D.A.S Audio Engineering Dept.
Line arrays are specifically designed so that when we assemble several units, the whole behaves as a single sound source. This is what sets them apart from conventional systems.
The horizontal format of the cabinets, the spacing between drivers, the crossover frequencies and the design of the high-frequency section are what make this behavior possible. In the mid and low sections of a line array, there are two characteristics worth starting with. The first is obvious at a glance: the transducers are arranged vertically, very close to one another.
The second can't be seen, but it comes up in any text on line arrays: the upper cutoff frequency of the drivers, which, as we'll see later, is an important part of the system design and can't be changed without hurting the system's performance. These two characteristics have more in common than it might first appear, and they could be explained together. For clarity, though, we've chosen to introduce them separately. Time to get down to… theory!
Ideal Characteristics of a Sound System
There are two acoustic characteristics a sound system should ideally have. The first is the ability to control vertical directivity, so that acoustic energy can be aimed where the audience is, keeping it from reaching places where it can cause problems (like theater ceilings) or being wasted when we're outdoors. The second is that the individual sound sources add together coherently, or efficiently, with the whole acting as a single source and producing even pressure distribution over distance. Below we'll explain in more detail why these two characteristics are desirable and how they are achieved.
Controlling Vertical Directivity: Why?
Figure 1 shows an example of a system with poor vertical directivity control. The cabinets are stacked vertically and as close together as possible, but the drivers reproducing the example frequency are far apart because of the cabinet's vertical design. The lobe at the top of the pressure map will cause a reflection that reaches the audience area late relative to the direct sound. This will undoubtedly hurt intelligibility.
In Fig. 2 we see a system that does have good vertical directivity control. It's clear that the energy is concentrated where the audience is.
Controlling Directivity: How?
The vertical coverage a system needs to cover only the audience area is usually not very large. How should we set up a system if we want to narrow its vertical coverage? There is a general principle in electroacoustics which says that the smaller the distance between drivers, the narrower the coverage becomes. Of course, frequency is also a factor in this phenomenon.
To illustrate this general principle, let's look at an example of what happens to the coverage of a complete system as the distance between cabinets gets smaller. This applies to any system; there is nothing specific to line arrays in this phenomenon. The laws of physics that apply to line arrays also apply to a conventional system.
Let's imagine several conventional systems in different configurations. In the first, the centers of the transducers are separated by a distance of two wavelengths; in the next, the distance is one wavelength; and in the last, the spacing is half a wavelength. The smaller the distance between transducers, the narrower the coverage and the more uniform the map.
In line arrays, we use this general principle to get narrow coverage by stacking the transducers vertically as close together as possible. The system's horizontal coverage will be that of a single loudspeaker.
Efficient Coupling: Why?
The ultimate effect of efficient coupling, or coherent summation, is that pressure distribution over distance is uniform. This is achieved by preventing secondary lobes from appearing in the array's vertical polar response. If we look at the coverage simulation images, we'll see that in some cases secondary lobes appear in the vertical polar response, while in others we could say there is a single main lobe.
In a theater, for example, the effect on pressure distribution over distance is what you would see in the images of the orchestra seating area in our example theater. In another possible scenario, you would see irregularities in the pressure distribution that correspond to the lobes of the polar response. In that case, the tonal balance heard at the mix position may have very little to do with what is heard in other areas of the theater.
Another possible case is one where the pressure distribution is more uniform because there are no lobes in the polar. A frequency response measurement at several positions will give more similar results than in the previous case.
Efficient Coupling: How?
Before explaining how efficient coupling is achieved in line arrays, it's worth pointing out something that isn't mentioned enough. In line arrays, the cone drivers reproduce only frequencies at which the transducer's polar response is omnidirectional. We'll use this concept later.
To get an idea of what a transducer's coverage will be as a function of frequency, we need to look at what is called the k·a factor, where k = 2pf/c and "a" is the radius of the loudspeaker.
When k·a is equal to or greater than two, secondary lobes appear and the coverage becomes too narrow to be useful in a line array.
With that said, to understand how to achieve efficient coupling we'll apply an acoustic principle we'll call the general principle, to emphasize that it applies to any sound source, whether line array or not. This general principle says that to achieve efficient coupling, the transducers must reproduce only frequencies whose wavelength is large compared with the distance between driver centers.
What you're probably asking yourselves now is: Specifically, how large must the wavelengths be relative to the distance between transducers for the coupling to be efficient? We'll answer that question at the end of the following explanation.
We've said that we don't want secondary lobes to appear in the vertical polar response; in other words, we want only one main lobe. That is the same as saying we have to design our system so that the first null appears at 90º off axis. That way there will be only one lobe, pointing toward the audience. To keep the math simple, let's work through an example with two cabinets.
Case 1. Suppose two cone drivers in two cabinets. On axis, both waves reach the listening position at the same time, so they add in phase, giving a sound pressure level 6 dB higher than that produced by a single source.
Case 2. Now suppose that at 15º off axis there is a path difference d = d · cos q. In our example, where the distance "d" between sources is 27 cm, the path difference d is 6.98 cm. This path difference represents a phase difference of 46.6º at the frequency of our example, which is 630 Hz. The resulting sound pressure will be 5.3 dB higher than that produced by a single sound source.
At 45º off axis. We see that at this angle the sound pressure is 1.1 dB lower than that produced by a single sound source. When the phase difference between two waves is 120º, the resulting pressure equals that of a single sound source. As the phase difference increases, the resulting pressure decreases, falling below that of a single source.
At 90º off axis. Both waves are out of phase, shifted by 180º. This logically results in total cancellation, because of the 180º phase difference and also because the pressure levels from both cabinets are the same at that point. Remember that the polar pattern of each transducer is omnidirectional, as stated above.
In other words, the way to prevent secondary lobes from appearing in the polar, which would produce a pressure distribution that isn't uniform over distance, is to limit the frequency band reproduced by each section to those frequencies for which the distance between drivers "d" is equal to or less than half the wavelength. The well-known equation:d <= l/2
The shortest wavelength each driver will reproduce (d = l/2) therefore corresponds to the upper cutoff frequency of that section in a line array. The wavelength at the cutoff frequency will thus be greater than the distance between drivers "d", exactly twice as great. The lower cutoff frequency will be even greater, as specified in the equation in Fig. 6, l >> d.
This shows why the cutoff frequency should never be changed in a line array. We run the risk of the cone drivers working at frequencies where secondary lobes appear, spoiling the uniformity of pressure over distance, which is one of the main advantages of line arrays.
Can We Use the Same Technique to Reproduce High Frequencies?
Obviously not. We've said that to get efficient coupling between sound sources and keep lobes out of the polar response, the distance between sources must be less than or equal to half the wavelength of the highest frequency to be reproduced. For high frequencies, the highest frequency is 20 kHz, and the wavelength at 20 kHz is 1.7 cm. There are no 0.85 cm high-frequency transducers powerful or efficient enough for professional sound reinforcement. So we'll have to come up with a different technique to solve the high-frequency problem in our line array system.
Ideally, for the highs we would want a continuous vertical sound source that produced an isophasic wavefront. A source like that would give vertical coverage similar to what we get from the mid and high sections of our line array, and secondary lobes would be avoided, since the whole surface would radiate in phase.
We can build a real system that approaches the ideal by stacking discrete rectangular sound sources vertically, as long as the spacing between them is such that the radiating surface is at least 80% of the total surface. Keep in mind that the discrete radiating surfaces will be separated from each other by the thickness of the enclosure, so a restriction must be placed on the ratio of total surface to radiating surface so that the whole approximates the ideal continuous source.
The Waveguide
To get a rectangular radiating surface from a compression driver with a circular output, we need a waveguide, which is the key component of a line array. In the D.A.S. Audio CA28, for example, the waveguide has an undulation and a curvature that is more pronounced in the center than at the top and bottom.
Otherwise, the wave would reach the center before the edges and we would have a curved wavefront, which is no good for a line array because it would cause interference between adjacent sources, producing lobes in the polar response.
The waveguide, then, equalizes the path lengths so that the distance from the driver's exit to the center and to the top and bottom edges of the radiating surface is the same.
This gives us an isophasic wave with narrow vertical coverage, avoiding interference with adjacent radiating surfaces, as we've already mentioned. Other waveguides use different techniques to achieve the same thing.
Key Characteristics of Line Array Systems
By way of summary, I think it's worth listing the three characteristics that set most line arrays (those using direct-radiating drivers) apart from conventional systems. If a line array system with direct-radiating drivers lacks any of these characteristics, it can't be expected to behave like a line array. They are:
1.- The cone drivers are mounted in a vertical line, as close together as is physically possible, which contributes to vertical directivity control.
2.- The highest frequency each cone driver should reproduce (the upper cutoff frequency) will be approximately the one corresponding to the wavelength defined by the equation:
d = l/2, where "d" is the distance between the centers of the drivers.
3.- The high-frequency section will have some type of waveguide that produces an isophasic or nearly isophasic wave (depending on the system design and its application).
