Abstract: This paper presents a comparative study of the
interactions between five commercial handset antennas and human-head tissue in
personal communications using the finite-difference time- domain (FDTD)
electromagnetic simulation approach. Various antennas used for cellular phones
such as the monopole, dipole and inverted-F antennas (IFA) have been considered
in the investigation. A heterogeneous and realistic head model has been
utilized to predict the effects of EM coupling to a human operator on the
antenna characteristics, such as input impedance, radiation patterns, and
radiation efficiency. The potential hazards posed by the antennas on the human
head have also been addressed by examining the specific absorption rate (SAR)
in the human tissue for 1 W of power radiated.
Keywords: Electromagnetic
Radiation, Finite-Difference Time-Domain Method (FDTD), Biological Effects, Cellular
Phone, and Mobile Communications.
I. Introduction
The
introduction of cellular communications technology has led to a growing
awareness of the vital role wireless systems playing in communication networks
[1]. With this ever-increasing role, the requirements placed on antenna design
are increasingly stringent.
Since
the cellular handphones are in close proximity to the human head while in use,
two important aspects that the antenna designer must account for are:
Ø
Will the proximity of the
person degrade the performance, i.e. antenna gain, radiation pattern and input
impedance matching?
Ø
Are there potential health
hazards to the user with the human head tissue exposed to electromagnetic
radiation?
Ø
How much difference is there
as different mobile phone radiate in the presence of human head?
Hence,
the designer must develop a highly-efficient, low profile antenna which can be
mounted on a hand-held transceiver and operated in the proximity of human
tissue. The various commercial antennas studied here include the monopole,
dipole and inverted F-antennas (IFA). For the monopole, both the Pan European
Cellular System-Group Speciale Mobile (GSM) and Personal Communications Network
(PCN) types have been considered and investigated. To gain a detailed
understanding of the antenna-tissue interaction, there exist a variety of
techniques which can be used to perform the required analysis, such as the
finite element method, the method of moments, and the finite-difference method,
each with its own strengths and weaknesses. Among these techniques,
considerable attention has been focused on the direct solution of Maxwell's
time-domain differential equations using the finite-difference time-domain
(FDTD) method for characterization of more complex radiating structures. As
stated by John B. Schneider and Kurt Shlager, the FDTD literature goes back to Kane Yee's 1966 paper. Since then,
there was one other publication in the 60's, a trickle of publications in the
70's, a stream in the 80's, and a flood in the 90's.
At best, they have catalogued a significant portion of published literature to
date although the database is not complete. Therefore, this paper here does not
intend to include a very lengthy list of publications.
In
this work, a well-developed physical model of the human head has been employed
together with detailed representations of handset-mounted antennas to allow for
accurate FDTD simulations of real-life scenarios. The first section of this
paper briefly introduces the background of this work. The second section
outlines the Yee algorithm, summarizes the various antenna configurations and
their dimensions used in this analysis, and tabulates typical human-head tissue
parameters. In the third section, results obtained are presented and discussed.
Finally, the work is concluded with some remarks.
II. Formulation of the Problem
A. FDTD Implementation
The
FDTD methodology originates from the Yee algorithm [2] which solves for both
electric and magnetic fields in time and space domains using the coupled
Maxwell's curl equations in their finite difference form. The volume of space
is discretised into lattice cells on a rectilinear grid. By employing a
discretization of the calculus operators in these equations, a set of algebraic
time-stepping relations are obtained, as given in [3].
In
making the FDTD calculations, certain general constraints and requirements must
be accounted for. The rule of thumb in selecting the cell size is that each
cell should be 1/(10l) or less at the highest
frequency (or shortest wavelength) of interest. For a 3-D rectangular grid, Dt must be of the order of the dimension of the structure such
that
(1)
where
Vmax is the maximum
velocity of light in the medium. Besides the constraint which wavelength
imposes on cell size, the small dimensions of the box must be taken into
consideration. There must also be sufficient number of cells to span the width
of the box. Hence, 3.20 mm cubical FDTD cells are chosen. From Equation (1),
the time step is given by
(2)
To
avoid the inaccuracies caused by reflections from the outer boundaries of the
finite computational space, the Mur absorbing boundary condition (ABC) [4] was
initially used to truncate the computational grid in the original XFDTD
software. More recently extended Berenger's PML boundary condition [5]-[7] is
then used in the computation using the modified XFDTD codes. In fact, the
difference of the results obtained using the two ABC's is not really
significant in this case. A 30-cell border is used to provide an adequate
absorption of the radiated fields.
B.
Design
Characteristics of IFA
Increased
efforts have been made to develop smaller, less obtrusive antennas for further
miniaturization of portable handsets. Hence, for the purpose of facilitating
operation, antennas that have small and low profile structures are suitable for
mounting on portable equipment. Among antennas that have such a structure, the
inverted F-antenna is one of the most promising.
The
geometry of the inverted F-antenna is illustrated in Figure 1. It basically
consists of a probe-fed, rectangular conducting plate of dimensions W´L suspended above the conducting chassis which acts as the
ground plane.
Fig.1:
Structure of the inverted F-antenna.
A
short circuiting strip is attached to one end of the suspended plate as this
configuration allows considerable reduction in the element resonant size. The
geometrical properties of the PIFA will influence the resonant condition of the
antenna due to the variation of the surface current flow on the planar element
when its dimensions vary. The relation between the resonant frequency and the
dimensions of the planar element has been shown [8] to be given by
h = 0.04 l, and L + W = 0.25 l (3)
where
l is the resonant wavelength.
The antenna can generally be matched to the 50 W feeding line through proper selection of the feed point and
shorting strip location.
C.
Antenna
Modeling
The
antenna geometries and dimensions for the various transceiver units are shown
in Figure 2. Length L is a
quarter-wavelength and thus depends on the frequency of operation. For GSM
(850-950 MHZ) and PCN (1750-1850 MHz) frequencies, L = 86.4 mm and 41.66 mm,
respectively. The dipole-mounted phone has a similar structure to that of the
monopole but it is center-fed instead of at the bottom and L is a half-wavelength.
Fig. 2: Geometry of a monopole, a side-mounted PIFA and
a back-mounted IFA on conducting box.
The
dimensions of the conducting box are the same for all the different antenna
configurations. An outer casing is included and modeled as a 3.2-mm thick
lossless dielectric with relative permittivity 2.
D. Human Head
Modeling
The
anatomical features of the human head and hand are modeled within the FDTD
framework by mapping the spatial location of the different tissues into a
permittivity and conductivity assignment in the computational grid. Magnetic resonance
images (MRI) were used to aid in the tissue classification and location.
Fig. 3: Side and rear views of the FDTD
head/hand/handset model.
The
two different views of the head/hand/handset configuration are shown in Figure
3 with the dimensions used in the FDTD computations. The hand is located 9.6 mm
away from the human head.
In
this paper, 5 groups of different tissue types are used in the Modeling of the
human head. Since the electrical properties (s, er) are frequency
dependent, the tissue parameters have been provided for both GSM and PCN
frequencies in Tables 1 and 2 below.
Table 1:
Tissue parameters for the human head at GSM frequencies.
|
Tissue type |
Density (r/kg
m-3) |
s/Sm-1 |
er |
|
fat, bone |
1850 |
0.0508 |
9.67 |
|
muscle |
1070 |
1.26 |
59.0 |
|
nerve, brain |
1030 |
1.05 |
52.7 |
|
eye |
1000 |
1.9 |
70.0 |
|
blood |
1000 |
1.18 |
62.0 |
Table 2:
Tissue parameters for the human head at PCN frequencies.
|
Tissue type |
Density (r/kg
m-3) |
s/Sm-1 |
er |
|
fat, bone |
1850 |
0.105 |
7.75 |
|
muscle |
1070 |
2.00 |
55.3 |
|
nerve, brain |
1030 |
1.65 |
46.0 |
|
eye |
1000 |
2.20 |
67.5 |
|
blood |
1000 |
1.25 |
62.3 |
E.
Specific
Absorption Rate
The
SAR quantifies the power absorbed per unit mass of tissue and is a fundamental
parameter used when discussing the health risks of electromagnetic power
absorption in the body. The SAR is defined for each cell as
(4)
where
Ex is the rms value of
the x-component of the sinusoidal electric field for a particular FDTD cell, sx is the corresponding
conductivity in S/m and rx is the corresponding
material density in kg/m3. The remaining terms are for the y- and
z-components of the same FDTD cell.
The
ANSI/IEEE C95.1-1992 RF Safety Guidelines [9] proposes a procedure to satisfy
the safety guidelines for uncontrolled environments that are defined as
situations where there is exposure of individuals who have no control of
exposure.
An
exposure condition can be considered to be acceptable if it can be shown that
it produces SAR below 0.08 W/kg as averaged over the whole body, and spatial
peak SAR values not exceeding 1.6 W/kg, as averaged over any 1 g of tissue
(defined as a tissue volume in the shape of the cube).
The
SAR quantity defined in Equation (4) computes the 1-voxel (cell) SAR which for
our simulation is 32.8 mm3. The average density of the human head is
approximately 1050 kg/m3 and hence, the 1-voxel SAR is only over
0.0034 g of tissue. Thus, the peak 1 voxel-SAR will be expected to grossly
overestimate the 1-g SAR. To obtain the peak 1-g SAR, the 1 voxel-SAR is
averaged over 3´3´3 FDTD cells which would approximate 1-g of tissue.
III. Results and Discussion
A.
l/4 GSM Monopole Antenna at 900 MHz
The
input impedance of the handset-mounted monopole is shown in Figure 4. The input
impedance is well matched at 47.4 W at the resonance frequency of 897 MHz. In the presence of
the human head, the resonance frequency is detuned to 851 MHz, a shift of 46
MHz, i.e. approximately 5% at GSM frequencies. The presence of the human head
also increases the input impedance of the monopole to 64 W at the resonance frequency. Hence, the impedance behavior
of the l/4 GSM monopole shows quite a
strong dependence on the surrounding environment.
Fig. 4:
FDTD results of Zin versus frequency f for a
GSM monopole alone and in the presence of the human head.
Figures
5 and 6 show the FDTD results of the radiation patterns for the zx- and zy-planes normalized to the maximum gain in the respective plane.
The outer circle denotes 0 dB and subsequent circles are in -10 dB divisions.
The handset-mounted monopole has a radiation pattern quite similar to that of a
l/2-dipole in free space. Like
the dipole, symmetry can be observed about the x- and y-axes for the zx- and zy-planes, respectively. However deviations occur because the
conducting box is longer than l/4 and the radiation behavior approximates that of an
asymmetric dipole as seen from the “butterfly-like” Eq pattern in the zy-plane.
The radiation pattern of the handset-mounted monopole is also dominantly q-polarized. As seen from Figures 5 and 6, |Eq|max is about 10 dB higher in both planes.
Fig. 5:
|Eq| and |Ef| in zx-plane for a GSM monopole only and in the presence of
human head.
In
the presence of the human head, the monopole's radiation pattern, like its
input impedance, is noticeably influenced. The radiation pattern remains
dominantly q-polarized.
Fig. 6:
|Eq| and |Ef| in zy-plane for a GSM monopole only and in the presence of
human head.
A
comparison of the radiation patterns (for both zx- and zy-planes) in the
half plane away from the head and the half plane of the head shows that,
predictably, less power is radiated in the head direction. The shadow effect of
the Eq pattern in the
z-direction for the zx-and zy-planes are about 5.3 and 6.1 dB
respectively.
A general decrease in gain is also observed with the human head present and this is expected since the human head attenuates the radiated power. This is especially pronounced in the q = 0o to 90o and the q = 270o to 360o region for the zx- and zy-planes respectively, which are along the direction of the head in their respective planes.
In
certain directions, a higher directive gain is obtained in the presence of the
human head. This phenomenon is less intuitive since there is a physical
explanation behind it. Although the body absorbs the radiated power to cause
attenuation of the radiated field, the induced currents inside the human head
also radiate EM fields (known as scattered fields). In some cases, a focusing
effect may occur and the radiated field is enhanced in a particular direction.
In
the presence of the human head, the radiation efficiency of the GSM monopole is
found to be 56.5% as compared with that of the GSM monopole in the absence of
the human head.
B.
l/4 PCN Monopole Antenna at 1800 MHz
From
Figure 7, it is observed that the input impedance is approximately 49.8 W at the resonance frequency of 1.8 GHz. In the presence of
the human head, the resonance frequency is once again shifted down, but this
time around by only 2.2% to 1.76 GHz. The impedance of the PCN monopole
increases to 52.5 W
at the new resonance frequency.
Fig. 7:
FDTD results of Zin versus frequency f for a PCN monopole alone and
in the presence of the human head.
The
far field radiation patterns of the handset-mounted PCN monopole are shown in
Figures 5 and 6. Similar effects as that of the GSM monopole are observed for
the lone handset-mounted PCN monopole. However, the polarization is now more
evenly distributed between q-
and f-polarizations with the
difference down to about 4 dB in both planes.
The
asymmetric dipole radiation behavior is again observed for the PCN monopole
though the “butterfly-like” Eq pattern for the GSM monopole is now slightly different. The
difference in the lobe structure occurs because at PCN frequencies, the
wavelength is smaller and the length of the conducting box relative to that of
the PCN monopole is larger than that relative to the GSM monopole.
Unlike
its input impedance, the radiation pattern for the PCN monopole is quite
sensitive to the proximity to the human head. A general decrease in gain is
observed as seen from Figure 8. This decrease in gain is more pronounced
compared to that of the GSM monopole, clearly observable by the greater
decrease of the | Eq| in the direction of the human head.
Fig. 8:
|Eq| and |Ef| in zx-plane for a PCN monopole only and in the presence of
human head.
Comparisons
of the radiation patterns in the half-plane away from the head and the
half-plane of the head shows a pronounced shadow effect in Figure 9. There is an
8.2 dB difference in the z-direction for both the zx- and zy-planes, which
is larger than that of the GSM monopole.
Fig. 9:
|Eq| and |Ef| in zy-plane for a PCN monopole only and in the presence of
human head.
The
radiation efficiency of the PCN monopole in the presence of the human head is
62.3%.
C.
l/2 Dipole Antenna at 900 MHz
Figure
10 shows the input impedance of the dipole. As seen, the two graphs are very
similar. There is still a reduction in resonance frequency from 896 to 890 MHz.
The detuning is minimal, only 0.67% compared to 5% for the GSM monopole. Hence,
the results imply that the human head exercises relatively little influence on
the input impedance of the dipole. This occurs because the antenna feed is
situated farther away from the human head.
Fig. 10:
FDTD results of Zin versus frequency f for a dipole alone and in the
presence of the human head.
From
the |Eq| plots of Figures
11 and 12, the |Eq| pattern of the
handset-mounted dipole is very similar to that of a l/2 dipole in free space. The zx-plane |Eq| pattern is identical, with equal gain in all directions,
while the zy-plane |Eq| pattern is only
slightly different with a notch along q = 0o and 180o. The difference is
attributed to the presence of the conducting box. Compared to the GSM and PCN
monopoles, the radiation patterns are less sensitive to the proximity of the
human head.
Fig. 11:
|Eq| and |Ef| in zx-plane for a dipole only and in the presence of human
head.
Fig. 12:
|Eq| and |Ef| in zy-plane for a dipole only and in the presence of human
head.
A
decrease in gain is still observed in the direction of the head, though the
decrease is less pronounced. The shadow effect between the two sides of the
head is only 3.7 dB for both the zx-
and zy-planes in the z-direction.
The
radiation efficiency of the dipole in the presence of the human head is
approximately 57.0%.
Side-Mounted PIFA at 900 MHz
The
input impedance graphs of the side-mounted PIFA is shown in Figure 13.
Frequency detuning is observed in the presence of the human head; the resonance
frequency decreases by approximately 10 MHz, i.e 1.1%, at GSM frequencies.
Fig. 13: FDTD
results of Zin versus frequency f for a Side-mounted PIFA alone and
in the presence of the human head.
From
the far field radiation plots, Figures 14 and 15, the radiation is distributed
between q- and f-polarizations.
The
radiation patterns follow closely the results from [10], where for the PIFA (in
the absence of the human head), symmetry is observed about the x- and y-axis in the zx- and zy-planes respectively. A reduction in
gain is observed in the presence of the human head. However, the human head
does not exercise much influence on the radiation pattern of the side-mounted
PIFA and the shadow effect is only about 2.1 and 1.6 dB in the z-direction for the two different
planes.
Fig. 14:
|Eq| and |Ef| in zx-plane for a side-mounted PIFA only and in the
presence of human head.
Fig. 15:
|Eq| and |Ef| in zy-plane for a side-mounted PIFA only and in the
presence of human head.
The
radiation efficiency of the side-mounted PIFA in the presence of the human head
is 48.3%.
D.
Back-Mounted PIFA at 900 MHz
The
graph of input impedance versus frequency for the back-mounted PIFA is shown in
Figure 16. The human head detunes the resonance frequency from 942 MHz to 895
MHz, approximately 5% at GSM frequencies. Thus, the effect of the human head on
the impedance matching of the back-mounted IFA is quite significant compared to
either the dipole or side-mounted PIFA.
Fig. 16:
FDTD results of Zin versus frequency f for a back-mounted IFA alone
and in the presence of the human head.
The
far field radiation patterns of the back-mounted IFA phone are shown in Figures
17 and 18.
Fig. 17:
|Eq| and |Ef| in zx-plane for a back-mounted IFA only and in the
presence of human head.
Fig. 18:
|Eq| and |Ef| in zy-plane for a back-mounted IFA only and in the
presence of human head.
From
the radiation plots, there is one clear distinction between the back-mounted
IFA and the other antennas previously investigated which makes it highly
desirable for personal communication. The Eq pattern in the zx-plane
for the antenna alone shows a lower gain in the direction of the head (f=0o to 90o). For the Eq-pattern in the zy-plane,
a notch is also seen in the direction of the human head at f=290o. This is in stark contrast with the other
antennas where symmetry about f=90o
can be observed for both the Eq plots. The directional radiation pattern exhibited by the
back-mounted IFA is mainly due to the metallic housing of the handset, which
lies between the antenna and the human head, acting as a shield. The shadow
effect is about 4.4 dB in both planes. The radiation efficiency of the
back-mounted IFA in the presence of the human head is 61.4%, which is
expectedly high since radiation to the head is reduced.
E.
Power
Absorption and SAR
E1: SAR Distribution
The
SAR distribution in two different cross sections (rear and side views) of the
human head for the various antennas is shown in Figure 19. The values for each
figure are normalized to the peak voxel value for that particular plane (as
opposed to a common value for all antennas) to give a clearer picture of the
distribution for each individual antenna. The SAR values are based on 1 W of
output for the different antenna configurations, which is typical of most
commercial cellular phones.
In
Figure 19, the antenna is beside the right ear and in each case, it is this
area where maximum energy absorption occurs. Energy is predominantly absorbed
in tissues such as the muscle and brain where the conductivity is higher. Lower
power deposition occurs in the skull since the conductivity of bone is low as
seen by the surrounding blue (-24 dB) layer. No hotspots deep in the head is
evident.
Fig. 19:
SAR distributions of the side and rear views inside the head model normalized
to their respective peak voxel values for 5 different antennas.
Comparing
the GSM monopole to that of the PCN, it is seen that the frequency of operation
of the antenna plays an important part in the SAR distribution. Power
absorption at PCN frequencies occurs more superficially as compared to GSM
frequencies. This occurs because as frequency increases, attenuation also
increases which in turn reduces the effect of any layering resonance and
results in an increasingly superficial deposition of energy. The results
obtained conform to the findings of [11], [12], [13], and [14].
The
amount of EM absorption on the hand relative to the head also varies for
different antennas. The IFA antennas have a larger physical area and with the
hand situated closer to them, a higher amount of EM radiation is absorbed in
the hand.
In
Figure 19, it is observed that the current distribution on the antenna and the
conducting box plays a significant part in the SAR distribution. For the
monopoles (GSM and PCN), the highest SAR distribution occurs at the regions
near the ear. For the dipole, the highest SAR distribution is concentrated in
the region near the temple, whereas for the IFA antennas, the SAR distribution
is more evenly spread.
From
Figure 19, the SAR in the eyes is relatively high for all the antennas which is
quite dangerous because the lens will undergo secondary heating from the energy
absorbed in the humor.
E2: Peak 1-g SAR and Average SAR for
Different Antennas
Table
3 shows the peak 1-g SAR and average SAR (averaged over entire head) for the
different antennas. From Table 3, it is seen that both the peak 1-g SAR and
average SAR for the monopoles and the side-mounted PIFA have exceeded the
safety limits of 1.6 W/kg and 0.08 W/kg respectively. With reference to the
peak 1-g SAR, the PCN monopole is the most dangerous to the human head and its
value is higher than that of the GSM monopole owing to the higher conductivity
of the tissues at PCN frequencies. A lower average SAR is observed for the PCN
frequencies because the penetration of radiation is deeper for the GSM monopole.
Table 3:
Peak 1-g SAR and average SAR for different Antennas
|
Type of Antenna |
Peak 1-g SAR |
Average SAR |
|
GSM monopole |
3.3061 |
0.1307 |
|
PCN monopole |
4.0178 |
0.1024 |
|
Dipole |
1.0521 |
0.0762 |
|
Side-mounted PIFA |
2.9838 |
0.1601 |
|
Back-mounted IFA |
1.3679 |
0.0520 |
Figure
20 shows the plot of average SAR (averaged over particular z-plane) versus
depth within the human head in z-direction. The depth is measured in terms of
number of cells, each representing a length of 3.2 mm. As seen from Figure 20,
the graph for the PCN monopole falls below that of the GSM after a depth of 8
cells.
Fig. 20:
Average SAR (averaged over particular z-plane) vs depth in the human head for
different antennas.
There
is a substantial reduction in SAR for both the dipole and back-mounted IFA. The
radiation absorbed by the human head falls within the stipulated safety limits.
Although the peak 1-g SAR of the dipole is lower than that of the back-mounted
IFA, its SAR averaged over the entire head is higher. This occurs because as
seen from Figure 20, the SAR distribution of the dipole is fairly constant over
the entire head whereas for the back-mounted IFA, SAR reduces at points deeper
in the head.
V. Conclusions
In
this paper, the salient issues related to the EM interaction between
handset-mounted antennas and the human head are studied using FDTD method. From
the simulations conducted, it is observed that the human head exercises a
noticeable effect on antenna input impedance, radiation patterns and efficiency
for various antennas, though the degree of influence varies from antenna to
antenna. The simulations also reveal that the SAR values for the monopoles and
the side-mounted PIFA exceed the safety limits stipulated by the ANSI/IEEE
C95.1-1992 RF Safety Guidelines if the users continuously communicate with
others using handsets over an hour. However, the SAR value does not exceed the
recommended safety limits if the continuous talking time is less than one hour
and the handset position is changed from one ear to the other in half an hour
time.
By
taking into account factors of both minimizing the power degradation inside the
human head and maximizing the antenna radiation, the back-mounted IFA is the
most ideal configuration which minimizes the effect of the radiation from the
phone on the human head (peak 1-g SAR 1.37 W/kg, average SAR 0.052 W/kg) and
vice versa (detuning of resonant frequency by 5%, shadow effect of 4.4 dB in
both planes and efficiency of 61.4%). Besides this, it also has a small and low
profile structure suitable for mounting on portable equipment to facilitate
operation.
References
[1]
M.A. Jensen
and Y. Rahmat-Samii, “Em interaction of handset antennas and a human in
personal communications”, Proc. IEEE,
vol. 83, pp. 7--17, 1995.
[2]
K. S. Yee,
“Numerical solution of initial boundary value problems involving Maxwell's
equations in isotropic media”, IEEE
Trans. Antennas Propagat., vol. 14, no. 3, pp. 302--307, 1966.
[3]
K. S. Kunz
and R. J. Luebbers, The Finite Difference Time Domain Method for
Electromagnetics, CRC Press, Boca Raton, FL, 1993.
[4]
G. Mur,
“Absorbing boundary conditions for the finite-difference approximation of the
time-domain electromagnetic-field equations”, IEEE Trans. Electromagn. Compat., vol. EMC-23, no. 4, pp. 377--382,
1981.
[5]
J.-P.
Berenger, “A Perfectly Matched Layer for the Absorption of Electromagnetic
Waves”, J. Comput. Phys., vol. 114,
no. 1, pp. 185--200, 1994.
[6]
J.-P.
Berenger, “Perfectly Matched Layer for the FDTD Solution of Wave-Structure
Interaction Problems”, IEEE Trans.
Antennas Propagat., vol. AP-44, no. 1, pp. 110--117, 1996.
[7]
Y C Lau, M S
Leong, and P S Kooi, “Extension of Berenger's PML boundary condition in
matching lossy medium and evanescent waves”, Electron. Lett., vol. 32, no. 11, pp. 974--976, May, 1996.
[8]
K. Kagoshima,
K. Tsunekawa, and A. Ando, “Analysis of a planar inverted F-antenna fed by
electromagnetic coupling”, in IEEE
Antennas and Propagat. Soc. Int. Symp., Chicago, IL, July 1992, vol. 3, pp.
1702--1705.
[9]
American National
Standards Institute, “IEEE C95.1-1992: American National Standard-Safety Levels
with respect to Exposure to Radio Frequency Electromagnetic Fields 3 kHz to 300
GHz”, Tech. Rep., Piscataway, NJ,
IEEE, 1991.
[10]
M. A. Jensen
and Y. Rahmat-Samii, “Performance analysis of antennas for hand-held
transceivers using FDTD”, IEEE Trans.
Antennas Propagat., vol. 42, no. 8, pp. 1106--1113, 1994.
[11]
S. Watanabe,
M. Taki, T. Nojima, and O. Fujiwara, “Characteristics of the SAR distributions
in a head exposed to electromagnetic fields radiated by a hand-held portable
radio”, IEEE Trans. Microwave Theory Tech.,
vol. 44, no. 10, pp. 1874--1883, 1996.
[12]
O. Fujiwara
and M. Nomura, “Correlation between spatial distributions of surface-SAR and
magnetic near-field in realistic head model for microwave exposure”, IEICE Trans. Commun., vol. E76-B, no. 7,
pp. 765--767, 1993.
[13]
O. Fujiwara
and M. Nomura, “Approximation of surface-SAR in a realistic head model for
microwave exposure using external magnetic near-field”, IEICE Trans. Commun., vol. E78-B, no. 2, pp. 140--144, 1995.
[14]
P. J.
Dimbylow, “Finite-difference time-domain calculations of absorbed power in the
ankle for 10-100 MHz plane wave exposure”, IEEE Trans. Biomed. Eng., vol. 38,
no. 5, pp. 423--428, 1991.