## Q-Factor Solution

STEP 0: Pre-Calculation Summary
Formula Used
Q Factor = 1/(2*Damping Ratio)
Q = 1/(2*ζ)
This formula uses 2 Variables
Variables Used
Q Factor - Q factor is non-dimensional characterization of the amount of damping; high Q indicates slow damping relative to the oscillation.
Damping Ratio - Damping Ratio in control system is defined as the ratio with which any signal gets decayed.
STEP 1: Convert Input(s) to Base Unit
Damping Ratio: 0.1 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Q = 1/(2*ζ) --> 1/(2*0.1)
Evaluating ... ...
Q = 5
STEP 3: Convert Result to Output's Unit
5 --> No Conversion Required
5 <-- Q Factor
(Calculation completed in 00.015 seconds)
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## Credits

Created by Nisarg
Indian Institute of Technology,Roorlee (IITR), Roorkee
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Chandigarh University (CU), Punjab
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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

## Q-Factor Formula

Q Factor = 1/(2*Damping Ratio)
Q = 1/(2*ζ)

## Explain the importance of Q-Factor?

The Q-Factor indicates energy loss relative to the amount of energy stored within the system. Thus the higher the Q the lower the rate of energy loss and hence oscillations will reduce more slowly, i.e. they will have a low level of damping and they will ring for longer.

## How to Calculate Q-Factor?

Q-Factor calculator uses Q Factor = 1/(2*Damping Ratio) to calculate the Q Factor, The Q-Factor formula is defined as a non-dimensional characterization of the amount of damping; high Q indicates slow damping relative to the oscillation. Q Factor is denoted by Q symbol.

How to calculate Q-Factor using this online calculator? To use this online calculator for Q-Factor, enter Damping Ratio (ζ) and hit the calculate button. Here is how the Q-Factor calculation can be explained with given input values -> 5 = 1/(2*0.1).

### FAQ

What is Q-Factor?
The Q-Factor formula is defined as a non-dimensional characterization of the amount of damping; high Q indicates slow damping relative to the oscillation and is represented as Q = 1/(2*ζ) or Q Factor = 1/(2*Damping Ratio). Damping Ratio in control system is defined as the ratio with which any signal gets decayed.
How to calculate Q-Factor?
The Q-Factor formula is defined as a non-dimensional characterization of the amount of damping; high Q indicates slow damping relative to the oscillation is calculated using Q Factor = 1/(2*Damping Ratio). To calculate Q-Factor, you need Damping Ratio (ζ). With our tool, you need to enter the respective value for Damping Ratio 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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