Modeling of infinite periodic arrays with dielectric volumes and quasi-3D oriented conductors

A new asymptotic extraction technique is used within the Method of Moments to model periodic quasi-3D arrays consisting of complex elements including vertical/horizontal conductors and dielectric volumes. The extraction uses special asymptotes closely connected to the actual Green's functions. These asymptotes can be used both for single elements and periodic arrays of elements. This step facilitates the simultaneous development of new features for both topologies. The modeling of periodic arrays composed of complex elements including horizontal/vertical con- ductors and dielectric volumes is of interest in difierent applications including antenna design, frequency selective surfaces and so on. The design of such arrays in many cases is facilitated if the modeling of a single element is also available. These two topologies can be very useful to estimate the mutual coupling in arrays. Nowadays there are several software tools available based on dif- ferent techniques that can be used to treat these two topologies. Some of the software tools are better suited to model single elements, while others are better suited to model antennas enclosed in an environment with periodic or waveguide boundary conditions. The switch between difierent software tools is not always straightforward because the input/output formats are very often in- compatible. Thus, it is of great interest to have a single code that is able to treat e-ciently these topologies using the same approach in both cases. The MoM method in combination with Mixed Potential Integral Equations (MPIE) has proven to be very e-cient in the modeling of conductors in layered structures (1). This approach is based on the construction of spatial Green's functions (GFs). This method can be used for a single element and a periodic array of elements. The GFs construction for a single element and for a periodic array encounters difierent types of problems despite that in both cases it is based on the Inverse Fourier Transform (IFT) of the same spectral GFs, which are known in a closed form. The IFT is expressed in terms of double integrals for a single element or in terms of double series for a periodic array. The convergence of the spectral GFs is normally insu-cient for a direct numerical evaluation. In the case of a single element, moreover, a special precaution should be taken to deal correctly with branch cuts and poles. In the case of a periodic array, these problems are avoided because the needed spectrum is discrete. This last difierence contributes enormously to the fact that the construction of the GFs is typically treated separately for a single element and a periodic array resulting in difierent algorithms and software codes. As a consequence available software tools are normally better suited for a single element or a periodic array. The aim of this paper is to report an e-cient algorithm and its implementation within a single code, with only minor difierences between a single element and a periodic array. This technique was consecutively applied to model periodic arrays only with horizontal conductors, and then with a combination of vertical and horizontal conductors. The application of this technique was shown at EUCAP 06 for horizontal conductors and at EUCAP07 for horizontal and vertical conductors. In this paper, dielectric volumes are included. The combination of vertical and horizontal conductors with dielectric volumes widens considerably the variety of topologies that can be modeled. 2. THEORY The MPIE in the MoM formulation requires the calculation of the GFs in the spatial domain for difierent source types (electric horizontal and vertical conductors and volumes). The algorithm to calculate them is quite cumbersome and its implementation needs a lot of efiort. The approach chosen in this paper relies on a strong resemblance between the two algorithms to calculate GFs for a single source and a periodic array of sources. The original algorithm for a single source is slightly adjusted in such a way that the periodicity of the elements can be implemented very easily.