Enter the frequency, resonant frequency, and quality factor into the calculator to determine the magnitude response in decibels (dB).
Magnitude Response Formula
The following formula is used to calculate the magnitude response of a system at a given frequency.
MR = 20 * log10(1 / sqrt(1 + (f / fr - fr / f)^2 * Q^2))
Variables:
- MR is the magnitude response (dB)
- f is the frequency at which the response is being measured (Hz)
- fr is the resonant frequency of the system (Hz)
- Q is the quality factor of the system
To calculate the magnitude response, use the formula above where MR is the magnitude response in decibels (dB), f is the frequency, fr is the resonant frequency, and Q is the quality factor.
What is Magnitude Response?
Magnitude response is a measure of how the amplitude of a system's output signal varies with frequency. It is often expressed in decibels (dB) and is used to characterize the frequency response of electronic filters, amplifiers, and other signal processing devices. The magnitude response can provide insights into the behavior of a system, such as its bandwidth, resonant peaks, and how it attenuates or amplifies signals at different frequencies.
How to Calculate Magnitude Response?
The following steps outline how to calculate the Magnitude Response.
- First, determine the frequency (f) at which the response is being measured in hertz (Hz).
- Next, determine the resonant frequency (fr) of the system in hertz (Hz).
- Next, determine the quality factor (Q) of the system.
- Next, gather the formula from above = MR = 20 * log10(1 / sqrt(1 + (f / fr - fr / f)^2 * Q^2)).
- Finally, calculate the Magnitude Response (MR) in decibels (dB).
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Frequency (f) = 500 Hz
Resonant Frequency (fr) = 1000 Hz
Quality Factor (Q) = 5
