The formula to calculate the magnitude response (MR) is:
\[ MR = 20 \log_{10}\left(\frac{1}{\sqrt{1 + \left(\frac{f}{fr} - \frac{fr}{f}\right)^2 Q^2}}\right) \]
Where:
Let's say the frequency (\( f \)) is 1000 Hz, the resonant frequency (\( fr \)) is 500 Hz, and the quality factor (\( Q \)) is 10. Using the formula:
\[ MR = 20 \log_{10}\left(\frac{1}{\sqrt{1 + \left(\frac{1000}{500} - \frac{500}{1000}\right)^2 \times 10^2}}\right) \]
We get:
\[ MR \approx -23.54 \text{ dB} \]
So, the magnitude response (\( MR \)) is approximately -23.54 dB.
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.
