[sdiy] [OT] Analog synths with 2 pole filters

[rburnett at richieburnett.co.uk]

> Going back to Scott Nordlund's comment, 2-pole filters definitely
> self-oscillate. After all, the typical "resonance" control on a SVF
> filter is actually a "damping" control, and if you  remove it, the
> filter can easily become an oscillator.

Hi all,

I think the reason that many 2-pole filters are seen not to be capable 
of self oscillation is down to the way in which they are actually 
implemented....

The moog 4-pole cascade goes into self-oscillation when the feedback 
gain reaches -4 (provided tolerances are tight and all of the 4 cascaded 
poles have exactly the same time-constant!)  You have to introduce some 
amplification into your circuit in order to achieve this gain of four 
times. And when you do this it is easy to design the circuit to allow 
the user to dial in just a little bit more gain (for example a gain of 5 
or 6) and therefore guarantee that the filter will start oscillating 
somewhere before the resonance pot reaches the very top of its available 
travel.

With the standard state-variable filter implementation of a 2-pole 
filter the resonance pot actually controls the damping in the 2nd order 
transfer function.  With the resonance pot at it's maximum setting there 
is no feedback from after the first-integrator, and the damping is zero. 
i.e. The filter is critically stable.  Just on the verge of 
self-oscillation.  It might oscillate, but then again it might not!  And 
to guarantee that the filter will oscillate you need to make the damping 
ever so slightly negative to push those complex poles into the 
right-half-plane and produce sustained oscillation.  It's easy to scale 
the amount of damping feedback around the first integrator over the 
range of 0 to +1 with a simple pot, but it's harder to design if you 
want to make this go slightly negative at the very top of the resonance 
pots travel to guarantee self-oscillation.

So, in summary, my point is that it's easy to make the moog 4-pole 
cascade capable of guaranteed self-oscillation because it just requires 
a little bit more gain where you already require a gain of 4 anyway.  In 
the case of the state-variable filter just taking the damping term down 
to zero is not enough.  The damping has to actually go slightly below 
zero, and this requires increased complication that most filter designs 
don't include.  That's my take on it anyway, I hope it helps the 
discussion :-)

-Richie,