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Closed Loop Gain Formula

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Closed-Loop Gain is the gain that results when we apply negative feedback to tame the open-loop gain. Check FAQs

A c = \frac{1}{β}

A_c - Closed-Loop Gain?β - Feedback Factor?

Closed Loop Gain Example

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With units

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Here is how the Closed Loop Gain equation looks like with Values.

Here is how the Closed Loop Gain equation looks like with Units.

Here is how the Closed Loop Gain equation looks like.

0.25 = \frac{1}{4}

0.25 = \frac{1}{4}

0.25 = \frac{1}{4}

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Closed Loop Gain Solution

Follow our step by step solution on how to calculate Closed Loop Gain?

FIRST Step Consider the formula

A c = \frac{1}{β}

Next Step Substitute values of Variables

∴

A c = \frac{1}{4}

Next Step Prepare to Evaluate

∴

A c = \frac{1}{4}

LAST Step Evaluate

∴

A c = 0.25

Closed Loop Gain Formula Elements

Variables

Closed-Loop Gain

Closed-Loop Gain is the gain that results when we apply negative feedback to tame the open-loop gain.

Symbol: A_c

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Closed-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.

Symbol: β

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Feedback Factor

Other formulas in Fundamental Parameters category

Go Transfer Function for Closed and Open Loop System

G s = \frac{C s}{R s}

Go Closed Loop Negative Feedback Gain

A f = \frac{A o}{1 + (β \cdot A o)}

Go Closed Loop Positive Feedback Gain

A f = \frac{A o}{1 - (β \cdot A o)}

How to Evaluate Closed Loop Gain?

Closed Loop Gain evaluator uses Closed-Loop Gain = 1/Feedback Factor to evaluate 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 evaluate Closed Loop Gain using this online evaluator? To use this online evaluator for Closed Loop Gain, enter Feedback Factor (β) and hit the calculate button.

FAQs on Closed Loop Gain

What is the formula to find Closed Loop Gain?

The formula of Closed Loop Gain is expressed as Closed-Loop Gain = 1/Feedback Factor. Here is an example- 0.25 = 1/4.

How to calculate Closed Loop Gain?

With Feedback Factor (β) we can find Closed Loop Gain using the formula - Closed-Loop Gain = 1/Feedback Factor.

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