# FW: digital contents

Don Tillman don at till.com
Sat Sep 21 09:25:43 CEST 1996

```   From: Haible_Juergen / Paolo Predonzani
Date: Thursday, 19. September 1996 15:06

I've been working on a numerical implementation of the Moog filter for
a month. The non-linearities I considered are the differential input
and the 4  current buffers.

Yes.

The non-linearities are a major problem because they are present in
every term of the (4th order) differential equation the filter obeys to.
This makes the poles move in the s-plane for constant cutoff freq and Q.
The small signal analysis shows 4 coincident poles in -p (open loop).
The large signal analysis shows that the poles move between -p and the
origin of the s-plane. The static open loop gain also varies.
Standard DSP filters rely on the fact that the coefficients of the
FIR/IIR filter are constant but this is not true for the Moog filter.

Yes indeed!  How much this dynamic tuning effect contributes to the
sound of the filter is unknown.  (Also whether the effect is
aesthetically pleasing or not.)

The algorithm I use could have been written in the 70's and can be
found
in many books on discrete-time control theory of that period.
Unfortunately it is very slow and has a poor conditioning (= noise).

Yeah, but this is about the only way there is to simulate
nonlinearities that dynamically affect tuning.

From: Haible_Juergen
Date: Fri, 20 Sep 96 14:51:00 PDT

This really caught my attention! So far I have only looked at the
nonlinearities as a cause of harmonics/distortion, and not shifting
poles as well! This would mean that the cuttof frequency changes
with signal input strength ...

True, but it also means that the distortion is much more bizarre than
a simple nonlinear curve.  You've got gain and phase-shift (!!!)
changing over the course of a single cycle.  And than adding feedback
on top of that.  Yow!

Now, this makes me question: (1) How are "poles" defined for
large signal analysis? I only know this concept for linear circuits.
How are they defined for nonlinear circuits? Time domain
response for a certain input signal, and then inverse fourier
transform? If so, for which input signal ??

Poles are really only defined for small-signal analysis -- they don't
begin to describe what happens when these sort of nonlinearities kick
in.

(2) How *far* would these poles move? Usually, the signal amplitude
thru the ladder is small in comparison with the bias current. (?)

Maybe not that small.  Overdriving the Moog filter is standard
operating procedure.  (That's a good way to get a more sinusoid wave
from a triangle.)

-- Don

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