# [sdiy] Pole Mixing

Andrew Simper andy at cytomic.com
Sun Apr 11 06:34:18 CEST 2021

```Also if you want to derive the frequency response yourself you solve these
equations for hs:

0 = g (in - lp1 - k lp4) - s lp1
0 = g (lp1 - lp2) - s lp2
0 = g (lp2 - lp3) - s lp3
0 = g (lp3 - lp4) - s lp4
hs = (m0 (in - k lp4) + m1 lp1 + m2 lp2 + m3 lp3 + m4 lp4) / in

Cheers,

Andy

On Sun, 11 Apr 2021 at 12:21, Andrew Simper <andy at cytomic.com> wrote:

> Hi David,
>
> I'm not sure you've got the correct frequency response on your page. You
> may have better luck with this:
>
> (g^4 (m0 + m1 + m2 + m3 + m4) + g^3 (4 m0 + 3 m1 + 2 m2 + m3) s +  g^2 (6
> m0 + 3 m1 + m2) s^2 + g (4 m0 + m1) s^3 +  m0 s^4) /
> (g^4 (1 + k) + 4 g^3 s + 6 g^2 s^2 + 4 g s^3 + s^4)
>
> where g is the cutoff in hz, and k is the resonance feedback with 4 being
> self oscillation, and the mixing terms are as follows:
>
> m0*(in - k*lp4) + m1*lp1 + m2*lp2 + m3*lp3 + m4*lp4
>
> Note that for the xpander uses inverting stages, I've used non-inverting
> stages, so each other mixing terms needs to be negative, eg:
>
> m0, -m1, m2, -m3, m4
>
> Cheers,
>
> Andy
>
> On Fri, 9 Apr 2021 at 06:24, David Moylan via Synth-diy <
> synth-diy at synth-diy.org> wrote:
>
>> Hi All.  I banged together a little web app to play around with filter
>> pole mixing, of the Oberheim Xpander type.  You can mix poles in varying
>> amounts and see the output magnitude shape as well as the transfer
>> function.  Y axis is Db and X axis is log scale based on normalized
>> frequency (so basically 1 equals the cutoff frequency).  Haven't done
>> phase plot yet.
>>
>> If you have an interest in this sort of thing check it out:
>>
>> https://expeditionelectronics.com/Diy/Polemixing
>>
>> Cheers.
>>
>> --
>> David Moylan
>> Expedition Electronics
>>
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>
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