[sdiy] Buchla 292c transfer function

[David G Dixon]

Hey Team,

A buddy asked me to lay out some custom boards based on the Buchla 292c
Lopass Gate.  Before I do that, I'm trying to understand this circuit.  I've
done an analysis of the transfer functions, and it is very interesting.

For this analysis, I replaced the 910pF cap of the original with the 1nF cap
found in the Thomas White/Dave Brown schematic:

http://modularsynthesis.com/nrm/lopass/djb-lopass_gate_schematic_mods.jpg

In VCF mode, at high frequencies (i.e., when R_vactrols << 4.7M), the
transfer function reduces to Sallen-Key with a damping factor of 0.5 (i.e.,
Q = 2, modest resonance) and an effective capacitor size of 2.2nF.

In VCA mode, the 4700pF capacitor is left floating and the input gain is
doubled.  Again, at high frequencies, the transfer function reduces to a
Sallen-Key with a damping factor of 1.67 (i.e., Q = 0.6, virtually no
resonance) and an effective capacitor size of 330pF (cutoff frequency 6.7
times higher).

I haven't plotted the transfer functions yet to see the effect of the 4.7M
resistor as a function of cutoff frequency (that's next) but already I can
see that this is a diabolically clever little circuit which shows a deep
understanding of filter fundamentals (as if there were any doubt).

If anybody has followed a similar path and would like to compare notes,
please email me privately.