Gain-Bandwidth Product Calculator

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Fundamental Parameters

Second Order System

✖Amplifier gain in mid band is a measure of the ability of a two-port circuit to increase the power or amplitude of a signal from the input to the output port.ⓘ Amplifier Gain in Mid Band [A_M]			+10% -10%
✖Amplifier Bandwidth is defined as the difference between the frequency limits of the amplifier.ⓘ Amplifier Bandwidth [BW]			+10% -10%

✖The gain-bandwidth product for an amplifier is the product of the amplifier's bandwidth and the gain at which the bandwidth is measured.ⓘ Gain-Bandwidth Product [G.B]

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Formula

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Gain-Bandwidth Product

Formula

`"G.B" = "modulus"("A"_{"M"})*"BW"`

Example

`"56.16Hz"="modulus"("0.78")*"72b/s"`

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Gain-Bandwidth Product Solution

STEP 0: Pre-Calculation Summary

Formula Used

Gain-Bandwidth Product = modulus(Amplifier Gain in Mid Band)*Amplifier Bandwidth
G.B = modulus(A_M)*BW
This formula uses 1 Functions, 3 Variables

Functions Used

modulus - Modulus of a number is the remainder when that number is divided by another number., modulus

Variables Used

Gain-Bandwidth Product - (Measured in Hertz) - The gain-bandwidth product for an amplifier is the product of the amplifier's bandwidth and the gain at which the bandwidth is measured.
Amplifier Gain in Mid Band - Amplifier gain in mid band is a measure of the ability of a two-port circuit to increase the power or amplitude of a signal from the input to the output port.
Amplifier Bandwidth - (Measured in Bit Per Second) - Amplifier Bandwidth is defined as the difference between the frequency limits of the amplifier.

STEP 1: Convert Input(s) to Base Unit

Amplifier Gain in Mid Band: 0.78 --> No Conversion Required
Amplifier Bandwidth: 72 Bit Per Second --> 72 Bit Per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

G.B = modulus(A_M)*BW --> modulus(0.78)*72

Evaluating ... ...

G.B = 56.16

STEP 3: Convert Result to Output's Unit

56.16 Hertz --> No Conversion Required

FINAL ANSWER

56.16 Hertz <-- Gain-Bandwidth Product

(Calculation completed in 00.020 seconds)

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Credits

Created by Payal Priya

Birsa Institute of Technology (BIT), Sindri

Payal Priya has created this Calculator and 600+ more calculators!

Verified by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

Urvi Rathod has verified this Calculator and 1900+ more calculators!

< 19 Fundamental Parameters Calculators

Angle of Asymptotes

Go Angle of Asymptotes = ((2*(modulus(Number of Poles-Number of Zeroes)-1)+1)*pi)/(modulus(Number of Poles-Number of Zeroes))

Bandwidth Frequency given Damping Ratio

Go Bandwidth Frequency = Natural Frequency of Oscillation*(sqrt(1-(2*Damping Ratio^2))+sqrt(Damping Ratio^4-(4*Damping Ratio^2)+2))

Damping Ratio given Percentage Overshoot

Go Damping Ratio = -ln(Percentage Overshoot/100)/sqrt(pi^2+ln(Percentage Overshoot/100)^2)

Percentage Overshoot

Go Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))

Closed Loop Negative Feedback Gain

Go Gain with Feedback = Open Loop Gain of an OP-AMP/(1+(Feedback Factor*Open Loop Gain of an OP-AMP))

Closed Loop Positive Feedback Gain

Go Gain with Feedback = Open Loop Gain of an OP-AMP/(1-(Feedback Factor*Open Loop Gain of an OP-AMP))

Damping Ratio or Damping Factor

Go Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))

Damped Natural Frequency

Go Damped Natural Frequency = Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2)

Gain-Bandwidth Product

Go Gain-Bandwidth Product = modulus(Amplifier Gain in Mid Band)*Amplifier Bandwidth

Resonant Frequency

Go Resonant Frequency = Natural Frequency of Oscillation*sqrt(1-2*Damping Ratio^2)

Resonant Peak

Go Resonant Peak = 1/(2*Damping Ratio*sqrt(1-Damping Ratio^2))

Steady State Error for Type Zero System

Go Steady State Error = Coefficient Value/(1+Position of Error Constant)

Steady State Error for Type 2 System

Go Steady State Error = Coefficient Value/Acceleration Error Constant

Steady State Error for Type 1 System

Go Steady State Error = Coefficient Value/Velocity Error Constant

Number of Asymptotes

Go Number of Asymptotes = Number of Poles-Number of Zeroes

Transfer Function for Closed and Open Loop System

Go Transfer Function = Output of System/Input of System

Damping Ratio given Critical Damping

Go Damping Ratio = Actual Damping/Critical Damping

Closed Loop Gain

Go Closed-Loop Gain = 1/Feedback Factor

Q-Factor

Go Q Factor = 1/(2*Damping Ratio)

< 25 Control System Design Calculators

Time Response in Overdamped Case

Go Time Response for Second Order System = 1-(e^(-(Overdamping Ratio-(sqrt((Overdamping Ratio^2)-1)))*(Natural Frequency of Oscillation*Time Period for Oscillations))/(2*sqrt((Overdamping Ratio^2)-1)*(Overdamping Ratio-sqrt((Overdamping Ratio^2)-1))))

Time Response of Critically Damped System

Go Time Response for Second Order System = 1-e^(-Natural Frequency of Oscillation*Time Period for Oscillations)-(e^(-Natural Frequency of Oscillation*Time Period for Oscillations)*Natural Frequency of Oscillation*Time Period for Oscillations)

Bandwidth Frequency given Damping Ratio

Go Bandwidth Frequency = Natural Frequency of Oscillation*(sqrt(1-(2*Damping Ratio^2))+sqrt(Damping Ratio^4-(4*Damping Ratio^2)+2))

Rise Time given Damping Ratio

Go Rise Time = (pi-(Phase Shift*pi/180))/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))

Percentage Overshoot

Go Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))

Time Response in Undamped Case

Go Time Response for Second Order System = 1-cos(Natural Frequency of Oscillation*Time Period for Oscillations)

Peak Time given Damping Ratio

Go Peak Time = pi/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))

First Peak Undershoot

Go Peak Undershoot = e^(-(2*Damping Ratio*pi)/(sqrt(1-Damping Ratio^2)))

First Peak Overshoot

Go Peak Overshoot = e^(-(pi*Damping Ratio)/(sqrt(1-Damping Ratio^2)))

Gain-Bandwidth Product

Go Gain-Bandwidth Product = modulus(Amplifier Gain in Mid Band)*Amplifier Bandwidth

Resonant Frequency

Go Resonant Frequency = Natural Frequency of Oscillation*sqrt(1-2*Damping Ratio^2)

Number of Oscillations

Go Number of Oscillations = (Setting Time*Damped Natural Frequency)/(2*pi)

Time of Peak Overshoot in Second Order System

Go Time of Peak Overshoot = ((2*Kth Value-1)*pi)/Damped Natural Frequency

Rise Time given Damped Natural Frequency

Go Rise Time = (pi-Phase Shift)/Damped Natural Frequency

Steady State Error for Type Zero System

Go Steady State Error = Coefficient Value/(1+Position of Error Constant)

Delay Time

Go Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation

Steady State Error for Type 2 System

Go Steady State Error = Coefficient Value/Acceleration Error Constant

Time Period of Oscillations

Go Time Period for Oscillations = (2*pi)/Damped Natural Frequency

Steady State Error for Type 1 System

Go Steady State Error = Coefficient Value/Velocity Error Constant

Setting Time when Tolerance is 2 Percent

Go Setting Time = 4/(Damping Ratio*Damped Natural Frequency)

Setting Time when Tolerance is 5 Percent

Go Setting Time = 3/(Damping Ratio*Damped Natural Frequency)

Number of Asymptotes

Go Number of Asymptotes = Number of Poles-Number of Zeroes

Peak Time

Go Peak Time = pi/Damped Natural Frequency

Q-Factor

Go Q Factor = 1/(2*Damping Ratio)

Rise Time given Delay Time

Go Rise Time = 1.5*Delay Time

< 12 Modelling Parameters Calculators

Angle of Asymptotes

Go Angle of Asymptotes = ((2*(modulus(Number of Poles-Number of Zeroes)-1)+1)*pi)/(modulus(Number of Poles-Number of Zeroes))

Bandwidth Frequency given Damping Ratio

Go Bandwidth Frequency = Natural Frequency of Oscillation*(sqrt(1-(2*Damping Ratio^2))+sqrt(Damping Ratio^4-(4*Damping Ratio^2)+2))

Damping Ratio given Percentage Overshoot

Go Damping Ratio = -ln(Percentage Overshoot/100)/sqrt(pi^2+ln(Percentage Overshoot/100)^2)

Percentage Overshoot

Go Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))

Damping Ratio or Damping Factor

Go Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))

Damped Natural Frequency

Go Damped Natural Frequency = Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2)

Gain-Bandwidth Product

Go Gain-Bandwidth Product = modulus(Amplifier Gain in Mid Band)*Amplifier Bandwidth

Resonant Frequency

Go Resonant Frequency = Natural Frequency of Oscillation*sqrt(1-2*Damping Ratio^2)

Resonant Peak

Go Resonant Peak = 1/(2*Damping Ratio*sqrt(1-Damping Ratio^2))

Number of Asymptotes

Go Number of Asymptotes = Number of Poles-Number of Zeroes

Damping Ratio given Critical Damping

Go Damping Ratio = Actual Damping/Critical Damping

Q-Factor

Go Q Factor = 1/(2*Damping Ratio)

Gain-Bandwidth Product Formula

Gain-Bandwidth Product = modulus(Amplifier Gain in Mid Band)*Amplifier Bandwidth
G.B = modulus(A_M)*BW

Why gain bandwidth product is important?

This quantity is commonly specified for operational amplifiers, and allows circuit designers to determine the maximum gain that can be extracted from the device for a given frequency (or bandwidth) and vice versa.

How to Calculate Gain-Bandwidth Product?

Gain-Bandwidth Product calculator uses Gain-Bandwidth Product = modulus(Amplifier Gain in Mid Band)*Amplifier Bandwidth to calculate the Gain-Bandwidth Product, The Gain-Bandwidth Product formula is defined as the product of the amplifier's bandwidth and the gain at which the bandwidth is measured. Gain-Bandwidth Product is denoted by G.B symbol.

How to calculate Gain-Bandwidth Product using this online calculator? To use this online calculator for Gain-Bandwidth Product, enter Amplifier Gain in Mid Band (A_M) & Amplifier Bandwidth (BW) and hit the calculate button. Here is how the Gain-Bandwidth Product calculation can be explained with given input values -> 56.16 = modulus(0.78)*72.

FAQ

What is Gain-Bandwidth Product?

The Gain-Bandwidth Product formula is defined as the product of the amplifier's bandwidth and the gain at which the bandwidth is measured and is represented as G.B = modulus(A_M)*BW or Gain-Bandwidth Product = modulus(Amplifier Gain in Mid Band)*Amplifier Bandwidth. Amplifier gain in mid band is a measure of the ability of a two-port circuit to increase the power or amplitude of a signal from the input to the output port & Amplifier Bandwidth is defined as the difference between the frequency limits of the amplifier.

How to calculate Gain-Bandwidth Product?

The Gain-Bandwidth Product formula is defined as the product of the amplifier's bandwidth and the gain at which the bandwidth is measured is calculated using Gain-Bandwidth Product = modulus(Amplifier Gain in Mid Band)*Amplifier Bandwidth. To calculate Gain-Bandwidth Product, you need Amplifier Gain in Mid Band (A_M) & Amplifier Bandwidth (BW). With our tool, you need to enter the respective value for Amplifier Gain in Mid Band & Amplifier Bandwidth 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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