Loudspeaker Array Low-Frequency Pattern Control using Filtered Array Technology™

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Array directivity control theory is not new. Olson’s Acoustical Engineering in 1940 discussed Gradient microphone arrays, and both it and Beranekís 1954 Acoustics have sections on line arrays. In the 1970s JBL offered two tapered and shaded line array systems, the 4375 and 4380 designed by George Augspuger. David Klepper, Topper Sowden, and others have used sophisticated line array designs for installed sound reinforcement system for several years.

Low cost DSP that conveniently provides the signal processing required for low frequency control, coupled with customer requirements dictating smaller arrays with tighter pattern control, has renewed interest in the concept. Simulation software aided design has further stimulated manufactures to offer solutions to the market.

JBL researched several approaches to controlling the low frequency pattern, including constructing full size arrays for proof of concept. Three of the most useful designs are presented here. Two are Halfwave Line Arrays, which provide good attenuation at 90° off-axis and propagate radiation into the audience area with half the rate of attenuation of a non “steered” cluster. That is, because of the directivity characteristics of the array SPL drops 3 dB with doubling of distance, not 6 dB. This provides more even coverage from front to back at low frequencies, previously a difficult problem. The third cluster is a Gradient Array. It uses a steering element behind the main cluster to null the main clusterís radiation directly below it. This can be very useful in houses of worship and other applications using lavalier or podium microphones located underneath the cluster. One other important advantage of this design is its compactness.

Section 2 of this paper describes how constructive interference works to provide pattern control and Section 3 details the cluster components, construction, signal processing parameters, and expected results.

2: Demonstration of Principle
In this section we will use very small loudspeakers to demonstrate interference concepts, and how they can be used for directivity control. The loudspeaker used is about one third the size of what would be used for sound reinforcement. Therefore the effects can be scaled in frequency: what occurs at 300 Hz in the model will be at 100 Hz for a cluster three times as large.

When two sound sources producing identical program are displaced relative to each other, they will combine to produce a unique interference pattern that depends on the observerís location. The interference pattern is a result of the different arrival times from the two sources. For a position directly on the common axis of the two sources, and equal distance from each of them, the relative combined response will simply be +6 dB louder than that of a single source alone. This is known as coherent summation of two signals. They are identical in phase and amplitude at all frequencies and thus combine to +6 dB.

Figure 1 (below) shows what occurs when an observer moves slightly off-axis of two sources. This example illustrates two different positions, the first position creates a condition where the path length difference results in a time displacement of 0.25 ms, the second 1 ms. The 0.25 ms difference will result in an apparent 180° phase shift for the frequency of 2 kHz and an apparent phase shift of 360° at 4 kHz. The frequency dependent phase shift introduced by the relative displacement of the two sound sources means that the sound cancels starting at 2 kHz, is reinforced at 4 kHz, cancels at 6 kHz, and so on every 2 kHz. This type of response is known as comb filtering because of its resulting frequency response. If the resulting displacement were 1 ms, then the fundamental cancellation is at 500 Hz, with summation and cancellation intervals of 500 Hz.

The interference (comb filtering response) occurring in an array of loudspeakers can be used to our advantage for directivity control. Figure 2 (below) is an example of four loudspeakers placed in a line with a 23.5-cm (9.25”) spacing, without filtering.

Here is the on-axis, 45°off-axis, and 90° off-axis response of a four element line array. The on-axis level goes up by +12 dB relative to a single element, and the 90° axis attenuation is increased to as much as 15 dB in the 400 Hz to 800 Hz octave band. However, the response is not uniform and would have an annoying sound due to the peak in the response at 1.6 kHz. Summation of elements and 1 create a primary interference notch in the 200 Hz to 300 Hz band. This would be expected because the spacing of the loudspeakers produces a 1.4 ms delay between the sound arrivals at the 90° off axis position. Each pair of loudspeakers will produce its own comb filter response that can be used for pattern control. Summation of elements 4 and 2 create a primary interference notch in the 400 Hz region, elements 4 and 3 in the 800 Hz region. If we use a set of bandpass filters on the array elements so that each pair is operated only over their primary notch bandpass, we could smooth the off axis response.