[sdiy] Moog filter self-FM questions

[Antti Huovilainen]

On Mon, 29 Mar 2010, cheater cheater wrote:

> I was looking through Tim's papers earlier. The animations were indeed
> very interesting and educative, I hope he makes more.
>
> I am afraid the complete Moog Filter paper from Tim is more than I can
> dedicate myself to this month.
>
> So guys, looking back at the original question..
> to what extent does the audio *really* modulate the cutoff?

If the transistors are reasonably well matched, it doesn't.

I'll use the digital equations to illustrate (as they're simple to write), 
but just assume the samplerate is "very large" and the same will apply to 
analog.

y = y + g*(tanh((x + Vo1)/2Vt) - tanh((y + Vo2)/2Vt)

(Vo1/Vo2 = previous/current pair offset voltage, 2Vt = 50mV, g = cutoff)

If Vo1 and Vo2 are large (10mV) and of opposite sign and the signal 
consists of large amplitude bass note and small amplitude high note, the 
result could be considered as the bass note modulating filter cutoff g 
for the high note. However, that ignores the higher harmonics produced by 
the tanh function. The required offset is also much larger than the 
transistor matching specified by Moog (2mV).

As the required conditions are relatively rare, it's much better to just 
consider the process as distortion. This way the result is valid for any 
signal and any combination of transistor pair offsets.

Antti

"No boom today. Boom tomorrow. There's always a boom tomorrow"
   -- Lt. Cmdr. Ivanova