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(AM)*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(AM)*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 00.004 seconds)

Credits

Created by Payal Priya
Birsa Institute of Technology (BIT), Sindri
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Vishwakarma Government Engineering College (VGEC), Ahmedabad
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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 Positive 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 Negative 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(AM)*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 (AM) & 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(AM)*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 (AM) & 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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