Some additional phase shifter questions to ponder

[Mark Hammer]

1) What is the "optimum" balance of fixed and swept stages?  We know that adding fixed phase-shift stages to a number of swept stages can add to the intensity of the effect while not requiring any additional control elements - essentially bigger bang for minimal buck.  A number of well-known many-stage phase shifters have fixed stages, such as the MXR Phase 100 and Maxon Rotary Phaser (6 swept and 4 fixed in each case), and the various Boss phasers built around the IR3109 chip (PH-2, RPH-10), and others.  The old orange Ross phaser uses a single fixed stage in the feedback loop to mimic regeneration in a 6-stage phaser, even though it is i many respects a 4-stager.  I've added a pair of fixed stages to commercial 4-stage phaser circuits with success, and Rick Holt has also incorporated fixed stages ito some of his elegant designs.

But at what point is the balance between fixed and swept stages inappropriate?  Is 4 swept and 6 fixed going to sound lousy?  Is there some maximum number of fixed stages one can use, or is there a ratio of fixed to swept stages, or is the "rule" that swept must always outnumber fixed in any sort of configuration?

2) When adding fixed stages, do they all have to provide phase shift starting at the same point, or in the same direction?  For example, one could have a quartet of fixed stages, as in the Phase 100, where the point at which 90-degrees shift is hit is dictated by the 22k/.01uf network feeding the non-inverting pin of each of the fixed stages.  OR one could have a pair of stages using a 22k/.022 network to move the starting point lower, and a second pair using the .01uf caps to add to that a bit higher up.  OR one could have a pair of fixed stages in lead mode (cap in series, resistor to ground) and another pair in lag mode (resistor in series, cap to ground), to distribute the phase shift more evenly across the spectrum.

3)  When more stages are added, where are the additional notches?  Are they added below the existing ones, or above?  I ask because I added a pair of fixed stages to a Ross/Ropez that was already sweeping very nicely, and waaayyyyyy up high.  The added stages make it sound like it doesn't sweep quite as high anymore.  One of the implications is that, when adding stages, one might wish to use slightly smaller cap values to compensate.

[frequencycentral]

Interesting points. I layed out a 4 x fixed stage PCB in 2010 and installed sockets for the caps. I hooked it up to a P90 and really found no benefit to it regardless of the cap values. The only real major win I've found with fixed stages (IMHO) is to achieve 4 stage type regen in a 2 x swept stage phaser stage (ie Causality 4).

[daverdave]

3)  When more stages are added, where are the additional notches?  Are they added below the existing ones, or above?  I ask because I added a pair of fixed stages to a Ross/Ropez that was already sweeping very nicely, and waaayyyyyy up high.  The added stages make it sound like it doesn't sweep quite as high anymore.  One of the implications is that, when adding stages, one might wish to use slightly smaller cap values to compensate.

I've been simulating phase shift networks using the common first order allpass on LTSpice, I set the cutoff of the highpass entering the non-inverting input to 1.59kHz roughly, as you'd expect, the phase shift passes through 90 degrees at this point.

What I found is that the notches appear before and after the cutoff set by the resistor and cap, with 2 stages you get a notch at the centre frequency where it passes through 180 degrees, 4 stages a peak where the in phase signals meet, with 2 nothes either side where the frequency cancels at 180 degrees and 540 degrees. 6 stages you get three notches, one at the cutoff, one below and one above.

I simulated it up to 24 stages, which produced 12 notches (well actually 13 for some reason, I'll have to think about that one). The notches are closer together near the cutoff on either side. This is due to the slope of the phase shift becoming less pronounced in the 'passband' and 'stopband' of the highpass.

I'll give changing the cutoffs a try, to simulate a sort of moving notch and fixed, the fixed should produce a notch at a fixed frequency, I'd say that if the fixed allpass stages are set to a high corner frequency then they'll attenuate the higher end, making the sweep sound as if it isn't reaching as high.

Think that's right anyhow, I might have missed a trick somewhere.

[daverdave]

Sorry, just thought I'd post this, it's the bode plot from the 24 stages mixed with the unaffected signal.
Not the best quality I'm afraid.



I simulated 6 stages with 4 stages set to 1.5kHz and 2 to 31.8Hz, heres the image:

[earthtonesaudio]

When choosing to add feedback to a simple 4-stager the sheer number of potential permutations is mind boggling:
-feedback from stage X output to Y input (16 different ways, not all of them work though)
-And any of these feedback methods can take the form of a simple resistor, or another allpass stage (lag or lead, swept or fixed).
That's just the tip of the iceberg at 80 possible feedback configurations for a "simple" phaser.

[earthtonesaudio]

Hope my last post didn't kill the mood.   

[Mark Hammer]

Not at all.  Personally, I'm just deep in cogitation about your post and dave's.

BTW, you forgot one form of feedback, which is used in the Boss AP-7, and that is to feed the phase-shifted signal all the way back to the input stage, rather than to any of the other phase-shift stages.

[earthtonesaudio]

Egad.  So any phase shift stage's output can be fed back to any input.  So for an n-stage phaser with an input mixer, but without an output mixer, we get (I think):

[(n+1)!*(n+1)!] combinations of feedback (including non-useful possibilities, such as sending the output of the first mixer back to its own input).  Four stages: 14400 permutations.

Same setup with the addition of an output mixer: 518400 permutations.  
I think it's safe to say there is some uncharted territory in phaser-land.

[frequencycentral]

I think it's safe to say there is some uncharted territory in phaser-land.

Yeah!