[sdiy] SVFs with different gains in the integrators

Donald Tillman don at till.com
Sun Dec 13 18:31:14 CET 2020

> On Dec 12, 2020, at 2:09 AM, Guy McCusker <guy.mccusker at gmail.com> wrote:
> The theory, if I have it right, is that with different integrator
> gains, the natural frequency is given by the geometric mean of the
> unity gain frequencies, and the Q is enhanced by something like the
> square root of the ratio of the gains. So you can vary Q without
> varying the bandpass feedback.

True.  But I'm not sure that's an advantage.

One of the big features of the State Variable Filter is that the frequency and Q are independent.  Compared to, say, varying the component values on a Sallen Key filter.  And if you want to make them dependent, it's a simple matter to patch it in.

Also note that the level of the bandpass output changes.

> The only use of this that I know about in synthesizers is the Serge
> Variable Slope filter (VCFS). The claimed varying slope is really
> varying the Q, so that the slope near the natural frequency changes;
> the asymptotic slope is still 12dB/Oct.

I'm not sure that's true.  Do we have schematics or anything to check?

> Incidentally, thinking about this always makes me smile at the
> marketing smarts of Serge in the 1970s. He marketed three filters:
> variable Q filter, variable slope filter, and variable bandwidth
> filter. Since Q and bandwidth are the same thing (one is the
> reciprocal of the other), and since the variable slope filter is
> actually varying the Q, all three of these are in fact variable
> bandwidth filters... but he managed to distinguish them by calling it
> three different things. Smart!

I'm not sure that's true, either.  It looks to me like Serge was seriously exploring new filter behaviors specifically for their ability to expand musical expression, each with different kinds of parameters to vary.  

So repurposing a Q parameter is the exact opposite of that.

But I'd love to see the schematics to know for sure.

  -- Don
Donald Tillman, Palo Alto, California

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