[sdiy] Sallen Key with input mixing to generate all shapes

[Andrew Simper]

Hey guys,

I've noticed many Sallen Key synth filters can generate different
responses by sticking the input into various points of the circuit,
but they only ever deliver a 1 pole high pass, and a very weak notch.
I've worked out the theory for generating all the same responses as
you can get by mixing the outputs of an State Variable, but instead
mixing the inputs to a Sallen Key. I've put together a technical paper
on it here:

https://cytomic.com/files/dsp/SkfLinearTrapezoidalSin.pdf

and I've sketched the basic structure of what is going on here (taking
an MS20 v2 type OTA Sallen Key as the basis):

www.cytomic.com/files/dsp/SkfInputMixing.jpg

the important voltages are:

vamp1 = (m0*v0) - (m1*v0 + v1)
vamp2 = (m1*v0 + v1) - (v2)
vcap1 = (v1) - (res*v2 + m2*(-v0))
vcap2 = (v2) - (m2*v0)

where m0 = low mix, m1 = band mix and m2 = high mix

Also for those interested in a digital implementation I've also
included in the paper is also a trapezoidal integrated linear circuit
model use state space increments and high precision coefficient
calculation.

Andy