Kvazistacionarni pristup za analizu mikrotalasnih vodova

Abstract

Analysis of microwave transmission lines is the main subject of research in the world for more than six decades. Since the day of stripline invention, back in 1949, and its modifications that followed in the forthcoming years, an "army" of scientists was trying to analyze it, simplify it and design new structures. These structures, due to their characteristics, have found wide application in microwave integrated circuits, for microwave filters and antennas design, delay lines, directional couplers, etc. Various numerical and analytical methods such as: the variational method, the method of moments, the boundary element method, the conformal mapping, the moving perfect electric wall method, the equivalent electrodes method etc. can be applied with more or less accuracy to the microwave transmission lines analysis. The aim of this doctoral dissertation is quasi TEM analysis of microwave transmission lines using the hybrid boundary method (HBEM). This method, developed at the Department of Theoretical Electrical Engineering in the Faculty of Electronic Engineering of Niš, is based on the equivalent electrodes methods and the point-matching method for the potential of the perfect electric conductor electrodes and for normal component of the electric field at the boundary surface between any two dielectric layers. Until now, it was applied to multilayered electromagnetic problems, grounding systems, electromagnetic field determination in the vicinity of cable terminations as well as magnetic field and force calculations of permanent magnets. In order to expand the field of method’s application, it is, for the first time, applied for the microwave transmission lines analysis. Single and coupled, shielded and open microwave transmission lines with homogeneous, isotropic single-layer and multilayer dielectrics were analysed in the examples presented. Structures with the ground planes of infinite width, but also the real cases – geometry with ground planes of finite width, the finite metallization thickness and substrate width, are also shown in this dissertation. The hybrid boundary element method has been proved to be a very simple, powerful and accurate procedure for microwave transmission lines analysis. The obtained system of linear equations is always well-conditioned, as the system matrix always has the greatest elements on the main diagonal. Quite good convergence for the desired parameters is achieved for only 700-1500 unknowns (equivalent electrodes). For the most examples, the convergence of results, calculation time, equipotential contours and distribution of polarized charges per unit length along boundary surfaces are shown in the tables and graphically. In order to validate the characteristic parameters results, obtained by the hybrid boundary element method, all the results will be compared to those obtained by software FEMM and FlexPDE as well as the results already reported in the literature. These results were shown in tables and graphically. The relative error for the characteristic impedance is less than 0.5 % in regards to the results obtained using the FEMM with few thousands elements and the uniform meshing technique. The computation time is even several times shorter than in the case of the analysis using the FEMM and FlexPDE. The real challenge for the author was to apply the hybrid boundary element method for analysis of microstrip transmission lines with Tellegen material (non-reciprocal bi-isotropic media). Unlike a wide range of literature that deals with the analysis of microwave transmission lines with isotropic dielectric, bi-isotropic media, due to their complexity, are not so common subject of research. The hybrid boundary element method was successfully applied for the analysis of such structures. Applying the hybrid boundary element method it is possible to analyze quickly, easily and sufficiently accurate the complex configuration of microwave transmission lines with isotropic and bi-isotropic substrate. In that way this dissertation represents a small contribution to the history of the development of methods for the analysis of microwave lines long more than 60 years.