[sdiy] Polymoog resonator question

Rutger Vlek rutgervlek at gmail.com
Thu Oct 11 19:27:50 CEST 2018

Hi David,

Great that you're working on this! I also had plans do build a resonator like along these lines, though probably would have changed things w.r.t. the original Moog version, most notably the option to have 12dB instead of 6dB slopes.

I read your email (below) a while ago and haven't found anyone directly replying to it. I may have missed it, but your findings and questions are interesting! 

I have a hypothesis on why Moog did it this way, with different gains for the LP/BP/HP outputs. It has to do with the expected power spectrum of the sounds typically used as an input. Most synth sounds (saw/tri/pulse) have a spectrum where most of the power resides in the fundamental and harmonics close to that. Towards the higher frequencies the power rolls of (e.g. isn't flat like the white noise spectrum). Given the resonator will receive such sounds at it's input, I can see it makes sense to balance the amplitude of the resonating frequency against that of the pass-band of the filter. So if you are in LP mode the filter passes all frequencies below the cutoff and resonates around the cutoff frequency. The resonance peak will have to be balanced against the typically rather bass-heavy remained of the input signal. With the HP mode, this is totally different, as in the pass-band only very little power remains, meaning that the resonance peak becomes masked less easily and risks being too dominant over the original high-end remainder of the spectrum. The BP being the neutral one also makes sense, as here there's little low nor high end to balance the peak against.

My suspicion is that if you prototype this idea, it will indeed turn out to be more musically sounding than making all outputs have the same gain. If I can find some time I'll rapid-prototype it for you (and others) on my Nord G2. It's a great platform for finding out such things.

What I still don't understand is why they did it inside the loop, rather than at the output. The only reason for being in the loop is if you wanted to affect frequency as well.... which isn't switching to a different range along with the LP/BP/HP is it?



On 6 okt 2018, at 07:15, David G Dixon wrote:

> 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
> frequencies?
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