math attack : feedback

[Uros]

----- Original Message ----- 
From: Martin Czech <czech at Micronas.Com>
To: <synth-diy at node12b53.a2000.nl>
Sent: Wednesday, April 19, 2000 5:43 PM
Subject: math attack : feedback


> If several bandpass sections are cascaded, and a feedback path
> goes from the last one back to the first, there is pole spread out.
> It is easy to show that the zeros stay at 0 (well, not exactly, we
> allready had that). I've looked at 2-8nd order, only one pole
> pair comes closer to the jw axis and will finally lead to oscillation.
> All other poles stay away.
> 
> Why is this so, I mean, is there a fundamental mathematical
> theorem behind that?
> 
> >From the measurement point of view we can say that a distinct
> oscillation is reached at some point, so a single pole pair
> makes sense, of course. However, I could imagine that more
> characteristic frequencys are possible.
> 
> m.c.

Well , I'm guessing ( only guessing , didnt checked out ) next thing :
when you put feedback around cascaded bandpass sections you change 
impedance that is seen by reactive elements in first and last sections
and by that chage positions of poles ( and zeroes ) that is contributed
by those reactive elements . So only two poles move . With increasing 
feedback Beta*A will reach unity and you go into selfoscilation .
Well , at least , thats what I think
regards
Uros