## Bandwidth Frequency given Damping Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
Bandwidth Frequency = Frequency*(sqrt(1-(2*(Damping Ratio^2)))+sqrt((Damping Ratio^4)-(4*(Damping Ratio^2))+2))
fb = f*(sqrt(1-(2*(ζ^2)))+sqrt((ζ^4)-(4*(ζ^2))+2))
This formula uses 1 Functions, 3 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Bandwidth Frequency - (Measured in Hertz) - Bandwidth frequency is the range of frequencies over which, the magnitude of frequency domain drops to 70.7% from its zero frequency value.
Frequency - (Measured in Hertz) - Frequency is defined as the number of occurrences of a repeating event per unit of time in control system applications.
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
Frequency: 23 Hertz --> 23 Hertz No Conversion Required
Damping Ratio: 0.1 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
fb = f*(sqrt(1-(2*(ζ^2)))+sqrt((ζ^4)-(4*(ζ^2))+2)) --> 23*(sqrt(1-(2*(0.1^2)))+sqrt((0.1^4)-(4*(0.1^2))+2))
Evaluating ... ...
fb = 54.9696597723011
STEP 3: Convert Result to Output's Unit
54.9696597723011 Hertz --> No Conversion Required
54.9696597723011 Hertz <-- Bandwidth Frequency
(Calculation completed in 00.003 seconds)
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## < 17 Second Order Systems Calculators

Time Response in Overdamped Case
Time Response for Second Order System = 1-(e^(-(Overdamping Ratio-(sqrt((Overdamping Ratio^2)-1)))*(Frequency*Time Period for Oscillations))/(2*sqrt((Overdamping Ratio^2)-1)*(Overdamping Ratio-sqrt((Overdamping Ratio^2)-1))))
Bandwidth Frequency given Damping Ratio
Bandwidth Frequency = Frequency*(sqrt(1-(2*(Damping Ratio^2)))+sqrt((Damping Ratio^4)-(4*(Damping Ratio^2))+2))
Time Response of Critically Damped System
Time Response for Second Order System = 1-e^(-(Frequency*Time Period for Oscillations))*(1+(Frequency*Time Period for Oscillations))
Rise Time given Damping Ratio
Rise Time = (pi-Phase Shift)/(Frequency*sqrt(1-Damping Ratio^2))
Maximum Overshoot
Maximum Overshoot = e^(-(Damping Ratio*Damped Natural Frequency)/(sqrt(1-(Damping Ratio)^2)))
Maximum Undershoot
Maximum Undershoot = e^(-(2*Damping Ratio*pi)/(sqrt(1-Damping Ratio^2)))
Time Response in Undamped Case
Time Response for Second Order System = 1-cos(Frequency*Time Period for Oscillations)
Peak Time given Damping Ratio
Peak Time = pi/(Frequency*sqrt(1-Damping Ratio^2))
Number of Oscillations
Number of Oscillations = (Setting Time*Damped Natural Frequency)/(2*pi)
Time of Peak Overshoot in Second Order System
Time of Peak Overshoot = ((2*Kth Value-1)*pi)/Damped Natural Frequency
Rise Time given Damped Natural Frequency
Rise Time = (pi-Phase Shift)/Damped Natural Frequency
Time Period of Oscillations
Time Period for Oscillations = (2*pi)/Damped Natural Frequency
Setting Time when Tolerance is 2 Percent
Setting Time = 4/(Damping Ratio*Damped Natural Frequency)
Setting Time when Tolerance is 5 Percent
Setting Time = 3/(Damping Ratio*Damped Natural Frequency)
Delay Time
Delay Time = (1+(0.7*Damping Ratio))/Frequency
Peak Time
Peak Time = pi/Damped Natural Frequency
Rise Time given Delay Time
Rise Time = 1.5*Delay Time

## < 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)

## < 19 Fundamental Parameters 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)

## < 17 Second Order System Calculators

Time Response in Overdamped Case
Time Response for Second Order System = 1-(e^(-(Overdamping Ratio-(sqrt((Overdamping Ratio^2)-1)))*(Frequency*Time Period for Oscillations))/(2*sqrt((Overdamping Ratio^2)-1)*(Overdamping Ratio-sqrt((Overdamping Ratio^2)-1))))
Bandwidth Frequency given Damping Ratio
Bandwidth Frequency = Frequency*(sqrt(1-(2*(Damping Ratio^2)))+sqrt((Damping Ratio^4)-(4*(Damping Ratio^2))+2))
Time Response of Critically Damped System
Time Response for Second Order System = 1-e^(-(Frequency*Time Period for Oscillations))*(1+(Frequency*Time Period for Oscillations))
Rise Time given Damping Ratio
Rise Time = (pi-Phase Shift)/(Frequency*sqrt(1-Damping Ratio^2))
Maximum Overshoot
Maximum Overshoot = e^(-(Damping Ratio*Damped Natural Frequency)/(sqrt(1-(Damping Ratio)^2)))
Maximum Undershoot
Maximum Undershoot = e^(-(2*Damping Ratio*pi)/(sqrt(1-Damping Ratio^2)))
Time Response in Undamped Case
Time Response for Second Order System = 1-cos(Frequency*Time Period for Oscillations)
Peak Time given Damping Ratio
Peak Time = pi/(Frequency*sqrt(1-Damping Ratio^2))
Number of Oscillations
Number of Oscillations = (Setting Time*Damped Natural Frequency)/(2*pi)
Time of Peak Overshoot in Second Order System
Time of Peak Overshoot = ((2*Kth Value-1)*pi)/Damped Natural Frequency
Rise Time given Damped Natural Frequency
Rise Time = (pi-Phase Shift)/Damped Natural Frequency
Time Period of Oscillations
Time Period for Oscillations = (2*pi)/Damped Natural Frequency
Setting Time when Tolerance is 2 Percent
Setting Time = 4/(Damping Ratio*Damped Natural Frequency)
Setting Time when Tolerance is 5 Percent
Setting Time = 3/(Damping Ratio*Damped Natural Frequency)
Delay Time
Delay Time = (1+(0.7*Damping Ratio))/Frequency
Peak Time
Peak Time = pi/Damped Natural Frequency
Rise Time given Delay Time
Rise Time = 1.5*Delay Time

## Bandwidth Frequency given Damping Ratio Formula

Bandwidth Frequency = Frequency*(sqrt(1-(2*(Damping Ratio^2)))+sqrt((Damping Ratio^4)-(4*(Damping Ratio^2))+2))
fb = f*(sqrt(1-(2*(ζ^2)))+sqrt((ζ^4)-(4*(ζ^2))+2))

## What is bandwidth?

Bandwidth is the difference between the upper and lower frequencies in a continuous band of frequencies. It is typically measured in hertz, and depending on context, may specifically refer to passband bandwidth or baseband bandwidth.

## How to Calculate Bandwidth Frequency given Damping Ratio?

Bandwidth Frequency given Damping Ratio calculator uses Bandwidth Frequency = Frequency*(sqrt(1-(2*(Damping Ratio^2)))+sqrt((Damping Ratio^4)-(4*(Damping Ratio^2))+2)) to calculate the Bandwidth Frequency, Bandwidth Frequency given Damping Ratio is defined as the Frequency value at which output drops by 3 dB of maximum response value, or reduces to (1/√2) of value at resonance. Bandwidth Frequency is denoted by fb symbol.

How to calculate Bandwidth Frequency given Damping Ratio using this online calculator? To use this online calculator for Bandwidth Frequency given Damping Ratio, enter Frequency (f) & Damping Ratio (ζ) and hit the calculate button. Here is how the Bandwidth Frequency given Damping Ratio calculation can be explained with given input values -> 54.96966 = 23*(sqrt(1-(2*(0.1^2)))+sqrt((0.1^4)-(4*(0.1^2))+2)).

### FAQ

What is Bandwidth Frequency given Damping Ratio?
Bandwidth Frequency given Damping Ratio is defined as the Frequency value at which output drops by 3 dB of maximum response value, or reduces to (1/√2) of value at resonance and is represented as fb = f*(sqrt(1-(2*(ζ^2)))+sqrt((ζ^4)-(4*(ζ^2))+2)) or Bandwidth Frequency = Frequency*(sqrt(1-(2*(Damping Ratio^2)))+sqrt((Damping Ratio^4)-(4*(Damping Ratio^2))+2)). Frequency is defined as the number of occurrences of a repeating event per unit of time in control system applications & Damping Ratio in control system is defined as the ratio with which any signal gets decayed.
How to calculate Bandwidth Frequency given Damping Ratio?
Bandwidth Frequency given Damping Ratio is defined as the Frequency value at which output drops by 3 dB of maximum response value, or reduces to (1/√2) of value at resonance is calculated using Bandwidth Frequency = Frequency*(sqrt(1-(2*(Damping Ratio^2)))+sqrt((Damping Ratio^4)-(4*(Damping Ratio^2))+2)). To calculate Bandwidth Frequency given Damping Ratio, you need Frequency (f) & Damping Ratio (ζ). With our tool, you need to enter the respective value for Frequency & 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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