Number of Resonant Cavities Calculator

✖Number of Oscillation refers to the occurrence of the oscillation.ⓘ Number of Oscillation [M]			+10% -10%
✖Phase Shift in Magnetron occurs due to the interaction between the electrons and the alternating electromagnetic field in the resonant cavity.ⓘ Phase Shift in Magnetron [Φ_n]			+10% -10%

✖Number of resonant cavities is defined as structure that supports standing waves at particular resonant frequencies, and can be used in various electromagnetic devices.ⓘ Number of Resonant Cavities [N]

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Formula

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Number of Resonant Cavities

Formula

`"N" = (2*pi*"M")/"Φ"_{"n"}`

Example

`"16"=(2*pi*"4")/"90°"`

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Number of Resonant Cavities Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Resonant Cavities = (2*pi*Number of Oscillation)/Phase Shift in Magnetron
N = (2*pi*M)/Φ_n
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Number of Resonant Cavities - Number of resonant cavities is defined as structure that supports standing waves at particular resonant frequencies, and can be used in various electromagnetic devices.
Number of Oscillation - Number of Oscillation refers to the occurrence of the oscillation.
Phase Shift in Magnetron - (Measured in Radian) - Phase Shift in Magnetron occurs due to the interaction between the electrons and the alternating electromagnetic field in the resonant cavity.

STEP 1: Convert Input(s) to Base Unit

Number of Oscillation: 4 --> No Conversion Required
Phase Shift in Magnetron: 90 Degree --> 1.5707963267946 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N = (2*pi*M)/Φ_n --> (2*pi*4)/1.5707963267946

Evaluating ... ...

N = 16.000000000003

STEP 3: Convert Result to Output's Unit

16.000000000003 --> No Conversion Required

FINAL ANSWER

16.000000000003 ≈ 16 <-- Number of Resonant Cavities

(Calculation completed in 00.004 seconds)

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Home » Engineering » Electronics » Microwave Theory » Microwave Tubes and Circuits » Klystron Cavity » Number of Resonant Cavities

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Created by Shobhit Dimri

Bipin Tripathi Kumaon Institute of Technology (BTKIT), Dwarahat

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< 14 Klystron Cavity Calculators

Average Microwave Voltage in Buncher Gap

Go Average Microwave Voltage = Input Signal Amplitude*Beam Coupling Coefficient*sin(Angular Frequency*Entering Time+(Average Transient Angle/2))

Maximum Input Voltage in Two Cavity Klystron

Go Maximum Input Voltage in Two Cavity Klystron = (2*Reflex Klystron Voltage*Bunching Parameter)/(Beam Coupling Coefficient*Average Transient Angle)

Average Distance between Cavities

Go Mean Distance Between the Cavities = (2*pi*Number of Oscillation)/(Phase Constant for N-cavities*Number of Resonant Cavities)

Phase Constant of Fundamental Mode Field

Go Phase Constant for N-cavities = (2*pi*Number of Oscillation)/(Mean Distance Between the Cavities*Number of Resonant Cavities)

Magnitude of Microwave Signal at Input Cavity

Go Magnitude of Microwave Signal = (2*Cathode Buncher Voltage*Bunching Parameter)/(Beam Coupling Coefficient*Angular Variation)

Velocity Modulation of Electrons in Klystron Cavity

Go Velocity Modulation = sqrt((2*[Charge-e]*High DC Voltage)/[Mass-e])

Conductance of Resonator

Go Conductance of Cavity = (Capacitance at Vane Tips*Angular Frequency)/Unloaded Q-factor

Beam Coupling Coefficient in Two Cavity Klystron

Go Beam Coupling Coefficient = sin(Average Transient Angle/2)/(Average Transient Angle/2)

Number of Resonant Cavities

Go Number of Resonant Cavities = (2*pi*Number of Oscillation)/Phase Shift in Magnetron

Induced Current in Catcher Cavity

Go Induced Catcher Current = Current Arriving at Catcher Cavity Gap*Beam Coupling Coefficient

Buncher Cavity Gap

Go Buncher Cavity Gap = Average Transit Time*Electron Uniform Velocity

Induced Current in Walls of Catcher Cavity

Go Induced Catcher Current = Beam Coupling Coefficient*Direct Current

Average Transit Angle

Go Average Transient Angle = Angular Frequency*Average Transit Time

Average Transit Time

Go Average Transit Time = Buncher Cavity Gap/Velocity Modulation

Number of Resonant Cavities Formula

Number of Resonant Cavities = (2*pi*Number of Oscillation)/Phase Shift in Magnetron
N = (2*pi*M)/Φ_n

What is Resonant Cavity?

A conducting surface enclosing a space in which an oscillating electromagnetic field can be maintained, the dimensions of the cavity determine the resonant frequency of the oscillation.

How to Calculate Number of Resonant Cavities?

Number of Resonant Cavities calculator uses Number of Resonant Cavities = (2*pi*Number of Oscillation)/Phase Shift in Magnetron to calculate the Number of Resonant Cavities, The Number of Resonant Cavities formula is defined as a structure that supports standing waves at particular resonant frequencies, and can be used in various electromagnetic devices, such as filters, amplifiers, and oscillators. Number of Resonant Cavities is denoted by N symbol.

How to calculate Number of Resonant Cavities using this online calculator? To use this online calculator for Number of Resonant Cavities, enter Number of Oscillation (M) & Phase Shift in Magnetron (Φ_n) and hit the calculate button. Here is how the Number of Resonant Cavities calculation can be explained with given input values -> 16 = (2*pi*4)/1.5707963267946.

FAQ

What is Number of Resonant Cavities?

The Number of Resonant Cavities formula is defined as a structure that supports standing waves at particular resonant frequencies, and can be used in various electromagnetic devices, such as filters, amplifiers, and oscillators and is represented as N = (2*pi*M)/Φ_n or Number of Resonant Cavities = (2*pi*Number of Oscillation)/Phase Shift in Magnetron. Number of Oscillation refers to the occurrence of the oscillation & Phase Shift in Magnetron occurs due to the interaction between the electrons and the alternating electromagnetic field in the resonant cavity.

How to calculate Number of Resonant Cavities?

The Number of Resonant Cavities formula is defined as a structure that supports standing waves at particular resonant frequencies, and can be used in various electromagnetic devices, such as filters, amplifiers, and oscillators is calculated using Number of Resonant Cavities = (2*pi*Number of Oscillation)/Phase Shift in Magnetron. To calculate Number of Resonant Cavities, you need Number of Oscillation (M) & Phase Shift in Magnetron (Φ_n). With our tool, you need to enter the respective value for Number of Oscillation & Phase Shift in Magnetron 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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