An enhancement of instruments for solution of general transmission line equations with method of lines, impedance-/admittance and field transformation in combination with finite differences

Abstract

The Method of Lines in combination with impedance/admittance and field transformation is used to analyze electromagnetic waves. The used cases are waveguiding structures in microwave technology and optics. The core of the theory is the solution of generalized transmission line equations (GTL). In the case of complex structures, a combination with finite differences (FD) can be used. The quality of this solution essentially depends on the effectiveness of the used interpolation of the differences. The individual steps of the FD are permanently linked to the steps of the fully vectorial impedance/admittance and field transformation, so standard libraries cannot be used. Two approaches based on the linear and quadratic interpolation were built into the impedance/admittance and field transformation in the past. However, the degree of improvement due to one or another kind of interpolation depends on the concrete behavior of the solution sought. In the case of complex structures, choosing the appropriate type of interpolation should be an effective aid. In this paper, an extension of the family of built-in methods is proposed—with the possibility of being able to build any known numerical method from the class of one-step or multi-step methods into the GTL solution. These can be higher-order methods, including fast explicit methods, or particularly stable implicit methods. The transmission matrices for the impedance/admittance and field transformation serve as the building site. To illustrate the procedure, some different methods are integrated into the GTL solution. The efficiency of the solutions is tested on some test structures and compared with each other and with existing solutions. The relevant waveguide specifics were discussed. Initial systematics and recommendations for users were derived.