Improved solution for mode coupling in different-sized circular apertures and its application

A solution for the mutual admittance between modes in identical circular apertures is extended to the general case of coupling between different-sized apertures. Two alternative representations for the mode coupling integrals are derived. One is a gamma-function series representation with a limited range of application. The other is an improved integral formulation which is better suited to numerical calculation than the original integrals and was obtained by means of an integral transform in the complex plane. The accuracy of this improved integral formulation is demonstrated by comparing computed results with measured data for a three-element test array. Excellent agreement is obtained between theory and experiment for both coupling coefficients and radiation patterns. Results are also presented for an eight-horn feed cluster for a reflector.