EQ bandpass filter: Q factor and bandwidth
When using the bandpass (or peak) filters of a parametric equalizer, you might be asking what is exactly the effect of the quality factor Q. You have probably noticed that a high Q curve is narrow, a low Q curve is wider and that the bandwidth is not linearly related to Q.
Here are some bandwidths in octaves and the corresponding Q.
|Q||N (bandwidth in octaves)|
N = LOG(SQRT((((2+(1/Q^2))^2)/4)-1)+(1/(2*Q^2))+1)/LOG(2)
Q = SQRT(POWER(2;N))/(POWER(2;N)-1)
explanations and useful calculators:
Bandwidth in octaves to Q factor (filter) conversion and vice versa
Q Factor and filter center frequency - Find -3 dB cutoff frequencies
See also RaneNote 170 (2008) by Dennis Bohn:
Bandwidth in Octaves Versus Q in Bandpass Filters