[sdiy] Moog filter self-FM questions

[Simon Brouwer]

Hi Antti,

Antti Huovilainen schreef:
> On Sun, 28 Mar 2010, cheater cheater wrote:
>
>> Simon,
>> thanks a lot for your email. Unfortunately some more explanation will
>> be necessary, I'm not smart enough yet to understand what you mean :-)
>> Some questions below..
>
> Read my paper on the non-linear digital emulation. It explains how the 
> ladder filter works for large signals.
This one, I suppose: http://www.qvoaudio.net/pdf/moog_filter.pdf . Very 
impressive.

>
> There is no self-fm, only nonlinearity within each of the 4 stages 
I humbly beg to differ. Not only the control current, but also the 
signal affects the series dynamic resistance of the two emitters in each 
section, changing the section's corner frequency. Allow me to attempt 
explaining that this is actually affirmed by the analysis in your paper.

Suppose the two transistors in fig. 3 were replaced by a linear 
resistor, with a resistance R that is inversely proportional to the 
control current, i.e. R=r/Ictl (with r a constant). So together with 
capacitor C you get a simple, linear RC filter section, driven by a 
current source. (In practice you would have to add some current sources 
to get rid of the control current, and now also It1=-It2, but all this 
would not affect the voltage across C)

With this modification, equation (6) would become: It1-It2=Ictl*Vc/r (6b)

Choosing 1/r as the slope of 2*tanh(Vc/2Vt) at Vc=0, equations (6) and 
(6b) are equivalent for small values of Vc. But for large Vc, 
2*tanh(Vc/2Vt) becomes smaller than Vc/r.

So to get the same result as in equation (6), you would have to make r, 
and thus the corner frequency of the RC section, dependent on the signal 
voltage Vc. Voila the "self-modulation".


This can of course be regarded as "only nonlinearity", but it is really 
something else than having four linear RC sections with tanh-distorted 
buffers in between. Another clue for this is equation (10), which shows 
that the dependence of dVc/dt is not only nonlinear on Vin, but also on Vc.

By the way, equation (10) would apply equally well to CEM3320 or SSM2040 
low pass filters in which the filter sections have individual feedback 
(see e.g.  http://www.electricdruid.net/index.php?page=info.cem3320)

-- 

Vriendelijke groet, 
Simon Brouwer.