**1. Introduction**

The excitation problem is of increasing importance at microwave frequencies [1]. Microwave antennas and other microwave devices are often fed by waveguides (rectangular, circular, and coaxial) or transmission lines (such as microstrips). In general, these devices are composite structures consisting of both conductive and dielectric elements. Therefore, the appropriate modeling of the waveguide excitation of such structures is of great interest. Such modeling in numerical methods is usually done by truncating the feed waveguide to create a waveguide port and formulate suitable boundary conditions (BC) imposed on the port. Such BCs should be able to launch an incident wave into the waveguide and absorb the reflected (in active mode) or received (in passive mode) wave without spurious reflections [2].

To date, most approaches to solving the waveguide port excitation (WPE) problem are based on volume discretization methods, such as the finite-element method (FEM) [1, 2], finite difference time domain (FDTD) [3–5], discontinues Galerkin time-domain (DGTD) [6], contour integral method (CIM) [7], etc. Most of these works use various modal absorbing boundary conditions (MABC) [4, 5], developed for time-domain methods as termination conditions imposed on the port.

At present, many electromagnetic (EM) problems are solved using surface integral equations (SIE) together with the method of moments (MoM) [8]. Within the framework of SIE, the WPE problem was first formulated as an aperture coupling problem for a conducting geometry, and the MoM solution for magnetic currents was obtained in the presence of a short-circuited conductive sheet [9]. This approach was then modified using the pseudo-image method for magnetic currents in addition to electric currents [10]. Further, MoM was applied to the waveguide port problems [11] and antenna radiation problems with aperture port excitation [12]. However, until recently, a MoM-based solution to the WPE problem for arbitrary geometries has been poorly represented in the literature. In our recent works [13–15], such a solution was obtained for radiation and coupling problems for various types of geometries.

This chapter generalizes the recently proposed MoM-based approach to WPE problems [13–15] on arbitrary conducting and composite geometries. The obtained approach combines the canonical aperture coupling approach with the EFIE-PMCHWT formulation for composite structures [16–22]. Each WPE problem in this approach is divided into equivalent sub-problems for internal and external regions, which are solved using the MoM. The internal WPE problems are solved using waveguide modal expansion in the port plane, while the external problems are solved using the equivalence principle to reduce these problems to the systems of algebraic equations for unknown electric and magnetic currents. The obtained solution also considers the problem of material junctions between adjacent surfaces, considered in [19–22].

The developed approach is validated on radiation and coupling problems for coaxial ports by comparing the simulated results with those from other approaches and measurements. In addition, this approach is applied to practical EMC problems for microwave antennas fed by coaxial ports. The MoM calculations were performed using the TriD numerical code incorporated in the EMCoS Studio software package [23].
