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A combined rigorous method is presented for the analysis of horn antennas with arbitrary cross section and general outer surface. The horn taper is described by the mode-matching (MM) method where the cross-section eigenvalue problem is solved by a two-dimensional (2-D) finite element (FE) technique. For the exterior horn surface including the radiating aperture, the application of the Kirchhoff-Huygens principle yields two expressions for the admittance matrix which are based on the electric (EFIE) and the magnetic (MFIE) field integral equation, respectively. The equations are solved numerically by the method of moments (MoM). For the preferred EFIE formulation, the eigenvectors of the last waveguide taper section and RWG functions for triangular patches are utilized as basis-functions for the magnetic or electric surface current densities, respectively. The presented method is verified by available reference values or measurements for a waveguide radiator with a peripheral choke, a conical and a rectangular horn. Its flexibility is demonstrated at the example of a conical ridged waveguide horn.Index Terms-Horn antennas, integral equation methods, method of moments, mode-matching methods.

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