poles and s-planes

[Martin Czech]

:::Hello good people of sdiy ,
:::there are several student questions I would like to ask :
:::What is s-plane position of poles and zeroes of  4pole moog and three pole
:::303 filters ?
:::I dont expect anyone to draw it and post it to list but can someone  please
:::tell me
:::where can I find it on net ? Also , root-locus diagrams ? On common sense
:::under normal conditions all poles should be imaginary , but what happens
:::with high resonance settings ? Selfoscilation ( instability ) should happen
:::when poles have just imaginary part in ideal conditions but in real cases
:::poles would enter ( more or less ) right half of s-plane , right ?
:::One of my professors told me that three pole transfer function is
:::inherently much , much more instable that two pole ?
:::Also he told me that instability could cause sqare wave oscilations not just
:::sine wave resonant oscilations . Has anyone experienced this in filters ?
:::And finaly are there any other three pole filters other than 303 ?
:::Was this discused earlyer ( I'm just two months on list ) ?
:::Thanks in advance
:::Uros

1.
I think for both filters (and ideal components) with no resosonace
all poles are real. The diode ladder loads each stage with the next,
so that in this case the poles are spread on the negative real axis.

As resonance increases, the 4pole moog poles spread out from one single
point into 4 orthogonal directions, with 45 DEG angle to the real axis,
this means two of them finally give oscillation by reaching the imag axis.

The loading in the diode ladder will change the symmetry of the pattern somehow,
I guess the leftmost pole-pair will differ from the right pair,
I guess it is not so resonantish, i.e. the imag part is smaller then
in the moog case.


All from my head, I know there is a root-locus for moog in EN,
but I never have seen an analysis for the diode ladder.

Somebody with CAD tools could do this very quickly, I think.

2.
The diode ladder has also four poles, but the stages load each other,
so the characteristic is less "sharp".

3.
Three pole filters I never heard or seen in commercial designs.
It is not so exiting, the third pole can never get away from
real axis.

4.
Of course, 3 poles finally make 3x90 DEG phase shift,
this is inherently more instable with feeback applied as a two pole.

In reality the number of poles is much larger, because all the active
and passive components add their characteristic. This is most noyiceable
when slow opamps are used. Discrete semeconductors are much faster.

This is why two poles filters always oscillate, the more the 
higher Fc is.

5.
No, the circuits will not get to squarish resonance, because
the amplitude limiting will happen in the first diff stage,
later on this will be filtered away, so that filters usually give
better sines then oscillators (with shapers).
At least the "vintage" circuits you mentioned.

6.
Yes, this was all covbered in detail in the past 5 years on
synth diy.

m.c.