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Noise in Avalanche Transit-Time Devices 1674 PROCEEDINGS OF THE IEEE, VOL. 59, NO. 12, DECEMBER 1971 for receiving arrays,” ZEEE Trans. Antennas Propagat. (Commun.), [22] C. J. Drane, Jr., and J. F. McIlvenna, “Gain maximization and VO~.AP-14, NOV.1966, pp. 792-794. controlled null placement simultaneously achievedin aerial array [9] A. I. Uzkov, ‘‘An approach to the problem of optimum directive patterns,” Air Force Cambridge Res. Labs., Bedford,Mass., antenna design,” C. R. Acad. Sci. USSR., vol. 35, 1946, p. 35. Rep. AFCRL-69-0257, June 1969. [lo] A. Bloch, R. G. Medhurst, and S. D. Pool, “A new approach to [23] R. F. Hamngton, “Matrixmethods for field problems,” Proc. the design of superdirective aerial arrays,” Proc. Znst. Elec. Eng., ZEEE, vol. 55, Feb. 1967, pp. 136-149. VO~.100, Sept. 1953, pp. 303-314. [24] J. A. Cummins,“Analysis of a circulararray of antennas by [ll] M.Uzsoky and L. Solymar,“Theory of superdirectivelinear matrix methods,” Ph.D. dissertation, Elec. Eng. Dept., Syracuse arrays,” Acta Phys. (Budapt), vol. 6, 1956, pp. 185-204. University, Syracuse,N. Y., Dec. 1968. [12] C. T. Tai, “The optimum directivity of uniformly spaced broad- [25] B. J. Strait and K. Hirasawa, “On radiation and scattering from sidearrays ofdipoles,” ZEEE Trans. Antennas Propgat., vol. arrays of wire antennas,” Proc. Nut. Elec. Con$, vol. 25, 1969. AP-12, July 1964, pp. 447-454. [26] A.T. Adams and B. J. Strait, “Modernanalysis methods for [13] D. K. Cheng and F. I. Tseng, “Gain optimization for arbitrary EMC,” ZEEEIEMC Symp. Rec., July 1970, pp. 383-393. antenna arrays,’’ ZEEE Trans. Antennas Propgat. (Commun.), [27] R. F. Harrington, Field Computation by Moment Methods. New VO~.AP-13, NOV.1965, pp. 973-974. York: Macmillan, 1968. [14] -, “Maximisation of directive gain for circular and elliptical [28] E. N. Gilbert and S. P. Morgan, “Optimum design of directive arrays,” Proc. Znst. Elec. Eng., vol. 114, May 1967, pp. 589-594. antenna arrays subjectto random variations,” Bell Syst. Tech. J., [15] E. I. Krupitskii, “On the maximum directivity of antennas con- vol. 34, May 1955, pp. 637-663. sisting of discreteradiators,” SOD.Phys.-Dokl., vol. 7, Sept. [29] M. D. Smaryshev, “Maximizing the directive gain of an antenna 1962, pp. 257-259. array,” Radio Eng. Electron. Phys. (USSR), vol. 9, Sept. 1964, pp. [16] F, R. Gantmacher, The Theory of Matrices, vol. I. New York: 1399-1400. Chelsea Publishing Co., 1960. [30] F. I. Tseng and D. K. Cheng, “Gain optimization for arbitrary [17] B. Das, “On maximumdirectivity of symmetrical systems of antennaarrays subject to randomfluctuations,” ZEEE Trans. Antennas Propgat., vol. AP-15, May 1967, pp. 356-366. radiators.” Radio Ena.I Electron. Phys. (USSR), vol. 10, June 1965, pp. 853-859. [31] D. K. Cheng and F. I. Tseng, “Optimum spatial processing in a [18] D. K. Cheng and F. I. Tseng, “Pencil-beam synthesis for large noisy environment for arbitrary antenna arrays subjectto random circular arrays,” Proc. Inst. Elec. Eng., vol. 117, July 1970, pp. errors,” ZEEE Trans. Antennas Propgat., vol. AP-16, Mar. 1968, 1232-1234. pp. 164-171. [19] P. D. Raymond, Jr., “Optimization of array directivity by phase [32] R. W. P. King, R. B. Mack, and S. S. Sandler, Arrays of Cylihdri- adjustment,” M.Sc. thesis, Elec. Eng. Dept., Syracuse University, cal Dipoles. Cambridge, England: Cambridge University Press, Syracuse, N. Y., June 1970. 1967. [20] F. B. Hildebrand, Methodr of AppIied Mathematics. Englewood [33] R. F. Harrington, “Antenna excitation formaximum gain,” IEEE Cliffs, N. J.: Prentice-Hall, 1965. Trans. Antennas Propgat., vol. AP-13, Nov. 1965, pp. 896-903. [21] E.A. Guillemin, The Mathematics of Circuit Atdysis. New [34] D. K. Cheng, “Antenna optimization criteria,” RomeAir Develop. York: Wiley, 1951. Cent., Cambridge, Mass., Rep. RADC-TR-71-156, Apr. 1971. Noise in Avalanche Transit-Time Devices AbstracCThe work performed onnoise in avalanche transit-titno de- of understanding of noise in these devices. It is hoped that this vices is reviewed and presented in detail. Both theoretical and experimen- review does not only have the advantage of consolidating this tal results on the noise mechanisms and performance of these devices when knowledge and arranging it systematically as to put the entire employed asoscillators, ampliflers, and self-oscillatingmixers are in- so cluded. Suggestions for further studies in this area are also given. field in perspective, but it also reveals unresolved problems and suggests new areas of investigation. I. IWRODUCTION The importance of noise studies in avalanche transit-time A. Object of the Review diodes cannot be overstated for two reasons. First,it is generally believed that the noisiness of avalanche diodes may limit their HE INCEPTION of every new electron device triggers a applications and represents their majorweakness in comparison detailed study of the various noise mechanisms in it and with other microwave devices.On the other hand, the largenoise Tways to reduce the noise. The literature on avalanche generation makes the avalanche diodean attractive noise source transit-time devices, which is nowsix years old, is no exception for microwave frequencies. and it worthwhileis to make a comprehensive review of the status Historically,noise studies in avalanchetransit-time diodes began almost as soon as the device became operational. The Manuscript received May 6, 1971. This work was supported by the earliest reported results of measurements of noise in avalanche- National Aeronautics and Space Administration under Grant NGL diode amplifiers andoscillators werethose of DeLoach and 23-005-183. Johnston [l ] who reported1) very large amplifier noise figures(50 The author is with the Electron Physics Laboratory, Departmentof Electrical Engineering, the University of Michigan, AM Arbor, Mich. to 60 dB), 2) reduction of noise figure with an increase in bias 48104. current, and 3) very large spectral linewidth (over 100 kHz for GUPTA : NOISE IN AVALANCHE TRANSIT-TIME DEVICES 1675 3-dBwidth). The first theories of noisein avalanche-diode TABLE I oscillators and amplifiers were both due to Hines [2], (31. Sub- APPLICATIONSOF AVALANCHE TRANSIT-TIMEDIODESAND stantial improvements have been madesince, both indevice noise CORRESPONDING CHARACTERIZATIONS OF NOISE performance and in sophistication of theories of noise in these PERFORMANCE UTLIZEDIN THISPAPER devices. Application of OneCommon Characteri- B. Sources of Noise in Avalanche Diodes Avalanchezation of Noise N etwork Diode PerformanceType Diode of Network The noise inan avalanche transit-time diode is primarily made up of three parts which are, in the order of their significance: Passive one-portnoise generator spectrum of current avalanche noise, frequency-converted noise, and thermal noise. fluctuations Avalanche noise, which is a type of shot noise, is the noise in Active one-portoscillator AMnoise FMandspectra carriercurrent generated by the inherently noisy avalanche Lineartwo-port small-signal amplifier noise figure multiplication process. Avalanche multiplicationacts much like a self-oscillatingmixer noise figure noisy amplifier,not only multiplyingthe original signal noise by aNonlinear two-port large-signal amplifier AM and FM noise of factor M (called the multiplication factor), but also by addingan output appreciable amount of noise to it. This noise addition is best described in terms of the statistical fluctuationsof M. To under- stand the origin of fluctuations in M, the avalanche mechanism combination noise is expectedto be small because the transit time must be considered in detail. Following the discussion of Hines of the carriers through thespace-charge region is of the order of [3], consider an avalanche region with a self-sustaining constant s, while the carrier lifetimeof excesscarriers isof the orderof current so that each carrier pair produces, on the average, exactly10-6 seven in direct gap semiconductors. one carrier pair by impact ionization.N Letbe the total numberof Flicker noise, on the other hand, has mostly been neglected carrier pairs present in the avalanche region on the average. Ifuntil the now on experimental grounds. Early workby Josenhans [4] history of one carrier pair in time is followed, it is found that its on X-band avalanche diodes showedno l/f effect in noise closeto “offsprings” are generated and swept out of the avalanche region the carrier, leading himto the observation that “no flicker noise at time intervals of T, on the average, where T, is the mean time was present in Read oscillators.” Ondria and Collinet [5] have interval between successive ionizations todue a single carrier pair. also reported the absence of 1,” behavior in FM noise spectra The chain ionization leadsto a pulse-train-like currentat the out- close to the carrier frequency, indicating that no flicker noise is put. The total current through the avalancheregion is then given present in avalanche diodes at low frequencies. More recently, by Ashley and Palka [6]have observed a 3-dB/octave slope in noise spectra close to the carrier in some Ku-band avalanche-diode I = Nqs/r+ (1) oscillators with a knee below 5 kHz, although the data are not where qsequals theelectronic charge. This current would appear consistent enoughto be conclusive. to be a constantif N is large, andT, is very small comparedto the Obviously, when the avalanche transit-time diodeused is as an period of the frequencies of interest. Now the sources of fluctua- amplifier or an oscillator the circuit in which itis embedded also tions inZare looked for. contributes to the totalnoise. Circuitlosses, impedance mismatch First of all fluctuations inM should be expected because each in the circuit, and noise in the nonreciprocal element (e.g., cir- carrier pair has a “probability”of ionization; i.e., the ionization culator)are all known to cause additional noise.However, process is notdeterministic. In terms of the previously mentionedavalanche diodes are very noisy devices, and it is generally be- model, this means that not all chainsof ionization are intennin- lieved that thenoise contributions fromall sources other than the able and uniform; some of them terminate (when a carrier pair diode can safely be neglected in estimatingthe noise behavior.
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