✖Amplitude of Signal which is entered into the O microwave tube.ⓘ Amplitude of Signal [V₁]			+10% -10%
✖Angular Frequency of Microwave Voltage denote the angular frequency of the microwave voltage applied across the gap.ⓘ Angular Frequency of Microwave Voltage [ω_v]			+10% -10%
✖Average Transit Time is the average time passed in the transient state.ⓘ Average Transit Time [τ]			+10% -10%
✖Entering Time refers to the instant at which an electron enters into the cavity.ⓘ Entering Time [t₀]			+10% -10%
✖Resonant Angular Frequency of the electromagnetic fields within a resonant cavity, such as the buncher gap.ⓘ Resonant Angular Frequency [ω_o]			+10% -10%
✖Buncher Gap Distance refers to the physical separation between the electrodes or structures that form the buncher cavity in a microwave device.ⓘ Buncher Gap Distance [d]			+10% -10%
✖Velocity of Electron is the rate of electron travels in the beam tube.ⓘ Velocity of Electron [v_o]			+10% -10%

✖Microwave Voltage in the Buncher Gap refers to the RF (radio frequency) voltage applied across the buncher gap in a microwave device.ⓘ Microwave Voltage in Buncher Gap [V_s]

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Microwave Voltage in Buncher Gap

Formula

`"V"_{"s"} = ("V"_{"1"}/("ω"_{"v"}*"τ"))*(cos("ω"_{"v"}*"t"_{"0"})-cos("ω"_{"o"}+("ω"_{"v"}*"d")/"v"_{"o"}))`

Example

`"4.2E^7V"=("5.5V"/("5.6rad/s"*"3.8e-8s"))*(cos("5.6rad/s"*"0.005s")-cos("4.3Hz"+("5.6rad/s"*"7m")/"9.3m/s"))`

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Microwave Voltage in Buncher Gap Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
V_s = (V₁/(ω_v*τ))*(cos(ω_v*t₀)-cos(ω_o+(ω_v*d)/v_o))
This formula uses 1 Functions, 8 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Microwave Voltage in the Buncher Gap - (Measured in Volt) - Microwave Voltage in the Buncher Gap refers to the RF (radio frequency) voltage applied across the buncher gap in a microwave device.
Amplitude of Signal - (Measured in Volt) - Amplitude of Signal which is entered into the O microwave tube.
Angular Frequency of Microwave Voltage - (Measured in Radian per Second) - Angular Frequency of Microwave Voltage denote the angular frequency of the microwave voltage applied across the gap.
Average Transit Time - (Measured in Second) - Average Transit Time is the average time passed in the transient state.
Entering Time - (Measured in Second) - Entering Time refers to the instant at which an electron enters into the cavity.
Resonant Angular Frequency - (Measured in Hertz) - Resonant Angular Frequency of the electromagnetic fields within a resonant cavity, such as the buncher gap.
Buncher Gap Distance - (Measured in Meter) - Buncher Gap Distance refers to the physical separation between the electrodes or structures that form the buncher cavity in a microwave device.
Velocity of Electron - (Measured in Meter per Second) - Velocity of Electron is the rate of electron travels in the beam tube.

STEP 1: Convert Input(s) to Base Unit

Amplitude of Signal: 5.5 Volt --> 5.5 Volt No Conversion Required
Angular Frequency of Microwave Voltage: 5.6 Radian per Second --> 5.6 Radian per Second No Conversion Required
Average Transit Time: 3.8E-08 Second --> 3.8E-08 Second No Conversion Required
Entering Time: 0.005 Second --> 0.005 Second No Conversion Required
Resonant Angular Frequency: 4.3 Hertz --> 4.3 Hertz No Conversion Required
Buncher Gap Distance: 7 Meter --> 7 Meter No Conversion Required
Velocity of Electron: 9.3 Meter per Second --> 9.3 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_s = (V₁/(ω_v*τ))*(cos(ω_v*t₀)-cos(ω_o+(ω_v*d)/v_o)) --> (5.5/(5.6*3.8E-08))*(cos(5.6*0.005)-cos(4.3+(5.6*7)/9.3))

Evaluating ... ...

V_s = 41704150.5848926

STEP 3: Convert Result to Output's Unit

41704150.5848926 Volt --> No Conversion Required

FINAL ANSWER

41704150.5848926 ≈ 4.2E+7 Volt <-- Microwave Voltage in the Buncher Gap

(Calculation completed in 00.004 seconds)

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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

Microwave Voltage in Buncher Gap Formula

What is the Buncher Gap?

The buncher gap is typically found in devices such as klystrons, traveling wave tubes (TWTs), and magnetrons, among others. Its function can vary slightly depending on the type of device, but generally, it plays a crucial role in controlling the electron beam's behavior to achieve desired signal characteristics.

How to Calculate Microwave Voltage in Buncher Gap?

Microwave Voltage in Buncher Gap calculator uses 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)) to calculate the Microwave Voltage in the Buncher Gap, The Microwave Voltage in Buncher Gap formula refers to the RF (radio frequency) voltage applied across the buncher gap in a microwave device such as a klystron or a traveling wave tube (TWT). Microwave Voltage in the Buncher Gap is denoted by V_s symbol.

How to calculate Microwave Voltage in Buncher Gap using this online calculator? To use this online calculator for Microwave Voltage in Buncher Gap, enter Amplitude of Signal (V₁), Angular Frequency of Microwave Voltage (ω_v), Average Transit Time (τ), Entering Time (t₀), Resonant Angular Frequency (ω_o), Buncher Gap Distance (d) & Velocity of Electron (v_o) and hit the calculate button. Here is how the Microwave Voltage in Buncher Gap calculation can be explained with given input values -> 4.2E+7 = (5.5/(5.6*3.8E-08))*(cos(5.6*0.005)-cos(4.3+(5.6*7)/9.3)).

FAQ

What is Microwave Voltage in Buncher Gap?

The Microwave Voltage in Buncher Gap formula refers to the RF (radio frequency) voltage applied across the buncher gap in a microwave device such as a klystron or a traveling wave tube (TWT) and is represented as V_s = (V₁/(ω_v*τ))*(cos(ω_v*t₀)-cos(ω_o+(ω_v*d)/v_o)) or 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)). Amplitude of Signal which is entered into the O microwave tube, Angular Frequency of Microwave Voltage denote the angular frequency of the microwave voltage applied across the gap, Average Transit Time is the average time passed in the transient state, Entering Time refers to the instant at which an electron enters into the cavity, Resonant Angular Frequency of the electromagnetic fields within a resonant cavity, such as the buncher gap, Buncher Gap Distance refers to the physical separation between the electrodes or structures that form the buncher cavity in a microwave device & Velocity of Electron is the rate of electron travels in the beam tube.

How to calculate Microwave Voltage in Buncher Gap?

The Microwave Voltage in Buncher Gap formula refers to the RF (radio frequency) voltage applied across the buncher gap in a microwave device such as a klystron or a traveling wave tube (TWT) is calculated using 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)). To calculate Microwave Voltage in Buncher Gap, you need Amplitude of Signal (V₁), Angular Frequency of Microwave Voltage (ω_v), Average Transit Time (τ), Entering Time (t₀), Resonant Angular Frequency (ω_o), Buncher Gap Distance (d) & Velocity of Electron (v_o). With our tool, you need to enter the respective value for Amplitude of Signal, Angular Frequency of Microwave Voltage, Average Transit Time, Entering Time, Resonant Angular Frequency, Buncher Gap Distance & Velocity of Electron 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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