Resonance and Bandwidth Question

[tomizzo]

So, I've been covering these concepts recently in a few of my classes, and I'm wondering if the bandwidth is always centered on the resonance frequency?

I assumed it was. However, in a recent problem given, it is shown that the bandwidth of a band-pass filter was not centered about the resonance frequency. I've been looking this up on the internet but couldn't find any info. Any help?

 

[rbj]

for a 2^nd-order biquad band-pass filter, in the log-frequency scale (not the linear-frequency scale), the resonant frequency is in the middle of pass band. that means if you pick the two bandedges (usually the -3.01 dB points, but it could be any level as long as it's the same for the upper bandedge and lower bandedge), the resonant frequency is at the geometric mean of the two bandedges. that is the same as saying that the log of the resonant frequency is at the arithmetic mean of the logs of the two bandedges.