What would you get by combining lead and lag allpass stages?

[Mark Hammer]

We're all quite familiar with allpass filter stages used for phase shifters.  The one we're most famililar with is the "lead" configuration, in which a highpass filter feeds the non-inverting input of an op-amp.  This can provide up to 90 degrees of phase shift, increasing from 0 to 90, as one approaches the asymptote dictated by the value of the capacitor and resistance to ground (or other reference point).  A FET or photocell is used to vary the resistance to ground to change where the maximum phase shift is introduced in each stage.

The other configuration is a "lag" allpass stage, in which the positions of the capacitor and variable resistance are switched around.  This provides for up to 90 degrees of phase shift for whatever is below the corner frequency, and reducing as one gets higher.

Because the value of a JFET's R is easier to control (as well as reduce distortion) when it goes to ground, and because the notches produced are more appealing when they are inserted into the harmonic content, as opposed to wiping out fundamentals, the topology we typically see is the "lead" form.

If one uses LDRs as the control element, rather than JFETs, though, or if one uses fixed phase-shift stages (i.e., a simple fixed resistor instead of a variable element), lag stages can also be used.

What I have never seen is something that employs BOTH lead and lag stages, such that total phase shift is more broadly distributed across the spectrum, instead of always having a maxima above some frequency.  I don't really have time to do the experiment at the moment, or the PSpice chops to simulate it.  So I was wondering if some of you more technically savvy types would have either the experience or knowledge or time to say what the result would be of combining lead and lag allpass forms in the same series of allpass stages.  I'll assume the cap and resistance values would be chosen prudently.  For instance, could their combination yield a different spacing of any notches produced?

I'm a curious little puppy.

[iainpunk]

This can provide up to 90 degrees of phase shift

a single first order allpass can flip 180 degrees.
basically the only difference between leading and lagging is if the frequency's below or above the break freq. are flipped. will sonically make no difference than adding an inverter.

cheers

[DrAlx]

The second circuit gives the inverse of the first. In other words, if you put the output of the first through a unity gain inverter you will get the exact same output as from the second circuit. And vice versa of course.

I have always found the lead/lag terminology misleading especially for low frequency signals near DC.
I call the bottom circuit phase lag (with zero lag at DC and 180 degree lag at infinity Hz), and I call the top circuit inverting phase lag.

The point being that for a signal near DC, the bottom circuit gives you an output waveform that looks like what you put in, just slightly delayed in time, hence "lag". With the top circuit, you get the exact same small time delay as the bottom circuit, but then the entire signal is also inverted. To think of the output waveform from the top circuit as somehow being a future version of the input (hence "lead") is what I think is misleading, pardon the pun. Those are capacitors, not flux capacitors

[Mark Hammer]

You'll get no quarrel from me regarding the confusing nature of the names for each type.  I had to Google around a bit to clarify them in the first place.

But let us say we had two "lead" stages whose lowest maxima would be 300hz (moving upwards from there as the resistance to ground gets lower), and two more "lag" stages with the same maxima at its highest point.  So in theory, we now have 360 degrees of phase shift (or 720 if one wants to calculate it that way) across the entire spectrum, from as close to DC as the circuit gets, up to the highest point in the overall passband.

The question becomes, I guess, does there have to be a minimum OR maximum frequency where the phase shift is applied in order for the effect to be produced?

[iainpunk]

probably better to keep the notches in the ''midrange'' between 300 and 3k.

a less-related, but still phaser question, how does a 4 stage phaser sound if you have one static allpass, and the 3 other allpass filters are controlled by a 3 output LFO with 120 degree out of phase pseudo-sinus waves...i wonder how that sounds...

cheers

[ElectricDruid]

I've always referred to them as highpass-based and lowpass-based all pass stages. At least like that I don't get them confused, since it's obvious.

My gut feeling is that this makes no difference, except to the final mixer that you use to get the notches.

In terms of the phase shift, it's the 90 degree point that you sweep up and down, and that's the same in both circuits. Otherwise it either goes from no-flip to flipped, or from flipped to no-flip. That makes a difference as to whether you're going to need a simple mixer or a differential mixer to add the dry signal back in (have we got a stray inversion in the wet path kicking around, basically) but otherwise doesn't make any odds.

This is more obvious if you think about the stages in pairs (which is after all what we need to make a notch). For a pair of LP stages you get a signal which is no-flip x no-flip at DC, via 180 degree shifted in the middle, up to flipped x flipped at the top. For the high pass version, it's flipped x flipped at DC, 180 degree shifted in the middle, and no-flip x no-flip at the top. Since 1 x1 = 1 and -1 x -1 = 1 as well, these are identical.
Mixing them up ("mixed doubles, anyone?") would only leave you with a stray inversion.