The hybridization of the Mode Matching Method and the Finite Element Method has been discussed in Chapter 1

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In this dissertation, the development of a hybrid numerical method Mode Matching-Finite Element-Spectral Decomposition (MM-FE-SD) for electromagnetic analysis and design of several devices has been investigated. In particular, attention has been focused on the design of complex devices with finite dimensions and thick FSSs optimized by means of a Genetic Algorithm.

The hybridization of the Mode Matching Method and the Finite Element Method has been discussed in Chapter 1; this part represents the guidelines of all this work and may be considered as a necessary introduction for a correct interpretation of the following chapters.

One of the key features of this formulation is the expansion of transverse electric and magnetic fields by using Tangential Vector Edge Elements (TVEE) which guarantees spurious-free solutions; indeed, this property is very important for an accurate numerical determination of the modal eigenvalues. A spectral criterion to determine the correct ratio between the number of FEM reconstructed and analytically derived modes is adopted.

Moreover the Mode Matching technique allows us to take into account several modes to correctly represent a generic discontinuity.

The hybrid MM-FE technique applied to the rigorous analysis of thick inductive Frequency Selective Surfaces (FSSs) has been presented in Chapter 2. These surfaces are realized by periodically perforating thick metallic screens with arbitrarily shaped apertures obtained as NURBS curves. The electromagnetic fields in the free-space region are expanded through a complete set of Floquet’s modes allowing us to reduce the analysis to a single periodicity cell; a set of waveguide modes is used inside the apertures and each mode is numerically determined through a FE procedure on edge elements. The optimized geometric characteristics of this kind of structures has been obtained by using a genetic optimization procedure, where the shape of the unit cell, the periodicities, the skewness angle and the thickness are the genes of the chromosome. This technique has shown that the convergence is faster for the optimization procedure applied to the unconventional FSS. Several numerical results have been proposed.

The application of the hybrid MM-FEM to the analysis of phased arrays of waveguide feeding a thick screen with arbitrary shaped apertures has been presented in Chapter 3.

Firstly, the infinite problem has been considered, next the MM-FE approach has been hybridized with the Spectral Decomposition method to allow the analysis of finite problem.

The active reflection coefficient has been computed as superposition of several different problems, each one corresponding to a spectral sample. The reflection coefficient, relative to any cell of the infinite array corresponding to the spectral sample is obtained by applying the MM-FE procedure. Polygonal arrangement of the single elements have been taken into account by using a closed-form Fourier transform. The hybrid methodology has been applied to the study of large finite phased array of horn antennas. A comparison of the results found by means of the hybrid MM-FEM approach with other methods and commercial software has been provided to show the effectiveness and the accuracy of the hybrid technique.

In Chapter 4 the same method has been extended to the analysis of thin FSSs of finite size.

In this case the Spectral Decomposition approach has been combined with a Method of Moments for thin periodic structures. Several example have been shown and compared with the results obtained by using commercial software.

Finally in the Chapter 5, a technique, based on a combination of the Mode Matching-Finite Element Method, Spectral Decomposition (MM-FEM-SD) and Method of Moments (MoM), to analyze large but finite array of waveguides, cascaded with an FSS with



dissimilar periodicity have been presented. It has been shown that, in order to accurately analyze such composite structure, the Generalized Scattering Matrix (GSM) of each subsystem has to be computed. To this aim, a relationship that maps the individual Floquet expansions of each subsystem with the global one has been established. The global GSM, relative to the global Floquet expansion, is filled by starting from the individual GSM of each subsystem. The GSM of the phased array is obtained by applying the MM-FE procedure, the GSM of the FSS is obtained by applying a MoM procedure. Several examples have been proposed to prove the effectiveness and the efficiency of this method.





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