[sdiy] Pole Dancing

[Donald Tillman]

On Jan 24, 2023, at 1:25 AM, Richie Burnett <rburnett at richieburnett.co.uk> wrote:
> 
> BTW, it's interesting to plot the RL of a State Variable Filter.  The poles move along circular arcs in the SVF when the resonance amount is altered. This is in contrast to the X-shaped lines for the moog ladder in the Stilson paper.  And... I just noticed that you can do this with the Javascript simulator on your web page too, using the second feedback slider!  Neat! :-)

Ah, good point; I forgot to mention that case.

To plot a State Variable Filter place two poles at the origin.  That's a SVF running open loop.  Then add negative s^0 feedback to tune it.  Without damping it's an oscillator.  So then add some negative s^1 feedback to set the Q.

To plot a Sallen-Key style filter, place two poles on the left real axis, and add positive s^1 feedback to set the Q.

Adding negative s^0 feedback raises the value of the s^0 coefficient, which has the effect of lowering the middle coefficients if you rescale the polynomial, thus raising the Q.

Adding positive s^1 feedback lowers the value of the s^1 coefficient directly, raising the Q.

  -- Don
--
Donald Tillman, Palo Alto, California
https://www.till.com