[sdiy] 4-pole SVF theory

[Neil Johnson]

Hi Tom,

> Can anyone point me at some good resources for state variable filter theory?

Books or online?  I prefer books, and I have quite a few.  Best to
find one that *you* can read, an author who's style fits with your
own.  One book I keep going back to is

Principles of Active Network Synthesis and Design
G. Daryanani

Long out of print but you can find it around the net. (google is your
friend, and 4shared provides).  if you have access, what could be the
founding paper on SVF is:

Kerwin, Huelsman, Newcomb: State-Variable Synthesis for Insensitive
Integrated Circuit Transfer Functions, IEEE J. Solid-State Circuits,
vol. SC-2, no. 3, Sept 1967.

They only show a 2-pole realisation, but the theory extends to as many
poles as you want.

> I've spent a long time playing with the classic 2-pole, 12dB oct SVF filter,
> and I think I get that now. So I want to move along. How do I convert it
> into a 4-pole filter? (without just sticking a second one on the end of the
> first one!)

You don't.  You design a 4-pole filter using the same basic principles
as for the 2-pole version.  The Riley paper that David pointed to
shows the basic structure.  If you can convert the diagram into a
transfer function in (s) then you're well on your way to designing a
4-pole (or 3-pole, 5-pole, 6-pole, etc) filter.

> Presumably there are good reasons why you don't see lots of 4-pole SVF
> filters around, otherwise I'd have thought it'd be the killer synth filter
> - LP, HP, BP outputs, independent Q control - cool, no? So what's wrong with
> it?

Cost is one.  Its the reason I went for 3-pole so that the entire
filter fits into a single SSM2164.  If I had gone for 4-pole then I'd
need some other OTA for the damping circuit.  Or you could do a 2-pole
filter with Q *and* a VCA as well.

Another is what is called sensitivity -- how sensitive the design is
to component tolerances.  The more stages you have stacked up then
generally the more sensitive the circuit is to component tolerances,
which will degrade the performance of the filter (e.g., the cutoff may
not be as sharp as you intended as the poles and zeroes aren't in
exactly the places they should be).

> Pleez, help me edukate meself!

First, learn to spell!

Cheers,
Neil
-- 
http://www.njohnson.co.uk