[sdiy] SVFs with different gains in the integrators
guy.mccusker at gmail.com
Tue Dec 15 14:24:06 CET 2020
> This simply implies that the denominator of a S-V filter changes from a normalized s^2 +(1/Q)s + 1 to s^2 + (A1/Q)s + A1A2 where the integrator gains change from 1 to A1 and A2 respectively, -1/Q is feedback VB to input, and the feedback from VL to input is -1. Just a modified 2nd-order, and the quadratic equation yields the exact new poles (hence the exact SHAPE of the frequency response) and corresponding (re-interpreted?) performance parameters. [For example, Omega-Zero moves from 1 to sqrt(A1A2) as someone here offered.] Everything should follow easily, obviously, and correctly. No magic in this - right?
I guess the interesting -- though admittedly not magical -- element of
this to me is that the Q of the transfer function you have written is
not given by the parameter called Q but by Q * sqrt(A2/A1), so the Q
of the filter is influenced by the ratio of the integrators' unity
gain frequencies as well as by the feedback from the bandpass. Andrew
Simper pointed out that this is also relevant to standard
implementations because presumably the two integrators are not
perfectly matched, though I suppose the influence of their mismatch is
not that great.
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