Although this subject has been covered here before, this month let’s do a quick refresher on options for P.A. subwoofer configurations, with links back to more in-depth articles.
While spaced Left/Right subs (see Fig. 1) are handy for one-off shows, these generally cause wave interference — a.k.a. comb filtering of the subwoofer polar response or uneven coverage — resulting in a level bump (power alley) down the center of the room. To see the sample subwoofer polar response of various subwoofer array configurations, check out the May 2019 issue of FRONT of HOUSE.
Mounting a subwoofer array on a very hard ceiling is a common solution for engineered P.A. installations. This overhead subwoofer array/box location maintains signal/time alignment to the main loudspeakers and provides more uniform coverage due to a smooth polar response and more uniform distance to all the listeners and also reduces clutter on the platform — both important benefits to most church and critical venue installations (such as music venues). To see an overhead subwoofer model coverage map, see the May 2018 issue of FRONT of HOUSE.
To improve “muddy” bass in a reverberant venue, you will need to lower the low/sub frequency reverberation acoustically with bass traps and/or install a directional cardioid sub-woofer (larger bass-horn or cardioid/gradient or end-fire sub array).
Remember that low-frequency wavelengths are very long (15 to 50 feet; see Fig. 2), so they wrap right around subwoofer cabinets. As is well known, single subs are almost omnidirectional, with only slightly more output in front, more with rising frequency. Even large dual-18” subs have little directivity, causing too much lost energy backstage, potential feedback and annoyance of onstage musicians and bystanders alike. Many subs are versatile, and can be configured either as an end-fire or gradient type of cardioid sub array. These sub arrays differ in the cost to deploy and how they are processed; the range of performance vs. cost choices are great, with many trade-offs in sub array sizes and options. In the case of end-fire sub arrays, size does matter.
Some Common Directional Sub Arrays
Let’s take another look at several different types of cardioid/directional subwoofer arrays used in sound reinforcement:
Broadside Arrays, (not shown) employ a number of woofers are arranged in a row, and the primary radiation is at right angles to the row. This had been the typical subwoofer array seen commonly at large concerts, spread out in a horizontal row (curve or line) or flown in a column.
Gradient Arrays (such as Fig. 3) use woofers are arranged and driven in specific ways to provide microphone-like directional patterns, usually cardioid or hypercardioid. Such arrays involve subwoofers with multiple drive channels that may contain delays, filters, and/or polarity inversions to achieve their results. Gradient arrays can be purchased as single boxes or separate sub boxes. For the theory on Gradient Subwoofer setup review the Sept. 2016 issue of FRONT of HOUSE.
End-fire Arrays (Fig. 4) have multiple sub boxes are arranged in a spaced row pointed in the desired direction of radiation, and driven in a successively delayed fashion, so as to create a very narrow pattern. The end-fire array is the sub equivalent of a shotgun microphone. End-fire arrays are less common, and most useful in long-throw applications, such as large venues.
Beamforming (not shown) is a technique by which the sound wave emitted by a large array can be aimed and shaped. In a beamformed array, the loudspeakers are driven separately (or in small groups), and each drive signal has its own delay and level (adding more cost to the array).
Gain Shading refers to modifying array drive parameters for the elements on or near the ends of the array, reducing the drive gain for one or more elements at either end of an array. For long arrays, shading takes the form of a gradual tapering of gain from 0 dB to about -6 dB over the last two or three elements at each end. While useful, this design is not the best value, so it’s not as popular.
Let’s compare how two types of sub arrays create attenuation (rejection) to the rear and sides of the array. The name “cardioid” means the same thing as it does for directional microphones: the polar response of the array has a heart-shaped pattern. Bennett Prescott, director of B&C Speakers North America says, “While technically this is describing a desired pattern shape rather than a specific type of array, it has become common in the live sound industry to describe gradient type subwoofer arrays as cardioid. An end-fire array is so named because a number of subs are arranged in a line and delayed so that they ‘fire’ in order, starting at the end farthest from the audience.”
Both methods create the desired off-axis attenuation, so some important questions are: at what direction, over how wide of a frequency range, at what size and cost? Gradient type cardioid arrays are less efficient than end-fire array designs, and time smear can be an issue (peaks can sound less impactful) with gradient-type cardioid arrays. Also, the reduced output at lower frequencies, from gradient-type cardioid sub arrays, requires additional LF equalization to compensate, thus reducing maximum output level. It is now also possible to model the direct sound for cardioid sub arrays in many programs. But due to lack of acoustical data, room modeling is not possible with subs. A very useful comparison of several variations on directional sub array models can be found a year back in the June 2019 FRONT of HOUSE, and many more sub arrays in Bob McCarthy’s excellent book Sound Systems: Design and Optimization.
David K. Kennedy operates David Kennedy Associates, consulting on the design of architectural acoustics and live sound systems, along with contract applications engineering and market research for loudspeaker manufacturers. Visit his website at immersive-pa.com.
Building a Simple Subwoofer Array
Creating a directional array begins with similar subwoofers, so that the relative phase of their baseline output is similar. Next, our two loudspeakers are separated in space. This can take several forms. One approach is to place the subwoofers one behind the other. This arrangement is a good option when stage height is low, but there is sufficient depth to the audience.
With one subwoofer placed behind the other, an appropriate spacing distance between them is close to a quarter-wavelength, or about 5 feet from the front of one cabinet front to the next. Another way to create this distance is to stack the subwoofers and turn one cabinet backwards. The spacing here is then the total distance the sound must travel around the cabinets.
The second cabinet, placed either behind or below the main subwoofer, provides the -20 dB rearward cancellation, as shown in Fig. 5, when the polarity of this second enclosure is inverted. The polarity reversal causes this “cancellation sub” to create pressure opposite the main subwoofer at all frequencies, with the result being a directional cardioid pattern. Opposite pressure is required for sound cancellation behind the array.
