[sdiy] Pole-mixing, Highpass filters, and switching the first stage off

[Tom Wiltshire]

On 6 Sep 2014, at 03:37, Andrew Simper <andy at cytomic.com> wrote:
> <snip>
> It looks like the Oberheim engineers figured this was the best approach
> to double the number of responses from the 8 inputs of the multiplexer
> to 16.

Yes, I suspect this is probably the only reason for doing it this way - you can use a 8-to-1 multiplexer and a single switch from a 4066 instead of a 16-to-1 multiplexer. There's some saving of resistors too. For example;

HP1 needs taps of 1,1,0,0 with the first stage turned off. Turning the first stage on in this situation gives you BP2 - Groovy!

However, I think this benefit is somewhat overplayed. The biggest savings would come from the outputs that use all four taps, like the HP3 mode, or the Phaser mode. But these tend to be the ones for which the alternative switch position doesn't produce anything special (what Olivier calls the "leftover modes").
The clearest examples of the first-stage switching are really the LP modes, where you can have a single resistor at the second stage and get LP2 and LP1 by switching the first stage on/off, and a single resistor at the fourth stage and get LP4 and LP3 by switching the first stage on/off. But these modes only require a single resistor anyway, so the benefit in terms of circuitry saved is minimal. 

> Here are some plots I did to show the difference between a true 4 pole
> cascade (4 1 pole high pass cascaded with feedback) and a 4 pole
> generated from pole mixing:
> http://www.cytomic.com/files/dsp/cascade-hp4-vs-lp4hpxtaps.pdf

Very interesting. I don't see anything there that would put me off - like Richie said, "good enough for music".

Perhaps the most significant difference between the lp4 with summed taps and the hp4 normalised is that the peak moves *up* with increasing resonance for the lp4, whereas it moves *down* a little bit for the true hp4. A dead giveaway!

Tom