[sdiy] multimode matrix filter question

David G. Dixon dixon at interchange.ubc.ca
Wed Oct 20 18:22:37 CEST 2010

> Have you spiced the various filter modes including the gain variability
> that will be present due to component tolerances?  I ran through a similar
> exercise years ago, and the frequency response is
> highly sensitive to component variation.

Yes, and I have also developed a mathematical model of the general case, and
put real resistor values in.  Certainly, some of the modes are quite
sensitive, particularly if the integers are large, but generally only when
resonance is increased.  For example, the 4P allpass mode has the following
gain ratios: {A,B,C,D,E} = {1,8,24,32,16}, and should give a perfectly flat
response with increasing resonance all the way up to self-oscillation.
Presuming that the "1" resistor is fixed (at, say, 100k), then there are no
standard 1% values to produce the other factors exactly.  For example, for
the "32" resistor, the closest standard values would be 3.09k and 3.16k.  It
would seem that one should be as good (or as bad) as the other, but in fact
it depends on which resistors are selected for the other factors.  For
example, I have found that the following combination of standard 1% values
should give the desired response very closely: {100k, 12.4k, 4.12k, 3.09k,
6.19k}.  However, with that particular combination, replacing the 3.09k
resistor with 3.16k kills the response at high resonance.

I can't really comment on opamp biases, offsets, and other tolerance factors
at this point.  Again, I think a lot of this will boil down to "suck it and
see".  However, hand-selection of the resistor values for some of the modes
will be critical.

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