THE D'APPOLITO 3/2 SPEAKER GEOMETRY
In his 1983 paper, "A geometric Approach to Eliminating Lobing Errors in Multiway Loudspeakers," Dr. Joseph D'Appolito found a way to create a symmetric vertical radiation pattern from speakers. Reading the work of Linkwitz, it occurred to him that a symmetrical positioning of 3 drivers in a 2-way design, used with a 3rd-order crossover, would produce the quuasi-spherical vertical response illustrated by the solid curved line (A) in Figure 7-4.
He found that, in order for the 3/2 geometry to work properly, the distance between the centers of the adjacent drivers should be kept close to one wavelength of the crossover's frequency, Fc. If you wish to calculate this distance in inches, divide the speed of sournd (13,503.94 inches/second) by the crossover frequency Fc. The elegance of the 3/2 driver arrangement is that some type of symmetrical vertical radiation pattern is produced no matter what crossover type is used.
Figure 7-4 shows two other symmetrical radiation patterns that can be produced using the D'Appolito 3/2 dirver geometry. A 2nd-order All-Pass (Linqkwitz-Riley) produces the large symmetric lobe shown as the slotted curved line (B). This type of radiation pattern is useful if you want your speaker to produce very little sound pressue in the off-axis regions, so that reflections from nearby walls and floors are greatly reduced.
The point/slotted curved line (C) shows a symmetric radiation pattern that is produced when a 3rd-order high-pass section of a crossover is combined with a 2nd-order low-pass section. This shows that the 3/2 geometry produces a symmetric radiation pattern even when used with a mixed-order crossover. It is of great benefit to speaker builders that the 3/2 geometry works with odd-order crossovers, even-order crossovers, or mixed-order crossovers.