DRAFT Recommended Practice for Measurements and ...

1/29/98 128 C95.3-1991 Revision — 2 nd Draft
10/98 Draft
D6. Theoretical Considerations for the Determination of SAR Associated with
Near-Field Exposures
The results of detailed mathematical analyses of the SAR distribution at different points
within a person's body, due to exposure to near-field sources, aid in estimating the order
of magnitude of the corresponding induced SAR. The corresponding exposure may or
may not be in the reactive near field of a radiator. The following considerations can aid
estimating the type of exposure (near- or far-field), and in the subsequent assessment of
the feasibility of estimating the internal SAR distributions in exposed personnel.
D6.1 Theoretical Considerations for Estimating RF Coupling and SAR
Associated with Reactive Near-Field Exposure.
Either reduced or enhanced absorption situations exist (see 5.6) for personnel exposed
to nonradiating, reactive near fields of a nearby source. One principal factor that
determines the relative magnitude of the induced SAR is the type and degree of coupling
between the RF source (an active radiator or passive radiator) and the exposed object.
For the case where the distance between the object (person) and the source is much
less than one wavelength, E and H exhibit a rapid decrease in amplitude with increasing
separation distance.
The characteristics of the reactive near-field region are described in 3.1.4. For a small
electric dipole antenna, the field strength at a point r can be expressed mathematically as
follows [D17]:
E
E
H
r
θ
φ
I0h e
− jkr ⎛ 2η
2
= ⎜ +
4π
⎝ d jωεd
2 3
⎞
⎟ cosθ
⎠
I0h j e
− jkr⎛
ωµ 1 η ⎞
= ⎜ + + ⎟ sin θ
(Eq D11 )
3 2
4π
⎝ d jωd d ⎠
I0h jk e
− jkr
=
⎛ 1
⎜ +
⎞
⎟ θ
π ⎝
2 sin
4 d d ⎠
where:
k = 2π λ
(1/m)
η = impedance of free space (377 Ω)
ε = permittivity of free space (F/m)
µ = permeability of free space (H/m)
h = length of the dipole (m)
I o = antenna current (A)
ω = angular frequency (radians/second)
λ = wavelength (m)
d = distance from the center of the dipole to the location of interest (m)
θ = angle between the axis of the dipole and the unit direction vector from the center of
the dipole to the point r.
Copyright © 1998 IEEE. All rights reserved. This is an unapproved IEEE Standards Draft,
subject to change.