sign in sign up
<<
Home , Harry Nyquist, Hendrik Wade Bode, Loop gain

THE OLDENBURGER MEDAL 1975 of the truly great esteem in which they are held by their colleagues Introduction and contemporaries. And for us in the ASME it seemed par­ ticularly fitting to honor especially a unique member of our own The ACD Honors Committee made the decision to present its Division who had not only contributed to its parochial concerns tff0 Oldenburger Medals in 1975 in consequence of some very and prestige but who also played a key role in the very formation special circumstances. of the organization meeting here today—IFAC—and of its Amer­ First, the 6th Triennial World Congress of the International ican affiliate, the American Automatic Control Council. Federation of Automatic Control was to be held in Cambridge/ This unusual man was Rufus Oldenburger: all American, but Boston in August partly in recognition of the U.S. Bicentennial a world figure, whom many of you remember vividly and fondly. Celebration which had begun with the 200th anniversary of the Thus not only was our new award to be named in his honor The Battles of Lexington and Concord. Rufus Oldenburger was him­ Oldenburger Medal, but he also became its first recipient in 1968. self instrumental in organizing IFAC and was very active in that Thus in this small gesture we trust he may have realized before organization. Moreover the ASME/ACD itself participates his untimely passing how much all in this room are beholden to actively in IFAC through the American Automatic Control him.

Council. Thus it was the intention of the Automatic Control Of the subsequent Oldenburger medalists, several are at this Downloaded from http://asmedigitalcollection.asme.org/dynamicsystems/article-pdf/98/2/125/5778038/125_1.pdf by guest on 29 September 2021 Division to honor that association by presenting before that IFAC Congress and I believe are also here in this auditorium. distinguished world body of delegates an Oldenburger Medal to If they are so present, we would appreciate their standing to be Hendrik Bode who lives and works in Cambridge and who recognized as I call our their familiar names: needed no introduction to that group. 1969: Nathaniel B. Nichols At the same time, the ASME was to hold its Winter Annual 1970: John R. Ragazzini Meeting in Houston in December. In this case it was felt possible 1971: "Doc" C. Stark Draper to have the second Oldenburger Medalist, , make 1972: Albert J. Williams, Jr. the trip from Harlingen, Texas to Houston to receive the award 1973: "Doc" Clesson E. Mason in person. 1974: Herbert W. Ziebolz In this way the pairing of these two "giants of via frequency response" as Oldenburger Medalists came about Now it has been our past custom to make this award at our very naturally. ASME annual meeting. Indeed we shall return to this custom The rest of the account of the two Award Ceremonies follows next wintei in making our award of a second 1975 Oldenburger below, together with some biographical material. Additional Medal to Harry Nyquist, another giant whose very name is documentation under the title "The Fundamental Contributions sufficient identification to all here assembled. of Nyquist and Bode to Automatic Control Theory" is planned But today at this very time and place, before a group singularly for the September issue of this Journal. able to appreciate and to honor him we wish to present an Olden­ burger Medal to one whose name, like Nyquist, is another "household word" throughout IFAC and the control profession The Presentation of The Oldenburger Medal across this planet. to In fact, I will let you guess his name from a few verbal clues Dr. Hendrik W. Bode taken verbatim from his landmark book finally appearing in OCCASION: declassified hard-covers just three short decades ago: ; The Oldenburger Medal was presented to Dr. Bode as a formal (a) design part of the Gth Triennial World Congress of IFAC, meeting at (6) and log frequency scale M.I.T. in Cambridge during the last week in August, 1975. The (c) margin and presentation occurred at a Plenary Awards Assembly held in (d) gain-phase relations M.I.T.'s Kresge Auditorium on August 27 (a magnificent sum­ (e) minimum phase condition and circuits mer afternoon) before approximately 800 IFAC delegates and (/) compensation friends. One should note that the brevity of the introductory remarks If you haven't guessed B-O-D-E as the household word, per­ and the response by the medalist was due to the limitation to haps you've missed something essential in automatic control just twenty minutes for the entire ceremony! This "telescoping" fundamentals! of an historic moment was not the intention of the ASME/ACD, This remarkable individual is thus already immortalized in but a result of IFAC scheduling of a clambake immediately fol­ that method of presenting frequency response data which bears lowing the award! his name. But the fact that these diagrams play such a vital and direct role in design process of active feedback control PRESENTATION REMARKS BY H. M. PAYNTER: made of real hardware better foretells his many additional lasting contributions to our peculiar art and craft. Thank you, Dr. Coales. The fertile notions for which we honor our medallist today Delegates and Friends: were brought forth during his four decades of service with , but most particularly, during the remarkable 1930's as I speak to you today on behalf of the President of The Ameri­ he and his associates wrestled with optimal designs of communi­ can Society of Mechanical Engineers, who is unable to be present cation systems based on fruitful marriages of passive filter cir­ in person today. cuits with active feedback , following the inventions Like solid-state technology and like science, the of H. S. Black and the disclosures of Nyquist's regeneration newly emergent field we are pleased to call automatic control is theory. still so young and vigorous that many of its leaders and pioneers Perhaps it was just our medallist's particular good fortune to are still alive and well; indeed many are here with us today at be the right man at the right place at the right time working this 6th Triennial World Congress of IFAC. on the right problem; in his modesty he will surely put it thU In conscious recognition of this remarkable fact, the Automatic way. Control Division of The American Society of Mechanical Engi­ So quite naturally those very signal shaping design procedures neers decided a decade ago to honor some of our heroic figures using active feedback circuitry which worked so well for com­ with a suitable award and medallion as a representative token munication systems in the 1930's, were equally successful when

Journal of Dynamic Systems, Measurement, and Control JUNE 1976 / 12S Copyright © 1976 by ASME applied to the control systems of the 1940's and the high-speed the solution of all problems in control theory, and of cour< computing systems of the 1950's. they didn't, they were at least highly suggestive. But our man's surest insights were to reveal so clearly and so It is worth noting that somewhat the same relation exist, permanently that even feedback and amplifiers could not per­ today. The growing sophistication of signalling theory, hayxl form miracles against Nature's inexorable energy constraints and now on Shannon's theorem and computer processing, matches causality conditions! It is this aspect of his work which is even the growing complexity of control problems. now bearing further fruit, perhaps unbeknownst to him, in high- My own contributions to this early signalling theory were energy particle and scattering theory of the 1960's and quite meager, but there were, of course, important contributions 1970's. from others. One thinks immediately of the Campbell-Fo^M But in our limited time we would all prefer to hear from our table pf Fourier transforms, or MacColl's book on servo-mecha­ medallist himself. nisms, for example. However, the outstanding name is clearly It is therefore my great personal pleasure to announce that on that of Harry Nyquist who is, I am told, also to receive the behalf of the Automatic Control Division of the ASMB that the Oldenburger Medal this year. Oldenburger Medal has been awarded to Dr. Hendrik W. Bode, Nyquist is outstanding both for the importance and the variety

Emeritus Gordon MacKay Professor of Systems Engineering at. of his contributions. Control theorists know him as the author Downloaded from http://asmedigitalcollection.asme.org/dynamicsystems/article-pdf/98/2/125/5778038/125_1.pdf by guest on 29 September 2021 . of the Nyquist stability criterion. Modern communications engi­ Would he kindly step forward to receive the award and hear neers base their calculations on the Nyquist sampling thcorcn the citation? and the Nyquist interval. Circuit theorists turn to the Nyquist formula for thermal noise in electrical circuits. In between times Citation he became the author of more than a hundred inventions. Nyquist was my senior by 12 or 15 years when I first joined To : "In recognition of his attain­ Bell Labs. I looked up to him almost from the start. I am very ments in advancing the science and technology of automatic much flattered to have my name coupled with his on this oc­ control and particularly for his development of casion. techniques that are widely used in the design of feedback control My last reason for special satisfaction with the award is that it systems." allows me to emerge with some grace from a hole I dug for my­ self in writing the "History of an Idea" paper. Most of the paper The Oldenburger Award Response was indeed historical, but I also tried to suggest the powiblo future, and my forecast was quite gloomy. I recall in particular by Hendrik W. Bode making the point that the best and easiest mathematics was 197S 0ld@nbur§@r Specialist probably in a sense "used up," and thus not available for the easy generation of technical results in the control field. In addi­ Thank you very much, Professor Paynter. I am both pleased tion I expressed some qualms about the viability of the partner­ and flattered at being awarded the Oldenburger Medal for 1975. ship of communication theory and control theory generally. The flattery we can take for granted, but I would like to say a This, I said, was a sort of shotgun marriage forced upon in hy few words about the reasons which make the occasion a particu­ the pressures of military problems in World War II. However, larly pleasant one for me. the partners in the marriage had different long-term interest*, These reasons stem primarily from the fact that my actual and perhaps it was time for them to go their separate ways— work in the control field was done so long ago—30 or 40 years so I said. ago. This makes anything I can say now necessarily retrospec­ Of course I could not have been more wrong. What one soea, tive. In fact, I wrote a retrospective paper under the title "Feed­ in going about these meetings, is a vigorous, lively field, full of back, the History of an Idea" in 1960, so that what I might say interest and thoroughly capable of absorbing inputs of many now must be retrospective at the second level, so to speak. The sorts and of extending to cover more and more of the critical 1960 paper, intended for an audience of circuit theorists, was problems in our modern world. The partnership is more viable focussed Strongly on amplifiers as used for than ever. I am delighted that it worked out this way, and want communications circuits, a subject to which I will return briefly formally to recant my early pessimism. Thank you again. later on. My first cause for satisfaction, then, is that there is anything surviving to be pleased about. In 30 or 40 years, one expects his ON HENDRIK W. BODE intellectual babies to be nibbled at and finally buried by a flood Further Comments by H. M. Paynter of better ideas. It is reassuring to find that even a little of one's Hendrik Bode has made many contributions to the field of work is still viable. One can feel he is enjoying a certain mild feedback amplifiers and automatic control which are further de­ immortality. tailed in a tribute entitled "The Fundamental Contributions of I find the 30-40 year perspective also comforting in another Nyquist and Bode to Automatic Control Theory" which will way. It gives me a better understanding than I might otherwise appear in the September, 1976 issue of this Journal. Uclnw have of the really significant elements in the long-term theoretical follows but a thumbnail account. development of the field. Professor Paynter pointed out the importance of the complex variable approach which of course BI63KAPHICAL NOTES: underlies my own work. It is worth noting, however, that before Hendrik Wade Bode was born December 24, 1905 in Madwon, one can have the complex variable approach at all we must have Wisconsin. After attending high school in Urbana, Illinois and converted the original randomly varying signals to an equivalent normal school in Tempe, Arizona, he received a B.A. in 1924 bundle of steady state sinusoids, using Fourier—later Laplace— and an M.A. in 1926 from . He became ft transforms. This is almost a philosophical matter involving a member of the technical staff of Bell Telephone Laboratories in basic question of what we mean by signalling anyway. The job 1926. Receiving a Ph.D. in Physics from was effectively done in the mid and late 1920's by J. R. Carson in 1935, he became, in turn, in charge of the Bell Labs Mathe­ of the AT&T Company and Vannevar Bush here at M.I.T., matics Research group from 1944 to 1952, director of Mathe­ starting more or less from Heaviside's original operational cal­ matics Research 1952 to 1955, and director of Research in Physi­ culus. With additional contributions from other sources, this cal Sciences from 1955 to 1958. In 1958, he became Vice Pru­ gave us a large stock of "worked examples," so to speak, from dent of Military Systems Engineering at Bell Labs, a post which the communications field. If they did not immediately lead to he held until his retirement in 1967. Upon that occasion he

116 / JUNE 1976 Transactions of the ASME brtntne Gordon MacKay Professor of Systems Engineering at arranged that the award would be accepted on his behalf by his Harvard University, continuing his activities in that field. grandson, Paul L. Monroe, followed by a response in the form of a tribute by John C. Lozier, of Bell Laboratories, who had HONORS: just completed his three year term as President of IFAC, who l)r. Bode has leceived the following honors and awards: was a close friend and colleague of Rufus Oldenburger, and who Presidential Certificate of Merit, 1948 as an "old boy" at Bell Labs, knew both Nyquist and Bode, IEEE Edison Medal, 1969 personally. Member, National of Science As a further treat at the dinner, we were privileged to have as Member, National Academy of Engineering guests a group of delegates from the Chinese Mechanical Engi­ , American Academy of Arts and Sciences neering Society of the People's Republic of China who were Fellow, IEEE, APS, SIAM nearing the end of a one-month U.S. tour of automatic control research and manufacturing establishments. In this way, no Publications and Patents: less than for Bode, Nyquist was honored in a truly international context! pr. Bode's publications include the following: Thus, while Dr. Nyquist could not be present in person at the Downloaded from http://asmedigitalcollection.asme.org/dynamicsystems/article-pdf/98/2/125/5778038/125_1.pdf by guest on 29 September 2021 1 Bode, H. W., "Future of Engineering Mathematics — A Dinner in his honor, Paul Monroe made a tape of Jack Lozier's Customer's View-Point," /. Eng. Educ, 52:189-99, 1961. speech. Paul's mother (and Nyquist's daughter), Helen Nyquist 2 Bode, H. W., "Reflections on the Relation Between Weekes, then carried the medal and citation, together with the Science and Technology," Basic Research & National Goals, tape and its transcription to her father in Harlingen, Texas. Wellington National Research Council, 41-76, Mar. 1965. 3 Bode, H. W., "Feedback — The History of an Idea," Besides Jack Lozier's remarks, we are reprinting by way of Brooklyn Polytechnic Inst., Research Inst., Proc. further response, Nyquist's Luncheon remarks made in 1953 on Sump- on Active Networks and Feedback Systems, 1961. the occasion of the ASME Frequency Response symposium or­ •1 Bode, H. W., and Shannon, C. E., "Simplified Derivation ganized by Rufus Oldenburger and later reprinted in Oldenbur- of Linear Least Square Smoothing and Prediction Theory," Pror. I.R.E., 38:417-425, Apr. 1950. ger's book Frequency Response which was dedicated to Harry 5 Bode, H. W., Network Analysis and Feedback Design, Nyquist. 1945 (book). 6 Bode, H. W., "Relations Between Attenuation and Phase Citation in Feedback Amplifier Design," Tech. JL, 19:421-54, Julv 1940. To HARRY NYQUIST: "In recognition of his attainments 7 Bode, H. W., "Variable Equalizers," Bell System Tech. in advancing the science and technology of automatic control JL, 17:229-244, Apr. 1938. and particularly for his development of the Nyquist stability H Bode, H. W., "Impedance and Energy Relations in Elec­ trical Networks," Physica, 5:143-144, Mar. 1938. criterion that is used extensively in the analysis and design of fl Bode, H. W., and Dietzold, R. L., "Ideal Wave Filters," feedback control systems." Bell System Tech. JL, 14:215-52, Apr. 1935. 10 Bode, H. W., "General Theory of Electric Wave Filters," ./. Math. & Pyhsics, M.E.T., 13:275-362, Nov. 1934. The Oldenburger Award Response 11 Bode, H. W., "A Method of Impedance Correction," Hell System Tech. JL, 9:794-835, Oct. 1930. An Appreciation of Harry Nyquist by Following is a list of 15 of the 25 U.S. Patents that have been John C. Losier fannled to Dr. Bode: Bell Laboratories Though Harry Nyquist is being honored with the Oldenburger PATENT NO. PATENT DATE SUBJECT Medal tonight for his work on the stability of feedback systems, <1) 2,744,224 5-1-56 Automatic Curve Follower with Vibrating Stylus I think we will gain a better perspective of his work if we go back (2) 2,455,035 11-30-48 Averaging Mechanism to 1928. This was the year that he published the now classic (3) 2,492,351 12-27-49 Smoothing Network paper entitled "Certain Topics in Telegraph Transmission M) 2,710,720 6-14-55 Computer Theory." This paper included the famous "Nyquist Rate" for (5) 2,367,711 1-23-45 Broad Band Amplifier pulse transmission. (6) 2,337,965 15-28-43 Coupling Networks (7) 2,342,638 2-29-44 Wave Transmission To appreciate this work fully we have to remember the state Networks of the art in telegraph transmission in 1928. (8) 2,315,040 3-30-43 Electric Wave At this time the primary design tool for the telegraph engineer Amplification (9) 2,249,415 7-15-41 Wave Filter was the pulse response of the system. Using the pulse response, (10) 2,123,178 7-12-38 Amplifiers one could see just how closely successive pulses could be spaced 01) 2,058,210 10-20-36 Wave Transmission without excessive intersymbol interference. For theoretical sup­ Networks port there was Heaviside's work showing the tie between the (12) 2,002,216 5-21-35 Wave Filters transient response and the frequency response. However in real (13) 2,035,258 3-24-36 Wave Filters (14) 1,944,209 1-23-34 Transmission Networks systems it is very difficult to determine the transient response (15) 1,828,454 10-20-31 Transmission Networks analytically, as Nyquist pointed out. This must have been a frustrating time for an engineer. He The Presentation of the Oldenburger Medal must have known instinctively that there was a maximum realiz­ to able pulse transmission rate for any real system, but he had no way of finding what this maximum might be. He must also have Dr. Harry Nyquist realized that there was a preferred shape to the frequency re­ OCCASION: sponse for realizing the maximum pulse rate, but there were no As indicated previously, the Oldenburger Medal was planned guidelines as to what form the prefered shape might take. The 'or presentation to Dr. Harry Nyquist on the occasion of the basis tools for exploring these questions were simply not available Eighth Annuai Oldenburger Award Dinner on the evening of to him. December 1, 1975 at the Sheraton Hotel in Houston, Texas. Though this situation might have been frustrating to an engi­ After plans had been made, it was realized that it would not in neer it provided a field day for gadgeteers. Their hope was to 'act be possible for Dr. Nyquist to be present in person to receive find some magic equalizer that could produce a narrow pulse the medal and to be "hassled" in our usual manner. It was then response over a narrow band system.

Journal of Dynamic Systems, Measurement, and Control JUNE 1976 / 127 However Nyquist's 1928 paper showed: involves the equalizing networks needed to properly shapo tl Nyquist diagram. F. B. ("Feed Back") Anderson, a colleague (a) That there was indeed a maximum pulse rate, and it was f Black, had plotted the gain and phase characteristics of all kind related to the bandwidth; of filters, hoping, like many others to find a network which had (ft) That this maximum pulse rate was numerically equal to sharp gain cutoff versus frequency, but little phase lag. twice the bandwidth; This is where Hendrick Bode came into the picture, [n (c) That these results were "substantially" independent of brilliant piece of analysis he showed that the attenuation and the number of pulse levels used. (Substantially was-the phase characteristics of physically realizable networks were v>. word Nyquist used.) lated, and that there was a minimum phase lag associated with He also showed a whole family of steady state gain, and phase each attenuation characteristic. Anderson's search was over characteristics that would permit the maximum pulse rate. With Bode's gain and phase relationships, one could now derive From reading the paper again recently, I was struck by the an equalizer that would shape the Nyquist diagram most ef­ realization that what he thought most important was that these fectively. results provided a steady state approach to the design of tele­ So Nyquist and Bode together transformed feedback amplifier graph transmission systems. Later he was to do much the same design from an art to a science; in doing so they laid the haaij Downloaded from http://asmedigitalcollection.asme.org/dynamicsystems/article-pdf/98/2/125/5778038/125_1.pdf by guest on 29 September 2021 thing for feedback amplifier design with his regeneration theory. for engineering. However the 1928 scene would not be complete without men­ tion of R.V.L. Hartley and his classic paper on "The Trans­ mission of Information." Hartley was director of research in telephone and telegraph systems at Bell Laboratories and his paper was also published in the B.S.T.J. in the next issue after Nyquist's paper. The Regeneration Theory Hartley took a different approach. He introduced the con­ by H. Nyquist cept of a unit or bit of information, showed how to find the in­ Luncheon address presented at the Frequency Response Symposium, held formation content of various kinds of signals, and also showed at the Annual Meeting, New York, N. Y., November 29-December 4, 1053, how to measure the capacity of a system to transmit these bits of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS. of information. His conclusion was that the capacity of a system From "Frequency Response/' Oldenburger, R., editor, The MacMillan Co. to transmit information is equal to the bandwidth over which the N.Y., Copyright THE AMERICAN SOCIETY OP MECHANICAL ENGINEER*, 195fl. frequency response is essentially uniform. So Nyquist, and Hartley between them made 1928 a vintage The following is an explanation of the circumstances which year for transmission engineering. Of course these results were led the author to write his 1932 paper on the "Regeneration obtained for systems in absence of noise, and also implicitly in Theory."i the absence of power limitations. It was left to For some years prior to the time of writing the paper in to take the next step and incorporate these constraints in his question, the technical departments of the Bell System had been "Mathematical Theory of Communications" some 18 years engaged in developing a carrier system for use in cables. Pre­ later. viously the long telephone circuits in cables had been confined I find it remarkable that only four years after Nyquist changed to the audible frequency range and this limited the number of telegraph transmission from an art to a science, he was to do circuits obtainable to three circuits per quad of conductors. This much the same for feedback systems with his 1932 paper on yield was limited further by the need for four-wire operation on "Regeneration Theory." the longest circuits. Four-wire operation means that the two di­ Harold Black had invented the feedback amplifier in the late rections of transmission required separate conduction paths. 20's. This work was very important because these feedback The net result was that for these long circuits eight conductors or amplifiers were the first amplifiers that promised a linearity of two quads were required to obtain theree telephone circuits. to one part in two thousand, as required for long distance carrier telephone systems. Multiplex Operation By 1932 Black and his colleagues were able to build remarkably good feedback amplifiers. However, as Nyquist pointed out in The carrier art as practiced on open wire circuits was well ad­ his paper, stability was something of a mystery. Some amplifiers vanced, and for such circuits it had resulted in substantial "sang" when the was increased, and others "sang" economy in conductor costs because a large range abovn the when the gain was decreased, no one really knew why. audible was used and this made multiplex operation possible. It As you know, Nyquist solved the mystery by showing that the was natural to think that similar carrier operation would be stability of a feedback loop could be determined from the locus applicable to cable circuits as well. But cable operation posi'd a formed by the polar plot of the open loop gain versus frequency. number of problems. Because the conductors were small the This became the so called Nyquist diagram. attenuation was large and this required close repeater sp'icins When his proof was questioned, Nyquist's answer was that it and special techniques for compensating for temperature efforts passed the test of a good proof; it explained the known results, on the attenuation. Because the conductors were close together and it stood up to experimental verification. Later another of there were new problems in coupling between circuits which had Nyquist's colleagues, Leroy MacColl, showed that Nyquist's to be taken care of. proof was related to the Cauchy integral theorem, and then Of these various problems, we are here concerned with the re­ everyone was happy. peater. Mr. Black proposed a negative feedback repeater and Of course the engineers were delighted with Nyquist's results proved by tests that it possessed the advantages which he had from the beginning. Not only was the stability mystery cleared predicted for it. In particular, its gain was constant to a high de­ up, but they could now determine the dynamic behavior of the gree, and it was linear enough so that spurious signals caused by closed loop system from the shape of the Nyquist diagram in the the interaction of the various channels could be kept within per­ neighborhood of the (1, 0) point. So again Nyquist had provided missible limits. a frequency response tool to solve transient behavioral problems, in this case problems of stability, damping, etc, in feedback loops. However feedback amplifier design was still something of an '"The Regeneration Theory," by H. Nyquist, Bell System Technical Journ art. One of the critical problems in feedback amplifier design Vol. 11, 1932, pp. 126-147.

128 / JUNE 1976 Transactions of the ASME l-'nr best results, the feedback factor, the quantity usually mal noise data, transmission, and negative feedback." I ,i,i\vii as pfi, had to be numerically much larger than unity. The Franklin Institute: 1960 is-iibility of stability with a feedback factor greater than unity "for his theoretical analyses and practical inventions in ...w puzzling. Granted that the factor is negative it was not the field of communications systems during the past nlivious how that would help. If the factor was minus 10, the forty years including, particularly, his original work in pffcrt of one round trip around the feedback loop is to change the the theories of telegraph transmissions, thermal noise in nrnitude 0f an original current from, say, 1 to —10. After a electrical conductors, and in the theory of feedback sys­ gerund trip around the loop the current becomes 100, and so tems." forth. The totality looks much like a divergent series and it was AIEE: Mervin J. Kelly Award 1961 not clear how such a succession of ever-increasing components National Academy of Engineers: 9th Founders Medal 1969 could add to something finite and so stable as experience had shown. Publications and Patents: Author's Part in the Problem Dr. Nyquist's publications include the following:

1 Nyquist, H., Rice, S. O., and Riordan, J., "Distribution of Downloaded from http://asmedigitalcollection.asme.org/dynamicsystems/article-pdf/98/2/125/5778038/125_1.pdf by guest on 29 September 2021 The missing part in this argument is that the numbers that Random Determinants," Quart. App. Math., 12:97-104, July describe the successive components 1, —10, 100, and so on, 1954. 2 Nyquist, II., and Pfleger, K. W., "Effect of the Quardature represent the steady state, whereas at any finite time many of Component in Single Sideband Transmission," Bell System Tech. the components have not yet reached the steady state and some JL, 19:63-73, Jan., 1940. of tlitm, which are destined to become very large, have barely 3 Nyquist, H., "Stabilized Feedback Amplifiers," Discussion reached perceptible magnitude. My calculations were princi­ of Paper by H. S. Black, Elec. Eng., 53:1311-21, Sept. 1934. 4 Nyquist, H., Regeneration Theory," Bell System Tech. Jl., pally concerned with replacing the indefinite divergent series 11:126-147, Jan., 1932. Oldenburger, R., ed., Frequency Response, rufwrred to by a series which gives the actual value attained at a 1956, p. 3. specific time I. The series thus obtained is convergent instead of 5 Nyquist, H., and Brand, S., "Measurement of Phase Dis­ divergent and, moreover, converges to values in agreement with tortion, Bell System Tech. JL, 9:522-549, July, 1930. 6 Nyquist, H., "Thermal Agitation of Electric Charge in tho experimental findings. Conductors," Phys. Rev., 32:110-113, July 1928. This explains how I came to undertake the work. It should 7 Nyquist, H., Shanck, R. B., and Cory, S. I., "Measure­ perhaps be explained also how it comes to be so detailed. In the ment of Telegraph Transmission," AIEE JL, 46:231-240, Mar., course of the calculations, the facts with which the term condi­ 1927; discussion, 385-386, Apr., 1927, AIEE Trans., 46:367-376; discussion, 376, Feb., 1927. tional stability have come to be associated, became apparent. 8 Hamilton, B. P., Nyquist, H., Long, M. B., and Phelps, One aspect of this is that it is possible to have a feedback loop W. A., "Voice Frequency Carrier Telegraph System for Cables," which is stable and can be made unstable by increasing the loop AIEE Jl. 44:213-218, Mar. 1925. loss. This seemed a very surprising result and appeared to re­ AIEE Trans., 44:327-332, Feb. 1925. quire that all the steps be examined and set forth in full detail. Elec. Comm., 3:288-294, Apr. 1925. Following is a list of 15 of the 138 U.S. Patents that have been ON HARRY NYQUIST granted to Dr. Nyquist:

Further Comments by H. M. Paynter PATENT NO. PATENT DATE SUBJECT Harry Nyquist has made many contributions to the field of (1) 2,749,508 6-5-56 Measurement of Trans­ feedback amplifiers and automatic control which are further de­ mission Time (2) 2,345,881 4-4-44 Correction of Distorted tailed in a tribute entitled "The Fundamental Contributions of Telegraph Signals Nyquist and Bode to Automatic Control Theory" which will (3) 2,291,555 7-28-42 Wave Transmission appear in the September, 1976 issue of this journal. Below fol­ (4) 2,300,133 10-27-42 Braod Band Amplifiers lows a thumbnail account. (5) 2,188,758 1-30-40 Transmission and Reception of Frequency Modulated BIOGRAPHICAL NOTES: Waves (6) 2,259,000 10-14-41 Transmission of Frequency Harry Nyquist was born in Nilsby, Sweden, February 7, 1889. Modulated Waves He received a BA and BS in E.E. in 1914 and an M.S. in 1915 (7) 2,184,978 12-26-39 Carrier Current Telegraphy from the University of North Dakota, followed by a PhD in (8) 2,135,596 11-8-38 Relay Circuit Physics from Yale in 1917. He was employed as a communica­ (9) 2,105,927 1-18-38 Gain Control System 1,926,169 9-12-33 Phase and Frequency tions engineer at A.T.&T. from 1917 to 1934, joining the Bell (10) Control Labs in that latter year. Dr. Nyquist retired from Bell Labs in (ID 1,915,440 6-27-33 Regenerative Amplifier and 1954. Method of Determining its Stability HONORS: (12) 1,887,599 11-15-32 Constant Current Dr. Nyquist is the recipient of the following honors and awards: Regulation Bell Telephone Laboratories: Service Award 1954 (13) 1,683,725 9-11-28 Phase Regulating System (14) 1,770,422 7-15-30 Phase Compensating Institute of Radio Engineers: Medal of Honor 1960 Networks "for contributions to quantitative understanding of ther­ (15) 1,565,491 12-15-25 Volume Control

Journal of Dynamic Systems, Measurement, and Control JUNE 1976 / 121