Sloped baffle

"So the question then becomes: Doesn't the presence of that inductive component of the driver impedance (especially in the case of the tweeter) cause a deviation from first order 6 db/octave behavior? And if so, to a degree that may audibly compromise phase and time coherence? And if so, is that or can that be compensated for in other aspects of the speaker's design?"
ABSOLUTELY, I had stated earlier that a simple cap seldom produces a 6db slope for that exact reason, no speaker that I've seen shows purely resistive(other than a ribbon). In the crossover, we can only lower impedance of a driver with compensation circuitry. A simple pad in series on a tweeter will raise impedance, but also cause you to need a new crossover. All this is the difference between electrical vs acoustical crossovers, cause & effect. 6, 12, 18 or 24 db per octave crossovers on paper, often end up being larger slopes because of the natural inductance, impedance and capacitance of a driver that must be taken into consideration in the design itself. In my experience without impedance compensation work, a driver with 6 db filters are still TYPICALLY 10 to 20 degrees out of phase... Any speaker that is with + or - 15 degrees of phase for its useable response curves in my mind IS phase coherent.

Bifwynne, I'd say that the cost is substantial but fair. The vendor is located in Colorado, and he came to my home in Arizona for the calibration and installation. I don't know if there is a trial program. The DEQX corrects the room acoustics, and it also corrects the speaker, as outlined in my previous post. The unit resides between my conventional preamp and the amps, but it also has full preamp capabilities if needed. A less expensive option deletes the preamp functions.

To answer Al's rephrased question or Bruces's origional, I'll give the example of the speakers I'm working with lately. The midwoofer is an inexpensive 5" that has a fairly nasty and fairly normal breakup around 5KHz and rolls off rapidly after that. The design I'm using it in is basically a flat baffle MTM (+++) with a low crossover point of about 1500 Hz. BSC is handled separately, but we won't get into that because that gets complex. The low pass is a first order (electrical) with an inductor.

By itself, no crossover, the woofer shows 30 degrees of phase shift by 1500 Hz even though it is nowhere close to rolling off. With the crossover, it's 120 degrees at the same point and nearly 180 degrees by 3000 Hz. It's the combined acoustic slope that matters and that's measured in Hz and dB. Phase is along for the ride.

Things get a bit more complicated. To attenuate the cone breakup 5K, which would still be audible, I added a "tweeked" Zobel. By that, I mean I oversized the cap and undersized the resistor so that it falls somewhere between a filter and impedance compensation. It also comes in handy to get phase dialed in. Tried but couldn't get a notch filter to work well in this case. Got it about 20 dB down.

As some of you might have guessed, for a tweeter to cross that low, it has to be particularly rugged and there's only a few I know that capable, particularly with only a second order high pass. Didn't want the crossover that low but that's where the combination wanted to be. It's already 6 dB down by the crossover point, which gets summed back, when drivers are in phase. The tweeter, with crossover, has begun rolling off from around 5000 Hz. Another "trick" was utilized to round the knee. By the tweeter's Fs (resonant frequency) it's down 20 dB. The tweeter's phase shift from 1500 Hz to 20K, before any baffle diffraction and with crossover, is only 60 degrees. Essentially, little to no phase shift without crossover. If you're still paying attention, you might think something's wrong with my math. Shouldn't second order shift 180 degrees? For a high pass, the phase shift is caused by capacitance, not inductance.

In order to get the driver's phase aligned, I needed to invert the polarity of the tweeter. By the way, this sims out to a 45 dB reverse null at 2m, so I think it's pretty much on target. Nicer is that it's consistent over a wide vertical and horizontal range and listening distances. Gently sloped plateau on the impedance phase to +30 (inductive) degrees maximum, which by most standards, is quite good.

That's a very simple example, even for a two-way. You should see what happens with real woofers. Remember the old spinning plates act, where a guy balanced plates on poles and ran around to keep them going while he added more plates? Now, tie the poles together with strings and springs and rods and hinges and that's speakers.

Why does so much discussion center around how "perfect" 6db per octave is? There is 90 phase shift at the crossover point and we can add on electrical and mechanical impedance changes in the drivers across their frequency range. So can't we fully expect some pretty significant deviations from "perfect phase" in the performance of any speaker, even with the first order crossover?

Next week, I'm planning to do some fact finding about the DEQX device. Short of outboard active crossovers, I'm starting to get the sense that mechanical (e.g., sloped baffles) and electrical (i.e., 1st order X-overs), at best, does rough justice. I'll be back.