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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]

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.

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]