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Application of Linear-Phase Digital Crossover Filters to Pair-Wise Symmetric Multi-Way Loudspeakers Part 2: Control of Beamwidth and Polar Shape
In part 2, we present an alternate simplified design technique that is based not on Part 1’s specification of frequency responses at arbitrary off-axis vertical angles, but on specification of the total shape and coverage angle (vertical beamwidth) of the polar patterns generated by pairs of separated point sources. Here we show that when only a single pair of drivers is operating at a specific frequency (Part 1 called these the “critical frequencies”), the spacing of these drivers is a constant distant apart in terms of acoustic wavelength. The design procedure of Part 2 simplifies that of part 1 by restricting the level of the forced-to-be-flat off-axis angle to -6 dB thus making it equal to the level of the polar beamwidth specification, i.e. beamwidth is defined as the angle between the 6-dB-down points from on axis. Thus restricted, Part 2 shows that the spacing of each pair of drivers at their critical frequencies should be in the range of 0.4 to 0.6 wavelength to yield well-behaved polar shapes with beamwidths in the range of 67º to 113º. Part 2 also shows that that spacing ratios between successive pairs of drivers should preferably be in the range of 2:1 to 2.5:1, but can extend out to 4:1, but at the expense of polar uniformity at angles beyond the 6-dB-down points.
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