Designing a speaker system for the do-it-yourself crowd has a number of problems, one of which is how to determine the acoustic center of the drivers. Of greater importance is the relative difference between acoustic centers (called relative acoustic offset). Knowing the absolute acoustic centers is useful if you intend to test a number of drivers without actually fabricating a baffle and mounting them. But if you know which drivers will be used and have access to a good measurement system and appropriate CAD software, it is possible to determine the relative acoustic offset without actually knowing the absolute acoustic centers.
My first experience with this was when I had access to LMS and, later, MLSSA in 1996. I was learning how to use them and CALSOD at the same time. I tried the typical physical-measurement techniques described in Speaker Builder and other books and magazines, but these never resulted in a good correlation between my optimized design and the subsequent measured combined responses. Also, I did not have good facilities for making and testing various baffles. I didn't even have a router for flush-mounting drivers.
I really did not need the absolute centers, but only the relative acoustic-center offset between them. How could I determine this? After much frustration, I came up with the idea (which I had never seen presented anywhere) of using relative offsets. I had a baffle with the drivers mounted, which would not change.
You determine the measurements for individual drivers, usually on each driver's axis, and import them into the CAD software. Then you add the relative offsets in the three axes, either by hand-measuring the cone depth, as some recommend, or by using the center of the voice coil. Why not, I thought, make a raw measurement of both drivers combined, from the same position? This would include the acoustic offset of both drivers. Now all I needed was a way to adjust one driver relative to the other for that specific microphone position.
Since I had the combined raw result, which intrinsically included the relative offset, all I needed were measurements of each driver taken individually, without moving the microphone. I could then import each measurement into CALSOD and use its capability of combining driver responses to compare the result against the combined raw measurement.
The procedure is to import each driver's raw measurements into the CAD program, model them, and create a single file (in the case of CALSOD) containing the two driver models. Then use the combined raw measurement as the reference against which the resultant CAD combined (system) result is compared. In CALSOD, the file is imported as an experimental curve. It is important to point out here that no crossover components can exist in the model. All of this is done using only the raw models.
I always measure the combined result on the tweeter axis, since that is my typical listening position. I leave the tweeter offset at 0. I then modify the woofer offset repeatedly until the combined result from CALSOD matches the measured result as closely as possible, with the emphasis on the area of the target crossover frequency. I do this because the acoustic centers of drivers vary with frequency.
I also use 1/6-octave smoothing in LAUD before I export the text file, thus getting rid of the minor fluctuations without changing the character of the curve significantly. This makes it simpler to model, doesn't impact the actual results, and makes for easier matching of the measured combined signal with the calculated combined curve.
I took the measurements with the woofer and tweeter connected in positive-phase polarity. It is possible to do it in any configuration, but you must be sure that the model in the CAD program properly reflects the connections to prevent it from being 180 degrees out of phase, which may not be obvious, depending on the drivers relative offset.
You can also determine the offset with measurement software alone, although I have never attempted to do so. I find that since I must model the drivers in CALSOD no matter what else I might do, it makes more sense to use the program. It is also much easier, because the iterative process required is much simpler. You edit the offset value in the file, reload it, and display the two curves.
As an example, consider a two-way system comprising a Dynaudio 20W75 and a Vifa D27TG-45. The individual raw measurements are shown in Figure 1 after importation into and modeling in CALSOD. Only the portion above 500Hz is shown, because I am interested only in the acoustic-center offset at the crossover point.
Figure 1: Individual Raw Driver Curves
Figure 2 shows the initial CALSOD summation curve, with both drivers' acoustic-center offset in the z-axis at 0. Figure 3 shows the summation with the "best guess" iterated resultant offset for this driver/baffle combination when the target crossover point is 2kHz. Compare the two figures to see how small variations can have a significant impact, especially if you wish to design a minimum-phase system using first-order crossover slopes.
Figure 2: Predicted vs. Measured Combined Response for Offset of 0
Figure 3: Predicted vs. Measured Combined Response for Iterated Best Guess Offset
The difference in this example is actually very small. The acoustic-center offset added was only 0.006m (CALSOD uses the metric system for distances), which is approximately 5/32". This is initially a surprising result for an 8" woofer, although the Dynaudio does have a rather shallow cone. The acoustic center of the Vifa at this low frequency may also be rather recessed. Since the typical acoustic-center curve tends towards additional recess as the frequency decreases, this should not be so surprising in the end.
Figure 4 shows the measurement using the optimized values for the final crossover. I wish to point out here that the crossover is actually one I derived from a 30° window of measurements. After determining the correct offset, I re-measure at -15°, 0°, and +15°, and average the result. Then I import this average for each driver and remodel it. I use this for the actual optimization for the final crossover, since this, to my ears, yields a more accurate-sounding system. The high-frequency upward tendency actually is seen only on-axis. The average is really closer to flat with this crossover.
Figure 4: Measured Responses of Optimization using Empirically Derived Offset
Figure 5 shows the optimized on-axis curve generated by CALSOD, with the imported on-axis measurement made using LAUD. You can easily see the close correlation, especially in the area of the crossover, 2kHz.
Figure 5: Predicted vs. Measured Optimized System Response
You can do this for any system, two-way or more. The procedure must be followed for each pair of drivers. For a three-way, it is probably necessary to make the measurements from the midrange or woofer position. You would then add the offset determined for the woofer to that of the midrange if the tweeter is left at 0. Then all three drivers will have the correct relative offsets.
One point to remember is that in the CAD program, you must enter the vertical offsets as well as any horizontal (lateral) offset. But this is academic, since these distances are usually known and are easily measured again in any case. Just be sure you enter them correctly into the CAD software before beginning the procedure I have described.
When done properly, measured results at the crossover point generally are within 0.5dB of the target curve. In three years of using this technique, I have never seen it fail to produce accurate, repeatable results.