The CLIO system was used to measure the impulse response of each individual driver, mounted in a test panel. Here I will use the impulse response for the tweeter/midrange combination (17.9 kb) as an example. The starting point for the time sample (or time-gate) used to derive the frequency response establishes the phase reference point. The reference point can be moved back and forth until the phase pattern is nearly flat (25.4 kb) vs. frequency. In the example the starting time, shown on the right-hand side of the CLIO window, is 3.85 milliseconds. Sound travels 1.32 meters in this time interval, so the phase reference is 1.32 meters in front of the calibrated microphone. By measuring the distance from the mike to the driver, the point is then determined relative to the driver. The reference point location for a flat phase pattern is shown for each of the three drivers as the red circles in the illustration on time-alignment (5.5 kb). With respect to these reference points, all three drivers have nearly equal phase patterns within their respective frequency bands. Therefore, with the reference points aligned on the same vertical plane, the sound from the three drivers will combine with near-perfect coherence in the forward direction. That was the technique used to determine the terracing dimensions. (Strictly speaking, I suppose this should be called phase-alignment, but the result is equivalent to time-alignment).
It is odd that the reference points are in front of the tweeter and midrange. Stefanos Albanidis has kindly shared measurements that he made on a similar tweeter using a later version of CLIO. His measurement shows the reference point is 1.4 cm behind the faceplate. He also stated that my version of the CLIO system may be measuring this incorrectly. As far as my speaker design is concerned, I only need to accurately know the relative distance between the points for the three drivers. This is correct as evidenced by the combined measurements of the drivers, even if the absolute location of the points are shifted.
Note added 3/19/98. Audiomatica kindly gave me a CLIO upgrade from v3.2 to v4.0. When I repeated the time-alignment measurement, this time the origin was right at the tweeter face-plate.
The correct geometrical alignment of the drivers is not sufficient to guarantee good time-alignment. The crossover design is also critical. This is discussed in detail in the section on system design. The example phase pattern for the tweeter and midrange includes the crossover, and shows that true time-alignment was achieved for the total system response.
The time alignment is perfectly accurate only at a height midway between the midrange and tweeter. (The woofer has relatively little effect on time-alignment). The geometry is designed so this height is at ear-level in the "sweet spot" where I sit. If I stand up instead of sitting, the path-lengths from the tweeter and midrange to my ears are no longer equal. For the geometry of my enclosure and room (7.2 kb), the difference in pathlength in this case is 1.13 inches. At a the crossover frequency of 3000 Hz, the sound from the tweeter and midrange will have a relative phase shift of 90 degrees due to this pathlength difference. However this is just part of the story. The 1st order crossover introduces a 90 degree phase shift also, and the net result is that the midrange and tweeter are 180 degrees out of phase at this point.
I computed the sound pressure (12 kb) along the vertical path 140 inches from the reference points shown in the geometry illustration, for 10 frequencies. The horizontal axis in these Figures is the response in dB; the vertical axis for the left-hand Figure is the vertical movement in inches above the point between the midrange and tweeter. The numerals adjacent to some of the curves are the frequency in kHz for the curve. For my system, the left-hand Figure, the 3 kHz curve has a null 19 inches above the midpoint as expected (this corresponds to the 23" dimension in the geometry illustration).
A D'Appolito array straddles the tweeter with two midrange drivers. This creates a virtual phase reference point in between the two midrange speakers, and eliminates lobing between the midrange and tweeter. However it creates new lobing between the two midrange speakers. These drivers are twice as far apart as the midrange and tweeter. However, with the same crossover the variation is less than with a single midrange, as shown in the right-hand Figure. For the D'Appolito Figure the vertical offset is relative to the tweeter. Since the phase shift introduced by the crossover is an important part of this behavior, these curves apply only to 1st order crossovers. I have not made any calculations for other orders.
Lobing is a fairly complicated phenomenon, and the calculations do not include the drop-off in driver response as the angle off axis increases. I measured the response of my system (46 kb) and the null for a vertical offset of 19 inches was there just as predicted (ain't engineering wonderful). The red curve is measured at the sweet spot, and the yellow curve at the elevated position.
The vertical size of the "sweet spot" is increased by decreasing the vertical spacing between the tweeter and midrange, so I put them as close as I could without creating a diffraction problem. For my purposes the "sweet spot" is large enough that lobing is not a problem. But I must say, after starting out very skeptical about the D'Appolito configuration, I have been converted into a believer. For an application where the "sweet spot" needs to be large vertically, it is clearly a superior arrangement with a 1st order crossover.
Shortly after writing this sentence, it finally occurred to me to calculate the response moving below the sweet spot. Normally, of course, the lowest my ear will be is when I am sitting down, which is why I didn't do this calculation the first time around. The D'Appolito array is symmetrical with respect to movement up or down, and the result for it is a flipped version of the graph already shown. However for the single midrange and tweeter, the situation is not symmetrical, because of the phase shift introduced by the crossover. The resulting curve for a downward movement (8.5 kb) shows a much broader sweet spot, and if anything it is a little better than the D'Appolito array. If I had made this calculation a few months ago, I probably would have built the speakers with the midrange above the tweeter. I think every speaker I have ever seen has the tweeter on top, and I just blindly followed tradition. It also did not occur to me that the crossover phase shift would introduce and asymmetry, until I actually did the calculations shown here. Oh well, live and learn.
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