Figure 1: The “tight-pack” array.

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

Figure 2: The “exploded” array.

• 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.

Figure 3: The “spherical” array.

• 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 4: Idealized radiation pattern.

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.

Figure 5: Optimum audience plane for a side-by-side array.

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.

Figure 6: Another optimum audience plane for a side-by-side 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 7: Yet another optimum audience plane for a side-by-side array.

Figure 8 shows the physical conflicts that occur when a tight-pack configuration is attempted. 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 8: Ideal versus physically realizable devices.

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 bec-omes 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.

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).

Figure 9: In a dream world...

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 10: The real world: our ideal array is no longer ideal.

Figure 11: Spherical arrays move the acoustic centers out from a common origin.

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. 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.

Figure 12: Low-Q arrayed on a sphere.

Figures 12 - 16 show the 3-D directivity balloons for several “real world” array configurations for frequencies in the voice range. The geometric origin is 1 meter for each array, a distance that is great enough to remove the physical conflicts between the devices.

Figure 12 shows an array of small sound columns that have the typical broad horizontal pattern and controlled vertical pattern. The lack of pattern control produces significant lobing at all but the highest frequency considered. At this frequency, the lobing becomes so dense that the response actually becomes smoother. Dense interference is a common technique used by sound system designers. As the lobe density is reduced (lower frequencies) the coverage becomes more uneven.

Figure 13: Arrayed on a sphere.

Figure 13 shows the resultant radiation patterns when the column loudspeakers are replaced with medium-format horns having a 60-degree nominal horizontal coverage pattern in the 2 kHz octave band. The coverage is much more even than in the previous example.

As with the previous array, these devices are positioned on the surface of a sphere by using a common distance back to a “virtual” physical origin. This arraying technique produces physically appealing arrays, but unfortunately does not compensate for the fact that the acoustic centers are not reconciled. As such, significant lobing is present in the radiation pattern at the lower octave centers where the radiated pattern is wider than the nominal coverage.

Figure 14: Center loudspeaker advanced by one foot.

Figure 14 shows the same configuration, but with the center loudspeaker advanced physically by one foot. This makes the array non-spherical, which (ironically) produces an improvement in the evenness of coverage in the 500 Hz and 2 kHz balloons.

Figure 15: Center loudspeaker advanced one foot and delayed .88 milliseconds.

Figure 15 shows the same configuration, but with the center device delayed electronically in an attempt to “compensate” for the

1-foot advance. This demonstrates that the acoustic center of a device is a physical characteristic and cannot be moved electronically. While a delay can certainly alter the radiation pattern of the array, it is not a direct substitution for the repositioning of a device.

Figure 16: Large-format horn array with coaxial high-frequency section.

Array performance can be improved by using devices whose directivity holds up to a lower frequency. This means a physically larger device. Figure 16 shows the result of substituting large-format 60-degree horns for the medium format devices in the previous figures. The increased pattern control in the 1 kHz and 2 kHz balloons is apparent. The bandwidths of these devices do not extend to 2 kHz, so the high frequency response was achieved with additional devices, coaxially mounted within the large-format horns.

Since using a larger format produces improved behavior, it is reasonable to expect that this improvement could be extended to lower frequencies if devices of sufficient physical size were used. Since the acoustic wavelength doubles when frequency is halved, the required size at 500 Hz would be twice that required at 1 kHz (8-foot mouth size!).