42. Application of Linear-Phase Digital Crossover Filters to Pair-Wise Symmetric Multi-Way Loudspeakers

Publication Date: 2007-09-06

Various methods exist for crossing over multi-way loudspeaker systems. These methods include those loosely classified as Linkwitz-Riley filters, constant-voltage filters, and D’Appolito configurations. All these methods do not provide broad-band constant-beamwidth or constant-directivity operation because their vertical radiation patterns change shape as a function of frequency. This paper describes a simple, non-iterative linear-phase crossover filter design technique that provides uniform frequency responses vertically off-axis for a given multi-way loudspeaker. Distances between the individual drivers, and desired off-axis attenuation are prescribed as input parameters for the design process, the outcome of which is a set of crossover frequencies and unique filter frequency responses in each band. In order to obtain wide-band constant-beamwidth, a loudspeaker array configuration composed of a single central tweeter surrounded symmetrically by pairs of lower-operating-frequency transducers arranged in a vertical line is required. Practical implementation issues are outlined in the paper by means of various design examples. Two design methods are presented in two-parts: Part 1: a general method which emphasizes flatness of arbitrary off-axis frequency responses and Part 2: a simplified method that emphasizes frequency uniformity of beam shape and coverage angle (vertical beamwidth) of the polar patterns.

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Horbach, Ulrich; Keele, Jr., D. B. (Don); 2007; Application of Linear-Phase Digital Crossover Filters to Pair-Wise Symmetric Multi-Way Loudspeakers Part 1: Control of Off-Axis Frequency Response [PDF]; Harman International Industries; Paper 3; Available from: https://aes2.org/publications/elibrary-page/?id=14199

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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Horbach, Ulrich; Keele, Jr, D.; 2007; Application of Linear-Phase Digital Crossover Filters to Pair-Wise Symmetric Multi-Way Loudspeakers Part 2: Control of Beamwidth and Polar Shape [PDF]; Harman Consumer Group; Harman/Becker Automotive Systems; Paper 12; Available from: https://aes2.org/publications/elibrary-page/?id=14208