MESFET Distributed Amplifier Design Guidelines

Transcription

1 268 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHIWQUES, VOL. MTT-32, NO. 3, MARCH 1984 MESFET Disribued Amplifier Design Guidelines JAMES B. BEYER, SENIOR MEMBER, IEEE, S. N. PRASAD, MEMBER, IEEE, ROBERT C. BECKER, JAMES E. NORDMAN, MEMBER, IEEE, AND GERT K. HOHENWARTER Absrac In hk paper, he anafysis of GGAS MESFET disribued amplifiers and a sysemaic approach o heir design are presened. The analysis focuses on fundamenal design consideraions and afso esablishes he maximum gain-bandwidh produc of he amplifier. The design approach presened enables one o examine he radeoffs beween he variables, such as he device, he number of devices, and he impedances and cuoff freqnency of he lines, and arrive a a design which gives he desired frequency response. Excellen agreemen is shown when he heoreically prediced response of a ypicaf amplifier is compared wih compuer-aided anafysis resuls, and good agreemen is shown wih previously published experimenal resuls. 1. INTRODUCTION T HE PRINCIPLE of disribued or raveling-wave amplificaion using discree ransisors is a echnique whereby he gain bandwidh produc of an amplifier may be increased. In his approach, he inpu and oupu capaciances of he ransisors are combined wih lumped inducors o form arificial ransmission lines. These lines are coupled by he ransconducances of he devices. The amplifier can be designed o give a fla, low-pass response up o very high frequencies. Disribued amplifiers using discree FET s have been demonsraed a microwave frequencies [1]-[5]. The raveling-wave ransisor, an ineresing variaion of he discree FET disribued amplifier, has also been proposed [6]. However, we will show in his paper ha he discree FET disribued amplifier, unlike he raveling-wave ransisor, can be designed o give fla response nearly up o he cuoff frequency of he lines. The opology of he disribued amplifier is paricularly suied o MMIC S because is passive circui predominanly consiss of inducors which can be realized in he form of shor lenghs of microsrip lines. Recenly, broad-band MMIC disribued amplifiers using GaAs MESFET S have been presened [1]-[3]. The design of he disribued amplifier involves a careful choice of he variables, such as he device, he number of devices, and he impedances and cuoff frequency of he lines, o obain he desired frequency response. Even hough several disribued amplifiers using MESFET S have been buil, a sysemaic design approach which enables one o examine he radeoffs beween he design variables has no been presened. The disribued amplifier has been exensively analyzed since i was firs proposed in 1937 by Percival [7]. We Manuscrip recewed June 14, 1983; revised December 12, This work was suppored by he Office of Navaf Researchunder Conrac NOO C The auhors are wih he Universiy of Wisconsin, Madison, Deparmen of Elecncaf and Compuer Engineering, DRAIN LINE TERM INAT ION A W:T T INPUT Fig. 1. Schemaic of FET disribued amplifier. GATE LINE TERMINATION 3 presen here only a limied sample of lieraure [8] [12]. The unified analysis of Chen [12] reas a general case disribued amplifier composed of image mached, nonuniform inpu and oupu ransmission lines and is he mos complee analysis currenly available. In his paper, we analyze he MESFET disribued amplifier by focussing on fundamenal design consideraions and presen a graphical design approach which enables one o examine he radeoffs beween he design variables and arrive a a design under he consrain of maximum gain bandwidh produc. The design approach will be illusraed by an example and he analyically prediced response will be compared wih he resuls obained by compuer-aided circui analysis. We will also compare he prediced response of a ypical amplifier wih previously published experimenal resuls. II. AMPLIFIER ANALYSIS A schemaic represenaion of he FET disribued amplifier is shown in Fig. 1. The gae and drain impedances of he FET s are absorbed ino lossy arificial ransmission lines formed by using lumped inducors as shown. The resulan ransmission lines are referred o as he gae and drain lines. The lines are coupled by he ransconducances of he FET s. An RF signal applied a he inpu end of he gae line ravels down he line o he erminaed end, where i is absorbed. As he signal ravels down he gae line, each ransisor is excied by he raveling volage wave and ransfers he signal o he drain line hrough is ransconducance. If he phase velociies on he gae and drain lines are idenical, hen he signals on he drain line add in he forward direcion as hey arrive a he oupu. The waves raveling in he reverse direcion are no in phase, and any uncanceled signal is absorbed by he drain-line erminaion /84/ $ IEEE

2 BEYER ef U/.: MESFET DISTRIBUTED AMFLIFIER DESIGN GUIDELINES 269 Cdg G [ + Cgs T - c ds $ i icds Ri ds a s i d* = ym Vc Ym = 9me j~ro Fig. 2. Simplified equivalen circui of a MESFET. Lg/2 where ~ is he volage a he inpu erminal of he amplifier and dg = Ag + j~g is he propagaion funcion, on he gae line. i4g are he aenuaion and phase shif per secion on he gae line, ag = l/r, Cg, is he gae-circui radian cuoff frequency, ancl UC= 2mfc is he radian cuoff frqquency of he ~nes. For cons~-k ype ransmission lipes, lie phase velociy is a well-known,funcion of he cuoff frequency fcof he line. By requiring gae and drain lines o have he same cuoff frequency, he phase velociies are consrained o be equal. Therefore, we ~d [13]. From (1) and (2), 10 can be expressed as I.= =:. 0 Ld/2 Ld I (3) TERMINATION LOAD The power delivered o he load and inpu power o he amplifier are given, respecively, by (b) Fig. 3. (a) Gae ransmission line. (b) Drain ransmission line. A simplified equivalen circui of a MESFET arrived a from ypical S-parieer measuremens a microwave frequencies [3] is shown in Fig. 2. R, is he effecive inpu resisance beween he gae and source erminals and Cg, is he gae-o-channel capaciance. Rd, and Cd, are he draino-source resisance and capaciance, respecively. C~g,is he drain-o-gae capaciance and g~ he ransconducance. In our analysis, he device will be considered unilaeral and Cdg will be negleced. The equivalen gae and drain ransmission lines are shown in Fig. 3(a) and (b). They are essenially loaded consan-k lines, wherein he parasiic resisances of he FET s are considered he dominan loss facors. The lines are assumed o be erminaed in heir image impedances a boh ends. The curren delivered o he load is given by I.= ~ gme-edz [ ~ <,,-(M% where VCkis he volage across $g$ of he k h r~sisor and 19d= Ad is he propagaion funcion on he drain line. Ad and Qd are he aenuaion and phase s~f per secion on he drain line. n is he number of ransisors in k=l he amplifier. ~ck can be expressed in erms of he volage a he gae erminal of he k h FET as [13] 1 (1) and ~0= ~h12re[%d] = d/cd[l (~/%)2] where Z~D and ZIG are he image impedances of he drain and gae lines [13]. Therefore, he power gain of he amplifier is G= g; R01R02 sinh2 [( Ad Ag)]e-n(~ +~g) ; (u/uc)2] sinh 2[+(A.-A,)] [ ( g )][ where Rol( = ~~) and R02( = ~~) are he characerisic resisances of he gae and drain lines, respecively. Consider an ideal impedance ransformer a he oupu por which ransforms R02 o he gae-line characerisic resisance Rol of he succeeding amplifier in a andem connecion of idenical amplifiers. Then, from (4), he magniude of he volage gain of a single amplifier sage can be shown o be %l(~ol~02) l 2sinh [ ~(Ad Ag)]e n(a~+ag)/ 2 (4) (5)

3 270 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. MTT-32, NO. 3, MARCH 1984 z,/2 zl/2 1! Z2 Fig. 4. A secion of consan-k line. From (5), one can show ha he number of devices which maximizes gain a a given frequency is [14] ln(-%/~g) p = Ad Ag (6) LA454C Q S k+ (a) A similar relaion was found by Podgorski and Wei [6] for he opimum gae widh of a raveling-wave ransisor. Therefore, i is clear ha in he presence of aenuaion, he gain of a disribued amplifier canno be increased indefiniely by adding devices. This propery of he disribued amplifier can be easily explained. As he signal ravels down he gae line, each ransisor receives less energy han he previous one due o aenuaion on he gae line. Similarly, he signal excied in he drain line by a ransisor is aenuaed by he subsequen line secions beween i and he oupu por. Therefore, addiional ransisors no only decrease he exciaion of he las device bu also increase he overall aenuaion on he drain line. The gain of he amplifier increases wih addiional devices unil he opimum number of devices a he given frequency is reached. Any device added beyond he opimum number is no driven sufficienly o excie a signal in he drain line which will overcome he aenuaion in he exra secion of he drain line. Consequenly, he gain of he amplifier begins o decrease wih furher addiion of devices. A. Aenuaion on Gae and Drain Lines The aenuaion on gae and drain lines is he criical facor conrolling he frequency response of he amplifier, as will be shown. The expressions for gae- and drain-line aenuaions can be derived from he propagaion funcion for he consan-k line, which is given by he relaion [15] cosh(a+@)=l+&. (7) 2 Z1 and Zz are he impedances in he series and shun arms of a secion of consan-k line as shown in Fig. 4, and A and Q are he aenuaion and phase shif per secion of he line. When aenuaion per secion is small ( <0.4 Np), one can derive from (7) he following expressions for aenuaion on gae and drain lines [13]: A.={* 8) u :Uoo, (b) Fig. 5. (a) Aenuaion on gae line versus normalized frequency. (b) Aenuaion on drain line versus normrdized frequency. x k+ where X~ = a/uc is he normalized frequency and. =/&{& The aenuaion on gae and drain lines versus frequency wih WC/wg and ud/ic as parameers are shown in Fig. 5(a) and (b), respecively. I is eviden from he figures ha he gae-line aenuaion is more sensiive o frequency han drain-line aenuaion. Furher, unlike aenuaion in he gae line, he drain-line aenuaion does no vanish in he low-frequency lii. Therefore, he frequency response of he amplifier can be expeced o be predominanly conrolled by he aenuaion on he gae line and he dc gain by he aenuaion on he drain line, as will be shown in he following secion. I is clear from (8) and (9) ha aenuaion on he gae and drain lines can be decreased by making uc/wg and Ud/u< small. Therefore, for a given u=, me has o choose a device having high ig and low ~d. B. Frequency Response Exending he analysis of Horon e al. [9], (8) and (9) can be rewrien as d / C (9) (11) d=m

4 : b.or 1 ldb 0.8 o=~.4, b=,16 Fig. 6. No&mfized frequency response of MESFET disribued amplifiers. 20- BEYER e al.: NmSFETDISTRIBUTED AMPLIFIER DESIGN GUIDELINES a=.6, b= < E oojj_uuj xk- where n I (12) and, (13) Using (10) and (11), one can derive from (5) he following expression for he normalized gain: 01 I I I I o 0. I 0 2 b- 0 3 Fig. 7. Fracional bandwidh curves. 0.4 () [ sinh ~ e~sinh b/(1 X~)l 2 - X ++(%: )x r l e [b/(l x;)l/*+ax;/ [1 +(4a2/n2 l)x~]lfq,,4) [1- X~] 2sinh~ b/(1- X~) /2- Si h( [l+;x r [ X 41+(%-l)X 11 where Ao, he dc gain,(he gain of he amplifier in he low-frequency limi), is given by. A._ gm(~ol~02)1 2S~(b)e-b 2sinh(b/n} I,, is eviden from (14) ha he normalized frequency,, (15) response (norm~zed gain,versus normalized frequency) of he amplifier is a funcion of he panrgneers a, b, and n. The a and b pariimeers are relaed o gae- and drain-line aenuaions, respecively. The dc gain of he amplifier is conrolled by he aenuaion on he drain line as spen in (15). From (14), one can deermine he normked frequency response of he amplifier for various values of a and b, as shown in Fig. 6. The value of n used is 4. For given values of a and b, he normalized response does no change appreciably wih n, for n greaer han 4, Therefore, he normalized frequency response of he amplifier is compleely characerized by he parameers a and b. We will show laer how he a and b values qre relaed o a paricular circui. By a proper choice of a and b parameers, he afiplifier can be designed o give a nearly fla response up o a frequency close o he cuoff frequency of he lines. This is he disinc advanage of he disribued amplifier using discree ransisors as compared o a raveling-wave ransisor proposed by Podgorski and Wei [6], whose gain monoonically decreases due o ransmission-line aenuaion. In he case of a disribued amplifier using discree ransisors, he rise in volage a he gae erminals oo,mpensaes o some exen he effec of gae-line aenuaion as he cuoff frequency is approached (see (2)). This can be seen if one views he lumped consan gae line as cascaded ms.pcions. The ransisor gae source erminals are cqnneced across he.?-secion erminals. I is well kno~ ha he image impedance of a resecion, and hence he gaesource volage, rises as he cuoff frequency is approached. How his effec c?m be used o obain nearly fla low-pass response ou o frequencies approaching he cuoff of he lines will be demonsraed. In order o. enable cascading of disribued amplifier sages, he individual amplifiers mus be designed o give a nearly fla gain response up o he, desired maximum frequency. This calls for an appropriae choice of a and b parameer values. An ideal frequency response is he one which is fla Wp o he cuoff frequency of he lines. However, depending on he values of a and b, he frequency response sars deviaing from he ideal response a a frequency below he cuoff frequency of he lines. In order o selec he required frequency response and corresponding a and b values, i is necessary o characerize hese

5 272 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. Mm-32, NO. 3, MARCH I.( ~ 0.5 ~X. ofldb 4fmax c1 o I \ o I I I I o Fig. 9. Normalized maximum gain-bandwidh produc curve. b- c o & \~o.;5 o 0.1 I I I 0 2 b Fig. 8. K= cons. curves. responses by heir degrees of flaness. We define he degree of flaness as he fracional bandwidh X = ~1 db/f., where fl dfi ishefrequency a which he gain of he amplifier falls belc~w he dc gain by 1 db, as shown in Fig. 6. The values of parameers a and b which give he same fracional bandwidh can be deermined from (14) by ieraion, and are ploed on he a b plane as shown in Fig. 7. These curves give he designer he values of a and b o choose from which yield he same fracional bandwidh. I is clear from Fig. 7 ha he flaness of response is quie sensiive o he parameer a, which conrols he aenuaion on he gae line. C. Gain-Bandwidh Produc One can derive he following relaion saring from (15) when b <0.4, [13]: & = (a@ /2e-~ (16) where j~= is he frequency a which he maximum available gain (MAG) of he FET becomes uniy [16]. I is also referred o as he maximum frequency of oscillaion of he FE?. ~~= is given by 0.30 The facor KX in (18) can be viewed as he gain-band 0.2!5 x widh produc of he amplifier normalized o 4~~=. The 020 value of KX can be found from Figs. 7 and 8. The maximum value can be shown o be abou 0.2. Fig. 9 shows,. o.io he normalized maximum gan-bandwidh produc curve 0.4 on he a b plane. By choosing he parameer values a and b o lie on his curve, one can design a disribued amplifier having maximum gain-bandwidh produc. given I follows ha he maximum gain-bandwidh produc is by o.fl del= 0.8 fmax. (19) I can be seen ha he maximum gain bandwidh produc of he disribued amplifier is consrained by he fm=of he device. From (19), one can show ha he frequency a which he gain of he disribued amplifier becomes uniy canno exceed 0.7 from.we have also confirmed his by he compuer-aided analysis of several disribued amplifiers. III. AMPLIFIER DESIGN Up o his poin, we have shown how he frequency response of he amplifier depends on a range of values of he parameers a and b, and we will now show how he choices of cuoff frequency and impedances of he lines, and paricular acive device and heir number consrain he values of a and hence he frequency response. The sysemaic design approach presened below will enable one o exapine he possible radeoffs beween he design variables and arrive a a suiable design. (13): The following relaions can be derived from (12) and find+ # gsr Equaion (16) can be expressed as Aofl z d~ = 4Kxfm* (17) (18) n =Wd ab. 4 Wg (20) (.0: a/b. (21) i)g~d where K = (ab)l/2e - b and ~1 ~~ = Xfc. Fig. 8 shows K = Equaion (20) defines he value of he produc ab in cons. curves on he a b plane. Equaion (18) gives he erms of he number of devices and he device characerisgain--bandwidh produc of a MESFET disribued ampli- ic frequencies (ag and ad). This equaion defines a family fier. I is dependen on he values of a and b, as well as he of hyperbolas on he a b plane as shown in Fig. 10. j~= of he FET. For a given MESFET, ~~a is fixed. Equaion (21) defines a family of lines on he a b plane as Therefore, (18) gives he gain bandwidh produc of he shown in Fig. 10. Each line corresponds o a cuoff amplifier for he chosen values of a and b. frequency (~ ) and characerisic resisances (Rol and R02)

6 BEYER e U/.: MESFET DISTRIBUTED AMPLIFIER DESIGN GUIDELINES \ \ [Ro:,.ffo;, f;] 1. I 1. I 0 0 0, 0 ). I ) b- Fig. 10. ab = cons. curves and a/b= cons. lines, of he. lines because hey are relaed as follows: f ==/& =T{& The poin of inersecion of a hyperbola defined by (20) and a line defined by (21) deermines an operaing poin on he a b plane. The value of X (fracional bandwidh) and K corresponding o his operaing poin can be obained from Figs. 7 and 8, respecively, since he coordinaes (a, b) of he poin are known. Then he dc gain (AO ) and bandwidh ( fl ~B ) can be obained from he following relaions: fl db = f. (22) 4KXfmm An=.. II db The frequency response of he amplifier can be obained from (14). The amplifier is now compleely defined in erms of he device, he number of devices, he cuoff frequency and he impedances of he lines, and he frequency response. Superposiion of Figs. 7, 8, and 10 will enable one o examine he radeoffs beween he design variables. We will now illusrae he design approach presened above by an example. A. Design Example Le us consider he design of a disribued amplifier using ypical 300-pm MESFET S which have he following characerisic frequencies: fg = CJg/2T = 84.2 GHz fd = 4.8 GHz fmm = 77.2 GHz../ Fig, 11. Design curves for he disribued amplifier using ypical 300-pm MESFET S. Le R01= ROZ.Therefore, we have Cg~= Cd~+ CP, since he cuoff frequencies of he lines are also consrained o be equal. CP is an exernal capaciance added o he device oupu capaciance Cd.. For he MESFET considered here, Cg~= 0.27 pf, Cd, = 0.11 pf, and Rd, = 300 L?.Therefore, we obain he following equaions: fi=l/2&,(cd~ + C,) =1.96 GHz (24) ab = ~=(5.82x10 3)n2 (25) a/b = ~ 2 =(6.06 x10-2 ) f:. (26) (4J cl+ The se of design curves consising of curves defined by (25), he lines defined by (26), fracional bandwidh curves (Fig. 7), and K = cons. curves (Fig. 8) are ploed on he a b plane as shown in Fig. 11. For an amplifier having Rol = Roz = 50 Q, fc = 23.6 GHz, and n =4, we obain he following values for a, b, X, and K from Fig. 11: a= O.56 b= O.17 x= 0.7 K= O.25. Therefore, he bandwidh of he amplifier is and he dc gain is f, d~ = Xfc = GHz A = 4KXfm= o fl db = 3.27 (10.29 db). The frequency response of his amplifier prediced by (14) and he response obained by using he sandard microwave circui analysis program are shown in Fig. 12. They are in good agreemen. The image erminaions are realized

7 274 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. MTT-32, NO. 3, MARCH : ~% -- -%, COMPUTER SIMULATION 01 I I I I I I I I I FREQUENCY (GHz) - \ ANALYTICAL i Jsh , O 18.0 FREQUENCY (GHz) + Fig. 14. Frequency response of he six-secion disribued amplifier Fig. 12. Frequency response of he four-secion disribued amplifier using ypicaf 300-pm MESFET S. o L I 1 IFig. 13. A shor lengh of microsripline and is equivalen circui. by using he sandard m-derived filer half secions a boh ends of he lines [13]. A careful sudy of Fig. 11 reveals ha for a given cuoff frequency (and hence he impedance of he lines), he gain of he amplifier can be increased by adding devices a he expense of bandwidh. On he oher hand, if he number of devices is decreased, one can obain a larger bandwidh by sacrificing gain. If he number of devices is fixed, a decrease in cuoff frequency (and hence an increase in he impedance of he lines) resuls in an increase in gain and reducion in bandwidh. B. ;Yome Pracical Design Consideraions ~esign of a disribued amplifier as discussed in his paper involves he design of he lumped inducors. As already menioned, he lumped inducors can be realized by shor lenghs of high-impedance rnicrosripline. A shor leng,h of microsripline and is equivalen circui are shown in Fig. 13. For a shor lengh 1( < Ag/7) of loss-free line, he inducance is given by =qf Zol (27) where ZO is he characerisic impedance of he microsripline, f is he frequency, and Ag is he wavelengh in he microsripline. The end capaciances are given by 1 c=2fzoag (28) The end capaciances can be absorbed ino gae and drain lines by aking hem ino accoun in he design of he ransmission lines. For a given ZO and highes frequency of operaion, he resricion on 1 limis he maximum realizable value of inducance. Even hough i is advanageous o increase ZO in order o achieve high inducance and low end capaciance values, a pracical limi is reached when he widh of he microsrip becomes oo small, resuling in excessive aenuaion in he microsrip. Also, he geomerical consideraions in he layou of he amplifier place a lower limi on he lengh of he inducors [13]. Anoher imporan consideraion in he design of microsrip inducors is he elecromigraion of he meal a high curren densiies. In order o preven elecromigraion, he curren densiy in he microsrip should be kep below a criical value, which is of he order of 105A/cm2 for gold. This requiremen places an addiional resricion on he design of microsrip inducors if hey mus carry dc curren o bias he FET s. The measured frequency response of a disribued amplifier [3] is shown in Fig. 14. The figure also shows he responses prediced analyically and by compuer-aided analysis. The analyically prediced response was obained by applying correcions for inpu and oupu reflecion coefficiens and aenuaion due o series resisance of he inducors. The analyically prediced frequency response is in good agreemen wih he response obained by compuer-aided analysis. The discrepancy beween he compuer-simulaed and measured responses was aribued o addiional losses in source grounding bars in he amplifier, and sligh differences beween he es FET s and he FET s in he amplifier [17]. IV. CONCLUSIONS The analysis of MESFET disribued amplifiers and a sysemaic approach o heir design has been presened. The analysis has revealed ha he ransmission-line aenuaion caused by he device parasiic resisances is he criical facor in he design of he amplifier. The analysis has also shown ha he gain bandwidh produc of he disribued amplifier can only approach he ~~u of he individual device. The graphical design approach presened enables one o examine he radeoffs beween he variables,

8 BEYER e al.: MESFET DISTRIBUTED AMPLIFIER DESIGN GUIDELINES 275 such as he device, he number of devices, and cuoff frequency and impedances of he lines, and arrive a a design which gives he desired frequency response. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] lu3femnces Y. Ayasli, R. L. Mozzi, J. L. Vorhaus, L. D. Reynolds, and R. A. Pucel, A monolihic GRAS 1-13 GHz raveling-wave amplifier; IEEE Trans. Microwave Theory., Tech., vol. MTT-30, VV , h]y Y. Ayasli, L. D. Reynolds, J. L. Vorhaus, and L. Hanes, Monolihic 2-20 GHz raveling-wave anmlifier. Elecron. Z,e.. vol. 18. no. 14, pp , July E. W. Srid and K. R. Gleason, A DC-12 GHz monolihic GaAs FET dkribued amplifier, IEEE Trans. Microwave Theory Tech., vol. MTT-30, pp , July J. A. Archer, F. A. Pez, and H. P. Weidlich, GaAs FET disribued amplifier; Elecron. Le., vol. 17, no, 13, p. 433, June W. Juzi, A MESFET disribued amplifier wih 2 GHz bandwidh, Proc. IEEE, vol. 57, pp , A. S. Podgorski and L, Y. Wei, Theory of raveling-wave ransisors< IEEE Trans. Elecron Devices, vol. ED-29, pp , Dec W. S. Percival, Thermionic vajve circuis, Briish Paen , Jan E. L. Ginzon, W. R. Hewle, J. H. Jasberg, and J. D. Noe, Disribued amplificaion; Proc. IRE, vol. 36, pp , Aug W. H. Horon, J. H. Jasberg, and J. D. Noe, Disribued amplifiers: PracicaJ consideraions and experimenal resulsfl Proc. IRE, VOL 38, pp , July H. G. Basse and L. C. Kelly, Disribued amplifiers: Some new mehods for conrolling gain/frequency and ransien responses in amplifiers having moderae bandwidhs, Proc. Ins. Elec. Eng., vol. 101, p.iii, pp. 5-14, D. G. Sarma, On disribued amplificaion, Proc. Ins. Elec. Eng., vol. 102B, pp , Sep W. K. Chen, Disribued amplificaion heory; in Proc..5h Annual Alleron Conf. Circui and Sysem Theory, (Universiy of Illinois, Urbana), 1967, pp J. B. Beyer, S. N. Prasad, J. E. Nordman, R. C. Becker, G. K. Hohenwarer, and Y. Chen, Wideband monolihic microwave amplifier sudyfl ONR Rep. NR , Sep J. B. Beyer, S. N. Prasad, J. E. Nordmars, R. C. Becker, and G. K. Hohenwarer, Wideband monolihic microwave amplifier sudy, ONR Rep. NR , July J. Zobel, Transmission characerisics of elecric wave-filers; Bell Sys. Tech. J., vol. 3, pp , P. Wolf, Microwave properies of Schoky-barner field-effec ransisor: IBM J. Res. Develop., vol. 14, pp , Mar E. W. Srid, privae communicaion. * James B. Beyer (M61 SM 79) was born in Horicon, WI, on July 7, He received he B. S.E.E., M. S., and Ph.D. degrees from he Universiy of Wisconsin, Madison, in 1957, 1959, and 1961, respecively. From 1950 o 1954, he served in he U.S. Navy as an elecronics echnician. Upon resuming his sudies in 1954, he held boh eaching and research appoinmens a he Universiy of Wisconsin. He has augh ccnrrsesin he area of elecromagneic heory, microwaves, anennas, and communicaions elecronics since his appoinmen o he faculy in In , he was a Visiing Professor a he Technicaf Uni~ersiy in Braunschweig, Germany. He is presenly engaged in research on microwave inegraed circuis, RF circuis and sysems, and anennas. Dr. Beyer is a member of Ea Kappa Nu and Sigma Xi. S. N. Prasad (S 79-M81) was born in Bangalore, India, on May 26, He received he B.E. degree in elecronics from Bangalore Universiy, India, in 1972, he M. Tech. degree in microwave and radar engineering from he Indian Insiue of Technology, Kharagpur, in 1974, and he Ph.D. degree in elecrical engineering from he Indian Insiue of Technology, Bombay, in From 1974 o 1975, he worked as a scienis in he Defense Research and Developmen Laboraory, Hvderabad, India. From 1980 o he held he appoinmen as a s;ien;s in Elecronics and Radar Developmen Esablishmen, Bangalore, India. Since 1982, he has been working as a Research Associae in he Deparmen of Elecrical and Compuer Engineering, Universiy of Wisconsin, Madison. He ii currenly engaged in research in he area of microwave inegraed circuis, and eaching a course in elecromagneic. His areas of ineres are microwave inegraed circuis, RF circuis, and anennas. * / Rober C. Becker was born in Madison, WI, on June 15, He received he B.S. degree in elecrical engineering in 1976, and he M.S. degree in 1980, boh from he Universiy of Wisconsin. From 1977 o 1979, he was employed by Rockwell Inernaional doing synhesizer design and cusom MSI conroller developmen. He is presenly compleing sudies for he Ph.D. degree in elecrical engineering. Mr. Becker is a member of Ea Kappa Nu. * James E. Nordman (S 61-M63) received he B.E.E. degree from Marquee Universiy, Milwaukee, WI, in 1957, and he M.S. and Ph.D. degrees in elecrical engineering from he Universiy of Wisconsin, Madison, in 1959 and 1962, respecively. In 1962, he joined he Universiy of Wisconsin, Madison as an Assisan Professor. His research ineress were in semiconducor device physics wih emphasis on he D-i-n diode. In 1967, he was on leav; a RCA Laboraories, Princeon, NJ, where he was involved in he developmen of niobium-based JoseDhson unnel juncions. He became Associa; Professor of Elecrical Engin;enng a Wisconsin in In 1972, he was a L Air Liquide, Grenoble, France, working on semiconducor barriers for Josephson juncions. Since 1974, he has been a Professor of Elecrical Engineering a Madison. He eaches courses on elecronic devices and maerials. His curren research ineress involve he use of high Tc films for Josephson devices, and he sudy of various device mechanisms in superconducors and semiconducors. * Ger K. Hohenwarer was born on March 20, 1950, in Frankfur, Wes Germany. He received he DipL-Ing. degree in eler@ical engineering from he Technische Universia Brarmschweig in Ocober Coninuing his educaion a he Universiy of Wisconsin, Madison, hemas graned he M. S.E.E. degree in Aug He is cu~enly working oward he Ph.D. degree in he area of applied superconduciviy. Mr. Hohenwarer is a member of Sigma Xi.

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