[sdiy] Obtaining Bandpass and High-Pass Functions From A Four-Pole Low-Pass

Andrew Simper andy at cytomic.com
Tue Oct 16 03:36:11 CEST 2018

You can generate a HP4 from a LP4 and an allpass. You can also generate a
HP4 from 5 taps of a 4 pole cascade, any form of cascade can be turned into
any other response. You need input + feedback, and then the 1st, 2nd, 3rd,
and 4th stage outputs. So you can make a bandpass core from HP1 -> HP1 ->
LP1 -> LP1, and then turn that into LP4, HP4 etc. The theory around this is
pretty simple, but I don't know exactly when it was first "discovered".

The Xpander compromised on some of the 4 pole modes because of the filter
chip they used. The resonance gain and summing with the input happened
inside the chip, so they had to use a cool trick to get that summed signal
outside the chip. They shorted the first capacitor to ground, and switched
the low pass of the first stage to a fixed gain (from memory!). So they
were only left with a 3 pole filter, had to run the self oscillation
calibration again since it needs more gain in 3 pole mode to self
oscillate, so they could only generate a 3 pole high pass.


On Mon, 15 Oct 2018 at 17:52, mark verbos <markverbos at gmail.com> wrote:

> Hallo,
> A while back there was talk about getting a hipass response using
> cancellation of a lopass filter. I was surprised to find out that you
> cannot simply cancel a 4 pole lopass to get a 4 pole hipass. In fact, I
> still can’t really understand why. But, I was reading Electronotes about
> something unrelated and I discovered an article about just this subject.
> In Electronotes #85 there is a technique for getting a 4 pole hipass from
> a 4 pole lopass by mixing all 4 pole outputs. I still don’t really
> understand the math, but it is proven in this article. As far as I can see,
> the Oberheim Xpander filter doesn’t ever get a 4 pole hipass. So, this may
> be the only implementation of one using pole mixing.
> Mark
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