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Power Gain of Two Cavity Klystron Amplifier Formula

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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. Check FAQs

P g = (\frac{1}{4}) \cdot ({(\frac{I o \cdot ω f}{V o \cdot ω q})}^{2}) \cdot ({β o}^{4}) \cdot R sh \cdot R shl

P_g - Power Gain of Two Cavity Klystron Amplifier?I_o - Cathode Buncher Current?ω_f - Angular Frequency?V_o - Cathode Buncher Voltage?ω_q - Reduced Plasma Frequency?β_o - Beam Coupling Coeffiecient?R_sh - Total Shunt Resistance of Input Cavity?R_shl - Total Shunt Resistance of Output Cavity?

Power Gain of Two Cavity Klystron Amplifier Example

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Here is how the Power Gain of Two Cavity Klystron Amplifier equation looks like with Values.

Here is how the Power Gain of Two Cavity Klystron Amplifier equation looks like with Units.

Here is how the Power Gain of Two Cavity Klystron Amplifier equation looks like.

1.6E-10 = (\frac{1}{4}) \cdot ({(\frac{1.56 \cdot 10.28}{85 \cdot 1.2E+6})}^{2}) \cdot ({7.7}^{4}) \cdot 3.2 \cdot 2.3

1.6E-10W = (\frac{1}{4}) \cdot ({(\frac{1.56A \cdot 10.28Hz}{85V \cdot 1.2E+6rad/s})}^{2}) \cdot ({7.7rad/m}^{4}) \cdot 3.2Ω \cdot 2.3Ω

1.6E-10 = (\frac{1}{4}) \cdot ({(\frac{1.56 \cdot 10.28}{85 \cdot 1.2E+6})}^{2}) \cdot ({7.7}^{4}) \cdot 3.2 \cdot 2.3

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Power Gain of Two Cavity Klystron Amplifier Solution

Follow our step by step solution on how to calculate Power Gain of Two Cavity Klystron Amplifier?

FIRST Step Consider the formula

P g = (\frac{1}{4}) \cdot ({(\frac{I o \cdot ω f}{V o \cdot ω q})}^{2}) \cdot ({β o}^{4}) \cdot R sh \cdot R shl

Next Step Substitute values of Variables

∴

P g = (\frac{1}{4}) \cdot ({(\frac{1.56A \cdot 10.28Hz}{85V \cdot 1.2E+6rad/s})}^{2}) \cdot ({7.7rad/m}^{4}) \cdot 3.2Ω \cdot 2.3Ω

Next Step Prepare to Evaluate

∴

P g = (\frac{1}{4}) \cdot ({(\frac{1.56 \cdot 10.28}{85 \cdot 1.2E+6})}^{2}) \cdot ({7.7}^{4}) \cdot 3.2 \cdot 2.3

Next Step Evaluate

∴

P g = 1.59887976488216E-10W

LAST Step Rounding Answer

∴

P g = 1.6E-10W

Power Gain of Two Cavity Klystron Amplifier Formula Elements

Variables

Power Gain of Two Cavity Klystron Amplifier

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.

Symbol: P_g

Measurement: PowerUnit: W

Note: Value can be positive or negative.

Formulas to find Power Gain of Two Cavity Klystron Amplifier

Cathode Buncher Current

Cathode Buncher Current refers to the current that flows through the cathode buncher circuit of a klystron or other microwave vacuum tube.

Symbol: I_o

Measurement: Electric CurrentUnit: A

Note: Value should be greater than 0.

Formulas to find Cathode Buncher Current

Angular Frequency

Angular Frequency of a steadily recurring phenomenon expressed in radians per second.

Symbol: ω_f

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

Formulas to find Angular Frequency

Cathode Buncher Voltage

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.

Symbol: V_o

Measurement: Electric PotentialUnit: V

Note: Value should be greater than 0.

Formulas to find Cathode Buncher Voltage

Reduced Plasma Frequency

Reduced Plasma Frequency is defined as the reduction in plasma frequency in the ionic level due to several reasons.

Symbol: ω_q

Measurement: Angular FrequencyUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Reduced Plasma Frequency

Beam Coupling Coeffiecient

Beam Coupling Coeffiecient refers to the parameter that quantifies the degree of interaction between the electron beam and the electromagnetic fields within the tube.

Symbol: β_o

Measurement: Propagation ConstantUnit: rad/m

Note: Value can be positive or negative.

Formulas to find Beam Coupling Coeffiecient

Total Shunt Resistance of Input Cavity

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.

Symbol: R_sh

Measurement: Electric ResistanceUnit: Ω

Note: Value can be positive or negative.

Formulas to find Total Shunt Resistance of Input Cavity

Total Shunt Resistance of Output 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.

Symbol: R_shl

Measurement: Electric ResistanceUnit: Ω

Note: Value can be positive or negative.

Formulas to find Total Shunt Resistance of Output Cavity

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How to Evaluate Power Gain of Two Cavity Klystron Amplifier?

Power Gain of Two Cavity Klystron Amplifier evaluator 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 evaluate 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 evaluate Power Gain of Two Cavity Klystron Amplifier using this online evaluator? To use this online evaluator 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.

FAQs on Power Gain of Two Cavity Klystron Amplifier

What is the formula to find Power Gain of Two Cavity Klystron Amplifier?

The formula of Power Gain of Two Cavity Klystron Amplifier is expressed as 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. Here is an example- 1.6E-10 = (1/4)*(((1.56*10.28)/(85*1200000))^2)*(7.7^4)*3.2*2.3.

How to calculate Power Gain of Two Cavity Klystron Amplifier?

With 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) we can find Power Gain of Two Cavity Klystron Amplifier using the 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.

Can the Power Gain of Two Cavity Klystron Amplifier be negative?

Yes, the Power Gain of Two Cavity Klystron Amplifier, measured in Power can be negative.

Which unit is used to measure Power Gain of Two Cavity Klystron Amplifier?

Power Gain of Two Cavity Klystron Amplifier is usually measured using the Watt[W] for Power. Kilowatt[W], Milliwatt[W], Microwatt[W] are the few other units in which Power Gain of Two Cavity Klystron Amplifier can be measured.

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Power Gain of Two Cavity Klystron Amplifier Formula

Power Gain of Two Cavity Klystron Amplifier Example

Power Gain of Two Cavity Klystron Amplifier Solution

Power Gain of Two Cavity Klystron Amplifier Formula Elements

Other formulas in Beam Tube category

How to Evaluate Power Gain of Two Cavity Klystron Amplifier?

FAQs on Power Gain of Two Cavity Klystron Amplifier

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