[sdiy] MOTM 440 4P LPF questions

[Lanterman, Aaron]

On Oct 31, 2011, at 12:00 PM, Thomas White wrote:

> Bassification... Okay I jest. It seems to boost the volume that would normally be lost when turning the resonance up with most filters. You end up with resonant filtering with more "punch" I'd say. Really keeps the low end portion of the sound that is the first to disappear when turning the res up. 

You can quantify the loss of volume. If you have four 1st-order sections in cascade, tuned to the same cutoffs, with negative feedback around all four (i.e. typical SSM2040 or Moog filter lader configurations), the gain at DC is 1/(1+K), where K > 0 is the gain of the negative feedback loop. Tracking the movement of the closed-loop poles shows that they hit the imaginary axis, hence goes unstable, at K=4 (of course there are practical effects that jiggle this.) So with no feedback, you get a gain of 1 at DC, and approaching max possible, you get a gain of 1/5 (i.e. an attention.)

I haven't looked at the MOTM 440 circuit or docs in a while but I'd guess Paul probably used that 1/(1+K) formula somewhere.

- Aaron