Since the earliest days of professional audio, users have needed more output, coverage and frequency response than a single loudspeaker transducer could provide. Even with dramatic increases in modern transducer performance, it would seem that combining multiple drivers together, whether for response, coverage, or output will be a perpetual fixture of the industry. Because of the limitations of drivers, much of the effort in professional loudspeaker design has been expended in combining multiple drivers in a single loudspeaker box, and then combining multiple boxes together into arrays.
For most of the history of sound reinforcement, the placement of boxes in an array meant a series of inevitable compromises in terms of evenness of coverage and deleterious interactions between boxes. Fairly recently, the increased power of digital signal processing has led to a class of loudspeakers where the interactions between drivers are encouraged, and rather than being something to avoid, instead are a powerful tool to shape the directional coverage of a loudspeaker system.
The idea of using an array of radiating elements to control direction is hardly a new idea. Anyone who had a television antenna on their roof, or used a “shotgun” microphone (Fig. 1), has used this principle in reverse. Here, the physical spacing and layout of the antenna’s receiving elements — or interference slots along the mic body — provide directional control. For a steerable loudspeaker, the physical placement of the elements, coupled with the processing to each driver, provides coverage control for the audience area. This can be taken as far as aiming the speaker’s output in a (slightly) different direction that the loudspeaker itself is facing.
That brings us to the topic of this month’s article, steerable arrays. Whether in the form of a cardioid low-frequency array, a digital column loudspeaker or a high-end concert P.A., the concept of processing to take advantage of tailored interactions (acoustical or electronic) between array elements is here to stay. The discussion of the calculations behind array steering is inherently mathematical, but we will avoid that here, instead providing an overview of general principles about how these arrays operate, and some of their limitations.
Segmenting the Audience
For a substantial fraction of audience layouts, vertically segmenting the audience makes the most sense. Audience members near to the loudspeaker array need comparatively low sound levels, and experience only small amounts of high frequency absorption. Audience members far from the array require greater output, and more compensation for high frequency absorption to maintain even coverage. Splitting an array into vertical zones, where the upper portion covers distant audience members, allows for tailoring the sound arriving at each audience cross-section in a more even manner. Thus, the majority of steerable loudspeakers (or arrays) have their drivers laid out vertically. Custom control of vertical dispersion and relative output to each audience segment is one of the major advantages for steerable array products.
Array Interactions
A principle of steerable arrays is that the drivers must be physically spaced in the plane they wish to control. This is why the majority of steerable arrays systems in the field arrange their driver configuration vertically. In concert with the above principle, a steerable array’s physical size must be some appreciable fraction of the wavelength of the frequency range where the control is to take place. One the wavelength becomes larger than the array, the pattern control is lost. No amount of processing can overcome the limitations behind the relative physical spacing of the drivers with respect to wavelength.
Steerable loudspeakers will never behave like a laser beam. Loudspeaker coverage patterns widen and narrow in a frequency-dependent manner. The variable performance of loudspeakers is a consequence of the huge range of wavelengths they are asked to reproduce. The shortest wavelengths in the domain of human hearing are less than an inch long, while the longest are tens of feet in length. The physics of acoustic waves dictates that they bend fairly easily around objects whose dimensions are comparable to (or smaller than) their wavelength. This behavior, known as diffraction, has been well understood for over a century, and no product or manufacturer has immunity from its effects. As a simple experiment, you can illustrate this for yourself by taking a loudspeaker, turning it so the drivers face away from you, and listening to it from behind. The mids, low mids and low frequencies will still be clearly audible behind the box, as they have bent around the loudspeaker enclosure.
At very short wavelengths, essentially high frequencies, the loudspeaker’s physical size will be sufficient to provide strong control over how sound travels. A useful guideline is that virtually all individual loudspeakers retain excellent directional control for frequencies above approximately 5 kHz. This is akin to saying that one can treat each loudspeaker driver as independent from its neighbors above 5 kHz. This also means that the physical processing applied to drivers in a steerable array at high frequencies has less effect on the surrounding drivers.
As wavelengths get longer, and frequencies get lower, the ability of an individual loudspeaker to provide directional control decreases. Sound bends around the edges of the box, and spills on the features around the loudspeaker. Sound also bleeds onto adjacent loudspeakers in the array. This means that the coverage behavior, and frequency response of a loudspeaker in the middle of an array, with other drivers above and below, is different from a driver near the top or bottom of the array. It also means that processing applied to individual boxes in the array is not independent, and will influence the entire array’s response.
The mathematical simulation of array behavior is complicated, and becomes even more so when aiming the sound in a specific direction is considered. Processing required to correctly influence the overall array response can be very unintuitive. While it is tempting to adjust the processing of a single driver pointed at a specific audience location, this can rarely be done in isolation without deleterious effects on the overall array response. It is in this range of inter-driver interaction where the steerable array designers work their magic.
In a steerable array, the designers utilize the physical spacing, time relationship(s) and volume relationship(s) between drivers to tailor their interactions with each other at every frequency. The choice of aiming processing is often driven by sophisticated computer algorithms that seek to increase the sound uniformity on the plane of the audience. Rather than the historical processing paradigm of making the on-axis response uniform a short distance from each speaker, the steerable array considers how the loudspeakers interfere at the plane of the audience, regardless of how strange the performance immediately adjacent to the array might seem. Ultimately, though, it is how the sound waves sum at the ears in the audience that matters.
What about Horizontal Coverage?
If most steerable loudspeakers segment the audience vertically, and then further tailor processing for optimal results at the audience plane, what then for these speakers in the horizontal plane? Here these speakers typically use more conventional means to provide directional control.
At low and mid frequencies, the wavelengths of sound are several feet long, bigger than the driver diameter. As the frequencies get higher, the driver’s dimensions become comparable to the wavelength of sound being reproduced. In this frequency realm, an interesting effect occurs where the driver’s coverage angle starts to narrow. As frequencies get higher, the driver becomes progressively more directional. Fig. 2 shows this effect graphically.
The driver in Fig. 2 becomes more directional because of phase, specifically the phase difference between sound waves that comes from different points on the speaker cone. Imagine that you are standing directly in front of the speaker driver listening. When you are standing directly in front of the speaker, the arrival time of the sound from points on the driver cone is uniform, as you are the same relative distance from both edges of the cone.
Now imagine standing off to the left of the loudspeaker driver and listening. Sounds from the left side of the speaker cone will arrive at you sooner than sounds from the right side of the speaker cone. This is because you are farther from the right side of the speaker cone than the left side. At low and midrange frequencies, this difference in distance is of little effect. The wavelengths are very long, and therefore the phase difference is minimal. However, when the wavelengths become shorter, comparable to the dimensions of the cone, the phase difference is quite high and the directivity becomes narrow (also depicted in Fig. 2).
Note that the phase difference of arrival from both sides of the cone is not dissimilar to the types of processing applied to create a steerable array, where one might manipulate the arrival phase for a specific range of frequencies. The difference here is that this phase differential is an inescapable consequence of the driver’s design, rather than some carefully applied digital manipulation.
Vertical Performance Limitations
Discussions on vertically arrayed sources, like those in a steerable array, typically begin with describing their behavior up close, usually at a distance no greater than the height of the array. Then the discussion moves to ever farther distances from the array. Conceptually, however, it is much easier to understand the behavior of a vertical array by starting at point very far from the array, and then moving closer.
Just like the Sun (a very large object indeed) appears as a small round ball in our sky, even a tall vertical array looks like a small dot when we move far enough away. At this extreme distance every driver in the vertical array is essentially the same distance away from us, and the array’s behavior is much like standing directly on axis of an individual driver like we discussed above. Technically stated, if perceived from far enough away, every array is like a point source.
As we move closer to the array, the relative distance between each individual driver to the listener increases due to simple geometry. The drivers at the far ends of the array are farther from us, and therefore increasingly out of phase at the listening position. The result is analogous to the effect of listening off-axis to a single driver. It is here in this range of “useful” phase differences, due to physical placement, where steerable array processing best works its magic.
For example, at high frequencies where the array is many wavelengths tall, there is a “beam” of in-phase energy on axis with the array. This is show in Fig. 3, where the angle of zero (0) degrees is on-axis with the array. Above and below the array, the phase differences force the drivers to cancel almost completely, resulting in narrow vertical coverage that causes high frequencies to essentially disappear once you move above or below the array’s height. In this frequency range, the processing of a steerable array might be used to increase the coverage angle by slightly delaying and/or attenuating the sound from the elements at either end of the array. It can also be used to smooth out the side lobes above and below the array.
Steering the Beam
The math applied to create the phase relationships at the audience plane for steerable arrays is not typically fixed in stone, and the algorithms can be re-run for different audience planes. Changing the locus of the in-phase arrival of the sound allows for some degree of control over the array’s beam angle purely using digital manipulation of the arrival times and levels at the desired location. This technique has limitations due the physical array configuration, but is a powerful tool. One important caveat with directional beam steering is that controlling the location of the primary lobe can lead to the creation of undesirable secondary lobes that bounce off roofs or get picked up in podium microphones. Further, at very high frequencies the directivity of a steerable array is controlled almost completely by the high frequency wave shaping device(s), and thus has no digital means to be steered in a direction other than where it is aimed.
Into the Future
The vast digital horsepower that underlies steerable arrays will continue to push the knowledge envelope of those working in the business. Computer algorithms generate DSP filter coefficients directly, and finite impulse response (FIR) filters can manipulate frequency and phase with fine granularity. Pro audio people will need to become more comfortable with heavy-duty prediction software, and develop a toolkit to perform precise venue surveys. The reward for accumulating this additional knowledge results in greater evenness in coverage, and more flexibility in the location of our P.A. systems.
