Mutual coupling effects of finite rectangular phased arrays

A rigorous integral equation formulation for the analysis of a phased array of flange-mounted waveguide apertures is given for a finite number of elements and nonuniform spacings. The resulting set of integral equations is reduced to a matrix equation called the coupling matrix which relates the coefficients of all the modes in all the waveguides to one another. The solution then yields the dominant mode reflection coefficient, coefficients of scattered modes and hence the field in each waveguide. The block-Toeplitz symmetry property for the uniformly spaced linear and rectangular grid arrays is utilized in the solution of the system of equations