Full-Wave Finite-Element Analysis of General Microwave Waveguides

Thesis brings a critical overview of so-far existing numerical methods based on finite elements and serving for the analysis of microwave transmission lines. On the basis of revealed problems, existing methods are originally modified. Attention is turned the the generality of developed approaches. The initial method is based on a functional of I. Huynen and A. Vander Vorst describing the distribution of EM field in a transmission line. Components of EM field are approximated by nodal-edge finite elementsand the functional is minimized with respect to unknown approximation coefficients. That way, a matrix equation is obtained, which is identical with the result of Galerkin method. Since accuracy of the finite-element method is crucially influenced by the quality of the discretization mesh, a detailed discussion is devoted even to this topic. Several meshes were proposed and their quality is tested using the reaction concept. Then an optimization method based on linear random search is proposed and the error of the solution is minimized. Since most CPU time is consumed by the solution of the general eigenvalue problem, efficiency of the method is increased using the complex hopping concept. Accuracy of the method is slightly lower. Since the classical finite-element method can be used for the analysis of closed structures only, a special spatial transformation was used to convert open structures to closed ones. Moreover, the transform is shown to behave the same way as perfectly matched layers.