[sdiy] Weird Serge Resonant Filter topology in upper bands

Donald Tillman don at till.com
Tue Dec 13 07:54:25 CET 2022

Hey Aaron,

I don't recognize it either.

And the filter circuit, as presented, doesn't make any sense.  If you work out the transfer function, it's not a bandpass filter; it's some highpass bandpass combo with a low Q.  And like you said, the opamp buffer doesn't make any sense either.

Hmmm, y'know... 

If the schematic was in error... 

And the filter's output signal was not the opamp output as shown, but instead tapping off of the RC network that leads to the opamp's + input, that would make more sense.

Something like this:

That's a proper bandpass filter.  And it would require a buffer.

  -- Don
Donald Tillman, Palo Alto, California

> On Dec 11, 2022, at 5:11 PM, Lanterman, Aaron D via Synth-diy <synth-diy at synth-diy.org> wrote:
> I’ve been looking at the Serge Resonant Filter:
> https://electro-music.com/wiki/pmwiki.php?n=Schematics.SergeResonantEqualizer
> The lower 7th bands are standard bandpass Multiple Feedback filters. But the 3 top band (see rightmost two on the bottom row, rightmost one on the top row) are something else weird I haven’t seen. They vaguely remember a Wein-bridge-style filter in the Boss SP-1 Spectrum pedal, but instead of having a capacitor in series in the positive feedback loop, Serge has it in series with the input. 
> Does anyone recognize this filter? I have an urge to give things names.
> I tried to work out the transfer filter under the assumption that the negative feedback is stronger than the positive feedback so “golden op amp” rules hold. But when I plot the frequency response of my transfer function, I get peaks that are way too broad — they’re more curves than peaks. So I’m doing something wrong somewhere. 
> My transfer function has a numerator of
> c*s*(r+rp*(1+r*c*s))*rn 
> And a denominator of
> rp*r^2*c^2*s^2 + (rp*2+rn)*r*c*s + rp 
> Where rn is the resistor in the negative feedback look, rp is the resistor in the positive feedback loop, and the input resistor and resistor to ground are the name and denoted by r.
> Serge doesn’t remember where he got the filter from. He said he went to this topology for the higher bands because limitations in the open loop gain bandwidth product prevented the MFB topology from working well at the higher frequencies.
> One interesting thing is he felt the need to add an op amp buffer at the output of the filter, which suggests to me that non ideal op amp effects are in play.
> Aaron Lanterman, Prof. of ECE, Georgia Tech
> My blog on Education and Innovation: https://edupocalypsenow.wordpress.com
> My blog on Electronics and Programming: https://lantertronics.blogspot.com
> My YouTube channel on Electronics and Programming: https://www.youtube.com/c/lantertronics

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