Closed Loop Gain Calculator

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Fundamental Parameters

Second Order System

✖The Feedback Factor of an op-amp application defines the fraction of the amplifier output signal fed back to the amplifier input.ⓘ Feedback Factor [β]

+10%

-10%

✖Closed-Loop Gain is the gain that results when we apply negative feedback to tame the open-loop gain.ⓘ Closed Loop Gain [A_c]

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Formula

✖

Closed Loop Gain

Formula

`"A"_{"c"} = 1/"β"`

Example

`"0.25"=1/"4"`

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Closed Loop Gain Solution

STEP 0: Pre-Calculation Summary

Formula Used

Closed-Loop Gain = 1/Feedback Factor
A_c = 1/β
This formula uses 2 Variables

Variables Used

Closed-Loop Gain - Closed-Loop Gain is the gain that results when we apply negative feedback to tame the open-loop gain.
Feedback Factor - The Feedback Factor of an op-amp application defines the fraction of the amplifier output signal fed back to the amplifier input.

STEP 1: Convert Input(s) to Base Unit

Feedback Factor: 4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_c = 1/β --> 1/4

Evaluating ... ...

A_c = 0.25

STEP 3: Convert Result to Output's Unit

0.25 --> No Conversion Required

FINAL ANSWER

0.25 <-- Closed-Loop Gain

(Calculation completed in 00.004 seconds)

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Created by Payal Priya

Birsa Institute of Technology (BIT), Sindri

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Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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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 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)

< 4 Feedback Characteristics Calculators

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))

Transfer Function for Closed and Open Loop System

Go Transfer Function = Output of System/Input of System

Closed Loop Gain

Go Closed-Loop Gain = 1/Feedback Factor

Closed Loop Gain Formula

Closed-Loop Gain = 1/Feedback Factor
A_c = 1/β

What is feedback amplifier?

The process of injecting a fraction of the output energy of some device back to the input is known as Feedback. It has been found that feedback is very useful in reducing noise and making the amplifier operation stable.

Depending upon whether the feedback signal aids or opposes the input signal, there are two types of feedbacks used - Positive Feedback and Negative Feedback.
The feedback in which the feedback energy i.e., either voltage or current is in phase with the input signal and thus aids it is called Positive feedback.

The feedback in which the feedback energy i.e., either voltage or current is out of phase with the input and thus opposes it, is called negative feedback.

How to Calculate Closed Loop Gain?

Closed Loop Gain calculator uses Closed-Loop Gain = 1/Feedback Factor to calculate the Closed-Loop Gain, The Closed Loop Gain formula is defined as the gain that results when we apply negative feedback to "tame" the open-loop gain. The closed-loop gain can be calculated if we know the open-loop gain and the amount of feedback (what fraction of the output voltage is negatively fed back to the input). Closed-Loop Gain is denoted by A_c symbol.

How to calculate Closed Loop Gain using this online calculator? To use this online calculator for Closed Loop Gain, enter Feedback Factor (β) and hit the calculate button. Here is how the Closed Loop Gain calculation can be explained with given input values -> 0.25 = 1/4.

FAQ

What is Closed Loop Gain?

The Closed Loop Gain formula is defined as the gain that results when we apply negative feedback to "tame" the open-loop gain. The closed-loop gain can be calculated if we know the open-loop gain and the amount of feedback (what fraction of the output voltage is negatively fed back to the input) and is represented as A_c = 1/β or Closed-Loop Gain = 1/Feedback Factor. The Feedback Factor of an op-amp application defines the fraction of the amplifier output signal fed back to the amplifier input.

How to calculate Closed Loop Gain?

The Closed Loop Gain formula is defined as the gain that results when we apply negative feedback to "tame" the open-loop gain. The closed-loop gain can be calculated if we know the open-loop gain and the amount of feedback (what fraction of the output voltage is negatively fed back to the input) is calculated using Closed-Loop Gain = 1/Feedback Factor. To calculate Closed Loop Gain, you need Feedback Factor (β). With our tool, you need to enter the respective value for Feedback Factor 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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