Investigation of distributed circuit theory with retardation for analysis of microwave characteristics of three dimensional conductor/dielectric structures

The recent progress in the field of high-speed digital circuit technologies and Monolithic Microwave Integrated Circuits (MMICs) has led to complex microwave circuit structures that exhibit strong dispersive behavior. Therefore, to model the dynamic behavior of electromagnetic properties of complex structures, the use of distributed circuit models in conjunction with numerical analysis is very promising. The starting point for the use of numerical models for field analysis is the generalization of field theory to circuit theory, to efficiently manage complexity. In this thesis, the equivalence between Kirchoffs current and voltage laws, and Maxwell's field equations, using retarded potentials and the method of moments (Galerkin's) technique, is established in the frequency domain. Retarded potentials are directly related to the current and charge sources and therefore both electric and magnetic fields can be determined [3].; Various numerical methods have been published in the literature that lead to circuit models of electromagnetic wave propagation, but a direct evaluation of equivalent circuit models and their characteristics using retarded potentials in the frequency domain and Kirchoff's laws has not been implemented previously. This work addresses the issue and shows the relationship between retarded potentials in field theory and Kirchoff's current and voltage laws resulting in equivalent circuit models. The resulting circuit models have been evaluated using various analytical formulae available in the literature and the scattering characteristics of several relevant structures have been obtained using circuit network analysis and are discussed.