JdM12EQ 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) |
|---|---|
| 0.267 | 4 |
| 0.326 | 3.5 |
| 0.404 | 3 |
| 0.511 | 2.5 |
| 0.667 | 2 |
| 0.920 | 1.5 |
| 1.414 | 1 |
| 1.707 | 5/6 |
| 2.145 | 2/3 |
| 2.871 | 1/2 |
| 4.318 | 1/3 |
| 8.651 | 1/6 |
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)
Thanks to
SengpielAudio
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
November 2016