ASM1 filter self oscillation

[Magnus Danielson]

Hi Gene and all the rest!

>      State-variable filters are notoriously unstable in the high-Q regions. 
>      I'm not exactly sure what the engineering reasons for this are, but it 
>      may have something to do with the fact that the state-variable goes 
>      into a higher-Q condition when feedback is *reduced*, but the 4-pole 
>      (cascaded integrator) filter goes into a higher-Q condition when 
>      feedback is *increased*.

Your rigth in a way.... but:

For a 2-pole statevariable you usually control the Q value by adjusting the
feedback from the first interator while keeping the feedback from the second
integrator at a fixed position. This has the advantage that you are in fact
adjusting the distance of the poles from the jw axis in a fully linear manor.
This means that a small feedback will give a small distance which means that 
the
filter is close to feedback. Greater feedback will increese the distance and
this makes the filter more damped/flat.
You can also adjust the feedback from the second integrator but this will have
a quite diffrent effect.

To make it a little clearer I will put it in a small formula. If b1 is the
feedback from the first integrator and b2 is the feedback from the second
intergrator will the summer output (HP) become

	                2
	               s
	H(s) = ------------------
	        2   b1       b2
	       s  - -- s - ------
	            RC     (RC)^2

	           b1
	sigmap = - --
	           RC

	     sqrt(-b2)
	rp = ---------
	        RC

	          1        -4b2 - b1^2
	omegap = -- sqrt ( ----------- )
	         RC             4

	    sqrt(-b2)
	Q = ---------
	        b1

The integrator constants RC will nicely scale the filter up and down as 
expected. The Q value is increesing as b1 is decreesing. Q is increesing when
b2 is increesing. Note that the b2 feedback must be negative for stability.

So, you can make a 2-pole state-variable have the same kind of feedback pot
action as an "traditional" 4-pole filter can. From a pure filter point of
view this kind of feedback is a bit uggly, but if it is what you want you may
have it.

Does that clears up the uncertainties Gene?

Note:
If integrators with inverse output is used then there is a few signchanges 
needed here and there.

>      The fact that the state-variable needs more feedback for less Q means 
>      that you can add a non-linear circuit that bypasses the Q pot, so that 
>      if the level of the bandpass output exceeds a certain level, then more 
>      feedback gets added, thereby reducing the Q a little. That's what's in 
>      the ASM-1 filter, copied straight out of the Oberheim SEM schematic. 
>      Some component value experimentation in that little circuit may be 
>      worthwhile.
>      
>      Since the 4-pole filter needs more feedback to self-oscillate, its Q 
>      pot acts like a feedback control on a tape echo. In other words, if 
>      the feedback is a tiny bit less than unity, the oscillation will 
>      eventually die away, but if the feedback is slightly more than unity, 
>      the oscillation will start to "run away". Unlike tape echo (which will 
>      deteriorate into VU-meter-crunching distorted echos), the 4-pole 
>      filter will tend to distort in the first integrator (the first pole), 
>      but the next three stages will round this off to a nice sine shape and 
>      the oscillation will maintain itself as a well-containted sine wave. 
>      Therefore you can set the resonance pot to a setting slightly over 
>      unity gain and have a stable sine wave oscillator.
>      
>      In the state variable filter, however, the filter's natural mode of 
>      operation (without any feedback) is crazy distorted self-oscillation. 
>      Feedback is used to "tone down" this out-of-control behavior, but 
>      right around the point of nice sine-waviness the Q pot is at such a 
>      low setting that the feedback signal is real tiny, and may be 
>      influenced by noise factors. I'm guessing here. I think that there are 
>      also some phase-shift versus frequency issues at work here as well - 
>      the ASM has some phase compensation capacitors at the 3080 inputs to 
>      combat these effects (per Electronotes) but alas it's really just a 
>      band-aid rather than a cure.

It all depends on how you apply feedback. If you want to go close to the
selfoscillating case you will have problems almost any way you do it, it's in
the nature of differential equations and not in the structure. If you don't
apply the minimal necessary feedback for a state-variable you have shown your
own lack of knowledge rather than the structures fault. The state-variable
design has been used with great success in several fullparametric EQs including
designs from Klark-Technish and TC Electronics.

>      An analogy could be to compare the state-variable filter to those new 
>      jet figher prototypes that are inherently unstable but use a computer 
>      fly-by-wire system to keep them from flipping out of control at any 
>      moment. The performance is very twitchy and quick, but within safe 
>      margins if the proper feedback is kept. As the feedback is reduced, 
>      the system becomes unstable.

The analogy is quite good, cause in the jet fighter (or rather, any airplane)
case you have earlier designed the system so that it inherentsly has the 
stability due to feedback is in the mechanical design but in modern designs
(including the Swedish JAS-39 Gripen which have showed a few designflaws but is
shaping up nowdays... many jokes around... no one killed even if there's been
a few chrashes) is the mechanical feedback moved over to a computer to ensure
stability. A similar description can also be used to describe the difference to
front and back driven cars... front drive cars have more stability due to
mechanical design. Normally have the poor driver act as the stabilizing 
feedback
processor... It will be interesting to see what modern DSP and individual wheel
force and steering will do to cars... there are people working on it.

The lesson is really, unless you have spent your time in good engineering and
trying to ensure control over stability you will sooner or later suffer
greatly for it.

Understanding the full concept of stability does also include some less 
apparent cases. Here's one example on how things can get wrong: In a 
commercial speaker
crossover filter they had also installed a few simple fixed EQs (just putting
them there is wrong, but that's another issue). I got one box onto my labbench
with a note that they heard "digital noise" (this is a analogue filter).
So, I started to measure the filter here and there and found that the signal
occured before the filter section... isolated it down to one of the EQs and 
then
found the reason: They had forgot to solder the ground side of an resistor 
which
caused the EQ to get a high amplification and turned it into a squarewave 
oscillator... one soldering and it was gone.

Put the poles on the rigth side for a while :)
Magnus