'unbalanced' or 'unmatched' sallen-key filter

[Eddododo]

I get that with, say, a linkwitz-riley filter/crossover/whatever, that mismatched components and therefore frequencies will cause trouble with the steep Q taking out 'chunks' between corner frequencies.

But with something like a sallen-key, if you have two independent pots to control the frequency sweep, instead of one dual-ganged pot, could you feasibly get some nuance and subtleties of tone out of it? Like a high-pass filter that rolls off the lows gently and then and the second frequency setting (lower) the slope increases, slamming the lowest lows out.

Is there a phase component to this unbalancing that makes this unfavorable?
Will there be a wierd/unpredictable ripple in the passed band that makes it unusable?

Or in other words, is there a reason NOT to do this?

[R.G.]

I get that with, say, a linkwitz-riley filter/crossover/whatever, that mismatched components and therefore frequencies will cause trouble with the steep Q taking out 'chunks' between corner frequencies.

But with something like a sallen-key, if you have two independent pots to control the frequency sweep, instead of one dual-ganged pot, could you feasibly get some nuance and subtleties of tone out of it? Like a high-pass filter that rolls off the lows gently and then and the second frequency setting (lower) the slope increases, slamming the lowest lows out.

You are of course, free to implement any filters in any way you like. However, there is considerable evidence that the universe is underpinned by math, and may in fact BE the equations that we are trying to discover. All of the named filter setups - Sallen-Key, Butterworth, Cauer, Yada, Yada - are solutions to the S-plane equations that describe a certain kind of rolloff. The need for perfectly matched components meeting these conditions is to get the filter you actually make with resistors, caps, ICs and so on to match the frequency and rolloff you wanted.

All of the filter responses that exist are points in a continuum of possible filters with different ratios between the components that are "matched" in named filters. If the real component values are not what the conditions said to be, then the real filter response will have diffent damping, passband ripple, falloff skirts, ultimate attenuation, and ripple in the stop band than you were intended. That's what the "matched" does for you.

The math gets even more complicated when you try to do a crossover, which is what you are describing. Getting a lowpass and a high pass to butt together nicely with no dropouts or peaks in output power as you cross from one to the other is more difficult that getting the highpass or lowpass filters to have the right responses to start with. So an error in either filter messes up the crossover region if flatness and smooth response is something you want.

It's really a question of how picky you are. If you're a hifi tweako, you won't stand for any crossover at all, and will demand full range *speakers* to avoid them. Good luck with that. If you're a guitarist, odd notches and bumps are part of the landscape, so hey, could sound GREAT, at least to some people and some values of 'great'.

But no, if you want to define a filter response ahead of time, and get out what you want, using components that don't meet the filter alignment math won't give you what you were trying to get.

Is there a phase component to this unbalancing that makes this unfavorable?

(1) getting a variation in frequency response requires using reactive elements (inductors and/or caps), as pure resistors are not frequency selective at all.
(2) there is an unavoidable phase shift associated with reactive components that is related to their frequency selectivity in concert with resistors. There is no good way to get around this, so all filters that change amplitude response have a changing frequency response as their amplitude changes. It's written into the math underpinning of the universe.
(3) unbalancing the alignment or component ratios just changes the predictability of the filter response, not whether or not you're getting phase and amplitude funnies
(4) whether or not this is unfavorable depends on YOUR ears

Will there be a wierd/unpredictable ripple in the passed band that makes it unusable?

The ripple in the passband, stop band, and damping will be different from that predicted by the alignment you were closest to. Whether or not this is unusable is a matter of taste, and as you know, there can be no disagreement about matters of taste.

[PRR]

> a sallen-key, if you have two independent pots to control the frequency sweep, instead of one dual-ganged pot, could you feasibly get

Re-iterating R.G.'s broad survey.....

"Two pots" probably implies a 2-pole filter.

A 2-pole won't have ripple like on a lake. Just one bump (or not).

I *think* these are all the same, whether values are "ideal" or "whatever". Plot response curves for very-high and very-low filter Q. I think all 2-poles will fall in this range and mostly track the "ideal" curve for some Q. (It is possible that two very offset poles gives a curve that is more like 1-pole down to some great attenuation, and then steepens to 2-pole.)

So what you are asking: I think you may as well stay with the ganged-pot, but add a Q pot to dial the bump/slump shape. With the unity-gain Sallen-Key, you design for Q of say 2 or 3, then run a low-value pot across the output and use that to dial-down the kick-back which gives the hi-Q bump. This plus your frequency should give all practical 2-pole curves from bump to a very slow slump.

When you get into higher-order filters...

You either have a *specific* curve-shape you need (just do math), or you cascade a bunch of 2-pole filters with adjustable F and Q and diddle until happy (or lost).

AFAIK, "all" higher-order filters can be composed of 2-pole filters. And in practice, they mostly are. A SSB filter for carrier telephony was 20 or 30 L-C pairs in a box the size of a cigarette carton. Later implementations were 2-pole Sallen-Key or similar cascaded with proper F and Q (often a 3rd pole is snuck between 2-pole elements to reduce opamp count). All the classic radio and most radar filters are 2-pole L-C filters lined-up to give desired effect. There's a few tricks-- center-tapping a coil to serve two 2-poles with fewer parts, the pi-tee connection used to push 'scopes faster than the circuits they will measure, coupled-pairs to flat-top an AM radio IF with fewer cans.

[Digital Larry]

I find this topic fascinating.   Part of that is due to the fact that I spend most of my audio twiddling time now on the digital side of the aisle.  Getting a different frequency response there is not much more than calculating a new set of coefficients.  No ordering parts, coming to grips with component values and tolerances, wondering if the gain-bandwidth product of such and such an op-amp will give me stabilty, and especially NO SOLDERING. 

You think it would be great huh?  But then you have to come to grips with the implementation you're using.  I'm fairly well entrenched with the Spin FV-1 which has its own set of limitations.  One of them I came across recently came from the desire to use a control knob input to sweep frequencies and Q.  If you do your bilinear transforms correctly, you'll find out that you need to calculate a sin() function, which the FV-1 doesn't support.  You could approximate it with the first few terms of a Taylor series expansion, but watch the instruction count!

Then I read a few more notes from the chip's designer.  He talks about musical results being more important than mathematical purity, and oh by the way, here's a 2-pole state variable structure that does let you use the control inputs directly to adjust frequency and Q.

After that, I have tried implementing some dynamic effects such as an envelope controlled filter.  You can do all sorts of things with the control signal to shift its curve and adjust the start and stop points.  But it's next to impossible to predict ahead of time what is going to float one's personal sonic boat.  So then one starts getting into experimentation, just brute force changing coefficients without wondering or worrying about the exact mathematical ramifications.

What I was doing last night was trying to get a Frank Zappa inspired sound that he got by using two Dynaflangers set to sweep in opposite directions following the input envelope, but high passed, so that it followed the envelope of the high frequency content to give a more "pillowy" sound.   Now it's a little hard to test here at home after the kids go to bed - I don't think Frank ever played at less than 130 dB.  However I can tell that (using his early 80's tone as a guide) that he really liked his flanger resonance WAY UP.  And while I can hear the flangers sweeping in response to the inputs, ah... (cough) it still doesn't sound quite like Frank.  Anyway I can still experiment without soldering, but at the same time I am not quite certain which direction to go with it.  Baby steps, Larry.

[Eddododo]

Thanks for the info as always.  Hard to tell if I feel more sure or lost,  subsequently     building blocks!

[R.G.]

"Lost" would be appropriate. Unlike some parts of electronics, good filter design really does require diving down into the equations to get real answers.  It's one of those places where the the paste-and-crayons explanations start to break down. At least it was for me. A very simple glossing over is OK, and necessary for a mental picture of what is happening, but the details, and especially getting out what you wanted at the start requires some work.

I highly recommend "The Active Filter Cookbook" by Don Lancaster. It's a whole book of a semitechnical glossing over that's about as compact as I've seen active filters taught that's not just paste and crayons. You're very unlikely to get an understanding of this with whatever someone is willing to type on an internet forum reply box.