A Study on the Stability and Numerical Dispersion of the Lumped-Network FDTD Method

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...

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Bibliographic Details
Published in:IEEE transactions on antennas and propagation 2009-07, Vol.57 (7), p.2023-2033
Main Authors: Gonzalez, O., Grande, A., Pereda, J.A., Vegas, A.
Format: Article
Language:English
Subjects:
Admittance
Antennas
Applied classical electromagnetism
Dispersion
Dispersions
Electromagnetic wave propagation, radiowave propagation
Electromagnetism
electron and ion optics
Exact sciences and technology
Finite difference method
Finite difference methods
Finite difference time domain method
Finite-difference time-domain (FDTD) methods
Frequency
Fundamental areas of phenomenology (including applications)
lumped elements
Mathematical analysis
Mathematical models
Microwave circuits
numerical dispersion
Numerical stability
Permittivity
Physics
Resistors
Stability
Stability analysis
Studies
Time domain analysis
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Summary: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 M th-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.
ISSN:0018-926X
1558-2221
DOI:10.1109/TAP.2009.2021907