Contributions to the time domain-finite difference method for the modeling of microwave structures.

Abstract

In this thesis, the Time Domain-Finite Difference (TD-FD) approach based on Maxwell's time dependent curl equations has been investigated with the objective to develop a numerical model for simulation of electromagnetic (EM) wave propagation phenomena, and to obtain S-parameters of guided wave transmission structures. The numerical model formulated as initial boundary value problem has been developed for both CW (single frequency) and pulse (wide band) propagations. The simulation property of EM field propagation is interpreted by considering the analogy between continuous and discrete characteristics of Maxwell's curl equations, the latter being derived from the leap-frog approximation scheme for local wave propagation. In an effort to relate the discrete wave propagation model to the continuous one, the geometrical meaning and the effects of the stability factor are introduced. The analysis of the leap-frog approximation under the plane wave condition shows that the TD-FD method is non-dissipative, which means that numerical energy is conserved during the simulated wave propagation. From the field distribution of numerical wave propagation, any physical parameters in the frequency domain can be extracted. This is done using the S-parameter extraction algorithm that has been developed for both the CW and pulse propagation cases. To accurately model EM wave propagation by the numerical process, convergence criteria for checking the global errors in the numerical procedure are also introduced by considering the physical properties, phase linearity and matching condition (standing wave) along a lossless waveguide with uniform cross-section. The physical properties used also confirm that Maxwell's equations can be separated into transverse and longitudinal parts in any uniform guide. The criteria serve as a basic building block for the analysis of more complex guiding structures. In the formulation of a computational domain for EM wave propagation solutions, artificial matching boundary conditions (MBC) are necessary to make the domain compact. A new wideband MBC has been introduced. The MBC is based on the concept of the transition operator used in modern control theory. An efficient local mesh refinement algorithm is also developed by using the concept of the characteristic and by enforcing boundary conditions for $\vec{E}$ and $\vec{H}$ fields at the interface of different mesh sizes. Numerical analysis results are presented to validate the various procedures when combined into a complete model. The objective of this study was to develop a TD-FD model of Maxwell's equations for EM wave propagation phenomena in continuous media. With this numerical model, almost all kinds of experiments can be done in complete freedom from experimental apparatus. Also, when probing the field distribution in an experiment, the numerical model provides excellent results without any field disturbance.