Design of Optimal Transducer Arrays

A generalized approach to the design of practical transducer arrays using recently developed mathematical optimization techniques is presented. The method generates the optimal array configuration and sets of element excitations to produce simultaneously a number of different three-dimensional patterns, which may be specified in any arbitrary planes. To ensure a practical design, the procedure is not limited to isotropic sources; it can also accommodate measured directivity characteristics of individual radiators. In addition, realistic bounds for all parameter values can be included. These variables are the location of the individual modules comprising the array and the excitation (amplitude and phase) of each module for each pattern. A computer program was written to implement this method, and two examples and of its use are presented: The first example treats the design of a linear array of eight isotropic radiators and shows that improvement over Dolph-Chebychev shading is possible; the second deals with a 12-element planar array required to produce, simultaneously, three patterns, each of which is specified in three planes.