## Closed Loop Gain Solution

STEP 0: Pre-Calculation Summary
Formula Used
Gain with Feedback = 1/Feedback Factor
Af = 1/β
This formula uses 2 Variables
Variables Used
Gain with Feedback - Gain with Feedback is the gain of the feedback amplifier, known as the closed-loop gain or the gain-with-feedback.
Feedback Factor - The feedback factor of an op-amp application defines the circuit performance.
STEP 1: Convert Input(s) to Base Unit
Feedback Factor: 4 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Af = 1/β --> 1/4
Evaluating ... ...
Af = 0.25
STEP 3: Convert Result to Output's Unit
0.25 --> No Conversion Required
0.25 <-- Gain with Feedback
(Calculation completed in 00.000 seconds)
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## Credits

Created by Payal Priya
Birsa Institute of Technology (BIT), Sindri
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## < 19 Fundamental Formulas Calculators

Bandwidth Frequency given Damping Ratio
Bandwidth Frequency = Frequency*(sqrt(1-(2*(Damping Ratio^2)))+sqrt((Damping Ratio^4)-(4*(Damping Ratio^2))+2))
Damping Ratio given Percentage Overshoot
Damping Ratio = -ln(Percentage Overshoot/100)/ sqrt((pi^2)+ln(Percentage Overshoot/100)^2)
Angle of Asymptotes
Angle of Asymptotes = (((2*Parameter for Root Locus)+1)*pi)/(Number of Poles-Number of Zeros)
Percentage Overshoot
Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))
Closed Loop Positive Feedback Gain
Closed-Loop Gain = Open Loop Gain of an OP-AMP/(1- (Feedback Factor*Open Loop Gain of an OP-AMP))
Closed Loop Negative Feedback Gain
Closed-Loop Gain = Open Loop Gain of an OP-AMP/(1+(Feedback Factor*Open Loop Gain of an OP-AMP))
Damping Ratio or Damping Factor
Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))
Gain-Bandwidth Product
Gain-Bandwidth Product = modulus(Amplifier Gain in Mid Band)*Amplifier Bandwidth
Damped Natural Frequency
Damped Natural Frequency = Frequency*(sqrt(1-(Damping Ratio)^2))
Resonant Peak
Resonant Peak = 1/((2*Damping Ratio)*sqrt(1-(Damping Ratio)^2))
Resonant Frequency
Resonant Frequency = Frequency*sqrt(1-2*(Damping Ratio)^2)
Steady State Error for Type Zero System
Steady State Error = Coefficient Value/(1+Position Error Constant)
Steady State Error for Type 2 System
Steady State Error = Coefficient Value/Acceleration Error Constant
Steady State Error for Type 1 System
Steady State Error = Coefficient Value/Velocity Error Constant
Number of Asymptotes
Number of Asymptotes = Number of Poles-Number of Zeros
Transfer Function for Closed and Open Loop System
Transfer Function = Output of System/Input of System
Damping Ratio
Damping Ratio = Actual Damping/Critical Damping
Closed Loop Gain
Gain with Feedback = 1/Feedback Factor
Q-Factor
Q Factor = 1/(2*Damping Ratio)

## Closed Loop Gain Formula

Gain with Feedback = 1/Feedback Factor
Af = 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 Gain with Feedback = 1/Feedback Factor to calculate the Gain with Feedback, 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). Gain with Feedback is denoted by Af 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 Af = 1/β or Gain with Feedback = 1/Feedback Factor. The feedback factor of an op-amp application defines the circuit performance.
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 Gain with Feedback = 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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