Digital Signal Processing Reference
In-Depth Information
space. As the distance from the radiation source increases, this energy is divided over
an increasing sphere surface area. In this connection we talk of the
radiation power
per unit area, also called
radiation density S
.
In a
spherical emitter
, the so-called
isotropic emitter
, the energy is radiated uniformly
in all directions. At distance
r
the radiation density
S
can be calculated very easily as
the quotient of the energy supplied by the emitter (thus the transmission power
P
EIRP
)
and the surface area of the sphere.
P
EIRP
4
πr
2
S
=
(
4
.
61
)
4.2.3 Characteristic wave impedance and field
strength E
The energy transported by the electromagnetic wave is stored in the electric and mag-
netic field of the wave. There is therefore a fixed relationship between the radiation
density
S
and the field strengths
E
and
H
of the interconnected electric and magnetic
fields. The electric field with electric field strength
E
is at right angles to the mag-
netic field
H
. The area between the vectors
E
and
H
forms the wave front and is at
right angles to the direction of propagation. The radiation density
S
is found from the
Poynting radiation vector
S
as a vector product of
E
and
H
(Figure 4.58).
S
=
E
×
H
(
4
.
62
)
The relationship between the field strengths
E
and
H
is defined by the permittivity
and the dielectric constant of the propagation medium of the electromagnetic wave. In
a vacuum and also in air as an approximation:
E
=
H
·
√
µ
0
ε
0
=
H
·
Z
F
(
4
.
63
)
Z
F
is termed the
characteristic wave impedance
(
Z
F
=
120
π
=
377
). Furthermore,
the following relationship holds:
E
=
S
·
Z
F
(
4
.
64
)
E
Radiation source
S
R
H
l
Figure 4.58
The Poynting radiation vector
S
as the vector product of
E
and
H
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