M. Celuch-Marcysiak

Wide-band S-parameter extraction from FD-TD simulations for propagating and evanescent modes in inhomogeneous guides

This paper proposes a new method of S-parameter extraction from finite-difference time-domain simulations. Unlike the previously published methods, the present method extracts the frequency-dependent mode impedance and propagation constant directly from the three-dimensional simulations. This makes it accurate and computationally effective in wide-band analysis. This paper provides examples of calculations including difficult cases of inhomogeneous or lossy structures, with the frequency band spanning below and above the cutoff frequency. Special attention is given to the S-parameter extraction for evanescent modes. It is shown that the available literature provides insufficient and sometimes confusing background in this regard. Thus, a new consistent theoretical background is presented.

Generalized TLM algorithms with controlled stability margin and their equivalence with finite-difference formulations for modified grids

Generalized TLM formulation based on modified grids of 2-D shunt nodes or 3-D expanded modes are proposed. Generalization consists of permitting flexible control of the numerical stability margin (and thus a time-step for a particular discretization), and of introducing enhanced models for curved boundaries. Formal equivalence between generalized TLM and FDTD algorithms based on the same grid is proved. Simple rules for transforming circuit models (from TLM to FDTD and vice versa) and for their equivalent excitation are given. It is demonstrated that the application of the generalized algorithm reduces computer resources required for the TLM analysis of a circular waveguide by an order of magnitude. >

A differential method of reflection coefficient extraction from FDTD simulations

A novel concept for accurate extraction of the reflection coefficient from electromagnetic simulations is proposed and implemented into the finite-difference time-domain (FDTD) method. It uses only the values of an arbitrary tangential E-field component and its derivative with respect to the longitudinal direction at one selected point, and of an arbitrary tangential H-field component and its derivative with respect to the longitudinal direction at another point. No a priori knowledge of reference impedances is needed, and the reflection coefficient is extracted from a single run of FDTD. The proposed method is directly applicable to arbitrarily shaped and inhomogeneous transmission lines.

On the nature of solutions produced by finite difference schemes in time domain

This paper is a review discussing properties of field solutions produced by various finite difference schemes in the time domain. Considered algorithms include standard FDTD as well as its modifications based on different sets of electromagnetic equations and/or different discretization in space. By developing their complete dispersion relations, conclusions are drawn regarding divergence, curl, and energy conserva tion by each of the emulated eigenmodes separately. This is in extension to previous works which were concerned with the total solution, and permits to formulate conditions for restricting the total solutions to physical uncoupled solenoidal and potential modes. Original classification of spurious modes for the time domain finite difference modelling is also proposed. It is shown that spurious compensating modes can propagate over the mesh in the case of penalty schemes with p≠0, and that spurious degenerate modes at high- and low-frequencies appear in the case of condensed node discretization. Copyright

On the effect of bilateral dispersion in inhomogeneous symmetrical condensed node modeling

We have detected bilateral dispersion in electromagnetic simulation of microwave circuits, based on the SCN modeling. Bilateral dispersion means that in eigenvalue analysis the calculated resonant frequencies may be overestimates as well as underestimates. We demonstrate that this effect is caused by nodal stubs representing inhomogeneous permittivity and permeability in the SCN. We introduce an exact analytic formula evaluating the SCN dispersion errors within arbitrary media, and we verify this formula by means of computational examples. We show that superiority of the SCN modeling (with respect to the ExpN modeling of the same cell size) in terms of the dispersion as exhibited for homogeneous circuits may practically vanish in the case of inhomogeneous circuits with big differences in media parameters. This effect should be taken into account when selecting one of the models for electromagnetic simulation. >

Formal Equivalence and Efficiency Comparison of the FD-TD, TLM and SN Methods in Application to Microwave CAD Programs

In this study, the Theorem of Equivalence of the FD-TD, TLM and SN methods in application to the analysis of microwave circuits is derived. Computer resources required by FD-TD, TLM and SN are thoroughly compared. The concepts of extended FD-TD and of mixed modelling are introduced.

A new efficient excitation scheme for the FDTD method based on the field and impedance template

We have presented a new excitation scheme for the FDTD analysis of guided wave problems. Tangential E-field components in the input plane are driven by elementary sources with both amplitude and output impedance determined by the modal template. This permits accurate FDTD simulations using only short sections of input feeds. For typical microwave circuits such as a patch antenna considered in the present paper, a reduction in computer resources by a factor of two is achieved. The templates are established automatically by the 2DV FDTD algorithm operated in an optimization loop. By using the 2DV rather than 3D FDTD template generation, we can easily consider a fundamental mode or any higher mode, and distinguish between two propagating modes such as an odd and even mode in the presented example of asymmetrical coupled microstrip lines.

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. >

Local stereoscopic field singularity models for FDTD analysis of guided wave problems

New local FDTD field singularity models have been proposed. In an extension to previous local models, not only radial field variations but also the geometry of field lines and the curvature of Ampere/Faraday integration surfaces are taken into account. The method is shown to provide the same order of accuracy as previously published specialised higher-order algorithms. Yet, contrary to those methods, the gain in accuracy is achieved practically without any increase of the computing time of FDTD simulations.

Effective time domain analysis of periodic structures

In the paper we introduce a new approach to the analysis of periodic structures such as corrugated transmission lines or slow wave structures. It is based on the time domain simulation (FD-TD or TLM) of only one period, with a special type of boundary conditions modelling its behaviour in the entire structure. Two versions of the new method are considered. The first one utilizes complex notation in the phase constant domain while the other one reduces calculations to real numbers. We show how the new approach has been applied to several practical cases producing excellent results.