[sdiy] Polymoog resonator question

David G Dixon dixon at mail.ubc.ca
Thu Oct 11 19:50:51 CEST 2018

Thanks, Rutger!  I have built the PCB to reproduce the original three
resonators fairly closely -- same gains, same frequency ranges, but with the
option of voltage control.  I have a fourth resonator that is a copy of the
high-frequency resonator, but which will cover the entire frequency range
(60 to 7500 Hz) given the same input voltage range.  With this I can see how
overlapping peaks sound.

To test uniform gains, all I have to do is swap out a few resistors (an easy
and pleasant task with my Hakko FR-300 desoldering gun).  If it sounds good
as it is, then I may not bother.

I have installed everything except the capacitors and the connector
hardware.  I got a fairly ill on Monday night (headcold plus pancreatitis --
not a nice combo) and didn't feel like finishing it.  I also searched (in
vain) for 5.6nF caps for the low resonator, and have since changed the
design to use (the much more common) 6.8nF caps.  I will finish it tonight,
however, so I expect to be back on SDIY with a vengeance tonight and/or
tomorrow.  I don't have a Jupiter 8 to put through it, so I won't be able to
recreate Ken Elhardt's setup, but I'll make do with my Doc Sketchy synth.
Or, maybe I'll try my Hammond digital organ through it.

> -----Original Message-----
> From: Rutger Vlek [mailto:rutgervlek at gmail.com] 
> Sent: Thursday, October 11, 2018 10:28 AM
> To: David G Dixon
> Cc: 'Donald Tillman'; synth-diy at synth-diy.org
> Subject: Re: [sdiy] Polymoog resonator question
> 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?
> Regards,
> Rutger
> 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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