[sdiy] Sallen-Key [was: Re: Digital pots as the gain element in a filter]

[Tom Wiltshire]

On 6 Jul 2011, at 01:58, <lanterma at ece.gatech.edu> <lanterma at ece.gatech.edu> wrote:

> On Jul 5, 2011, at 10:09 AM, Tom Wiltshire wrote:
> 
>> I've used the Sallen-Key design loads of times, for anti-alising filters and such like, but it wouldn't have been my first choice for a synth filter since the cutoff and Q are so mixed up together. Presumably he untangles that in the code somewhere.
> 
> They're untangled if you keep the resistor values the same - i.e. if you make them your variable element, but raise or lower the effective resistance of both equally. In that case you can control the Q with the amount of feedback. The Buchla LPGs and the Korg MS-20 use this approach. Although, the MS-20 isn't strictly an original Sallen-Key, because there's an added buffer; I've been calling it a "Bach" variation, as in some dude I found cited in some paper, not J.S. or any of his many relatives.
> 
> - Aaron

Can I ask you a bit more about this, Aaron?

In the following paper:

	http://focus.ti.com.cn/cn/lit/an/sloa024b/sloa024b.pdf

Section 3.4 (bottom of page 5) gives equations for an equal-components version of the Sallen-Key filter, and says that in this situation, the Fc and Q are independent (yay!).

The equations given are:

	Fc = 1 / (2.Pi.R.C)
	Q = 1 / (3 - K)

Now, K I can't find a nearby reference too. It's mentioned earlier on in relation to the gain (back on page 4)

	K = 1 + R4/R3, where R4 and R3 are the gain resistors providing feedback to the -ve input.

Is this what you meant? In this equal components version, does the Q only depend on the gain? Presumably, altering the gain also...umm...alters the gain? By which I mean passband gain.

If this is right, it's still not entirely useful as a synth filter. You get to choose - quiet and no resonance, or loud and resonant, but you can't have it all ways. I suppose this can be compensated, but that demands another control element, which reduces the benefit somewhat.

Thanks,
Tom




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