848) Some PROCEEDINGS OF THE IRE Notes on the History Mlay of Parametric Transducers* W. W. MUMFORDt, FELLOW, IRE Summary-This paper summarizes briefly the chronology of the development of parametric transducers. The early works of Michael Faraday (1831), F. Melde (1859), and Lord Rayleigh (1883) are cited as mechanical examples and the pioneering work of L. Kiihn, J. Zenneck, E. F. W. Alexanderson and R. V. L. Hartley are cited as electrical examples. A very brief resum6 of selected contributions follows, dating from the work on H. Q. North's diodes in 1945 to the present flurry of excitement beginning in 1954, created by the development of the Signal Corps-Bell Laboratories Task 8 varactor diodes. A list of 200 selected references is included. T -I HE recent interest in amplifiers which derive their gain from variable reactance circuit elements stems chiefly from the development of low-loss variable-capacitance diodes. There are two reasons for this interest. One reason is the fact that such amplifiers have low noise and the other is that the diodes are expected to have extremely long life. Either one of these properties is adequate justification for the excitement currently rampant throughout the world concerning the exploitation of this "new" type of amplifier, but, with two good reasons readily apparent, this excitation is doubled. Mystery seemed to invade the thoughts of people when the scientists announced this new type of anmplifier which was called a variety of names, such as: "Parametric Amplifier," "Reactance Amplifier" and "MAVAR" (Modulator Amplifier by Variable Reactance).1 Some of this mi-iystery could have been avoided had the moderni men known or mentioned that the principle underlying the miiechanism whereby electrical amplification was effected was an old principle. This principle may be broadly stated thus: The energy of an oscillating system may be increased by supplying energy at a frequency which differs from the fundamental freqbuency of the oscillator. One mechanical illustration of this principle is the simple pendulum. The child in the swing learns that he can "pump up" the amplitude of the oscillation of the swing by lowering his center of gravity on the down swing and raising it on the up swing. He thus "pumps" at twice the frequency of the swing. Who knows when this was invented? Could it have been in prehistoric times by a monkey swinging by his tail from the branch of a tree? Faraday, Melde and Lord Rayleigh have published observations and calculations concerning this principle. Quoting Lord Rayleigh, "Faraday, . . . with great ingenuity and success (upon exaim-iiiiing) . . . the crispations upon the surface of water which oscillates vertically, arrived at the conclusion experimentally that * Original manuscript received by the IRE, November 17, 1959; revised manuscript received, February 1, 1960. t Bell Telephone Labs., Whippany, N. J. These three names are considered herein to be synonymous and to apply to any device which derives its gain from the pumping of a I variable reactance. there were two complete vibrations of the support for each complete vibration of the liquid. Crispations (may be) observed upon the surface of liquid in a large wine glass or finger glass which is caused to vibrate in the usual manner by carrying the moistened finger round the circumference. All that is essenitial to the production of crispations is that the body of liquid with a free surface be constrained to execute a vertical vibration. Faraday's assertion that the waves have a period double that of the support has beeni disputed, but it may be verified in various ways." Faraday's work was published in 1831 and Lord Rayleigh verified his conclusions sixty years later, also with considerable ingenuity. The double period oscillation of the water is not readily proven by casual observation. The following example of the principle, reported by Melde in 1859, is, however, readily observed and understood. Quoting again from Lord Rayleigh, "Perhaps the best known example is that form of ?Melde's experiment in which a fine string is maintainied in transverse vibrationl by connecting one of its extremities with a vibrating prong of a massive tuning fork, the direction of motion of the point of attachment being parallel to the length of the string. Unider these circumstances . .. the string may settle down into a perimianent and vigorous vibration, whose period is the double of that of the fork." Lord Rayleigh anialyzed and experimented with this and other similar mechanical phenomenia in 1887. This led to anialogous experimnenits with electrical circuits. The electrical principle is readily understood by the following simple explaniatioin. Suppose that we have a capacitor formed by two metal plates separated by air. Assume that a charge exists on the capacitor. The plates will be attracted to each other because of the equal anid opposite charges so that to separate the plates requires work. Uponi separating the plates, say to twice the original distance, the capacitaince will be reduced to half its original value and, hence, the voltage mlust be twice the original value, since the charge upoIn the plates remains the same. The electrostatic energy, however, has been doubled, since it is proportionial to the square of the voltage and directly proportioinal to the capacitanice. The eiiergy required to separate the plates Inow appears as electrostatic energy in the capacitor. Now suppose that the capacitor is combinied with an inductor to form ain oscillating circuit. The voltage on the capacitor will reach a imaxiniui-ii value twice each cycle. Now if, on each half cycle, the capacitance is decreased when the voltage is ml-aximum aind increased when the voltage is zero, net energy will be imiparted to the oscillations since Ino electrical enlergy is used to restore the capacitor to its original value wheni the voltage is zero. 1960 Mumford: Some Notes on the History of Parametric Transducers 849 It appears to me that the fundamental principle . . will find its Similarly, it is apparent that energy could be imother problems in connection with radio frequency application parted to the circuit had the inductance been varied in circuits. Onetothat suggests itself immediately is the amplification of the appropriate phase. This electrical principle was ex- incoming signals. panded to include frequencies other than the two-to-one Alfred N. Goldsmith pointed out the advantages of ratio and the resulting device was used successfully in magnetic amplifier over the direct-curAlexanderson's radio telephone communication betweeni Berlin and doubler employed by Kuhn. frequency rent-controlled Vienna prior to World War I. This was described by that the magnetic amplifier Forest commented Lee De L. Kuhn in 1915. Prof. J. Zenneck, E. F. W. Alexandermodulator than as a high-power was more practical far son and R. V. L. Hartley pioneered with theoretical and used to ob500 audion amplifiers the ensemble of over experimental contributions within the next few years. ComElectric 11 kw the Western by tain at Arlington Alexanderson called these devices "Magnetic Ampliwill situation the can that however, "No one say, pany. fiers," a name which remains with us today. The objecor three years in one, two materially be altered very not tive then was to modulate a continuous wave arc transmitter by means of a nonlinear inductance or saturable after we learn how to build oscillions for large power 10 kw each. That will create a very difreactance. Here the voice currents constituted the sig- outputs, say 5 or ferent situation." nal, and the carrier was the pump. The resulting sideThus, there appears to be very old prior art on banids were radiated, together with the pump (or its harboth as modulator and amplifier. HowMAVAR, monic in some cases). I quote the following fromn a paper delivered by ever, the interest in magnetic amplifiers as radio freE. F. W. Alexanderson at an IRE meeting in New York quency modulators subsided quickly with the advent of the high-power vacuum tube modulators. The "difCity onl February 2, 1916: ferent situation" predicted by Lee De Forest in FebruThe name "Magnetic Amplifier" has been given to a device for ary, 1916, did, indeed, come to pass. controlling the flow of radio frequency currents because this name In the 1920's and '30's, interest developed in subseems to describe its function when it is used for radio telephony oscillations in electrical circuits containing a harmonic be used for a device can As the same better than would any other. variety of other purposes, the above name may in some cases not variable reactance. These "parametric" oscillations seem too appropriate. However, the essential part of the theory that exist at any one of f/n frequencies, where n is the will be given refers to the amount of amplification which is possible could fraction of the fundamental frequency. In subharmonic of attainment and the methods of securing a higher ratio of amplification than would be given by the device in its simplest form. ... 1954 Von Neumann and Goto independently recognized The ratio of amplification is proportional to the ratio between a phase ambiguity existed in the subharmonic the frequency of the radio current and that of the controlling current. that oscillations and that this ambiguity could be utilized in logic circuits. Goto calls this device a "parametron." (This conclusion was verified by R. V. L. Hartley and About thirty years after the pioneering work of subsequently by Manley and Rowe.) Kuhn, Zenneck, Alexanderson, and Hartley on inductive Alexanderson, in the discussion, also suggested am- reactance modulators, interest developed in capacitance plification of incoming signals by cascaded stages of up- reactance modulators at microwave frequencies. The conversion, rectification and up-conversion, etc. The failure of reciprocity in some crystal converters obname of Alexanderson's device withstood the rigors of served in the middle 1940's by L. Apker of General time. Currently, however, we recognize its radio fre- Electric Co., Schenectady, N. Y., and R. N. Smith of quency version as a type of parametric amplifier, rePurdue University, Lafayette, Inc., and the peculiar actance amplifier, or MAVAR. behavior of welded contact germanium diodes made by In Alexanderson's magnetic amplifier, the chief inter- H. Q. North of General Electric Co., Schenectady, est resided in the mode of operation in which the input N. Y., was interpreted to mean that the contact capacsignal was in the voice frequency band and the useful ity varied with bias. H. C. Torrey of the Massachusetts output power was taken in some radio frequency band. Institute of Technology Radiation Laboratory, CamThus it was a modulator or up-converter. bridge, Mass., gave a thorough discussion of the theory Alexanderson presented curves to show that negative of nonlinear capacity converters. resistance effects could exist. Quoting again from his M. C. Waltz and R. V. Pound at the MIT Radiation 1916 paper: Under some conditions "instability and Laboratory observed negative IF conductance when generation of self-excited oscillations" can exist. "This units like North's were used. Pound gave many interis a condition that must be avoided for telephone con- esting details about measured power and gain and also trol; whereas it may have useful applications for other measured negative IF conductance. He obtained a 10purposes." (One useful application, pointed out by db gain and reasoned that such a receiver should have Eugene Peterson in 1930, was the negative resistance a better noise figure than that of a conventional coInstraight-through amplifier, in which the negative re- verter which has conversion loss. He was unable, howsistance effect was enhanced by the suppression of fre- ever, to achieve this. quencies higher than the pumping frequency.) In 1948, A. van der Ziel and, in 1949, V. D. Landon Louis Cohen, in a communicated discussion of the also derived the MAVAR gain relationships; the former paper, said: also pointed out the low-noise figure possibilities. 850 May PROCEEDINGS OF THE IRE In 1952, C. F. Edwards observed nonreciprocal behavior in converters when he used R. S. Ohl's bombarded silicon diodes which exhibited variable capacitance as well as variable resistance characteristics. This observation again triggered a sequence reminiscent of the North diode sequence of the 1940's in which Apker, Smith, Pound, and Waltz reported the experimenetal results and Torrey, van der Ziel, and Landon derived the theory. Corresponding names for the early 1950 sequence are Ohl, Edwards, Manley, and Rowe. However, ini neither of these sequences was a very low-loss variable capacitance diode available and hence the gain was limnited and the noise figure was not especially good. In 1954, the United States Signal Corps sponsored a project at Bell Telephone Laboratories, Murray Hill, N. J., to develop semiconductor devices. In the second interim report of this now famous "Task 8," A. E. Bakaniowski published his derivation of the nonlinear capacitor as a mixer. The work of Bakaniowski, Cranna and Uhlir led to the discovery of a technique for making low-loss units. The technique of making low-loss silicon diode varactors or varicaps advanced rapidly and interest in these new units began to expand. In the meantime, H. Suhl discovered that variable reactance in the microwave range was obtained in ferrite materials when properly excited by a pumping frequency. He proposed using this effect to obtain parametric amplification and discussed suitable materials in the paper published in 1957. M. T. Weiss verified Suhl's proposal experimentally. M. E. Hines and H. E. Elder succeeded in demonstrating gain and oscillationis in a reactance amplifier which used silicon varactors and suggested several microwave circuits for up-converters and negative resistance amplifiers. Their work stimulated activity in microwave applications of "varactor" diodes.2 In 1957, Heffner aiid Wade considered theoretically the noise, gain and bandwidth of parametric amplifiers. Early in 1958, the low-noise properties predicted by theory were verified experimentally at the Bell Telephone Laboratories at 6000 mc by Uenohara anid at 380 mc by Engelbrecht. Salzberg at Airborne Instrumenits Laboratory, Mineola, N. Y., and Heffner and Kotzebue at Stanford University, Stanford, Calif., also achieved low-noise performance working at 1 mc and 1200 Illc, respectively. Miyakawa in Japan, Cullen in England and Tien and Suhl in America considered the amplificationi anid frequency conversion in propagating circuits in which the variable reactors were distributed along a tranismission line while Bloom, Chang and Wittke of RCA Laboratories, Princeton, N. J., took up the theory of parametric amplification and discussed the new approaches to am- 2 It should be pointed out that, unknown to Hines and Elder, Kita and Fujii in Japan had been successful in demonstrating gain and oscillations at microwave frequencies independently while working with variable capacitance diodes in 1954. plification of microwaves. Bloom and Chang also discussed the case of low frequency pumping. R. S. Engelbrecht at Bell Telephone Laboratories designed a traveling wave UHF parametric amplifier using varactor diodes and achieved over 200-mc bandwidth at UHF with 8 to 10 gain. MTIeasurements indicated an "astronom-iy" iioise figure of one db, correspondinig to a "radar" noise figure of about 3.5 db. (This compares favorably with the best commercially available vacuum tube, whose noise figure is about 5 db.) In the meantime, Adler of Zenith, Chicago, Ill. (in June, 1957), suggested a niovel principle of signlal amplification using a pumped electroni beam, and Bridges (in February, 1958) suggested and constructed a parametric amplifier using the variable reactance of a floating drift tube klystron. Louisell and Quate discussed the capabilities of this type of amplifier, and Adler demonstrated that the conclusions conicerninig the lownoise capabilities were indeed correct. He achieved a noise figure capability of 1.4 db, of which 0.4 db represented the loss in the iniput coupler. The developmenit of the vacuumi tube in AlexandersonIs time curtailed the interest in radio frequency parametric transducers. Thirty or so years later, the invenition of the transistor then dimiinished the interest in vacuum tubes. But the interest in radio frequenicy parametric transducers was resurrected by the developmiienit of the low-noise variable capacitance diode, aind this resurrection, in turn, has stimulated the interest in vacuum tubes as parametric tranisducers. What is the next cycle in this see-saw pattern? LIST OF SELECTED REFERENCES ON PARAMETRIC AMPLIFIERS (To JULY, 1959) 1. M. Faraday, "On a peculiar class of acoustical figures; and oni certain forms assumed by a group of particles upon vibrating elastic surfaces," Phil. Trans. Roy. Soc., London, vol. 121, pp. 299-318; May, 1831. 2. F. Melde, "Uber erregung stehender Welleni eiiies fadenformeigen Korpers," Ann. der Physik u Chemnie, Ser. 2, vol. 109, pp. 193-215; month, 1859. 3. J. W. Strutt, Lord Rayleigh, "On the crispations of fluid resting upon a vibrating support," Phil. Mulag., vol. 16, pp. 50-53; July, 1883. 4. J. W. Strutt, Lord Rayleigh, "OIn the miainiteniance of vibrations by forces of double frequency, and on the propagation of waves through a medium enidowed with a periodic structure, " Phil. Mag., ser. 5, vol. 24, issue 147, pp. 145-159; August, 1887. 5. J. W. Strutt, Lord Rayleigh, "Theory of Souniid,'"Macmillan anid Co., Ltd., London, England, 2nd edition, vol. 1, 1894; vol. 1, 1896. 6. R. Goldschmidt, "Reduction of hysteresis losses by highfrequency ctirrents," Elektrotech. Z., vol. 31, pp. 218-221; March, 1910. 7. L. Kuhn, "Uber ein neves radiotelephoniische system," Jahr. fiir dracht. Teleg. und Telephone, vol. 9, pp. 502-534; June, 1915. 8. J. Zenneck, "A contribution to the theory of magnetic frequency doublers," presented at IRE meeting, New York, N. Y.; September, 1915. 9. E. F. W. Alexanderson, "A magnetic amplifier for radio telephony," PROC. IRE, vol. 4, pp. 101-149; April, 1916. 10. E. F. W Alexanderson, U. S. Patent #1,206,643. 11. R. V. L.Hartley, U. S. Patent #1,287,982. 12. B. van der Pol, "On relaxation-oscillatioiis,' Phil. Mag., ser. 7, vol. 2, pp. 987-992; November, 1926. 13. E. Peterson, "Atomic physics and circuit theory," Bell Labs. Record, vol. 7, pp. 231-233; February, 1929. 1960 851 Mumford: Some Notes on the Ilistory of Parametric Transducers 14. R. V. L. Hartley, "A wave mechanism of quantum phenomena," Phys. Rev., vol. 33, p. 289; February, 1929. (Abstract.) 15. E. Peterson, "Magnetic wave amplifying repeater," U. S. Patent #1,884,844. Filed March 30, 1929, issued October 25, 1932. 16. E. Peterson, "Magnetic Amplifier," U. S. Patent #1,884,845. Filed September 13, 1930, issued October 25, 1932. 17. W. R. Bennett, "New results in the calculation of modulation products," Bell Syst. Tech. J., vol. 12, pp. 228-243; April, 1933. 18. B. van der Pol, "Nonlinear theory of electric oscillations," PROC. IRE, vol. 22, pp. 1051-1086; September, 1934. 19. W. R. Bennett and R. M. Kalb, "Ferromagnetic distortion of a two-frequency wave," Bell Syst. Tech. J., vol. 14, pp. 322-359; April, 1935. 20. L. Mandelstam, N. Papalexi, A. Andronov, S. Chaikin, and A. Witt, "Expose des recherches recentes sur les oscillations nion lineares," Tech. Phvs. U.S.S.R., vol. 2, pp. 2-134; 1935. 21. G. Gorelik, "Ph6norlnnes de resoniance dans les systemes linieaires a paranmtres periodics," Tech. Phys. U.S.S.R., vol. 2, no. 2-3, pp. 135-180; 1935. 22. R. V. L. Hartley, "Oscillations in systems with noni-liniear reactance," Bell, Syst. Tech. J., vol. 15, pp. 424-440; July, 1936. 23. W. L. Barrow, D. B. Smith, and F. A;. Baumann, "A fnrther study of oscillatory circuits having periodically varying parameters," J. Franklin Inst., vol. 221, pt. I, pp. 403-416; pt. II, pp. 509-529; March, 1936. 24. L. W'. Hussey and L. R. Wrathall, "Oscillations in an electromagnetical systeml," Bell Syst. Tech. J., vol. 15, pp. 441-445; July, 1936. 25. R. N. Smith, "The Theory of Mixers in Terms of Measurable Mixer Constants," NDRC Rept. No. 14-259, Purdue University, Lafayette, Ind.; March 24, 1944. 26. L. Apker, "Note on Reciprocity Failure in Crystal Mixers," NDRC Rept. No. 15-931-16, Contract OEMSR-931, General Electric Co.; March 9, 1945. 27. L. Apker, E. Taft, and J. Dickey, "Theory of a Double Mixer for Spectrum Analyzer Applications," NDRC Rept. No. 931-17, 15-931-16, General Electric Co.; April 2, 1945. 28. H. C. Torrey, "Theory of the Negative IF Conductance of North's Welded Contact Germanium Rectifiers," RL Rept. No. 55, Mass. Inst. Tech., Cambridge, Mass.; May 22, 1945. 29. N. Minorski, "On parametric excitation," J. Franklin Inst., vol. 240, pp. 25-46; July, 1945. 30. L. C. Peterson and F. B. Llewellyn, "The performance and measurements of mixers in terms of linear network theory," PROC. IRE, vol. 33, pp. 458-476; July, 1945. 31. H. Q. North, "Properties of welded contact germanium rectifiers," J. Appl. Phys., vol. 19, pp. 912-923; November, 1946. 32. J. M. Manley and E. Peterson, "Negative resistance effects in saturable reactor circuits," Trans. AIEE, vol. 65, pp. 870-881; December, 1946. 33. N. W. McLachlan, "Theory and Applications of Mathieu Functions," Oxford University Press, New York, N. Y., pp. 69-70, 274-275; 1947. 34. F. Rockett, "The electron art," Electronics, vol. 21, pp. 136-195; January, 1948. 35. H. C. Torrey and C. A. Whitmer, "Crystal Rectifiers," M.I.T. Rad. Lab. Ser., McGraw-Hill Book Co., Inc., New York, N. Y., vol. 15; 1948. 36. M. C. Waltz, "Negative i-f conductions," in "Crystal Rectifiers," H. C. Torrey and C. A. Whitmer, M.I.T. Rad. Lab. Ser., McGraw-Hill Book Co., Inc., New York, N. Y., vol. 15, p. 401; 1948. 37. R. V. Pound, "Microwave Mixers," M.I.T. Rad. Lab. Ser., McGraw-Hill Book Co., Inc., New York, N. Y., vol. 16; 1948. 38. A. van der Ziel, "On the mixing properties of nonlinear condensers, " J. A ppl. Phys., vol. 19, pp. 999-1006; November, 1948. 39. C. L. Cuccia, "The electron coupler," RCA Rev., vol. 10, pp. 270-33; June, 1949. 40. V. D. Landon, "The use of ferrite cored coils as converters, amplifiers and oscillators," RCA Rev., vol. 10, pp. 387-396; September, 1949. 41. W. R. Bennett, "A general review of linear varying parameter and non-linear circuit analysis," PROC. IRE, vol. 38, pp. 259263; March, 1950. 42. J. M. Manley, "Some general properties of magnetic amplifiers," PROC. IRE, vol. 39, pp. 242-251; March, 1951. 43. H. S. Tsien, "Engineering Cybernetics," McGraw-Hill Book Co., Inc., New York, N. Y.; 1954. 44. J. von Neumann, "Non-linear capacitance or inductance switching, amplifying and memory organs," U. S. Patent #2,815,488. Filed April 28, 1954, issued December, 1957. 45. D. Leenov, Bell Telephone Labs., Murray Hill, N. J., Interim Repts. on Task 8, Signal Corps Contract No. DA-36-039s65589; 1954 to present. 46. S. Kita and T. Fujii, "Microwave amplification by use of crystal diode," ECL Internal Rept.; February, 1954. Annual Convention, Inst. of Elec. Commun. Engrs., Japan; October, 1954. 47. W. P. Mason and R. F. Wick, "Ferroelectrics anid the dielectric amplifier,"PRoc. IRE, vol. 42, pp. 1606-1620; Novenmber, 1954. 48. E. Goto, "New parametron circuit elemenit usinig non-linear actance," Kokusai, Den. Den. Kenkyu Shiryo; November, 1954. mixer," 2nd 49. A. E. Bakanowski, "The non-linlear capacitor Interim Rept. on Task 8, Crystal Rectifiers, Signal Corps Project 2-7-323A; December 31, 1954. 50. R. J. Duffin, "Impossible behaviour of noni-linear networks," re- as a J. Appl. Phys., vol. 26, pp. 602-605; April, 1955. 51. E. Goto, "On the application of parametrically excited nonilinear resonators," J. Elec. Commun. Engrs., Japan, vol. 38, pp. 770-775; October, 1955. 52. S. Oshima, Enomoto and W;atanabe, "Oscillation theory of parametron and method of measurinig non-linlear elements," Kokusai, Den. Den. Kenkyu Shiryo; November, 1955. 53. A. van der Ziel, "Theory of shot noise in junlctioIn diodes and jUnlctioIn tranlsistors," PROC. November, 1955. 54. S. Oshima, "Introduictioni 55. 56. 57. 58. 4, S. to 4; December, 1955. Oshima, "General remarks IRE, vol. 43, pp. 1639-1646; parametron," Denshi Kogyo, vol. p. on a circuit," Denshi parametroni Kogyo, Special issue. H. Yamada, "A parametron circuit examiined from the point of mathematical logic," Denshi Kogyo, Special issue. A. C. Macphersoni, "An analysis of diode mixer consisting of non-liniear capacitance and conductance and ohmic spreadinig resistance,' NRL Rept. 4667; February 13, 1956. L. J. Giacoletto and J. O'Connell, "A variable capacitanlce maniium diode for U.H.F.," RCA Rev., March, 1956, also 221-238. "Transistors I," RCA Lab., Princetoni, N. J.; F. Dill and L. Depian, "Semicotnductor capacitance amplifier," 1956 IRE CONVENTION RECORD, pt. 3, pp. 172-174. A. Uhlir, Jr., "High-frequency shot noise in p-n junctions," PROC. IRE, pp. 44, 557-558; April, 1956. M. Vadnjal, "Resonanit dielectric amplifier," Alta Frequenza, vol. 25, pp. 211-232; June-August, 1956. A. Uhlir, "Frequency conversion and computation with p-n juinction devices," Sixth Interim Tech. Rept. Task 8, Crystal Rectifiers, Signal Corps Contract No. DA-36-039sc-5589, ch. 1; June 15, 1956. Al. H. Higa, "Theory of non-linear coupling in a novel ferroelectric device," J. Appl. Phys., vol. 27, pp. 775-777; July, 1956. A. Uhlir, Jr., "Possible uses of non-linear capacitor diodes," Bell Telephone Labs., Eighth Interim Rept. on Task 8, Signal Corps Contract No. DA-36-039-565589; July 15, 1956. J. M. Manley add H. E. Rowe, "Sonie general properties of non-linear elements Part I. General energy relations," PROC. IRE, vol. 44, pp. 904-913; July, 1956. J. E. Pippin, "Frequency doubling and mixing in ferrites," PROC. IRE, vol. 44, pp. 1054-1055; August, 1956. A. Uhlir, Jr., "Two-terminal p-n junction devices for frequency conversion and computation," PROC. IRE, vol., 44, pp. 11831192; September, 1956. A. E. Bakanowski, "Small signal admittance measurements for a retarding field diode," Ninth Interim Tech. Rept. on Task 8, Crystal Rectifiers, Signal Corps Contract DA 36-039sc-5589, ch. 2; October 15, 1956. H. Suhl, "The theory of ferromagnetic resonance at high signal powers," J. Phys. Chem. Solids, vol. 1, pp. 209-227; September ger- pp. 59. 60. 61. 62. on 63. 64. 65. 66. 67. 68. 69. /October, 1956. 70. H. Suhl, "The nonlinear behavior of ferrites at high microwave frequencies," PROC. IRE, vol. 44, pp. 1270-1284; October, 1956. 71. H. Takahashi, "The Parametron," Tsugakkat Shi, vol. 39, p. 72. 73. 74. 75. 76. 77. 78. 79. 56; 1956. C. F. Edwards, "Frequency conversion by means of a nonlinear admittance," Bell Syst. Tech. J., vol. 35, pp. 1403-1416; November, 1956. A. C. Macpherson, "An analysis of the diode mixer consisting of nonlinear capacitance and conductance and ohmic spreading spreading resistance," IRE TRANS. 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