Angel Vegas

Analyzing the stability of the FDTD technique by combining the von Neumann method with the Routh-Hurwitz criterion

This paper addresses the problem of stability analysis of finite-difference time-domain (FDTD) approximations for Maxwells equations. The combination of the von Neumann 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.

Computation of resonant frequencies and quality factors of open dielectric resonators by a combination of the finite-difference time-domain (FDTD) and Prony's methods

Open dielectric resonators using the FD-TD (finite-difference time-domain) method are analyzed. Resonant frequencies and quality factors are calculated using Pronys method instead of the classical fast Fourier transform. In this way, reductions of up to two orders of magnitude are achieved in computation time. The results obtained are in good agreement with those reported by other authors.<<ETX>>

FDTD modeling of wave propagation in dispersive media by using the Mobius transformation technique

This paper introduces a technique for finite-difference time-domain modeling of wave propagation in general Mth-order dispersive media. Ohms 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 Yees 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.

A treatment of magnetized ferrites using the FDTD method

The finite-difference-time-domain (FDTD) method is extended to include magnetized ferrites. The treatment of the ferrite material is based on the equation of motion, using Gilberts approximation of the damping term. The validity of the formulation is verified by applying it to the calculation of propagation constants in waveguides containing ferrites with transverse magnetization. The results for a rectangular waveguide filled with ferrites and those for a rectangular waveguide loaded with a centered ferrite slab are compared with the exact results, showing good agreement.<<ETX>>

Numerical dispersion and stability analysis of the FDTD technique in lossy dielectrics

Two different extensions of the finite-difference time-domain (FDTD) method for the treatment of lossy dielectrics are considered: the time-average (TA) and the time-forward (TF) difference schemes. An analytical study of the stability properties and numerical dispersion of these schemes is presented. The stability analysis is based on the Von Neumann (Fourier series) method, while the numerical dispersion properties are established in terms of the numerical permittivity of discrete lossy dielectrics. The analytical stability limits are compared with those obtained numerically in previous works. The accuracy of the two schemes is compared by computing the reflection coefficient of a lossy dielectric slab.

An extension of the lumped-network FDTD method to linear two-port lumped circuits

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-Amperes 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.

Full-Wave Hybrid Technique for 3-D Isotropic-Chiral-Material Discontinuities in Rectangular Waveguides: Theory and Experiment

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 wave guides 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 filled partially with the isotropic chiral material. The scattering parameters were also measured. The predicted and measured scattering parameters were in reasonably good agreement.

Study on the stability and numerical dispersion of the FDTD technique including lumped inductors

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.

FDTD Modeling of Chiral Media by Using the Mobius Transformation Technique

This letter introduces a new technique for finite-difference time-domain (FDTD) modeling of electromagnetic wave propagation in frequency-dispersive chiral media. First, Maxwells curl equations are discretized according to Yees scheme. Then the constitutive relations, expressed in the Laplace domain, are discretized using the Mobius transformation technique and appropriate digital-processing methodologies. The resulting formulation is explicit and preserves the second-order accuracy of the conventional FDTD technique. To show the validity of the method, the reflection and transmission coefficients of a chiral slab are computed and compared to the exact results, with good agreement being obtained

Modelling multiple discontinuities in rectangular waveguide partially filled with non-reciprocal ferrites

This work analyzes multiple 3D discontinuities between rectangular ferrite-loaded waveguides. Each uniform section of waveguide is analyzed by means of Schelkunoffs 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 well with measurements. >