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Loudspeaker Arrays: Ideas, Data & Solutions In Solving Horizontal Coverage Problems
Facts and myths regarding tight-pack and spherical arrays

A loudspeaker array is a collection of loudspeakers that is assembled to achieve a coverage pattern that cannot be achieved with a single device.

Arrays are most commonly implemented to achieve a wide horizontal coverage pattern from a position on or above the stage.

The “perfect” array would be a collection of loudspeakers whose radiation pattern was indistinguishable from a single (hypothetical) device that provided the needed pattern for the audience area.

Many attempts have been made to solve the horizontal coverage problem. These include:

• The “tight-pack” array ­ a collection of loudspeakers packed tightly together to emulate a single loudspeaker (Figure 1).

• The “exploded” array ­ technically not an array, but a group of devices that are separated by a sufficient physical distance large enough to reduce the acoustic coupling between the devices (Figure 2). Devices can be tilted at a downward angle.

• The “spherical” array ­ a group of devices with a common mouth distance to a virtual point of origin, placing them on the surface of a virtual sphere (Figure 3).

Figure 1, 2 and 3. (click to enlarge)

All of these side-by-side array topologies have merits if implemented properly. Let’s take a look at some facts and myths regarding the tight-pack and spherical arrays, and (hopefully!) provoke some thought about the horizontal coverage problem.

The balloon plots in this article were generated using EASE. They represent the approximate response of an array generated using the manufacturer-supplied EASE loudspeaker data.

Figure 4: Idealized radiation pattern. (click to enlarge)

Since real-world loudspeakers are inherently more complex than the EASE data representation, the simulations are “best case.”

The best-case response of any horizontal array could be described with the balloon plot of Figure 4. The plot is of three 60-degree horizontal devices arrayed side-by-side to provide a 180-degree horizontal radiation pattern.

NEED AN ARRAY?

Because a horizontal array attempts to achieve a wider coverage pattern than can be achieved with a single device, it makes sense to consider what such a coverage pattern would be useful for.

If the array is radiating equal sound energy to all points within its horizontal pattern, then even coverage is achieved only if all listeners in the horizontal plane are at a similar distance from the array.

Figures 5-7 show the audience planes that can be covered evenly with a side-by-side array.

We will proceed with the assumption that the goal of the array is to evenly cover one of these audience area shapes.

Note that if the array were tilted (i.e. above the stage), the audience plane would need to have the same tilt.

Such an audience plane is unlikely, so the “exploded” array is normally used this application.

Figure 5, 6 and 7: Optimum audience planes for a side-by-side array. (click to enlarge)

Figure 8 shows the physical conflicts that occur when a tight-pack configuration is attempted.

Figure 8: Ideal versus physically realizable devices. (click to enlarge)

If the acoustic centers could be reconciled physically, then a coherent wavefront could be achieved without the requirement of the sum of the individual radiation patterns being 180 degrees (Figure 9). Unfortunately, such a localized acoustic center is not possible for much of the spectrum in practice due to the required physical size of transducers that can radiate significant acoustic power.

It is necessary to de-centralize the components to a degree that doesn’t require the devices to occupy the same position in space. This process also moves the acoustic centers, and our “ideal” array is no longer ideal (Figure 10).

Figure 9: In a dream world…  Figure 10: The real world: our ideal array is no longer ideal. (click to enlarge)

The performance of a tight-packed array will depend on the degree to which the designer is able to reconcile the acoustic centers to a common point. Because a physical solution becomes more difficult with increasing frequency (shorter wave-lengths), the performance of tight-pack arrays will transition to that of a spherical array at some frequency.

Table 1: Maximum physical distance between acoustic centers of adjacent devices. (click to enlarge)

Table 1 shows the maximum physical distance bet-ween acoustic centers of adjacent devices that allow in-phase energy summation (less than one-quarter wavelength).

The spherical array moves the acoustic centers out from a common origin and uses a radiation pattern that minimizes the overlap bet-ween adjacent devices.

Figure 11 shows the ideal case, which would yield a “dead” zone in the overlap area. In practice, the opposite happens, since all loudspeakers spill some acoustic energy outside of their rated coverage patterns.

Figure 11: Spherical arrays move the acoustic centers out from a common origin. (click to enlarge)

The result is a “lobing” three-dimensional radiation pattern and an acoustic response riddled with comb filters at any single listener position.

It is interesting to note that the number of lobes in the radiation pattern is determined by the separation of the acoustic centers, not by the coverage angles of the devices that form the array.

Tighter patterns can reduce the level differences between the peaks and nulls, but they don’t reduce the number of peaks and nulls. Array performance is not judged by the absence of lobes, but by the relative level difference between the peaks and the nulls.

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