Investigations on numerical techniques based on integral equation for the analysis and design of microwave devices in space applications

Abstract

Among all the numerical methods described in the technical literature and implemented in the electromagnetic (EM) full-wave simulators, this Ph. D. dissertation is focused on the Multimode Equivalent Network (MEN) technique. The main objective of this doctoral thesis is to extend the state of the art in the MEN context. This technique is based on the individual characterization of the discontinuities present in the structure. For each discontinuity, it starts by imposing the boundary conditions to obtain the relevant integral equations (IEs) that model the problem. After solving the IEs, the discontinuity is then characterized through an equivalent network, where the interactions between the modes on both sides of the discontinuity are rigorously account for by an impedance or admittance coupling matrix. Finally, the individual MENs are conveniently combined to perform the analysis of the complete device. This technique was originally developed for the analysis of waveguide components, where the excitations are the guided modes on both sides of the discontinuities. This formulation is revisited in this document as starting point. Several mechanisms to increase the computational effciency of this technique for waveguide analyses are also proposed in this doctoral thesis. Then, in order to extend the functionality of this technique and adapt it to other technologies that are nowadays commonly used in certain applications (such as microstrip or stripline), we develop in this doctoral thesis the MEN formulation for single-layer and multilayer planar components. We start formulating the MEN representation for zero-thickness discontinuities composed of rectangular obstacles, containing lateral ports in the transverse plane. This development is based on an electric MEN approach. The introduced lateral excitations are employed to model the coaxial connectors that normally excite the planar shielded structures. The excitation of the components through these ports is the most important difference with respect to the MEN formulations for waveguide problems. It allows to analyze planar devices where the excitation of the structures is lateral, instead of through guided modes (as in waveguide components). Then, we extend this analysis to zero thickness discontinuities that contain lateral ports and are formed by arbitrarily shaped metallizations. This is possible thanks to the combination of the magnetic MEN technique with the Boundary Integral-Resonant Mode Expansion (BI-RME) method. This extension allows the analysis of a large variety of microwave planar components using the MEN approach. In this development, internal ports are also considered for inter-connection purposes. Based on this MEN formulation, we detail how to consider ohmic losses in the discontinuity when the magnetic approach is used. Finally, we extend the MEN technique to the analysis of multilayer boxed planar microwave circuits that are built using a thick metallization. This formulation is particularly necessary when the thickness of the metallization becomes electrically large. All the proposed MEN extensions have been programmed in MATLAB. To validate the formulations, we select certain microwave components as examples and we analyze them running our MATLAB MEN codes. Then, we compare the simulations to different commercial software results, measurements from prototypes (if they are available) and results from the technical literature. In addition, several microwave fflters have been designed in this document. They are implemented in different technologies (rectangular waveguide, thick metallic bars and microstrip) for different applications. These fflters have been also simulated using the MEN formulations proposed in this doctoral thesis. All these numerical results show good agreement with respect to other full-wave EM tools and measurements, thereby fully validating the MEN extensions proposed in this thesis. Finally, an optimization module has been added to the MEN codes and allows the design of microstrip components using the MEN formulation.