Bandwidth of Negative Resistance Parametric Amplifier (NRPA) Calculator

✖The coupling coefficient γ is defined as the ratio of the modulated negative resistance at the pump frequency to the capacitance of the nonlinear element.ⓘ Coupling Coefficient [γ]			+10% -10%
✖Idler frequency in Negative Resistance Parametric Amplifier is the third frequency that is generated as a result of mixing the two input frequencies.ⓘ Idler Frequency [f_i]			+10% -10%
✖Signal frequency is defined as the frequency of a signal that is containing information.ⓘ Signal Frequency [f_s]			+10% -10%
✖Gain of NRPA (Negative Resistance Parametric Amplifier) is proportional to the negative resistance generated by the LC circuit in an Parametric Amplifier.ⓘ Gain of NRPA [G_NRPA]			+10% -10%

✖Bandwidth of NRPA (Negative Resistance Parametric Amplifier) refers to the range of frequencies over which the parametric amplifier can effectively amplify a signal.ⓘ Bandwidth of Negative Resistance Parametric Amplifier (NRPA) [BW_NRPA]

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Formula

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Bandwidth of Negative Resistance Parametric Amplifier (NRPA)

Formula

`"BW"_{"NRPA"} = ("γ"/2)*sqrt("f"_{"i"}/("f"_{"s"}*"G"_{"NRPA"}))`

Example

`"0.02759Hz"=("0.19"/2)*sqrt("125Hz"/("95Hz"*"15.6dB"))`

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Bandwidth of Negative Resistance Parametric Amplifier (NRPA) Solution

STEP 0: Pre-Calculation Summary

Formula Used

Bandwidth of NRPA = (Coupling Coefficient/2)*sqrt(Idler Frequency/(Signal Frequency*Gain of NRPA))
BW_NRPA = (γ/2)*sqrt(f_i/(f_s*G_NRPA))
This formula uses 1 Functions, 5 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Bandwidth of NRPA - (Measured in Hertz) - Bandwidth of NRPA (Negative Resistance Parametric Amplifier) refers to the range of frequencies over which the parametric amplifier can effectively amplify a signal.
Coupling Coefficient - The coupling coefficient γ is defined as the ratio of the modulated negative resistance at the pump frequency to the capacitance of the nonlinear element.
Idler Frequency - (Measured in Hertz) - Idler frequency in Negative Resistance Parametric Amplifier is the third frequency that is generated as a result of mixing the two input frequencies.
Signal Frequency - (Measured in Hertz) - Signal frequency is defined as the frequency of a signal that is containing information.
Gain of NRPA - (Measured in Decibel) - Gain of NRPA (Negative Resistance Parametric Amplifier) is proportional to the negative resistance generated by the LC circuit in an Parametric Amplifier.

STEP 1: Convert Input(s) to Base Unit

Coupling Coefficient: 0.19 --> No Conversion Required
Idler Frequency: 125 Hertz --> 125 Hertz No Conversion Required
Signal Frequency: 95 Hertz --> 95 Hertz No Conversion Required
Gain of NRPA: 15.6 Decibel --> 15.6 Decibel No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

BW_NRPA = (γ/2)*sqrt(f_i/(f_s*G_NRPA)) --> (0.19/2)*sqrt(125/(95*15.6))

Evaluating ... ...

BW_NRPA = 0.027590178482894

STEP 3: Convert Result to Output's Unit

0.027590178482894 Hertz --> No Conversion Required

FINAL ANSWER

0.027590178482894 ≈ 0.02759 Hertz <-- Bandwidth of NRPA

(Calculation completed in 00.004 seconds)

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< 13 Parametric Devices Calculators

Power Gain of Down-Converter

Go Power Gain Down-Converter = (4*Idler Frequency*Output Resistance of Idler Generator*Output Resistance of Signal Generator*Ratio Negative Resistance to Series Resistance)/(Signal Frequency*Total Series Resistance at Signal Frequency*Total Series Resistance at Idler Frequency*(1-Ratio Negative Resistance to Series Resistance)^2)

Output Resistance of Signal Generator

Go Output Resistance of Signal Generator = (Gain of NRPA*Signal Frequency*Total Series Resistance at Signal Frequency*Total Series Resistance at Idler Frequency*(1-Ratio Negative Resistance to Series Resistance)^2)/(4*Signal Frequency*Output Resistance of Idler Generator*Ratio Negative Resistance to Series Resistance)

Noise Figure of Parametric Up-Converter

Go Noise Figure of Up-Converter = 1+((2*Diode Temperature)/(Coupling Coefficient*Q-Factor of Up-Converter*Ambient Temperature)+2/(Ambient Temperature*(Coupling Coefficient*Q-Factor of Up-Converter)^2))

Bandwidth of Negative Resistance Parametric Amplifier (NRPA)

Go Bandwidth of NRPA = (Coupling Coefficient/2)*sqrt(Idler Frequency/(Signal Frequency*Gain of NRPA))

Bandwidth of Parametric Up-Converter

Go Bandwidth of Up-Converter = 2*Coupling Coefficient*sqrt(Output Frequency/Signal Frequency)

Power Gain for Parametric Up-Converter

Go Power Gain for Up-Converter = (Output Frequency/Signal Frequency)*Gain Degradation Factor

Output Frequency in Up-Convertor

Go Output Frequency = (Power Gain for Up-Converter/Gain Degradation Factor)*Signal Frequency

Gain-Degradation Factor

Go Gain Degradation Factor = (Signal Frequency/Output Frequency)*Power Gain for Up-Converter

Pumping Frequency using Demodulator Gain

Go Pumping Frequency = (Signal Frequency/Power Gain of Demodulator)-Signal Frequency

Power Gain of Demodulator

Go Power Gain of Demodulator = Signal Frequency/(Pumping Frequency+Signal Frequency)

Power Gain of Modulator

Go Power Gain of Modulator = (Pumping Frequency+Signal Frequency)/Signal Frequency

Signal frequency

Go Signal Frequency = Pumping Frequency/(Power Gain of Modulator-1)

Idler Frequency using Pumping Frequency

Go Idler Frequency = Pumping Frequency-Signal Frequency

Bandwidth of Negative Resistance Parametric Amplifier (NRPA) Formula

Bandwidth of NRPA = (Coupling Coefficient/2)*sqrt(Idler Frequency/(Signal Frequency*Gain of NRPA))
BW_NRPA = (γ/2)*sqrt(f_i/(f_s*G_NRPA))

What is Negative Resistance Parametric Amplifier (NRPA)?

A Negative Resistance Parametric Amplifier (NRPA) is an electronic amplifier that is based on the principle of negative resistance. Unlike traditional amplifiers, which use positive resistance to amplify a signal, an NRPA uses an active device that generates a negative resistance at a certain frequency. This negative resistance can be used to amplify signals at that frequency.

How to Calculate Bandwidth of Negative Resistance Parametric Amplifier (NRPA)?

Bandwidth of Negative Resistance Parametric Amplifier (NRPA) calculator uses Bandwidth of NRPA = (Coupling Coefficient/2)*sqrt(Idler Frequency/(Signal Frequency*Gain of NRPA)) to calculate the Bandwidth of NRPA, The Bandwidth of Negative Resistance Parametric Amplifier (NRPA) formula is defined as the range of frequencies over which the amplifier can effectively amplify a signal. In an NRPA, the bandwidth is typically determined by the resonance frequency of the LC circuit used to generate the negative resistance. Bandwidth of NRPA is denoted by BW_NRPA symbol.

How to calculate Bandwidth of Negative Resistance Parametric Amplifier (NRPA) using this online calculator? To use this online calculator for Bandwidth of Negative Resistance Parametric Amplifier (NRPA), enter Coupling Coefficient (γ), Idler Frequency (f_i), Signal Frequency (f_s) & Gain of NRPA (G_NRPA) and hit the calculate button. Here is how the Bandwidth of Negative Resistance Parametric Amplifier (NRPA) calculation can be explained with given input values -> 0.02759 = (0.19/2)*sqrt(125/(95*15.6)).

FAQ

What is Bandwidth of Negative Resistance Parametric Amplifier (NRPA)?

The Bandwidth of Negative Resistance Parametric Amplifier (NRPA) formula is defined as the range of frequencies over which the amplifier can effectively amplify a signal. In an NRPA, the bandwidth is typically determined by the resonance frequency of the LC circuit used to generate the negative resistance and is represented as BW_NRPA = (γ/2)*sqrt(f_i/(f_s*G_NRPA)) or Bandwidth of NRPA = (Coupling Coefficient/2)*sqrt(Idler Frequency/(Signal Frequency*Gain of NRPA)). The coupling coefficient γ is defined as the ratio of the modulated negative resistance at the pump frequency to the capacitance of the nonlinear element, Idler frequency in Negative Resistance Parametric Amplifier is the third frequency that is generated as a result of mixing the two input frequencies, Signal frequency is defined as the frequency of a signal that is containing information & Gain of NRPA (Negative Resistance Parametric Amplifier) is proportional to the negative resistance generated by the LC circuit in an Parametric Amplifier.

How to calculate Bandwidth of Negative Resistance Parametric Amplifier (NRPA)?

The Bandwidth of Negative Resistance Parametric Amplifier (NRPA) formula is defined as the range of frequencies over which the amplifier can effectively amplify a signal. In an NRPA, the bandwidth is typically determined by the resonance frequency of the LC circuit used to generate the negative resistance is calculated using Bandwidth of NRPA = (Coupling Coefficient/2)*sqrt(Idler Frequency/(Signal Frequency*Gain of NRPA)). To calculate Bandwidth of Negative Resistance Parametric Amplifier (NRPA), you need Coupling Coefficient (γ), Idler Frequency (f_i), Signal Frequency (f_s) & Gain of NRPA (G_NRPA). With our tool, you need to enter the respective value for Coupling Coefficient, Idler Frequency, Signal Frequency & Gain of NRPA 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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