On the foundations of the transmission line matrix method

The foundations of the TLM method with symmetrical condensed node in the original formulation of Johns for the solution of three-dimensional electromagnetic field problems are investigated in this dissertation. It is shown that the mapping between the discretized electromagnetic field components and the TLM wave pulses determines the asymptotic convergence rate of the TLM algorithm. For this, the convergence of the original symmetrical condensed node TLM formulation introduced by Johns is proved for the first time. The proof is achieved in three steps. First, the appropriate function spaces providing a suitable norm for proving convergence are constructed. Second, the cell-centred field-mapping is applied at every iteration step yielding a mapping induced finite difference scheme, which is the well known Lax-Friedrichs scheme. Third, it is shown using norm estimations that the difference between the TLM scheme and this mapping induced finite difference scheme approaches zero for the discretization approaching zero. It emerges that using a cell-centred field-mapping results in convergence of order 0.5. Other work has shown that using a bijective boundary oriented field-mapping gives second order convergence. This influence of the field-mapping on the asymptotic convergence order is verified in a numerical experiment. Furthermore, the suitability of the recently proposed Alternating Transmission Line Matrix Method for the solution of electromagnetic field problems is discussed. The application's part of this dissertation deals with the characterization of planar microwave components using the TLM method. A TLM algorithm for considering first order dispersive media is derived. The influence of dielectric losses of the adhesive that is used to embed chips into multichip module (MCM) substrates on the transmission properties of such MCM interconnects is investigated applying this TLM algorithm. Further, the influence of substrate losses on the properties of planar microwave transformers, which are used in mobile communication amplifiers, is investigated. For this layered absorbers for the truncation of the computational domain have to be implemented. The TLM characterization of a simplified transformer indicates a potential use of such transformers up to 50 GHz. The lossy substrate has a negligible influence on the transformer characteristics up to 30 GHz.SIGLEAvailable from: http://tumb1.biblio.tu-muenchen.de/publ/diss/ei/2000/rebel.html / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman