## Power Gain of Two Cavity Klystron Amplifier Solution

STEP 0: Pre-Calculation Summary
Formula Used
Power Gain of Two Cavity Klystron Amplifier = (1/4)*(((Cathode Buncher Current*Angular Frequency)/(Cathode Buncher Voltage*Reduced Plasma Frequency))^2)*(Beam Coupling Coeffiecient^4)*Total Shunt Resistance of Input Cavity*Total Shunt Resistance of Output Cavity
Pg = (1/4)*(((Io*ωf)/(Vo*ωq))^2)*(βo^4)*Rsh*Rshl
This formula uses 8 Variables
Variables Used
Power Gain of Two Cavity Klystron Amplifier - (Measured in Watt) - Power Gain of Two Cavity Klystron Amplifier refers to the increase in power level achieved by the amplifier when compared to the input power level.
Cathode Buncher Current - (Measured in Ampere) - Cathode Buncher Current refers to the current that flows through the cathode buncher circuit of a klystron or other microwave vacuum tube.
Angular Frequency - (Measured in Hertz) - Angular Frequency of a steadily recurring phenomenon expressed in radians per second.
Cathode Buncher Voltage - (Measured in Volt) - Cathode Buncher Voltage is the voltage applied to the cathode of a klystron tube to produce a bunched electron beam that interacts with the resonant cavity of the klystron to produce microwave power.
Reduced Plasma Frequency - (Measured in Radian per Second) - Reduced Plasma Frequency is defined as the reduction in plasma frequency in the ionic level due to several reasons.
Beam Coupling Coeffiecient - (Measured in Radian per Meter) - Beam Coupling Coeffiecient refers to the parameter that quantifies the degree of interaction between the electron beam and the electromagnetic fields within the tube.
Total Shunt Resistance of Input Cavity - (Measured in Ohm) - Total Shunt Resistance of Input Cavity in a microwave tube refers to the combined electrical resistance presented by all components connected in parallel to the input circuit of the cavity.
Total Shunt Resistance of Output Cavity - (Measured in Ohm) - Total Shunt Resistance of Output Cavity in a microwave tube represents the cumulative electrical resistance across all components connected in parallel to the output circuit of the cavity.
STEP 1: Convert Input(s) to Base Unit
Cathode Buncher Current: 1.56 Ampere --> 1.56 Ampere No Conversion Required
Angular Frequency: 10.28 Hertz --> 10.28 Hertz No Conversion Required
Cathode Buncher Voltage: 85 Volt --> 85 Volt No Conversion Required
Reduced Plasma Frequency: 1200000 Radian per Second --> 1200000 Radian per Second No Conversion Required
Beam Coupling Coeffiecient: 7.7 Radian per Meter --> 7.7 Radian per Meter No Conversion Required
Total Shunt Resistance of Input Cavity: 3.2 Ohm --> 3.2 Ohm No Conversion Required
Total Shunt Resistance of Output Cavity: 2.3 Ohm --> 2.3 Ohm No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Pg = (1/4)*(((Iof)/(Voq))^2)*(βo^4)*Rsh*Rshl --> (1/4)*(((1.56*10.28)/(85*1200000))^2)*(7.7^4)*3.2*2.3
Evaluating ... ...
Pg = 1.59887976488216E-10
STEP 3: Convert Result to Output's Unit
1.59887976488216E-10 Watt --> No Conversion Required
1.59887976488216E-10 1.6E-10 Watt <-- Power Gain of Two Cavity Klystron Amplifier
(Calculation completed in 00.004 seconds)
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## < 23 Beam Tube Calculators

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Microwave Voltage in the Buncher Gap = (Amplitude of Signal/(Angular Frequency of Microwave Voltage*Average Transit Time))*(cos(Angular Frequency of Microwave Voltage*Entering Time)-cos(Resonant Angular Frequency+(Angular Frequency of Microwave Voltage*Buncher Gap Distance)/Velocity of Electron))
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RF Output Power = RF Input Power*exp(-2*RF Attenuation Constant*RF Circuit Length)+int((RF Power Generated/RF Circuit Length)*exp(-2*RF Attenuation Constant*(RF Circuit Length-x)),x,0,RF Circuit Length)
Repeller Voltage
Repeller Voltage = sqrt((8*Angular Frequency^2*Drift Space Length^2*Small Beam Voltage)/((2*pi*Number of Oscillation)-(pi/2))^2*([Mass-e]/[Charge-e]))-Small Beam Voltage
Power Gain of Two Cavity Klystron Amplifier
Power Gain of Two Cavity Klystron Amplifier = (1/4)*(((Cathode Buncher Current*Angular Frequency)/(Cathode Buncher Voltage*Reduced Plasma Frequency))^2)*(Beam Coupling Coeffiecient^4)*Total Shunt Resistance of Input Cavity*Total Shunt Resistance of Output Cavity
Characteristic Impedance of Coaxial Line
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Plasma Frequency
Plasma Frequency = sqrt(([Charge-e]*DC Electron Charge Density)/([Mass-e]*[Permitivity-vacuum]))
Total Energy Stored in Resonator
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Total Electron Beam Current Density = -DC Beam Current Density+Instantaneous RF Beam Current Perturbation
Total Electron Velocity
Total Electron Velocity = DC Electron Velocity+Instantaneous Electron Velocity Perturbation
Total Charge Density
Total Charge Density = -DC Electron Charge Density+Instantaneous RF Charge Density
Reduced Plasma Frequency
Reduced Plasma Frequency = Plasma Frequency*Space Charge Reduction Factor
Power Obtained from DC Power Supply
DC Power Supply = Power Generated in Anode Circuit/Electronic Efficiency
Power Generated in Anode Circuit
Power Generated in Anode Circuit = DC Power Supply*Electronic Efficiency
Maximum Voltage Gain at Resonance
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Rectangular Microwave Pulse Peak Power
Pulse Peak Power = Average Power/Duty Cycle
AC Power Supplied by Beam Voltage
AC Power Supply = (Voltage*Current)/2
DC Power Supplied by Beam Voltage
DC Power Supply = Voltage*Current

## Power Gain of Two Cavity Klystron Amplifier Formula

Power Gain of Two Cavity Klystron Amplifier = (1/4)*(((Cathode Buncher Current*Angular Frequency)/(Cathode Buncher Voltage*Reduced Plasma Frequency))^2)*(Beam Coupling Coeffiecient^4)*Total Shunt Resistance of Input Cavity*Total Shunt Resistance of Output Cavity
Pg = (1/4)*(((Io*ωf)/(Vo*ωq))^2)*(βo^4)*Rsh*Rshl

## What is Two Cavity Klystron Amplifier?

A Two Cavity Klystron Amplifier is an electron tube utilized for microwave amplification, functioning through the principle of velocity modulation. Its operation involves several key components. Firstly, an electron gun emits a stream of electrons. These electrons then traverse through a resonant cavity where they encounter an electric field inducing velocity modulation. This modulation causes the electrons to form groups with alternating high and low velocities. Subsequently, the bunched electrons pass through a series of resonant cavities, interacting with the microwave signal to be amplified.

The power gain of a two-cavity klystron amplifier is a critical parameter in determining its performance in applications such as RF amplification, signal processing, and radar systems. It reflects the effectiveness of the amplifier in boosting the power of input signals and is often a key consideration in the design and evaluation of microwave systems.

## How to Calculate Power Gain of Two Cavity Klystron Amplifier?

Power Gain of Two Cavity Klystron Amplifier calculator uses Power Gain of Two Cavity Klystron Amplifier = (1/4)*(((Cathode Buncher Current*Angular Frequency)/(Cathode Buncher Voltage*Reduced Plasma Frequency))^2)*(Beam Coupling Coeffiecient^4)*Total Shunt Resistance of Input Cavity*Total Shunt Resistance of Output Cavity to calculate the Power Gain of Two Cavity Klystron Amplifier, The Power Gain of Two Cavity Klystron Amplifier formula refers to the increase in power level achieved by the amplifier relative to the input power level. Power Gain of Two Cavity Klystron Amplifier is denoted by Pg symbol.

How to calculate Power Gain of Two Cavity Klystron Amplifier using this online calculator? To use this online calculator for Power Gain of Two Cavity Klystron Amplifier, enter Cathode Buncher Current (Io), Angular Frequency f), Cathode Buncher Voltage (Vo), Reduced Plasma Frequency q), Beam Coupling Coeffiecient o), Total Shunt Resistance of Input Cavity (Rsh) & Total Shunt Resistance of Output Cavity (Rshl) and hit the calculate button. Here is how the Power Gain of Two Cavity Klystron Amplifier calculation can be explained with given input values -> 1.6E-10 = (1/4)*(((1.56*10.28)/(85*1200000))^2)*(7.7^4)*3.2*2.3.

### FAQ

What is Power Gain of Two Cavity Klystron Amplifier?
The Power Gain of Two Cavity Klystron Amplifier formula refers to the increase in power level achieved by the amplifier relative to the input power level and is represented as Pg = (1/4)*(((Iof)/(Voq))^2)*(βo^4)*Rsh*Rshl or Power Gain of Two Cavity Klystron Amplifier = (1/4)*(((Cathode Buncher Current*Angular Frequency)/(Cathode Buncher Voltage*Reduced Plasma Frequency))^2)*(Beam Coupling Coeffiecient^4)*Total Shunt Resistance of Input Cavity*Total Shunt Resistance of Output Cavity. Cathode Buncher Current refers to the current that flows through the cathode buncher circuit of a klystron or other microwave vacuum tube, Angular Frequency of a steadily recurring phenomenon expressed in radians per second, Cathode Buncher Voltage is the voltage applied to the cathode of a klystron tube to produce a bunched electron beam that interacts with the resonant cavity of the klystron to produce microwave power, Reduced Plasma Frequency is defined as the reduction in plasma frequency in the ionic level due to several reasons, Beam Coupling Coeffiecient refers to the parameter that quantifies the degree of interaction between the electron beam and the electromagnetic fields within the tube, Total Shunt Resistance of Input Cavity in a microwave tube refers to the combined electrical resistance presented by all components connected in parallel to the input circuit of the cavity & Total Shunt Resistance of Output Cavity in a microwave tube represents the cumulative electrical resistance across all components connected in parallel to the output circuit of the cavity.
How to calculate Power Gain of Two Cavity Klystron Amplifier?
The Power Gain of Two Cavity Klystron Amplifier formula refers to the increase in power level achieved by the amplifier relative to the input power level is calculated using Power Gain of Two Cavity Klystron Amplifier = (1/4)*(((Cathode Buncher Current*Angular Frequency)/(Cathode Buncher Voltage*Reduced Plasma Frequency))^2)*(Beam Coupling Coeffiecient^4)*Total Shunt Resistance of Input Cavity*Total Shunt Resistance of Output Cavity. To calculate Power Gain of Two Cavity Klystron Amplifier, you need Cathode Buncher Current (Io), Angular Frequency f), Cathode Buncher Voltage (Vo), Reduced Plasma Frequency q), Beam Coupling Coeffiecient o), Total Shunt Resistance of Input Cavity (Rsh) & Total Shunt Resistance of Output Cavity (Rshl). With our tool, you need to enter the respective value for Cathode Buncher Current, Angular Frequency, Cathode Buncher Voltage, Reduced Plasma Frequency, Beam Coupling Coeffiecient, Total Shunt Resistance of Input Cavity & Total Shunt Resistance of Output Cavity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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