KOULOURIDIS AND NIKITA: STUDY OF COUPLING BETWEEN HUMAN HEAD AND CELLULAR PHONE

63

is the radian frequency,  and

are the free-space permit-

tivity and permeability, respectively. A perfectly conducting ar-

bitrarily shaped wire excited by a voltage imposed at a feeding

gap of length  models the antenna. The time dependence of

and it is suppressed

the field quantities is assumed to be

throughout the following analysis.

First, the Green's function of the three-layer sphere is de-

termined as the response of this object to the excitation gener-

ated by an elementary dipole of unit dipole moment, external to

the sphere. Thus, the following expression for the electric type

and in

Green's function inside the layered sphere

the air region

is obtained [14]:

(1)

Fig. 1. Schematic diagram of a three-layer spherical head model exposed to

where  and  are the well-known spherical wave vectors [12],

the radiation of: (a) arbitrarily shaped wire antenna and (b) helical antenna (not

drawn in scale).

,  are scalar coefficients computed in [14] and

,

, 2, 3 is the wavenumber in the th region. Also

for

tool for checking the accuracy of FDTD simulations which are

, 2, 3 and

for

.

then used to solve the electromagnetic dosimetry problem for a

The antenna of the problem under consideration is modeled

heterogeneous anatomically correct human head model exposed

by applying the MoM. The geometry of an arbitrarily shaped

to a handheld terminal equipped with a normal-mode helical an-

wire antenna, in the global Cartesian coordinates system Oxyz

tenna. Furthermore, in this paper emphasis is placed on the com-

(Fig. 1), is parametrically described as [15],

parative study of power absorption between heads of adults and

(2)

children, and extensive simulations based on both Green/MoM

and FDTD techniques are carried out.

where is a real valued parameter.

The rest of the paper is organized as follows. In Section II,

For the problem of the wire antenna treated in this paper, since

the mathematical formulation of the hybrid Green/MoM tech-

its diameter is usually substantially less than the radiation wave-

nique is presented, while in Section III, details of FDTD sim-

length, the thin wire approximation (TWA) can be adopted [16].

ulations for the cases studied in this paper are given. In Sec-

Thus, the current on the surface of the antenna wire is supposed

tion IV, the head and antenna models used in the simulations

to flow parallel to its curved axis. The antenna is then subdivided

are described. In Section V, the necessary checks for the vali-

into a number of  curved segments,

in length, centered at

dation of the Green/MoM technique are presented, followed by

points

,

. The electric field

numerical results concerning the absorption by the head and the

at a point  lying in any region

, is expressed by

antenna performance for specific canonical exposure problems,

means of the corresponding Green's function

i.e., layered spheres and helical dipoles at 1710 MHz based on

Green/MoM and FDTD simulations. Finally, results of FDTD

simulations for a realistic exposure problem, i.e., an MRI-based

(3)

human head model exposed to a handset equipped with a small

helix-monopole operating at 1710 MHz, are presented.

where  is the unknown current coefficient flowing along the

curved th segment of the antenna wire and  is the unit vector

II. GREEN/MOM TECHNIQUE: MATHEMATICAL FORMULATION

tangent to the wire antenna,

AND ANALYSIS

The problem under consideration is shown in Fig. 1. A three-

(4)

layer sphere with radii  ,  , and

is used to model the head.

The relative complex permittivity of each layer is  ,  , and  ,

respectively. The magnetic properties of the layers are defined

. Free space is assumed for the ex-

Then, the boundary conditions for the tangential electric

as

, where

terior of the sphere with wavenumber

field component vanishing on the conducting surface of the