ECE 662 – Microwave Electronics

Klystrons

March 31, April 7, 2005

General Characteristics

• Efficiency about 40%

• Power output– Cw: 1MW – Pulsed: 100MW @ 10 GHz– Power Gain 15 to 70 dB– Frequency 100 GHz

• Characteristics– High pulse and CW power– Medium bandwidth (2-15 %)

General Characteristics

cavity). theoffrequency

resonant the(also operated be tois tubeheat which t

(period) 1/f d/v ime transit treduces d small Also

particles. of streams themodulate to

on acceleratifor fields E strong thereforesmall (d)

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:d spacing, with grids

buncher ebetween th voltageGap cavity.buncher

of inalsinput term toapplied is signal Microwave

(m/s) V10593.0 /mV e 2v

V voltage,dchigh by dacceleratefirst Electrons

0

011s

06

00

0

Input Cavity

+

Input Cavity

Bunching of Electrons

Time/Distance Applegate Diagram

Beam coupling coefficient

BSin A sin -2{} brackets that theNote

B)}(A cos)B(A ){cosω(E/)m/e( v v

)d/(2vωB and )d/(2vωtωAlet

}tω cos)d/vωtω){cos(ω(E/)m/e( v v

gap theacross timed/vtt

)tω costω (cos )ω(E/)m/e( v v:Integrate

zt sin eE/dt)vm(dF :electronson Force

0

000

0000

001

010

Beam coupling coefficient

gap.modulator ough theransit threlectron tinstant

average the),v2/d(tupon dependingelectron

oelectron t from sexit varieupon elocity electron v

current beam ofcomponent ac circuit toexterior

in inducedcurrent ac of ratio cavity input theof

tcoefficien coupling Beam d/2v

)d/2vsin( where

)v2/dt(sin )v/d( E )m/e(v

)v2/dt(sin )d/2vin(s )ω(E/)m/e(2 v v

00

0

0

0000

0000

Electron Bunching Process

The net result of beam transit through the cavity is a sinusoidalBeam velocity modulation at cavity frequency

Faster electrons “catch” up with slower electrons. At a certainDistance L the electrons have “bunched” together. Here (at L)A second cavity is placed in order to induce microwave fieldsIn the “output” of “catcher” cavity.

Electron Bunching Process

The distance from the buncher grid to the location of the of dense electron bunching for the electrons at tb is L = v0 (td -tb). Distances for electrons at ta and tc areL = vmin (td -ta) = vmin (td -tb+/(2)) (1)L = vmax (td -tc) = vmax (td -tb-/(2)) (2), wherevmin= v0 {1-(V1)/(2V0)}; V0 =½(m/e)(v0

2), V1 =Ed, andvmax= v0 {1+(V1)/(2V0)}; equations (1) and (2) becomeL = v0(td -tb)+{v0 /(2)-v0[(V1)/(2V0)](td-tb)-v0[(V1)/(2V0)]/(2)}L = v0(td -tb)+{-v0 /(2)+v0[(V1)/(2V0)](td-tb)+v0[(V1)/(2V0)]/(2)}

Electron Bunching Process

For electrons at ta, tb, and tc to meet at the same distance L means that terms in both brackets {} must = 0. thereforetd -tb = [(2V0)/(v0 V1)][v0 /(2)][1-(V1)/(2V0)] ~ V0/V1, L ~ v0V0/V1 (space charge neglected & not max degree of bunching)Transit time in the field free region between grids is T = t2 - t1 = L/ v(t1) = T0 {1 - [(V1)/(2V0)] sin [t1 - (d)/(2v0)]}where T0=L/v0 and used (1 + x)-1 ~ 1- x; In radiansT = t2 - t1 = L/ v0 - X sin [t1 - (d)/(2v0)], whereX = (L/ v0) [(V1)/(2V0)] = Bunching parameter of a Klystron

Electron Bunching ProcessAt the buncher gap a charge dQ0 passing through at a time interval dt0 is given by dQ0 = I0 dt0 = i2 dt2, by conservation of charge, where i2 = current at the catcher gap.

t2 = t0 + + T0 {1 - [(V1)/(2V0)] sin [t0 + (d)/(2v0)]}dt2 / dt0 = 1 - X cos [t0 + (d)/(2v0)]i2 (t0) = I0 / {1 - X cos [t0 + (d)/(2v0)]} = current arriving at catcher.Using t2 = t0 + + T0 ,i2 (t2) = I0 / {1 - X cos [t2 - (L/v0) - [(d)/(2v0)]}

Plot i2 for various X (corresponding to different L providing and (V1)/(2V0 ) are fixed.)

Electron Bunching Process Electron bunching corresponds to current peaks that take place and for X 1; i2 is rich in harmonics of the input frequency which is the resonant frequency of both cavities. (Klystron can be run as a harmonic generator).Beam current at the catcher is a periodic waveform of period 2/ about a dc current. expand i2 in a Fourier Series:

)t(d tnsin i1

b

)t(d tn cos i1

a ,)t(d i2

1a

)tnsinbtncosa(ai

222n

222n220

2n1n

2n02

Electron Bunching Process

kind 1 offunction Besselorder n )nX(J where

]v/Ln)v2/(dn[sin )nX(J I2b

]v/Ln)v2/(dn[ cos )nX(J I2a

Ia ;i Insert

stthn

00n0n

00n0n

002

Cavity Spacing

beam. in the harmonics of presence the todue LL

before. from L, 1.15V

Vv682.3L

or V2

LV

v 1.841X

1.841X when amplitude Maximum

).X(JI2I of magnitude a hascavity catcher

at thecurrent beam theofcomponent lFundamenta

)]T(t[n cos )nX(J I 2 I i

opt

1

00opt

0

1

0max

10f

02n1n

002

Catcher Cavity

(X)J I 2 β I I

of magnitude a hascatcher in the

inducedcurrent ofcomponent lfundamenta and

thenidentical are cavitiescatcher andbuncher If

gap.catcher oft coefficien coupling beam

)](t[ c (X)J I 2 β i i

100f0induced 2

0

0

0210020induced 2

i

Tos

Phase of catcher gap voltage must be maintained in such a way that the bunched electrons as they pass through the grids encounter a retarding phase. Thus kinetic energy is transferred to the field of the catcher grid. The fundamental component of the induced current is given by:

Catcher Cavity- Output Power

LBshoSH

220SH2

20out

R//R //RR where

V I β (1/2) R )I( (1/2) P

Rsho = wall resistance of catcher cavityRB = beam loading resistanceRL = external load resistanceRSH = effective Shunt resistanceI2 = If = fundamental component of the beam current at the catcher cavityV2 = fundamental component of the catcher gap voltageOutput power delivered to the catcher and the load is given by

Efficiency and Mutual Conductance of Klystron

0

00

1

0

20

0

m

00011100

1

.ind2m

02

020

00

220inout

V

IG ,

X

)X(J

v

L

G

G

X)L/v)(/V2(V use ;V/)X(J I 2

V

i

input v

ioutput induced G e,conductanc Mutual

30% to15 efficiency practiceIn

58% efficiency then ,V V and

(0.582) I 2 I and 1 β perfect, is coupling If

.V I

V I β (1/2)/PP Efficiency

max

Output of Klystron

2LSH

L2

SH210SHmv

000

SH0

102

0

1

SH20

1

2v

0

20

0

m

0

20

0

m1

)RR(2

RR)](J I 2[ & R G 2 A

resistance beam /R

R R

)(J

V

R I

V

VA Gain,

316.0G

G

1.841Xat output maximumFor

2

1

G

G ;

2

1)(J X, small

XP

dcIV

X

XVoltage

v

L

v

L

X

Xfor

L

Reflex Klystron OscillatorCan make an amplifieroscillate by providingregenerative feedbackto input terminals.Simpler is reflex - singlecavity oscillator, but lower power, 10-500mW,1-25 GHz, 20-30 % eff.Widely used in radars.

Key here is to have electrons be repelled such that they return to thegap in the form of a bunch. Time electron of velocity vi spends in thegap-repeller space dr is given by

)Ve(V / )d vm (2 r0ri

Reflex Klystron OscillatorThe t1 electrons seeaccelerating phase and penetrate farthest into gap-repeller space.The t3 electrons seedecelerating phase and spend least timein gap-repeller space.Note they all return when Rf is maximum in accelerating phaseto give energy back to gap fields.

Reflex Klystron Oscillator

Average transit time should correspond to (N+3/4) cycles of Rf time where N=0, 1, 2, 3. Optimum positive feedback at cavity resonance, f, occurs when

Theoretical Output Characteristicsof a typical X-band reflex Klystronfor a fixed accelerator voltage, V0.

f

N

VV

dVem

VVe

dmv

r

r

r

rr

)4/3(

)(

)/(22

)(

2

0

0

0

0

Frequency, f, changes slightly with repeller voltage - more tuning bymechanically adjusting the cavity. In general: High Q, Low BW.

Reflex Klystron OscillatorFollowing the same analysis of the 2-cavity klystron amplifier, the bunching parameter for the reflex is

)4/3N(2 used ,)4/3N)(2(

X2

V

V (1), From

)X(JIV2/)I(V load todelivered PowerP

)X(JI2I component, lFundamenta

cavity of on walls collected

and fieldrepeller by returned oelectron t some

for timet where)tcos()X(JI2i

i current, beam and (1) ,V2

VX

r0

1

10121ac

102

2r2102

2r0

1

Reflex Klystron Oscillator

)4/3N(

(X)J X

P

P Efficiency

I VPP ;)4/3N(

(X)J X I VP

1

dc

ac

00dcin100

ac

Note the peak is atX=2.408, X J1(X)=1.25