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[I31 P. Revesz, M. Wittmer, J. Roth, and J. W. Mayer, Epitaxial regrowthof Ar-implanted amorphous silicon, J. A p p l . P h y s . , vol. 49, p. 5199,1978.[14] J. Ga rrido, E. Calleja, and J. Piqueras, Deep centers introduced byargon implantation bombardment in n-type silicon, Solid-State Elec-t ron . , vol. 24, p. 1121, 1981.

The Input Gap Voltage of a KlystronJ. R M. VAUGHAN

Abstract-Following the discovery that several large-signal kljstronprograms did not agree on the value of the RF voltage at the inprt gapof a klystron, the question was examined afresh. Available textbookswere found to make restrictive assumptions about matching and/ortuning of the input cavity, assumptions which are no longer accep :able.A formula was derived, in terms of cold test parameters and drivepower, that correctly apportions the power between dissipation, reflec-tion, and beam loading, thereby determining the RF gap voltage.

I. INTRODUCTIONIt might be thought that theproblem of calculating the input gapRF voltage of a klystron in terms of the cavity parameters, the 3eam

loading, and the drive power, was solved more than thirty year:, ago.If it was, the solution appears to have been lost, at least in someinfluential quarters: the writer ecently discovered that he had threedifferent computer programs, and an analysis by R. S. Symonf un-published), no two of which gave the same answer to his appal entlystraightforward problem. As shown in Table I, the differences weresubstantial.

Clearly, these programs cannot all be satisfying conservation ofenergy, and the detuned V, value for SLACKLY is obviously notshowing even the same functional dependence n tuning as thr: oth-ers.

Textbooks did not prove helpful; mostly they date from a timewhen klystrons were regarded as single-frequency or very-nwrow-band devices, and make restrictive assumptions: Warneckc. andGuenard [ l ] allow for detuning, but assume that the input cavity ismatched at resonance; Collin [2] assumes that the input cavity istuned but not matched; Hamilton et al. [3] tacitly assume that thecavity is both matched and tuned. For broad-band klystrons nei-ther of these restrictions is acceptable.

An acceptable solution must include the effects of cavity mis-match on or off resonance and of beam loading and detuning, andmust correctly divide the available drive power between the avitylosses, the real power transferred to the beam, and the reflsctedpower. We shall assume that the input line is matched at the gen-erator end, and that the generator itself is unaffected by reflsctedpower. It was found that Symons solution included everything ex-cept the beam detuning, but it was expressed in terms of normalklystron design parameters that are not directly accessible to rnea-surement. It was considered desirable to have a solution expr-ssedas far as possible in terms of Qs, VSWRs, and other parameterswhich can be measured directly with the klystron in the opeiatingand nonoperating states.The beam loading conductance GB and susceptance BB d3 notmeet this condition of direct measurability; they can be calct latedfrom formulas given by Gewartowski and Watson [4] or witf con-siderably more difficulty) from the relativistic formulation by Craig[5]. This calculation is subject toconsiderable uncertainty, be :ause

Manuscript received January 22, 1985; revised June 5 1985.The author is with Litton Electron Devices, San Carlos, CA 940701.

TABLE I

PRCGRPM A U T M N S ) 1 v 3SLACKLY D R u s s e l l l T .W e s s e l - B e r g 90.1 105.2 8 . 4J P N D I S K H Yonezaua, Y O ka za k i S L A C ) 164 8 160.6 5 5 . 5SSKLY* R V a u g h a n 51.9 52.5 23 3--- R.S. Syrnons 119.0 117.5 52.7NOTES: V j , V , , V3 a r e h e rms vol tagesa t h eco l d e s o n a n t r eq u en cy ,a t the hotresona nt reque ncy, and detuned 2 from coldreson-

a n ce e s p ec t i ve l y ,a l lwi th beam on. The ata f o r t h e e s tR/Q=lOO, QE=IOO Q = l O O O Pi n = l W, fo=296 MHz .case were 90 kV, 54 Amp, a=.9525 m b=.762 on d=l.0312 cm,

*This i s no t he Same as h e program of t h e same name byP. T a l l e r i c o a t Los Alamos.

2510 IEEE FRANSACTIONS ON ELECTRON DEVICES, VOL. ED-32, NO. 11, NOVEMBER 198

0018-9383/85/113~0-2510 01.00 985 IEEE

the gap ength g has to be fudged to allow for the fringing of thfields in the ungridded gaps that are now almost universally usedThere is no general agreement on what fudge factor to use. Thproblem is discussed in a companion paper [6].Initially, we shall assume that values for GBand BB are knownbut an unexpected result of this analysis was a method of findinGB and BE, and also RlQ and the effective transit angle , fromeasurements made only on the completed tube. This developmeis given in Section I11 below.

11. CALCULATIONF THE GAP VOLTAGEThe known parameters are assumed to be the cavity cold resonant frequency fo the cold unloaded andexternal Qs, Q, an

QE, the shunt resistance R/Q, the beam admittance GB jBB,anthe available drive power Pi, t frequencyf.Then the fractional detuning is

A = - f fojoand the detuning due to the beam is

We define a beam-loading Q

and a hot unloaded Q

Then the conductance seen from the line is

Note thatQE is not nvolved in 5); this is the point at which at leasome of the programs appear to have gone wrong. The corresponding conductance GE is across the cavity as seen from the interactgap, but it is not across the cavity as seen from the line. Rather, is behind the observer.The terminal susceptanceBT has two components, the cavity anbeam susceptances

B - - + B p2sT - RlQThen the total admittance seen from the line is

The equivalent conductance of the drive line is

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lEEERANSACTIONSNLECTRONEVICES, VOL. ED-32, NO. 11, NOVEMBER 1985 2511

and the assumption that this line is matched at the generator endimplies that this must be its characteristic admittance. In reality, aline of some, standard admittance will be used, but one connectedby some form of transformer, which we assume to be ideal, so thatit leaves (8) still valid.The complex reflection coefficient is then

and the input VSWR is

We now have all the quantities required to define the r m s inputgap voltage satisfying conservation of energy

2l + uvr=-J Pi uQd RJQ>. 1)

For this formulation, the values corresponding to Table I are V , =118, V2= 121, V = 50 V.111 CALCULATIONOF R IQ , GB AND B B FROM HOT TESTMEASUREMENTSLet us now. assume that we do not know the effective values ofR l Q , loT G B , and Bu, but that we can assume a tria l value of 100for R IQ , and first-cut values for the other three based on Gewar-towski and Watsons analysis, with some reasonable fudge factor.We assume that we have an operable tube, and equipment for mak-

ing normal cold test measurements in the drive line with the beameither on or off. With the beam off we can identify fo and can mea-sure Q and QE if they are not alreadyknown. Turning on the beam,but staying at fo we measure he new VSWR uOH, nd find thereflection coefficient magnitude from

IPOHI = uOHOOH +At this frequency, 6 = 0 BT = B E , and the terminal admittance is

The complex reflection coefficient is thenGE GT BB

PO = GE GT BB

1 1 1 B B R / Q )QE Q, QB

Using 2) we have

We can now measure hB by finding the hot resonant frequency f Band

6 B = B fa6Equation 14) is then an equation for Q B n termsof known quan-tities. While it would no doubt be possible to express the solution

explicitly by rationalizing and then taking the modulus, it seemsmuch easier to solve it by iteration, using a first trial value for Q Bfrom 3) and the first estimates mentioned above for GBand R l Q .The right-hand side of 14) seems to be just about proportional toQB, and the left-hand side is known from 12), so that very fewiterations are needed to find Q B to 3 significant figures-the dataare unlikely to justify more.Eliminating R l Q from 2 ) and 3), we have

But from Gewartowski andWatsons equationsB , 2 sin 0 e 1 cos eGB 2 1 cos e 0 sin 0

02= cot .

Hence the effective transit angle isBT = 2 atan - 0 .5 / 6B Q B ) . 18

Since this is calculated from the deviation caused by the beam, itis the naturally fudged value which we sought earlier.

Given the dc beam conductance G o =ZolVo) , we can now cal-culate GBand BB from

and RlQ is given by 3)RlQ 11GBQp 21)

Equation 2) can be used as a check on R IQ , except in the casewhen O T is close to K where 2) becomes indeterminate.REFERENCES

[l] R. Warnecke and P. Guenard, Tubes a Modulation de Vitesse. Paris:Gauthier-Villars, 1951, p. 269.[2]R.E.Collin, Foundations for MicrowaveEngineering. NewYork:McGraw-Hill, 1972, p. 469.[3] D. R. Hamilton, J. K. Knipp, and J. B . H. Kuper, Klystrons and Mi-crowave Triodes Radiation Lab. Series, vo l . 7 New York: McGraw-Hill, 1948, p. 251.[4] J. W. Gewartowskl and H. A.Watson,, Principles of ElectronTubes. Princeton, NJ: D. van Nostrand, 1965, p. 212.

[ 5 ] E . J. Craig, The beam loading admittance of gridless klystron gaps,ZEEE Trans.ElectronDevices, vol. ED-14, no. 5 pp. 273-278; andcorrection in vol. ED-16, no. 1, p. 139, Jan. 1969.[6] J. R. M. Vaughan, A model for the klystron cavity gap, ZEEE Pans.Electron Devices, this issue, pp. 2482-2484.

Correction to Measurement of Diffusion Length,Lifetime, and Surface Recombination Velocity inThin Semiconductor LayersFRANKLIN N. GONZALEZ AND ARNOST NEUGROSCHEL

In the above paper, 1) should read

Manuscript received August 8, 1985.F. N. Gonzalez and A. Neugroschel, ZEEE Trans . Electron Devices,vol. ED-31, no. 4, pp. 413-416, Apr. 1984.