[sdiy] Pole Dancing
rburnett at richieburnett.co.uk
Tue Sep 18 21:34:20 CEST 2018
That's cool Don. Great programming, and thanks for sharing. I've had this
on my "to do" list for sometime, but can strike it off now someone else has
done it well.
I'm used to using MATLAB to produce root locus plots for control-loop
stability, etc, but this web interface is much more intuitive and
I always found it fascinating how the Moog filter's poles move as global
feedback is applied around the ladder. Particularly how poles that are
slightly spread out on the real axis due to component tolerances "pair up"
with their nearest neighbour and then split again to form *two resonant
(complex) pairs*. It is interesting to me because the 4-pole moog filter
with resonance applied actually behaves like two cascaded 2-pole filters
with different cutoff and resonance values. As the poles split in the
classic X formation, the two that make a dash for the jw axis are highly
resonant and dominate the frequency response, and the two that head
leftwards are still slightly resonant but are at a higher natural frequency
and very highly damped. It's useful to break up the response like this for
digital modelling because digital filters are rarely realised in orders
higher than 2 for stability, numerical accuracy and computational efficiency
reasons. So it's interesting to see that a 4-pole Moog LPF can be modelled
with two cascaded 2-pole resonant LPFs, and that the parameters of these two
cascaded 2-pole IIR filters are not the same!
I think this is where Roland went wrong with a lot of their early VA synth
filters. The 2-pole filter setting sounded good, but for the 4-pole filter
setting they just sent the audio through two identical cascaded 2-pole
digital filters, which results in a very broad resonant peak that sounds
thin, weedy and very nasal. That is not how a real 4-pole ladder (or
cascaded OTA) filter with global feedback behaves when the resonance is
turned up, and your JS app clearly shows that!
From: Donald Tillman
Sent: Tuesday, September 18, 2018 6:44 PM
To: synth-diy mailing list
Subject: [sdiy] Pole Dancing
Since we've been talking about filters lately...
There are several classes of active filters (state variable, gyrator, etc.),
but one that's especially interesting is where you start with a passive RC
filter, with poles on the real axis, and apply feedback, liberating the
poles into the wonderment of the complex plane.
Root Locus Demo of Real Poles with Feedback
Have fun with it. Tell me what you think. Ask questions. Explore.
Donald Tillman, Palo Alto, California
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