This book presents the topic in electromagnetics known as Transmission-Line Modeling or Matrix method-TLM. While it is written for engineering students at graduate and advanced undergraduate levels, it is also highly suitable for specialists in computational electromagnetics working in industry, who wish to become familiar with the topic. The main method of implementation of TLM is via the time-domain differential equations, however, this can also be via the frequency-domain differential equations. The emphasis in this book is on the time-domain TLM. Physical concepts are emphasized here before embarking onto mathematical development in order to provide simple, straightforward suggestions for the development of models that can then be readily programmed for further computations. Sections with strong mathematical flavors have been included where there are clear methodological advantages forming the basis for developing practical modeling tools. The book can be read at different depths depending on...

The Transmission-Line Modeling (TLM) Method in Electromagnetics

This paper presented direct derivations of the TLM symmetrical condensed node (SCN) and hybrid symmetrical condensed node (HSCN) from Maxwell's equations by using centered differencing and averaging. Direct correspondence between the TLM and finite difference method is established. The node scattering matrices and field expressions are given for the general case with graded mesh and anisotropic materials including both electric and magnetic losses. It is found that the TLM SCN and HSCN always have 2nd-order accuracy regardless of a uniform or graded mesh discretization of the space. >

Direct derivations of TLM symmetrical condensed node and hybrid symmetrical condensed node from Maxwell's equations using centered differencing and averaging

Much progress has been made in the use of computational electromagnetics for the analysis of electromagnetic compatibility (EMC) problems during recent years. This paper reviews the improvements in some of the most important techniques of the field: the method of moments, the finite-difference time-domain method, the finite-element method, the transmission-line matrix method, and the partial-element equivalent-circuit method. The results of computer codes on the basis of such methods have to be validated, and some of the respective possibilities are addressed.

Numerical Electromagnetic Field Analysis for EMC Problems

The application of the transmission line matrix and the finite-difference time-domain methods for two and three dimensional numerical modelling of ground probing radar (GPR) is the subject of this thesis. Basic principles of GPR are discussed at the outset and the suitability of the chosen approach for its numerical simulation is demonstrated. Efficient absorbing boundary conditions are introduced in the two dimensional formulation of the transmission line matrix in order to limit the computational domain. Their performance is evaluated and it is demonstrated that by using different forms of implementation they can perform similarly or better than the finite-difference time-domain method. Two dimensional models are used to study the effects of the constitutive parameters of the subsurface to the GPR signals and the limits of horizontal and vertical resolution as well as responses from common geological targets. A solution to the instabilities introduced by absorbing boundary conditions in the three dimensional transmission line matrix method using the symmetrical condensed node is reported as a modification of an existing formulation. The good performance of this absorbing boundary condition in free-space scattering problems is demonstrated using a scattering field transmission line matrix model. Three dimensional models based on these numerical techniques are used to study the GPR responses from small localized targets and the advantages and disadvantages of different orientations of the transmitting and receiving antennas. The potential benefit of the use of magnetic field sensors in ground probing radar is demonstrated using the three dimensional finite-difference time-domain model. Comparisons between the two formulations studied for the simulation of ground probing radar are reported.

The investigation of transmission-line matrix and finite-difference time-domain methods for the forward problem of ground probing radar

A new ‘multigrid’ interface is presented for the connection of fine and coarse TLM meshes. The interface is defined as an electrical connection and thus may be used unmodified with any type of TLM, and with guaranteed stability and losslessness. The connection supports correct propagation at any angle to the interface.

New multigrid interface for the TLM method

An alternative symmetrical condensed node has been developed for which the iterative time step is independent of the ratio of grading on the TLM mesh. The new mode has fewer stubs than the previous node and is shown to have a reduced velocity error for axial propagation.

Hybrid symmetrical condensed node for the TLM method

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. A basic TLM model of straight multiconductor lines is developed first, followed by the derivation of a general multiconductor junction model suitable for describing more complex configurations. Sample numerical results are presented to confirm validity and efficiency of the model.

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.

A compact TLM model is presented for efficient computer simulation of electromagnetic field propagation through airflow aperture arrays in metal equipment boxes. The model permits modelling of air-vents with significant perforation depth using computational cells larger that the individual apertures. Validations of the proposed model are presented.

Compact TLM model for air-vents

An extension to the TLM method allowing efficient modelling of perforated metal screens is presented. This model permits simulation of emission from shielded enclosures with small apertures, such as air-vents, using computational cells that may be larger than the individual apertures. The TLM scattering algorithm is given and numerical validation of the proposed model is presented. (2 pages)

R. Scaramuzza

Papers

Hybrid symmetrical condensed node for the TLM method

A fully integrated multiconductor model for TLM

A fully integrated multiconductor model for TLM

Compact TLM model for air-vents

TLM modelling of perforated thin metal screens