DRAFT Recommended Practice for Measurements and ...

1/29/98 123 C95.3-1991 Revision — 2 nd Draft
10/98 Draft
The FDTD method solves Maxwell’s differential equations at each cell edge at discrete
time steps. Since no matrix solution is involved, electrically large geometries can be
analyzed. FDTD solutions for three dimensional complex biological geometries involving
millions of cells have become routine, e.g., studies of SAR distributions associated with
exposure to hand-held radio transceivers [Gandhi, et al.,1996; Gandhi and Chen, 1995;
Jensen and Rahmat-Samii, 1995; Dimbylow and Mann, 1994; Luebbers, et al., 1992].
FDTD may be used for both open region calculations, e.g., SAR and current distributions
induced in the human body under plane-wave exposure conditions [Gandhi, et al., 1992],
or closed regions, such as within a TEM cell. Commercial FDTD software is available
from several sources, with some of these also offering FDTD meshes for human heads
and bodies. These commercial packages provide a graphical user interface for viewing
the FDTD mesh. Some provide interactive mesh editing while others allow for import of
objects from CAD programs.
The actual FDTD calculations may be excited in different ways. Most commonly the
electric fields on one or more mesh edges are determined by an analytical function of
time, such as a gaussian pulse or sine wave. This then acts as a driven voltage source
which, for example, may be used to excite an antenna such as a short monopole on a
metal box to approximate a hand-held radio transceiver. This monopole antenna could
be driven by a driven voltage source located on the mesh edge at the monopole base
next to the top of the box. Both [Kunz and Luebbers, 1993] and [Taflove, 1995] describe
methods for modeling RF sources. A variety of FDTD sources, including current
sources, are described in [Picket-May, et al., 1994]. Alternatively a plane wave may be
incident on the object as the excitation source.
The time variation of the excitation may be either pulsed or sinusoidal. The advantage of
the pulse is that the response for a wide frequency range can be obtained. For accurate
results, however, the frequency dependent behavior of the biological materials must be
included in the calculations. Methods for doing this are well known [Kunz and Luebbers,
1993; Taflove, 1995] so that transient electromagnetic field amplitudes for pulse
excitation can be calculated, e.g., (FD) 2 TD [Furse, et al., 1994]. When the results at a
single frequency or at a few frequencies are all that is desired, sine wave excitation is
preferred. This is especially true if results for the entire body are needed, such as the
SAR distribution, since storing the transient results for the entire body mesh and applying
Fast Fourier transformation (FFT) to calculate the SAR versus frequency requires
extremely large amounts of computer storage.
D5.7.1. Cell size and time-step size requirements. The choice of cell size is
critical in applying FDTD. It must be small enough to provide accurate results at the
highest frequency of interest, and yet be large enough to keep resource requirements
manageable. Cell size is directly affected by the dielectric properties of the materials
present. The greater the permittivity and/or conductivity the shorter the wavelength at a
given frequency and the smaller the cell size required. Once a cell size is selected, the
maximum time step is determined by the Courant stability condition. After the cell size is
determined, a problem space large enough to encompass the scattering object, plus
space between the object and the outer absorbing boundary, is determined. From the
number of Yee cells needed and the number of time steps required, resource
requirements can be estimated (see D5.7.2).
Copyright © 1998 IEEE. All rights reserved. This is an unapproved IEEE Standards Draft,
subject to change.