ece 662 – microwave electronics klystrons march 31, april 7, 2005
TRANSCRIPT
![Page 1: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/1.jpg)
ECE 662 – Microwave Electronics
Klystrons
March 31, April 7, 2005
![Page 2: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/2.jpg)
![Page 3: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/3.jpg)
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 %)
![Page 4: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/4.jpg)
![Page 5: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/5.jpg)
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)
VV t),ω( sinVV
: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
![Page 6: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/6.jpg)
![Page 7: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/7.jpg)
Input Cavity
+
![Page 8: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/8.jpg)
Input Cavity
![Page 9: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/9.jpg)
![Page 10: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/10.jpg)
Bunching of Electrons
![Page 11: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/11.jpg)
Time/Distance Applegate Diagram
![Page 12: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/12.jpg)
![Page 13: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/13.jpg)
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
![Page 14: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/14.jpg)
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
![Page 15: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/15.jpg)
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.
![Page 16: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/16.jpg)
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)}
![Page 17: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/17.jpg)
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
![Page 18: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/18.jpg)
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.)
![Page 19: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/19.jpg)
![Page 20: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/20.jpg)
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
![Page 21: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/21.jpg)
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
![Page 22: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/22.jpg)
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
![Page 23: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/23.jpg)
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:
![Page 24: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/24.jpg)
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
![Page 25: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/25.jpg)
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
![Page 26: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/26.jpg)
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
![Page 27: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/27.jpg)
![Page 28: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/28.jpg)
![Page 29: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/29.jpg)
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
![Page 30: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/30.jpg)
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.
![Page 31: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/31.jpg)
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.
![Page 32: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/32.jpg)
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
![Page 33: ECE 662 – Microwave Electronics Klystrons March 31, April 7, 2005](https://reader035.vdocuments.mx/reader035/viewer/2022081506/56649f445503460f94c65a9d/html5/thumbnails/33.jpg)
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