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Effective Performance of Bessel Arrays
The Bessel array is a configuration of five, seven, or nine identical loudspeakers in an equal-spaced line array that provides the same overall polar pattern as a single loudspeaker of the array. The results of a computer simulation are described, which uses point sources to determine the effective operating frequency range, working distance, efficiency, power handling, maximum acoustic output, efficiency-bandwidth product, and power-bandwidth product of the array. The various Bessel configurations are compared to one-, two-, and five-source equal-spaced equal-level equal-polarity line arrays. As compared to a single source, a five source Bessel array is 14% (0.6dB) more efficient, can handle 3.5 (+5.4dB) more power, and has 4 times (+6dB) the maximum midband acoustic output power, and is usable for omnidirectional radiation up to the frequency where the overall length is 11 wavelengths long. As compared to a two-source equal-level in-phase array, a five-source Bessel array is 43% (2.4dB) less efficient, can handle 1.75 (+2.4dB) more power, has the same maximum midband acoustic output power, and is usable for omnidirectional radiation 10 times higher in frequency. A working distance of 20 times the length of the Bessel array was assumed, with the length of the Bessel array (center-to-center distance of outside sources) being four times that of the two-source array. Analysis reveals that the three Bessel arrays have equal maximum acoustic output, but that the five-element Bessel array has the highest efficiency and power-bandwidth product. The seven- and nine-source Bessel arrays are found to be effectively unusable, as compared to the five-source array, due to much lower efficiency, requirement for more sources, and poor high-frequency performance. Judging polar peak-to-peak ripple and high-frequency response, the performance of the Bessel array is found to improve in direct proportion to the working distance away from the array. Unfortunately the phase versus direction and phase versus frequency characteristics of the Bessel array are very nonlinear and make it difficult to use with other sources.
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