math attack : feedback

[Martin Czech]

Well, from the practical point of view it is clear that the bandpass
configuration will pick out the center frequency for oscillation,
and also gain/phase plots say this.

I just wonder why all other poles seem to stay far away from jw-axis,
regardless of filter order. This was a bit surprising.

It all boils down to look for the zeros of a special type of polynom
in the complex plane.

m.c.

:::> >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
:::
:::