Contains research objectives and reports on three research projects.U.S. Navy (Office of Naval Research) under Contract Nonr-1841(49)U.S. Air Force under Air Force Contract AF19(604)-5200Lincoln Laboratory, Purchase Order DDL-B22

Bers, Abraham

Litwin, R.

Morse, D. L.

Rummler, W. R.

Smullin, Louis D.

DSpace@MIT

VIII. MICROWAVE ELECTRONICSProf. L. D. Smullin Prof. A. Bers W. R. RummlerProf. H. A. Haus D. L. Morse W. K. RushforthR. B. McCulloughRESEARCH OBJECTIVESWe shall continue our work on the theory of wideband, high-power klystrons, andon wideband circuits for klystrons and traveling-wave tubes.1. We shall be studying multigap, klystron output cavities in an attempt to realizebandwidth of 20 per cent at the megawatt power level.2. The wideband-buncher klystron analysis will be extended to other configurationsthan the one illustrated in this report.3. The X-line will be studied experimentally to determine its applicability to high-power traveling-wave amplifiers at one extreme, and to millimeter tubes at the other.L. D. SmullinA. BROADBAND-BUNCHER KLYSTRONW. H. Watson and R. E. Holady (1), of Litton Industries, Inc., have described anovel wideband klystron which they call the "Skirtron." This is shown in Fig. VIII-1, inwhich the frequency responses of the various cavities are indicated.The input cavity (No. 1) is a simple reso-nant circuit, very heavily loaded by the inputcircuit, and tuned to a resonant frequencyT 23 15? COLLECTOR f < fo where fo designates the center of theBEAME ii frequency band that is of interest. The inter-]i f--- /In--r t--/--I NPUT )  OUTPUT mediate cavities are located at a distancef I = Xq/2 beyond the input cavity, where X qis the effective plasma wavelength in thefl fo fo fi fbeam. Each of these is tuned to a commonFig. VIII-1. Schematic of "Skirtron" frequency fi>f . They are heavily loaded bywideband klystron. resistive loss, are not coupled electromag-netically, and are spaced a distance 13 zX /20 apart. The output cavity is located q2 = q/4 beyond the last intermediate cavity.It is of a wideband variety, having a passband centered on f . (The design of such an out-put cavity is still a serious problem, but that matter is not a part of this discussion.)The over-all frequency response of such a tube is reported to be very flat over abandwidth of 10 per cent, or so, while the gain remains fairly high, approximately 30 db.This research was supported in part by Purchase Order DDL-B222 with LincolnLaboratory, a center for research operated by M.I. T., which is supported by theU.S. Air Force under Air Force Contract AF19(604)-5200; and in part by the U.S. Navy(Office of Naval Research) under Contract Nonr-1841(49). Reproduction in whole or inpart is permitted for any purpose of the United States Government.(VIII. MICROWAVE ELECTRONICS)Watson and Holady (1) say that the flat bandwidth results from the multiplication of thecomplementary skirts of the input and intermediate cavity characteristics, whence thename "Skirtron." They have not made it clear why the gain is so high with the cavitiesso heavily loaded. The spacings fl are small, and f2 Xq/4 is the distance to theoutput cavity.We have carried out a small-signal, space-charge wave analysis of this con-figuration. Our analysis actually predicts large gain and bandwidth, which is inagreement with their experiments. It is possible, also, to reduce the length of thefirst drift-tube from X q/2 to 3 = q/20 without substantially affectingthe tube performance.Consider the system shown in Fig. VIII-2. If the cavity gaps are short, 0 << 1, wegcan assume that the beam leaving the input gap carries an ac kinetic voltage U 1 = -MV 1,where M = 1 is the gap coupling coefficient, and V 1 is the gap voltage. The convectioncurrent at this plane may be ignored (a good approximation).The group of intermediate cavities may be treated as a multigap klystron (1, 2). Or,if these cavities are assumed to be very close together, the system will behave like areactive-medium amplifier (Easytron). In the second case, with many intermediatecavities very close together, the beam emerges with relatively large velocity modula-tion as compared with the current modulation. We haveU 1nn2 /2W.1 1where Z = (2Vo /Io )(q/), ' i is the intermediate-cavity resonant frequency, and Qi isthe Q of the cavities. For a in the neighborhood of wi, Un/JnZo >> 1.The gain of the continuous intermediate section goes as U cC U eaz whereP pea = Ren 1/21-e 1- W 2 1/Figure VIII-3 is a qualitative plot of the gain versus frequency for lossless, and lossy,continuous intermediate structures, and for a structure consisting of a finite number ofcavities with small, but nonzero, spacing (f1). The gain of such a structure may bevery high, even with heavy loading (low Q ).Calculations were made of the small-signal gain of a hypothetical tube with the fol-lowing characteristics:UnBEAM I I JI I i I I iINPUT--INTERMEDIATECAVITIESFig. VIII-3.S COLLECTORIOI IOUT PUTWideband-buncher klystron.Q. = 0Gain-frequency characteristics of continuous (Easytron)resonant structures and discrete structures.1 2 34BEAM 4I i II  iS14INPUT -INTERMEDIATECAVITIESI COLLECTOROUTPUT-6 -5 -4 -3 -2 -1Wideband-buncher klystron.15M Vgi YoREAL PART-- IMAGINARY PARTI 2 3 4 5-I // HALF- BANDWIDTHS FROMCENTER FREQUENCY OF-/ INTERMEDIATE CAVITIESReal and imaginary parts of beam current (I5) at the output cavity.Fig. VIII-4.Fig. VIII-2.Fig. VIII-5.(VIHI. MICROWAVE ELECTRONICS)Vo = 140 kv Gap transit angle, ped = 0. 5Io = 71 amps Gap radius, per = 0. 63P = 107 watts R/Q = 70X = 25 cm R = 5. 5 X 105 ohmso shuntX = 145 cm Cavity spacing 1 0.05 qq 01 = 2rr 1/qInput cavity loaded to QL = 10 by the sourceThree intermediate cavities loaded to QL = 10 by lossThe beam excitation at the output of the last idler cavity in Fig. VIII-4 can be shown (2)to beMV = l-j6(01 z)-5(01 z)2+j(O 1 z)3MV 1 1Z)11Yo M 1 j3+41 lzl)-jo1z)2where z = (MZ) Zo; M. = 1 is the intermediate gap coupling coefficient; Z., is theimpedance of loaded, intermediate cavities; and Z is the characteristic impedance ofthe electron beam.The ac current, I5, was found to have a maximum amplitude at a distance 02q = 740beyond the last intermediate cavity. The real and imaginary parts of 15 versus w areshown in Fig. VIII-5.The output power of the tube is given byI 1 212 22 Iv I 11i52 115  y 5 2 V 12L 2G 2G 2GL o owhere G L is the load conductance, assumed to be equal to the beam conductance; G =Io/V o , and y 5 is a transadmittance relating V 1 and 15. The input power to the tube isgiven byP. - l2 (G +Gin 2 sh efIn order to load the input cavity to a very low Q, the generator conductance must be verylarge, and there is a large reflection mismatch. Thus the available gain is defined asPower out of tube Y5() 2Gsh +Ge LAvailable generator power 4 G 0 L(where L 1 is the input reflection loss (0<L 1 <1). For the case considered, L 1 was -18 db(VIII. MICROWAVE ELECTRONICS)at the input-cavity resonant frequency.Figure VIII-6a shows a curve computed with the input cavity tuned 3 half-bandwidths-5 -4 -3 -2 -1 0 I 2 3f f.-BANDWIDTHS OF INTERMEDIATE CAVITIES(a)GAIN(DB)302010Q 10-7 -6 -5 -4 -3 2 I 0 I 2fi fAw HALF-BANDWIDTHS OF INTERMEDIATE CAVITIES(b)Fig. VIII-6. Gain-frequency characteristic of wideband-buncher klystronwith input cavity tuned to f and idler cavities to fi .below the intermediate cavities. A bandwidth of approximately 15 per cent, and a gainof approximately 29 db, are indicated. In Fig. VIII-6b, the input cavity is tuned 4 half-bandwidths below f.. It can be seen that decreasing the bandwidth of the intermediatecavities somewhat (raising their gain at Af = 0) would result in a fairly flat responseover a bandwidth of approximately 20 per cent.When the input gap is lengthened to 0gl = 2, the electronic loading Ge is increased,and an ac current is induced at the output of the input gap. This current does not appre-ciably affect the ratio 15 /Vgi , but allows a much better power match at the input cavity.GAIN (DB)4030Qi= 10-7 -6 -5 -4 -3 -2 -1 0 I 2fl fiA6) HALF- BANDWIDTHS OF INTERMEDIATE CAVITIESFig. VIII-7. Gain-frequency characteristic of wideband-buncher klystron withinput cavity tuned to fl and idler cavities to fi. Transit angle ofinput gap is increased to 2 radians to make Gej appreciable.The effect is a shifting of the whole gain curve upward, which allows greater separationin frequency of the input and intermediate cavities and still maintains acceptable gain.The calculated gain versus bandwidth curve for the input cavity (Qinput = 6 2/3) tunedGAIN (DB)2010-7 -6A, HALFQi= 10I I I(VIII. MICROWAVE ELECTRONICS)5 half-bandwidths below the intermediate cavities is shown in Fig. VIII-7. The peakgain is approximately 39 db, and the bandwidth is very nearly 6 half-bandwidths of anintermediate cavity, or approximately 30 per cent.L. D. Smullin, D. L. MorseReferences1. W. H. Watson and R. E. Holady, a paper presented at the 1959 Electron DevicesMeeting, Washington, D.C., Oct. 29-30, 1959 (unpublished).2. A. Bers, Interaction of electrons with electromagnetic fields of gaps with appli-cation to multicavity klystrons, Sc.D. Thesis, Department of Electrical Engineering,M.I.T., June 1959.B. SPACE-CHARGE MODE THEORY OF MULTICAVITY KLYSTRONSIn Quarterly Progress Report No. 55, pages 65-70, we presented the theory of inter-action between an electron stream and the electromagnetic fields of a gap. The multi-cavity klystron will be considered to consist of a succession of such gaps. Except forthe electron stream, the gap circuits will be assumed to be uncoupled.The gap interaction can be summarized in the convenient matrix form=II = I, II gII =I---- --- (1)g = g -Ig YeL gwhere I, II, and g refer to reference planes as shown in Fig. VIII-8, and, in the notationof the previous report (1),B(1 VkB= ; B(k) = (2)B (n) ID D (k) e eF() D(nk Zok sin Y -jD L . • D =-----------------------e e" D(n jYok sin 0 k cos Ok(3)(k) kK = ; K = (4)(n) Y NK It ok kMk (M + Mk) C (5)k 2 +k -kkREFERENCE PLANES/ ELECTRON BEAMIILMID-PLANE OF GAP(0)v lIg+ IIFig. VIII-8. Schematic representation of the gap region of interaction:(a) reference planes in the gap region; planes I and II arelocated where the gap fields are zero; (b) multiport repre-sentation of the interaction; the independent transmissionlines represent the diagonal drift transformations. Planes(-) and (+) are, respectively, just at the left and right of g.S I II I Iv / I I I VD G D I(n) I Ig I (n)Yey (n) +I 'I (nSI II I1I - + TFig. VIII-9. Equivalent circuit at thegap terminals.Fig. VIII-10. Equivalent circuit in the beamwhen I = -Y Vg c g4VIgn2 3 n-I nFig. VIII-11. Equivalent circuit in thebeam for a single-modetransformation through asymmetric gap.Fig. VIII-12. Schematic representation ofmulticavity klystron. Thelocation of the mid-plane ofeach gap is shown.(VIII. MICROWAVE ELECTRONICS)1Nk (M+k - Mk) Ck (6)F = F(1 ) .(n)] • r(k) = (Y N M )  (7)g = =g =g ok k kM =1( M k + M Kk (8)k k - k) k (9)The superscripts 1 ... k... n and subscript k refer to the various space-chargemodes, and Yet has been defined previously (1). The formulation of Eqs. 1-9 places inevidence the importance of choosing the mid-plane of the gap as a reference. Equation 1can be rewrittenB D 0 1 K D 0 B= II = gII 0 ]Ig I(0)I 0 1 r Y 0 1 Vwhich has the drift and gap parameters separated as shown in Fig. VIII-lb.a. The Equivalent Circuit at the GapFrom Eq. 1, the short-circuit gap current isI = F B = X (Y N' V + M I (k)(11)where the subscript (minus) denotes the plane just preceding the mid-plane of the gap.The gap circuit is loaded by Ye. The real part of Yef is given byGe -4 +ok M k 2- M-k 2Ck Kk (12)The imaginary part of Yea is, similarly, a sum of Bef k over all the modes (1). Theequivalent circuit at the gap terminals is shown in Fig. VIII-9.b. Equivalent Circuit in the BeamWhen the gap circuit is representable by an admittance Y , thenI = -Y V (13)g c gThe transformation of the excitation in the beam is found from Eqs. 1 and 13:BII [DgII G Ig] =I (14)100(VIII. MICROWAVE ELECTRONICS)G = I + K (-Z) r= = -g g =gZ = 1g Y + Yc Yetand I is theis containedidentity matrix.in the matrixK(1) r (1)=g gK=g=gThe mixing of the modes, which occurs because of the gap,.. .. K(1) (n )k(n) r(n)=g =gK(n) (l)=g =g(17)whereY .N! M.K(i) (j) 0j 3 1i= g = g Y N! Y .N.o] 3 o 1M! M.3 1Y . N. M!01 1 3(18)The equivalent circuit for Eq. 14 is shown in Fig. VIII-10.For a single mode, Eq. 15 becomes simplyS-Y MN' Z -MM' Zo g gG =------------ (19)-Y2N' NZ 1 -Y M' NZo g o gIf the gap is symmetric [that is, (M/C) = (M'/K) and (N/C) = (N'/K)], the equivalentcircuit for Eq. 14 is a loaded gyrator, as shown in Fig. VIII-11. This was pointed outby R. B. McCullough.c. Multicavity Klystronsi. Cascade formulationThe schematic of a multicavity klystron is shown in Fig. VIII-12. It consists of asuccession of gaps of arbitrary characteristics. The gain of the multicavity klystron isproportional to the transfer admittance Ign/Vg l , which can be written with the aid ofEqs. 1, 4, 7, and 14.gn= D G D G D GD KV = gn=n- l ,n =n-l =n-2,n-1 =n-2 =23 =2 =12 glgl(20)101where(15)(16)(VIII. MICROWAVE ELECTRONICS)ii. Two-gap transfer admittanceConsider two gaps as shown below:Vgl I2g2Let2g -g2 Vg2=0 Vg2 = 2 g Z 2where Z is as defined by Eq. 16. We define the two-gap transfer admittanceI2g1 glWith the use of Eqs. 2-9, Eq. 22 becomesY21 =-exp(-jee l , 2) I [Yo(M 1 N2 + M2 N 1 ) cos 612 + jYo(M 1 M + N 1 N2) sin 612] ( k )(23)The subscripts could, clearly, apply to any two gaps.iii. Feedforward formulationsA different approach to the determination of the multicavity klystron gain is to con-sider the output as a linear combination of the outputs resulting from excitations in allthe gaps. If we consider that the outputs are the result of the two main signal transfermechanisms in the device - drifting and interaction with gap fields - we can write thetransfer functions for any number of gaps by inspection. For example, the transferadmittance for a three-cavity klystron,I 2I3g3is given by102(21)(22)L|(VIII. MICROWAVE ELECTRONICS)1 3g= Y21Y32Z2 + Y31V(24)We note that the first term is an interaction, or cascade, term, the second is a drift,or feedforward, term. Similarly, for a four-cavity klystron,VglI 2the transfer admittance is given by(25)y 2 1Y 3 2 Y4 3 Z 2 Z 3 + Y3 1 Y4 3 Z 3 + Y2 1 Y4 2 Z 2 + Y4 1V-1The excitation in the beam at any plane can also be found by inspection.the beam excitation after four gaps,VgIFor example,B=4+is given byB g4+Vgl K 4 [Y2 1 3 2 4 3 Z 2 Z 3 Z 4 + K 4 [y 3 1 y4 3 Z 3 Z 4 ]+ K 4 [Y2 1Y4 2 Z 2 Z 4 ]+ 43 21Y3223 +K 4 [Y4 1 Z 4] + D4 3 3 [Y3 1Z 3]+D 4 2 _2 [Y 2 1 Z 2 ] +D 4 1 K 1In general, for an n-cavity klystron, by the feedforward formulation, we haveI TT n-l kng V Y(k+l),(k-l) kVgl k k k p=2(27)yp,(p- 1 ) Z10314g3 4(26)a I I I I H(VIII. MICROWAVE ELECTRONICS)where the first sum is over all possible types of k, that is, k = 0, k = 2, 3 ... n - 1,k = all pairs, k = all triplets, etc., k = all intermediate gaps; the second sum is a cyclicpermutation over all the k's of one type; H denotes a product, and H k denotes a productwith the k t h member missing.A. BersReferences1. A. Bers, Space-charge mode theory of gap interaction, Quarterly ProgressReport No. 55, Research Laboratory of Electronics, M.I.T., Oct. 15, 1959, p. 65.C. THE X-LINE SLOW-WAVE STRUCTUREThe X-line is a periodic structure consisting of wires or bars across a circulartube. The wires are alternately rotated back and forth through an angle a, as shownin Fig. VIII-13 (if a = 0 we have a simple ladder line). The phase shift per section wasfirst determined by cold measurements, and later by beam probe measurements. Thecold tests consisted of measurements of the resonances of structures having variousnumbers of wires. Some idea of the field configuration was obtained by observing theshift of resonant frequency as a small metal bead was pulled through the structure,either along the axis or on some line parallel to it.Except for the case when a = 0, this structure has no transverse planes of symmetry.Therefore it is not possible to measurethe resonances of an elementary cell, andthereby deduce the upper and lower cutofffrequencies of the various passbands. Inthis respect, it resembles an interdigitalline. An experimental determination ofthe w - 3 diagram must be made with alarge enough number of elements to makethe end effects unimportant. Figure VIII-14S4 shows the natural frequencies of resona-tors consisting of various numbers ofFig. VIII-13. Elementary X-line struc- wires, with a = 900. It is clear thatture. 6 pairs give the cutoff frequencies withvery good accuracy. Figure VIII-15 is anw - p plot for the nine-pair resonator, taken from the data of Fig. VIII-14. A strikingfeature of the A - p diagram is the large angle with which the curve appears to approachthe upper and lower cutoff points.Figure VIII-16 illustrates the effect of varying the angle, a, between the wires, from104"0" MODE LINE *-- - -- *- - ---2 *3, 6 a/ , 9 -112I / /2134 56 7 9PAIRS OF CROSSED ELEMENTSFig. VIII-14. Resonances of an X-line structureof pairs of crossed wires.(a=900) versus numberO 2 4 6 8 10 12 14 16 18 x 180:PHASE SHIFT ALONG THE UNIT CELLFig. VIII-15. w - P diagram of X-line (a=900).105TM0 1WIRE LENGTH = DIAMETER OF THE TUBE - 5.08 CMDISTANCES BETWEEN WIRES = 0.46CMLENGTH OF THE CAVITY = 7CM7 + 6 WIRESPHASE SHIFT ALONGTHE WHOLE STRUCTURE137 127ISHORTEDwi 0117 107 97r 87 77 67 57 47 37I I I II I I I II I I Il I I I l , IIII II III II-27 17II I Iw LIii U_a uI- U071I II I III,2 2.5 3 3.5 4 4.5 5f (xmc)Fig. VIII-16. Effect of angle a on resonant-frequency pattern of X-line.7000600050004000zwwat 3000U_2000100050 100 150 200 250 300f. mc/sec, (VOLTS)1/2Fig. VIII-17. - 1 diagram of X-line determined by electron-beam interaction.106cnw 903: 7560w4 5*30 °D 15-ljzI III II III(VIII. MICROWAVE ELECTRONICS)00 to 900. The structure that was measured had 13 wires. It will be observed that thisstructure has a fundamental backward-wave space harmonic, and thus should be suitablefor use as a backward-wave oscillator. The advantage of this structure over the simpleladder line lies in its much greater bandwidth.Dr. R. C. Hergenrother, of the Spencer Laboratories, Raytheon Corporation, hasconstructed an X-line backward-wave oscillator. He has kindly loaned it to us to makeelectron-beam interaction measurements of the w - P diagram (1). The beam is operatedwell below the starting current for backward-wave oscillation (<1 ma). At some fixedinput frequency, the beam voltage is varied and points at which the rf output powerchanges are noted, and plotted as in Fig. VIII-17.L. D. Smullin, W. R. Rummler, R. LitwinReferences1. D. A. Watkins and A. E. Siegman, Helix impedance measurements using anelectron beam, J. Appl. Phys. 24, 917-922 (1953).107

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