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

[Donald Tillman]

> On Dec 20, 2014, at 11:54 PM, Andrew Simper <andy at cytomic.com> wrote:
> 
> 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.

This would be the Nyle Steiner design, here:

    Voltage-tunable active filter features low, high, and bandpass modes
    Nyle Steiner
    Electronic Design, Dec 6, 1974
    http://yusynth.net/archives/ElectronicDesign/N-Steiner-VCF-1974.pdf

    A Super Simple Three-moode Simultaneous Input, Variable Resonance, Voltage Controlled Filter for Signal Processing
    Nyle Steiner
    AES Convention, Nov 1977
    http://www.ka-electronics.com/images/pdf/Steiner_Filter.pdf

> 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.


The classic example of this is the Fleischer and Tow design:

    Design Formulas for Biquad Active Filters Using Three Operation Amplifiers
    P. E. Fleischer and J. Tow
    Proceedings of the IEEE, May 1973

The F&T schematic is confusing, so you have to redraw it, spinning it one opamp counterclockwise, so it makes more sense.  And then you have to add an extra resistor to get rid of that silly bandpass dependency, and invert two signals for polarity consistency, and then you have a SVF with separate low pass, band pass, and high pass inputs.


> I've put together a technical paper
> on it here:
> 
> https://cytomic.com/files/dsp/SkfLinearTrapezoidalSin.pdf

Yours seems to be somewhat similar to the Fleischer and Tow design (with the changes I noted) but with your as+b/s+1 blocks replacing the integrators, and some tweaks to make that work.  

That's very interesting, I have not seen it done that way before.

  -- Don

--
Don Tillman
Palo Alto, California
don at till.com
http://www.till.com
650 888-9632