[sdiy] Hand-matching capacitors for filter stages

[Richie Burnett]

Hi Tom,

> So the question is - does anyone match capacitors for filters?

I honestly wouldn't bother taking time to match capacitors in a VCF. 
Variations in the capacitor values only move the real poles of the filter 
slightly.  This alters the knee point (-3dB) point for each pole of the 
filter when there is no feeback (no resonance.)  All a spread of capacitor 
values will do is make the combined knee point slightly softer and more 
gradual.  However, if you think about it, it is very soft and gradual anyway 
with no feedback.

When you add feedback to poles will group together to form oscillatory pairs 
pretty much as they would if all the capacitors were identical.  The pole 
spreading due to capacitor value variation only alters the amount of 
feedback required to achieve a particular amount of resonance.  A VCF with 
perfectly matched pole positions will self-oscillate with slightly less loop 
gain than one with its pole positions spread out.  But, you generally have a 
resonance pot to adjust this parameter by ear anyway.

Given that things like transconductance of OTAs will also have a tolerance 
and temperature coefficient, I think that matching of capacitors is not 
worth the effort in a VCF.  If you're not convinced you only have to look at 
Tim Stinchombes analysis of ladder filters.  He shows that the TB-303 ladder 
filter behaves pretty much like any other normal ladder filter regardless of 
the oversized capacitor at the bottom of the ladder.  I guess these 
topologies for VCFs were successful *because* they are tolerant of component 
spread!

-Richie,