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

[Ian Fritz]

Andrew --

Cool stuff -- thanks for putting it up.  I have a third order filter (the 
Threeler) that uses the same Sallen Key-like blocks.  I get various 
responses by switching the stages between LP and HP and taking the outputs 
from all three stages.  So filter orders 1, 2, and 3, both HP and LP are 
available, along with a variety of bandpass responses.  Several people have 
said it is the best filter ever!

Ian
http://home.comcast.net/~ijfritz/MiscProj/Threeler.htm


At 12:54 AM 12/21/2014, Andrew Simper wrote:
>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
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