Design HPklystrons

8/12/2019 Design HPklystrons

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TALLERICO: DESIGN CONSIDERATIONS FOR MULTICAVITY KLYSTRON 375In addi tion , he following quantiti es have beende-

fined :uo , the dc beam velocityup d G o ,he radian plasma frequencya = MV,,,/ Vo, the modula tion coefficient

P O the dc space-charge density0, the permit tivity of free spaceM , the gap coupling coefficient [ 5 1

The electronphase is measuredwith espect o ahypothetical wave which travels at the dc bea m veloc-ity; thus

W Zuocp = t. 7 )

ber of charge grou ps is used to simulate the continuo uselectron flow. Eachchargegroupcarries wo ndices,which have the following meanin g: i denot es the axialplane of th e int erac tion region i=0, 1 , 2 , ) ; j de-notes theentrancephaseof theelectron j= l , 2 , . . ,m) .

Th e differenceequationsareobtainedby etainingonly the first two terms in the Taylor series expansionof theworkingequations.Equations (3) and (4) thenbecome, in difference form,

andTheouriermpli tude s of thearmonicurrentsre 'AYuu


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376 IEEE TRANSAGTIONS ON ELECTRON DEVICES, JLTYE 1971culation are therefore m, A y , w,/w, uo/c , a , y a , and b / a .I n addition, if a multicavity klystron is being analyzed,one must specify the drift ength , a , and Q o foreachcavity.

~ \ ~ C M E R I C A L ESULTSThe electron phase formalism greatly facilitates the

solution of the equations since the steady-sta te solutionis found directly. However, these relations are not validin regions where the electron trajectories change rapidlywithin an electronwavelength ( Xe= 2nuo /w ) and huscannotbe used tocalculateelectron rajectories n aoutpu t gap. Mihr an has proposed the merit figure

which closely approximates the efficiency in a klystron.Here Emins the kinetic energy of the slowest electronat the y plane being considered, and E,,, is the energywhich corresponds to the dc beam velocityo his meritfigure hows th at good bunch ing i.e., a high funda-mental ha rmonic content of the beam current) can onlyyield high conversion efficiency when the energy spreadin the stream is small. Mihran presents arguments onthe easonableness of (18), bu t he final ustificationmustreston heagreementbetweenexperimentandcalculated results. Equation 18) is used to estimate theconversion efficiency in this work, but n a nonrelativis-tic analysis a simpler relation may be used:

Numerical calculations to determine the merit figurefor the wo-, hree-, nd our-cavityklystronshavebeen performed in the present investigation. The largestmerit figures invariably occurred with a substantial R Fvoltage on the first cavity; hence, one or moreow-levelcavities would have o precede he arge-signal powerextractionsectionsconsideredhere.The inearspace-charge wave heory may be used to design the small-signal portion of the amplifiers.

Unless specified otherwise, 32 electrons per R F cycleand an integrat ion incremen t given by (15) were usedin the numerical calculations.Two-Cavity Resul ts

The wo-cavity klystron can beeasilyanalyzedbythe linear space-charge wave theory [S I provided thatthe input signal is small enough. Thus, two-cavity cal-culations provide a good check on the R F space-chargeforces and the solution method. Kumerical results for aseries of calculations in which a1 was varied are shownin Fig. 1 . 2 For small values f a he fundamental current

of Z/h , .2 The notation Li means that the dist ance is measured in units

1.2//--

//

////

//

/ /

OY0 I .2 .3 4 .5 .6 .7a LOFig. 1. Upper curves: maximum merit figure and fundamental har-monic current versusa for the two cavity klystron. Lower curvethe normalizeddistance a t which hesemaximaareachieved.r a = 0 . 7 6 3 3 , wp/w=0.38198, k e = 0 . 5 1 2 , b / a = 0 . 7 . )

reaches a maximum at one-quarter of a reduced space-chargewavelengthfrom he nputgapand hemaxi-mum magnitude agrees well with the small-signal pre-diction :

For larger values of a the fundament al current is lessthan hesmall-signalprediction. It can, howev er, ex-ceed the ballistic heorymaximum [ l ] . Anotherpre-diction of the ballistic heory is that any large a willyield the same conversion efficiency, although the mer itfigure shows th at th e fficiency is strongly dependent ona and reaches a maximum a t a =0.35.

I t is important o note hat he working equations[(13) and (14) 3 do not contain he plasma frequencyreduction actor,but ince heGreens unctionac-counts for the finite radial geometry, the fundamentalharmoniccurrent(forsmallsignals)reaches its maxi-mum at the proper distance.Three-Cavity Results

The hree-cavityklyst ron is specifiedby thebeamvariables w,/w, u o / c , y a , and the following paramete rs:

011 the input cavity normalized voltage,012 the cent er cavit y normalized voltage,QZ the phase angle of the admi ttance of t he secondLl the ength of the irstdrift ength n educed

cavity, and

plasma wavelengths.I n Figs. 2-4 mer it igurecontoursareshown orafamily of three-cavity amplif iers for ai s of 0.05, 0.1, and0.2, respect ively. The mer it figure is plotted as a func-tion of the relative bunching voltage 0 1 2 and the phaselag - 4 % of t he second cavity. The beam parameters innonnormalized variables are


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TALLERICO:DESIGN CONSIDERATIONS FOR MULTICAVITY KLYSTRON 377

.s

. 2 + -450

I

'0 4 .8 1.2 1.6 2.0 2.4-@2, RADIANS

Fig. 2. Merit figure contours on the a2-G2 plane for thethree-cavity klystron. a1=0.05, L1=0.1255.)

'0 .0 1.2 1.6 2.0 2.4-a2 ADIANS

Fig. 3 Meri t figure contours on the aa-@2 plane for thethree-cavity klystron. a1 0 .1 , L1=0.1255.)

' I tOC0 .4 .0 1.2 1.6 2.0 24

--IP2,R-Fig. 4. Meritigureontours on the plane forhethree-cavity klystron. (a1 0 .2 , L1 0.1255.)

I m . l .2.4.a .I .I5 .2 .25 3LI

Fig. 5 . Merit figure versus L1 for the three-cavity klystronwith a1 as the parameter. (as=0.4, On= -1.4.)

m-.-.-a-,2

.os0 .I .IS .20 2 5 .30LI

Fig. 6 . Normalized saturation length versus L for the three-cavityklystron with a1 as the parameter. (as=0.4, @Z = .4.)

2a = 2 g inw = 2n X 8 0 5 X lo6 ad/s

V, = 87 000 V on the anode, andIo=32 AL I - ~ 10.5 in (0.1255 reduced plasma. wavelengths).

The beam variabl es in normalized units are shown nthe capt ion of Fig. 1. The maximum merit figure can beseen o ncrease from 0.54 to over 0.60 as a1 is madelarger , illus trating the gain-efficiency compromise. Themaximum merit figure for all al s is a t a2 =0.35 , as inthe two-ca vity case; however , the phase becomes morecriticalas he argermerit igurecasesareachieved.This is in agreement with previous knowledge that thepenultimatecavitymustbehigh-Qand unedabovethe drive frequenc y for maximum efficiency.

Fig. 5 shows the effect f the first drift length on merifigure for the three-cav ity klystron , while Fig. 6 showsthecorresponding econddrift engths a t which themaximummerit igure is achieved. I n these tudiesaz=0.4 and @ 2 = -1.4. The larg est meri t figures again


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FIRS T DRIFTPACEECOND DRIFT SPACE

IEEE TRANSACTIONS ON ELECTRON DEVICES, J U N E 1971

............ . o/ . ' .&....... I. .

....a- -- , ee l , az/x,=0.198 z/Aq ..I18IT 2 t 2 0 * in

Fig. 7 . Velocity-phasediagrams or he hree-cavityklystron atvarious locations in the drift spaces. (a1=0.2, Ll =0.2 , az=0.4,ap = .4.)

occur for large (XI : the surprisi ng feature f Fig. 5 is thatthe me rit figure increases steadily with LI . This occurssince the long drift length increases the harmonic cur-rent and reduces the velocity spread on the beam as i tentershe second cavity.One would expecthatLl=O.25 would be too long an input drift length for ahigh-efficiency klystron. The fact that the radial motionhas been gnored may well account or hegenerallyincreasing merit figure as L1 is made larger. The generaltrend shown in Fig. 5 is true; however, the author doesnot trust these results for L1>0.2 due to th e confined-flow electronic model.3 The experimental klys tron to bedescribed below used L I=0.16 and the results were inagreement with the computed predictions. Fig. 6 indi-cate s that a normalized drift length Lz = 0.1 to 0.125 isoptimum for the high a1 cases.

The velocity-phase diagrams for allf the caseswhichyieldedahighmerit igurewere ound obesimilar.Fig. 7 shows the velocity-phase diagrams for a typicalhighmeritfigurecase. The eft colu mn of figures arethe velocity-phase diagrams a t various drift distanceswithin the first drift tube. The first two diagrams howthenitialmodulation ndhemodulation at z/X,=0.0762.Large-signalnonlineareffectsappear in thethird frame (z/X,=O.1564); here the electrons near thebunch center + = T ) are all traveling near the dc beamvelocity.Thespace-charge forces areaccelerating he

3 Note added in proof. Recent three-dimensional calculations bythe author indicate that forinite magnetic focusing ields the curvesof Fig. 5 all reach a maximum for LI=O.2.

0 2 4 6ELECTRON HASE

40

0 2

0.15

0.190.0500 2 4 6 8

ELECTRON HASE( b )

Fig. 8. (a)Electronphaseversusnormalizeddistance or he firstdrift space of the klystron of Fig. 7. (b) Electron phase versusnormalized distance for the second drift space of the klystron ofFig. 7 .

electro ns in front of the bunch + >A ) and deceleratingthose immediately behind the bunch center. This causea second harmonic to be added to the velocity distribu-tion as shown in the third diagram. The last diagramshows the situation just prior to the second gap. Th ecorresponding Applega te diagram (with the dc compo-nent of velocityremoved) is shown in Fig. 8(a). Thefour igures in the secondcolumn of Fig. 7 show hedevelopment of the electron bunch in the second driftspace. The first figure is the velocity modulation m-mediately after he second gap. The second harmoniccomponent of the velocity modulation reduces the totalvelocity spread of the bunch in the region f phase from2 . 7 to 3.8 rad.Thenext wodiagramsare aken forfurther distances along the second drift tube; while thelast diagram is the velocity phase plot drawn near thesaturati on plane. The modified App legate diagram forthe second drift space is shown in Fig. 8(b).

These esultsemphasize henecessity of hav ing alarge voltage n he pre-penultimate cavity as well asthe penultimate. For high efficiency the bunch mus t be


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TALLERICO: DESIGN CONSIDERATIONS FOR MULTICAVITY KLYSTRON 379shaped by at least two large-signal (a2 0.1) cavities tomaximize the bunching while maintaining aow velocityspread.Four-Cav i ty Resu l t s

Th e ta sk of finding an optimum configuration withfour large-signal cavities is formidable. Using the meritfigure, there are still seven variables (al, L1, az, @ 2 L2a 3 and a3)which must beexamined. The beam var-iables are all held at the sa me valu es as out lined n th etwo-cavity section above. A subroutine was writte n forthe large-signalcodewhichwouldautomaticallystepany one of the par ameters of the second or third cavityto seek a maximum along a one dimensional path. Th enumber of combinations is still so large that one cannothope to systematically study the entire parameter space.

Fig. 9 shows merit figure contoursn the a2 -@2 planefor a family of four -cav ity klys trons. The merit figurereaches 0.67 for a n the range of 0.15 to 0.2 and with@z = .4 rad.This is asubstantial mprovement of18 percent over the corresponding three-cavity calcula-tion. Thus i t is advantageous to have three large-signalcavities befo re the output s ection. I t is likewise well totune the penultimate and the pre-penultimate cavitieshigher than the drive frequency to achieve the properphaseangle.Thesecavitiesmusthaveahigh Q torealize theproper mpedanceat heoptimumphaseangles.

An optimum merit figure for the four-cavity klystronwas found as follows. Th e six parameter s L1, a 2 a2, 20 1 3 and @ 3 were each varied (one t a time) and set to thebestvalue whichgave he argestmerit igure.Thisoptimization procedure gives first order approximationto the best parameter settings.

The highest meri t igure was reached with the follow-ing parameters: a l=O. l ,Ll=0.1646, a2=0.15, aZ=1.4,L~=O.1515,3 =0.4, and = 1.4. The mer it figurewas0.689 in a tota l leng th of 0.4401 reduced plasma wave-lengths. Extensive calculations were only performed inthe four-cavity case for a1= 0.1. The t ren d of t he meri tfigure increasing as the tota l gain is decreased was ob-served as in the three-cavity cases.

Lien [ 7 ] has reported his work on a klystron in whichonecavity is tunednear he secondharmonic of thedrive frequency. This method has he advantage hattheecond-harmonicelocityomponent,whichsnecessary oachieve hehighest efficiencies, canbeadded by he cavity rather han by he space-chargeforces. The second-harmonic voltage and phase can bearbitrarily etbycontrolling hecavity mpedance.The four-cavity s ituation in which the second cavi ty istunednear hesecondharmonicwasstudied n hisprogram. The energy chang e at thin second-harmonicgap is

Apj = a ( p 0 1) sin (2& 2 + a0 , (21)

.4--

au 2 3--

f ]I ..0.0 .4 .a 1 2 1.6 2.0 2.4-@2Fig. 9. Merit figure contours on the a - plane for a four-cavityklystron. (a l=O. l ,L1=0.1255, L~=0.127 , s=0.4, % = 1.4.)2.0.

SATURATION

1 5 ,,-----I--// /e---*1.0- lkl\/ / I

.5.-

z/x qFig. 10. Harmonic currents and merit figure versus distance for afour-cavityklystron. (a1 0.1, LI=0.165,a2=0.15, + z = -1.4,La=0.152, a3=0.4, &=1.4.)

where all symbols have he same meaning as in (12).The highest merit figure was achieved with th e follow-ing parameters: al=O.l , Ll=O.1255,a=0.16thesecond-harmonic cavity voltage), @2 = 0 . 8 , Lz 0.077,a3 =0.4, and 3 = .4. This resultedn a merit figureof0.712 in a total length of 0.3499 wavelengths. The meritfigure improvement over the best results with four fun-damental cavities is modest; however, there is the ap-preciable reduction in the total tube lengthf 20 percent(0.09wavelengths)when hesecond-harmoniccavityis used. I n either configuration it is necessary to precedethe large-signal cavities by two or three gain cavities;thus, the overall percentage length reduction is not asdramatic.Theoptimumphaseang le of the econd-harmonic cavity is 0.8 rad , which implies tha t the cav ityshould be tuned somewha t below th e second harmonicof the drive frequency . This point is in agreement withthe re sults of Lien.

Fig. 10 shows he variation of the meri t figure andfirst woharmonic urrent mplitudes orhe ourfundamental-cavity klystrons described above, and thesame nformation is shown nFig. 11 for hecase in


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380 EEEE TRANSACTIONS ON ELECTRON DEVICES, JU N E 977

,,r SATURATIONPLANE 7

Fig. 11. Harmonic currents and merit figure versus distance for afour-cavity klystron with the second cavity tuned near the secondharmonic of the drive frequency. (al=0.1, L1=0.126, aZ=0.16,=0.8, L2=0.077, aa=0.4, @ = 1.4.)

which the second cav ity is tuned near the second har-monic. In the latte r case , the bunc hing in the seconddrift space is almost entirely at t he second harmonic;thus the fundame ntal current amplitud e hardly growsin this drift space. The second harmonic amplitude isgreater than the dc current at the saturation plane inboth cases. Th e Applega te diagra ms for these interac-tionsareshown nFigs. 12 and 13,respectively.Theasymmetry is caused by he var iati on of the mass ofthe electrons with velocity. Since the gaps have beenassumed to be thin, the flight lines can have discontinui-ties in their slopes a t each gap. In both cases the slowelectrons in the last drift space bunch more quickly andreach a maximum density a t a shorter distance hanthe faster electrons. In the conventional klystron (Fig.12), the electrons are always forced towards the centralelectron (4 = R ) a t each gap. This bunching around Rcauses th e repulsive space -charge forces to be very effi-cient n hefinaldriftspaceand his imits he finalam ou nt of bunching. With a second-harmonic cavity,two bunches are formed in the second drift space, onenear 2.0 rad and the other near4.8 rad, leaving the areanear q5 T with a sparse electron population. Then inthe final drift space the two bunches converge towardsthecentralelectronsand hespace-charge orcesarenotas effective a t inhibiting hebunchingprocess.Anothe r way of looking at the mecha nis m of the effi-ciency improvement shown in Fig. 13 is that after thesecond drift space, both bunches aret phases where thegap fields are high . This allows most of the e lect rons toexperience a arge and favorable velocity modulation.This modulation effectively overcomes the space-chargeeffects.

A very long penultimate drift length also produces ararefac tion of the flight-line diagram near + = R . Thusthe mechan isms for the meri t figure mprovement are

ELECTRON PHASEFig. 12. Electron phase versus distance for the klystron of Fig. 10.

Y 3

9.-0-

2.-

0-.4-

YI.e

070 2 4 6 8ELECTRONPHASE

Fig. 13. Electron phase versus distance for the klystron of Fig. 11.

similar in bothcases,although hebunchingprocesscan be controlled better with the second-harmonic cav-ity. The second-harmonic cavityllows a shorter overal llength to be used for a high-efficiency kly stron; this' isan important advantageor low-frequency applications.

COMPARISONF THEORYND EXPERIMENTSThe above resu lts were used to design a high-power

klystronfor he Los AlamosMesonPhysicsFacility.Themajorklystron equireme nts for hisapplicationare the following.

Drive frequency 805 M H zPeak power output 1 . 25 MWDuty factor 12 percent


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TALLERICO: DESIGN CONSIDERATIONS FOR MULTICAVITY KLYSTRON 381l i0-0 2 4 6 8 Ib I2 i l k 18

POWER INPUT,WFig. 14. Calculated power ransfer curves for he L5120Awith cavity frequency and Q as the parameters.

8174809 811 813 815 81719F3 (MHz)

Fig. 15. Merit figure contours on he F3 F4plane for the L5120A.

Gain 50 d BMinimum efficiency 45 percentPower tra nsfer curv e as smooth a s possibleMaximumcceleratingoltage 86 kVBandwidth 4 M H z .

The designwasaccomplished as follows. The beamdiameterwaschosen so that henormalizedplasmafrequency with a 0.7 b / a ratio became w,/w =0.38. Thefirst wo drift engths were set at L1=LZ=O.125 froma small-signalgaincalculation.UsingFig. 5 , a hirdlength of La =0.16 was chosen. Some calculated powertransfercurveswithvarious hird-and ourth-cavitytunings are shown n Fig. 14. These computed resultsindicate that the third cavity shouldbe unlo aded; how-ever, he ubebuildersdecided o oad hefirst hreecavities o educe heeffects of manufacturing oler-ances and to provide a means of selectively loading anyhigher order cavity modes. The third- and fourth-cavityfrequencies were determined from the calculations sum-marized in Fig. 15. The mer it figure is shownon heF3-F4 plane, and the dashed curves the locus of 50-dB

00 10 20 x 40 50POWER INPUT, W

Fig. 16. Theoretical and experimental power transfer curvesfor the L5120A. (S IN 2005, V0=86kV 10=33 A.)TABLE I

SUMMARYF L5120A DESIGNDATA.BEAMVOLTAGE86 kV; BEAMCURRENT2 ANormalized

harmonicNormalized Drift currentvoltage at lengthmplituderequencyCavityaturation (inches) I ~ I / I O / (MHz) R/Q1 0.00710.52 0.0385 0 805 10510.53 807 900.1384.3.1215 8154 0 457 7.6.6727 821 80805 1.3718 805 70

gain. Th e region under and to the right of the gain lin eis the area where the saturate d gain is grea ter than 50dB , he specified minimum .Theoperatingpoint ofF3 =815 MHz and F4=821 M H z was chosen, yieldinga merit figure of 0.55.The cy of the first cavity s too small to permit a directapplication of the large-signal equations. Thus the cy inthe second cavity was calculated according to the small-signal method and then a large-signal, four-cavity cal-culation was made. The only drawbackf this approachis that the large-signalffects of the tuni ngof the secondcavity cannot be found. F2 was set a t 807 MH z, basedonprevious xperiencewithargeklystrons for theStanford linear accelerator.

Th e calculated and actual performance f the L5120Aare shown in Fig. 16. K O adju stme nts of th e cavity fre-quencies from the calculated values were needed. Theparamet ers for this klystron are listed in Table I .

The theoreticalndxperimentalowerransfercurves for two other klystrons are shown in Figs. 17 an18 . Two experime ntal curves are shown in Fig. 1 7 fortwo etti ngs of the focus mag netcurrent.The 14-Acurrent yields the most output power and this is com-pared to the theory.

n all cases the calculat ed o utput power is between 4


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IEEE TRANSACTIONS ON ELECTRON DEVICES, J U N E 1971

V 84 5 k Vv 2 9 . 4 A

0 5 IO 15POWER INPUT, W

Fig. 17. Theoretical and experimental power transfer curves for theVA-862A with magnet current as the parameter. ( S I N 104.)

-----.// / .

.1.2.-

V,,=aOkV&826. 5A

POWER O U T P U T WFig. 18. Theoretical and experimental power transfer curves for the\A-862A with beam voltage as the paramete r. (S IN 105.)

t

PEAK INCIDENT INPVTPOWER,WFig. 19. Reflected input power versus ncident nput powerfor the L5120. ( S J N 2004R, V0=86 kV, I0=40 A.)

and 10 percentgreater han hatactuallyobserved.This discrepancy s probably due to the fact that undermost conditions the merit figure is an optimistic mea-sure of efficiency. The agr eem ent s very good, especiallysince the flow is no t confined. Some of these tubes havean isolated collector, which allows the intercepted cur-rent to bemeasuredeasily.Typically he nterceptedcur ren t at sat ura tio n is about one-tenth of the beamcurrent. Thewiggles on some experimental curves (suchas Fig. 18) are caused by reflected electrons returningto the input gap. This hypothesis is verified by Fig. 19whichshows he orwardand eflectedpower at heinpu t cavi ty of an L.5120 klystron. The VSWR of thecavity depends on the drive level, which indicates th atfor some drive evels the returning electrons cause morepower to be reflected into the generator.

SUMMARYN D CONCLUSIONSThe major results of this investigatio n are that for a

high-efficiency klys tron he following condi tionsmustbe met.

1) At east wocavities, inaddition o heoutputcavi ty, must have a normalized gap voltag e of a 20.1.

2) An appreciable second-harmonic component mustbe present on the electron velocity as the beam entersthe penultimate cavity. This component can arise fromeither a second-harmonic cavity or a long drift space.

Th e large-signal equations presented here have beenapplied to several different klystrons and the calculatedsaturatedou tput power is between 4 and 10 percentgreater han hemeasuredvalues.The confined flowdiskmodel of theelectron flow andMihransmeritfiguremethod of estimating heconversion efficiencyare therefore shown to be valid concep ts for the designand analysis of high-powered klystrons.

ACKNOWLEDGMENTThe authorwishes to thank L. . Fox of Litton Indu s-

triesand 0 . C. Lundstrom of VarianAssociates ortheir work in the design and productionf the klystronsreferred to in this paper.

REFERENCES[ l ] S. E. W ber,Ballisticanalysis of a two-cavity initebeamklystron, IRE Trans.ElectronDevices, vol. ED-5,Apr. 1958,pp. 98-108.---, Large-signalanalysis of the multicavity klystron, IRETrans.ElectronDevices, vol. ED- 5, Oct. 1958, pp. 306-315.J . E. Rowe, NonlinearElectron- Wuoe InteractionPhenomena .New York: Academic Press, 1965.T. G. NIihran, T he effect of d rift ength ,beam adiusandperveance on klystron power conversion fficiency, IEEE T r a n s .Electron Deoices, vol. ED-14, Apr. 1967, pp. 201-206.

A. H. W . Beck, Space-ChavgeWaves. New York:Pergamon,1958.[6]S. Wallander, Large-signal computer analysisf klystron waves,I n t . J . E l e c t r y . , vol. 24, Feb. 1968, pp. 185-196.[7] E. L.Lien,High efficiency klys tronamplifier,presented at1969 IEE E Int . Ele ctro n Devices Meeting, Washington, D. C.,Oct. 30, 1969.

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