V. Trenkic

Development of a general symmetrical condensed node for the TLM method

A general symmetrical condensed node (GSCN) for the transmission line modeling (TLM) method, with six different link line characteristic impedances, six stubs, and six lossy elements is described for the first time. It unifies all the currently available condensed nodes into a single formulation and provides the basis for the derivation of an infinite set of new nodes, including nodes with improved numerical characteristics. The GSCN is derived in two ways: (1) from an equivalent network model and (2) directly from Maxwells equations using central differencing and averaging. The direct correspondence established between the GSCN TLM and a finite difference scheme for Maxwells equations provides a rigorous theoretical foundation for all available TLM methods with condensed nodes.

Theory of the symmetrical super-condensed node for the TLM method

This paper describes a novel time-domain node for the TLM method. It has the unique feature of modeling arbitrary inhomogeneous media on a generally graded rectangular TLM mesh without using stubs. Variations in material properties and arbitrary aspect ratios of mesh cells are modeled by allowing different characteristic impedances in a cell, maintaining impulse synchronism throughout the mesh. The complete theory of the new node is given and its implementation on a general TLM mesh is discussed. Numerical results for a canonical resonator loaded with dielectric layers are presented for different grading cases. Substantial savings in computer storage and run-time as well as improved accuracy compared to the uniform mesh are achieved when an appropriate nonuniform grading of the TLM mesh is used. >

A fully integrated multiconductor model for TLM

A fully integrated model of coupling between the electromagnetic field and multiconductor cabling is developed using the transmission line matrix (TLM) method. In this model, the multiconductor cables are represented by multiconductor transmission lines which connect to the general TLM mesh.

Optimization of TLM schemes based on the general symmetrical condensed node

A general symmetrical condensed node (GSCN) for the transmission-line modeling (TLM) method is derived from first principles, based on the establishment of a mapping between field quantities and voltage pulses, averaging at the node centers quantities at the boundaries and differencing of Maxwells equations. The degrees of freedom offered by this formulation permit the development of adaptable nodes, where the mix of stubs and links can be chosen in a manner to optimize the dispersion characteristics. Results are shown confirming that the adaptable nodes can reduce substantially the dispersion and remove polarization-dependent errors.

Analytical expansion of the dispersion relation for TLM condensed nodes

A method for obtaining analytical solutions of the general transmission line modeling (TLM) dispersion relation for condensed node schemes is described. Exact analytical forms of the dispersion relation for currently available nodes are derived, enabling the efficient study of dispersion solutions without resorting to a numerical solver. Using these analytical relations, the range and behavior of propagation errors are fully explored and visualized, not only for propagation along the axes and diagonals or in a coordinate plane, but for arbitrary angles of propagation in three-dimensional space. Comparisons are presented of the numerical performance of different TLM condensed node schemes.

On the time step in hybrid symmetrical condensed TLM nodes

New formulas for the maximum permissible time step in TLM hybrid nodes modeling anisotropic media are introduced and analyzed. It is shown that the value of the time step in most cases can be higher than that suggested by the minimum node dimension. The chosen value of the time step has significant impact on the dispersion characteristics of the hybrid symmetrical condensed node. >

Dispersion analysis of a TLM mesh using a new scattering matrix formulation

An equivalent scattering matrix for the TLM symmetrical condensed node is derived by rearranging the order of node ports. The new matrix is given in a partitioned form with zero blocks on the main diagonal. It enables a transformation of the general dispersion relation from a 12th- to a 6th-order eigenvalue equation, thus significantly simplifying the problem of finding a closed algebraic form of the dispersion relation for the symmetrical condensed node. >

Advanced node formulations in TLM-the adaptable symmetrical condensed node

The paper describes the development of a class of adaptable symmetrical condensed (ASCN) transmission-line modeling (TLM) nodes. The parameters and numerical properties of the ASCN are expressed in terms of arbitrary weighting functions which can be selected in a manner that minimizes dispersion and improves accuracy. It is shown that this approach is effective and can be used to optimize nodal properties according to problem requirements.

Dispersion of TLM condensed nodes in media with arbitrary electromagnetic properties

New analytical closed forms of the dispersion relation for TLM condensed nodes modelling general materials (stubbed symmetrical condensed node, symmetrical super-condensed node) are presented and validated by numerical results. The range of dispersion errors and bilateral behavior are fully explored and practical guidance is offered to users.<<ETX>>

A graded symmetrical super-condensed node for the TLM method

A novel node for use in simulations by the transmission-line modelling (TLM) method is described. Unlike existing nodes, it contains no stubs but it is capable of modelling inhomogeneous media using a variable or graded mesh. The theoretical development of the new node is described and results from simulations are presented showing the accuracy and a considerably increased computational efficiency compared to conventional nodes.<<ETX>>