I don't get over here much but I just dropped by. I like what you're doing very much. I hope I'm not out of line to drop a few ideas here.
I've been making DI-matched two-way speakers like this for well over a decade, nearer to two decades. I like this approach and I applaud you guys and your efforts.
Points in no particular order:
1.
Tweeter compensation
The R1/R2/C1 compensation circuit I use does two things. It gives 6dB/octave HF augmentation after an initial shelf of flat response. The way it gets that initial shelf is by providing specific damping to the high-pass filter. It's actually slightly underdamped, which raises the bottom end a little. The end result is the curve we want - a conjugate of the driver's power response.
Tweeter Compensation
2.
Woofer directivity
Woofer directivity collapses generally as a function of wavelength and radiator diamater. But the radiator isn't flat so cone profile (including dust cap) plays a part too. It also is smaller than the frame, i.e. 15" woofers have diameter of 12-13" or so. So in the end, directivity is a collapsing cone but you cannot assume a 12" midwoofer will have the directivity of a 12" flat round radiator. It would be closer to that of an 9-10" round radiator.
3.
Source locations and crossover topology
Tweeter horns (or waveguides, if you prefer the name) have a length that sets the source location back. This represents a fixed delay. Direct radiating woofers are also set back some fixed amount, by virtue of the fact they are cone shaped. Another fixed delay.
Then there are reactive offsets. The woofer's voice coil inductance, cone mass and driver suspension create a changing reactance that makes a changing acoustic phase. The cabinet has an impact too, but not significant at crossover frequencies for a DI-matched two-way. Horns, whether conical CD or any other have a reactive element in addition to diaphragm mass and voice coil inductance. The horn tends to make the system less reactive at high frequencies, but at low frequencies it usually has some ripples.
All of this has to come together in the crossover for summing to be flat. In my experience, the woofer and tweeter in a system like this usually work better with an asymmetrical crossover, one with different slopes or different apparent crossover points, or both. Just by looking at the physical offsets, many conclude that the woofer should be crossed over with a higher slope to compensate for the longer path length of the horn. In my experience, this is rarely the case because a horn of the right size to DI match isn't that much longer than the distance to the woofer's acoustic center, and the woofer has electro-mechanical characteristics that delay it more.
For example, my four Pi loudspeaker has 3rd order slopes for both woofer and tweeter, but the woofer has values that roll it off around 1.3kHz and the tweeter has values that bring it in a little later, around 1.6kHz. A second order crossover on the woofer works pretty well too. Fourth order is OK, but insertion loss adds up. Third/third and 1.3kHz and 1.6kHz works best for me. See the response curve at the link below:
four Pi performance data
(four Pi speaker with JBL 2226 and B&C DE250 on H290 horn flare; Optional components can be Eminence Omega 15 and/or Eminence PSD2002)
4.
Vertical directivity, round horns verses rectangular horns
When a tweeter is placed on the baffle above the woofer, lobes form above and below the front axis. Depending on the position, the lobes will generally be somewhere between 20 and 25 degrees or so. This makes the maximum vertical coverage angle be 40 t0 50 degrees before the nulls cause non-uniform response. That's why I've always championed the use of rectangular horns for DI matched speakers. You can match the horizontal pattern around 90 degrees, which is a nice spread. The vertical pattern will be limited by the null angle, so it makes sense to mate a horn with that vertical pattern, generally 40 or 50 degrees.
Coverage of DI matched speakers
If you use a 90 degree axisymmetrical horn, the pattern narrows sharply in the vertical through the crossover region and then widens back up above it. The off-axis response shows a sharp dip in the crossover region. To avoid this, it always seemed to me to be a better idea to use a horn with vertical pattern that matches the null angle. Small horns don't generally have much pattern control at low frequencies but in this case, the null angles tend to punctuate pattern cutoff. Some (many) rooms have lively ceiling reflections too, so a narrow vertical pattern is a benefit. Clap your hands and listen for the ping from the ceiling. A narrow verical pattern helps reduce this.
]
:
