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Cardioid/Directional Subwoofer Arrays, Part 1

by David Kennedy • in
  • May 2019
  • Tech Feature
• Created: May 8, 2019

In the May, 2018 FRONT of HOUSE, Vince Lepore asked if flown sub arrays would cover better at his church and still “hit like they did on the floor,” and should they be Left and Right, or Centered? He showed a pair of sound model coverage graphics that showed the much smoother coverage from a flown and centered sub array.

Fig. 1: The effect of two widely-spaced sub boxes can result in irregular response. Image courtesy PreSonus

A central/flown sub array offers the best SPL far-field efficiency — along with smoother (more even) sub-frequency coverage, due to all the arrays being more equal distance to all the listeners. This sub configuration is also a better choice than Left and Right subs, as it provides a close coupling with a central/flown main array, and performs well (by avoiding interference) in spite of not being closely coupled to L/R mains. As many sound techs have learned, widely spaced Left/Right subwoofers (Fig. 1) can produce wave interference (comb filtering), which causes peaks and nulls across a venue at different frequencies.

Fig. 2: Wavelengths increase dramatically at lower frequencies

This month, let’s take a look at several different cardioid/directional sub arrays. Remember, LF wavelengths are very long (10 to 50 feet, Fig. 2), so they wrap right around sub cabinets. As is well known, single subs are almost omnidirectional, with only slightly more output in front, with rising frequency (Fig. 3). Even large dual-18 subs have little directivity, sending too much energy backstage, and creating potential feedback and annoying 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.

Fig. 3: Polar plots of conventional omnidirectional subs at 31 Hz, 63 Hz and 125 Hz. Image: Bob McCarthy

‡‡         Directional Subwoofer Technologies

Much of what we know about subwoofer arrays is based on directional radio antenna arrays and the work of audio pioneers such as Harry Olson, Ph.D. Beginning nearly a century ago, Olson was a prolific inventor and engineer, and was awarded more than 100 patents for many types of audio equipment.

In live sound, there are several kinds of cardioid/directional sub arrays:

Fig. 4: Meyer MAPP image of broadside subs placed across stage front, shown at 31 Hz. Image: Bob McCarthy

Broadside Arrays, (Fig. 4) in which 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 sub/array configuration seen most commonly, either spread out in a horizontal row (curve or line) or flown in a column.

Fig. 5: Response of gradient sub array. Image courtesy PreSonus

Gradient Arrays, (Fig. 5) in which subs are arranged and driven in specific ways to provide microphone-like directional patterns, usually cardioid or hypercardioid. Such arrays involve subs with multiple drive channels that may contain delays, filters, and/or polarity inversions to achieve their results. Gradient arrays may be purchased as single boxes, or created from separate sub boxes.

Fig. 6: Response of basic end-fire sub array. Image courtesy PreSonus

End-fire Arrays, (Fig. 6) employ multiple sub boxes 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 have been less common, and most useful in long-throw applications such as large venues.

Beamforming is a technique by which the sound wave emitted by a large array can be aimed and shaped. In a beamformed array, the sub drivers 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 means 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 2 or 3 sub/drivers at each end. While useful, this design is not the best value.

‡‡         Options, Options, Options…

Sub array options involve: SPL, size, uniform directivity and cost. So what are cardioid sub arrays? 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 as shown in Fig. 5).

Bennett Prescott, director of B&C Speakers NA 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 (gradient and end-fire) 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 arrays have a very stable pattern due to their polarity inversion.

‡‡         Types of Cardioid/Gradient Arrays

Fig. 7: Conventional omnidirectional sub (top); Fulcrum Acoustic’s Passive Cardioid sub (center); active cardioid sub at bottom. Image from Fulcrum Acoustic

Passive cardioid subs by Fulcrum Acoustic (Fig. 7) use special tuned ports on the rear of the sub to create the cardioid polar shape, and are more cost-effective, needing as few as a single woofer and one amp, but their SPL and rear rejection is less than active cardioid subs.

Some cardioid subs provide directivity by using front VLF (Very-Low-Frequency) driver(s) along with a rear VLF driver

Cardioid-gradient arrays are moderately cost-effective. Requiring as few as two woofers and two amp channels, these can provide active cardioid low-frequency directivity.

Fig. 8: d&b audiotechnik’s J-INFRA sub has one rear-facing 21” driver and two front-firing 21” woofers

Meyer Sound offered the first commercially available cardioid sub array design, the PSW-6 (including six woofers and electronics) about two decades ago. There are now several one-box brand-name cardioid subs with two to three woofers, in a variety of driver sizes and quantities, such as d&b audiotechnik’s J-INFRA (Fig. 8).

Fig. 9: The author’s variation on the three-box cardioid array.

However, a directional subwoofer can also be created with arrays of two or more conventional sub cabinets. Also, by slightly varying the delay for the rear sub driver, it is possible to vary the polar pattern to fit your exact usage. There are now several one-box branded active subs with “cardioid mode” — providing the built-in electronics — but needing additional subs to complete the sub-array. Fig. 9 shows a custom variation on the three-box cardioid array.

Gradient arrays can often be built within the same footprint as a traditional array. Cardioid/gradient arrays, using forward and rearward facing subs, can be assembled vertically or horizontally, subs stacked one on top of another or laid side by side, in a line, some facing the audience and about one-third facing backwards.

Fig. 10: Two popular 3-box cardioid arrangements, set up side by side.

Fig. 10 shows the popular three-box cardioid array. Although many concert events have used this popular cardioid sub array (with one-third facing backwards), such sub arrays can lose their cardioid directivity at maximum sound level, as they are limited by the number of rear-facing woofers.

The trade-off with a gradient sub array is reduced output as frequency drops; since one sub-woofer is polarity inverted, as the wave-lengths get longer (play lower in freq.), the subs begin to behave like a single source and cancel in all directions.

In practice, this reduction in output is not critical as long as the array is built with a reasonable number of drivers and center-frequency in mind. So, remember that 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 require additional LF equalization to compensate, thus reducing maximum output level.

“Gradient arrays only work when their dimensions are small with respect to wavelength. They are the opposite of end-fire arrays, which must be large in order to work. The reason for this is that gradient loudspeakers work by controlling pressure differences between the different parts of the sound wave, and must be small enough to work within the wave,” said Jeff Berryman, senior scientist with Electro-Voice.

‡‡         Understanding End-fire Sub Arrays

Fig. 11: Resulting 63 Hz polar pattern from a 4-box, in-line end-fire configuration, with 2.9 ms delay applied to the second sub, 5.8 ms to the third and 8.7 ms to the farthest front-facing sub. Image: Bob McCarthy

End-fire arrays (Fig. 11) have their own set of pro and cons. According to Bennett, “The primary advantage is near-perfect addition in the forward direction, and the primary disadvantage is the physical space required to implement them. Additionally, as subs are added to the line, more separate delay taps are required, which may require more amplifier or processor channels than are available on-site or in the project budget. Most importantly,” he added, “an end-fire array depends entirely on phase interaction to create rejection. Therefore, if reduced in size, it has a different pattern at each frequency, as the wavelengths involved are different at every frequency. This can create uneven off-axis frequency response, leaving an issue of where in the audience area to equalize the PA system.”

End-fire arrays are more efficient, so they play louder than gradient sub arrays.

For more details on end-fire sub arrays, see: bobmccarthy.com/phase-wavelengths-the-end-fire-cardioid-array-made-visible. For more on various cardioid sub arrays and larger variations of directional sub arrays, see Bennett Prescott’s excellent article, “Advanced Sub Techniques,” at bennettprescott.com.

So, if more ideal polar patterns (almost-cardioid) are desired from an end-fire array, it will require more space, woofers, amplifiers and thus more budget than a gradient (cardioid) array, but the payoff is higher SPL and better impact.

‡‡         The Payoff!             

By building more directional sub arrays, sound energy can be reduced on the stage, ceiling and walls, and focused on the audience, where it works better (sounding more intimate and impactful).

Next month, we will delve deeper into PC modeling of directional subwoofer
arrays.

For Further Reading:

For further insights and test results on the efficiency of flown versus ground-stacked subwoofer configurations, see AES Paper #10051 “On the Efficiency of Flown vs. Ground Stacked Subwoofer Configurations,” (authored by Etienne Corteel, Hugo Coste Dombre, Christophe Combet, Yoachim Horyn and François Montignies of L-Acoustics) and presented at the 145th Convention in New York City, October 2018. Note: The paper is available free to AES members or E-Library subscribers (or purchase by non-members) through the AES E-Library at www.aes.org/e-lib/

David Kennedy specializes in the design of architectural acoustics, AV systems and custom loudspeaker arrays. Since 1980, he has designed more than 300 auditorium sound systems, including churches, schools and performing arts centers. Visit him at www.line-arrays.com.

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