[sdiy] Filter terminology question

[Magnus Danielson]

From: "David Reichert" <dreichert at sympatico.ca>
Subject: RE: [sdiy] Filter terminology question
Date: Thu, 20 Nov 2003 20:41:20 -0500
Message-ID: <000a01c3afd0$9338afd0$6401a8c0 at Sysyphus>

> 
> Whilst we're on the topic, does anyone understand how to compute the
> cutoff frequency and Q from a given transfer function?

Um, yes...

If you crack your transfer function roots open, and know the pole positions it
is actually quite simple.

Say that we have a pole pair s = o +/- jw, then since w = 2*pi*f we have

      w
f  = ----
 c   2*Pi

where as the Q is slightly more complex:
      _____
    \/o²+w²
Q = -------
      -2o

This is actually not quite accurate for undamped systems (Q > 0.707) since the
-3 dB point will move due to the resonant rise in responce, but I think these
formulas give an another form of accurateness which you want anyway.

Cheers,
Magnus