Power Gain of Two Cavity Klystron Amplifier Calculator

✖Cathode Buncher Current refers to the current that flows through the cathode buncher circuit of a klystron or other microwave vacuum tube.ⓘ Cathode Buncher Current [I_o]			+10% -10%
✖Angular Frequency of a steadily recurring phenomenon expressed in radians per second.ⓘ Angular Frequency [ω_f]			+10% -10%
✖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.ⓘ Cathode Buncher Voltage [V_o]			+10% -10%
✖Reduced Plasma Frequency is defined as the reduction in plasma frequency in the ionic level due to several reasons.ⓘ Reduced Plasma Frequency [ω_q]			+10% -10%
✖Beam Coupling Coeffiecient refers to the parameter that quantifies the degree of interaction between the electron beam and the electromagnetic fields within the tube.ⓘ Beam Coupling Coeffiecient [β_o]			+10% -10%
✖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 Input Cavity [R_sh]			+10% -10%
✖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.ⓘ Total Shunt Resistance of Output Cavity [R_shl]			+10% -10%

✖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.ⓘ Power Gain of Two Cavity Klystron Amplifier [P_g]

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Formula

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Power Gain of Two Cavity Klystron Amplifier

Formula

`"P"_{"g"} = (1/4)*((("I"_{"o"}*"ω"_{"f"})/("V"_{"o"}*"ω"_{"q"}))^2)*("β"_{"o"}^4)*"R"_{"sh"}*"R"_{"shl"}`

Example

`"1.6E^-10W"=(1/4)*((("1.56A"*"10.28Hz")/("85V"*"1.2e6rad/s"))^2)*(("7.7rad/m")^4)*"3.2Ω"*"2.3Ω"`

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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
P_g = (1/4)*(((I_o*ω_f)/(V_o*ω_q))^2)*(β_o^4)*R_sh*R_shl
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

P_g = (1/4)*(((I_o*ω_f)/(V_o*ω_q))^2)*(β_o^4)*R_sh*R_shl --> (1/4)*(((1.56*10.28)/(85*1200000))^2)*(7.7^4)*3.2*2.3

Evaluating ... ...

P_g = 1.59887976488216E-10

STEP 3: Convert Result to Output's Unit

1.59887976488216E-10 Watt --> No Conversion Required

FINAL ANSWER

1.59887976488216E-10 ≈ 1.6E-10 Watt <-- Power Gain of Two Cavity Klystron Amplifier

(Calculation completed in 00.004 seconds)

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Created by Zaheer Sheik

Seshadri Rao Gudlavalleru Engineering College (SRGEC), Gudlavalleru

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< 23 Beam Tube Calculators

Microwave Voltage in Buncher Gap

Go 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))

RF Output Power

Go 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

Go 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

Go 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

Go Characteristic Impedance of Coaxial Cable = (1/(2*pi))*(sqrt(Relative Permeability/Permittivity of Dielectric))*ln(Outer Conductor Radius/Inner Conductor Radius)

Phase Velocity in Axial Direction

Go Phase Velocity in Axial Direction = Helix Pitch/(sqrt(Relative Permeability*Permittivity of Dielectric*((Helix Pitch^2)+(pi*Diameter of Helix)^2)))

Total Depletion for WDM System

Go Total Depletion for a WDM System = sum(x,2,Number of Channels,Raman Gain Coefficient*Channel Power*Effective Length/Effective Area)

Average Power Loss in Resonator

Go Average Power Loss in Resonator = (Surface Resistance of resonator/2)*(int(((Tangential Magnetic Intensity Peak Value)^2)*x,x,0,Radius of resonator))

Plasma Frequency

Go Plasma Frequency = sqrt(([Charge-e]*DC Electron Charge Density)/([Mass-e]*[Permitivity-vacuum]))

Total Energy Stored in Resonator

Go Total Energy Stored in Resonator = int((Permittivity of Medium/2*Electric Field Intensity^2)*x,x,0,Resonator Volume)

Skin Depth

Go Skin Depth = sqrt(Resistivity/(pi*Relative Permeability*Frequency))

Carrier Frequency in Spectral Line

Go Carrier Frequency = Spectral Line Frequency-Number of Samples*Repetition Frequency

Total Electron Beam Current Density

Go Total Electron Beam Current Density = -DC Beam Current Density+Instantaneous RF Beam Current Perturbation

Total Electron Velocity

Go Total Electron Velocity = DC Electron Velocity+Instantaneous Electron Velocity Perturbation

Total Charge Density

Go Total Charge Density = -DC Electron Charge Density+Instantaneous RF Charge Density

Reduced Plasma Frequency

Go Reduced Plasma Frequency = Plasma Frequency*Space Charge Reduction Factor

Power Obtained from DC Power Supply

Go DC Power Supply = Power Generated in Anode Circuit/Electronic Efficiency

Power Generated in Anode Circuit

Go Power Generated in Anode Circuit = DC Power Supply*Electronic Efficiency

Maximum Voltage Gain at Resonance

Go Maximum Voltage Gain at Resonance = Transconductance/Conductance

Return Loss

Go Return Loss = -20*log10(Reflection Coefficient)

Rectangular Microwave Pulse Peak Power

Go Pulse Peak Power = Average Power/Duty Cycle

AC Power Supplied by Beam Voltage

Go AC Power Supply = (Voltage*Current)/2

DC Power Supplied by Beam Voltage

Go DC Power Supply = Voltage*Current

Power Gain of Two Cavity Klystron Amplifier Formula

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 P_g 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 (I_o), Angular Frequency (ω_f), Cathode Buncher Voltage (V_o), Reduced Plasma Frequency (ω_q), Beam Coupling Coeffiecient (β_o), Total Shunt Resistance of Input Cavity (R_sh) & Total Shunt Resistance of Output Cavity (R_shl) 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 P_g = (1/4)*(((I_o*ω_f)/(V_o*ω_q))^2)*(β_o^4)*R_sh*R_shl 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 (I_o), Angular Frequency (ω_f), Cathode Buncher Voltage (V_o), Reduced Plasma Frequency (ω_q), Beam Coupling Coeffiecient (β_o), Total Shunt Resistance of Input Cavity (R_sh) & Total Shunt Resistance of Output Cavity (R_shl). 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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