[sdiy] Q?

[Czech Martin]

I was sure that I know what the quality factor Q of a filter is, and how it is defined.
Until I tried to write it up and do the math.
After some days I think I found it.

Most texts skip this topic and simply state that it be like it is.
Or explain it only for one example circuit.

Now, what is your way to introduce Q?

My way was to start with a 2nd order bandpass , and define Q as the ratio of peak frequency
versus f1-f2 , where f1 and f2 are the -3dB or half power frequencies.
This works consitently for Q between +inf. and 0.
Then: compare the numerator of the transfer function of any other 2nd order system with that 2nd order bandpass
and if equal, you define it to have the same Q. Of course both must be "normalized" in the same way,
i.e. best would be to write them in the canonical form, as b*s**2+a*s+1.
Q is then sqrt(b)/a.


Are there other ways to do it?

m.c.