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.

A New Approach to the Modeling of Anisotropic Media with the Transmission Line Matrix Method

“…xx /ε 0 = σ m zz /µ 0 . This relation between the electric and the magnetic conductivity ensured propagation without frequency dispersion, which allowed for the prediction of a common attenuation factor for all frequencies in the case of plane wave propagation [2,29]. In this example, the specific values of both conductivity terms had been chosen for an attenuation factor of exp(−1) after travelling 100 nodes.…”

“…These twelve ports are termed the link lines, and they are mainly responsible for propagation. It is worth noting that connections at the node center are not actual connections; they are to be understood in a formal sense instead, in order to reproduce the coupling existing in the original differential equations governing the phenomenon, which is Maxwell's equations in this work [2]. On occasion, additional capacitive, inductive, or electric and magnetic loss lines are also formally connected at the node center to allow for a specific control of properties such as the electric permittivity, magnetic permeability, or electric and magnetic conductivity [3,4].…”

Importance of the singular constitutive parameters of cylindrical cloaks: illustration on the anticloak concept

“…The global node in Fig. 1 can be split into three subnodes, each one representing a component of the Maxwell's equations [19]. It is worth mentioning that two supplementary infinite stubs could be added to the node to describe magnetic losses, but since no magnetic losses are present in the structure under consideration, they will not be included to rule out an unnecessary increase in the computational requirements.…”

Time domain simulation of electromagnetic cloaking structures with TLM method

“…This particular version of 2D nodes is explained by the fact that most of the TLM effort has been concentrated on the design of general 3D condensed nodes. It has been only in later years that general condensed and lossy condensed nodes in 2D problems have been reported in the literature [17,18], independently defining permittivity, permeability, together with electric and magnetic losses in a node with arbitrary length along each Cartesian direction. In this situation, we propose using the technique described in [18,19] to design a 2D condensed node with a minimum number of inductive and capacitive stubs appropriately connected so as to model not only usual materials but also metamaterials with negative permittivity and/or permeability values.…”