Analysis and design of field patterns of multidimensional structures

A simplification of the analysis and design of field patterns of multidimensional structures is presented. Application of the method of moments (MoM) to the analysis problem yields a matrix description of the structure - the admittance matrix. The excitation is represented by a voltage matrix. The product of the admittance matrix with the voltage matrix gives the current on the structure. Use of the MoM has been well established for several decades with known advantages: mutual coupling between array elements is taken into account and no unreasonable assumptions need to be made regarding the current distributions on the wires. Next, the array factor and the source distribution are related through discrete Fourier transform reducing much of the work done in the analysis and synthesis of point source arrays. With this procedure, a single matrix relates the structure excitation and the far field pattern. With proper manipulation on this matrix, according to the number of field points and feed points, it´s possible to obtain the feed voltages for a desired pattern. This communication describes theory in three dimensional structures of parallel wires. The effectiveness of the proposed method is illustrated with known examples of arrays in one and two dimensions.