# [sdiy] Pole Mixing

David Moylan dave at expeditionelectronics.com
Sun Apr 11 14:39:03 CEST 2021

```Sorry, meant to say "I'll verify with" David Dixon's spreadsheet.

On 4/11/21 8:34 AM, David Moylan via Synth-diy wrote:
> A bit hard to follow here, Andrew. Your main transfer function looks
> the same to mine if g=1, except that you have the k term included in
> the denominator but not the numerator.  In general, my denominator
> looks like yours with the k term, and in the numerator the feedback
> only changes the term on s^0 which goes from
>
> a - b + c - d + e;
>
> to
>
> (a * (1 - k)) - b + c - d + e;
>
> David Dixon shared his Excel spreadsheet with me, so verify with that
> as well.
>
> Dave
>
>
> On 4/11/21 12:21 AM, Andrew Simper 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 <mailto: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
>>     <https://expeditionelectronics.com/Diy/Polemixing>
>>
>>     Cheers.
>>
>>     --
>>     David Moylan
>>     Expedition Electronics
>>
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>
> --
> David Moylan
> Expedition Electronics
>
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--
David Moylan
Expedition Electronics