[sdiy] SVFs with different gains in the integrators

[Bernard Arthur Hutchins, Jr]

As very recently posted, an analog integrator SEEMS to have a transfer function T(s) = A/sRC where RC is a time constant and A is a SUPPOSED ”gain”, BUT it is a one-parameter term (A/RC)(1/s) – an unending/unbending 45 degree slope which can be thought of as varying up/down (gain) OR left/right (frequency):


http://electronotes.netfirms.com/AN353.pdf


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?


-Bernie




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