Analytical prediction of radiation from a multi-element variable-directivity spherical loudspeaker array and construction and measurement of a prototype

Abstract

An analysis of radiation from a spherical surface with twelve radiating spherical caps oriented in a dodecahedral arrangement is performed. The approach generalizes the classical single cap solution by utilizing spherical trigonometry transformations to create many spherical caps in different orientations. The calculations include far-field directivity, surface impedances, and net radiated power for a variety of cap motions within the spherical array. Simulations show how well the discrete caps can produce monopole, dipole, and higher mode directivity patterns. Relative motions of the caps are calculated that best simulate these individual radiation modes. The frequency ranges for accurate reproduction of these radiation modes using discrete caps are quantified, and the role of large cap sizes to extend the range is shown. At higher frequencies, the phase interference between discrete cap radiators cause the intended radiation patterns to break down in complicated ways. A prototype 12-element spherical speaker enclosure has been constructed, with the help of a 3-D printer, and tested in an anechoic chamber. The configuration of typical cone loudspeakers creates constraints on the practical design of spherical speakers, limiting the radiating area fraction. Driver design changes to allow more compact spherical speakers with extended frequency range are suggested.