[sdiy] Polymoog resonator question

David G Dixon dixon at mail.ubc.ca
Sat Oct 6 07:15:51 CEST 2018

So, I've done the Bode plot analysis of the Polymoog Resonator.  The results
were a bit surprising to me (and I confirmed them with Multisim).

The surprise is that the LP output has a pretty high gain (about 13dB) at
low frequencies, while the HP output has pretty low gain (about -7dB) at
high frequencies.  The BP output looks normal, with a corner frequency gain
of about 0.85dB at the minimum resonance.  Of course, all three amplitude
responses have equal magnitude at a normalized frequency of 1, whereas the
normalized corner frequency is at 0.316.  This means that the resonating
frequency has dramatically different gains from the three filter outputs at
maximum resonance (HP 12.8dB, BP 22.8dB, LP 32.8dB).  This means that the LP
output is going to suffer from crazy clipping with low-frequency signals at
high resonance.

All of this weird behaviour is the direct consequence of that 10% loop gain
factor.  If the input and loop gains are set to unity (by making the two
feedback resistors equal to the input resistor, 22k), then the three
responses all give equal peak gains at all resonances.  It remains to be
seen how this will affect the sound, but I fear that the resonator as
designed by Moog will simply be too loud on the LP setting.  I guess I'll
just have to build it with sockets for those resistors (and the capacitors,
since the corner frequencies will all change by a factor of 3.16) and hear
for myself which way is superior.

Does anyone else have any opinions on this matter?  Does anyone have any
insights as to why the Polymoog resonator design may or may not be superior
to three bog-standard unity-gain SVF circuits at the same corner

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