Closed-Loop Gain as Function of Ideal Value Calculator

✖The feedback factor of an op-amp application defines the circuit performance.ⓘ Feedback Factor [β]			+10% -10%
✖The loop gain is calculated by imagining the feedback loop is broken at some point and calculating the net gain if a signal is applied.ⓘ Loop Gain [Aβ]			+10% -10%

✖Closed-loop Gain is the gain that results when we apply negative feedback to "tame" the open-loop gain.ⓘ Closed-Loop Gain as Function of Ideal Value [A_cl]

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Formula

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Closed-Loop Gain as Function of Ideal Value

Formula

`"A"_{"cl"} = (1/"β")*(1/(1+(1/"Aβ")))`

Example

`"1.590798"=(1/"0.454")*(1/(1+(1/"2.6")))`

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Closed-Loop Gain as Function of Ideal Value Solution

STEP 0: Pre-Calculation Summary

Formula Used

Closed-Loop Gain = (1/Feedback Factor)*(1/(1+(1/Loop Gain)))
A_cl = (1/β)*(1/(1+(1/Aβ)))
This formula uses 3 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 circuit performance.
Loop Gain - The loop gain is calculated by imagining the feedback loop is broken at some point and calculating the net gain if a signal is applied.

STEP 1: Convert Input(s) to Base Unit

Feedback Factor: 0.454 --> No Conversion Required
Loop Gain: 2.6 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_cl = (1/β)*(1/(1+(1/Aβ))) --> (1/0.454)*(1/(1+(1/2.6)))

Evaluating ... ...

A_cl = 1.59079784630445

STEP 3: Convert Result to Output's Unit

1.59079784630445 --> No Conversion Required

FINAL ANSWER

1.59079784630445 ≈ 1.590798 <-- 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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National Institute Of Technology (NIT), Hamirpur

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< 4 Basic Characteristics Calculators

Summing Amplifier

Go Output Voltage of Summing Amplifier = -(Feedback Resistance/Input Resistance of Summing Amplifier)*(sum(x,1,Number of Input Voltages of Summing Amplifier,Input Voltages of Summing Amplifier))

Gain with Feedback of Feedback Amplifier

Go Gain with Feedback = (Open Loop Gain of an Operational Amplifier)/Amount of Feedback

Closed-Loop Gain as Function of Ideal Value

Go Closed-Loop Gain = (1/Feedback Factor)*(1/(1+(1/Loop Gain)))

Amount of Feedback Given Loop Gain

Go Amount of Feedback = 1+Loop Gain

< 15 Negative Feedback Amplifiers Calculators

Feedback Signal

Go Feedback Signal = ((Open Loop Gain of an Operational Amplifier*Feedback Factor)/(1+(Open Loop Gain of an Operational Amplifier*Feedback Factor)))*Source Signal

Error Signal

Go Error Signal = Source Signal/(1+(Open Loop Gain of an Operational Amplifier*Feedback Factor))

Gain at Mid and High Frequencies

Go Gain Factor = Mid Band Gain/(1+(Complex Frequency Variable/Upper 3-dB Frequency))

Signal-to-Interference Ratio at Output

Go Signal to Interference Ratio = (Source Voltage/Voltage Interference)*Gain Factor

Lower 3-DB Frequency in Bandwidth Extension

Go Lower 3-dB Frequency = 3-dB Frequency/(1+(Mid Band Gain*Feedback Factor))

Upper 3-DB Frequency of Feedback Amplifier

Go Upper 3-dB Frequency = 3-dB Frequency*(1+Mid Band Gain*Feedback Factor)

Output Current of Feedback Voltage Amplifier Given Loop Gain

Go Output Current = (1+Loop Gain)*Output Voltage/Output Resistance

Gain with Feedback of Feedback Amplifier

Go Gain with Feedback = (Open Loop Gain of an Operational Amplifier)/Amount of Feedback

Output Signal in Feedback Amplifier

Go Signal Output = Open Loop Gain of an Operational Amplifier*Input Signal Feedback

Output Resistance with Feedback Current Amplifier

Go Output Resistance of Current Amplifier = Amount of Feedback*Output Resistance

Output Resistance with Feedback Voltage Amplifier

Go Output Resistance of Voltage Amplifier = Output Resistance/(1+Loop Gain)

Input Resistance with Feedback Current Amplifier

Go Input Resistance with Feedback = Input Resistance/(1+Loop Gain)

Closed-Loop Gain as Function of Ideal Value

Go Closed-Loop Gain = (1/Feedback Factor)*(1/(1+(1/Loop Gain)))

Feedback Factor of Feedback Amplifier

Go Feedback Factor = Input Signal Feedback/Signal Output

Amount of Feedback Given Loop Gain

Go Amount of Feedback = 1+Loop Gain

Closed-Loop Gain as Function of Ideal Value Formula

Closed-Loop Gain = (1/Feedback Factor)*(1/(1+(1/Loop Gain)))
A_cl = (1/β)*(1/(1+(1/Aβ)))

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 as Function of Ideal Value?

Closed-Loop Gain as Function of Ideal Value calculator uses Closed-Loop Gain = (1/Feedback Factor)*(1/(1+(1/Loop Gain))) to calculate the Closed-Loop Gain, The Closed-loop gain as function of ideal value 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_cl symbol.

How to calculate Closed-Loop Gain as Function of Ideal Value using this online calculator? To use this online calculator for Closed-Loop Gain as Function of Ideal Value, enter Feedback Factor (β) & Loop Gain (Aβ) and hit the calculate button. Here is how the Closed-Loop Gain as Function of Ideal Value calculation can be explained with given input values -> 1.590798 = (1/0.454)*(1/(1+(1/2.6))).

FAQ

What is Closed-Loop Gain as Function of Ideal Value?

The Closed-loop gain as function of ideal value 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_cl = (1/β)*(1/(1+(1/Aβ))) or Closed-Loop Gain = (1/Feedback Factor)*(1/(1+(1/Loop Gain))). The feedback factor of an op-amp application defines the circuit performance & The loop gain is calculated by imagining the feedback loop is broken at some point and calculating the net gain if a signal is applied.

How to calculate Closed-Loop Gain as Function of Ideal Value?

The Closed-loop gain as function of ideal value 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)*(1/(1+(1/Loop Gain))). To calculate Closed-Loop Gain as Function of Ideal Value, you need Feedback Factor (β) & Loop Gain (Aβ). With our tool, you need to enter the respective value for Feedback Factor & Loop Gain 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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