[sdiy] filter resonance

[Antti Huovilainen]

On Thu, 11 Nov 2004 jays at aracnet.com wrote:

> Has anyone put together anything saying what type of feedback and 
> scaling works best with different filters?

For Moog-like filters that have four RC sections in series (Moog, most 
CEMs, most SSMs), you feed back the output inverted to the input. This 
works because each section adds 45 degrees of phase shift at cutoff freq 
which means total phase shift of 180 degrees. Inverting provides another 
180 degrees, making the feedback positive at cutoff freq. As each section 
decreases amplitude by 3dB at cutoff, you need to scale feedback by 4x to 
make 0..1 feedback go from zero resonance to self oscillation.
Another trick you can play is to sum part of the input before the 
inversion (but after scaling) to adjust how much passband gain decreases 
when increasing resonance.

You might want to check my recently published paper about emulating the 
moog filter (with nonlinearities), "Non-linear Digital Model of the Moog 
Ladder Filter", published at DAFX04. The paper is online at
http://dafx04.na.infn.it/DAFx04_Proceedings.htm (go to contents, click 
page number 61 in the list).

For Korg MS-20, you feed back the output (non-inverted) to the _bandpass 
input_ (yes, MS-20 filter natively has lowpass, bandpass and 1-pole 
highpass inputs). Bandpass input does not produce any phase shift at 
cutoff frequency so resonance is done with normal positive feedback. The 
scaling for self oscillation is 2x. (I'll publish something on this too 
once I get it written)

Antti

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