1. ECE 662 – Microwave Electronics
Klystrons
March 31, April 7, 2005

3. General Characteristics
Efficiency about 40%
Power output
Cw:  1MW
Pulsed:  10 GHz
Power Gain 15 to 70 dB
Frequency  100 GHz
Characteristics
High pulse and CW power
Medium bandwidth (2-15 %)

5. General Characteristics

7. Input Cavity +

8. Input Cavity

10. Bunching of Electrons

11. Time/Distance Applegate Diagram

13. Beam coupling coefficient

14. Beam coupling coefficient

15. Electron Bunching Process
The net result of beam transit through the cavity is a sinusoidal
Beam velocity modulation at cavity frequency 
Faster electrons “catch” up with slower electrons. At a certain
Distance L the electrons have “bunched” together. Here (at L)
A second cavity is placed in order to induce microwave fields
In the “output” of “catcher” cavity.

16. 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 are
L = vmin (td -ta) = vmin (td -tb+/(2)) (1)
L = vmax (td -tc) = vmax (td -tb-/(2)) (2), where
vmin= v0 {1-(V1)/(2V0)}; V0 =½(m/e)(v02), V1 =Ed, and
vmax= v0 {1+(V1)/(2V0)}; equations (1) and (2) become
L = 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)}

17. 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. therefore
td -tb = [(2V0)/(v0 V1)][v0 /(2)][1-(V1)/(2V0)] ~ V0/V1,
L ~ v0V0/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 radians
T = t2 - t1 = L/ v0 - X sin [t1 - (d)/(2v0)], where
X = (L/ v0) [(V1)/(2V0)] = Bunching parameter of a Klystron

18. Electron Bunching Process
At 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.)

20. 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:

21. Electron Bunching Process

22. Cavity Spacing

23. Catcher Cavity
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:

24. Catcher Cavity- Output Power
Rsho = wall resistance of catcher cavity
RB = beam loading resistance
RL = external load resistance
RSH = effective Shunt resistance
I2 = If = fundamental component of the beam current at the catcher cavity
V2 = fundamental component of the catcher gap voltage
Output power delivered to the catcher and the load is given by

25. Efficiency and Mutual Conductance of Klystron

26. Output of Klystron

29. Reflex Klystron Oscillator
Can make an amplifier
oscillate by providing
regenerative feedback
to input terminals.
Simpler is reflex - single
cavity oscillator, but
lower power, mW,
1-25 GHz, % eff.
Widely used in radars.
Key here is to have electrons be repelled such that they return to the
gap in the form of a bunch. Time electron of velocity vi spends in the
gap-repeller space dr is given by

30. Reflex Klystron Oscillator
The t1 electrons see
accelerating phase and penetrate farthest into gap-repeller space.
The t3 electrons see
decelerating phase
and spend least time
in gap-repeller space.
Note they all return
when Rf is maximum
in accelerating phase
to give energy back to gap fields.

31. Reflex Klystron Oscillator
Theoretical Output Characteristics
of a typical X-band reflex Klystron
for a fixed accelerator voltage, V0.
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
Frequency, f, changes slightly with repeller voltage - more tuning by
mechanically adjusting the cavity. In general: High Q, Low BW.

32. Reflex Klystron Oscillator
Following the same analysis of the 2-cavity klystron amplifier, the
bunching parameter for the reflex is

33. Reflex Klystron Oscillator
Note the peak is at
X=2.408, X J1(X)=1.25