Hi Ollie,

> I see, you want to get an explicit expression of the phase-
> frequency relation of your filter.
> I doubt that you can derive this expression directly from the
> transfer function of a filter.

Yes you can, as I posted before: tan^-1 im(H(wj))/re(H(wj)). (Aaargh, I see I'm being forced into it!) - it is pretty nasty, here it is for the 5th stage o/p:

tan^-1(-5*w + 3*k*w - 5*w^3 - k*w^3 + 14*w^5 + 22*w^7 + 7*w^9 - w^11)/
(1 + k - 7*w^2 - 3*k*w^2 - 22*w^4 - 14*w^6 + 5*w^8 + 5*w^10)

So plug in frequency, w, and k (resonance), and get the phase back.

[Mostly via Mathematica + time courtesy of not being able to get into work due to snow!]

> To derive such a phase-frequency relation, one needs a formula
> which relates the phase of the "incoming" frequency to the phase
> of the "outgoing" frequency.

This is given by the transfer function, see above!

> So you could think of a system where a harmonic oscillator with

<<snip lots of stuff I have no intention of trying to understand, as I don't see the relevance>>

There are lots of good books out there on active filters if you want to learn more: _my_ particular favourite is 'Design of Analog Filters', Schaumann & van Valkenburg, OUP

(Sorry everyone else for the algebra overload - especially
Florian :-) - back to what you were doing!)

Tim
__________________________________________________________
Tim Stinchcombe

Cheltenham, Glos, UK
www.timstinchcombe.co.uk