Analysis of circular waveguide antennas including the outer wall geometry with a spherical-wave formulation of the boundary contour-mode-matching method

A new mode-matching method is presented for the rigorous analysis of circular waveguide antennas including an arbitrarily shaped outer antenna geometry with symmetry of revolution. The uniform modal expansion formulation uses cylindrical wave functions for the homogeneous waveguide region, whereas for the inhomogeneous outer region with the more general boundary contour, spherical waves are utilized. This formulation achieves high efficiency and only a few modes are required for adequate convergence. The mode-matching at the aperture yields directly the modal scattering matrix of the complete antenna and the wave amplitude coefficients of the spherical modes for a given excitation. To show the usefulness of the method, the E-, H-plane and cross-polar patterns of an open circular waveguide with finite wall-thickness and finite length are calculated for the minimum cross-polarization value and compared with results obtained by the moment method. Excellent agreement is observed. Moreover, the theory is verified by comparison with measurements of the return loss vs. frequency of a circular waveguide antenna with a circular flange of finite length.<>