Symmetrical Condensed TLM Node Research Articles

Accurate propagation computation through metamaterial RAM structures using modified 3D SCN transmission line matrix method for different incidence angles

In this paper, a validation study for the metamaterial accurate modelling using the electromagnetic numerical transmission line matrix (TLM) computation method is presented. In our work, the three-dimensional symmetrical condensed node (SCN) TLM algorithm has been modified to fully simulate non-linear and dispersive metamaterial structures. The modification code principles have been explained theoretically. The propagation computation using our modifying TLM code has been tested for a metamaterial ground slab loaded by split ring resonator structure. The tested structure acts as a metamaterial radar absorber. Moreover, experimental measurements were carried out and compared to the computed ones. The results confirmed the good agreement between measured and TLM computed results. Furthermore, the propagation computation was confirmed by measuring the backscattering for different incident angles which demonstrate very good agreement for our modified TLM code. The measurement results confirm the versatility and power of the modified SCN TLM algorithm to handle metamaterial structures.

Modeling of electromagnetic waves propagation in nonlinear optical media using HSCN-TLM method

In this paper, we propose a hybrid symmetrical condensed node TLM approach for the simulation of optical media under femtosecond regime. The formulation is based on the piecewise linear recursive convolution (PLRC) technique, voltage sources and the introduction of the variable admittance concept. Optical solitons with Kerr and Raman nonlinearities are simulated using this novel approach.

Numerical modeling of microstriplines with substrates with arbitrarily varying thickness with the use of the TLM method

AbstractThe symmetrical condensed‐node TLM method is used for the analysis of microstrip lines with substrates of arbitrary varying thickness. This numerical technique has been efficiently used for the computation of the propagation constant and the characteristic impedance of this structure. Moreover, it has been demonstrated that the shape of the microstrip substrate is also an important parameter for controlling the values of its characteristic impedance. The validity of the obtained results is proved by comparisons with those obtained from the literature. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 34: 48–51, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10369

A Z-transform-based absorbing boundary conditions for 3-D TLM-SCN method

In this paper, an efficient absorbing boundary condition (ABC) constructed in the Z-transform domain [i.e., Z-transform-based absorbing boundary conditions (Z-ABCs)] for the three-dimensional symmetrical condensed-node transmission-line matrix method is presented. Numerical results indicate that the Z-ABCs show better performance than the conventional Higdon's ABC in suppressing instability caused by spurious modes.

Modified conducting boundaries in symmetrical condensed node (SCN) transmission line matrix (TLM) modelling

Previously in the symmetrical condensed node TLM (SCN-TLM) method conducting boundaries have been placed at the interface between two cells. The author describes modifications that can be made to the SCN that enable a conducting boundary to go through the centre of the cell. The modified TLM method is compared with the traditional TLM method, and with data available in the literature for a waveguide iris. The results reveal enhancement in the convergence of the results as the cell size is reduced.

A fast spatial-domain method for the suppression of excitation-induced spurious modes in SCN TLM

An efficient method for the suppression of excitation-induced spurious modes in the symmetrical condensed node (SCN) transmission-line matrix (TLM) method is presented for the general case of dielectric, anisotropic, or lossy media in planar structures. A special mapping of the field-excitation onto the wave amplitudes of the TLM algorithm completely prevents the emanation of the spurious modes. The application of the mapping in the k-/spl omega/ space can be done for waveguides with low computational effort. The method is generalized for planar structures with high spatial frequencies of the field at the discontinuities. We use precomputed field templates at the entrance of the three-dimensional (3-D) structures. The mapping is mainly done in the space domain based on the quasi-TEM propagation of the guided waves to keep the computational effort low. Instead of the four-dimensional (4-D) k-/spl omega/ transformation, only independent one-dimensional (1-D) transformations to the wave coefficient of the conductors direction and /spl omega/ are necessary. In the case of propagation with low dispersion, the expenditure can be further reduced to 1-D transformations with respect to /spl omega/. The efficiency of the present method is demonstrated by investigation of a coplanar waveguide and a triplate waveguide.

Modeling of general constitutive relationships in SCN TLM

The modeling of general constitutive relationships in SCN (symmetrical condensed node) TLM is presented. The technique consists of decoupling the impulse scattering at the nodes from equations describing the medium by using equivalent node sources with state-variable formulation of the constitutive relationships. The procedure requires few modifications of TLM. Numerical examples are presented.

Comments on "A class of symmetrical condensed node TLM methods derived directly from Maxwell's equations" [with reply

In the original paper, LoVetri and Simons [see ibid, vol.41, p. 1419-28,1993] derive the three-dimensional symmetrical condensed node TLM algorithm using a characteristic based field decomposition of Maxwell's equations. The goal and eventual result of the investigation was to present a mathematically sound method for deriving the TLM scattering and transfer events directly from Maxwell's equations (without recourse to the approximation of space by a mesh of transmission lines). The statement made by Krumpholz and Russer, that the original derivation is erroneous, is not valid and the two specific points they raise are considered.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A pair of hybrid symmetrical condensed TLM nodes

This letter reports the development of a new time-domain hybrid symmetrical condensed TLM node. The new node can accommodate a graded mesh and model lossy anisotropic media described by diagonal tensors. The generalisation of an existing hybrid node to accommodate anisotropic media is also presented. The two hybrid nodes are complementary and provide the same computational advantages over the symmetrical condensed node originally proposed by Johns (1987). >

A new frequency domain symmetrical condensed TLM node

This paper reports the development of a new symmetrical condensed TLM node derived directly in the frequency domain. The new node can accommodate a graded mesh and can model lossy anisotropic media described by a static conductivity tensor along with complex permittivity and complex permeability tensors. The frequency domain TLM method is used to generate modal dispersion curves for microwave and millimeter wave guiding structures. The results compare the new node to existing time domain symmetrical condensed nodes. >

General electromagnetic scattering analysis by TLM method

The symmetrical condensed node TLM method is applied to the problem of electromagnetic scattering from objects illuminated by a plane wave at off axis angles of incidence. A mesh division algorithm is described for implementing the plane wave source. Good agreement with measured data is demonstrated.

One-way equation absorbing boundary conditions for 3-D TLM analysis of planar and quasi-planar structures

Absorbing boundary conditions based on one-way wave equations (formulated by Higdon for FD-TD analysis) have been investigated and implemented for the 3-D Symmetrical Condensed Node TLM analysis of dispersive microwave and millimeter-wave structures. Very low reflections over a wide frequency band have been obtained by concatenating two and three first-order boundary operators. Numerical stability of the absorbing boundary conditions with different discretizations of the boundary operators (derivatives) has been studied. It has been found that numerically stable algorithms can be obtained with proper discretizations. These excellent stable absorbing boundary conditions can considerably reduce the computational domain, thus making possible the 3-D TLM analysis of planar and quasi-planar structures with moderate computer resources. The scattering parameters computed using these boundary conditions for microstrip via holes and shorting pins compare well with the available data. >

Circuit model for a symmetrical condensed TLM node

AbstractAn equivalent circuit for a symmetrical condensed TLM node is presented. The basic circuit has twelve ports and consists of 24 1:1 ideal transformers. Three additional conductances model the conductivity of the medium. The circuit is extended with additional ideal transformers giving six ports for short‐circuit and open‐circuit stubs which model the permittivity and permeability of the inhomogeneous medium. The scattering matrix of the 18‐port network is determined symbolically by solving a set of linear circuit equations. The matrix agrees with previously published results for a symmetrical condensed TLM node, obtained from Maxwell's equations.

Consistent finite difference modelling of Maxwell's equations with lossy symmetrical condensed TLM node

AbstractA propagator integral interpretation for general TLM processes is presented and applied to discretized Maxwell's equations. The approach provides exact algebraic solutions of finite difference equations along a quite universal scheme.Specifically, Johns's process based on the symmetrical condensed node is reconstructed and generalized as a clear‐cut FD algorithm. The fields computed are exact time‐domain solutions of the FD equations, provided that total voltages and currents are evaluated and stub quantities are not externally excited. Losses are very naturally incorporated into the TLM algorithm.The structural similarity of the TLM process (properly operated) with the propagator integral appears just as fundamental as general and should have further applications.

A transformed symmetrical condensed node for the effective TLM analysis of guided wave problems

A transmission line matrix (TLM) algorithm for the effective solution of arbitrary guided wave problems is proposed. The algorithm uses an appropriately transformed symmetrical condensed node (SCN) introduced herein. In comparison with the previous SCN TLM formulation for the analysis of guiding structures, the approach maintains equivalent accuracy and generality while providing a 50% gain in terms of required computer memory and time. The advantages of the new algorithm are verified by means of several examples, including full-wave analysis of waveguides filled with anisotropic and lossy media. >

A class of symmetrical condensed node TLM methods derived directly from Maxwell's equations

A series of general transmission line matrix (TLM)-type methods, which include the symmetrical condensed node method, are derived directly from Maxwell's curl equations without recourse to transmission line models. Written as a system of conservation laws, Maxwell's equations in 3-D plus time are decomposed along the orthogonal characteristic directions of a rectangular grid. The Riemann invariants in this method correspond to the voltage pulses of the TLM method. A new method of handling inhomogeneous media is proposed based on a new transfer event. The dispersive nature of these schemes is also investigated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

New TLM technique for steady-state filed solutions in three dimensions

A new steady-state technique is presented for the 3-D symmetrical condensed TLM node. A waveguide problem is modelled to test the theory and an electromagnetic diffusion problem is modelled as a case where steady-state TLM is more efficient than time-domain TLM

Representation of symmetrical condensed TLM node

A new and simple transmission line junction to represent the symmetrical condensed TLM node is presented. The required scattering is achieved without the use of ideal transformers, though at the expense of a redefinition of the ports. The junction is intended as a conceptual model, but with minor modifications could actually be built.

Modelling of materials with electric and magnetic losses with the symmetrical condensed tlm method

The modelling of materials that include both electric and magnetic losses by the TLM method using the symmetrical condensed TLM node is described. The new scattering matrix for the node with losses is given and numerical results are presented which display the high degree of accuracy available with this model.

Numerical Results for the Symmetrical Condensed TLM Node

Numerical calculations have been made in order to test the accuracy of the recently derived three-dimensional symmetrical condensed TLM node for electromagnetic. Demonstrations of its use in these areas are given. Analysis of dispersion characteristics shows that the velocity error bound for the new symmetrical condensed node is likely to be less than that for the expanded node. Predictions of the surface currents on an F-111 aircraft due to the scattering of an incident plane wave are in good agreement with other computed codes and measurements. Lastly, the introduction of, stubs into tbe scattering node allows generalization to a cylindrical mesh, which is tested by finding coaxial cavity modes.