Klystron - MICROWAVE ENGINEERING ALL NOTES ATTACHED WITH THE TOPIOCS MENTIONED ABOVE. PDF

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Summary

MICROWAVE ENGINEERING ALL NOTES ATTACHED WITH THE TOPIOCS MENTIONED ABOVE....

Description

Klystron Oscillator(Reflex Klystron): Schematic Diagram & Velocity Modulation or Applegate diagram:

Principle of Operation:  If a fraction of the output power is fed back to the input cavity and if the loop gain has a magnitude of unity with a phase shift of multiple of 2, the Klystron will oscillate. 

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A 2-cavity klystron oscillator is usually not constructed because when the oscillation frequency is varied the resonant frequency of each cavity and the feedback phase shift must be readjusted for a positive feedback. The reflex Klystron is a single cavity Klystron that overcomes the disadvantages of the 2-cavity Klystron oscillator.

The electron beam injected from the cathode is first velocity modulated V(t1) by the cavity gap voltage. Here the cavity gap voltage is the microwave noise field(r.f. field) generated due to d.c. voltage in the cavity circuit. Electrons emerging from the gap are either accelerated or decelerated or no change in velocity depending upon the part of the rf cycle during which it crosses the gap. The faster electrons travel further in the repeller space as compared to slower one and take longer time to return. These velocity modulated electrons will be turned back towards the cavity by the repeller voltage(VR = -dc voltage) and then pass through the cavity gap in bunches that occur once per cycle. The repeller voltage(VR) and repeller space(L) are so adjusted in such a way that the electrons spread over a half cycle of oscillations leaving the modulating gap (d) with different velocities return back to the gap in the form of bunch at a time which corresponds to the positive peak of the rf cycle of the cavity resonator. On this return journey the bunched electrons pass through the gap during the retarding phase of rf field, lose their kinetic energy and give up the rf field in the cavity. When the energy delivered by the bunched electrons to the cavity is greater than the energy loss in the cavity, cavity could sustain the oscillations at the resonant frequency of the cavity.

Oscillator output energy is taken from the cavity through coupling loop.

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The electrons are finally collected by the walls of the cavity or other grounded metal parts of the tube.

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Quantitative Analysis: Velocity Modulation, bunching and arrival times:-

The electron entering the cavity gap(d) from the cathode at z=0 and time t=t0 is (assumed to have uniform velocity) given by �0 = 0.953 � 106 �0 m/s -------------------------1 The same electron leaves the cavity gap at z = d at time t = t1 with velocity �(�1 ) is given by

� �1 = �0 1 +

�� �1 2�0

sin ��1 −

�� 2

------------------2

The same electron is forced back to the cavity at z = d and time t = t2 by the retarding electric 󰇍 is given by � = �� +�0 +�1 sin �� -----------------3 field � �

assumed to be constant in the z-direction. The force equation for one electron in the repeller region is given by �

�2 � ��2

=− �� = − �

�� +�0 ----------------------------(4) �

Where � =− ∇� is used in the z direction and �1 sin �� ≪ (�� + �0 ) Integrating equation 4 twice we get �=

−�(�� +�0 ) 2��

(� − �1 )2 + � �1 � − �1 + �----------------------------5

On the assumption that the electron leaves the cavity gap at z = d and time t1 with a velocity of � �1 and returns to the gap at z = d and time t = t2, then at t=t2, z=d, equation (5) becomes

0=

−�(�� +�0 ) (�2 2��

=> � �1 = =>

− �1 )2 + � �1 �2 − �1 ---------------------(-6)

−� �� +�0 2��

(�2 − �1 )

�2 − �1 = �' ��� =� �

2��

� +�0

=

2�� � �� +�0

�0 1 +

� �1 �

�� �1 2�0

sin ��1 − 2� �

� �

1 ��1 − � -----------------7 �2 − �1 = �' = �' 0 1 +2� � sin 2 0

Where

2���0 � �� +�0

= �' 0 , is the round-trip dc transmit time of the center-of- the bunch electron.

Multiplying equation (7) through radian frequency ‘ω’ we get � �2 − �1 = ��' 0 1 +

�

�� �1

2�0

=> � �2 − �1 = �' 0 +

sin ��1 − 2�

�� �1 '

2�0

� 0 sin ��1 −

�� 2

------------------------8

Where �' 0 = ��' 0 i.e., the round trip dc transit angle of the center-of-the bunch electron & �� �1 ' �0 2�0

= �' , is the bunching parameter of the reflex klystron oscillator.

Transit time and Mode Number: “In order for the electron beam to generate a maximum amount of energy to the oscillations, the retarding electron beam must cross the cavity gap when the gap field is maximum retarding”. In this way, a maximum amount of kinetic energy can be transferred from the returning electrons to the cavity walls. It is seen from the applegate diagram that for a maximum energy transfer, the round trip transit angle, referring to the center of the bunch, must be given by: 1

� �2 − �1 = ��' 0 = 2 f (n - ) T 4

1

�

= (n - 4)2 = N . 2 = 2n - , 2

where, T =

1 �

, time period of r.f. voltage across the gap.

& n = any positive integer for cycle number �

& N = (n - ), is the number of modes, or called mode number. � Where, n = 1, is known as

3

mode,

4

N = 2 , is known as 1 N = 3 , is known as 2

3 4 3 4

mode, mode and so on. 1

Note: The optimum transit time for the bunch to arrive at the cavity is: (n - ) cycles after the 4

beam initially left the cavity....