Klystrons - Prof. Ragavendra PDF

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Prof. Ragavendra...

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KLYSTRONS Klystron is a specialized linear beam vacuum tubes. There are two types of Klystrons. They are (i)

Two cavity klystron

(ii)

Reflex klystron

Two cavity klystron are used as low power microwave amplifier and reflex klystrons are used as low power microwave oscillator.

Two cavity Klystron

Fig. Two Cavity Klystron Amplifier Figure shows the two cavity klystron amplifier. It has two cavities namely Buncher cavity and Catcher cavity. High velocity electrons are injected from the cathode. Then these electrons enter into the buncher cavity. The RF input to be

amplified is applied to the buncher cavity. As soon as the electron beam elenter into the buncher cavity, it undergoes velocity modulation. We know that modulation is a process in which the carrier is varied in accordance with the input signal. In the buncher cavity the velocity of the electron beam is varied in accordance with the RF input voltage. When the RF input voltage is maximum, then velocity of the electron beam increases and when the RF input voltage is minimum, then the velocity of the electron beam decreases. This is known as velocity modulation. The density of the electrons changes cyclically with time. When the velocity of the electron beam decreases, the kinetic energy of the electrons is transferred to the field of the second cavity. The electrons then emerge with the reduced velocity and finally terminate at the collector. The buncher cavity gap width “d” is selected in such a way that the time taken by the electron beam to pass through this gap width “d” is less than T/4. Where T is the total period of the input RF signal V1sinωt . Reentrant cavities (Resonant Frequencies) A reentrant cavity is one in which the metallic boundaries extend into the interior of the cavity. One of the commonly used reentrant cavities is the coaxial cavity.

Fig. Coaxial Cavity and its equivalent. Buncher cavity and Catcher cavity are reentrant cavities. The input impedance to each shorted coaxial line is given by 𝑍𝑖𝑛 = 𝑗𝑍0 tan(𝛽𝑙)

Where l= Length of the coaxial cable

1 𝜇 √ ln(𝑏/𝑎) 2𝜋 𝜖 b = Radius of the outer cylinder 𝑧0 =

a = Radius of the inner cylinder Inductance of the cavity is given by 2𝑋𝑖𝑛 𝜔 1 𝜇 𝑏 √ ln ( ) tan(𝛽𝑙) 𝐿= 𝜋𝜔 𝜖 𝑎 𝐿=

The capacitance is given by

At resonance 𝜔𝐿 = 1/𝜔𝐶𝑔

𝜖𝜋𝑎2 𝐶𝑔 = 𝑑

𝜔𝐿 =

1

𝜇 𝑏 ) tan(𝛽𝑙) √ ln ( 𝑎 𝜋 𝜖 1 𝑏 1 𝜇 = √ ln ( 𝑎) tan(𝛽𝑙) 𝜔𝐶𝑔 𝜋 𝜖

𝑏 1 𝜇 𝑑 √ ln ( = ) tan(𝛽𝑙) 𝜔𝜖𝜋𝑎2 𝜋 𝜖 𝑎 𝑑

𝜇 𝜔𝜖√ 𝜋𝑎2 𝜖

=

1 𝑏 ln ( ) tan(𝛽𝑙) 𝑎 𝜋

1 𝑑 𝑏 ) tan(𝛽𝑙) = ln ( 𝑎 𝜔√µ𝜖𝜋𝑎2 𝜋 𝑣=

1

√𝜔𝜖

𝑑𝑣 𝑏 1 ) tan(𝛽𝑙) ln ( = 𝑎 𝜔𝑎 2 𝜋 tan(𝛽𝑙) =

𝑑𝑣 𝑏 ln ( 𝑎) 𝜔𝑎 2

The above equation is a tangent function , it has infinite number of solutions. Therefore, this type of reentrant cavity can support infinite number of resonant frequencies.

VELOCITY MODULATION PROCESS The velocity of electron beam is varied in accordance with the RF input voltage. This is known as velocity modulation.

Figure show the RF input voltage Vs=V1 Sin(ωt). Let the, velocity of the electron = 𝑣0 = √

2𝑒𝑉0 𝑚

, where V0 = High DC Voltage.

V1...