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IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 46, NO. 1, FEBRUARY 2004
Fig. 4. Current distributions along the helical dipole radiating in the proximity of a homogeneous head model for a feeding voltage of 1 V. Results produced with
Green/MoM and FDTD techniques.
V. NUMERICAL RESULTS AND DISCUSSION
TABLE II
PEAK SAR VALUES AND ABSORBED POWER IN HOMOGENEOUS AND
A. Validation of the Green/MoM Technique
THREE-LAYER SPHERICAL HEAD MODELS EXPOSED TO NORMALMODE
HELICAL DIPOLE ANTENNA AT 1710 MHZ. THE TOTAL RADIATED
In order to check the convergence and stability of the devel-
POWER IS 125 MW. RESULTS PRODUCED WITH GREEN/MOM
TECHNIQUES
AND FDTD
oped Green/MoM numerical code, several trials have been per-
formed by varying the number of spherical wave vectors used to
express the fields inside the sphere layers and in the air region
and by increasing the number of segments of the antenna wire.
To assure convergence of the obtained solution at any point in
space, a number of 3565 wave vectors ((1)) is required, while
a significantly lower number
of wave vectors is needed
for computations at far-field points. The number of segments
required to model the wire antenna depends on its total length
and complexity of its shape. For the specific helical dipole sim-
ulations considered here, a number of 500 segments has been
found sufficient to assure convergence of the obtained solution.
An additional check referring to the energy conservation has
been performed by comparing the input power computed at the
voltage of 1 V. The corresponding input impedance was found
feeding gap, to the sum of the power absorbed by the head and
.
the power radiated in the antenna far field. An excellent agree-
The maximum values of local SAR, SAR averaged over 1
ment has been observed (difference less than 1%).
or 10 g of tissue, and the power absorbed by the head have
been computed for the four canonical problems and are shown
B. SAR Computations and Antenna Performance
in Table II. It can be noticed that similar values of maximum
The Green/MoM technique has been used to study canonical
SAR (local or averaged) are observed in children and adults
exposure problems at 1710 MHz. Simulations have been carried
head models. As far as the total absorbed power is considered, a
out for four spherical head models, namely homogeneous and
90%95% of the helical dipole input power is absorbed by chil-
three-layer spheres simulating adults and children heads, ex-
dren or adults head models.
posed to the helical dipole of Fig. 2(a). A separation distance of
Penetration curves showing the SAR variation along -axis,
5 mm between helical antenna and spherical head models
that is "from one ear to the other" of the spherical head models,
has been considered.
have also been computed and the local SAR values normalized
to the maximum SAR value, as computed by the Green/MoM
For the case of the helical dipole radiating in the presence of
technique, are presented in Fig. 5. Since the diameter of the
the adult homogeneous spherical head model, the spatial dis-
children's head models is smaller, the SAR value at the opposite
tribution of the current along the antenna wire as a function of
from the phone head side is higher than the corresponding one
ratio, where is the curvilinear coordinate along the wire,
in the adults head models.
has been calculated and is presented in Fig. 4, for a feeding