for the flutter fading. This is accomplished without a corresponding loss of signal- to-noise ratio since, of course, noise is rejected, too. Fortunately, flutter fading does not seem to be associated prominently with greatly depressed field intensity so the failure to secure signal-to-noise im- provement with flutter fading does not appreciably penalize the MUSA as a means of extending operation through periods of depressed field conditions. VI. Recapitulation The MUSA receiving system described in this paper is the culmina- tion of some four years effort to determine the extent to which receiving antenna directivity may be carried to increase the reliability of short- wave transatlantic telephone circuits. ^^ Fundamental experimental studies of wave propagation were made with particular emphasis upon how the waves arrive. Based upon the results of these studies a system was evolved in which a new technique of phasings was required. The result is a steerable antenna whose signal-to-noise advantage is seven to eight decibels compared with the largest fixed antenna that can be employed effectively. By analyzing this improvement and comparing the various contributing factors with theory, it is possible to estimate that a system three times larger than the experimental one will yield an additional four to five decibels, and will perform better consistently. In addition to the signal-to-noise improvement a 5' Potter and Peterson, "The Reliability of Short-Wave Radio Telephone Cir- cuits," BellSys. Tech. Jour., vol. 15, pp. 181-196, April, 1936. A MULTIPLE UNIT STEERABLE ANTENNA 417 substantial improvement in quality is obtained by reducing the distortion associated with selective fading. It is both interesting and important to note that whereas so often one advantage is gained only at the expense of another, in the MUSA system the best quality im- provement and the greatest signal-to-noise advantage are obtained together, without compromising. The system developed is expensive and might be thought to illustrate the law of diminishing returns. As a part of a point-to-point radio- telephone system, however, it has certain compensating features not mentioned thus far. One of these is the broad frequency band feature. With essentially aperiodic unit antennas the MUSA possesses a broad frequency range; i.e., the directional pattern, despite its sharp- ness, is substantially the same over a band of a hundred or more kilo- cycles provided the terminal equipment is made sufficiently broad. (See Appendix I.) The broad-band feature is important for its possi- bilities in multiplexed operation of telephone circuits; i.e., it makes possible, insofar as the antenna system is concerned, the adaptation of some of the carrier telephone methods to radio circuits. It is to be expected that, excepting certain critical cases, fairly large percentage frequency bands will follow virtually the same paths. This assump- tion was verified by a few experiments in which pulses were received simultaneously from GBS (Rugby, 12,150 kilocycles) and GBU (Rugby, 12,290 kilocycles) 140 kilocycles apart. These tests showed that, although the pulse fading was, of course, not synchronous, the angles involved were alike. Another compensating feature of the MUSA receiving system is that, with suitable terminal equipment, reception may be carried on from several points at once provided they lie within the horizontal angular range of the unit antenna. Some sacrifice in vertical angular selec- tivity occurs but this is confined to low angles where it is least im- portant. Certain features of the system make for economies in plant cost. The fact that a great many components are identical permits manu- facturing economies. Also, spare units need be provided only for a few vital functions, since the failure of one of the many similar parts does not disrupt service. The development of steerable directivity has thus far been concerned with receiving antennas. In receiving, one has the obvious ad- vantage of having, in the monitoring branch, a criterion to dictate the steering adjustments. The lack of such a direct criterion for adjusting transmitting directivity does not, however, rule out the possibility, at 418 BELL SYSTEM TECHNICAL JOURNAL some future time, of a MUSA transmitting system. That horizontal steering of transmitting directivity may be decidedly important is strongly suggested by observations made on transmissions from Dav- entry in which significant effects upon flutter fading have been found to be associated with the orientation of the directional transmitting antennas. Acknowledgment The experiments described in this paper necessarily involved the coordinated effort of many individuals, in both the British Post Ofiice and the Bell System, and their help has been appreciated. Mr. E. Bruce had charge of the design of the rhombic antennas and trans- mission lines, and Messrs. L. R. Lowry and W. M. Sharpless had im- portant parts in the various phases of the work. The authors are particularly indebted to Mr. R. K. Potter who contributed much through his keen interest throughout the entire work. Appendix I Broad-Band Characteristic of the MUSA The frequency characteristic of the MUSA may be calculated from (3). Frequency and angle appear only in the form 2Tra{v — cos 5) where a is inversely proportional to frequency. By writing the equation Iv - cos 5] = ^^-^ — ^— [u - COS (5 -f A5)] we express the angular shift, from 5 to (5 + A5), of a given point on the directional pattern as the frequency is varied from/ to (/ + A/). This equation may be rewritten as . , A/ V — cos 8 1 + - / u - cos (5 + A6) ■ As an example consider A/ — 200 kilocycles, / = 10 megacycles, 5 = 30 degrees, and i; — 1.05. Then A8 = — 0.4 degree. For lower values of 8, A5 becomes still smaller. The frequency characteristic expressed in terms of percentage band and angular shift given by the above equation is independent of the size of the MUSA. It relates to the over-all length of the system, how- ever, by the fact that for greater lengths a given angular shift has more effect. A MULTIPLE UNIT STEERABLE ANTENNA 419 The broad band of the MUSA reflects the fact that, with the terminal at the "leeward" end as assumed heretofore, the delay of the space paths is nearly the same as that of the transmission-line paths so that if the antenna outputs are phased to add at one frequency they will nearly add at other frequencies. If the terminal is located at the center of the MUSA to economize on transmission line, the frequency range is greatly reduced. The broad band may be regained, however, by delays introduced in the receiving equipment. With a center loca- tion, the antennas in the forward and rearward sections of the MUSA must have their phases shifted oppositely, and, unless certain other compensating networks are provided, the two phase shifts must be coupled in different phase relations for different wave-lengths. Abstracts of Technical Articles from Bell System Sources Modern Theater Loud Speakers and their Development} C. Flanna- GAN, R. Wolf, and W. C. Jones. Although many of the basic ideas involved in the operation of present-day loud speakers were conceived during the early stages of the development of the telephone, it was not until the advent of the vacuum tube amplifier that these principles were applied to the design of structures capable of delivering sufficient acoustical power to be audible throughout a room or auditorium. Having reached this stage, however, the developments that culminated in the sound reproducing systems employed with present-day sound pictures came in rapid succession. These developments have em- braced all phases of loud speaker design, with the result that systems are now available that convert from 25 to 50 per cent of the electrical input into acoustical output, and maintain conversion efficiencies of this order of magnitude over a frequency range of 50 to 10,000 cps. These systems are so designed as to be capable of reproducing the recorded sound at intensities that not only greatly enhance the dramatic effect of the presentation in the theater, but also open entirely new fields in recording. All these improvements have been attained with a reduction in distortion and improved fidelity of the reproduced sound. The directional properties of the loud speakers also have been markedly improved, with the result that the better quality of reproduction achieved is available throughout the entire seating area and the undesirable beam effects previously experienced have been eliminated. Power System Faults to Ground — Part I: Characteristics} C. L. GiLKEsoN, P. A. Jeanne and J. C. Davenport, Jr. The results of an extensive oscillographic study of power-system faults to ground are presented herewith. While this study was made primarily to obtain data useful in inductive coordination problems, the results are believed to be of general interest as well. They provide data on such items as frequency of occurrence of ground-current disturbances, their monthly distribution, duration, cause, method of clearance, and wave-trace characteristics. Data on fault resistance are given in part II, a companion paper. ' Jour. S. M. P. E., March 1937. ^Elec. Engg., April 1937. 420 ABSTRACTS OF TECHNICAL ARTICLES 421 Direct Recording and Reproducing Materials for Disk Recording} A. C. Keller. Recently materials for direct recording and repro- ducing work have been improved so that they are now suitable for many uses. These materials, as they are available on the market, are classified chemically into five groups and measurements are given of frequency characteristic, surface noise, life, distortion, etc. These data have been taken with both lateral and vertical recording, ^ Jour. Acous. Soc. Amer., April 1937. Contributors to this Issue Edwin H. Colpitts was introduced to readers of the Journal — if it can be said that he needed an introduction — in the April issue. Karl K. Darrow, B.S.. University of Chicago, 1911; University of Paris, 1911-12; University of BerHn, 1912; Ph.D., University of Chicago, 1917. Western Electric Company, 1917-25; Bell Telephone Laboratories, 1925-. Dr. Darrow has been engaged largely in writing on various fields of physics and the allied sciences. C. B. Feldman, B.Sc, University of Minnesota, 1926; Teaching Fellow, University of Minnesota, 1926-28; M.Sc, University of Minne- sota, 1928. Bell Telephone Laboratories, 1928-. Mr. Feldman has been engaged in short-wave radio receiving. His work has been mainly on transmission lines, antennas, and wave propagation problems. H. T. Friis, E.E., Royal Technical College in Copenhagen, 1916; Columbia University, 1919-20. Research Department, Western Electric Company, 1920-24; Bell Telephone Laboratories, 1925-. Mr. Friis' work has been largely in connection with radio reception methods and measurements. He has published papers on vacuum tubes as generators, radio transmission measurements and static interference. As Radio Research Engineer he now directs studies of new methods of short-wave reception. W. P. Mason, B.S. in Electrical Engineering, University of Kansas, 1921 ; M.A., Columbia University, 1924; Ph.D., 1928. Bell Telephone Laboratories, 192 1-. Dr. Mason has been engaged in investigations on carrier transmission systems and more recently in work on wave transmission networks, both electrical and mechanical. John Riordan, B.S., Sheffield Scientific School, Yale University, 1923. American Telephone and Telegraph Company, Department of Development and Research, 1926-34; Bell Telephone Laboratories, 1934-. Mr. Riordan's work has been mainly on problems associated with inductive effects of electrified railways. R. A. Sykes, Massachusetts Institute of Technology, B.S. 1929; M.S. 1930. Columbia University, 1931-33. Bell Telephone Labora- tories, Research Department, 1930-. Mr. Sykes has been engaged in the application of piezoelectric crystals to selective networks, and more recently in the use of coaxial lines as filter elements. 422 VOLUME XVI OCTOBER, 1937 number 4 THE BELL SYSTEM TECHNICAL JOURNAL DEVOTED TO THE SCIENTIFIC AND ENGINEERING ASPECTS OF ELECTRICAL COMMUNICATION Resistance Compensated Band-Pass Crystal Filters for Use in Unbalanced Circuits — W. P. Mason 423 Magnetic Generation of a Group of Harmonics —E. Peterson, J. M. Manley and L. R. Wrathall 437 The Vodas— S. B. Wright 456 Radio Telephone Noise Reduction by Voice Control at Receiver — C. C. Taylor 475 Transmitted Frequency Range for Circuits in Broad-Band Sys- tems—/f. A. Affel 487 The Dielectric Properties of Insulating Materials — £. J. Murphy and S. O. Morgan 493 Variable Frequency Electric Circuit Theory with Application to the Theory of Frequency-Modulation — John R. Carson and Thornton C. Fry 513 Irregularities in Broad-Band Wire Transmission Circuits •^Pierre Mertz and K. W. Pfleger 541 Technical Digests — Transoceanic Radio Telephone Development — Ralph Bown . . . 560 A Negative -Grid Triode Oscillator and Amplifier for Ultra -High Frequencies— il. L. Samuel 568 Addendum — Radio Propagation Over Plane Earth— Field Strength Curves —Charles R. Burrows 574 Abstracts of Technical Papers 578 Contributors to this Issue 581 AMERICAN TELEPHONE AND TELEGRAPH COMPANY NEW YORK 50c per Copy $L50 per Year THE BELL SYSTEM TECHNICAL JOURNAL Published quarterly by the American Telephone and Telegraph Company 195 Broadway, New York, N. Y, iiiiiiiitiiiiniiiiiiiiiiiiiiiniiniiii Bancroft Gherardi A. F. Dixon D. Levinger R. W. King, Editor EDITORIAL BOARD H. P. Charlesworth O. E. Buckley M. J. Kelly W. Wilson F. B. Jewett O. B. Blackwell H. S. Osborne J. O. Perrine, Associate Editor lllllilliriiiMliiniilillllilinilllll; SUBSCRIPTIONS Subscriptions are accepted at $1.50 per year. Single copies are fifty cents each. The foreign postage is 35 cents per year or 9 cents per copy. iiiiiiiiiiiniiiiriiiiiiiiinniiiiiim Copyright, 1937 American Telephone and Telegraph Company PRINTED IN U. S. A< The Bell System Technical Journal Vol. XVI October, 1937 No. 4 Resistance Compensated Band-Pass Crystal Filters for Use in Unbalanced Circuits By W. p. MASON In this paper are discussed several types of crystal band-pass filters which can be used in unbalanced circuits. These types of filters are all resistance compensated, i.e., the resistances associated with the filter elements are in such a position in the filter that they can be effectively brought to the ends of the filter and combined with the terminal resistances with the result that the dissipation produces an additive loss for the filter characteristic and does not affect the sharpness of cut-off attainable. It is shown that all these types of networks can be reduced to three lattice types of crystal filters, and the formulae for these three networks are given. A comparison is given between the characteristics obtainable with resistance compensated crystal and electrical filters and a conclu- sion regarding their comparison given by V. D. Landon * is shown to be incomplete. I. Introduction TN a recent paper ^ a description is given of a number of wave filters -^ employing quartz crystals as elements. Most of these filters were of the lattice type and hence were inherently balanced. For some purposes, however, such as connecting together unbalanced tubes, it is desirable to obtain a filter in an unbalanced form and it is the purpose of this paper to show several forms for constructing resistance com- pensated band-pass crystal filters which will give results similar to those described previously. Another purpose is to give a numerical comparison between the characteristics obtainable with resistance compensated crystal and electrical filters. II. A Comparison of the Performance Characteristics of Crystal vs. Coil and Condenser Filters In order to show the properties of resistance compensated crystal filters it is instructive to give a comparison between the types of characteristics which can be obtained by using crystal and coil and ' "Electrical Wave Filters Employing Quartz Crystals as Elements," W. P. Mason, B. S. T. J., July, 1934, p. 405. 423 424 BELL SYSTEM TECHNICAL JOURNAL condenser filters. The quartz crystal filter considered here is shown on Fig. 1. By using the balancing resistance Rx of Fig. 1 the crystal filter can be made entirely compensated for coil resistance ; i.e. the resistance associ- ated with the coils of the network is in such a place in the network that y 1 ■ •-1 h ^JOOC> T 1-2 o \' ( C,=r Rx> Fig. 1 — A bridge T quartz crystal filter. it can be effectively brought to the ends of the filter and combined with the terminal impedances with the result that the effect of the dissipa- tion in the coils is only to produce an additive loss for the filter charac- teristic and does not affect the sharpness of cut-off attainable. In fact Fig. 2 — Electrical network equivalent to crystal filter of Fig. 1. if the filter works into a vacuum tube the dissipation in the coil can be used to terminate the filter completely, and introduces no loss. For the electrical filter, however, the dissipation introduced by the electrical elements which replace the crystal is not compensated and causes a considerable distortion of the pass band which becomes more prominent as the band width is narrowed. To show this let us consider RESISTANCE COMPENSATED BAND-PASS CRYSTAL FILTERS 425 the network of Fig. 2. In analyzing such networks it is usually more convenient to reduce them to their equivalent lattice form and apply network equivalences holding for lattice type networks. This can be done by applying Bartlett's Theorem ^ which states that any network which can be divided into two mirror image halves can be reduced to an equivalent lattice network by placing in the series arms of the lattice a two-terminal impedance formed by connecting the two input terminals of one half of the network in this arm and short-circuiting all of the cut wires of the network, and in the lattice arm placing the same network with all its cut wires open-circuited. Applying this process to Fig. 1, a lattice network equivalent to the network of Fig. 1 is that shown on Fig. 3. In this network the capacitances can be considered as sub- Fig. 3 — Lattice equivalent of crystal filter of Fig. 1. stantially dissipationless and if the network representing the crystal can also be considered dissipationless, the resistance introduced by the coils can be effectively brought outside the lattice and incorporated with the terminal resistances. This follows from the fact that an inductance with an associated series resistance can just as well be represented over the narrow-frequency range of the filter by an in- ductance paralleled by a much higher resistance. The impedance of an inductance and resistance in series and the impedance of an inductance and resistance in parallel are given by the expressions Ri + jooLi = R^ijwL^ R^L^ + jwL^R^ i?2 + joiLi Ri^ + co^W (1) * "Extension of a Property of Artificial Lines," A. C. Bartlett. Phil. Mag., 4, pp. 902-907, Nov. 1927. 426 BELL SYSTEM TECHNICAL JOURNAL Defining Q, the ratio of reactance to resistance, asQ — ooLijRi, we have R, = i?i(l + Q') ; L2 = Li(l + 1/(32). (2) This relation holds strictly only for a single frequency, but over a narrow-band filter the relation holds quite accurately. Employing this conception, the lattice network can be reduced to that of Fig. 4 in which a resistance R parallels each arm of the lattice. Fig. 4 — Filter showing paralleling resistance. This is made possible by the adjustable resistance Rx which is fixed at such a value that the parallel resistance associated with the inductance Li + 2L2 is equal to that associated with Li. Then by employing the two lattice equivalents shown on Fig. 5, first proved by the writer,' it is c c A/W-- (a) r V^ 1 "l V\A ^ (b) Fig. 5 — Lattice network equivalences. ' Reference 1, page 418. RESISTANCE COMPENSATED BAND-PASS CRYSTAL FILTERS 427 possible to take these resistances outside the lattice and combine them with the terminating impedance, leaving all the elements inside the lattice dissipationless. The two remaining arms of the lattice have the impedance characteristic shown on Fig. 6A . A lattice filter has a pass band when the two impedance arms have opposite signs and an at- tenuation band when they have the same sign. When the impedance of two arms cross, an infinite attenuation exists. Hence the character- istic obtainable with this network is that shown on Fig. 6B. Next let us consider an electrical filter in which coils and condensers take the place of the essentially dissipationless crystal. In this case the dissipation due to Li and L2 can be balanced as before and the only question to consider is the effect of the dissipation associated with L3 and C3. In a similar manner to that employed for the coil we can show Fig. 6 — Characteristics obtainable with the crystal filter of Fig. 1. that a series tuned circuit with a series resistance Ri is equivalent to a second series tuned circuit having the same resonant frequency as the first shunted by a resistance Ri where where Q = 1 C0C4 CO 1 - -— 2 R, (3) At two frequencies for which the absolute values of the reactances are the same and therefore the value of Q equal, it is possible to replace the series resistance by a shunt resistance and hence compensate it by varying the resistance Rx. Since, however, the reactance of the tuned circuit varies from a negative value through zero to a positive value over the pass band of the filter, the value of this shunt resistance is not 428 BELL SYSTEM TECHNICAL JOURNAL even approximately constant and hence the filter cannot be resistance compensated throughout the band of the filter. It can, however, be compensated at the frequencies of infinite attenuation and high losses can be obtained at these frequencies. The effect of the lack of resistance compensation throughout the band can best be shown by a numerical computation of the loss of an electrical filter as compared to that for a crystal filter. A practical example has been taken of a filter whose band width is 12 kilocycles wide with the mean frequency at 465 kilocycles. In order to obtain the best (2's with reasonably sized coils an arrangement suggested by R. A. Sykes is used. The coils L\ are obtained by using the two equal wind- ings of a coupled coil series aiding so that Li equals the primary induct- ance plus the mutual inductance. Since in an air core coil all of the dissipation is associated with the primary inductance and none with the mutual this gives a high Q for Li. The inductance L2 neutralizes the negative mutual inductance —M and supplies in addition a small positive inductance. The Q of this combination is poor but it makes unnecessary the use of a high resistance Rx for balancing purposes. By this method a much higher effective Q is obtained than can be obtained by a single coupled coil or by three separate coils. The calculated curve for the electrical filter assuming Q's of 150 for all the coils is shown on Fig. 7 by the dotted lines. A similar curve for a crystal filter is shown on Fig. 7 by the full lines. As is evident the effect of the coil dissipation is to round off the edges of the pass band and to limit the effective discrimination between the passed and attenuated bands. This result does not agree with that given by Landon,"* who in a recent paper makes a comparison between the results obtained with crystal and electrical filters which appears to be somewhat misleading. It is stated in this paper that the electrical filter circuits given are com- pletely resistance compensated and "in crystal filters in which the crystal is confined to the rejector meshes of the network, the limitation is about the same as for electrical filters." By referring to the curves of Fig. 7 it is readily seen that high losses can be obtained outside the pass band with resistance compensated electrical filters, ^ but that the *"'M Derived' Band-Pass Filters with Resistance Cancellation," Vernon D. Landon, R. C.A. Review, Oct. 1936, Vol. 1, No. 2, Page 93. * The use of resistance for compensating and balancing the attenuation in electrical filters has been worked out bv H. W. Bode and S. Darlington (see U. S. patents 2,002,2 16, 1 ,955,788, 2,029,014,'2,035,258). The first work was done for low- and high- pass filters but it was later extended also to band-pass filters. Some of these results are analogous to those of Landon, while others give a better compensation within the transmitted band. The use of the resistance in the crystal filter of Fig. 1 was sug- gested by Mr. Darlington. RESISTANCE COMPENSATED BAND-PASS CRYSTAL FILTERS 429 ^u 35 , 1 , 30 / / \ 25 ^*=c=. ^ 1 \ \ -^ ^ 1 20 15 \ 1 ll \ 10 I \ 1 1 / / RESISTANCE COMPEN SATED CRYSTAL FILTE ASSUMING Q'S of ISC THE ELECTRICAL COI R-^ / / / t 1 EL _r^si ECTRICAL FILTER, RE- iTANCE COMPENSATED THE PEAK FREQUEN- ES. ALL COILS HAVE A Q OF 150 5 IN 1 \ \ \ / / / / 1 ^'^ 1 ^' \ / 0 450 455 460 465 470 475 480 FREQUENCY IN KILOCYCLES PER SECOND 490 Fig. 7 — Numerical comparison between the loss characteristics of a crystal filter and a coil and condenser filter. 430 BELL SYSTEM TECHNICAL JOURNAL pass band of the filter is seriously distorted unless elements, such as crystals, are used which have negligible dissipation. III. Band-Pass Resistance Compensated Crystal Filters All of the wide-band resistance compensated crystal filters proposed so far can be shown to be equivalent to the two general types of lattice crystal filters shown on Fig. 8. For example the crystal filter of Fig. 1 was shown to be equivalent to the lattice type filter of Fig. 8 (b) in which the crystals in the lattice arms are left out. Fig. 8 — Wide-band lattice crystal filters. In the lattice filters of Fig. 8 the number of crystals employed can be cut in half by employing in two similar arms a crystal with two pair of equal plates. It can be shown that such a crystal used in similar arms is equivalent to two identical crystals of twice the impedance of the crystal used as a single plate and having the same resonance frequency. Hence the lattice filters of Fig. 8 are as economical of elements — except for two condensers — as an unbalanced type filter. For some purposes, however, such as connecting together unbalanced tubes, it is desirable to obtain a filter in an unbalanced form. Also, at high frequencies the crystals become quite small and hence it becomes difficult to divide the RESISTANCE COMPENSATED BAND-PASS CRYSTAL FILTERS 431 plating on such crystals. It is the purpose of this section to list a number of filters of the unbalanced type which are equivalent to the lattice filters of Fig. 8. They do not have as general filter character- La 2 2Q, C3 Qi -^w^ K _Vu^ -^r^Ry^ 2[z=l ±l2C2 (a) -^w^ 20| HOh ^u^^^- 'C| 'C| Jl2 2 (b) 0,4= 5^L, 02 Fig. 9 — Wide-band bridge T crystal filters. istics as the equivalent lattice networks but for a number of purposes are satisfactory. Fig. 9 shows four bridge T crystal filters which are equivalent re- 432 BELL SYSTEM TECHNICAL JOURNAL spectively to the lattice crystal filters of Fig. 8. The equivalent lattice configurations are shown on Fig. 9. The first two filters have series coils which inherently give low-impedance filters. The second of these is equivalent to the filter of Fig. 8 (a) with one pair of the crystals eliminated. If the inductance L^ were eliminated from Fig. 9 (a) or (b) the filters will be resistance compensated, for all of the resistance will be on the ends of the filter. Furthermore if a small amount of coupling is allowed between the two end coils, the effect of this will be to intro- duce the small coil L2/2 in the desired place as can be seen from the T network equivalent of a coupled coil as shown on Fig. 10. Further- more if the coils are air core, no dissipation is associated with the mutual inductance and hence if coupled coils are used the networks still have a resistance balance. Similarly the filters shown on Figs. 9 (c) and (d) are equivalent to the high-impedance type filter shown on Fig. 8 (b) with all crystals present or with crystals missing from the lattice arms. By -^WD^-i-^WO"^- PIM SIM PS-M PS-M S+M PS-M P+M Fig. 10 — T and tt network equivalences of a transformer. employing coils with a small amount of mutual inductance these types can also be made with a resistance balance. They can also be made to balance for physical coils by employing the resistances shown. It is obvious from the equivalent lattice structures that these networks have limitations on band widths and allowable attenuation which are not present for the original lattice structures of Fig. 8. However, for filters whose pass bands are less than the maximum pass bands, useful results can be obtained. Another method for obtaining results similar to that obtainable in a lattice network is to use a hybrid coil with series aiding secondaries which are connected to a crystal and a condenser as shown on Fig. 11. This circuit, which has been used extensively to provide a narrow band crystal filter in telegraph work, was invented first by W. A. Marrison ^ of the Bell Telephone Laboratories. Under certain circumstances this configuration can be shown to give results similar to the narrow-band « Patent 1,994,658 filed June 7, 1927, granted March 19, 1935. RESISTANCE COMPENSATED BAND-PASS CRYSTAL FILTERS 433 lattice filter of Fig. 12. A hybrid coil with series aiding windings con- nected to two impedances 2Zi and 2Zi as shown by Fig. \2)A can be shown to be equivalent to the circuit of Fig. \2>B in which a lattice Fig. 11 — A three-winding transformer crystal filter. network with the branches Zi and Zi is placed in series with the trans- forming network and the series terminating inductances. Hence if the hybrid coil has nearly a unity coupling between its secondary coils and Fig. 12 — A narrow-band lattice crystal filter. the remainder of the transformer is designed to work into the impedance of the filter, the network of Fig. 11 is equivalent to the narrow-band lattice filter of Fig. 12 with crystals removed from the lattice arms, plus A B Fig. 13 — An equivalent circuit for a three-winding transformer and network. 434 BELL SYSTEM TECHNICAL JOURNAL a transformer. As usually used, however, the impedance of the trans- former is much lower than that of the filter and as a consequence the band-pass characteristic of the filter is lost. As a result the network passes only a single frequency and gives results similar to those obtain- able with a very sharply tuned circuit. By placing a crystal in the other arm of the network as shown by Fig. 14, '^ this configuration can be made equivalent to the filter shown in -'ig. 12. It is obvious from the equivalence of Fig. 13 that the configurations of Fig. 11 and Fig. 14can also be used togiveawide-bandfilter. This follows since the series inductances can be taken inside the lattice and the low- impedance crystal filter of Fig. 8 (a) results. The Q of the coils included in the filter will ordinarily not be high since the inductance is obtained by a difi"erence of primary and mutual inductances, and a better result will be obtained by making the secondary coupling high and including physical coils in series with the crystals. Fig. 14 — A three-winding transformer crystal filter with two crystals. We see then that all of the resistance compensated wide-band filters are equivalent to the lattice filters of Figs. 8 and 12, and all their design equations are known when the design equations of the equivalent lattices are calculated. This requires two steps, first the calculation of the spacing of the resonant frequencies of the network to give the required attenuation and secondly the calculation of the element values from the known resonances by means of Foster's theorem. Such calculations are familiar in filter theory and hence only the results are given here. The results are given in Tables I, II, and III for the network of Figs. 8 (a) , 8 (b) and 12 respectively. These values are given in terms of the characteristic impedance Zo of the filter at the mean frequency, the lower and upper cut-ofif frequencies /i and/2 respectively and the 6's of the network. These last are parameters which specify ' This configuration is covered by patent 2,001,387 issued to C. A. Hansell. RESISTANCE COMPENSATED BAND-PASS CRYSTAL FILTERS 435 TABLE I where Element Formula Lo ZoMf2' + fi'B) 2irfx{h- mU'A +fi'C) Li ZoWM + /i^C) 2irhU2 - mh' + fi'B) T » Z^imA{\ +B) - C) + 2f,\h^C + fi^BCJ 27r/,/2(/2 - fi?(f2 + fiKf2'A + UC:\C{AB - C) T . Z„ZfM + VmC + jx\B{A + C) - C)J 2^M2{f2 - /i)^(/2 + finf2' + UB){AB - C) Co if2- mf2'A ■\-f,^CY 2irZ,UhU2KA{\ +B) - C) + 2f,^f2'C + UBC2 r. {f2 - fl){f2' + UB)^ 27rZo/i/2[/2M + 2f,^f2'C + fiKBiA + C) - O] c (AB- C)C(f2 - f:)Hf2 + f,y 2wZofif2U2'iA{l +B) - C) + 2M,^C + fi'BC2ii + B) r. {AB - C)(/2 - /,)K/2 + fxY 2xZo/,/2[/2M + 2m,^C + UiB{A + C) - CniA + C) ^1 + ^2 + bz; B = bibi + bibi + Ms; C = bibzbs', h _ foo 2/A2 &»=Vl V 2/2; « = 1,2,3 TABLE II Element Formula Element Formula T n Zo(/2 - /l)(^ + C) 2;r/./2(l + 5) Co ih-^ + f,^B)f2 27rZo/l(/2-/l)(/2M+/i2C) T , Zo(/2 -/.)(! +B) 2wfrMA + C) Ci (/2M + /i^C)/, 2TZof2(.f2 - fl){f2^ + fl^B) T « Zo(A + C)(f2'A +UC)' Cj U2 - mu + f^yciAB - c) 27r/,/2(/2 - /.)(/2 + fi)'C{AB - C) 27rZo/l/2(/2M + /i2C)(^ + C)2 T , Zo(l +5)(/22 + /i^5)2 C3 (/2 - U){h + h)KAB- C) 27r/,/2(/2 - /i)(/2 + hY{AB - C) 27rZo/,/2(l + 5)^/2^ + h^B) where A = ii + 62 + bz; "" -Xl _/^„2//^2' B = bibi + 61^3 + ^2^3; « = 1, 2, 3 C = bib^bz; 436 BELL SYSTEM TECHNICAL JOURNAL TABLE III Element Formula Element Formula Co /.(fci + W C2 bMf2-' - /.=') 27rZo(/22 + /i^iiia) 27rZo/l/2H6l + 62) Cn' /2* + fi^bM iTrZof.mbi + b2) Xi ^0(/2* + /l2i'l62)2 2^flf2'{bl + b2){f2' - U) c, (&. + b2)(f2' - /,^) Z.2 Zof2Hbl + b2) 27rZo/,(l +b,b2){f2'+fl^blb2) 27rf,bMU - U) -Vl^ /=°.V/i' /=».V/2'' =v^ -/«2V/r /^2-//2^ the location of the attenuation peaks of the network with relation to the cut-off frequencies and are given by the expression : ^"=Vf /^nW f^nVf2" n = I, 2, 3, where / 00 „ is the frequency of infinite attenuation. These tables give the design formulae for the networks of Figs. 8 and 12. To obtain the equations for a network having crystals in the series arms alone, it is only necessary to let bs = 0. If one of the peaks of the filter of Fig. 8 (a) is placed at infinity — which results when ^2 = /2//1 — the two coils will have equal values and by the theorem illustrated by Fig. 5 can be brought out to the ends of the filter, simplifying the construction. In a similar manner if one of the peaks of the filter of Fig. 8 (b) is placed at zero frequency, i.e. 62 = 1, the two shunt inductances are equal and can be brought out to the ends of the filter. The design equation of the narrow band filter of Fig. 12 with the lattice crystals replaced by condensers can be obtained from Table III by letting 62 = 0. Magnetic Generation of a Group of Harmonics* By E. PETERSON, J. M. MANLEY and L. R. WRATHALL A harmonic generator circuit is described which produces a number of harmonics simultaneously at substantially uniform amplitudes by means of a non-linear coil. Generators of this type have been used for the supply of carrier currents to multi-channel carrier telephone systems, for the synchronization of carrier fre- quencies in radio transmitters, and for frequency comparison and standardization. A simple physical picture of the action of the circu t has been derived from an approximate mathematical analysis. - The prin- cipal roles of the non-linear coil may be regarded as fixing the amount of charge, and timing the charge and discharge of a con- denser in series with the resistance load. By suitably propor- tioning the capacity, the load resistance, and the saturation in- ductance of the non-linear coil, the amplitudes of the harmonics may be made to approximate uniformity over a wide frequency range. The sharply peaked current pulse developed by condenser discharge passes through the non-linear coil in its saturated state and so contributes nothing to the eddy current loss in the core. In this way the efficiency of frequency transformation is main- tained at a comparatively high value for the harmonics in a wide frequency band, even with small core structures. The theory has also been adequate in establishing a basis for design, and in evalu- ating the effects of extraneous input components. I. Outline of Development ' I ""HE use of non-linear ferromagnetic core coils to generate har- -'' monies started with a simple type of circuit due to Epstein ^ which appeared in 1902. AppHcation of the idea was not made to any great extent until it was elaborated by Joly ^ and by Vallauri ^ in 1911. The frequency multipliers thus developed were limited to doublers and to triplers, polarization being required for the doubler. In these, as well as in subsequent developments, single and polyphase circuits were used, and various arrangements were adopted for the structure of the magnetic core and for the circuit, by which unwanted components were balanced out of the harmonic output path. Later developments had to do with improvements in detail, and with the generation of higher harmonics in a single stage and in a series of stages. The applications * Presented at the Pacific Coast Convention of A. I. E. E., Spokane, Washington, September 2, 1937. Published in Elec. Engg. August 1937. 437 438 BELL SYSTEM TECHNICAL JOURNAL of perhaps greatest importance were to high power, long-wave radio- telegraph transmitters, where the fundamental input was obtained from an alternator. Other applications of the idea of harmonic pro- duction by magnetic means have been made in the power and com- munication fields/ It appears that these circuits were all developed primarily to generate a single harmonic. Comparatively good efficiencies were obtained, values from 60 to 90 per cent being reported for the lower harmonics. The theory of frequency multiplication was investigated by a number of workers, among whom may be mentioned Zenneck ^ and Guillemin.^ The latter, after analysis which determined the optimum conditions for the generation of any single harmonic, found experimentally that the efficiency of harmonic production decreased as the order of the har- monic increased. He obtained efficiencies of 10 per cent for the 9th harmonic, and 3 per cent for the 13th harmonic of 60 cycles. Where the circuits are properly tuned and the losses low, free oscilla- tions may be developed. The frequencies of these free oscillations may be harmonic, or subharmonic as in the circuit described by Fallou ; ^ they may be rational fractional multiples of the fundamental, or in- commensurable with the fundamental, as in Heegner's circuit.^ The amplitudes of these free oscillations are usually critical functions of the circuit parameters and input amplitudes, and where the developed frequencies are not harmonic, they are characterized by the fact that the generated potentials are zero on open circuit. The theory of the effect has been worked out by Hartley.^ It is presumably this effect which is involved in the generation of even harmonics by means of an initially unpolarized ferromagnetic core, an observation which has been attributed to Osnos.^'^ II. Circuit Description The harmonic producer circuit which forms the subject of the present paper differs from those mentioned in that it is designed to generate simultaneously a number of harmonics at approximately the same amplitude. Harmonics developed in circuits of this type have been used for the supply of carrier currents to various multi-channel carrier telephone systems, for synchronizing carriers used in radio transmitters, and for frequency comparison and standardization. Only odd harmonics are generated by the harmonic producer when the core of the non-linear coil is unpolarized, as is the case here. To generate the required even harmonics, rectification is employed. This is accomplished by means of a well balanced copper oxide bridge, which provides the even har- monics in a path conjugate to the path followed by the odd harmonics. MAGNETIC GENERATION OF A GROUP OF HARMONICS 439 A typical circuit used for the simultaneous generation of a number of odd and even harmonics at approximately equal amplitudes is shown schematically in Fig. 1. Starting with the fundamental frequency Fig. 1 — Circuit diagram of channel harmonic generator. input, a sharply selective circuit (F) is used to remove interfering com- ponents, and an amplifier {A) provides the input to the harmonic generator. The shunt resonant circuit (LoCo) tuned to the funda- mental serves primarily to remove the second harmonic generated in the amplifier. The elements CiLi are inserted to maintain a sinusoidal current into the harmonic producer proper, as well as to tune out the circuit reactance. "#iii»MHl>i Fig. 2 — Cathode ray oscillogram of output current wave form with fundamental input current as abscissa. 440 BELL SYSTEM TECHNICAL JOURNAL L-2. is a small permalloy core coil which is operated at high magnetiz- ing forces well into the saturated region. The circuit including L2, C2, and the load impedance, which is practically resistive to the desired harmonics, is so proportioned that highly peaked current pulses rich in harmonics flow through it. Two such pulses, oppositely directed, are produced during each cycle of the fundamental wave, the duration of each being a small fraction of the fundamental period. The typical output wave shown in Fig. 2 was obtained by means of a cathode ray oscillograph, the ordinate representing the current in the load re- sistance, and the abscissa representing the fundamental current into the coil. The desired odd harmonics are selected by filters connected across the input terminals of the copper oxide bridge. The even har- monics are obtained by full-wave rectification in the copper-oxide bridge. They appear at the conjugate points of the bridge, and are connected through an isolating transformer to the appropriate filters. Thus the harmonics are produced in two groups, with the even harmon- ics separated from the odds to a degree depending largely upon the balance of the copper-oxide bridge, as well as upon the amount of second harmonic passed on from the amplifier. In this way the re- quired discrimination properties of any filter against adjacent harmonics are reduced to the extent of the balance. A particular application of the circuit described above to the genera- tion of carriers for multi-channel carrier telephone systems uses a fundamental frequency of 4 kc, from which a number of harmonics are developed. Of these the 16th to the 27th are used as carriers. A photograph of an experimental model of this carrier supply system * is shown in Fig. 3. The top panel includes an electromagnetically driven tuning fork serving as the highly selective circuit {F), the amplifier {A), the output stage of which consists of a pair of pentodes in push-pull, and the tuned circuit LqCq. The next panel includes the elements L\C\, Li, C2, B, and T, together with a thermocouple and meter terminating in a cord and plug for test and maintenance purposes. The last two panels include the twelve harmonic filters, with test jacks and potentiometers for close adjustment of the output of each harmonic. A few of the more interesting performance features are given in Fig. 4. The harmonic power outputs shown in Fig. 4a represent measurements at the input terminals of the filters. The variation observed is produced by the non-uniform impedances of the filters. When these are corrected, the variations due to the harmonic generator proper are less than ± 0.2 db from the 16th to the 27th harmonic. Outside this region the amplitudes gradually decrease to the extent * Developed by J. M. West. MAGNETIC GENERATION OF A GROUP OF HARMONICS 441 Fig. 3— Carrier supply unit, furnishing twelve harmonics of 4 kc. (experimental model). of 4 db at the 3d and 35th harmonics, and 11 db at the fundamental and the 61st harmonic. The variation of harmonic output with change of ampHfier plate potential is given for the two harmonics indicated in Fig. 4&. Figure 4c shows the 104 kc. output as a function of the 4 kc. input. Arrows are used to indicate normal operating points. The input amplifier is operated in an overloaded state so that beyond a critical input, the fundamental output of the amplifier and 442 BELL SYSTEM TECHNICAL JOURNAL :3h UJI- o5 Q-i " o d 18 < >,^ r" >, ^ 60 64 68 76 80 84 88 92 96 100 FREQUENCY IN KILOCYCLES PER SECOND 104 108 112 (A) 104 KC '^ 140 150 160 170 Eb IN VOLTS (B) -35 -30 -25 -20 -15 -10 -5 0 5 10 4-KILOCYCLE INPUT IN DECIBELS ABOVE I MILLI-WATT (C) Fig. 4 — Performance curves of channel harmonic generator. {A) Harmonic outputs; {B) Variation of 16th and 26th harmonics with ampUfier plate potential; (C) Variation of 26th harmonic with fundamental input. Fig. 5 — Construction of experimental non-linear coils used for harmonic generation, showing core forms, magnetic tape, wound coils, and assembled units. MAGNETIC GENERATION OF A GROUP OF HARMONICS 443 the harmonic output corresponding are but little affected by change of input amplitude. With a linear amplifier the harmonic output current would vary roughly as the four-tenths power of the input current. Another application involving higher frequencies has been made to the generation of the so-called "group" carriers used in conjunction with a coaxial conductor.^^ There odd harmonics of 24 kc. from the 9th to the 45th are used. The circuit differs from Fig. 1 in that the copper oxide bridge is omitted, and the non-linear coil is provided with two windings to facilitate impedance matching. The performance of an experimental model is similar to that of the generator described above. A notion of the physical size and construction of the non- linear coils used may be had from the photographs of Fig. 5. In both applications the required harmonics are generated at ampli- tudes high enough to avoid the necessity for amplification. III. Theory of Operation The analysis of operation of the harmonic generating circuit de- scribed above meets with difficulties, since a high degree of non-linearity is involved in working the coil well into its saturated region. To avoid these difficulties, an expedient is adopted by which the hysteresis loop is replaced by a single-valued characteristic made up of connected linear segments ^ as shown in Fig. th. It is then possible to formulate a set of linear differential equations with constant coefficients, one for each linear segment. The solutions are readily arrived at and may be pieced together by imposing appropriate conditions at the junctions, so that a solution for the whole characteristic is thereby obtained. From this solution the wave form of current or voltage associated with any circuit element may be calculated. Resolution of the wave form into components may then be accomplished by an independent Fourier analysis. The assumed B-H characteristic of Fig. 66 is made up of but three segments. While it is manifestly a naive representation of a hysteresis loop, it will be shown by comparison with experiment that the main performance features of harmonic generators may be reproduced by this crude model. It will be noted on Fig. db that the differential permeability of the assumed non-linear core, a quantity proportional to dB/dH, takes on one of two values, determined by the absolute value of the magnetizing force. These are designated by n in the permeable region and ;u« in the saturated region. The corresponding inductances are L20 and Lit, -^20 being many times greater than Lis. The values of current through the coil at which the differential inductance changes are designated ± Iq, 444 BELL] SYSTEM TECHNICAL JOURNAL I — v^A^ — ^1 — nm~^ C2 © , ^2 I| J (NON LINEAR)' i2 e^2 lL2 (A) B, 1-20 -2 L2S 1 Bm^l / L2S y 0 lo H (B) -pt Fig. 6 — Diagrams illustrating operation of the harmonic generator. {A ) Harmonic generator circuit; (B) Differential inductance and flux density of assumed non-linear coil as functions of magnetizing force; (C) Variation with time of currents in primary and secondary meshes, and in non-linear coil; (D) (E) (F) Equivalent circuits of the harmonic generator for the three time intervals indicated. corresponding to the magnetizing forces ± Ho. With this simple representation of the non-Unear inductance, the operation of the circuit shown in Fig. 6a will be described over a complete cycle of the funda- mental input wave. The current flowing in the input mesh is made practically sinusoidal by tuning Z-i, Ci. If now we start at the negative peak of the sinus- oidal input current of amplitude /i and frequency p/lw, the non-linear MAGNETIC GENERATION OF A GROUP OF HARMONICS 445 coil is worked in the saturated state where its inductance Lis is low. Since the resistance of the winding is small, the potential drop across the coil is correspondingly small. The current i^ which charges the condenser C2, assuming the latter to have zero charge at the start, is therefore negligible as indicated in Fig. 6c. This state of affairs is maintained until the current through L2 reaches the value — /q, at time tc. At this point the inductance of the coil increases suddenly to L20 and the voltage across the coil tends to increase. Hence the current i^ increases and C2 is charged much more rapidly than in the preceding interval. Charging continues until the current through the coil increases through /o at time td- At that time, the coil inductance returns to the low saturation value L^s, and the potential across the coil decreases. The condenser potential is no longer opposed by the poten- tial drop across the coil and the condenser discharges through R2 and Lis ; ii reverses its direction, maintaining the coil in the saturated region. The form and duration of the sharply peaked discharge pulse charac- teristic of this type of harmonic generator are determined by the values of the elements just mentioned. The resistance, capacity, and satura- tion inductance effectively in circuit are adjusted to permit the current to rise to a high maximum, to damp the pulse, and to shorten the pulse duration to the point at which the highest harmonic required reaches the desired amplitude. Under the working conditions which will be assumed in the following, this insures that the pulse dies away before the end of the half-cycle as shown in Fig. 6c. At that time the currents and potentials are the same, except for reversals of sign, as those at the start, so that the current wave consists of an alternating succession of these pulses. Equivalent circuits for the three respective time inter- vals of a half-cycle are shown in Figs. 6d, 6e, 6/. The similarity of the load current wave form derived above to that experimentally observed and shown in Fig. 2, is to be noted. The course of events described above parallels closely conclusions drawn from the mathematical analysis. This picture attributes to the coil L2 a sort of switching property which permits the condenser C2 in the load circuit to be charged and discharged alternately. The charge starts when the large inductance L20 is switched across the primary and secondary meshes, thus permitting energy to flow from the primary circuit into the condenser C2. This corresponds to that part of the wave described above during which the load current slowly rises as the charge accumulates on C2. Discharge starts when the large inductance L20 is switched out and the much smaller inductance Lis is switched in. This sharply reduces the voltage across L2, and the condenser is dis- charged through the load resistance and the saturation inductance. 446 BELL SYSTEM TECHNICAL JOURNAL During this interval the secondary circuit is practically isolated from the primary. The switching process is sustained by the alternations of the sinusoidal primary current and is periodic, as we have seen, since similar conditions exist at the start of each pulse. The times at which switching occurs are those at which the current through the coil passes through the critical values (dz /o) where the inductance changes. Since the narrow discharge pulse provides the principal contribution to the higher harmonics in which we are interested, and since this discharge takes place in the secondary independently of the primary, the elements of the secondary mesh during discharge determine the form of the output spectrum. From this viewpoint we may regard the con- denser as the source of energy for these harmonics and hence as a possible location for equivalent harmonic generator e.m.f.'s. In this light, the discharge circuit becomes a half-section of low-pass filter terminated in resistance i?2, with L2s as the series element and C2 as the shunt element. IV. Quantitative Results of Analysis To connect the three solutions which hold for the three linear regions of the B-H characteristic, conditions at the junctions are introduced which lead to transcendental equations. These may be solved graph- ically when definite values are assigned to the circuit parameters. From these may be obtained the maximum value Qm of charge on C2 which is reached at the end of the charging stage. By plotting a representative group of these final charges over a range of parameters ordinarily encountered, an empirical equation has been deduced for Qm as follows : C„ = V2f(f»)"-(,c*)..»(f;)- C) For the usual operating conditions the narrow peaked discharge part of the current pulse is most important in the determination of the higher harmonics (say beyond the 9th) with which we are concerned here. The charging interval then may be neglected in calculating the higher harmonics. The form of the discharge pulses is determined by the parameters PC2R2 and k, where k = UsjRi^Ci. The familiar criterion for oscillation in a series circuit containing inductance, capacity and resistance may be expressed in terms of k. If ^ > I, the discharge is an exponentially decaying oscillation; if MAGNETIC GENERATION OF A GROUP OF HARMONICS 447 k — \, the discharge is an exponentially decaying pulse. This last condition is the one assumed in the description of operation given above. If the discharge is oscillatory, and if further the second peak is large enough, the current through the coil may become less than 7o during the discharge interval. Thus L^ will return to its larger value, and recharging of the condenser will result. This process may lead to large and undesired variations in the amplitudes of the harmonics. To maintain the frequency distribution as uniform as possible over the frequency range of interest, the circuit parameters are usually adjusted so that recharging does not occur. Harmonic analysis shows that the nth harmonic amplitude under the above assumptions is given by I{n) = ^^Z"^^^- , (2) VI + (1 - 2k){npC2R2Y + k^npC^R^Y where n is odd. This expression neglects the contributions due to the charging stage, which are usually small for harmonics higher than the ninth. The corresponding harmonic power output is ^IWR,^ W, 2 1 + (1 - 2k)inpC2R2y + k\npC2R2Y' where Wo is a convenient parameter which does not vary with n and hence serves as an indication of the power of the output spectrum. It is related to W, the total power delivered to the load resistance, by the equation, Wo=-pC2R2W. IT For purposes of calculation. Wo may be found from (1) and (2) to be Wo = ^' pBrAdH, ( f-° ) "' {pC2R2y-' ( ^ ) "■' watts, (4) where 1-20 = ^ ' -^1 = ^-^Nlild, and N is the number of turns wound on the toroidal core of diameter d cm. and cross-sectional area A cm.} 448 BELL SYSTEM TECHNICAL JOURNAL In Fig. 7 the power spectrum is shown by plotting Wn in db above or below Wq as a function of npdRi for several values of k. These curves illustrate the degree of uniformity obtainable in harmonic am- $ -6 K=2.0\ ^^ 1.0 ^ 0.75 0.5 "^^ ^ bv. V-^ ^ ^ \ "-^ h^ ^ -^ \ \ \ ^^"S ^ * \ \ \ 02 0.4 0.6 1.0 1.2 1.4 npC2R2 1.8 2.0 2.2 Fig. 7 — Harmonic power spectrum plotted from eq. (2) as function of npdRi with k as parameter. plitudes under different conditions. It may be shown from (3) that Wn has a maximum with respect to n when k is greater than \, if 1 npC^Ri = T V^ — I, and that its value at this point is A number of relations may be derived from these equations which are useful for design purposes. Thus the form of harmonic distribution is fixed by k and pCiRt- The output power for a given magnetic ma- terial worked at a given fundamental magnetizing force then depends solely upon the volume of core material. Finally, the impedance is fixed by the number of turns per unit length of core. If the impedances desired for primary and secondary circuits differ, separate windings may be used for each circuit. MAGNETIC GENERATION OF A GROUP OF HARMONICS 449 V. Calculated and Observed Performance In order to make practical use of the results given above, we need some basis for deriving the assumed parameters of the non-linear coil from the physical properties of the magnetic materials used in harmonic producers. The fact that the actual magnetization curve is a loop instead of a single-valued curve as assumed requires increased power input to the circuit to provide for the hysteresis and eddy losses in the core. Other than this, the principal remaining effect of the existence of a loop is a lag in the time at which the pulses occur, an effect which is of no great moment in determining the form or magnitude of the resulting pulses. The next point requiring consideration is the effect introduced by the assumed abrupt change of slope contrasted to the smooth approach to saturation actually observed. While no rigorous comparisons can be drawn, the effect of the more gradual approach to saturation was ap- proximated analytically by introducing an additional linear segment between the permeable region and each saturated region of the B-H characteristic, at a slope intermediate between the two, so as to form a B-H characteristic of five segments in place of the original three. The solutions for these two characteristics were found to yield negligibly small differences in the amplitudes of the higher harmonics. It was inferred from this result that no substantial change would be introduced by a smooth approach to saturation. Finally, the actual B-H characteristic has a slight curvature in the saturated region, while the analysis considered a small linear variation. A rough approximation for the effect of this curvature, which leads to fair agreement with experiment, consists in taking for L^s the average of the actual slope, from its minimum value reached during the dis- charge peak down to the point at which the slope is one-tenth maxi- mum. To this is added the linear inductance contributed by the dielectric included within the winding. To summarize then, the harmonic outputs obtained from the analysis with the assumed B-H characteristic may be brought into line with experimental observations by the introduction of quantities ob- tained from actual B-H loops at appropriate frequencies and magnetiz- ing forces. In these the maximum slope found on the loop is taken for L20, the average slope over the saturated region is taken for Lis, and the energy corresponding to the area of the real B-H loop must be added to that originally supplied the harmonic generator input. A comparison between measured and calculated harmonic distri- butions obtained with a 4-kc. fundamental input is shown in Fig. 8. In this case the harmonic distributions were measured for four different 450 BELL SYSTEM TECHNICAL JOURNAL values of the secondary condenser d as shown by the plotted points. The power output of each harmonic is plotted in terms of the quantity npCiR-i. Calculated values are indicated by dashed lines. It is observed that while the agreement between calculation and experiment 20 — — „^ THEORETICAL * ■---. ^c: ^ FUNDAMENTAL (4 KILOCYCLES) MAGNETIZING FORCE :^ 8.1 OERSTEDS — — "^Si ^^ **"*• ^ -v "^ <"^>,., >^C 2 IN MICRO- fs^ARADS — _r:: ^-^ •^-. '^ V^«* ^^ 0.008^^ \ :ici^ "^^ ^^^ "^ Z^ \ ^-v \ ^S, s ■^-k ^ -\ \ V, ^ .^;:^ ^-> \ \ ^ N 0.002 \ N. ^ ^x "n N^ ^V s 0.001 V ^x 1.2 1.6 npC2 R2 2.8 3.0 Fig. 8 — Comparisons of calculated and measured harmonic distributions, plotted as functions of npdRi, with C2 as parameter. is perhaps as good as could be expected for the two highest curves, a substantial divergence is noticed in the two lowest sets ; the forms of the two sets are significantly different, and it seems that the divergence might become even greater at larger values of npdRi than those shown. Upon examination of the equations, however, it turns out that the conditions existing for the lowest pair of curves are just those for which recharging occurs, so that the conditions for which the equations were framed hold no longer. The calculated distributions might be expected to be too low for the higher harmonics, since we have taken an average value for the saturation inductance. This means that the peak of the discharge pulse will be sharper than that calculated, with a corresponding effect upon the higher harmonics. MAGNETIC GENERATION OF A GROUP OF HARMONICS 451 Another comparison between calculated and observed values is shown in Fig. 9 for a fundamental input of 120 kc. with two values of resistance load. Fair agreement is observed over the greater part of the frequency range which extended to 5 MC. The distribution curve for the smaller resistance load undulates as the load resistance is re- duced, since multiple oscillations and recharging are then promoted, in consequence of which the output power tends to become concentrated in definite bands of harmonics. In general, agreement within a few db is found over a wide range of circuit parameters when working into a resistance load, provided that recharging does not occur. 30 I J. 26 a 14 FU MAG^ .__ _ 1 NDAMENTAL (l20 KILOCYCLES) vJETIZING FORCE = 9.8 OERSTEDS ~"~--— . ■^^^- '^'"'^l ^ -§ ^ V :;^ N "•"^ ^'^-^. R2=3I00 — ' R 2= 1370 X ^"-- 1.6 2.0 2.4 npCaRz 3.2 3.6 4.0 Fig. 9 — Comparisons of calculated and measured harmonic distributions plotted as functions of npCiRi, with R^ as parameterl When the resistance termination is replaced by a bank of filters as it is in practice, the resistance termination is approximated over the frequency band covered by the filters. Where the band is wide the results obtained do not differ greatly from those with the pure resist- ance load, but when only a few harmonics are taken off by filters and the impedances to the other harmonics of large amplitude vary widely over the frequency range, then the wave form of the current pulse is substantially altered, with corresponding effect upon the frequency distribution, and the calculations for a pure resistance termination do not apply. A difficulty sometimes arises in getting a desired value of funda- mental current into the coil. Under certain circuit conditions the current amplitude is found to change rapidly as the input voltage is smoothly varied. This phenomenon has been described by various terms such as Kippeffekt, ferro-resonance, and current-hysteresis.^* If the operating point is located close to one of these discontinuities, the 452 BELL SYSTEM TECHNICAL JOURNAL fundamental input and harmonic output may vary widely with small changes in supply potentials and circuit parameters. This troublesome source of variation may be avoided in a number of different ways, of which the simplest is to increase the resistance of the resonant mesh. In the present case this is effectively accomplished without sacrificing efficiency by using pentodes, which have high internal resistances, in the amplifier stage connected to the resonant mesh. The efficiency of power conversion from fundamental to harmonics may be found from the fundamental power input to the circuit, as derived from measurements on a cathode ray oscillograph, and from the total harmonic output measured by means of a thermocouple. The maximum efficiency obtainable with the low-power circuits described in the second section is in the neighborhood of 75 per cent, and decreases with increasing fundamental frequency because of the increased dissi- pation due to eddy currents. It should be noted that this figure does not include losses in the primary inductance Li. When only a few harmonics are used, the efficiency of obtaining this useful power naturally drops to a much lower value, which for the particular cases mentioned in the second section, is between 15 and 25 per cent. VI. Effect of Extraneous Components In any practical case the fundamental input to the harmonic pro- ducer is accompanied by extraneous components introduced by cross- talk, by modulation, or by an impure source. Thus if the fundamental is derived as a harmonic of a base frequency, small amounts of adjacent harmonics will be present. Or if the amplifiers are a.-c. operated, side- frequencies are produced differing from the fundamental by 60 cycles and its multiples. Extraneous components of this sort in the input modulate the fundamental and produce side-frequencies about the harmonics in the output. When the harmonics are used as carriers, the accompanying products must be reduced to a definite level below the fundamental if the quality of the transmitted signal is to be un- impaired. The requirements imposed by this condition can be calcu- lated by simple analysis, the results of which agree rather well with experimental values. The method of analysis used is to consider the extraneous component at any instant as introducing a bias ^^ to the non-linear coil. The primary effect of a small bias (h) is to shift the phase of the discharge pulse by =F bIHi radians, //] being the amplitude of the fundamental magnetizing force. The sign of the shift alternates so that intervals between pulses are alternately narrowed and widened. MAGNETIC GENERATION OF A GROUP OF HARMONICS 453 The effect of this shift on the harmonics produced may be found by straightforward means in which the ampHtude of any harmonic is expressed in terms of the bias. Hence when the extraneous component or components vary with time, the sidebands produced may be evalu- ated when the bias is expressed by the appropriate time function. If the bias is held constant, the wave is found to include both odd and even harmonics, the amplitudes of which are given by In ^ I(n) \cosnb/Hi\, = I{n) |sin nhlH,\, (n odd) , 1 (n even),] (5) I(n) being the harmonic distribution in the absence of bias as given by eq. (2). If the extraneous input component is sinusoicjal, we have b = Q sin (qt + ^). (6) Substituting this expression for b in the equation for the harmonic com- ponents yields odd harmonics of the fundamental, and modulation products with the angular frequencies mp ± Iq, which may be grouped as side-frequencies about the odd harmonics. The amplitude of the wth (odd) harmonic is In = Hn) nQ and the amplitude of the modulation product mp ± Iq is 'm, ±i I(m) Ji H, ,{m-^l odd). (7) (8) where Ji{x) is the Bessel function of order /. Considering the side-frequencies about the wth harmonic, the largest and nearest of these are {n -\- \)p — q and {n — \)p -\- q, n being odd. The ratio of the amplitudes of either side-frequency to the nth harmonic is In ±1. Tl In J,\{n ± \)QIH{\ JoinQIH,) (9) on the assumption that the harmonic distribution in the neighborhood of n is uniform so that I{n ± 1) = I{n). If the arguments of the Bessel functions are less than four-tenths, a good approximation to the right member of eq. (9) is (« ± l)Q/2IIi. Hence with sufficiently small values of interference, the sidebands produced are proportional 454 BELL SYSTEM TECHNICAL JOURNAL to the amplitude of the interference, and increase linearly with the order of the harmonic. These relations apply to harmonic generators which produce sharply peaked waves in general, and are not peculiar to the magnetic type. Neighboring modulation products involving the interfering com- ponent q more than once have much smaller amplitudes in normal circumstances than the product considered above. Because of the tuning in the input mesh, interfering components far removed in fre- quency from the fundamental are greatly reduced and the most troublesome interference is likely to be close in frequency to the fundamental. It may be noted that where the interference is produced by amplitude modulation of the fundamental, so that two interfering components enter the input, the distortion produced may be approximated by doubling the amplitudes of the side-frequencies produced by one of the interfering components. If the disturbance is the second harmonic of the fundamental, the effect is nearly the same as that for constant bias, and the relations (5) may be used if h is taken as the amplitude of the second harmonic magnetizing force. 4.4 Fig. 10 — 73rd and 74th harmonic amplitudes as functions of direct current flowing through non-linear coil. Ordinate is ratio of harmonic amplitude with bias indicated, to that of 73rd harmonic with zero bias. Abscissa is harmonic number multiplied by the ratio of bias to fundamental. Dashed lines calculated from eq. (5), full lines measured. To illustrate the effects of d.-c. bias, Fig. 10 shows the amplitudes of the 73d and 74th harmonics of 4 kc. as functions of the parameter nQ/Hi. The agreement between measured and calculated values indicates that the most important effects of bias have been included in the simple analysis. MAGNETIC GENERATION OF A GROUP OF HARMONICS 455 References 1. E. T. Z.,v. 25, p. 1100, 1904. 2. C. R., V. 152, p. 856, 1911. 3. E. T. Z., V. 32, p. 988, 1911. 4. Cantwell, Elec. Engg., v. 55, p. 784, 1936. 5. Proc. I. R. E., V. 8, p. 468, 1920. 6. Arch.f. EL, v. 17, p. 17, 1926, and Proc. I. R. E., v. 17, p. 629, 1929. 7. Rev. Gen. d'El., v. 19, p. 987, 1926. 8. Zeit.f. Fernmeldetechnik, v. 5, p. 115, 1924. 9. Peterson, Bell Labs. Record, v. 7, p. 231, 1929. 10. Kasarnowski, Zeit.f. Phys., v. 30, p. 225, 1924. 11. Espenschied and Strieby, Elec. Engg., v. 53, p. 1371, 1934; Bell Sys. Tech. Jour., V. 53, p. 654, 1934. 12. Elmen, Elec. Efigg., v. 54, p. 1292, 1935; Bell Sys. Tech. Jour., v.l5, p. 113, 1936. 13. Casper, Hubmann and Zenneck, Jahrbuch, v. 23, p. 63, 1924; Rouelle, C. R., v. 188, p. 1392, 1929. 14. Peterson and Llewellyn, Proc. I. R. E., v. 18, p. 38, 1930. The Vodas * By S. B. WRIGHT Since the first transatlantic radio telephone circuit was opened for service over ten years ago, an increasing number of voice- operated switching devices has been added to the international telephone network. All of these have the common purpose of preventing echo and singing effects due to arranging the facilities to give the best possible transmission, even under difficult radio conditions. Differences in the design and performance of the several types of devices suggest that the advantages and dis- advantages of each be made available. The characteristics of two types of "vodas" used on circuits connecting with the United States are described in this paper. For reference purposes, a complete list of Bell System papers re- lating to these devices is included. Introduction 'TpHE interconnection of ordinary telephone systems by means of -'- long radio-telephone links presents some unique and interesting technical problems. Since radio noise is often severe as compared with that in wire lines, radio transmitter power capacity is relatively large and expensive, and it is in general economical to control the speech volumes so that the radio transmitter will be fully loaded and thus the effect of noise minimized for a given transmitter power rating. This volume control, to be fully effective, calls for voice-operated switching devices to suppress echoes and singing. This paper describes the measures which have been developed for use at radio-wire junctions in the United States. They are based upon an arrangement called a "vodas." This word, devised to fill a need for verbal economy, is formed from the initial letters of the words "z;oice- operated crevice anti-ringing"; and thus implies not only a suppressor of feedback or singing, but also automatic operation by voice waves. The general principles and applications of the vodas have been discussed from time to time in various papers listed at the end of this text. The present paper goes somewhat more into detail regarding the transmission performance of the vodas, including a description of an improved form of circuit which discriminates between line noise and the syllabic characteristics of speech. * Presented at the Pacific Coast Convention of A.I.E.E., Spokane, Washington, September 2, 1937. Published in Elec. Engg., August, 1937. 456 THE VODAS 457 Historical Background The two-way problem in telephony began with the invention of the telephone itself, and was the subject of considerable pioneering activity during the latter part of the nineteenth century. The invention of the amplifier brought about new problems when applied in a repeater for two-way operation. Even before a practical repeater had been devised, inventors visualized controlling the direction of transmission through amplifiers in a line by relays controlled from switches associated with the subscribers' instruments, an idea which is in use today on airplanes and small boats and in special circuits where this type of two-way operation is practicable. It is also used by amateur radio telephone operators. But for public telephone service more rapid and automatic control of two-way conversation is preferable. To control the direction of transmission in a manner that would meet public convenience, invention progressed through the early part of the twentieth century toward devices for switching the speech paths automatically by voice waves. During this period, long distance radio telephony was first demonstrated to be practical on a one-way basis. From that time until the first transatlantic radio telephone circuit was placed in service on January 7, 1927, anti-singing voice-operated devices underwent a process of development aimed at meeting the requirements of two-way radio telephone service. The vodas was one result. Since 1927, improvements have been made in cheapening and simplifying the equipment and in making a vodas that will operate better on speech and not so frequently on noise. It has also been possible to arrange a vodas so as to permit using the same privacy apparatus for both directions of transmission, thereby saving the cost of duplicate apparatus. The Radio Telephone Problem The conditions encountered when joining two-wire two-way circuits by radio links are illustrated in Fig. 1 in which (o) shows a connection between two subscribers, W and E, while {b) shows the paths of direct transmission and echo when E talks. In addition to the talker and listener echoes which arise in such a connection, singing can occur around the closed circuit CAFGDBC if the amplification is great enough. Also, when the same frequency band is used to transmit in both directions, two cross-transmission paths AB and DF are set up, and echoes and singing can take place around the end paths ABC and DFG. Any echoes or singing are of course primarily due to reflections of energy at points of impedance irregularities in the two-wire plant, including the subscribers' telephones themselves. 458 BELL SYSTEM TECHNICAL JOURNAL r r ^ / I ^1 L^ I A L w THE VODAS 459 In wire circuits, simple hybrid coils and echo suppressors ^ are usually adequate to prevent such effects because the gains are not increased to provide for loading the circuit with energy when speech is weak, and also because the cross-transmission paths are absent. In long radio circuits, however, singing may result from the adjustments of amplification made to load the radio transmitter in case of weak speech and thus override noise, even though separate frequency bands are used in the two directions. Moreover, it is desired that the users of the service have as good transmission over the entire connection, including these radio links, as that to which they are accustomed in their own wire telephone systems, and even better transmission may be desired owing to differences in the language habits of the sub- scribers. Consequently, the overall transmission efficiencies of inter- continental radio circuits are sometimes better than those of the best land lines in the areas to be interconnected. Fundamentals of Vodas Operation A voice-operated device to suppress singing effects can be designed to have three possible arrangements: 1. The terminal can normally be blocked in one direction and con- nected through in the other. 2. Both directions of transmission can normally be blocked and activated in either direction but not both directions by the voice waves. 3. The circuit can remain activated in the last direction of speech and blocked in the other direction. Where there is no noise on the transmission system under con- sideration any of these three arrangements will give satisfactory opera- tion as there is then nothing to prevent making the voice-operated devices as sensitive as may be necessary to obtain full operation on weak as well as on strong voice waves. If there is any noise on the system which tends to operate the device it is necessary to make it less sensitive to avoid false operation. A point may be reached where the sensitivity is so low that the weakest parts of speech will not cause operation, and the weak consonants will be lost. The reduction in articulation has been found to be proportional to the time occupied by these lost or "clipped" sounds.^ If the device is located at a point in the circuit where the signal-to- noise ratio coming from one direction is poorer than that coming from the opposite direction it is obvious that a considerable advantage will be gained by using arrangement 1, since the device may be pointed in ^ See references at end of text. 460 BELL SYSTEM TECHNICAL JOURNAL THE VODAS 461 the direction in which the normally blocked path is exposed to the better signal-to-noise ratio and the normally activated path is exposed to the poorer signal-to-noise ratio. The vodas is, of course, arranged so that the normally blocked (transmitting) side is exposed to the land lines, which are usually quieter than the radio links. In the receiving side, the device can be less sensitive because there is no need for having it completely operated under control of the voice waves. All that is necessary is to have this side sensitive enough to operate in response to comparatively large voice or noise waves which might otherwise, after reflection and passage into the outbound path, result in false operation of the more sensitive side associated with this path. In the vodas the principle of balance is used to keep the reflected currents small and thus allow the sensitivity of the normally activated device to be further reduced if necessary. Where a high degree of balance is not obtained and when noise from the radio limits the sensitivity of the receiving device it is sometimes necessary, particularly for weak outgoing volumes, to reduce the incoming volume so as to prevent echoes from operating the normally blocked transmitting side. This echo limitation is primarily due to noise in the radio link, reflections from the two-wire plant and weak volumes from the subscribers. It is difficult to produce any large improvement in talker volumes and balance; so it would appear that the solution of the difficulty would probably come from the direction of improving radio transmission. Some benefit has also been obtained by reducing the effect of radio noise on the vodas with special devices of which the "Compandor" '''• ^^ and the "Codan" ^^'2" are examples. More re- cently, use has been made of a new voice-controlled device called a "Noise Reducer" -^' '^^ which reduces the received noise between speech sounds. Vodas Design — Type A Control Terminal Figure 2 shows a schematic diagram of a vodas * arranged to use the same privacy device for both transmitting and receiving. This is the type used on transatlantic and other long routes. Since the operation of this arrangement has been described before, ^^ it will not be repeated here. The diagram of the relay circuit in Fig. 3 shows how various time actions are obtained. Relays 1, 2, 4 and 5 are operated from battery Bi when the ground contact of relay TM is opened. Thus the travel time of any relay armature is not a factor in securing fast initial * The vodas apparatus, together with the volume control devices and technical operator's circuits, go to make up what is called a Type A Control Terminal. 462 BELL SYSTEM TECHNICAL JOURNAL 1 ui 1 cc to -> ^^ - (J THE VODAS 463 operation. When the armature of relay TM reaches its left-hand contact, relay Hi operates and delays release of the relay train even if TM is at once restored to normal. Hi is delayed in releasing by the time required to charge condenser Ci. The final release of relays 1 and 4 is then controlled by the time constant of an auxiliary circuit involving relay H2 and condenser C2, while that of relays 2 and 5, which is made later so as to suppress delayed echoes, is controlled by the circuit charging C3. On the receiving side, condenser C4 is ad- justable so as to permit the technical operator to select the shortest release time for suppressing the delayed echoes in a given land line extension. Fig. 4 — Type A control terminal at San Francisco. The vodas control terminal of the A type ^ used at New York con- sists of a line of technical operating positions with cross-connections to other lines of equipment containing the delay units, repeaters, vodas amplifier-detectors and privacy apparatus. Figure 4 shows an arrangement of a single terminal at San Francisco. The control bay is placed between two line testing bays on the left and two trans- mission testing bays on the right of the operating lineup. The dis- tributing frame is in the center of the picture; and repeaters, ringers and privacy apparatus are shown at its left. At the extreme left is the vodas bay. 464 BELL SYSTEM TECHNICAL JOURNAL Syllabic Vodas — Type B Control Terminal The desire for a cheaper control terminal than the Type A led to the development of a second type, known as Type B, in which the vodas employs the same fundamental principles. In this vodas added protection against false operation from line noise is secured by the use of a new principle in voice-operated devices, called "syllabic" operation. It is observed that in many types of noise a large component of the long-time average power is steady. Speech, however, comes as a series of wave combinations of relatively short duration. These facts suggested a device which distinguishes between the rates of variation of the envelopes of the impressed waves. This is accom- plished by a filter in the detector circuit which passes the intermodu- lated components of speech in the syllabic range, but suppresses those of line noise which are above or below this range. Figure 5 shows a schematic diagram of the application of this device to a Type B control terminal. The privacy switching circuits are omitted from this drawing, as are also the circuits for delaying the release of the relays. In comparing this drawing with Fig. 2, it will be seen that relays 1, 2 and 3 perform the same functions, but the transmitting branch of the vodas consists of two portions, one a sensitive detector with a syllabic frequency filter, which on operation increases the sensitivity of the second portion. Considering the action of Fig. 5 on transmitted speech, the output of the sensitive detector of the syllabic device is a complex function of the applied wave having intermodulated components in the range passed by the tuned input circuit, together with a d-c. component and various low frequency components set up by the syllabic nature of the speech. There are also various components of any noise waves which may be present including a d-c. component. The first step in getting rid of the noise is to pass the detector output through a re- peating coil which blocks the d-c. component of both the speech and noise, but passes frequencies above about 3^ cycle per second. The resulting waves enter the low-pass filter, the output of which contains frequencies between 3^ and 25 cycles per second, which "syllabic range" is between the d-c. component of zero frequency and the fundamental frequency of the line noise. These syllabic frequency currents cause momentary operations of relays (/) and (F). Relay (7) operates when a speech wave is commencing and relay (F), which is poled oppositely, operates while the impulse is dying out, thus sending current out of the filter in the opposite direction. Operation of either (7) or (F) effectively inserts gain ahead of the upper detector, thereby THE VODAS 465 466 BELL SYSTEM TECHNICAL JOURNAL Fig. 6— Technical operator at Forked River, N. J., using a type B control terminal to establish a circuit between a steamship and a shore telephone operator. THE VODAS 467 increasing the sensitivity of relay {K), when speech is present. Even if the noise is strong enough to operate relay {K) over the upper branch when the gain is inserted, the release of relay {F) at the end of a speech sound will remove the gain and permit {K) to fall back. Thus, it is possible to work relay {K) more sensitively on weak speech than would be possible without the syllabic device. Figure 6 shows a photograph of a B-type terminal in ship-to-shore service at Forked River, New Jersey. The vodas and volume control apparatus are in the left-hand cabinet. The right-hand cabinet contains privacy apparatus, a signaling oscillator and a vodas relay test panel. Performance In any system employing voice-operated devices it is necessary for the time actions to provide for to-and-fro conversation with a minimum of difficulty when the subscribers desire to reverse the direction. The electromagnetic relays used in the vodas have advantages over other types of switching arrangements which have been proposed in that they (1) operate and release at definite current values, (2) have fast operating and constant releasing times, (3) have their windings and their contacts electrically separated, thus simplifying the circuits, and (4) operate in circuits having low impedances. The operating times of the two types of vodas are shown in Fig. 7 as a function of the strength of suddenly-applied single-frequency sine waves in the voice range. These measurements were made with a capacitance bridge.^ The sensitivities of the two types were adjusted so that observers noted an equivalent amount of clipping. The Type A vodas was provided with a 20-millisecond delay circuit; the Type B had no delay. For the Type A vodas, the operating time is quite small and constant just above the threshold of operation. For weak inputs the operating time of the syllabic device is de- termined by relay (/) and the filter, as shown in Fig. 7. As the suddenly-applied input is increased, a point is reached where the less sensitive detector operates relay {K), reducing the operating time from around 20 milliseconds to values comparable to those of the Type A. The operation was also tested on waves formed by applying simul- taneously two sine waves of equal amplitude but slightly different frequencies. These waves were recorded on an oscillograph, together with a d-c. indication of the operation of each of the vodas relays, with the sensitivities adjusted the same as for Fig. 7. The time from the beginning of a beat wave (null point) to the time of operation was measured from these oscillograms and plotted against various values of 468 BELL SYSTEM TECHNICAL JOURNAL total applied voltages. Figure 8 shows the results for a 5-cycle-per- second difference between the two frequencies. Negative values of time indicate that the path was cleared before the beginning of the wave, and these occur only with the Type A vodas due to the delay circuit. The curves for frequency differences of less than 5 cycles per second show more clipping and greater differences between the devices, while those for greater frequency differences show less time clipped and less difference between the two types of vodas. In the case of weak waves it is evident that the syllabic will give less clipping 40 36 28 12 ■ — 1 TYPE B 1 TYPE A \ \J "i^ -| \ \ V — u -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6 INPUT IN DECIBELS (RELATIVE TO I MILLIWATT) Fig. 7 — Vodas operating times with sine waves suddenly applied. because the energy of the wave does not rise to the value required to operate the Type A device until after the syllabic device has operated; and for very weak waves the Type A does not operate at all. In the case of strong waves, the Type A vodas is better due to its delay circuit. However, since the clipped time is greater on weak sounds than on strong ones, the two types give performances on speech which are judged to be equivalent. A comparison of operation of the two types of vodas on a speech wave is shown in Fig. 9. Reading from left to right, the middle trace of this oscillogram shows the wave recorded by saying the word THE VODAS 469 "six" over a telephone circuit transmitting a band of frequencies from about 800 to 2000 cycles per second, which is the range normally effective in operating the vodas. The upper trace shows the point at 60 52 ^V. "-. -. "-. -12 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 INPUT IN DECIBELS (RELATIVE TO I MILLIWATT) Fig. 8 — Operation on a 5-C.P.S. sine wave. which the syllabic Type B device operated and the lower trace shows the point at which the Type A device operated. Since the speech wave shown was used to operate both devices, the reduction of clipping 470 BELL SYSTEM TECHNICAL JOURNAL by the delay circuit in the Type A vodas was not recorded. However, the effect of a transmission delay of 20 milliseconds is shown by sub- tracting 20 milliseconds from the point at which operation occurred. This is indicated on the oscillogram for both devices. It is concluded that on this wave the syllabic device without a delay circuit would give about the same clipping as the Type A vodas with its delay circuit. Figure 8 indicates that the Type A would be better for stronger speech and the Type B would be better for weaker speech. The advantage of a delay circuit in either case is evident. It is evident from this analysis that the reason for using delay circuits is not primarily because the relays are slow in operating. When the sensitivity is limited by noise, clipping of initial consonants can occur with infinitesimal operating times. One way of reducing the clipping is to use long releasing times so that the relays remain OPERATE POINT TYPE B TIME """•"' " y OPERATE POINT TYPE A Fig. 9 — Oscillogram of the word "SIX," illustrating clipping and its reduction by a delay circuit in the transmission path. operated between syllables. This has the disadvantage of making it harder for the opposite talker to break in. To avoid this difficulty, the relays in the vodas are given releasing times that permit the distant speech to break in about one sixth of a second after a United States talker ceases to speak. One advantage of delay circuits is to reduce the clipping of initial consonants and thus permit using short releasing times, thereby making it possible to reverse the circuit more readily. In addition, delay circuits permit using a lower relay sensitivity which has two advantages. First, more noise can be tolerated without causing false operation. Second, more received volume can be delivered without the echoes causing false operation of the normally blocked trans- mitting side. The advantage of artificial delay of various amounts has been determined by using different types of normally blocked arrangements THE VODAS 471 to find the relation between the delay and the sensitivity required to produce given amounts of clipping of initial sounds. The results are shown for a Type A vodas in Fig. 10. The curves for the syllabic device are similar. The set-up was arranged so that various delays could be inserted in either the transmission circuit (Delay X) or the relay circuit (Delay Y). The left ends of the curves indicate that when delay Y is used, that is, when the net operating time of the relay is great, a point will be reached where no reasonable increase in CD "J -25 ^3 \ DELAY X , 1 40 — *- — 1 > \ 1 CIRCUIT FOR OPER ATING RELAY I n' J -35 DELAY Y \ V - L^ 1 ^ 1 -in 25 20 15 10 5 0 \ CLIPPING JUST ^N.^NOT ICE ABLE ^N ^-^., ^^^ ^. MODERATE . CLIPPING L^ ^^--., ^ -10 -5 0 5 10 X MINUS Y IN MILLISECONDS Fig. 10 — Typical delay vs. sensitivity for certain clipping effects. sensitivity is sufficient to prevent intolerable clipping. The value of 20 milliseconds of delay X as compared to zero is equivalent to an increase of about 5 db in sensitivity for a given amount of noticeable clipping. A reasonable release time is of value in preventing clipping, as it causes the relays to remain operated not only for trailing weak endings of sounds, but also when the energy is temporarily reduced by inter- mediate consonants which may be comparable with noise. Delayed release is also important when it is required to maintain the blocked condition while delayed echoes are being dissipated. For these 472 BELL SYSTEM TECHNICAL JOURNAL echoes, the hangover or release times should be constant for various applied voltages. In the vodas, the change in release time over a wide range of inputs is less than 1 per cent. Adjustments are made by varying the condensers and resistances of the auxiliary circuits shown in Fig. 3. Typical values obtained by this method are indicated in Fig. 11. V) 120 80 ? 60 40 < 20 0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 RELEASE CIRCUIT CAPACITY IN MICROFARADS Fig. 11 — Release time vs. capacitance. The vodas amplifier-detectors have broadly tuned input circuits to exclude by frequency discrimination many of the frequencies induced by power sources and those which are unnecessary for speech opera- tion. The sensitivity- frequency characteristic is shown on Fig. 12. LONG ^^ ^ ^ ^ ^" MEDIUN f^ SHORJ^ ^ / ^ \ / N \ / / \ \, O ill <=> -8 / \ V z / \ > H IP / \ s 1-14 UJ ^ -le / \ -v^ / _i y -18 ^^ ^ _ SYLLABIC RANGE 0.5 TO 25 'X' ^ i/ TEL EPHO ANSE NF -20 / R -22 / 400 800 1200 1600 2000 FREQUENCY IN CYCLES PER SECOND 2400 2800 Fig. 12 — Sensitivity -frequency characteristics of the vodas. THE VODAS 473 This figure also shows the relatively narrow frequency range passed by the repeating coil and syllabic frequency filter of the Type B vodas. Operating Attendance To insure proper operation of a vodas a technical operator ^ is in attendance. He is provided with circuits which enable him to talk and monitor on the circuit as indicated in Figs. 2 and 5. His duties include adjusting the sensitivity of the receiving relays for the par- ticular value of radio noise existing and adjusting the transmitting and receiving speech volumes by the aid of potentiometers and volume indicators. He selects the proper hangover time and coordinates the operation of the circuit as a whole with the distant end. At times, he may be required to increase the sensitivity of the transmitting side of the vodas in the case of talkers with poor ability to operate relays or to decrease the sensitivity when weak volumes are supplied from land lines with more than the usual amount of noise. Summary The vodas is used in radio telephony to switch the voice paths rapidly to and fro, and thus prevent echoes and singing that would otherwise occur at unpredictable times. It is also used to save privacy apparatus by permitting the use of the same apparatus for both directions of transmission. The performance characteristics of the electromagnetic relays used in the vodas are very suitable in that they have small operating and constant releasing times. Improved performance of the voice-operated relays in the presence of line noise can be secured by the use of a syllabic type of vodas which discriminates between the characteristic voltage-time envelopes of the noise and speech waves. Laboratory and field tests indicate that this device, even without delay circuits, gives slightly better performance on most conditions than the original vodas with delay. When provided with a transmitting delay circuit, the syllabic device is decidedly better than the older vodas. References The International Bibliography on the Coordination of Radio Telephony and Wire Telephony is given in the C.C.I.F. Green Book Volume I of the Proceedings of the Xth Plenary Meeting, held at Budapest, September 1934. Below is a chronological list of Bell System papers relating to the vodas. 1. "The Limitation of the Gain of Two-Way Telephone Repeaters by Impedance Irregularities," George Crisson, Bell Sys. Tech. Jour., Vol. 4, No. 1, January, 1925, pp. 15-25. 474 BELL SYSTEM TECHNICAL JOURNAL 2. " Echo Suppressors for Long Telephone Circuits," A. B. Clark and R. C. Mathes, A.I.E.E., Jour., Vol. 44, No. 6, June, 1925, pp. 618-626; Elec. Commun., Vol. 4, No. 1, July, 1925, pp. 40-50; A.I.E.E., Trans., Vol. 44, 1925, pp. 481^90. v3. "The New York-London Telephone Circuit," S. B. Wright and H. C. Silent, Bell Sys. Tech. Jour., Vol. 6, No. 4, October, 1927, pp. 736-749. 4. "Echo Elimination in Transatlantic Service," G. C. Crawford, Bell Lab. Record, Vol. 5, No. 3, November, 1927, pp. 80-84. 5. "Bridge for Measuring Small Time Intervals," J. Herman, Bell Sys. Tech. Jour., Vol. 7, No. 2, April, 1928, pp. 343-349. 6. "Problems in Power-Line Carrier Telephony," W. B. Wolfe and J. D. Sarros, A.I.E.E., Jour., Vol. 47, No. 10, October, 1928, pp. 727-731 ; ^.7.£.E., Trans., Vol.48, 1929, pp. 107-113. 7. "A Carrier Telephone System for Power Lines," C. F. Boeck, Bell Lab. Record, Vol. 7, No. 11, July, 1929, pp. 451-458. 8. "Voice-Frequency Equipment for the Transatlantic Radio Telephone," J. A. Coy, Bell Lab. Record, Vol. 8, No. 1, September, 1929, pp. 15-20. 9. "Effects of Phase Distortion on Telephone Quality," J. C. Steinberg, Bell Sys. Tech. Jour., Vol. 9, No. 3, July, 1930, pp. 550-556. 10. "Electrical Delay Circuits for Radio Telephony," R. T. Holcomb, Bell Lab. Record, Vol. 9, No. 5, January, 1931, pp. 229-232. 11. "Acoustic Delay Circuits," W. P. Mason, Bell Lab. Record, Vol. 9, No. 9, Mav, 1931, pp. 430-432. 12. "The Time Factor in Telephone Transmission," O. B. Blackwell, Bell Sys. Tech. Jour., Vol. 11, No. 1, January, 1932, pp. 53-66; Bell Lab. Record, Vol. 10, No. 5, January, 1932, pp. 138-143; A.LE.E., Trans., Vol. 51, 1932, pp. 141-147. Elec. Engg., Vol. 50, No. 10, October, 1931, pp. 902-903 (Abstract). 13. "Two-Way Radio Telephone Circuits," S. B. Wright and D. Mitchell, Bell Sys. Tech. Jour., Vol. 11, No. 3, July, 1932, pp. 368-382; LR.E., Proc, Vol. 20, No. 7, July, 1932, pp. 1117-1130. 14. "A Telephone System for Harbor Craft," W. K. St. Clair, Bell Lab. Record, Vol. 11, No. 3, November, 1932, pp. 62-66. 15. "Voice Frequency Control Terminals for Caribbean Radio Systems," W. A. MacMaster, Bell Lab. Record, Vol. 11, No. 12, August, 1933, pp. 369-374. 16. "Certain Factors Limiting the Volume Efficiency of Repeatered Telephone Circuits," L. G. Abraham, Bell Sys. Tech. Jour., Vol. 12, No. 4, October, 1933, pp. 517-532. 17. "The 'Compandor' — An Aid Against Static in Radio Telephony," R. C. Mathes and S. B. Wright, Elec. Engg., Vol. 53, No. 6, June, 1934, pp. 860-866; Bell Sys. Tech. Jour., Vol. 13, No. 3, July, 1934, pp. 315-332. 18. "The Voice-Operated Compandor," N. C. Norman, Bell Lab. Record., Vol. 13, No. 4, December, 1934, pp. 98-103. 19. "Ship-to-Shore Radio in Puget Sound Area," E. B. Hansen, Elec. Engg., Vol. 54, No. 8, August, 1935, pp. 828-831. 20. "Marine Radio Telephone Service," F. A. Gifford and R. B. Meader, Commun. & Broadcast Engg., Vol. 2, No. 10, October, 1935, pp. 9-11, 15. Tech. Digest in Bell Sys. Tech. Jour., Vol. 14, No. 4, October, 1935, pp. 702-707. 21. "A Noise Reducer for Radio Telephone Circuits," N. C. Norman, Bell Lab. Record, Vol. 15, No. 9, May, 1937, pp. 281-285. 22. "Radio Telephone Noise Reduction by Voice Control at Receiver," C. C. Taylor, this issue of Bell Sys. Tech. Jour.; Elec. Engg., August, 1937. Radio Telephone Noise Reduction by Voice Control at Receiver * By C. C. TAYLOR In listening to speech transmitted over radio circuits, the noise arriving in the intervals between the signals may be annoying. There is also evidence that the intelligibility is reduced due to this noise shifting the sensitivity of the ear. Reducing the noise occurring in the intervals of no speech should therefore improve reception. This paper gives the underlying requirements for a device to accomplish this type of noise reduction and describes the action of a typical " noise reducer." Laboratory and field tests are described which show that its use is equivalent to an improvement in signal- to-noise ratio which reaches a maximum value of about 5 db. It also reduces false operation of the voice-operated relays used on long radio telephone connections. Introduction TN transmitting speech over radio telephone circuits there are a -*- number of conventional methods of increasing the signal with respect to the noise. Examples of such methods are the use of higher power, directive antennas, diversity reception and filters to narrow the received frequency band. In addition, there are other methods of a special character which reduce the effect of the noise interference with the speech transmission. One example of such a device limits the noise interference by eliminating the high peaks of noise of very short duration and depending upon the persistence of sensation of speech in the ear to bridge the gaps. Another method diminishes the noise in intervals of no speech. This is the method which will be discussed here. Speech and Noise Considerations Speech signals may be represented by a group or band of frequencies occupying a certain interval of time. In using the conventional method of narrowing the received frequency band, filters eliminate all noise outside the band actually required. In fact we sometimes go beyond this and remove some of the outer frequency components of * Presented at the Pacific Coast Convention of A. I. E. E., Spokane, Washington, September 2, 1937. Published in Elec. Engg., August, 1937. 475 476 BELL SYSTEM TECHNICAL JOURNAL speech which are weak and submerged in the noise and therefore contribute little or nothing to the intelligibility. Experiments have shown the effect on voice transmission of removing portions of the frequency range.^ Articulation tests were used to afford a quantitative measure of the recognizability of received speech sounds. These show that the upper frequencies may be cut off down to about 3000 cycles without serious reduction in articulation. After such treatment, as the noise level increases, the weaker and less articulate sounds become more and more submerged in the noise and additional reduction in the detrimental effect of the noise is required. In addition to the speech waves covering a frequency band they occupy intervals of time. The unoccupied intervals between the speech sounds contain noise. Reduction of the noise reaching the ear in these intervals has been found to result, under certain conditions, in an improvement in speech reception. This may possibly be explained by considering the characteristics of the ear.^ It has been shown that noise present at the ear has the effect of shifting the threshold for hearing other sounds or has a deafening effect. That is, there is a reduction of the capacity of the ear to sense sounds in the presence of noise. For example, if a person has been listening to a noise for a certain period, his ear is made insensitive so that speech signals following are not so easily distinguished. The ear has a sensory build- up time, that is, a time needed for the noise to build up to a steady loudness. By reducing the noise in the intervals of no speech the average threshold shift seems to be diminished. Aside from this the presence of the noise tends to distract the attention from the perception of the speech. Removal of noise during the intervals of no speech tends to reduce this effect. Requirements In considering the elimination of the noise during these intervals it is necessary to bear in mind certain characteristics of speech. ^ Speech waves may be regarded as nonperiodic in that they start at some time, take on some finite values and then approximate zero again. In connected speech it is usually possible to approximately distinguish between sounds and to ascribe to each an initial period of growth, an intermediate period which in some cases approximates a steady state and then a final period of decay. The duration intervals of various syllabic sounds vary from about .03 to as much as .3 or .35 second. When noise is high the weaker initial and final sounds become obscured so that they contribute little to the intelligibility. ^ See end of paper for references. RADIO TELEPHONE NOISE REDUCTION 477 In connected speech, silent intervals occupy about one-fifth to one- third of the total time. Also there are frequent intervals when the sounds are rather weak. However, if we attempt to suppress noise during all these intervals, experience shows that the suppression be- comes too obvious, and the speech is apt to sound mutilated. For this reason the function of any device to be used for reduction of noise in the intervals between speech is to operate rather quickly to remove suppression and pass the speech and approximately to sustain this condition for sufficient periods to override weaker intervals so that obvious speech distortion does not occur. To reduce the noise in the intervals between speech it is necessary to depend for control upon either the speech itself or upon some auxiliary signal usually under the control of the speech at some point in the circuit where the signal-to-noise ratio is better. This latter condition is illustrated on a circuit where the carrier is transmitted only during speech intervals. The carrier then acts as an auxiliary signal which operates a device at the receiver to remove loss.*- ^ The device to be discussed below utilizes the speech itself at the receiver to perform this function. In using the speech in this way it is obvious that control can be accomplished only when the speech energy sufficiently exceeds the noise energy so that the presence of the speech is distinguishable. The device could operate abruptly as, for example, a relay which removes a fixed loss in the operated position and restores it when non-operated. Experience indicates that the use of such a device makes the suppression too obvious if it is to follow the speech sounds closely. It is desirable, then, to perform this reduction by more or less gradually removing loss as the speech increases to accentuate the difi^erence between levels of speech sounds and levels of noise which occur in the gaps between speech. Noise Reducer This kind of performance has been secured in a device known as a noise reducer. A comparison of the action of the noise reducer and a relay having similar maximum loss is shown in Fig. 1. This figure shows the input-output characteristics of these devices over the voice amplitude range to which they are subjected on a radio circuit. The noise reducer may be likened to a relay with a variable loss, the loss not varying instantaneously but over a short period of time. The loss, for any short period, may be any value within the loss range and the device has, therefore, been likened to an elastic or shock absorbing relay. The noise reducer has no loss for strong inputs, considerable loss for weak inputs and changes this loss gradually over a short interval of 478 BELL SYSTEM TECHNICAL JOURNAL time. It introduces loss in the absence of speech but reduces this loss in proportion to the amplitude and duration of waves impressed upon it. The time required for the loss change is such that abruptness of noise change is absent and very short impulses of static do not effec- uj -20 -28 -36 4 // vo LUME-REGULA SPEECH RANG TED / ^/ E / {/ / // ^ 1 / /, / / / / / r / r / f / / 1 ( NO LOSS /'' DEVICE / X / \ // / / / / / / y / f 1/ / 4' / / / > -5^ / >> ^ /'■ RELAY SWITCHING 25 DECIBELS LOSS / / 1 V-* l*>1 ( / / NOISE reducerX? / y^ i' / . / / -28 -24 -20 -16 -12 -8 -4 0 4 8 12 16 lOOO-CYCLE INPUT IN DECIBELS (RELATIVE TO I MILLIWATT) Fig. 1 — Input-output comparison of noise reducer and voice-operated relay. tively control the loss. This contrasts with a very fast limiter acting on high-peak crashes only. The noise may control the loss if its average amplitude is strong enough. Therefore, the control is made adjustable so that the noise RADIO TELEPHONE NOISE REDUCTION 479 waves are not permitted to control for any noise condition within the range of usefulness of this device. Thus the noise in the absence of speech is always reduced and the portions of the initial and decay periods of the speech sounds which are also reduced vary with this adjustment for noise intensity. Of course, if the speech-to-noise ratio becomes too small or if other transmission conditions interfere, an improvement becomes impossible. Circuit Arrangement Figure 2 shows the circuit of the noise reducer in simplified schematic form.^ Incoming waves pass from left to right through the fixed pad, INPUT REDUCTION '-W\^^W-l VsA 4iN MAX. MIN. 9 — *^^ 4 OUT OUTPUT RECTIFIER 0-P 6+P Fig. 2 — Simplified schematic of noise reducer. the vario-losser and the amplifier to the output. At the input, part of these waves pass through the reduction control branch circuit which includes a variable resistor, an amplifier and a rectifier. The direct current produced by the rectifier is applied through the condenser and resistance filter to the copper-oxide losser circuit. For current below a threshold value, no appreciable change occurs in the losser and the loss introduced is about 20 db. As input increases, rectified current reaches a value where the loss begins to change rapidly. It becomes 0 db at an input about 20 db above the point at which the loss starts to change. The design is such that the loss remains substantially constant for higher inputs. 480 BELL SYSTEM TECHNICAL JOURNAL The varid-Iosser makes use of the resistance variation with current of copper-oxide rectifier disks. This variable resistance shunts a fixed resistance in series with the windings of a repeating coil as shown in Fig. 2. The maximum loss is determined by the fixed resistance when small current is flowing through the disks while the varying loss is determined by the shunting copper-oxide resistance which decreases rapidly with increasing current above a threshold value until a low value is reached. The minimum loss is limited by the output of the control tube approaching a maximum and the shunting resistance becoming so small that additional decrease affects the loss inappreciably. The variable resistor setting in the reduction control circuit de- termines the input amplitude at which reduction begins and therefore the point above which the loss remains substantially constant. If there is a difference in amplitude between speech and noise, the reduction Fig. 3 — noise reducer panel. control may be so adjusted that the noise on the circuit, when no speech is present, is appreciably reduced. The action then is as follows : In the absence of speech, noise is reduced usually the maximum value of 20 db; during intervals of lower speech amplitudes the loss decreases in proportion to the increase in amplitude, and during speech of high amplitude both noise and speech are transmitted without loss. As the noise encroaches upon the range of speech amplitude, it becomes necessary to reduce greater amplitudes, thereby also further reducing the weaker parts of speech. The noise reducer is contained on a 1\ inch panel for relay rack mounting. Figure 3 gives a front view. The panel contains the reduction control resistor and an In-Out key which, in the Out position, gives the device a fixed loss. Both resistor and key may be duplicated external to the panel with the wiring arranged to give remote control. RADIO TELEPHONE NOISE REDUCTION 481 Characteristics Figure 4 gives the 1000-cycle input-loss characteristic for three settings of the reduction control. For any setting, there is an input volume above which the loss remains constant, while for volumes below this the loss increases with decreasing input until the maximum loss is reached. The volume regulated speech range encountered on radio circuits at some point in the circuit which is 5 db above reference volume as measured on a volume indicator is indicated as extending from + 13 db to — 17 db referred to 1 milliwatt for the purpose of showing approximate corresponding speech amplitudes. ^ -^ — ' — - nr ^ '' ^ 2 4 6 8 10 12 14 V y / / r / / / / / / / / / / /minimum /medium / MAXIMUM / / / / f > / / 16 / / \ /OLUME-REGULA SPEECH RANG TED / 18 20 22 / E / y / ' 24 -40 -36 -32 -28 -24 -20 -16 -12 -8-4 0 4 8 12 16 20 1000-CYCLE INPUT IN DECIBELS (RELATIVE TO I MILLIWATT) Fig. 4 — Loss versus input for several settings of the reduction control. Figure 5 shows oscillograms giving the input and output charac- teristics of noise for maximum reduction and of speech for maximum, medium and minimum reduction. The upper trace is the input and the lower trace the output. The middle trace is not used. It will be noted by inspecting the In and Out traces at the beginning and ending of the word "bark" that there is some distortion in speech for the maximum reduction condition, but very little distortion for minimum reduction. Maximum reduction would be used only in case of high noise where this distortion is less objectionable than the noise. 482 BELL SYSTEM TECHNICAL JOURNAL RADIO TELEPHONE NOISE REDUCTION 483 Performance Laboratory tests have been made in an attempt to evaluate the advantages to be gained by the use of the noise reducer. It was shown that, for the rather Hmited and controlled conditions which were tested, definite advantage can be observed in judgment tests of the effectiveness of speech transmission through noise with and without the noise reducer. This advantage is of the order of magnitude of 3 to 5 db at the border line between commercial and uncommercial conditions on the noisy circuit. This figure is in approximate agreement with results obtained from records of performance on commercial connections. A curve is available which shows the approximate relation between percentage lost circuit time and transmission improvement for a long-range short- wave radio telephone circuit.*^ From the records of lost circuit time as affected by the noise reducer use, an improvement of 4 db is obtained from this curve. Observations were made and records kept for twelve months of the use of the device at the land terminal of the high seas ship-to-shore circuit and for shorter periods on New York-London circuits. These observations indicate that the noise reducer most satisfactorily reduces objectionable effects where the interference consists of noise of a fairly steady character. As might be expected it is somewhat less effective on crashy static. If the noise is very low there is no improvement; as the noise increases the benefit increases up to a certain point; when the noise amplitudes begin to approach too closely the peak amplitudes of the voice waves it becomes impossible to distinguish between them without producing objectionable speech distortion and there is again no advantage. Where volume fading is present there is a tendency to accentuate the volume changes and it becomes necessary to adjust the reduction control to limit this. Otherwise this effect may offset the possible noise improvement. The operating practice is to adjust the reducer control circuit for each noise or transmission condition so that optimum reception as judged by the technical operator is obtained. The general rule is to use the minimum reduction possible. Use of Noise Reducer with Voice Switched Circuits On radio telephone circuits for connection to the land telephone system, control terminal equipment is used at the junction of the land lines and the two one-way radio channels (one transmitting the other receiving) necessary for two-way communication. In making this connection a widely used method is one in which the two-wire land circuit is normally connected to the receiving radio channel and is 484 BELL SYSTEM TECHNICAL JOURNAL z o to UJ „ to< ii CCCO OQ UJ < o 52 o O 2<0 Oiii Z— ' 2o OUJ act I I i UJUJ . RADIO TELEPHONE NOISE REDUCTION 485 switched to the transmitting channel when the land subscriber talks. This switching is done by voice-operated relays. ''• ^ The noise reducer in addition to improving the intelligibility of the speech received protects these voice-operated relays against false operation by the received noise. Figure 6 shows the application of the noise reducer to such a control terminal. Speech entering the terminal from the left goes through the upper branch of the circuit, with volume regulating means and privacy apparatus, to the radio transmitter. Speech received from the distant terminal enters at the lower right from the radio receiver and proceeds through the privacy apparatus, the noise reducer, receiving regulating network and amplifier to the two-wire line. Outgoing speech operates the transmitting path and disables the receiving path. Incoming speech operates the receiving amplifier detector, which disables the transmitting amplifier detector, thus preventing singing and reradia- tion of received waves. Without the noise reducer the receiving relay may be operated by noise in the receiving path and such operation to an excessive extent will interfere with outgoing speech. To avoid this effect, it is custom- ary to reduce its sensitivity so that noise may not operate it. This results in the weaker speech parts also failing to operate the receiving relay. This weak speech and noise returned to the transmitting path through the land line connection may be strong enough to operate the transmitting relays and thus cut off incoming speech. This is avoided by reducing the volume to the land line. Therefore, any device which reduces noise in the receiving path in the absence of speech effects an improvement not only in the switching operation but also in the received volume. By placing the noise reducer in the receiving path false operation is diminished and volume increases of 5 to 15 db are realized. The noise reducer is applied to the receiving side of the terminal beyond the privacy apparatus so that it does not introduce any distortion in the privacy portion of the circuit. It is placed ahead of the receiving amplifier detector, thereby reducing noise between words which might affect the operation of this relay apparatus. Summary The noise reducer, which is a voice controlled variolosser with limited and controllable action, has been provided for use on short- wave radio telephone circuits and has proved to be a valuable and relatively inexpensive means of securing noise reduction. Improved reception is obtained for many of the transmission conditions experi- enced on such circuits. This results in better intelligibility to the 486 BELL SYSTEM TECHNICAL JOURNAL subscriber, greater margin in the operation of two-way radio telephone circuits and a reduction of difficulties in the wire plant caused by connection to noisy radio circuits. References 1. "Speech and Hearing," H. Fletcher, D. Van Nostrand Co., 1929. 2. "Effects of Phase Distortion on Telephone Quality," J. C. Steinberg, Bell Sys. Tech. Jour., July, 1930. 3. " Ship-to-Shore Radio in Puget Sound Area," E. B. Hansen, Elec. Engg., Vol. 24, No. 8, August, 1935. 4. "A Telephone System for Harbor Craft," W. K. St. Clair, Bell Laboratories Record, November, 1932. 5. "A Noise Reducer for Radio Telephone Circuits," N. C. Norman, Bell Labora- tories Record, May, 1937. 6. "The Reliability of Short-Wave Radio Telephone Circuits," R. K. Potter and A. C. Peterson, Jr., Bell Sys. Tech. Jour., July, 1934. 7. "Two-Way Radio Telephone Circuit," S. B. Wright and D. Mitchell, Bell Sys. Tech. Jour., July, 1932. 8. "The Vodas," S. B. Wright, this issue of the Bell Sys. Tech. Jour.; Elec. Engg., August, 1937, Transmitted Frequency Range for Circuits In Broad-Band Systems By H. A. AFFEL IN utilizing the broad frequency ranges which the newer carrier systems can transmit the telephone engineer has a problem of choice in band width per channel to be allotted to speech currents. A sufficient width is vital to faithful speech reproduction ; and desire for better telephone service always recommends an increase in band width over past practice. A reasonable balance, however, must ob- tain between various economic factors; and there must always be considered the relation between a proposed system and the other parts of the telephone plant, and also the trend of the art. The message band widths and the channel spacing which have been chosen by the Bell System for various new systems are summarized and discussed in this paper. These systems are expected to play a large part in the future growth of its long distance plant; and the reasons underlying this choice may therefore be of general interest. Different broad band systems are under development: A 12-channel system for use on open-wire lines employing frequencies up to 140,000 cycles, a 12-channel system for use on 19-gauge pairs in existing toll cables using frequencies up to 60,000 cycles, and a coaxial system capable of transmitting frequencies up to a million cycles or more, from which it is proposed to obtain 240 or more channels. In the different systems noted above, terminal apparatus is em- ployed which has many common features : The different channels are uniformly spaced at 4000-cycle intervals ; the same band filters are used in the ultimate channel selecting circuits; and the derived voice circuit band widths are substantially identical for all channels of all systems. The transmission frequency characteristic of a single link of such systems, in accordance with present designs, is shown on Fig. 1. A curve for five similar links connected in tandem is also indicated. Based on a 10 db cutoff as compared with 1000-cycle transmission, a single-link band extends from approximately 150 to 3600 cycles, and a five-link band extends from about 200 to 3300 cycles. There is, of course, no fixed relationship between the channel spacing and the frequency range of the derived voice-frequency circuit. This is largely a matter of economics in the design of a particular system. 487 488 BELL SYSTEM TECHNICAL JOURNAL The 4000-cycle channel spacing would permit obtaining a narrower band width with some simplification in the selecting circuits. With further development in selecting circuits, it is believed that it would permit obtaining a somewhat wider band or, if desired, a reduction in the cost of apparatus, maintaining the same band. The band chosen initially for the new systems is believed to be a desirable and forward-looking step in the direction of improving the quality of speech transmission, a continuing trend which is as old as u 0 1 1 FIVE , LINK ' S-rSTEM / ; 1 1 , /siMCLE y LINK SYSTEM I 1 1 J 1 / 1 y I 1000 2000 3000 FREQUENCY-CYCLES PER SECOND Fig. 1 — Transmission frequency characteristics of broad-band systems. telephony itself. Figure 2 shows typical band characteristics which mark the progress of transcontinental telephony since 1915. For shorter distances, the band widths have, of course, generally been wider than indicated on this series of curves. In the case of carrier systems the band depends on the number of links. The curve shown for 1937 is for the broad-band systems, estimated on the basis of a three-link connection. The increase in band width is achieved without material increase in cost, since in situations which favor their use, broad-band systems provide circuits which are substantially more economical than other alternatives, and the improvement can therefore be obtained by giving up only a small portion of the savings which the systems themselves make possible. If, as in some older types of systems, it had been chosen to maintain a standard of 250 to 2750 cycles for a single-link connection in the broad band systems, this could have been accom- plished by the use of a channel frequency spacing of about 3000 cycles. The wider transmission band is therefore obtained by a sacrifice in TRANSMITTED FREQUENCY RANGE FOR CIRCUITS 4SQ the ratio of approximately 3:4 in the number of channels obtained within a griven frequenc\" range. However, this does not mean a 4:3 increase in the cost per circuit. The amount is considerably less than this — depending somewhat on the type of s^^stem. In the pro- posed coaxial system, which appears to be a favorable example, where the attenuation increases roughly as the square root of the frequency, a frequency band increased by one-third means that for repeaters of a given t>pe and amplification the number of repeaters is multiplied by approximately y^; that is to say, approximately 15 per cent more repeaters are required. Furthermore, the line and terminal apparatus costs are not changred in a case of this kind, and since they constitute a major part of the total cost, the net increase in cost for the wider 0 ' 1000 2000 3000 ♦OOC FREQUENCY- CYCLES PER SECOND Fig. 2 — Representative transmission frequency characteristics of 3000-mile toll circuits. band width will be considerably less than 15 per cent — about five per cent in the case of the longer systems where the terminal apparatus costs are a small factor, and only a per cent or two in the case of the ver>- short systems where the terminal apparatus costs predominate. In the ideal case, using substantially perfect transmitters and re- ceivers, articulation is improved as the upper limit in frequency transmission is raised, as shown in Fig. 3. The increase in transmission performance, which a step from 2750 to 3300 cycles, or 3600 c>-cles for a single link, makes possible, is evidently still on the part of the band width-articulation relationship where a measurable increase in articulation may be expected. An improvement in band width accord- ingly reduces the eflPort needed to interchange ideas, since fewer repe- 490 BELL SYSTEM TECHNICAL JOURNAL titions occur and attention can be somewhat relaxed. It also enhances the naturalness of the received speech, and so makes the conversation more pleasing as well as easier. It should be noted also that the pro- posed broad-band systems will transmit frequencies approximately 50 to 100 cycles lower than earlier systems, which, while not contributing appreciably to articulation, has the effect of increasing naturalness. When applied in the telephone plant, the resultant effect of a given increase in band width will of course depend on the other parts of the circuit, and the transmission characteristics of the transmitters and receivers. Improved transmitters and receivers are now being applied O 60 — \ ^- \ y/^ HIGt- Fl PASS .TER \ /Lo / F W PAS LTER S / \ / \ / ^ V / \ / / 0 1000 2000 3000 4000 5000 CUTOFF FREQUENCY OF FILTERS - CYCLES PER SECOND Fig. 3 — Effect of cutoff frequency on syllable articulation. rapidly in the Bell System. They have much better transmission characteristics than earlier types and an effective upper frequency of transmission for the new station set which is well above 3000 cycles, as shown on Fig. 4. The toll connecting trunks are important links in a typical overall connection, and here also there has been a continued trend to provide wider band circuits. Figure 5 shows the transmission frequency char- acteristics of representative types of toll connecting trunks which are being commonly installed at present. Both non-loaded and loaded trunks are shown on the figure. Of course, in the non-loaded case, there is no definite cutoff frequency. The curve for the loaded trunk TRANSMITTED FREQUENCY RANGE FOR CIRCUITS 491 shows a reasonably long trunk having a 5 db loss at 1000 cycles (6.4 miles). In practice, of course, the trunk length may vary from a 2000 3000 FREQUENCY-CYCLES PER SECOND Fig. 4 — New station-set characteristics (including two one-mile 24-gauge loops con- nected by distortionless trunk). > 5 I- 58 LOADED^^ T ^ 0 1000 2000 3000 4000 5000 FREQUENCY-CYCLES PER SECOND Fig. 5 — Toll connecting trunk characteristics. fraction of a mile to 10 miles or more, with a corresponding effect on the transmission characteristic. It will be noted that the effective 492 BELL SYSTEM TECHNICAL JOURNAL cutoff of the loaded trunk shown is about 3500 cycles based on a 10 db cutoff point. Other types of loading, which will also be em- ployed, will have still higher cutoff points. Evidently the band widths of the broad-band circuits, toll connecting trunks, and new station sets are well matched. Laboratory and field tests have been made with circuits simulating the cutoff of the new broad-band systems and using various types of station sets, including the new standard. These indicate that raising the cutoff from 2750 cycles to 3600 cycles is equivalent to making a reduction of 3 to 4 db in the net overall loss of the circuit. Raising the cutoff from 2750 cycles to 3300 cycles is equivalent to a lesser reduction. With older types of instruments which reproduce speech less faithfully, this difference is also less, and of course, with instru- ments providing transmission up to considerably higher frequencies, the difference is greater. It will be appreciated, of course, that the wider speech band which will be made available in the new broad-band systems will not be fully effective in all telephone connections unless other toll circuits and toll connecting trunks and station sets are provided with improved trans- mission frequency characteristics. From a practical standpoint it is obvious that in a large telephone plant improvements cannot be made in all parts at one time. They must be introduced gradually as new systems and apparatus are applied, and with a far-sighted concern for future trends. The Dielectric Properties of Insulating Materials By E. J. MURPHY and S. O. MORGAN This paper gives a qualitative account of the way in which dielectric constant and absorption data have been interpreted in terms of the physical and chemical structure of materials. The dielectric behavior of materials is determined by the nature of the polarizations which an impressed field induces in them. The various types of polarization which have been demonstrated to exist are listed, together with an outline of their characteristics. I. Outline of the Physico-Chemical Interpretation OF THE Dielectric Constant THE development of dielectric theory in recent years has been along such specialized lines that there is need of some correlation between the newer and the older theories of dielectric behavior to keep clear what is common to both, though sometimes expressed in different terms. The purpose of the present paper is to outline in qualitative terms the way in which the dielectric constant varies with frequency and temperature and to indicate the type of information regarding the structure of materials which can be obtained from the study of the dielectric constant. The important dielectric properties include dielectric constant (or specific inductive capacity), dielectric loss, loss factor, power factor, a.c. conductivity, d.c. conductivity, electrical breakdown strength and other equivalent or similar properties. The term dielectric behavior usually refers to the variation of these properties with frequency, temperature, voltage, and composition. In discussing the dielectric properties and behavior of insulating materials it will be necessary to use some kind of model to represent the dielectric. The success of wave-mechanics in explaining why some materials are conductors and others dielectrics suggests that it might be desirable to use a quantum-mechanical model even in a general outline of the characteristics of dielectrics, but for the aspects of the theory of dielectric behavior with which we are immediately concerned here the behavior predicted is essentially the same as that derived on the basis of classical mechanics. However, in the course of the description of the frequency-dependence of dielectric constant we shall have occasion to make a comparison between the dispersion 493 494 BELL SYSTEM TECHNICAL JOURNAL and absorption curves for light and those for electromagnetic dis- turbances in the electrical (i.e., radio and power) range of frequencies. The difficulty is then met that the quantum-mechanical model is the customary medium of description of the absorption of light. But, since the references to optical properties will be only incidental and for comparative purposes, there is little to be lost, even in this domain in which quantum-mechanical concepts are the familiar medium of description, in using the pre-quantum theory concepts of dispersion and absorption processes. Thus a model operating on the basis of classical mechanics and the older conceptions of atomic struc- ture will be sufficient for our present purposes. On the wave-mechanical theory of the structure of matter a di- electric is a material which is so constructed that the lower bands of allowed energy levels are completely full at the absolute zero of temper- ature (on the Exclusion Principle) and at the same time isolated from higher unoccupied bands by a large zone of forbidden energy levels.^ Thus conduction in the lower, fully occupied bands is impossible because there are no unoccupied energy levels to take care of the additional energy which would be acquired by the electrons from the applied field, while the zone of forbidden energy levels is so wide that there is only a negligible probability that an electron in the lower band of allowed levels will acquire enough energy to make the transition to the unoccupied upper band where it could take part in conduction. The bound electrons in a completely filled and isolated band of allowed levels can, however, interact with the applied electric field by means of the slight modifications which the applied field makes in the potential structure of the material and hence in the allowed levels. On the other hand in the older theory of the structure of matter the essential condition which makes a material a dielectric is that the electrons and other charged particles of which it is composed are held in equilibrium positions by constitutive forces characteristic of the structure of the material. When an electric field is applied these charges are displaced, but revert to their original equilibrium positions when the field is removed. In this account of the behavior of di- electrics this model will be sufficient, but no essential change in the relationships which will be discussed here would result if a translation were made to a model based upon quantum-mechanics. When an electric field is impressed upon a dielectric the positive and negative charges in its atoms and molecules are displaced in opposite directions. The dielectric is then said to be in a polarized ' Cf., for example, Gurney, "Elementary Quantum Mechanics," Cambridge (1934); (Herzfeld, "The Present Theory of Electrical Conduction," Electrical Engi- neering, April 1934. DIELECTRIC PROPERTIES OF INSULATING MATERIALS 495 condition, and since the motion of charges of opposite sign in opposite directions constitutes an electric current there is what is called a polarization current or charging current flowing while the polarized condition is being formed. For the case of a static impressed field a charging current flows in the dielectric only for a certain time after application of the field, the time required for the dielectric to reach a fully polarized condition. If the material is not an ideal dielectric, but contains some free ions, the current due to a static impressed field does not fall to zero but to a constant value determined by the conductivity due to free ions. More important than the static is the alternating current case, where the potential is continually varying and where, consequently, there must be a continuously varying current. The dielectric behavior of different materials under different con- ditions is reflected in the characteristics of the charging or polariza- tion currents, but since polarization currents depend upon the applied voltage and the dimensions of condensers it is inconvenient to use them directly for the specification of the properties of materials. Eliminating the dependence upon voltage by dividing the charge by the voltage, we have the capacity (C = Q/V); and the dependence upon dimensions may be eliminated by using the dielectric constant, defined as e = C/Co, where C is the capacity of the condenser when the dielectric material is between its plates and Co is the capacity of the same arrangement of plates in a vacuum. The dielectric constant is then a property of the dielectric material itself. The term "dielectric polarization" is used to refer to the polarized condition created in a dielectric by an applied field of either constant or varying intensity. The polarizability is one of the quantitative measures of the dielectric polarization; it is defined as the electric moment per unit volume induced by an applied field of unit efi"ective intensity. Another quantitative measure of the dielectric polarization is the molar polarization; this is a quantity which is a measure of the polarizability of the individual molecule, whatever the state of ag- gregation of the material. The concept of polarizability is as fundamental to, and plays about the same role in, the theory of dielectric behavior as does the concept of free ions in the theory of electrolytic conduction. Just as the con- ductivity of a material is a measure of the product of the number of ions per unit cube and their average velocity in the direction of a unit applied field, so the polarizability is a measure of the number of bound charged particles per unit cube and their average displacement in the direction of the applied field. 496 BELL SYSTEM TECHNICAL JOURNAL In the early Investigations of dielectrics two distinct types of charg- ing current were recognized, the one in which the charging or dis- charging of a condenser occurred practically instantaneously and the other in which a definite and easily observable time was required. A charge accumulating in a condenser in an unmeasurably short time was variously referred to as the instantaneous charge or geometric charge or the elastic displacement. The current by which this charge is formed was called the instantaneous or geometric charging current, and similarly the terms instantaneous dielectric constant or geometric dielectric constant were used to describe the property of the medium giving rise to the effect between the condenser plates. An even wider variety of names has been used for the part of the charge which formed or disappeared more slowly. Among these are residual charge, reversible absorption, inelastic displacement, viscous displacement and anomalous displacement. The modern theory still recognizes these two distinct types of condenser charges and charging currents but the simple descriptive designations rapidly-forming or instantaneous polarizations and slowly-forming or absorptive polarizations will be adopted here, as they seem sufficient and to be preferred to terms which have more specialized connotations as to the mechanism upon which the behavior depends. The properties of these two types of charging currents and the dielectric polarizations corresponding to them appear prominently in the theories of dielectric behavior. The total polarizability of the dielectric is the sum of contributions due to all of the different types of displacement of charge produced in the material by the applied field. Constitutive forces characteristic of the material determine both the magnitude of the polarizability and the time required for it to form or disappear. The quantitative measure of the time required for a polarization to form or disappear is called the relaxation-lime. In the following a description will be given of the physical processes involved in the formation of dielectric polari- zations, indicating the effect of chemical and physical structure upon the two quantities, magnitude and relaxation-time, which determine many of the properties of dielectric polarizations of the slowly-forming or absorptive type. The magnitude of the polarizability ^ of a dielectric can be expressed in terms of a directly measurable quantity, the dielectric constant e, by the relation 47r (e -f 2) It is sometimes convenient to use the polarizability and the dielectric DIELECTRIC PROPERTIES OF INSULATING MATERIALS 497 constant interchangeably in the quaUtative discussion of the magnitude of the dielectric polarization. In dealing with alternating currents the fact that polarizations of the absorptive type require a time to form which is often of the same order of magnitude as, or greater than, the period of the alternations, results in the polarization not being able to form completely before the direction of the field is reversed. This causes the magnitude of the dielectric polarization ELECTRICAL FREQUENCIES OPTICAL FREQUENCIES Fig. 1 — Schematic diagram of variation of dielectric constant and dielectric absorption with frequency for a material having electronic, atomic, dipole and interfacial polarizations. and dielectric constant to decrease as the frequency of the applied field increases. An example of this variation of the dielectric constant with frequency is shown in the radio and power frequency section of the curve plotted in Fig. 1. It is often convenient to refer to the mid- point of the decreasing dielectric constant-frequency curve as the relaxation-frequency; this frequency fm is very simply related to the relaxation- time r, for the theory of these effects shows that/^ = l/27rr. 498 BELL SYSTEM TECHNICAL JOURNAL Various types of polarization can be induced in dielectrics: There should be an electronic polarization due to the displacement of electrons with respect to the positive nuclei within the atom; an atomic polari- zation due to the displacement of atoms with respect to each other in the molecule and in certain ionic crystals, such as rock salt, to the displacement of the lattice ions of one sign with respect to those of the opposite sign; dipole polarizations due to the effect of the applied field on the orientations of molecules with permanent dipole moments; and finally interfacial (or ionic) polarizations caused by the accumula- tion of free ions at the interfaces between materials having different conductivities and dielectric constants. Electronic Polarizations A classification of dielectric polarizations into rapidly-forming or instantaneous polarizations and slowly-forming or absorptive polariza- tions has been made. Instantaneous polarizations may be thought of as polarizations which can form completely in times less than say 10~^° seconds, that is, at frequencies greater than 10'" cycles per second or wave-lengths of less than 1 centimeter, and so beyond the range of conventional dielectric constant measurements. The electronic polari- zations are due to the displacement of charges within the atoms, and are the most important of the instantaneous polarizations. The polarizability per unit volume due to electronic polarizations may be considered to be a quantity which is proportional to the number of bound electrons in a unit volume and inversely proportional to the forces binding them to the nuclei of the atoms. The effect of number of electrons and binding force is illustrated by a comparison of the values for the polarizability per unit volume of different gases; for the number of molecules per unit volume is inde- pendent of the composition of the gas. Thus, although a c.c. of hydrogen with two electrons per molecule has the same number of electrons as a c.c. of helium, which is an atomic gas with two electrons per atom, the quantity e — 1, that is the amount by which the di- electric constant is greater than that of a vacuum, is nearly four times as large for hydrogen as for helium. This shows that in hydrogen the electrons are in effect less tightly bound to the nucleus than in helium, resulting in a larger induced polarization. Nitrogen has a larger dielectric constant than either hydrogen or helium because it has 14 electrons per molecule. Some of these are tightly bound as in helium and some are more loosely bound as in hydrogen. The dielectric constant of liquid nitrogen is 1.43, which is much higher than the value 1.000600 for the gas. This is due to the fact DIELECTRIC PROPERTIES OF INSULATING MATERIALS 499 that the number of molecules, and consequently of bound charges, per unit volume is much greater in the liquid than in the gas. How- ever, the molar polarization, a quantity which is corrected for varia- tions in density, is the same for liquid as for gaseous nitrogen. The time required for the applied field to displace the electrons within an atom to new positions with respect to their nuclei is so short that there is no observable effect of time or frequency upon the value of the dielectric constant until frequencies corresponding to absorption lines in the visible or ultra-violet spectrum are reached. For con- venience in this discussion the frequency range which includes the infra-red, visible and ultra-violet spectrum will be called the optical frequency range while that which includes radio, audio and power frequencies will be called the electrical frequency range. For all fre- quencies in the electrical range the electronic polarization is indepen- dent of frequency and for a given material contributes a fixed amount to the dielectric constant, but at the frequencies in the optical range corresponding to the absorption lines in the spectrum of the material, the dielectric constant, or better the refractive index, changes rapidly with frequency, and absorption appears. (The justification for using refractive index n and dielectric constant e interchangeably for the qualitative discussion of the properties of dielectric polarizations fol- lows from the relation, e = n^, which is known as Maxwell's rule. This is a general relationship based upon electromagnetic theory and is applicable whenever e and n are measured at the same frequency no matter how high or low it may be.) The electronic polarization of a molecule may be regarded as an additive property of the atoms or of the atomic bonds in the molecule, and may be calculated for any dielectric of known composition with sufficient accuracy for most purposes. Within any one chemical class of compounds such as, for example, the saturated hydrocarbons or their simple derivatives, in which all of the bonds are C — H, C — CorC — X, the calculated values agree with the measured to within a few per cent. For other classes of compounds — for example, benzene, in which there are both single and double bonds such calculations must be corrected for the fact that some of the valence electrons have their binding forces and hence their polarizabilities altered in the double bond as compared to the single bond. Such values of electronic polarization, usually called atomic refractions, have been determined for all of the different types of bonds from the vast amount of experi- mental study of refractive indices of organic and inorganic compounds. In some materials the electronic polarization is the only one of importance. For example, in benzene the dielectric constant is the 500 BELL SYSTEM TECHNICAL JOURNAL same at all frequencies in the electrical range and is equal to the square of the optical refractive index. This must mean that the only polari- zable elements of consequence in CeHe are electrons which are capable of polarizing as readily in the visible spectrum, where the refractive index is measured, as at lower frequencies where dielectric constant is measured. The refractive index in the visible spectrum provides the means of determining the magnitude of electronic polarizations, for other types of polarization are usually of negligible magnitude when the frequency of the impressed field lies in the visible spectrum. For materials having only electronic polarizations the dielectric properties are very simply dependent upon the chemical composition and the temperature, and are independent of frequency in the electrical frequency range. In many materials, however, there are also other polarizations which can form at low frequencies but not at high ; these are characterized by more complex dielectric behavior. Atomic Polarizations Included among the polarizations which may be described as in- stantaneous by comparison with the order of magnitude of the periods of alternation of the applied field in the electrical frequency range are those arising from the displacement of the ions in an ionic crystal lattice (such as rock salt) or of atoms in a molecule or molecular lattice. In some few materials, for example the alkali halides, sufficient study has been made of the infra-red refractive index to provide data on the atomic polarizations, but for most substances little is known about them. What is known has in part been inferred from infra-red absorp- tion spectra and in part from the infra-red vibrations revealed by studies of the Raman effect. Atomic polarizations are distinguished from electronic polarizations by being the part of the polarization of a molecule which can be at- tributed to the relative motion of the atoms of which it is composed. The atomic polarizations may be attributed to the perturbation by the applied field of the vibrations of atoms and ions having their character- istic or resonance frequencies in the infra-red. Atomic polarizations may be large for substances such as the alkali halides and other in- organic materials, but are usually negligible for organic materials. The exact value of the time required for the formation of atomic polarizations is unimportant in the electric range of frequencies with which we are primarily concerned. The essential thing is that atomic polarizations begin to contribute to e(or n^) at frequencies below approximately 10^^ seconds — that is, in the near infra-red and that below about 10^" cycles per second, where the optical and electrical DIELECTRIC PROPERTIES OF INSULATING MATERIALS 501 frequency ranges merge, atomic polarizations contribute a constant amount to e(or w^) for a given material. The atomic polarization is determined as the difference between the polarization which is meas- ured at some low infra-red or high electric frequency and the electronic polarization as determined from refractive index measurements in the visible spectrum. The electronic and atomic polarizations are considered to comprise all of the so-called instantaneous polarizations; that is, the polariza- tions which form completely in a time which is very short as compared with the order of magnitude of the periods of applied fields in the electrical range of frequencies. The Debye Orientational Polarization The remaining types of polarization are of the "absorptive" kind, characterized by relaxation-times corresponding to "relaxation- frequencies" in the electrical range of frequencies. These polariza- tions include the important type which is due to the effect of the applied field on the orientation of molecules with permanent electric moments, the theory of which was developed by Debye. Among the other possible polarizations of the absorptive type are those due to inter- facial effects or to ions which are bound in various ways. Debye,^ in 1912, suggested that the high dielectric constant of water, alcohol and similar liquids was due to the existence of permanent dipoles in the molecules of these substances. The theory which Debye based upon this postulate opened up a new field for experimental investigation by providing a molecular mechanism to explain dielectric behavior which fitted into and served to confirm the widely held views of chemical structure. Debye postulated that the molecules of all substances except those in which the charges are symmetrically located possess a permanent electric moment which is characteristic of the molecule. In a liquid or gas these molecular dipoles are oriented at random and therefore the magnitude of the polarization vector is zero. When an electric field is applied, however, there is a tendency for the molecules to align themselves with their dipole axes in the direction of the applied field, or, put in another way, to spend more of their time with their dipole axes in the direction of the field than in the opposite direction. This dipole polarization is superimposed upon the electronic and atomic polarizations which are also induced by the field. The theory as developed by Debye accounts for the ob- served difference between the temperature and frequency dependence of the dipole polarizations and the instantaneous polarizations. While the latter are present in all dielectrics, the dipole polarizations can 2 P. Debye, Phys. Zeit., 13, 97, (1912); Verh. d. D. phys. Ges., 15, 777 (1913). 502 BELL SYSTEM TECHNICAL JOURNAL occur only in those made up of molecules which are electrically asymmetrical. Polar molecules (that is molecules with permanent electric moments) are, by definition, those in which the centroid of the negative charges does not coincide with the centroid of the positive charges, but falls at some distance from it. All materials must be classed either as polar or non-polar, the latter class including those which are elec- trically symmetrical. Some simple examples of non-polar molecules METHYL CHLORIDE (CH3 Cl) Fig. 2 — Methane and carbon tetrachloride are non-polar molecules each having four equal vector moments whose sum is zero. Methyl chloride is polar because the sum of the vector moments is not zero. are H2, N2, O2, CH4, CCI4 and CeHe. In these molecules each C — H, C — Cl or other bond may be regarded as having a vector dipole mo- ment of characteristic magnitude located in the bond. Where the sum of these vector moments is zero the molecule will be non-polar. Both CH4 and CCI4 meet this requirement but CH3CI is polar because the C — Cl vector moment is considerably greater than the resultant of the three C — H vectors. (See Fig. 2.) Polar molecules are the rule and non-polar the exception. DIELECTRIC PROPERTIES OF INSULATING MATERIALS 503 In the discussion of dipole polarizations it has frequently been pointed out that non-polar materials usually obey the general relation- ship i = n^ whereas for polar materials such as H2O, NH3 and HCl this rule is apparently not obeyed. Water, for example, has n^ = 1.7 and e = 78. This apparent discrepancy arises because the refractive inde.x as measured in the visible spectrum is usually compared with the dielectric constant as measured in the electric range of frequencies. Non-polar materials usually have only electronic polarizations and these can form both in the optical and in the electrical frequency ranges, but the dipole polarizations can form and contribute to the dielectric constant only in the electrical frequency range; this is the most frequent source of the above mentioned discrepancy. The general relationship t = v} should apply for any material at any fre- quency provided e and n are measured at the same frequency. The refractive index of water when measured with electric waves,^ for example, at a million cycles, is found to be slightly less than 9, the square of which agrees very well with the observed value e = 78. However, it does not always follow that when e > w^ the molecules of which the material is composed have permanent dipole moments, for this condition can also result from the presence of any slowly-forming or absorptive polarization or of a large atomic polarization. Experi- mental investigations based upon the Debye theory have shown, however, that in the case of water and many other familiar compounds the orientation of dipole molecules actually accounts for the high dielectric constant. The Debye theory shows that the magnitude of the dipole polariza- tion of a material is proportional to the square of the electric moment of the molecule, which, as has been pointed out, may be regarded as the vector sum of a number of constituent moments characteristic of the individual atoms or radicals of which the molecule is composed, or alternatively, of the bonds which bind these atoms into molecules or more complex aggregates. The very great amount of experimental study of the Debye theory has shown that the NO2 and CN groups have the largest group moments while CO, OH, NH2, CI, Br, I and CH3 have progressively smaller group moments. The value 34 for the dielectric constant of nitrobenzene (CeHsNOa), as against 5.5 for chlorobenzene (CeHsCl), 2.8 for methyl benzene (C6H5CH3) and 2.28 for benzene (CeHe), which is non-polar, are evidence of the large differences in the magnitudes of these group moments and the large part that dipole moments can play in determining the dielectric constant. 3 Drude, "Physik des Aethers," Stuttgart (1894), p. 486. 504 BELL SYSTEM TECHNICAL JOURNAL Another point regarding molecular structure shown by such studies is that it is not only the presence of polar groups in the molecule but also their position which determines the electric moment of the mole- cule. This is nicely illustrated by the dichlorobenzenes, of which there are three isomers. As is shown in Fig. 3, ortho-dichlorobenzene, having the two substituent groups in adjacent positions, is the most asymmetrical of the three compounds, and consequently has the high- Fig. 3 — Ortho dichlorobenzene being the more asymmetrical has a higher electric moment than the meta isomer; the para isomer which is symmetrical has zero electric moment. est electric moment, /x = 2.3. The meta compound has about the same moment as monochlorobenzene, /x = 1.55. The para compound, however, is symmetrical and has zero electric moment because the CI atoms are substituted on opposite sides of the benzene ring so that their vector moments cancel. These values of electric moment are reflected in the values of dielectric constant which are respectively 10, 5.5 and 2.8 for the three isomeric dichlorobenzenes. DIELECTRIC PROPERTIES OF INSULATING MATERIALS 505 Dielectric studies of this kind have also shown, for example, that H2O is not a symmetrical linear molecule, H — O — H, but rather a triangular structure 0<( . CO2 on the other hand, being non-polar, is determined to be a linear molecule O = C = O. Thus, dielectric measurements interpreted by the Debye theory have become estab- lished as one of the standard means of studying molecular structure. Since dipole polarizations depend upon the relative orientations of molecules, rather than upon the displacement of charges within the atom or molecule, the time required for a polarization of this type to form depends upon the internal friction of the material. Debye expressed the time of relaxation of dipole polarizations in terms of the internal frictional force by the equation: where ^ is the internal friction coefficient, 7/ is the coefficient of viscosity, a the radius of the molecule and T the absolute temperature.^ This latter expression, because it depends on Stokes' law for a freely falling body, is rigidly applicable only to gases or possibly to dilute solutions of polar molecules in non-polar solvents in which the polar molecules are far enough apart that they exert no appreciable influence on each other. Applying this equation to the calculation of the relaxation-time of the orientational polarizations in water at room temperature we obtain T = lO""^** seconds, assuming a molecular radius of 2 X 10~^ cm. and taking the viscosity as 0.01 poises.* The relaxation-frequency corre- sponding to this relaxation-time is about 1.6 X 10^ cycles/sec, agreeing with the results of experimental studies on water which show that in the range of frequencies extending from 10^ to 10^^ cycles the dielectric constant decreases from its high value to a value approxi- mately equal to the square of the refractive index. Thus the drop in dielectric constant occurs in the frequency range which corresponds to the calculated value of the relaxation-time. Similar experiments on dilute solutions of alcohols ^ in non-polar solvents yield values of r of about 10~^ seconds. The shortest relax- ation-times which dipole polarizations can have are probably not ^ P. Debye, "Polar Molecules," Chem. Cat. Co., 1929, p. 85. * The viscosity of a liquid in poises is given by the force in dynes required to maintain a relative tangential velocity of 1 cm. /sec. between two parallel planes in the liquid each 1 cm.^ in area and 1 cm. apart, the distance being measured normal to their surfaces. 6 R. Goldammer, Phys. Zeit., 33, 361 (1932). 506 BELL SYSTEM TECHNICAL JOURNAL much less than the order of 10~^^ seconds, since in general either the internal friction or the molecular radius of materials having polar molecules will be greater than those of water, resulting in longer relaxation-times. No long-time limit can be placed on the relaxation- times which dipole polarizations may have, for they are limited only by the values which the internal friction can assume. For materials, such as glycerine, which tend to become very viscous at low tempera- tures the time of relaxation of the dipoles may be a matter of minutes. Studies of the dielectric constant of crystalline solids, to be discussed in a later paper, show also that in some cases polar molecules are able to rotate even in the crystalline state, where the ordinary coefficient of viscosity has no meaning because the materials do not flow. In connection with the dielectric properties we are concerned only with the ability of the polar molecules to undergo rotational motion and it is likely that in these solids, which constitute a special class, the internal frictional force opposing rotation of the molecules is small even though the forces opposing translational motion may be very large. The particular equation for the calculation of the time of relaxation given above obviously does not apply to solids. In discussing the three types of polarizations which have been considered thus far, it has been pointed out that the magnitude of the dielectric constant depends upon the polarizability of the material. Each type of polarization makes a contribution to the dielectric constant if the measuring frequency is considerably below its relax- ation-frequency. However, if the frequency of the applied field used for measuring the dielectric constant is too high the presence of polarizations with low rela.xation-frequencies will not be detected. Thus the refractive index of water in the visible spectrum is 1.3 and therefore gives no evidence whatever of the presence of permanent dipoles. This is due to the fact that the H2O molecules do not change their orientations rapidly enough to allow fields which alternate in direction as rapidly as those of light to cause an appreciable deviation from the original random orientation which prevails in the absence of an applied field. The band of frequencies in which the dielectric constant decreases with increasing frequency because of inability of the polarization to form completely in the time available during a cycle, is called a region of absorption or of anomalous dispersion. The discussion of this characteristic of dielectric materials forms an important part of dielectric theory. The term anomalous dispersion is no doubt usually thought of in connection with the anomalous dispersion of light: when the refractive index of light decreases with increasing frequency the DIELECTRIC PROPERTIES OF INSULATING MATERIALS 507 material is said to display anomalous dispersion in the range of fre- quencies concerned. However, in a paper published in 1898 Drude ^ applied this term to the decrease of dielectric constant with increasing frequency in the electrical range of frequencies. The justification for this extension of the original application of the term is very direct for electromagnetic theory shows that the dielectric constant and the refractive index of a material are connected by the general relationship e = w^ whatever the frequency of the electromagnetic disturbance. As the dispersion of light by a prism is due to the variation of its re- fractive index with frequency, the use of the expression anomalous dispersion to refer to the decrease of dielectric constant with increasing frequency is consistent and has become generally accepted. Interfacial Polarizations The polarizations thus far considered are the main types to be expected in a homogeneous material. They depend upon the effect of the applied field in slightly displacing electrons in atoms, in slightly distorting the atomic arrangement in molecules and in causing a slight deviation from randomness in the orientation of polar molecules. The remaining types of polarization are those resulting from the heterogeneous nature of the material and are called interfacial polariza- tions. Interfacial polarizations must exist in any dielectric made up of two or more components having different dielectric constants and conductivities except for the particular case where €172 = 6271, 7 being the conductivity ^ and the subscripts referring to the two components. Heterogeneity in a dielectric may be due to a number of causes, and in the case of practical insulating materials is probably the rule rather than the exception. Impregnated paper condensers and laminated plastics are obvious examples of heterogeneous dielectrics. Paper is itself a heterogeneous dielectric, consisting of water and cellulose. In all probability the plastic resins are also heterogeneous, and cer- tainly so if they contain fillers. Ceramics, being mixtures of crystalline and glassy phases, are also heterogeneous. The simplest case of interfacial polarization is that of the two-layer dielectric, that is, a composite dielectric made up of two layers, the dielectric constants and conductivities of which are different. Max- well showed that in such a system the capacity was dependent upon the charging time. This is due to the accumulation of charge at the interface between the two layers, for this charge must flow through a ^ P. T)T\ide,Ann.d. Physik, 64, 131 (1898), "Zur Theorie der anomalien elektrischen Dispersion." * In this expression 7 represents the total a.c. conductivit>-, a quantity which depends on the frequency. 508 BELL SYSTEM TECHNICAL JOURNAL layer of dielectric whose resistance may be high enough that the inter- face does not become completely charged during the time allowed for charging. For the alternating current case this implies a decrease of capacity with increasing frequency, which is equivalent to the anoma- lous dispersion which has been described for the case of dipole polariza- tions. It should be particularly emphasized that the term anomalous dispersion describes a type of variation of dielectric constant with frequency which can be produced by a number of different physical mechanisms. The two-layer dielectric is of less interest than a generalization of this type of polarization which includes heterogeneous systems com- posed of particles of one dielectric dispersed in another. This type of heterogeneous dielectric is of considerable importance since such systems represent the actual structure of many practical dielectrics. Such a generalization of the two-layer dielectric has been made by K. W. Wagner ^ who developed the theory for the case of spheres of relatively high conductivity dispersed in a continuous medium of low conductivity. The conditions for the existence of an interfacial polarization are, as in the two-layer case, that 6172 + ^271, where the symbols have the significance just given. This type of polarization, which is variously referred to as an interfacial polarization, an ionic polarization and a Maxwell -Wagner polarization, shows anomalous dispersion like other absorptive polarizations. When the particle size is small as compared with the electrode separation it may be treated as a uniformly distributed polarization. The magnitude and time of relaxation of interfacial polarizations are determined by the differences in e and 7 of the two components. There is a widely prevalent opinion that this type of polarization always has such long relaxation-times as to be observed only at very low frequencies. While this is true for mixtures of very low-con- ductivity components, the general equations show that for the case where one component has a high conductivity — for example equal to that of a salt solution — the dispersion may occur in the radio frequency range. Several special types of interfacial polarization have been proposed to explain the dielectric properties of various non-homogeneous di- electrics where something regarding the nature of the inhomogeneity is known. The dielectric constant of cellulose, for example, receives a contribution from an interfacial polarization due to the water and dissolved salt which it contains. Experimental evidence indicates that an aqueous solution of various salts is distributed through the 9 K. W. Wagner, Arch. f. Elektrotechn., 2, pp. 374 and 383. DIELECTRIC PROPERTIES OF INSULATING MATERIALS 509 cellulose in such a way as to form a reticulated pattern which may correspond to the pattern formed by the micelles or to some feature of it. An interesting feature of this structure is that the conductance of the aqueous constituent can be changed by varying the moisture content or the salt content of the material and the efifect on the di- electric constant observed.^" Frequency Dependence of Dielectric Constant As has been pointed out, each of the different types of polarization may contribute to the dielectric constant an amount depending upon the polarizability and its time of relaxation. The upper curve in Fig. 1 shows schematically the variation of the dielectric constant (or of the square of the refractive index) for a hypothetical material possessing an interfacial polarization with relaxation-frequency in the power range, a dipole polarization with relaxation frequency in the high radio frequency range and atomic and electronic polarizations with dispersion regions in the infra-red and visible respectively. If polariza- bility were plotted, instead of e (or w^), the curves would be of the same general form but of different magnitudes, because of a relationship between the two given earlier. At the low-frequency side of Fig. 1, the dielectric constant curve has its highest value, usually called the static or zero-frequency dielectric constant. Here all of the polarizations have time to form and to contribute their full amount to the dielectric constant. With increasing frequency e begins to decrease as the relaxation-frequency of the interfacial polarization is approached and reaches a constant lower value (called the infinite-frequency dielectric constant) when the applied frequency is sufficiently above the relaxation-frequency of the polarization that it has not time to form appreciably. It is this decrease of e with frequency which is called anomalous dispersion. The horizontal arrows across the top of Fig. 1 indicate the frequency region in which the various types of polarizations indicated are able to form and contribute to the dielectric constant. At still higher frequencies we see that e again decreases as the relaxation-frequency of the dipole polarization is approached, and again reaches a constant lower value as the frequency becomes too high for the field to affect appreciably the orientation of dipoles. This second region of anomalous dispersion is similar to the first, which was due to interfacial polarizations. It has been shown as occurring at a higher frequency, but it should be emphasized that the frequency ranges chosen to illustrate anomalous dispersion in Fig. 1 " Murphy and Lowry, Jour. Phys. Chem., 34, 594 (1930). 510 BELL SYSTEM TECHNICAL JOURNAL are purely arbitrary. Anomalous dispersion due to dipole polariza- tions has been observed at power frequencies while that due to inter- facial polarizations has been observed at radio frequencies. The two types of polarizations may in fact give rise to anomalous dispersion in the same frequency range in a given dielectric. Proceeding to still higher frequencies in Fig. 1 other regions of dispersion appear in the infra-red and visible spectrum. These regions show a combination of normal optical dispersion, in which the dielectric constant, or better now the refractive index, increases with frequency, and anomalous dispersion in which it decreases. The dispersion in the visible range of frequencies is predominantly normal (anomalous dispersion being confined to relatively narrow frequency bands) whereas in the electrical range the reverse is true, normal dispersion not being observed ; the infra-red represents an intermediate region. Dipole and interfacial polarizations are not represented in the dispersion in the optical range, the dielectric constant (or refractive index) in the visible being due to electronic polarizations and in the infra-red to electronic and atomic polarizations. The curves plotted in Fig. 1 are merely schematic and the relative magnitudes of the different contributions to the dielectric constant are therefore arbitrary. However, experimental results indicate that the contribution eg of the electronic polarization to the dielectric constant is limited to values between 2 and 4 except for certain in- organic materials, since very few organic solids or liquids are known which have refractive indices in the visible spectrum which are greater than 2 or less than 1.4. The contribution e^ of atomic polarizations to the dielectric constant is in general small and is usually negligible, as has been indicated on the curve, although the possibility exists of special cases occurring in which the infra-red refractive indices are very high. The contributions tp and «/ of dipole and interfacial polarizations to the dielectric constant may vary greatly from one material to another, depending upon the symmetry of the molecule and the physical structure of the dielectric. From the above men- tioned limitations on the contribution to the dielectric constant which can be expected from electronic and atomic polarizations, it is apparent that the explanation of values of e higher than 3 to 4, at least in organic materials, requires the existence of some absorptive polarization such as arises from dipoles or interfacial effects. Thus all of the liquids which have high dielectric constants such as H2O (78), alcohol (24), nitrobenzene (34) have been shown to contain polar molecules. The lower part of Fig. 1 shows a maximum in the absorption for each type of dielectric polarization. The absorption, at least in the DIELECTRIC PROPERTIES OF INSULATING MATERIALS 511 electrical frequency range, is due to the dissipation of the energy of the field as heat because of the friction experienced by the bound charges or dipoles in their motion in the applied field in forming the polariza- tions. The theory of dispersion shows that the dielectric constant and absorption are not independent quantities but that the absorption curve can be calculated from the dielectric constant vs. frequency curve and vice versa. The absorption maximum is greatest for those materials showing the greatest change in dielectric constant in passing through the dispersion region. Thus a material having a high di- electric constant must have a large dielectric loss at the frequency at which e has a value half way between its low and high-frequency values. Though the quantum theory is necessary for the explanation of many optical and electrical phenomena a simple explanation, sufficient for our purposes, of the general form of the curves of dielectric constant vs. frequency in the infra-red and visible spectrum may be given in terms of the Lorentz theory of optical dispersion. In this theory the form of the dispersion curves depends upon the variation with frequency of the relative importance of the inertia of the typical electron and of the frictional forces and restoring forces acting upon it. For electronic polarizations the frictional or dissipative force is negligible, except in the narrow frequency interval included in the absorption band, and the inertia and restoring force terms predominate. For the atomic polarizations the frictional force is larger and the absorption region extends over a wider interval of frequencies. P'or dipole and inter- facial polarizations the influence of inertia is entirely negligible as compared with the frictional or dissipative forces so that in effect these polarizations may be thought of as aperiodically damped. Temperature Dependence of Dielectric Constant The dielectric constant of a material is a constant only in the ex- ceptional case. Besides the variation with frequency which has been considered the dielectric constant varies with temperature. Elec- tronic polarizations may be considered to be unaffected by the tempera- ture. The refractive index does indeed change with temperature but this is completely accounted for by the change of density, and the molar refraction is independent of temperature. The atomic and ionic vibrations are, however, affected by temperature, the binding force between ions or atoms being weakened by increased temperature. This factor of itself would yield a positive temperature coefficient for the atomic polarizations but the decrease in density with the increase in temperature acts in the opposite direction. The result is that calculation of the temperature coefficient of atomic polarizations 512 BELL SYSTEM TECHNICAL JOURNAL usually yields zero or slightly positive values. What experimental data there are indicate small positive temperature coefficients for atomic polarizations. One of the principal achievements of the Debye theory of dipole polarizations has been the manner in which it explains the large negative temperature coefficients of polarization of many liquids. Debye showed that the variation of polarization with temperature could be expressed by the relation P = A -{■ {BIT), in which the constant ^ is a measure of the instantaneous polarizations which are independent of temperature and 5 is a measure of the dipole polariza- tions. In a liquid or gas the molecules are continuously undergoing both translational and rotational motion, and the result of this thermal motion is to maintain a random orientation of molecules. The action of the electric field in aligning the dipoles is opposed by the thermal motion which acts as an influence tending to keep them oriented at random. As the temperature decreases, the thermal energy becomes smaller and the dipole polarization becomes larger, resulting in a negative temperature coefficient of dielectric constant. The effect of temperature upon interfacial polarizations has not been experimentally investigated to an extent at all comparable with that of dipole polarizations. However, interest in the interfacial or ionic type of polarization has increased considerably in the past few years, and it has applications of some importance. Among these is diathermy which is becoming of considerable importance as a thera- peutic agency. The foregoing qualitative description of the behavior of the di- electric constant and the type of information regarding molecular structure which has been derived from it will be followed in the next section by the derivation of some of the quantitative relationships which are common to all polarizations of the absorptive type. Variable Frequency Electric Circuit Theory with Application to the Theory of Frequency-Modulation By JOHN R. CARSON AND THORNTON C. FRY In this paper the fundamental formulas of variable frequency electric circuit theory are first developed. These are then applied to a study of the transmission, reception and detection of frequency modulated waves. A comparison with amplitude modulation is made and quantitative formulas are developed for comparing the noise-to-signal power ratio in the two modes of modulation. FREQUENCY modulation was a much talked of subject twenty or more years ago. Most of the interest in it then centered around the idea that it might afford a means of compressing a signal into a narrower frequency band than is required for amplitude modu- lation. When it was shown that not only could this hope not be realized,* but that much wider bands might be required for frequency modulation, interest in the subject naturally waned. It was revived again when engineers began to explore the possibilities of radio trans- mission at very short wave lengths where there is little restriction on the width of the frequency band that may be utilized. During the past eight years a number of papers have been published on frequency modulation, as reference to the attached bibliography will show. That by Professor E. H. Armstrong f deals with this subject in comprehensive fashion. In his paper the problem of discrimination against extraneous noise is discussed, and it is pointed out that important advantages result from a combination of wide frequency bands together with severe amplitude limitation of the received signal waves. His treatment is, however, essentially non- mathematical in character, and it is therefore believed that a mathe- matical study of this phase of the problem will not be unwelcome. This the present paper aims to supply by developing the basic mathe- matics of frequency modulation and applying it to the question of noise discrimination with or without amplitude limitation. The outstanding conclusions reached in the present paper, as regards discrimination against noise by frequency modulation, may be briefly summarized as follows: * See Bibliography, No. 1. t See Bibliography, No. 12. 513 514 BELL SYSTEM TECHNICAL JOURNAL (1) To secure any advantage by frequency modulation as distin- guished from amplitude modulation, the frequency band width must be much greater in the former than in the latter system. (2) Frequency modulation in combination with severe amplitude limitation for the received wave results in substantial reduction of the noise-to-signal power ratio. Formulas are developed which make possible a quantitative estimate of the noise-to-signal power ratio in frequency modulation, with and without amplitude limitation, as compared with amplitude modulation. It is a pleasure to express our thanks to several colleagues who have been helpful in various ways: to Dr. Ralph Bown who in a brief but very incisive memorandum, which was not intended to be a mathe- matical study, disclosed all the essential ideas of the quasi-stationary method of attack; to Mr. J. G. Chaffee,* who has been conducting experimental work on frequency modulation in these Laboratories for some years past, by means of which quantitative checks on the accuracy of some of the principal results have been possible; and to various associates, especially Mr. W. R. Bennett and Mrs. S. P. Mead, for detailed criticism of certain portions of the work. I In the well-known steady-state theory of alternating currents, the e.m.f. and the currents in all the branches of a network in which the e.m.f. is impressed involve the time / only through the common factor e'"' where i = V— 1 and co is the constant frequency. To this fact is attributable the remarkable simplicity of alternating current theory and calculation, and also the fact that the network is completely specified by its complex admittance Yiioi). Thus, if the e.m.f. is £g'"', the steady-state current is 7,3 = EY{ioi)e''^K (1) In the present paper we shall deal with the case where the frequency is variable, and write the impressed e.m.f. as E^xpli f'n{t)dt). (2) : r n{t)dt j . ^(t) will be termed the instantaneous frequency. This agrees with the usual definition of frequency when il is a constant; it is the rate of change of the phase angle at time /; and in addition the interval T between adjacent zeros of sin Xil{t)dt or cos J'^{t)dt is approximately 7r/i2(/) in cases of practical importance. * .See Bibliography, No. 11. VARIABLE FREQUENCY ELECTRIC CIRCUIT THEORY 515 Instead of dealing with an arbitrary instantaneous frequency ^{t) we shall suppose that Q{t) = CO + mW, (3) where co is a constant and ij.(t) is the variable part of the instantaneous frequency. In practical applications yu(/) will be written as \s(t) where X is a real parameter and the mean square value s^ of s{t) is taken as equal to 1/2. Other restrictions on ^t(/) will be imposed in the course of the theory to be developed in this paper. Fortunately these restrictions do not interfere with the application of the theory to important problems. The steady-state current as given by (1) varies with time in precisely the same way as the impressed e.m.f. When the frequency is variable this is no longer true. On the other hand, formula (1) suggests a "quasi-stationary" or "quasi-steady-state current" component, Igss, defined by the formula I,ss = E Y(i^) -expli C' ndt \ , (4) which corresponds exactly to (1) with the distinction that the ad- mittance is now an explicit function of time. We are thus led to examine the significance of I^ss as defined above and the conditions under which it is a valid approximate representation of the actual response of the network to a variable frequency electromotive force, as given by (2). We start with the fundamental formula of electric circuit theory.^ Let an e.m.f. F(t) be impressed at time / = 0, on a network of indicial admittance A{t); then the current /(/) in the network is given by /(/) = f^Fit - r)-A'{T)dT. (5) X Here A'(t) = dldt-A(t) and it is supposed that ^(0) = 0. (This restriction does not limit our subsequent conclusions and is introduced merely to simplify the formulas. Furthermore ^(0) is actually zero in all physically realizable networks.) Omitting the superfluous amplitude constant E we have F{1) = exp(i rndt) = exp ( iwt + i I iJLdt J , (6) ^ See J. R. Carson, "Electric Circuit Theory and Operational Calculus," p. 16. (7) (8) 516 BELL SYSTEM TECHNICAL JOURNAL F{t — t) — exp i{t — T)ui -}- i \ iidri \ = exp i(t — t)(jo -\- i \ fj-dri — i | ixdri L Jq J l-T = exp [^S2(/)]-exp — tcor — i \ lJ-{t — T\)dTx Substituting this expression in (5) for F{t — t) and writing exp ( - j r ix{t - Ti)dTi j = AI{t, t), we have for the current in the network / = e'-^^'^'- r Af(t, T)e-''''A'(T)dr. (9) We now split the integral into two parts, thus: J ft /^OO /•(» 0 Jo J t The second integral on the right represents an initial transient which dies away for sufficiently large values of time, t, while the infinite integral represents the total current, /, for sufficiently large values of /. We have therefore / = e'^^dt. r M{t, T)e-'^'A'{T)dT + It (10) Jo = F(*co, /)e'^«''' + It, where M(t, T)e-'-'A'(r)dr. (11) 0 The transient current,^ It, is then given by /j, = g'-y^-i^ r M{t, r)e-''^'A'{T)dT. (12) The foregoing formulas correspond precisely with the formulas for a constant frequency impressed e.m.f. ; these are I.s = e'"' r e-'-^A'{T)dr, Jo (10a) ^Hereafter the transient term It of (10) will be consistently neglected and the symbol / will refer only to the quasi-stationary current. VARIABLE FREQUENCY ELECTRIC CIRCUIT THEORY 517 FM = r e-'^^A'{T)dT, (Ua) Jo It = e' (r)dT, (12a) to which the more general formulas reduce when ij. — 0 and conse- quently M — \. We have now to evaluate Y(iio, t) as given by (11). We shall assume tentatively, at the outset, that ;u = \s{t) has the following properties : \s{t) <, (33) (j) = ojcT + wr + /3(co) + dc\ ^(0) = ^'(0) = 0, so that / = E exp {ioicf + id') r I Y{ioic + ^"co) |e-^^(")E(*"w)e''"'Vw, (34) 1/ — 00 where /' = / — r is the "retarded" time and 6' = d — dc. Formula (34) is identical with (25) but is expressed in the "retarded" time. Now we can expand the function I F(t'co, + ^)|e-^^("> in powers of w ; thus where (^ 1 + co^J I F(ic..)| + E r„(co.)co", rnM =-,\^\ Y{io:c + ic^) 1 e-^^^-) I nl [ dcoc J u =0 522 BELL SYSTEM TECHNICAL JOURNAL and by substitution in (34) we get I = E&^p(i r ^{T)dT + id'\ X I ( 1 + ^s(n~) I Y(ico.)\ + E^CnCO , (35) which corresponds precisely with (29) except that it is expressed in terms of the retarded time t'. If the transducer introduces a large phase delay, (35) may be much more rapidly convergent than (29) and should be employed in preference thereto. Corresponding to (30) we may write F(ico, + ic.)6-^-^(") = U^^^\\ Y(iu>,) I + R, which defines the remainder. Then I = Eexpli r ndr + id' where + E exp (ico/ + id')D{t'), (36) D{t') ^ r R(coc,co)-F(icc)e-''^''do^. (37) iJ — CO Formulas (36) and (37) correspond precisely with (31) and (32) and the same remarks apply. II The foregoing will now be applied to the Theory of Frequency Modulation. A pure frequency modulated wave may be defined as a high frequency wave of constant amplitude, the "instantaneous" frequency of which is varied in accordance with a low frequency signal wave. Thus PF = exp q coc/ + X s(t)dt I Jo (38) is a pure frequency modulated wave. Here coc is the constant carrier frequency and s{t) is the low frequency signal which it is desired to transmit. X is a real parameter which will be termed the modulation index. The "instantaneous" frequency is then defined as It is convenient to suppose that s(t) varies between ± 1; in this case VARIABLE FREQUENCY ELECTRIC CIRCUIT THEORY 523 the instantaneous frequency varies between the limits OJc ± X. In all cases it will be postulated that X <> coa. We shall now examine in more detail the concept of "instantaneous" frequency and the conditions under which it has physical significance. The instantaneous frequency is, as stated, coc + \s(t) ; a steady-state analysis is of interest and importance. To this end we suppose s(t) = cos o)t so that oj is the frequency of the signal. Then the wave (38) may be written ^iwct ) ^QQ I - sin wt ) -\- i sin I - sin cot y > , and, from known expansions, 00 W ^ Y. /„(X/co)g'("'+"")', (40) n=— 00 where /„ is the Bessel function of the first kind. Thus the frequency modulated wave is made up of sinusoidal components of frequencies Wc zt WW, W = 0, 1, 2, • • •, CO. If X/oj >>> 1 (the case in which we shall be interested in practice) the terms in the series (40) beyond n = X/co are negligible; this follows from known properties of the Bessel functions. In this case the frequencies lie in the range COc ± nco = OJc ± X, 524 BELL SYSTEM TECHNICAL JOURNAL which agrees with the result arrived at from the idea of instantaneous frequency. On the other hand, suppose we make X so small that X/co (57) \ wi /[ \coi -\- \ cos a -sit) / J ' or, to a first order, 1+ — cos a- sit) -\- l^^sin' a- s'{t). (58) coi Z coi The second term is the recovered signal and the third term is the first order non-linear distortion. Inspection of the foregoing formulas shows at once that, for detection by straight rectification, the following conditions should be satisfied: (1) X/wi must be less than unity. (2) The terminal network should be as nearly as possible a pure reactance to make the phase angle a as nearly zero as possible. 528 BELL SYSTEM TECHNICAL JOURNAL (3) To minimize both linear and non-linear distortion it is necessary that the sequence A, (IV (1- be rapidly convergent from the start. The first term of (58) is simply direct current and has no significance as regards the recovered signal. When we come to consider the problem of noise in the next section, we shall find that its elimination is important. This can be efi'ected by a scheme which may be termed balanced rectification. Briefly described the scheme consists in termi- nating the transducer in two frequency detectors ji and y^ in parallel ; these are so adjusted that 3'i(icoc) = — y^iiooe) and dyi/dc^c = dyz/dojc. oji is therefore of opposite sign in the two frequency detectors. The rectified outputs of the two parallel circuits are then differentially combined in a common low frequency circuit. Corresponding to (58), the resultant detected output is 2 — cos a- sit). (59) This arrangement therefore eliminates first order non-linear distortion, as well as the constant term. Rectification is the simplest and most direct mode of detection of frequency-modulated waves. However, in connection with the problem of noise reduction other methods of detection will be considered. Note As a specific example of the foregoing let the terminal frequency detector, specified by the admittance y{iui), be an oscillation circuit consisting simply of an inductance L in series with a capacitance C. Then /. x ■ [C COJOJR where wr^ = l/LC. Then, if ojc/cor is nearly equal to unity, that is, if we have approximately, Wfi = (1 + 5)coc, |5|«1, J_ ^ n\ y{ioic) = 7^ ZCOR — iOc VARIABLE FREQUENCY ELECTRIC CIRCUIT THEORY 529 Formula (42) thus becomes I = yiiooc) • F(«a)c) -exp ii I ^dtj-l 1+ ^' + ^' }• (cOiJ — 03 c)^ In order that the distortion shall be small it is necessary that X <3C \WR — COc\. If the two networks yi and y^ are oscillation circuits so adjusted that Ci/Li = C21L2, cofi^ = (1 + 5)co. = I/VlIG, Wfij = (1 — d)cOc = IHL2C2, then the combined rectified output of the two parallel circuits is proportional to X'J j^ C3 j^ C5 1^ "T 7^^ "T^ "T 7T TS -!-•••• 5-co, ' (5-0;^)' (5-co,)5 Thus the constant term and the first order distortion are eliminated in the low frequency circuit. IV The most important advantage known at present of frequency- modulation, as compared with ow;^/*7z^e-modulation, lies in the possi- bility of substantial reduction in the low frequency noise-to-signal power ratio in the receiver. Such reduction requires a correspondingly large increase in the width of the high frequency transmission band. For this reason frequency-modulation appears to be inherently restricted to short wave transmission. In the discussion of the theory of noise which follows, it is expressly assumed that the high frequency noise is small compared with the high frequency signal wave. Also ideal terminal networks, filters and detectors are postulated. In view of the assumption of a low noise power level, the calculation of the low frequency noise power in the receiver proper can be made to depend on the calculation of the noise due to the typical high fre- quency noise element -4„exp {iwct + *Wn^ + iQ^- (60) 530 BELL SYSTEM TECHNICAL JOURNAL Corresponding to the noise element (60), the output of the ideal frequency detector is - i\ r sdt\\. (61) Since the expression exp ( iwnt -\- idn — i\ i sdt ] occurs so frequently in the analysis which is to follow, it is convenient to adopt the notation fin = W„ — \s(t), JQ,ndt = Wnt — X I 0 Jq sdt. (61a) With this notation and on the assumption that ^„ ower for the frequency interval coi < co„ < C02 is, by the Fourier integral energy theorem, ' dcCn=- (C02 - C0i)iV2. (6b) The Fourier integral energy theorem states that, if in the epoch 0 < ^ ^ r, the function /(/) is representable as the Fourier integral /(/) =- r F(o:)-cos (oit + d(c^))do}, Ob) VARIABLE FREQUENCY ELECTRIC CIRCUIT THEORY 537 then (Sb) Replacing (46) by (5b) to take care of the distributed noise, the noise term of {3b) becomes cos f X / 5C?M • — I (OJO + C0„ + IJLS)- cos {oint + 9n)d0}n + sin ( X I 5C?/ j • — I (coo + con + iJLs) -sin (co„/ + dnjdcon. {%) Now this noise in the low frequency circuit is passed through a low pass filter, which cuts off all frequencies above coa. Wo is the maximum essential frequency in the signal s(t). It is therefore necessary to express (96) as a frequency function before calculating the noise power. To this end we write the Fourier integrals ( X r sdn = - n Fc cos {oit + do)doi, (106) cos sm (\Csdt\ = -CF, sin (co/ + e,)doi. (116) We note also that ''^ F, cos {oit + dM<^, (126) A fxs • cos ( X I ^'^^ ) ~ \'Tf sii^ ( ^ I sdt\ _ 1 r";. ~ ""Jo M5 • sin / X I ^^^] — ~ \^f cos ( ^ I sdt\ = - f" ^ F, sin (co/ + dc)dui. (136) Substituting (106), (116), (126) and (136) in (96) and carrying through straightforward operations, we find that the noise is given by 2-2 I Fpdw j I Wo + co„ + -CO j COS ((co — C0„)/ + Gp)d(X>n N r* /^-(c.-a,o) / ^ \ + Tr^ I -^m^W I COo + W„ — -CO COS ((cO + OoJ/ + Qm)du>n, ^■^ Jo J-(.+.,) V ^ / (146) ^See "Transient Oscillations in Electric Wave Filters," Carson and Zobel, B. S. T. J., July, 1923. 538 BELL SYSTEM TECHNICAL JOURNAL where F^^ = FJ" + F,' + 2FcFs cos (dc - 6^), (156) FJ = Fo^ + F32 - 2FcF, cos {do - e,). (16&) The limits of integration of w„ are determined by the fact that, CO — con in the first integral of (146) and w + co„ in the second, must lie between ± coai all other frequencies are eliminated by the low pass filter. From formula (146) and the Fourier integral energy theorem, the noise power Pn is given by JTN = . ^rp I Pp-do) I I COo + C0„ + - CO 1 doOn t/0 i/oj— w^ \ ' + ;r"^ I -^m^^^ I OJo + C0„ - -CO (/C0„. (176) 4T^rj^ J-(co+co„) V ^ ^ Integrating with respect to co„, we have Pn = ^ I cfcof [(coo + (1 + '^)co)2 + ico„2]F^2 + [(coo - (1 + ^)C0)'^ + |C0„2]F„2| ^ (18^,) where v = /x/X. Replacing Fp^ and Fm^ in (186) by their values as given by (156) and (166), we get P^=-^ \ ('^O' + (1 + VY^' + \^a'){F-' + F.')do: + 4-^ (1 + v)cooo^FcFs cos (0, - 0,)c?co. (196) 'r ^ Jo To evaluate (196) we make use of the formulas, derived below c^ + F/)do: = 1. (206) H''"' -^ rco2(F.2 + F.2)^co = XV = Ps, (216) wFcFs cos (^c - ^.)^co -^ 0 as r -^ 00 . (226) Substitution of (206), (216), (226) in (196) gives for large values of T Pn = (W + coo^ + (1 + v)2X2?)co„iV2. (236) Here, for convenience, we have replaced N-Jtv^ of (196) by N~, so that N^ of (236) may be defined and regarded as the high frequency noise power level. VARIABLE FREQUENCY ELECTRIC CIRCUIT THEORY 539 It remains to establish formulas {20b), (21b) and (22b). From the defining formulas (lOb) and (lib) and the Fourier integral energy theorem, we have — I FcMo) = y, I cos^ ( X I sdt j dt, -y I F,-d<^ ^ T i ^^^^ ( ^ r ^(/n dt. (24b) Adding we get (206). Now differentiate (106) and (116) with respect to t and apply the Fourier integral energy theorem ; we get -^ / "" ic^Fc-do: = Y^ r^ ^-s^ sin2 ( X T sdt \ dt, —^ j (ji^FM^Ji = -^ I X"-J"" COS" ( X j sdt ""Tjo ^Jo \ Jo (256) and, by addition, we get (216). To prove (226) we note that (1 + ijls) cos sdt r-)-^^-(\f = cos ( X I sdt]-\- sdt -;r[ Fc cos (oot -\- dc) -{- - 00 Fs COS (ut + 9s) X i^c^ + + 2 ^ coF.F, cos (9c - ds) X 1/2 cos (co/ + )(/co. (266) Consequently, by the Fourier integral energy theorem, r (1 + ns)^ cos2 ( X r sdt\dt ^ r r F.2 + (^ y'co-7^.2 +2^0,^,7^, cos (^^ - ^s) i_ r^ (fco (276) and 1 r^ Tp \ fjiS- cos- ( X I sdt ] dt ^T\t)l coFcF, COS (0c - ^O^'^- (286) 540 BELL SYSTEM TECHNICAL JOURNAL By simple transformations (286) becomes 1 r" -^ oiFcFs cos {dc — Qs)di>: ^ Xs + — sin ( 2X I sdt \ 0 as r ^ 00 , (296) since by hypothesis s = 0. We note for reference that -^r PcFs sin {do - eM^ = 2T f ^^" ( ^^ f ^^^ ) '^^' ^^^^^ Bibliography 1. Carson, J. R., "Notes on the Theory of Modulation," Proc. I. R. E., 10, pp. 57-64, Feb.,..1922. 2. Roder, H., "Uber Frequenzmodulation," Telefunken-Zeitung, 10, pp. 48-54, Dec, 1929. 3. Heilmann, A., "Einige Betrachtungen zum Problem der Frequenzmodulation," Elek. Nach. Tech., 7, pp. 217-225, June, 1930. 4. Van der Pol, B., "Frequency Modulation," Proc. I. R. E., 18, pp. 1194-1205, July, 1930. 5. Ecicersley, T. L., "Frequency Modulation and Distortion," Exp. Wireless and Wireless Engg., 7, pp. 482-484, Sept., 1930. 6. Runge, W., "Untersuchungen an amplituden- und frequenz-modulierten Send- ern," Elek. Nach. Tech., 7, pp. 488-494, Dec, 1930. 7. Roder, H., "Amplitude, Phase and Frequency-Modulation," Proc. I. R. E., 19, pp. 2145-2175, Dec, 1931. 8. Andrew, V. J., "The Reception of Frequency Modulated Radio Signals," Proc. I. R. E., 20, pp. 835-840, May, 1932. 9. Barrow, W. L., "Frequency Modulation and the Effects of a Periodic Capacity Variation in a Non-dissipative Oscillatory Circuit," Proc. I. R. E., 21, pp. 1182-1202, Aug., 1933. 10. Barrow, W. L., "On the Oscillations of a Circuit Having a Periodically Varying Capacitance; Contribution to the Theory of Nonlinear Circuits with Large Applied Voltages," Proc. I. R. E., 22, pp. 201-212, Feb., 1934, also M. I. T. Serial 97, Oct., 1934. 11. Chaffee, J. G., "The Detection of Frequency-Modulated Waves," Proc. I. R. E., 23, pp. 517-540, May, 1935. 12. Armstrong, E. H., "A Method of Reducing Disturbances in Radio Signaling by a System of Frequency-Modulation," Proc. I. R. £., 24, pp. 689-740, May, 1936. 13. Crosby, M. G., "Frequency Modulation Propagation Characteristics," Proc. I. R. E., 24, pp. 898-913, June, 1936. 14. Crosby, M. G., "Frequency-Modulated Noise Characteristics," Proc. I. R. E., 25, pp. 472-514, April, 1937. 15. Roder, H., "Noise in Frequency Modulation," Electronics, 10, pp. 22-25, 60, 62, 64, May, 1937. Irregularities in Broad-Band Wire Transmission Circuits By PIERRE MERTZ and K. W. PFLEGER The efifects of inhomogeneities along the length of a wire trans- mission circuit are considered, affecting its use as a broad-band transmission medium. These inhomogeneities give rise to reflec- tions of the transmitted energy which in turn cause irregularities in the measured sending or receiving end impedance of the circuit in its overall attenuation, and in its envelope delay. The irregu- larities comprise departures of the characteristic from the average, in an ensemble of lines, or departures from a smooth curve of the characteristic of a single line when this is plotted as a function of frequency. These irregularities are investigated quantitatively. TX riRE transmission circuits in their elementary conception are ^ ^ considered as perfectly uniform or homogeneous from end to end. Actually, of course, they are manufactured in comparatively short pieces and joined end to end, and there is a finite tolerance in the deviation of the characteristics of one piece from those of the next and also from one part of the same piece to another. A real transmission circuit therefore has a large number of irregularities scattered along its length which reflect wavelets back and forth when it is used for the propagation of a signal wave. When a cable pair, coaxial conductor, or similar medium is used for broad-band transmission it is important to know how these irregularities influence the transmission character- istics of the medium. The transmission characteristics which will be studied are the im- pedance, the attenuation, the sinuosity of the attenuation (to be defined), and the delay distortion. The derivations for the first two characteristics parallel substantially those published by Didlaukis and Kaden (ENT, vol. 14, p. 13, Jan., 1937). They are set forth here for completeness of presentation because the steps in them illustrate the more complicated steps in the derivation of the last two characteristics. When the characteristic impedance changes from point to point, its variation from the average characteristic impedance for the whole length of conductor forms the irregularities which produce reflections. Assume that successive discrete elementary pieces of the circuit are homogeneous throughout their length, that the lengths of these ele- mentary pieces are equal throughout the length of the whole circuit, and that there is no correlation between the deviations from average 541 542 BELL SYSTEM TECHNICAL JOURNAL characteristic impedance of any two elementary pieces. This repre- sents a first approximation to the problem. It is fairly accurate for pairs in ordinary cable in which the outstanding irregularities are devia- tions, from the average, between whole reel lengths; and in which the lengths of the successive spliced pieces (reel lengths) are at least roughly the same. There are irregularities in some coaxial conductors in which the impedance change is gradual rather than abrupt from one element to the next, and in which the elements can vary in length along the line. For these cases the approximation is a little over-simplified. However, although this somewhat affects the echo wavelets as computed from the impedance deviations along the line, Didlaukis and Kaden, as referred to above, have shown that it does not affect the ratio between the echo wavelets, suitably averaged, reaching the receiving end and those, similarly averaged, returning to the sending end. With the above assumptions there will be some correlation between the reflections at the two ends of an elementary length. If, for example, this length happens to be high in characteristic impedance the reflection at one end will tend greatly to be the negative of that at the other end. For this reason we are going to break up the reflection into two parts, at a point between any two successive elementary lengths of circuit — one part from one length of the circuit to an infinitesimal length of cable of average characteristics inserted between the two elementary lengths — and the other from this infinitesimal piece to the next elementary length of circuit. There is then 100 per cent correla- tion between the reflections at the two ends of a given elementary length (one being exactly the negative of the other) ; but there is no correlation between the reflections from any one elementary length to its adjacent infinitesimal piece of average cable, and the reflections from any other elementary length to its adjacent piece. This same treatment is used in the calculation of certain types of "reflection" crosstalk. The departure in characteristic impedance in the usual transmitting circuit in the higher frequency range, where the irregularities are most important, results essentially from deviations in the two primary con- stants of capacitance and inductance, each per unit length. There is a certain correlation between these, inasmuch as the capacitance devia- tion is contributed to both by differences in the dielectric constant of the insulation and by differences in the geometrical size, shape, and relative arrangement of the conductors; and the inductance deviation is contributed to by the latter alone. If there were no deviation in dielectric constant there would be no deviation in velocity of propaga- IRREGULARITIES IN WIRE TRANSMISSION CIRCUITS 543 lion (phase or envelope), which (at the higher frequencies) is inversely proportional to the square root of the product of the capacitance by the inductance. Consequently the portion of the fractional deviation in capacitance which is due to geometrical deviations correlates with an equal and opposite fractional deviation in inductance. Since in prac- tice the contribution from the geometrical deviation is apt to be dominating, that due to the variation in dielectric constant will be neglected and the above correlation assumed as 100 per cent. The standard deviation of the capacitance of the successive ele- mentary lengths, as a fraction of the average capacitance, will be designated as 8. The secondary constant of the line most affected by these irregulari- ties is the sending end (or similarly receiving end) impedance. If we consider a large ensemble of lines of infinite length of similar manufac- ture (and equal average characteristics and 8) but in which the indi- vidual irregularities are uncorrelated, then the sending end impedances of these lines, measured at a given frequency, also form an ensemble. The standard deviation of the real parts in this latter is ^AKr^, and that of the imaginary parts ^AKi^. In general, the departure in the impedance of one individual line from the average will vary with frequency; and perhaps over a moder- ate frequency range a sizeable sample can be collected which is fairly typical of the ensemble of the departures at a fixed frequency in the interval. If this is the case, and if at the same time the average im- pedance varies smoothly and slowly with frequency, and the standard deviation of the ensemble of departures also varies smoothly and slowly with frequency, then the standard deviation of the sample of departures over the moderate frequency interval is substantially equal to that of the ensemble of departures at a fixed frequency in this inter- val. (It is clear that this disregards exceptional lines in the ensemble, characterized by regularity in the array of their capacitance deviations, for which these conditions do not hold.) Under the circumstances where this observation is valid it makes it possible to correlate measure- ments on a single line, provided it is not too exceptional, with theory deduced for an ensemble. The irregularities in the transmission line will also affect its attenua- tion. If again we consider an ensemble of lines and measure the at- tenuation of each at a given frequency these attenuations will also form an ensemble. It will be found in this case, as will be demonstrated further below, that the average attenuation is a little higher than that of a single completely smooth line having throughout its length a characteristic 544 BELL SYSTEM TECHNICAL JOURNAL impedance equal to the average of that for the irregular line. This rise varies slowly with frequency. The standard deviation of the at- tenuation will also include not only the efifect of the reflections which we have been considering but in addition one caused by the fact that the attenuations of the successive elementary pieces are not alike, and hence their sum, aside from any reflections, will also show a distribu- tion. This additional contribution will vary only very slowly with frequency. The standard deviation will be vAAi^ + AA2^ where A represents the losses in the total line, the subscript 1 indicates the con- tribution due to the reflections, and the subscript 2 that due to the distribution of the individual attenuations. The same observation may be made about the attenuation that was made about the terminal impedance, as regards measurements made at one frequency on an ensemble of lines and measurements over a range of frequencies on one line; except that the contribution to the deviation caused by the distribution of individual attenuations varies so slowly with frequency that on each individual line it will look like a displacement from the average attenuation, over the whole frequency range. For the purposes of the present paper only the contributions from the reflections will be computed. When this information on irregularities is being used by a designer of equalizers he is interested in two characteristics: first, how far each attenuation curve for a number of lines will be displaced as a whole from the average; and second, how "wiggly" each individual curve is likely to be. While the observations above give the general amplitude of the latter they do not tell how closely together in frequency the individual "wiggles" are likely to come. To express this, the term "sinuosity " has been defined as the standard deviation of the difi^erence in attenuation (for the ensemble of lines) at two frequencies separated by a given interval A/. By the previous observations this can be extended to the attenuation difl^erences for successive frequencies separated by the interval A/, for a range of frequencies in a single line. When the transmission line is used for certain types of communica- tion, notably for telephotography or television, it is important to equalize it accurately for envelope delay as well as attenuation. The envelope delay is defined as T = d^/do) (1) where /3 is the phase shift through the line and co is 2x times the fre- quency. For an ensemble of lines, the envelope delay at a given frequency will also form an ensemble, the standard deviation of which will be VaT^. By the observations which have already been made IRREGULARITIES IN WIRE TRANSMISSION CIRCUITS 545 the same standard deviation also holds for the envelope delay depar- tures over a range of frequencies on one line. Let Fig. 1 represent a line of the type we have been discussing. The successive t/'s represent the reflection coefficients between succes- sive elementary pieces of line. As mentioned before, to avoid correla- tion, each 77 is broken up as shown into two h's, representing reflections between the elementary pieces and infinitesimal lengths of average line. The main signal transmission will flow as shown by the arrow a in Fig. 1. In addition there will be single reflections as shown by the arrow h. Following the assumptions we have set up, this really con- sists of two reflections from infinitesimally separated points. Further there will be double reflections, that is reflections of reflections, as shown by c. Here again each reflection point, according to our assump- tions, consists of two infinitesimally separated ones. There will be a variety of double reflections according to the number of elementary lengths between reflection points. Finally there will be triple, quad- ruple and higher order reflections which are not shown. The wave amplitude after reflection is cut down by the reflection coefficient. Consequently, even though there are more of them, the total of any given higher order reflections can always be made smaller than that of lower order reflections by a small enough reflection coefficient. We will here study only small reflection coefficients and therefore neglect all reflections of higher order than needed to give a finite result. For effects on the impedance this means neglect of all but. first-order reflec- tions. For the other effects studied it means neglect of all but first- and second-order reflections. The reflection coefficient between two successive impedances (one being K), is, approximately h = AKJilK). (2) Following our earlier assumptions, namely that the principal cause of impedance departures lies in geometrical irregularities, and that these may be expressed in terms of capacitance departures, ^ = ^, or h = ^, or Vp=6/2. (3) K C IC Consequently the reflection coefficients are real, namely, they intro- duce no phase shifts other than 0 or tt in the reflections. The irregularities in sending-end impedance have been computed in Appendix I from the single reflections of the type h in Fig. 1, The 546 BELL SYSTEM TECHNICAL JOURNAL iicn ix:: ix:: \^: II PuJuJ H^^ seT^ I ;, 31 'Hi I »- ll.< I- _ • o\8 K K 2\' (4) where 0 is the phase shift in radians in two elementary lengths, e is the attenuation in nepers of two elementary lengths, and 5 is, as men- tioned before, the standard deviation in C measured as a fraction of C. It will be noted that as a consequence of the single reflections, the ir- regularities in impedance vary as the first power of 5. The irregularities in attenuation have been computed in Appendix II from the double reflections of the type c in Fig. 1. It is found, as mentioned before, that there is a net rise in average attenuation caused by the reflections, equal, in nepers, to 2/4 where n is the number of elementary lengths in the total line. Con- sidering the factor in parentheses in the expression above, although the term e is not usually wholly negligible compared with the term <^^/2, nevertheless the latter is dominating and sets the order of magnitude of the factor. If the e is disregarded, the expression can easily be put in terms of the impedance irregularities, giving r Va^ L K A, (6) where A as before represents the loss in the total line. The standard deviation in the loss in nepers, when finally simplified, is, for the reflections, Vir-^. (7) Expressed in terms of the impedance irregularities, this amounts to 4m^[^]^\. (8) It will be noted that these irregularities in the attenuation vary with the square of b, or the square of the impedance irregularities. This is a consequence of the double reflections, and will continue to hold for the sinuosity and irregularities in envelope delay. It will also be noted 548 BELL SYSTEM TECHNICAL JOURNAL that in this form the equation is independent of e, <^, and n. It is in this case that Didlaukis and Kaden found that the result is independent of whether the reflection points are sharp and equally spaced or not. The sinuosity has been computed in Appendix III. When finally simplified and measured in nepers, it amounts to V(AA.-ArO^ = ^^A/. (9) Expressed in terms of the impedance irregularities this amounts to v(nr^^ = [ ?]' J^-^' ^'"^ where T is, as mentioned before, the envelope delay of the whole line, in seconds. In computing the above it is only the components of the echoes which are in phase (or tt radians out of phase) with the main transmission which affect the results. If the echo components at right angles to the main transmission are considered, they will give phase shifts in the resultant signal wave. Further, an echo component whose ratio to the main transmission is x will, when tt radians out of phase with it, give a loss of x nepers; and when at right angles to it, a phase shift of x radians. Now the distribution of echo components in phase (or tt radians out of phase) with the main transmission is substantially the same as that of components at right angles to it. Consequently the sinuosity is also numerically equal to the standard deviation of the difference in phase shifts at two frequencies separated by the given interval A/. Therefore if the interval is called Aco/2x and the resulting numerical value of the sinuosity is divided by Aw it will give the standard deviation of the envelope delay. This is (11) J 2Va The quantity which has been used in considering the suitability of a line from a delay standpoint for transmitting pictorial signals is its envelope delay distortion, or maximum departure in delay each way from a fixed average in the frequency band studied. If we make the usual assumption that the maximum departure ordinarily met (strictly speaking, except in about 3 cases out of 1000) is three times the standard deviation, then the delay distortion contributed by the ir- regularities is ± 3 times the expression given in equation (11). IRREGULARITIES IN WIRE TRANSMISSION CIRCUITS 549 Expressed in more usual units, the results given in equations (6), (8), (10), and (11) are repeated here. Rise in average attenuation (db) = Standard deviation in attenuation (db) = Sinuosity (db per kilocycle) = 0.0256 Delay distortion (microseconds) = ± 4.42 Va^ K K _ K aL, (6') V4.343aL, (8') -vz Va K vz ^[a (10') (11') where L = length of the line in miles, a = attenuation of the line in db per mile, T = envelope delay of the line in microseconds per mile. In order to convey a notion as to possible orders of magnitude of these effects of irregularities, and how they vary with changes in the parameters, a few calculations have been tabulated below for some hypothetical lines. K Circuit Length, Miles Attenuation, db per Mile Rise in Average Loss, db Standard Deviation in Loss, db Sinuosity, db for Interval of 1 Kc. Delay Distortion, Micro- Seconds rioo {.^ 0.05 0.10 0.005 0.007 0.2 X 10-3 0.15 " ±0.01 ±0.01 1 per cent < [lOOO u 0.5 1.0 0.015 0.02 0.7 " 0.5 " ±0.04 ±0.03 [100 {.I 0.2 0.4 0.02 0.03 0.9 " 0.6 " ±0.05 ±0.03 2 per cent < [lOOO u 2.0 4.0 0.06 0.08 3. 2. ±0.15 ±0.1 Note: T = 6 micro-seconds per mile. Appendix I Impedance In Fig. 1 the circuit is divided into n homogeneous elementary lengths. For a current of unit value traveling down the circuit at the junction of the yfeth and (k + l)th elementary lengths, the reflected 550 BELL SYSTEM TECHNICAL JOURNAL wave is hk — hk+\, (1) where hk denotes the reflection coefficient (assumed to be a real number) between the impedance of the ^th elementary length and the average impedance. However, if the current starts with unit value at the sending end, then the wave has to be multiplied by the factor g-'^^/^ [^ reaching the point of reflection, where P is the propagation constant per two ele- mentary lengths. In returning to the sending end the reflected wave is again multiplied by a like amount so that its value on arrival there becomes (hk - hk+i)e-''P. (2) The totality of echoes returning to the sending end is £6 = - Ai + L (hk - hk+i)e-''P = Z hk(e~'^P - g-^-^+O- (3) Let g-p = g-e+i4> ^ Be^^ (4) When n is large, it is permissible to use the assumption that k has co for its upper limit in the above summation. The real part of Eb is accordingly 00 Ebr = L hk[B^ cos k(i> - 5*-i cos {k - 1)0]. . (5) k=l By the same method as described for the more complicated case in Equation 15, Appendix II: 00 1^7 = ^ £ [52*= C0S2 k(t> - 252^-1 COS H COS { (/^ - 1)0} + 52A:-2cos2 {(yfe - 1)0}]. (6) This series may next be evaluated, giving: pT^ _ fe^ / 1 - 2^ COS 0 + ^2 1 _ ^2 \ "' 2\ 1-^2 "^ 1 + 25 COS 0 + 52; ■ ^'^ In a similar manner it follows for Ehi, the imaginary part of Eh, that P^ ^ ^2 / 1 - 2J3 COS (/> + 52 1 _ ^2 X '* 2V 1-52 1 +25COS0 + 52/ ■ ^^^ IRREGULARITIES IN WIRE TRANSMISSION CIRCUITS 551 Then, replacing e and neglecting higher-order terms in 4> and e, which are small, and putting li^ — 8^/4:, equations (7) and (8) become rKKy 4e AKi' = 4EbiKKy 4e A/Ai^.2 ^AKi'' \4>\b K K 2^e 552 BELL SYSTEM TECHNICAL JOURNAL Appendix II A ttenuation The following is a derivation of the standard deviation of the real part of the echo currents (which are received in phase with the direct transmission) over a circuit such as has been assumed in Appendix I. Accordingly, the reflected wave at the junction of the kth and {k + l)th homogeneous elementary lengths, for a current of unit value traveling down the circuit at this point, is: hk — hk+i. (1) This wave returns toward the sending end and in turn suffers partial reflections. Consider this secondary reflection at the point between the jth and (j + l)th lengths where j < k. The wave arriving at the point in question is (hk - hk+i)e-P^'-^-^'\ (2) The fraction of this wave which is reflected back again is - (hi - //./+i), (3) so that the wave which starts back from this point in the same direction as the original wave is: - (hi - h,-^^)(hk - hk+i)e-P^'-^^i\ (4) In traveling to the junction of the ^th and (k -\- l)th lengths it is again multiplied by e~^'-''~^'"^ so that the echo which is joined to the unit wave is therefore given by - (hi - hi^,)(hk - //,+i)e-^(*-'). (5) U m = k — j, this echo is — (hj — hi+i)(hj+m — hj+„,+i)e~"'^ when m > 0. (6) The sum of all the echoes for a given value of m > 0 is: n — m - e-'^P Z (hj - hi+i)(hi+m - hj+m+i) = - e-^^Hm- (7) 3=0 When w = 0, a slightly different treatment is necessary. Let the circuit be represented as in Fig. 1. A unit current traveling down the circuit will suffer a reflection loss at each junction so that the current passing through the junction is (1 — r],) times the current entering. The ratio of the current received IRREGULARITIES IN WIRE TRANSMISSION CIRCUITS 553 to the current that would be obtained without reflection loss is -^ = (1 - r7o)(l - 7?0(1 - 772)(1 - 7?3) • • • (1 - y)n), (8) -10 where the double reflected echoes of the previous type (w > 0) are omitted. The echo which is joined to the unit wave when m = 0 is A/ / - Jo h h (9) Logey- = Loge j = -y , when A/ is small. (10) Since A7 " " -y- = Loge n (1 - r?,) = E Log. (1 - 7/,) (11) ^0 ,=0 ;=0 and Log. (1 - r?) = - 7? - vV2 - 7,3/3 • . •, (12) therefore the echo is given as follows in nepers: - L (vi + viV2+ ..-) J=0 = — \i— hi + hi — hi + hi — h + hs ■ ■ • — hn + //n] - ^ Z (hj - h^+iY. (13) ;=o The first term is zero. The sum of all the echoes is -lliihj-h^+iy]- Ze-^H^ l ■^ j=0 J Jn=l = - n E (/^,- - h,+iy I - i'H^B-e^-t (14) I- "^ ;=0 -^ ».=1 The in-phase component of these echoes is Ecr= -\IZ {hi - hi+iY I - L HmB^ cos w0, (15) assuming /?'s may be taken as real and as having a symmetrical distri- bution curve about zero, the square of whose standard deviation may be denoted by h^. We will consider the distribution curve of Hm, which also is real. The average value of a function H{h) in a given distribution is equal to 554 BELL SYSTEM TECHNICAL JOURNAL the integral of the product of the function by the frequency of occur- rence for each value of it, divided by the integrated frequency of oc- currence alone. The frequency of occurrence of individual values of the function is the same as that of the corresponding values of its argument, and hence can be written as F(h)dh where F{h) is the distri- bution function of the variable h. The average value of Hm is therefore Hn, HI HmFiF2 • • • FndhidJh • • • dhn = I I • • • I E (^j - hj-+i){hj+„, - hi+m+i) X F1F2 ■ ■ ■ Fndhidh2 ' ' -dhn, (16) where Fk is the distribution curve of hu, and £ .£ Fkdhk = 1, kkFidhk = 0. Assuming the /z's all have equal distribution curves: hk^Fkdhk = /^^ except that since ho = 0 and A„+i = 0, then JiQ^Fodho = 0, and Likewise except that X X X }l~ n+\F n+ldh. n+i = 0. r hk'Fkdhk = h\ »y — 00 ho'^Fodho = 0, ■ 1. (27) The average value of Ecr is equal to the sum of the average values of its terms. Applying the results for Ho, Hi, and Hm, we obtain Ear = - Wo - HiB cos 0 = - [1 - 5 cos (l>']nh\ (28) (EcrY = II - 2B COS (f> -\- B^ cos2 Y X ^1^2 • • • FndhidJh • • • dhn J J J ^ p=0 g=0 X F1F2 • • • Fndhidhi • ' ' dhn /»/•/-» n n n — m + • • • I E ^'^ (cos m4>) £ E {K - h^iY J J J m=l p=0 g=0 X {hq — hq+i){hg+„t — hg+m+i)FiF2 • • • Fndhidhz • • • dhn + J j j ZZ ■S'-+' (cos ;'0)(cos sct>) n—r n—s X ZZ {hp - hp+i)(hp+r - hp+r+l){hq - hq+i) p=0 g=0 X (hq+g — hg+s+i)FiF2 • • • Fndhidhz • • • dhn. (30) Multiplying the factors containing the A's as indicated in (30) gives terms containing hahbhjid where the subscripts denote some integer such as the value for ^, ;^ + 1, ^ + ^, 2, 2+1' Q -\- s, etc. When 556 BELL SYSTEM TECHNICAL JOURNAL there is equality among subscripts so that the terms become hi^h-^ or hj^ the integration gives {h?y or A^, respectively. However, if such equality does not exist, or if one of the subscripts is zero or w + 1, the integration gives zero. By integrating term by term in the manner above indicated, adding the results, and finally thereafter putting r = m and s = m, the following result is obtained: EJ -^ (1 - Bcos ct>yn¥ + n^ - 1 - 2(n^ + n - 2)B cos + 2{n - \)B^ cos 20 + {n^ + 4n - 6)B^ cos ^ 0 + \ H (6w — 6m)B^"' cos- m \ - 8 I Y. {n - m - D^^'^+i cos { {m + 1)0} cos m0 1 + 2 I I^ (w - w - l)52'»+2cos [{m + 2)0) cosm0 1 W. (31) If the distribution of the lis is assumed to be a normal distribution, then: ¥ = 3(^2)2. (32) Making this substitution and subtracting {EcrY gives: ■tLcr yJ-icr) 3n - 1 - Sin - ^)B cos 0 + 2(w - 1)^2 ^qs 20 + WJ52 C0S2 0 + ] Z! (6» — 6m)52m (,Qg2 ^0 I -8|E(w-m- i)52-+i (^ cos { (2m + 1)0} COS 0 + 2 Z (^i-?w- l)-5' 2 ' 2 , /cos { (2m + 2)0} COS 20 )} h^\ (33) When n is large, it is permissible to use the assumption that m has <» for its upper limit in the above summations. It is likewise permissible to neglect terms in the result which do not contain the factor n. Accordingly, (EcrY = 3+^2 cos2 0 + 2 + 4 (I - B cos 0)2 1 - j52 (I + B cos 0) 1 + ^2 ^ 25 COS nh"^. (34) IRREGULARITIES IN WIRE TRANSMISSION CIRCUITS 557 The echo current which is joined to the unit received wave affects the final resultant and therefore the effective loss of the line. From equation (28), neglecting higher-order terms, the attenuation of the whole line is increased (in nepers) by e + (f)^ \ nb"^ (35) The standard deviation of the attenuation (A, in nepers), from equa- tion (34) and neglecting higher order terms, is a/(A - A)2 = "sTT (36) Appendix III Sinuosity The following is a derivation of the sinuosity of the attenuation, defined as the standard deviation of the difference A(/ -f A/) — A(/). Here A(/) is the loss in the circuit at the frequency, /. For practical purposes, the difference of the expression Ecr — Ecr at two discrete frequencies is d(Ecr — Ecr) X = df A/, (1) whose standard deviation will be derived below. From values of Ec and Ecr given in Appendix II we obtain J-'CT J-'C 3=0 Y, UmB"' cos mcf) j-.d{B COS0) " + [_! - B cos 4>']n¥, (2) diB™' cos m4>) df A/ , d cos(f) .\dB] n¥ { B —^ h (cos 0) -jj } , y-^ rr \ T, d COS md) , , , dB^ + H Hm{ B^ + (cos m) -jj A/ nh^{BQ s'm (f) — D cos 0) + 2] niH„, X (B^'Q sin mcf) - B"'-^ cos w0) A/, (3) 558 BELL SYSTEM TECHNICAL JOURNAL where Q = d(t>/df and D = dB/df. X2 = f f r X'^1^2/^3- • • Fndhidh^dh ■■• dhn = { ^ r nW\BQ sin y{^f)^ X F1F2 • • • Fndhidhz ■ • • dhn + f j f 2n¥(BQ sln(j> - D cos ) X E mHm(B"'Q sin w0 - 5™-iD cos w0) L m=l X (AfyFiFi ■ ■ ■ Fndhidh2 ••• dhn /* /^ /% n n + 1 I • • • I Z L r^(-B'-() sin r0 - B'-^ D cos r0) X {B'Q sin 50 - 5^-12) cos 50) n — r n — s Z Z i.K - hp+i) p=0 g=0 X (/?p+r — hp+r+l)(hq — hq+i){hg+s " ^^g+s+l) (A/)= X F1F2 • • ■ Fndhidho • • • dhn. (4) By methods similar to those employed in Appendix II it follows that = [ X2 = {BQ sm4> - D cos (f>y¥ + - 2(BQsm4> - Z> cos 0)2 + (52Q2 _[_ X)2)(3 _ 85 COS 0 + {652 - 2^4} cos2 0 + B') -(<2^-S)( 1- (1 - 52)3 1 + 652 - 354 52 /V (1 + 25 COS 0 + 52)3 65(1 + 52) cos 0 + 652(1 + 52) cos2 0 + 45^ cos« 0 (1 + 25 COS 0 + 52)3 {6(1 + 52) cos 0 + 45 cos2 0 + 85} sin 0 1 - 2BQD (1 + 25 cos 0 + 52)3 X {h^y^ n{Afy. (5) When the distribution of the h's is normal, this expression can be IRREGULARITIES IN WIRE TRANSMISSION CIRCUITS 559 simplified by noting that The sinuosity may be obtained from X^ as follows: (6) AA - AA = A(/ + A/) - A(/) - { A(/ + A/) - A(/) } (7) = A(/ + A/) - A(/+A/) - A(/) + A(7) (8) - EM + A/) - Ecrif + A/) - EM) + EM)- (9) Consequently, ' ^^ ~ (10) \(AA - AA)2 = VP. Therefore the sinuosity, expressed in nepers, is V(AA - AA)2 = SsHn, where, in accordance with equations (5) and (6) : 1 (11) S + (BQ sin cj) - D cos 0)^ (B^Q^ + D^)(3 - 8B cos 0 + {6B^ - 2B'} cos^ 0 + B') - Q'- D' 1 - (1 - 52)3 1 + 6^2 _ 3^4 B^J\^ (1 + 25 cos 0 + ^2)3 65(1 + 52) cos (A + 652(1 + 52) cos2 + 45-'' cos^ «^ 25(3D and (1 + 25cos0 + 52)3 (6(1 + 52) cos (j) + 4B cos2 0 + 85} sin 0 (1 + 25 cos , and neglecting those higher than needed to give a finite result, it is found that 8eV2l In general, D is negligible compared to Q and the sinuosity is -\'(AA - AA)2 8eV2^ (A/). (14) (15) Transoceanic Radio Telephone Development * By RALPH BOWN TEN years have elapsed since the opening to public use on January 7, 1927, of the first long distance radio telephone circuit. This form of intercontinental communication has now come into practical business and social use. A network of radio circuits interconnects nearly all the land wire telephone systems of the world. The art has passed through the pioneering stage and is well into a period of growth. The technical side of this development, which the present paper reviews, divides naturally into four categories. The first covers those factors which made possible the beginning of commercial radio tele- phony.^ In the second are the things without which its rapid growth and wide expansion could not have occurred. In the third, are a few incidental but interesting or valuable technical features. The fourth considers future improvements now in view. Essential Initial Developments Radio telephony presents difficulties in addition to those existing in radio telegraphy because: (1) The communication is two-way, and the radio system must be linked in with the wire telephone systems and available to any telephone instrument; (2) The subscriber cannot deliver himself of his message until the connection is actually estab- lished, and on this account delay due to unfavorable transmission con- ditions is less tolerable; (3) The grade of transmission required to satisfy the average telephone user is higher than that tolerable in aural tone telegraph reception by an experienced operator. These requirements emphasized the need for accurate and quantita- tive knowledge of radio transmission performance as a basis for en- gineering radio telephone systems. There was at the same time a similar need for transmission data in the engineering of early radio broadcast installations. The effort brought to bear on these twin prob- lems resulted in the development of practical field methods of measuring * Digest of a paper presented at the Spring Convention of the Institute of Radio Engineers, New York, May 10, 1937, and published in full in Proc. I. R. E., September, 1937. 1 A description of the early years of radio telephone development preceding exten- sive commercial application, together with a discussion of the origins of the whole art, will be found in companion paper "The Origin and Development of Radio Telephony," by Lloyd Espenschied, published in Proc. I. R. E., September, 1937. 560 TRANSOCEANIC RADIO TELEPHONE DEVELOPMENT 561 radio signal strength and radio noise. The employment of long dis- tance radio telephony in commercial use was preceded by experimental operation and tests which gave a considerable fund of statistical in- formation covering the cyclical changes characteristic of overseas radio transmission. The realization that a relatively high degree of reliability was essen- tial to success discouraged any attempt at commercial service until high-power transmission on a practical basis was assured by the inven- tion of a method of making water-cooled tubes. In searching for the most efficient way of applying the power made available by water-cooled tubes telephone engineers were led to the employment of a method which had already been successfully used in high-frequency wire telephony. This method, now well known to radio engineers, is called single-sideband suppressed-carrier transmis- sion. As compared with the ordinary modulated carrier transmission, it increases the effectiveness of a radio telephone system by about 10 to 1 in power. This accrues partly because none of the power capacity of the transmitter is used up in sending the non-communication bearing carrier frequency and partly because the narrower band width permits greater selectivity and noise exclusion at the receiver. A very important final element was also necessary to prevent voice- frequency singing through residual unbalances and around the entire radio link when wire circuits and radio channels are connected together. Recourse was again had to a device newly worked out for wire telephone transmission. By associating together and electrically inter- locking several of the voice current operated switching devices which had been developed for suppressing echoes on long wire lines, an ar- rangement now commonly known as a "vodas"^ was developed. When the subscriber talks, his own speech currents, acting on the vodas, cause it to connect the radio transmitter to the wire line and at the same time to disconnect the radio receiver. When the same sub- scriber listens the connection automatically switches back to the re- ceiver. No singing path ever exists. The amplification, in the two oppositely directed paths can be adjusted substantially independently of each other, and constant full load output from the radio transmitters is secured. With this device it became possible to connect almost any telephone line to a radio system and to adjust amplification so that a weak talker over a long wire line could operate the radio transmitter as effectively as a strong local talker. 2 This word, "vodas," Is synthesized from the initial letters of the words "voice- operated device, anti-singing." 562 BELL SYSTEM TECHNICAL JOURNAL Developments Essential to Growth The first long distance radio telephone circuit operated (and it still operates) between the United States and England with long-wave transmission at about 5000 meters. We did not then, and we do not today, know how any considerable amount of intercontinental radio telephony could have been accomplished with circuits of this kind. The frequency space available in the long-wave range would accom- modate comparatively few channels. The high attenuation to over- land transmission and the high noise level at these wave-lengths pre- clude their satisfactory use for very great distances or in or through tropical regions. The discovery that short waves could be transmitted to the greatest terrestrial distances and could be satisfactorily received in the tropics came at a most opportune time. Short-wave transmission not only released the limitations on distance and location inherent to long waves but also opened up such a wide range of frequency space as to give opportunity for an extensive growth in numbers of both radio telegraph and radio telephone circuits. Short waves further encouraged the growth of radio telephony by making it cheaper. Thus, it became possible to make directive antenna struc- tures of moderate size which increased the effectiveness of transmission many times, thereby reducing the transmitter power required for a given reliability of communication. Short waves were the indis- pensable element without which material growth could not have oc- curred, but there were other significant things. An important desideratum in telephony is privacy. Commercial radio telephony would have been severely hampered if privacy systems had not been developed to convert speech into apparently meaningless sounds during its radio transit. Another item of great aid in promoting growth was the development of methods of accurate stabilization of transmitted frequencies. The first effect of this was to eliminate the extreme distortion which charac- terized early short-wave telephone transmission and which was found to be due to parasitic phase or frequency modulation effects in the transmitters. As the number of radio communication facilities, both telegraph and telephone, grew, accurate stabilization of frequency be- came a necessity in order to permit effective utilization of the available frequency space without mutual interference between stations. Later Technical Advances The "rhombic" antenna is mechanically simple and electrically nearly aperiodic, covering a wide wave-length range efficiently. It TRANSOCEANIC RADIO TELEPHONE DEVELOPMENT 563 has radically changed the character of the physical plant and invest- ment necessary to the employment of directivity in short-wave transmitting and receiving. In Hawaii and the Philippines on circuits to the United States the "diversity" method of reception is used wherein three individual separated antennas and receivers with interlocked automatic gain controls are combined to produce a common output having less distor- tion and noise than a single receiver. The effects of distortion in short-wave circuits are avoided to some extent by an arrangement called a "spread sideband system," which has been used on circuits between Europe and South America. By raising the speech in frequency before modulation the speech sidebands are displaced two or three kilocycles from the carrier and many of the product frequencies resulting from intermodulation fall into the gap rather than into the sidebands. On the Holland-Java route a system is being used whereby more than one sideband is associated with a single carrier or pilot frequency, each such sideband representing a different communication. An improved signal-to-noise ratio is given by a device called a "compandor" ^ employed on the New York-London long wave circuit. It raises the amplitude of the weaker parts of the speech previous to transmission. In depressing these raised parts to their proper relative amplitude, after reception, the compandor also depresses the accumu- lated radio noise. Present Outlook The foregoing makes it evident that many fundamental engineering problems have been solved and that the pioneering stage of the service, when its possibility of continued existence might reasonably have been in doubt, has definitely been passed. In looking toward the future we find that the greatest needs are for improvement in reliability and in grade of service, accompanied by reduced costs. Improving the reliability struggles against the fact that short wave transmission varies through such a wide range of effectiveness, and seems to be so much influenced by the sun. We have not only a daily cycle in the transmission of a given frequency but also an annual cycle and beyond this an eleven-year cycle associated with the change in sunspot activity. Superimposed upon these are erratic and occa- sionally large variations associated with magnetic storms. ^ The synthetic word "compandor" is a contraction of the compound word "com- pressor-expander," which describes the effects the device has on the volume range of speech. 564 BELL SYSTEM TECHNICAL JOURNAL A statistical study of the data secured from operation of transoceanic radio telephone circuits over the past several years has given valuable help in engineering circuits to meet a given standard of reliability. This study has shown that the percentage of lost time suffered on a circuit appears to follow a probability law and that its relation to the transmission effectiveness of the circuit in decibels is given by a straight line when plotted to an arithmetic probability scale. Such a relation tells us, for example, that if a circuit as it stands suffers 15 per cent lost time, the lost time can be reduced to a selected lower value, say 5 per cent, by improving the circuit a definite amount, in the assumed case 10 decibels. It then becomes possible, by making engineering cost studies of the various available ways of securing the necessary number of decibels improvement in performance, to choose the most economical one. This approach is being applied to study of the radio telephone circuits extending outward from the United States. Some of the tech- nical possibilities which are being considered for improving these cir- cuits are discussed below. The performance of a radio telephone circuit may be changed by dynamically modifying the amplification or other characteristics of the circuit in accordance with the speech transmitted. The compandor already mentioned is an example of this kind of improvement on long waves. Further developments particularly suited to the vagaries of short-wave transmission are possible. The operation of the vodas, or voice-operated switching device linking the wire and radio circuits, is adversely affected by noise. Methods are being investigated for using single frequencies, called "control tones," transmitted alongside the speech band and under the control of speech currents, to give more positive operation of the switching devices and reduce the adjustment required. The transmission improvement of about 9 decibels (about 10 : 1 in power) offered by single-sideband suppressed-carrier transmission has been delayed in its application to short-wave transmission partly be- cause of the high degree of precision in frequency control and selectivity necessary to its accomplishment. In recent years successful apparatus has been developed and proved satisfactory in trials. The introduction of single sideband into commercial usage is already in progress. Turning now from the transmitting to the receiving end, one funda- mental way to reduce noise in radio telephony is to employ sharper directivity. It has been found by observation that there is a limit to which directivity, as ordinarily practiced, can be carried to advantage. It is easy to design antennas so sharp that at times very large improve- ments in signal-to-noise ratio are secured. But it is found that at other TRANSOCEANIC RADIO TELEPHONE DEVELOPMENT 565 times these antennas are actually poorer than are much less sharply- directive systems. Such observations also indicate a wide variation in the performance of antennas as regards selective fading, and the signal distortion accompanying it. The result of all this work has been the development of a system based on an entirely new approach to the problem of sharp directivity and of telephone receiving. This system is called a MUSA System, the word MUSA being synthesized from the initial letters of the descriptive words Multiple Unit Steerable Antenna. An outline of the principles and methods is given below. By sending short spurts or pulses of short-wave radiation from one side of the Atlantic, and receiving on the other side, it has been observed that each spurt may be received several times in quick succession. But these echoes do not arrive like successive bullets from the same gun, all following the same path. They come slanting down to the receiver from different angles of elevation, these vertical angular directions remaining comparatively stable. While the signal received at each of the individual directions may be subject to fading, the fading is somewhat slower and is not very selective as to frequency. The signal component coming in at a low angle takes less time in its trip from the transmitter than a high angle component. Evidently the low- angle paths are shorter. All these facts fit in well, on the average, with the ideal geometrical picture of waves bouncing back and forth between the ionosphere and the ground and reaching the receiver as several distinct components which started out at different angles, have been reflected at different angles, and have suffered different numbers of bounces. The ordinary directive antenna is blunt enough in its vertical receiv- ing characteristic to receive all or nearly all of these signal components at once. Because of their different times of transit the various com- ponents do not mix well but clash and interfere with one another at the receiver. This shows up as the selective fading and distortion which characterize short-wave reception much of the time. The MUSA method remedies this trouble. The MUSA provides extremely sharp directivity in the vertical plane. By its use a vertical angular component can be selected individually. It consists of a number of rhombic antennas stretched out in a line toward the transmitter and connected by individual coaxial lines to the receiving apparatus. The apparatus is adjustable so that the vertical angle of reception can be aimed or "steered " to select any desired com- ponent as a telescope is elevated to pick out a star. The antennas re- main mechanically fixed. The steering is done electrically with phase 566 BELL SYSTEM TECHNICAL JOURNAL shifters in the receiving set. By taking several branch circuits in parallel from the antennas to different sets of adjusting and receiving apparatus the vertical signal components may be separated from each other. Nature breaks the wave into several components and jumbles them together. The first function of the MUSA system, as just described, is to sort the components out again. Its second function is to correct their differences so that they may be combined smoothly into a replica of the original signal. To do this the received wave components are separately detected and passed through individual delay circuits to equalize their differences in transit time. They are then combined to give a single output. As compared with a simple receiver the MUSA receiving system gives (1) improvement in signal-to-noise ratio, as a result of the sharp directive selectivity of the antenna ; (2) improvement against selective fading distortion, by virtue of the equalization of the time differences between the components before they are allowed to mix; and (3) improvement against noise and distortion, because of the diversity effect of combining the several components. Fortunately, it is found that the directive selection and the delay compensation adjustments correct for one frequency are satisfactory for a considerable band of frequencies adjacent thereto. Thus there is offered the possibility of receiving a number of grouped channels through one system and the prospect appears not only of improved transmission but also of reduced cost per channel. The possibility of grouping channels at the transmitting station may be conceived on the basis of either "multiple" or "multiplex" trans- mission. In the multiple arrangement each channel has its own an- tenna and its individual transmitter whose frequency is closely spaced from and coordinated with the adjacent channels of the group. In "multiplex" transmission, the channels are aggregated into a group at low power and handled en bloc through a common high-power amplifier and radiating system. Particularly in the multiplex case, there are possibilities of important economies if the technical problems are satisfactorily solved. Passing a multiplicity of channels simultane- ously through a common-power amplifier involves interchannel inter- ference due to modulation products which is not met with when only one channel is present. Severe requirements are thereby placed on the distortion characteristics of the power amplifier. It seems a fair conclusion that the tendency in the engineering solu- tion of the problems of economy and growth in radio telephone de- velopment (and perhaps also radio telegraph development) will be toward channel grouping methods, especially for backbone routes I TRANSOCEANIC RADIO TELEPHONE DEVELOPMENT 567 between important centers where large traffic may develop. This will be a considerable departure from past practice which has resulted in the existing system of scattered frequency assignments. It is to be hoped that the obvious difficulties in rearranging frequency assign- ments will not prove so unyielding as to preclude putting new engineer- ing developments into service. A Negative-Grid Triode Oscillator and Amplifier for Ultra- High Frequencies * By A. L. SAMUEL ^ I ^HE author describes three negative-grid triodes of unusual design A which operate both as oscillators and as amplifiers at ultra-high frequencies. The power output of the smallest tube as an oscillator at 1500 megacycles is 2 watts, and is still capable of an output of 1 watt at 1700 megacycles with an oscillation limit of 1870 megacycles cor- responding to a wave-length of 16 centimeters. This tube also offers possibilities as an amplifier at frequencies as high as 1000 megacycles. Such capabilities of the negative-grid triode are notable since this de- vice has appeared to lag behind the magnetron as an oscillator at fre- Fig. 1 — Experimental double-lead tubes. quencies of above roughly 500 megacycles, while the only successful power amplifiers which have been described for frequencies of the order of 300 megacycles are multi-element tubes. The triode as used at radio frequencies differs from the multi-element tube chiefly in the manner in which interaction is prevented between the input and output circuits. This is obviously a circuit limitation, as contrasted with the electron transit time limitation which has received so much attention. The greatest opportunity for improvement seems to be in the direction of improved circuit design. The tubes described in this paper were developed from this point of view. Sample tubes are shown in Fig. 1 . They differ from previous designs * Digest of a paper presented before International Scientific Radio Union April 30, 1937 at Washington, D. C. Published in Proc. I. R. E., October, 1937. 568 NEGATIVE-GRID TRIODE OSCILLATOR AND AMPLIFIER 569 primarily in the lead arrangement. From the section view of one of these tubes, shown in Fig. 2, it will be observed that the grid and plate elements are supported by wires which in effect go straight through the Fig. 2 — Section view of one of the double-lead tubes. tube envelope providing two independent leads to each of these ele- ments. The filament leads are at one end only and one of these leads is extremely short. This unusual lead arrangement possesses a number of unique advantages. Fig. 3 — Typical oscillator circuit. A typical oscillator circuit is shown in Fig. 3. Here the tube is mounted at the center of a half-wave Lecher system. This arrange- ment provides a higher natural frequency circuit than that of the 570 BELL SYSTEM TECHNICAL JOURNAL quarter-wave Lecher system formed by removing one set of leads. Since only half of the total charging current to the inter-electrode capacitances flows through each set of leads, the losses due to the lead resistances are also reduced. In the tubes under discussion the electron transit time limitation has been met by the use of extremely small inter-electrode spacings so that full advantage may be taken of the increased frequency range. For the purpose of confirming the above conclusion, efficiency curves have been obtained on the large size tube, as shown in Fig. 1, when operated both single- and double-ended. The results are shown in Fig. 4. It will be observed that the efficiencies for double-ended operation are always higher than for the single-ended case over the range covered by the experimental data. In fact, usable outputs are obtained at frequencies well beyond the point where the single-ended tube fails to operate. The ratio of the cut-off frequencies for the two tubes happens to be 1.23 for the particular conditions under which these data were obtained. Output and efficiency curves for the large size tube are shown in Fig. 5. The values of 60 watts at 300 megacycles and 40 watts at 400 megacycles compare quite favorably with outputs reported from radiation-cooled magnetrons. When the problems of modulation and the complications of the magnetron's magnetic field are considered, the advantages of the negative-grid triode become more apparent. The improvement in power output made possible by this departure in design is illustrated by the comparison plot shown in Fig. 6. The double-lead arrangement is also responsible for an increase in the upper frequency limit at which stable operation as an amplifier may be secured. The primary cause for instability of the triode amplifier is the inter- action between the input and output circuits which results from the admittance coupling between these circuits provided by the grid-plate capacitance. A second source of coupling is that caused by common impedances in the two circuits in the nature of the self and mutual inductance of the tube leads. At moderately high frequencies this latter coupling is usually of negligible importance. Stable operation is thus possible when suitable means are provided to compensate or "neutralize" the admittance coupling. At ultra-high frequencies lead-impedance coupling can no longer be neglected. It may, of course, be minimized by the use of short leads. The ultimate solution is to provide independent leads for the input, output and admittance neu- tralizing circuits. The double-lead tube is an attempt to fulfill these conditions. It will be observed that the only common impedance NEGATIVE-GRID TRIODE OSCILLATOR AND AMPLIFIER 571 remaining is that caused by one filament lead and that this lead is extremely short. In the present investigation the method of neutralizing admittance coupling has been that disclosed by H. W. Nichols in U. S. Patent 30 *>^ ^^ »^^ 20 ^ v^ \ ^ DOUBLE-END OPERATION • ^^^ 10 SINGLE-END OPERATION ^»\ ^^ ^\ -^ >^^ 0 \^ >w "^ Nk^ 200 250 300 350 400 450 500 550 FREQUENCY IN MEGACYCLES PER SECOND Fig. 4 — Comparison plot of output efficiency for the large tube when operated^single- ended and double-ended. LU o 80 nr iij Q. 70 z >- 60 V UJ u sn u. ai 7 40 < IT) 1- 30 <• ^ PLATE DISSIPATION -^ D WATTS D WATTS ^*'"^«> ^^ "^ ^UTPUT ^__ \ \ ^■"" ■"■-- ~-^^ OUTPUT — ""-t— \ ^^ —— — nriT^ ^ rr^ --^^ N \, EFFICIENCY ttr^v ^^ V '«^ -^ ^ 20 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 FREQUENCY IN MEGACYCLES PER SECOND Fig. 5 — Output and efficiency as a function of frequency for the large tube. 1,325,879 and involves the resonating of the offending admittances at the desired operating frequency so that the resulting parallel admit- tance is reduced to a very low value. This takes the form of an in- ductance connected between the grid and plate of the tube and adjusted 572 BELL SYSTEM TECHNICAL JOURNAL to resonate with the grid-plate capacitance. For ease of adjustment a somewhat lower fixed inductance may be used and tuned by the ad- justment of a small variable condenser in parallel. This form of neutralization is commonly referred to as "coil" neutralization. At ultra-high frequencies where unavoidable inductances are already present in the form of lead inductances, this "coil" scheme possesses 100 80 60 50 40 30 20 < ? 10 I- 3 8 Q. H 8 6 5 4 \ \, \ V \ \, N \ ■^-v^ \ \ \\ \ N0.304A \ \ LARGE TUBE \ •H V \ \ \. "^ \ \ \\ S \ \ \ s \ \ ^^ \ N. \ \ NO. 3I6A'^ i- s N \ \ N s 'intermediate V \ -\ TUBE \ \ \ \ \ \ \ ->,,\-SMALLTUBE 1 \ \ \ \ n L ^ \ \\ \ \ \ \ \ 100 200 300 500 1000 2000 3000 FREQUENCY IN MEGACYCLES PER SECOND Fig. 6 — Comparison plot of the outputs of the double-lead tubes and of commercially available tubes. outstanding advantages over the more usual "capacitance" schemes. These advantages become even more pronounced with the availability of the double-lead tube. Verifying this analysis, a "coil- neutralized" two-stage amplifier using two of the largest size tubes was found to yield an output of 60 watts at 144 megacycles for Class B operation. Stability, distortion, and band width were quite comparable to the results obtained on a NEGATIVE-GRID TRIODE OSCILLATOR AND AMPLIFIER 573 pentode of similar rating. A four-stage amplifier employing the inter- mediate tube gave comparable results and although experimental data are not yet available, it seems reasonable to assume that the small size tube will permit of stable operation as an amplifier at frequencies as high as 1000 megacycles. The double-lead tube is therefore seen to possess a number of distinct advantages, both as oscillator and as amplifier, in the frequency range from 100 megacycles to 1000 megacycles. While the ultimate limit to which such developments may be pushed is still a matter of conjure it seems safe to predict that the triode will be able to meet the demands of the circuit designer at least for some time to come. Addendum to "Radio Propagation Over Plane Earth — Field Strength Curves" By CHAS. R. BURROWS IN the paper of the above title in the January 1937 issue of the Bell System Technical Journal, an approximation which was not ex- plicitly pointed out was made in deriving equation (17). A note from Mr. K. A. Norton* of the Federal Communications Commission points out that equation (17) does not give a reasonable result when r = 1, The explanation is that two terms which are unimportant except near the transmitter when the ground is a perfect dielectric were deleted. The complete equation is 2E W 1 1 + r2 ' 1 1 _ ^g(27r) M S,"0 ATTENUATION FACTOR (^/2Eo) 576 BELL SYSTEM TECHNICAL JOURNAL The situation in the immediate vicinity of the antenna is more clearly represented in Fig. 3A in which the attenuation factor is plotted against distance in wave-lengths. This allows inclusion of curves for € = 1 (i.e. for the earth replaced by air) and e = oo (which is equiva- lent to perfectly conducting earth). Comparison of these curves with the broken lines which are replotted from Fig. 2 shows that for dis- 10 \^ 3 -e=- 8 a 0 0 ) 6= 1 -X V e ^ A ^ • . \ A e = 0 \ M L 5 ° \ ^ ^ \ N^ \ 2 W V N^ 6 = 00 v_> ■?^ — — ' >^ >^y ^ y~- VS, ■^•> \/ >r *< ' V o ""^"""^-^ .^80 \ / ''S s "■^^^T^ 30 ^~- n =. \ /\ ,^ "^^ \ :i^\^ v'o ^Va, V. > K' ^^■\ A n 1 '0 0.02 0.05 0.1 0.2 0.5 1 2 3 4 DISTANCE IN WAVELENGTHS, d/\ Fig. 3A — Variation of attenuation factor with distance in wave-lengths for trans- mission over a dielectric plane. For d/\ small, ^/-. = C-iT)/(W- The broken curves are replots of the curve for ()= oo from Fig. 2. tances greater than a wave-length the main effect of using the curves of Fig. 2 is to ignore the presence of the oscillations in the curves. For a perfect dielectric the amplitudes of these oscillations do not decrease below ± l/e^/2 even at great distances as can be seen from equation (19). The presence of some conductivity causes these oscillations to be damped out. For example, a ^ of 5 reduces the amplitudes of these oscillations within the first four wave-lengths to a value too small to show on the figure. ADDENDUM TO "RADIO PROPAGATION OVER PLANE EARTH" 577 The second paragraph of the footnote referring to equation (17) should read : The differential equation given by Wise for ^IIo becomes ~ ^A'dd^'^ dd~d) ^^^ ^ \ r+72 ^ r=^* L 2^ddj\ "•■ {2widl\y J j ^''' when the value of >> = (1 + t^)4IIo is substituted in his equation (7) and the result divided by 1 + r^. The i of this paper is equal to — J in Wise's paper. By inter- changing ^1 and k-i in Wise's equation (7) and proceeding along parallel lines the corresponding equation of DYVo = y/{l + t-) is found to be 4Ti^\dd^^ dddj ° V 1 + r2 1 - r* L 2wid/X "^ {2irid/Xy J / °" Adding these two relations gives an expression for I —-7^ ")" j^ ) H, where n = 2{A + D)no, which when substituted in the above equation for E and the result divided by 2Eo, where Eo = — 240iw'^Tlo/'X, gives equation (17). Since Eq is the inverse distance component of the free space field, this relation for Eq follows from equation (11). In the last line of the footnotes on page 51 read 2/(1 + t^) for 2/(1 - r"). Abstracts of Technical Articles from Bell System Sources What Electrons Can Tell Us about Metals} C. J. Davisson. Some general statements are made about electron waves and electron diffraction, three typical investigations in which electron diffraction has been employed are described, and the technique of a new type of electron crystal analysis is discussed. Relation between Loudness and Masking} Harvey Fletcher and W. A. MuNSON. A functional relationship between the loudness of a sound and the degree to which it masks single frequency tones, that is, the masking audiogram of the sound, is developed. A loudness- masking function is determined experimentally. From tlris loudness- masking relationship the loudness of a sound can be computed by simply integrating the area under the masking audiogram plotted on a special chart. Comparisons of computed and observed loudness levels are shown for a number of sounds and serve to illustrate the precision to be expected from the method. Finally, the results of a large number of masking tests are given in the form of masking con- tours, which enable one to predict the masking audiogram of a sound from measurements of its intensity spectrum. Coupling between Parallel Earth-Return Circuits under D.-C. Tran- sient Conditions} K. E. Gould. In tests conducted in connection with several d.-c. railway electrifications, the induced voltages re- corded in paralleling communication circuits at times of short circuit on the railway have shown marked divergences from values computed on the basis of uniform earth resistivity and a rate of change of earth current determined from measurements in trolley and rail circuits. Due to the numerous factors which might contribute to these divergen- ces, such as non-uniform division of transient current along the tracks and associated return conductors, the presence of shielding conductors along or near the right-of-way, etc., it was felt that a better under- standing of the problem of induction under d.-c. transient conditions could be obtained by experimental studies of the transient coupling between parallel earth-return circuits, free from the effects of shielding conductors, and with concentrated, rather than distributed, grounds. The study described in this paper was undertaken for this purpose. 1 Jour, of Applied Physics, June 1937. ^ Jour. Acous. Soc. Amer., July 1937. ^ Electrical Engineering, September 1937. 578 ABSTRACTS OF TECHNICAL ARTICLES 579 The locations for the tests were selected to provide a reasonably large range of earth resistivity; also, at one location it was known that the earth structure departed substantially from uniformity. At each of these locations d.-c. transient coupling tests were performed in which transient currents, approximately of the form encountered during faults on d.-c. railway electrifications, were produced in an earth- return circuit, herein referred to as the primary, and measurements were made of the resultant voltages in earth-return circuits, herein called secondary circuits, parallel to and at separations from the primary circuit of from 50 or 60 to 2,000 feet. In addition to the d.-c. transient tests, measurements were made at each location of the steady state a.-c. coupling, in magnitude and phase angle, over a range of frequencies from 20 or 30 cycles to 3,200 cycles. From these a.-c. measurements the transient voltages were computed for a number of cases by evaluating the Fourier integral. The results of the a.-c. coupling tests were useful also in helping to explain, in a general way, the departures of the measured transient voltages from the voltages computed for uniform earth resistivity. The measured transient voltages and voltages computed (1) from the a.-c. coupling measurements and (2) on the basis of a uniform earth resistivity, are shown for several representative cases in figures accompanying the paper. The Shunt-Excited Antenna.'^ J. F. Morrison and P. H. Smith. The paper describes an arrangement for exciting a vertical broadcast antenna with the base grounded. Construction economy results through the elimination of the base insulator, the tower lighting chokes, and the usual lightning protective devices. The coupling ap- paratus at the antenna end of the transmission line is reduced to an extent which may make unnecessary a separate building for its pro- tection. Greater freedom from interruptions resulting from static discharges is expected. The performance of the design is substan- tially the same as that obtained from the antennas now in general use. The paper describes experimental work done, results obtained, and inferences to be drawn from them. A mathematical appendix is attached. Some Fundamental Experiments with Wave Guides.^ G. C. South- worth. This paper describes in considerable detail the early ap- paratus and methods used to verify some of the fundamental properties of wave guides. Cylinders of water about ten inches in diameter and *Proc. I.R. £., June 1937. ^Proc. I.R. £., July 1937. 580 BELL SYSTEM TECHNICAL JOURNAL four feet long were used as the experimental guides. At one end of these guides were launched waves having frequencies of roughly 150 megacycles. The lengths of the standing waves so produced gave the velocity of propagation. Other experiments utilizing a probe made up of short pickup wires attached to a crystal detector and meter enabled the configuration of the lines of force in the wave front to be determined. This was done for each of four types of waves. For certain types the properties had already been predicted mathematically. For others the properties were determined experimentally in advance of analysis. In both cases analysis and experiment proved to be in good agreement. The Dependence of Hearing Impairment on Sound Intensity.^ John C. Steinberg and Mark B. Gardner. This paper discusses the measurement of hearing loss for levels of sound that were well above the deafened threshold and hence were audible to the deafened person. In the tests, observers having unilateral deafness, i.e., one impaired and one normal ear, balanced a tone heard with the deafened ear against the tone heard with the normal ear. For some persons, the impaired ear heard less well than the normal ear for all sound levels. For others, tones which were well above the deafened threshold were heard about equally well with either ear. In other words, such deaf- ened ears tended to hear loud sounds with normal loudness. It was found that this type of deafness could be represented quantitatively on the assumption that it was due to nerve atrophy. Loudness judgments for a normal ear in the presence of noise were found to be similar to judgments by a nerve deafened ear. Relations, based on the loudness properties of normal ears, have been extended to represent the loudness heard by deafened ears. ^ Jour. Acous. Soc. Amer., July 1937. Contributors to this Issue H. A. Affel, S. B. in Electrical Engineering, Massachusetts Insti- tute of Technology, 1914; Research Assistant in Electrical Engineering, 1914-16. American Telephone and Telegraph Company, Engineering Department and the Department of Development and Research, 1916-34; Bell Telephone Laboratories, 1934-. As Assistant Director of Transmission Development, Mr. Afifel is engaged in development work connected with^carrier telephone and telegraph systems. Ralph Bown, M.E., 1913; M.M.E., 1915; Ph.D., 1917, Cornell University. Captain, Signal Corps, U. S. Army, 1917-19. American Telephone and Telegraph Company, Department of Development and Research, 1919-34; Bell Telephone Laboratories, 1934-. As Radio Research Director, Dr. Bown is concerned wuth radio development problems. He is a Past President of the Institute of Radio Engineers. Charles R. Burrows, B.S. in Electrical Engineering, University of Michigan, 1924; A.M., Columbia University, 1927; E.E., Univer- sity of Michigan, 1935. Research Assistant, University of Michigan, 1922-23. Western Electric Company, Engineering Department, 1924- 25; Bell Telephone Laboratories, Research Department, 1925-. Mr. Burrows has been associated continuously with radio research and is now in charge of a group investigating the propagation of ultra-short waves. John R. Carson, B.S., Princeton, 1907; E.E., 1909; M.S., 1912. American Telephone and Telegraph Company, 1914-34; Bell Tele- phone Laboratories, 1934-. As Transmission Theory Engineer for the American Telephone and Telegraph Company and later for the Labora- tories, Mr. Carson has made substantial contributions to electric circuit and transmission theory and has published extensively on these subjects. He is now a research mathematician. Thornton C. Fry, A.B., Findlay College, 1912; A.M., University of Wisconsin, 1913; Ph.D., 1920; Instructor in mathematics. University of Wisconsin, 1912-16. Mathematician, Western Electric Company, 1916-24; Bell Telephone Laboratories, since 1924. Lecturer electrical engineering, M.I.T., 1927; Lecturer mathematics, Princeton, 1929-30. Dr. Fry's work in the Laboratories has been of a mathematical character, 581 582 BELL SYSTEM TECHNICAL JOURNAL J.M.Manley, B.S. in Electrical Engineering, University of Missouri, 1930; Bell Telephone Laboratories, 1930-. Mr. Manley has been en- gaged principally in theoretical studies of non-linear electrical circuits. W. P. Mason, B.S. In Electrical Engineering, University of Kansas, 1921 ; M.A., Columbia University, 1924; Ph.D., 1928. Bell Telephone Laboratories, 192 1-. Dr. Mason has been engaged in investigations on carrier transmission systems and more recently in work on wave transmission networks, both electrical and mechanical. Pierre Mertz, A.B., Cornell University, 1918; Ph.D., 1926. American Telephone and Telegraph Company, Department of De- velopment and Research, 1919-23, 1926-34; Bell Telephone Labora- tories, 1934-. Dr. Mertz has been engaged in special problems In toll transmission, chiefly In telephotography and television. S. O. Morgan, B.S. In Chemistry, Union College, 1922; M.A., Princeton University, 1925; Ph.D., 1928. Western Electric Company, Engineering Department, 1922-24; Bell Telephone Laboratories, 1927-. Dr. Morgan's work has been on the relation between dielectric properties and chemical composition. E. J. Murphy, B.S., University of Saskatchewan, Canada, 1918; McGIU University, Montreal, 1919-20; Harvard University, 1922-23. Western Electric Company, Engineering Department, 1923-25; Bell Telephone Laboratories, 1925-. Mr. Murphy's work Is largely con- fined to the study of the electrical properties of dielectrics. E. Peterson, Cornell University, 1911-14; Brooklyn Polytechnic, E.E., 1917; Columbia, A.M., 1923; Ph.D., 1926; Electrical Testing Laboratories, 1915-17; Signal Corps, U. S. Army, 1917-19. Bell Telephone Laboratories, 19 19-. Dr. Peterson's work has been largely In theoretical studies of carrier current apparatus. K. W. Pfleger, A.B., Cornell University, 1921 ; E.E., 1923. Ameri- can Telephone and Telegraph Company, Department of Development and Research, 1923-34; Bell Telephone Laboratories, 1934-. Mr. Pfleger has been engaged in transmission development work, chiefly on problems pertaining to delay equalization, delay measuring, tem- perature effects In loaded-cable circuits, and telegraph theory. A. L. Samuel, A.B., College of Emporia (Kansas), 1923; S.B. and S.M. in Electrical Engineering, Massachusetts Institute of Tech- nology, 1926. Instructor in Electrical Engineering, Massachusetts CONTRIBUTORS TO THIS ISSUE 583 Institute of Technology, 1926-28. Bell Telephone Laboratories, 1928-. Mr. Samuel has been engaged in research and development work on vacuum tubes. C. C. Taylor, B.S. in Electrical Engineering, Colorado College, 1917. American Telephone and Telegraph Company, Long Lines Department, 1920-28; Department of Development and Research, 1929-34. Bell Telephone Laboratories, 1934-. Mr. Taylor's work has been concerned with radio-wire systems. L. R. Wrathall, B.S., University of Utah, 1927; Graduate School, 1927-28. Bell Telephone Laboratories, 1929- Mr. Wrathall has been engaged in the study of non-linear reactances. S. B. Wright, M.E. in Electrical Engineering, Cornell University, 1919. Engineering Department and Department of Development and Research, American Telephone and Telegraph Company, 1919-34; Bell Telephone Laboratories, 1934-. Mr. Wright is engaged in trans- mission development of radio systems. r:i,' '1;: !■ ' ',('.'. I'v'r'' ..,'.t..;'i'n)i .,H ^Mm ■sm m tiimimtisidmt,aiM