## Closed Loop Positive Feedback Gain Solution

STEP 0: Pre-Calculation Summary
Formula Used
Closed-Loop Gain = Open Loop Gain of an OP-AMP/(1- (Feedback Factor*Open Loop Gain of an OP-AMP))
Ac = Ao/(1- (β*Ao))
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.
Open Loop Gain of an OP-AMP - Open Loop Gain of an OP-AMP is gain of an op-amp without feedback. It is denoted as A.
Feedback Factor - The feedback factor of an op-amp application defines the circuit performance.
STEP 1: Convert Input(s) to Base Unit
Open Loop Gain of an OP-AMP: 4000 --> No Conversion Required
Feedback Factor: 4 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Ac = Ao/(1- (β*Ao)) --> 4000/(1- (4*4000))
Evaluating ... ...
Ac = -0.250015625976624
STEP 3: Convert Result to Output's Unit
-0.250015625976624 --> No Conversion Required
-0.250015625976624 <-- Closed-Loop Gain
(Calculation completed in 00.000 seconds)
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Indian Institute of Technology,Roorlee (IITR), Roorkee
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## < 10+ Fundamental Formulas Calculators

Bandwidth Frequency given Damping Ratio

## Bandwidth Frequency given Damping Ratio

Formula
"f"_{"b"} = "f"*((sqrt(1-(2*("ζ"^2))))+sqrt(("ζ"^4)-(4*("ζ"^2))+2))

Example
"54.96966Hz"="23Hz"*((sqrt(1-(2*("0.1"^2))))+sqrt(("0.1"^4)-(4*("0.1"^2))+2))

Calculator
LaTeX
Bandwidth Frequency = Frequency*((sqrt(1-(2*(Damping Ratio^2))))+sqrt((Damping Ratio^4)-(4*(Damping Ratio^2))+2))
Angle of Asymptotes

## Angle of Asymptotes

Formula
"ϕ"_{"k"} = (((2*"K")+1)*pi)/("P"-"Z")

Example
"951.4286°"=(((2*"18")+1)*pi)/("13"-"6")

Calculator
LaTeX
Angle of Asymptotes = (((2*Parameter for Root Locus)+1)*pi)/(Number of Poles-Number of Zeros)
Damping Ratio or Damping Factor

## Damping Ratio or Damping Factor

Formula
"ζ" = "c"/(2*sqrt("M"*"K"_{"spring"}))

Example
"0.188147"="16"/(2*sqrt("35.45kg"*"51N/m"))

Calculator
LaTeX
Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))
Gain-bandwidth Product

## Gain-bandwidth Product

Formula
"G.B" = "modulus"("A"_{"M"})*"BW"

Example
"56.16Hz"="modulus"("0.78")*"72b/s"

Calculator
LaTeX
Gain-Bandwidth Product = modulus(Amplifier Gain in Mid-band)*Amplifier Bandwidth
Damped Natural Frequency

## Damped Natural Frequency

Formula
"ω"_{"d"} = "f"*(sqrt(1-("ζ")^2))

Example
"22.88471Hz"="23Hz"*(sqrt(1-("0.1")^2))

Calculator
LaTeX
Damped natural frequency = Frequency*(sqrt(1-(Damping Ratio)^2))
Resonant Peak

## Resonant Peak

Formula
"M"_{"r"} = 1/((2*"ζ")*sqrt(1-("ζ")^2))

Example
"5.025189"=1/((2*"0.1")*sqrt(1-("0.1")^2))

Calculator
LaTeX
Resonant Peak = 1/((2*Damping Ratio)*sqrt(1-(Damping Ratio)^2))
Resonant Frequency

## Resonant Frequency

Formula
"ω"_{"r"} = "f"*sqrt(1-2*("ζ")^2)

Example
"22.76884Hz"="23Hz"*sqrt(1-2*("0.1")^2)

Calculator
LaTeX
Resonant Frequency = Frequency*sqrt(1-2*(Damping Ratio)^2)
Number of Asymptotes

## Number of Asymptotes

Formula
"N"_{"a"} = "P"-"Z"

Example
"7"="13"-"6"

Calculator
LaTeX
Number of Asymptotes = Number of Poles-Number of Zeros
Transfer Function for Closed and Open Loop System

## Transfer Function for Closed and Open Loop System

Formula
"G"_{"s"} = "C"_{"s"}/"R"_{"s"}

Example
"0.458333"="22"/"48"

Calculator
LaTeX
Transfer Function = Output of System/Input of System
Closed-loop Gain

## Closed-loop Gain

Formula
"A"_{"f"} = 1/"β"

Example
"0.25"=1/"4"

Calculator
LaTeX
Gain-with-feedback = 1/Feedback Factor

## Closed Loop Positive Feedback Gain Formula

Closed-Loop Gain = Open Loop Gain of an OP-AMP/(1- (Feedback Factor*Open Loop Gain of an OP-AMP))
Ac = Ao/(1- (β*Ao))

## 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 Positive Feedback Gain?

Closed Loop Positive Feedback Gain calculator uses Closed-Loop Gain = Open Loop Gain of an OP-AMP/(1- (Feedback Factor*Open Loop Gain of an OP-AMP)) to calculate the Closed-Loop Gain, The Closed Loop Positive Feedback Gain formula is defined as a type of feedback in a control system where the output of the system is fed back and added to the input, resulting in an amplification of the input signal. This can result in unstable behavior, such as oscillation or runaway conditions, if not properly designed or controlled. Closed-Loop Gain is denoted by Ac symbol.

How to calculate Closed Loop Positive Feedback Gain using this online calculator? To use this online calculator for Closed Loop Positive Feedback Gain, enter Open Loop Gain of an OP-AMP (Ao) & Feedback Factor (β) and hit the calculate button. Here is how the Closed Loop Positive Feedback Gain calculation can be explained with given input values -> -0.250016 = 4000/(1- (4*4000)).

### FAQ

What is Closed Loop Positive Feedback Gain?
The Closed Loop Positive Feedback Gain formula is defined as a type of feedback in a control system where the output of the system is fed back and added to the input, resulting in an amplification of the input signal. This can result in unstable behavior, such as oscillation or runaway conditions, if not properly designed or controlled and is represented as Ac = Ao/(1- (β*Ao)) or Closed-Loop Gain = Open Loop Gain of an OP-AMP/(1- (Feedback Factor*Open Loop Gain of an OP-AMP)). Open Loop Gain of an OP-AMP is gain of an op-amp without feedback. It is denoted as A & The feedback factor of an op-amp application defines the circuit performance.
How to calculate Closed Loop Positive Feedback Gain?
The Closed Loop Positive Feedback Gain formula is defined as a type of feedback in a control system where the output of the system is fed back and added to the input, resulting in an amplification of the input signal. This can result in unstable behavior, such as oscillation or runaway conditions, if not properly designed or controlled is calculated using Closed-Loop Gain = Open Loop Gain of an OP-AMP/(1- (Feedback Factor*Open Loop Gain of an OP-AMP)). To calculate Closed Loop Positive Feedback Gain, you need Open Loop Gain of an OP-AMP (Ao) & Feedback Factor (β). With our tool, you need to enter the respective value for Open Loop Gain of an OP-AMP & Feedback Factor and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Closed-Loop Gain?
In this formula, Closed-Loop Gain uses Open Loop Gain of an OP-AMP & Feedback Factor. We can use 1 other way(s) to calculate the same, which is/are as follows -
• Closed-Loop Gain = Open Loop Gain of an OP-AMP/(1+(Feedback Factor*Open Loop Gain of an OP-AMP))
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