Tweeter Crossover Circuit We'll the crossover design began it's life as a electrical third-order butterworth at 2,000 hz. However, from my first listening period, I could tell all was not right. They had a very perceptable harshness which was noticable at all but low volumes. Upon careful examination, I found that the issue was driver overlap. See, the woofer responds upwards to 4000 hz, while the tweeter begins to roll-off at 2,000 hz. This means with an electrical third order, acoustically it's more a third/fourth or third/fifth. So I went back to the drawing board and crafted up a second order filter for the tweeter. Now the roll-offs should match, third/third. Here is a jpeg-sketch of the tweeter's first x-over.  Here is the improved second order. Okay so I sat down to another listening session only to find that they sounded very midrange forward, not harsh mind you, but like a crispness was missing. Once again, I returned to the drawing board. After almost six hours of hard thought and numerous cups of coffee, I had the answer. It was so simple it that I felt stupid after it's discovery. 
 

The Resultant -3 Decibel Slope Problem A third order filter meets at a point three decibels below the reference level, now a second order meets six decibels below the reference level. What I was hearing was a -3 decibel terminated slope from 2,000 hz to 4,000 hz. Now many speakers have a three decibel dip in the area and sound just fine. However, they have a gentle slope, this slope is abruptly terminated by the woofer's full output at 2,000 hz. This is where I first discovered the law that states: For every correction you make to an electrical crossover, another problem of lesser effect will emerge. You can end up with an excellent crossover, just you have to be willing to settle in some manner. This is exactly why most designers will take a "near perfect" driver with a flat response so as to avoid this area of give and take. So my next step was to simply remove the -3db attentuation ciruit from the crossover. But see the above law, this was bound to generate another problem of lesser effect. It sure did. Above the slope the tweeter was +3db above the reference level of 87 db. The speaker sounded bright and rather obnoxious. So I had to develop a circuit to remove the slopes effect. It ended up as a simple LR circuit in series with the crossoover. Here is the revised crossover.  Now the speaker sounded relaxed and natural. It was slightly bright, but that has more to do with my earlier choices in crossover design with the diffraction loss step.  Now we can discuss the woofer's circuit. 

Midbass Crossover Circuit This was a breeze in comparison to the tweeter's circuit. In fact, it remained unchanged throughout the entire crossover refinement process. The only point of issue with it's design is the diffraction compensation circuit. I only choose to use a -3 decibel step filter, not a -6 like any textbook would tell you. I cite room-effect as my reasoning for not using a full -6db step. Since the speaker's are designed to by placed one to two feet from a wall, they are truly radiating into a quasi-half space. Here is a diagram to help with my explanation, it is a top view of a loudspeaker placed slightly off the wall.  Note the lengths x and y on the diagram. Full diffraction loss occurs at the frequency with a quarter wavelength equal to y. You can use this equation.  F6 = 3375/x (where x is in inches) When x is a short distance (say 12-18 inches), diffraction loss will be replaced by the well-known wall-dip effect. This manifests itself as a -3 decibel dip between 100 and 300 hz. This is why I choose to use a -3 decibel step instead of a full -6. Here is the first circuit. It has a diffraction loss RL, a standard butterworth third order filter at 2,000 hz and impedance compensation. 

The Final Low-pass Circuit The first x-over sounded good, but was subject to a hollowness, probably caused by the large phase variance of the circuit itself. So, citing the law that less is more with crossovers, I adjusted the circuit to it's final form. Here it is...

Now the phase difference between woofer and tweeter at 2,000 hz approximated 90 degrees. This is required for a two -3db outputs to sum flat. With the previous circuit, it was closer to 45 degrees, which would explain why the speaker sounded agressive, since the two outputs would sum closers to +2db at 2,000 hz.

Design Notes With the final crossover, the prestige sounds slightly forward, but over all very neutral. When placed near to the rear wall, (offset 6-18") it gets it's required bass boost and sounds very full. Experimentation is needed to determine the appropriate distance, too close sounds dull, and too far sounds thin.