[sdiy] CEM VCF transconductance stage difference!

[Magnus Danielson]

Scott Nordlund skrev:
> I think that once resonance is applied, an offset in one of the filter
> stages will be relatively insignificant.  Negative feedback (resonance)
> pushes each pair of poles together to form a conjugate pair, detuning
> one pole would mean that more feedback is required to form that
> conjugate pair (between the detuned poles) and that it would be offset
> by half of the detuning amount (or at least that's what my
> understanding of root locus would lead me to believe).

You are correct. If all roots have the same real position, they will 
expand out from that in the shape of a circle. The sign of the feedback 
will control which orientation the poles will have on the circle. For a 
4-pole design positive feedback gives poles at +/- 45 degrees and +/- 
135 degrees while negative feedback gives poles at 0, +/- 90 degrees and 
180 degrees. If the poles where not quite on mark (they never are), they 
will gather first and then expand out as expected but with a slightly 
skewed position and shape.

> I think the popular "TB-303 has a 3-pole filter that gives it a
> characteristic sound" rumor has been debunked already.  If I recall
> correctly it's more likely done for stability reasons (?).

Meaningful control-range in a cheap design?

> This was covered in the recent analysis of transistor/diode ladder filters
> that was posted to this list, but I can't cite/reference it in more detail
> because it's not on this computer.
> 
> Anyway I think the different transconductance of one stage would be
> directly equivalent to a different capacitor value.  Probably this could be
> undone (to what effect?) by using a larger capacitor on that one stage.

Certainly, as they form a ratio.

> Independent detuning of filter stages is an interesting idea, though
> I'd imagine an analog implementation would present its own difficulties
> (four matched exponential amplifiers?).  Detuning two stages by the same
> amount might give an interesting effect under resonance.  Detuning one
> stage by a large amount would make a three pole filter with no resonance,
> and then as resonance is increased it would make a genuine two pole
> resonant filter (rather than a 4-pole filter tapped at the second stage)
> with two negligible (?) poles in the stop band.  Neat idea.

No, not quite. The main effect would become that it would shift the 
point of feedback where the "star configuration" expands out. It would 
however essentially behave as a normal filter.

You will shift the frequency and point of expansion with detuning.

To create the type of effects you are describing I think you would need 
to tap the stage at different points for the feedback to achieve what 
you described.

Cheers,
Magnus