[sdiy] Reverse-exponential VCAs

[David G. Dixon]

> <<At this point, presuming a similar gain block on every filter
> stage, the filter will begin to self-oscillate. >>
> 
> I guess I am missing something, I do not see a feed back loop in the
> diagram.  I believe that self oscillation requires a positive feedback
> loop.

This is just a tiny part of the whole filter circuit.  One of these hangs
off of every filter stage, which also includes a separate VCA (as a VC
resistor), an integrator, and an inverter (which is the source of the two
signals of opposite polarities).  Hence, the entire filter cascade involves
8 VCAs (two 2164s) and 12 opamps, not counting the various auxiliary circuit
bits.  The output of the fourth gain block feeds back to the first filter
stage, as usual.

The difference is that every filter stage has a resonance amplifier, not
just the fourth stage, and the resonance VC is "reverse-exponential" rather
than linear (or even exponential, as in the case of Neil Johnson's 3P SVF).
I've only shown one of the resonance amps from the first three stages.  The
fourth one has a slightly different arrangement of resistors.  All four
resonance amps generate a gain of sqrt(2) at the onset of self-oscillation,
which gives the requisite overall gain product of 4 (sqrt(2) to the fourth
power).  

> 
>                                V_c
>                                 |      |--[ 13k7 ]--|
>                                 |      |            |
> (+) Signal --> [ 33k0 ] --> 2164 VCA ----> Summer ----> Out
>                                        |
> (-) Signal --> [ 33k0 ] -------------->|
>       |                                |
>       |------> [ 13k7 ] -------------->|