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A numerical dispersion analysis of the alternating-direction implicit finite-difference time-domain method for transverse-electric waves in lossy materials is presented. Two different finite-difference approximations for the conduction terms are considered: the double-average and the synchronized schemes. The numerical dispersion relation is derived in a closed form and validated through numerical simulations. This study shows that, despite its popularity, the accuracy of the double-average scheme is sensitive to how well the relaxation-time constant of the material is resolved by the time step. Poor resolutions lead to unacceptably large numerical errors. On the other hand, for good conductors, the synchronized scheme allows stability factors as large as 100 to be used without deteriorating the accuracy significantly. Index Terms--Alternating-direction implicit finite-difference time-domain (FDTD) method, lossy media, numerical dispersion, stability.

The lumped-network finite-difference time-domain (LN-FDTD) technique is an extension of the conventional FDTD method that enables the incorporation of linear one-port LNs in a single FDTD cell. This paper studies the stability and the numerical dispersion of this technique. To this end, an isotropic medium that is uniformly loaded with LNs in the x-direction is considered as a working model. The stability analysis, based on the von Neumann method, is performed for general Mth-order LNs and closed-form stability conditions are derived for some particular cases. The numerical dispersion relation is obtained for plane-wave propagation in the proposed LN-loaded medium. It is shown that LNs can be interpreted in terms of an effective frequency-dependent permittivity and, as a consequence, the LN-loaded medium can be viewed as a uniaxial medium. The numerical admittance of the LNs is also obtained showing that, as a side-effect of the time discretization, the LN parameters become frequency-dependent, e.g. for the resistor case, the resistance becomes a function of the frequency. Index Terms--Finite-difference time-domain (FDTD) methods, lumped elements, numerical dispersion, stability.

Numerical results obtained using a full-wave hybrid technique (comprising a new formulation of the coupled-mode method and the mode-matching method) for treating 3-D isotropic-chiral-material discontinuities in rectangular waveguides with perfect electrically conducting walls were compared with experimental data. For that purpose, samples of an isotropic chiral material were manufactured as composite materials. These samples were then fully characterized in the X-band. The measured constitutive parameters were used in the full-wave hybrid technique to predict the scattering parameters of three different structures--each a waveguide rifled partially with the isotropic chiral material. The scattering parameters were also measured. The predicted and measured scattering parameters were in reasonably good agreement. Index Terms--Chiral material, coupled-mode method, discontinuities, generalized scattering matrix, mode-matching method, rectangular waveguide, scattering parameters, vector network analyzer.

This paper introduces an extension of the original finite-difference time-domain (FDTD) method for modeling double-negative media characterized by high-order frequency-dependent permittivity and permeability. The approach basically consists of adding electric and magnetic current densities to Maxwell's curl equations and considering Ohm's law as a constitutive relationship. Current densities are discretized by using a weighted average in time and Ohm's law by applying the Mobius transformation technique. The extended FDTD formulation is validated and its numerical features are carefully examined. More specifically, analytical stability conditions are derived for several types of double-negative media and the numerical dissipation issue is discussed. In addition, the numerical dispersion equation for general high-order double-negative media is given and the order of accuracy of the scheme is studied. Finally, the definition of numerical refractive index is addressed and it is shown that, when the discretization parameters of the problem ate not properly chosen, a negative refractive index may become a positive one in the discrete world, thus changing the physics of the problem. Index Terms--Double-negative media, finite-difference time-domain (FDTD) methods, Mobius transformation, numerical dispersion, stability.

The lumped-network finite-difference time-domain (LN-FDTD) technique is an extension of the conventional finite-difference time-domain (FDTD) method that allows the systematic incorporation of linear one-port lumped networks (LNs) into a single FDTD cell. This paper presents an extension of the LN-FDTD technique, which allows linear two-port (TP)-LNs to be incorporated into the FDTD framework. The method basically consists of describing a TP-LN by means of its admittance matrix in the Laplace domain. By applying the Mobius transformation technique, we then obtain the admittance matrix of the TP-LN in the Z-transform domain. Finally, appropriate digital signal-processing methodologies are used to derive a set of difference equations that models the TP-LN behavior in the discrete-time domain. These equations are solved in combination with the Maxwell-Ampere's equation. To show the validity of the TP-LN-FDTD technique introduced here, we have considered the equivalent circuit of a chip capacitor and a linear circuit model of a generic metal--semiconductor field-effect transistor. These LNs have been placed on a microstrip gap and the scattering parameters of the resulting hybrid circuit have been computed. The results are compared with those obtained by using the electromagnetic simulator Agilent HFSS in combination with the circuital simulator ADS, and with those calculated by ADS alone. For the chip capacitor, experimental measurements have also been carried out. The agreement among all the simulated results is good. Generally speaking, the measured results agree with the simulated ones. The differences observed are mainly due to the influence of the subminiature A connectors and some mismatching at the ports. Index Terms--Finite-difference time-domain (FDTD) methods, global modeling, lumped networks (LNs).

A study of the stability and numerical dissipation of the finite-difference time-domain technique including passive and active lumped elements has been reported recently by Thiel and Katehi. In particular, three different formulations for lumped inductors were analyzed: the explicit, semi-implicit, and implicit schemes. The implicit scheme was identified to be the same as the formulation previously introduced by Piket-May et al., and its dissipative nature was modeled by a series resistor. In this paper, we perform a numerical dispersion analysis of the above-mentioned schemes, which has not been reported thus far. Other numerical properties of these schemes such as the stability are also discussed. The dispersion analysis allows the numerical impedance of the lumped inductor to be defined or, alternatively, to show that a region of lumped inductors can be interpreted as a dielectric material with a frequency-dependent permittivity. Special attention is given to the implicit scheme. For this scheme, three main conclusions are drawn, i.e., 1) the formulation introduced by Piket-May et al. does not correspond to the implicit scheme, but to the explicit one, 2) the implicit scheme is unconditionally stable for a range of inductance values, and 3) by means of the dispersion analysis, it is shown that the dissipative nature of the implicit scheme is more naturally modeled by a parallel resistor. Index Terms--Finite-difference time-domain (FDTD) methods, lumped inductors, numerical dispersion, stability.

This paper introduces a technique for finite-difference time-domain modeling of wave propagation in general Mth-order dispersive media. Ohm's law in the Laplace domain with an Mth-order rational model for the complex conductivity is considered as a constitutive relation. In order to discretize this model, the complex conductivity is mapped onto the Z-transform domain by means of the Mobius transformation. This leads finally to a set of difference equations that is consistent with Yee's scheme. The resulting formulation is explicit, it has a second-order accuracy, and the need for additional storage variables is minimal. The numerical stability problem is discussed and the numerical dispersion equation for Mth-order media is given. Index Terms--Dispersive media, FDTD methods, Mobius transformation.

Linear-prediction (LP) techniques are used to accurately and efficiently compute the frequencies and damping factors of microwave resonant structures from their transient response, which was previously obtained by using the finite-difference time-domain (FDTD) method. The LP equations are formulated in terms of a total least squares (TLS) problem and are solved by using the singular-value decomposition (SVD) algorithm. This approach confers robustness to the LP method, improves the spectral resolution, and provides a simple criterion for selecting the order of the LP model. We illustrate these characteristics of the LP method by applying it to two types of problems: the determination of the propagation constants of waveguides loaded with lossy dielectrics, and the calculation of the resonant frequencies of cylindrical cavities loaded with dielectric ring resonators. Index Terms - FDTD, Maxwell solver, numerical methods.

A formulation for the FDTD treatment of partially magnetized ferrites is presented. It is based on the derivation of a system of time-domain differential equations from an empirical expression of the permeability tensor, normally used for designing microwave devices. This approach is applied to the full-wave analysis of waveguides loaded with partially magnetized ferrites.

A novel procedure for the FDTD formulation for dispersive media is proposed. With this procedure, a dispersive medium is modeled as a time-invariant discrete system described in terms of its state-space equations. These equations are suitable for direct incorporation into the FDTD algorithm, allowing the wave propagation in general nth-order linear dispersive media to be analyzed by the FDTD method.

This work analyzes multiple 3-D discontinuities between rectangular ferrite-loaded waveguides. Each uniform section of waveguide is analyzed by means of Schelkunoff's method with improved convergence. Combining this method with the mode matching method allows the analysis of multiple discontinuities to be simplified. The theoretical results obtained in this way agree quite web with measurements.

This paper addresses the problem of stability analysis of finite-difference time-domain (FDTD) approximations for Maxwell's equations. The combination of the yon Nenmann method with the Routh-Hurwitz criterion is proposed as an algebraic procedure for obtaining analytical closed-form stability expressions. This technique is applied to the problem of determining the stability conditions of an extension of the FDTD method to incorporate dispersive media previously reported in the literature. Both Debye and Lorentz dispersive media are considered. It is shown that, for the former case, the stability limit of the conventional FDTD method is preserved. However, for the latter case, a more restrictive stability limit is obtained. To overcome this drawback, a new scheme is presented, which allows the stability limit of the conventional FDTD method to be maintained. Index Terms--Dispersive media, FDTD methods, Routh's methods, stability analysis, von Neumann method.