[sdiy] 4 Pole state-variable filters

[Neil Johnson]

> Are there any good references in text or online on 4-Pole
> state-variable filters?

Mmmm... the Format has a 4-pole filter that does LP/HP IIRC, but it is
made of 4 cascaded sections that are switched in either as LP or HP and
giving outputs at 6/12/18/24dB (but without frequency compensation, so the
cut-off freq falls as you move up the filter chain...)  Technically this
is not a state-variable filter, just a filter chain.

I'm currently working on an 18dB state-variable filter (LP/BP/HP at the
SAME time, unlike the Formant).  The maths gets a bit hairy, especially
for determining the feedback circuit for resonance, but not impossible.
For 24dB you just need another pole section and some trickier maths.

Why did I choose 18dB?  I wanted to use the SSM2164 quad VCA from Analog
Devices.  With one VCA used for Q I was left with three gain cells.  A
standard 12dB design would leave one left over, so I challenged myself to
design an 18dB filter just to use up the extra gain cell.  Early results
"sound"  promising.  Needs another weekend of tinkering to sort out the
feedback circuit for stable oscillation (yes it oscillates, down to a few
mHz).

I would certainly recommend the SSM2164 as a versatile quad VCA.  Another
idea I had was a combined 12dB VCF + VCA all in one (3 gain cells for VCF,
one for VCA).  Maybe something for a single-board analogue module???

Anyway, if you need any tips on maths let me know.  When my filter is done
I'll write up all the theory as well so others can see how it works.  Its
not too bad if you're familiar with s-plane math.

Good luck,
Neil

--
Neil Johnson :: Computer Laboratory :: University of Cambridge ::
http://www.njohnson.co.uk          http://www.cl.cam.ac.uk/~nej22
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