Graphics Programs Reference
In-Depth Information
and when
V
represents the entire hemisphere, Eq. (8.10) is modified to
2π
A
e
λ
2
2π
θ
3
φ
3
G
----
N
Beams
>
-----------
≈
------------
≈
(8.11)
8.2. Near and Far Fields
The electric field intensity generated from the energy emitted by an antenna
is a function of the antenna physical aperture shape and the electric current
amplitude and phase distribution across the aperture. Plots of the modulus of
the electric field intensity of the emitted radiation,
E
θφ
(
,
)
E
θφ
, are referred to as
)
2
the
intensity pattern
of the antenna. Alternatively, plots of
(
,
are called
the
power radiation pattern
(the same as
P
θφ
(
,
)
).
Based on the distance from the face of the antenna, where the radiated elec-
tric field is measured, three distinct regions are identified. They are the near
field, Fresnel, and the Fraunhofer regions. In the near field and the Fresnel
regions, rays emitted from the antenna have spherical wavefronts (equi-phase
fronts). In the Fraunhofer regions the wavefronts can be locally represented by
plane waves. The near field and the Fresnel regions are normally of little inter-
est to most radar applications. Most radar systems operate in the Fraunhofer
region, which is also known as the far field region. In the far field region, the
electric field intensity can be computed from the aperture Fourier transform.
Consider a radiating source at point O that emits spherical waves. A receiving
antenna of length is at distance away from the source. The phase differ-
ence between a spherical wave and a local plane wave at the receiving antenna
can be expressed in terms of the distance
d
r
δ
r
. The distance
δ
r
is given by
2
d
--
r
2
δ
r
=
AOOB
=
+
r
(8.12)
and since in the far field
rd
»
, Eq. (8.12) is approximated via binomial expan-
sion by
d
2
8
r
2
d
2
r
----
-----
δ
r
=
r
1
+
1
≈
(8.13)
It is customary to assume far field when the distance
δ
r
corresponds to less
than
116
⁄
of a wavelength (i.e.,
22.5°
). More precisely, if
2
δ
r
=
⁄
8
r
≤
λ 16
⁄
(8.14)
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