Effective Performance of Bessel Arrays
The Bessel array is a configuration of 5, 7, or 9 identical speakers in an equal-spaced line array that provides the same overall polar pattern as a single speaker of the array. This study reports the results of a computer simulation, using points sources, to determine the effective operating frequency range, working distance, efficiency, power handling, maximum acoustic output, efficiency-bandwidth product, and power-bandwidth product, etc., of the array. The various Bessel configurations are compared to 1, 2, and 5 source equal-spaced equal-level equal-polarity line arrays. As compared to a two-source equal-level in-phase array, a five source Bessel array is 2.4 dB less efficient, can handle 1.75 (+2.4 dB) 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 twenty times the length of the Bessel array was assumed, with the length of the Bessel array (center to center measurement) 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 7 and 9-source Bessel arrays are found to be effectively unusable, as compared to the 5-source Bessel, 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 working distance away from the array. Unfortunately, the phase vs. direction and phase vs. frequency characteristics of the Bessel array are very non-linear and make it difficult to use with other sources.
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