[sdiy] SVFs with different gains in the integrators

[Michael E Caloroso]

Part of the challenge of multiple integrators in a SVF is uniform
tracking of the integrators IE matching.  Oberheim used a hand
matching process for their OTAs in their SEM and OB-X.  Not perfect
but in those polyphonics you're hard pressed to hear a difference.

Oberheim never published the matching procedure but I did find a test
circuit in the Elektor Formant Music Synthesizer book May 1977 pg58 by
C. Chapman which is online.  Basically for each OTA you're setting
Iabc to 50/100/200 microamps, measuring Vout at each Iabc point, then
plotting Iabc vs Vout to find matching OTAs.  I wrote out the
procedure to show to Dave Rossum at a NAMM show a few years back and
he confirmed the procedure.

MC

On 12/12/20, Andrew Simper <andy at cytomic.com> wrote:
> Hi Guy,
>
> With a perfectly linear filter with no noise, spreading out the integrators
> just changes the cutoff, damping, and band pass gain of the filter compared
> to a regular SVF. Real world filters won't have perfectly matched cutoffs,
> so it's probably useful to understand the impact of this in regular SVF
> design as well. If cutoff1 < cutoff2 from my quick working the equations
> are:
>
> cutoff_spread = sqrt(cutoff1)*sqrt(cutoff2)
> gain_band_spread = gain_band*cutoff_spread / cutoff1
> damping_spread = damping*cutoff_spread / cutoff1
>
> This is probably easiest to understand with an example. If you generate a
> regular SVF biquad response, where the gain_low, gain_band, and gain_high
> are the amounts of gain applied to the low, band, and high outputs of the
> SVF, you have:
> cutoff = 3000 hz
> damping = 2
> response = (gain_low*cutoff*cutoff + gain_band*cutoff*s + gain_high*s*s) /
> (cutoff*cutoff + cutoff*damping*s + s*s)
>
> then you can match this with the spread out SVF:
> cutoff1 = 1000 hz
> cutoff2 = 9000 hz
> gain_band_spread = gain_band*3
> damping_spread = 2*3
> response = (gain_low*cutoff1*cutoff2 + gain_band_spread*cutoff1*s +
> gain_high*s*s) / (cutoff1*cutoff2 + cutoff1*damping_spread*s + s*s)
>
> In an actual circuit with noise and non-linearities the filter will sound
> different to a regular SVF.
>
> Cheers,
>
> Andy
>
> On Sat, 12 Dec 2020 at 18:09, Guy McCusker <guy.mccusker at gmail.com> wrote:
>
>> In Chris McDowell's recent thread I made an off-hand remark about
>> setting up an SVF with different gains in the integrators. I don't
>> know how well-known this is but I'm wondering what list members know
>> about the history and use of this idea in synthesizers.
>>
>> 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.
>>
>> 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. Are there any other examples?
>> Does anyone know any more of the history of this idea?
>>
>> 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!
>>
>> Guy.
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>