On the circuit description of TLM nodes

Abstract

Classically in the transmission line matrix (TLM) method, the non-existence of a simple and straightforward circuital description of Maxwell equations has only been associated with three-dimensional (3D) nodes describing general phenomena. On the contrary, except for some specific works available in the literature, a direct and simple transmission line circuit is usually employed for describing the full node. This single circuit allows derivation of the scattering matrix and other quantities for nodes in two-dimensional (2D) situations by simply using transmission and reflection coefficients for this circuit. The non-existence of such a simple circuital representation also for general 2D and even for one-dimensional (1D) TLM nodes is considered in this paper. As with the 3D cases, the use of coupled transmission line circuits is required in general 2D and 1D cases, instead. Therefore, except for some particular situations, the classical transmission and reflection coefficients of a single transmission line circuit are not valid for obtaining the scattering matrix or other quantities associated with these 2D nodes.

Keywords:

• Numerical modelling
• TLM method
• Electromagnetic wave propagation

Acknowledgements

This work has been supported in part by the ‘Ministerio de Educación y Ciencia’ of Spain under project reference FIS2004-03273 cofinanced with FEDER funds of the European Union. The authors also thank A. Espinosa for her help in preparing the manuscript.