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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. [ABSTRACT FROM AUTHOR]

This Letter introduces a novel impedance boundary condition (IBC) for the matched termination of waveguide ports in finite-difference–time-domain (FDTD) simulators. It is based on approximating the wave impedance by a rational function over the frequency band of interest. To show the validity of the proposed IBC, the reflection coefficient of a wideband matched 90° H-plane corner in rectangular waveguide is computed. The results obtained, which are less than -45 dB over the whole waveguide band, are in good agreement with those obtained by a commercial finite-element simulator. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 34: 151–155, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10400 [ABSTRACT FROM AUTHOR]

Introduces a technique for finite-difference time-domain modeling of wave propagation in dispersive media. Consideration of Ohm's law in the Laplace domain with an Mth-order rational model for the complex conductivity; Utilization of the Mobius transformation technique; Description of the resulting formulation.

At the pre- and post-processing stages of a finite-difference time-domain (FDTD) simulation, important tasks are carried out that require knowledge of the port data (propagation constants, fields, impedances, and so on) of the problem structure. This paper introduces a 2D finite-difference frequency-domain (FDFD) eigenvalue formulation specifically tailored for the computation of port data to be used in conjunction with the 3D-FDTD method. A key feature of the proposed FDFD scheme is that it leads to the same numerical dispersion equation as that of the 3D-FDTD method. This means that, for a given frequency, the numerical propagation constants and mode patterns calculated by the two methods are identical. This is desirable for preserving the accuracy of the FDTD simulation. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 45: 1–3, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20704 [ABSTRACT FROM AUTHOR]

In this paper, the characteristics of layered structures (photonic or electromagnetic bandgaps), including chiral media, are studied by means of two different numerical methods, one in the time domain (finite differences in the time domain, FDTD) and the other in the frequency domain (coupled-mode method, CMM). The results (reflection and transmission coefficients for a plane wave normally incident over a layered structure) obtained by means of both well different techniques are practically identical. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper studies the stability and numerical dispersion of an extension of the original finite-difference time-domain (FDTD) method to incorporate magnetized ferrites. This extension is based on discretizing the ferrite equations by means of central differences and averages. Both partially magnetized and saturated ferrites are considered. With the aim of studying the numerical features of the resulting FDTD algorithms, we have considered the propagation of plane-waves along longitudinally magnetized ferrite materials. This is a simple 1D problem that enables the numerical properties of the algorithms to be studied analytically. A von Neumann stability analysis shows that the stability condition of the original FDTD method is preserved and that the algorithms do not exhibit numerical dissipation. The accuracy of the numerical results is not deteriorated with respect to those obtained in the demagnetized case. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

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 are not properly chosen, a negative refractive index may become a positive one in the discrete world, thus changing the physics of the problem. [ABSTRACT FROM AUTHOR]

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-Ampère'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. [ABSTRACT FROM AUTHOR]