The above figure exhibit the response of the band pass filter. fL = Lower cut off frequency = 100 HzfH = Higher cut off frequency = 10K HzGain at the fH is 15 dBWhat will be the Q factor of the filter?
Question
The above figure exhibit the response of the band pass filter. fL = Lower cut off frequency = 100 HzfH = Higher cut off frequency = 10K HzGain at the fH is 15 dBWhat will be the Q factor of the filter?
Solution
The Q factor of a bandpass filter is calculated using the formula:
Q = f0 / (fH - fL)
where: f0 is the resonant frequency, fH is the higher cut-off frequency, and fL is the lower cut-off frequency.
In this case, the resonant frequency f0 is the geometric mean of fH and fL, which is sqrt(fH * fL).
So, first calculate f0:
f0 = sqrt(fH * fL) = sqrt(10K Hz * 100 Hz) = sqrt(1,000,000) = 1K Hz
Then, calculate Q:
Q = f0 / (fH - fL) = 1K Hz / (10K Hz - 100 Hz) = 1K Hz / 9.9K Hz = 0.101
So, the Q factor of the filter is approximately 0.101.
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