Aperture impedance of flared horns

The method of moments is often used when solving for the mutual coupling in arrays of aperture antennas. For elements that are waveguides or gradually flared horns, the aperture fields can be approximated by a finite sum of waveguide modal functions. To solve for the flared horn case, an approximation for the aperture impedances of the modes in the horn is needed. The WKB approach can be used to find these impedances, but this technique has an important limitation. It is known to fail in the vicinity of its turning points. The turning point is the cutoff point of the mode being considered. To overcome this limitation a different technique, the spherical mode approach, is discussed. This approach has no cutoff problems and works well for conical and pyramidal horns. Comparisons between the impedances and the resulting dominant mode reflection coefficient found using the two techniques are presented to illustrate this point.