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In-Depth Information
4π
θ
3
φ
3
-----------
G
D
≈
(8.4)
where
θ
3
and
φ
3
are the antenna half-power (3-dB) beamwidths in either
direction.
The antenna power gain and its directivity are related by
G
=
ρ
r
G
D
(8.5)
where is the radiation efficiency factor. In this topic, the antenna power
gain will be denoted as
gain
. The radiation efficiency factor accounts for the
ohmic losses associated with the antenna. Therefore, the definition for the
antenna gain is also given in Eq. (8.1). The antenna effective aperture
ρ
r
A
e
is
related to gain by
G
λ
2
4π
A
e
=
----------
(8.6)
where
λ
is the wavelength. The relationship between the antennaÓs effective
aperture
A
e
and the physical aperture
A
is
A
e
=
ρ
A
(8.7)
0
≤≤
ρ
1
is referred to as the aperture efficiency, and good antennas require
(in this topic
ρ
ρ
→
1
ρ
=
1
is always assumed, i.e.,
A
e
=
A
).
Using simple algebraic manipulations of Eqs. (8.4) through (8.6) (assuming
that
ρ
r
=
1
) yields
4π
A
e
λ
2
4π
θ
3
φ
3
------------
-----------
G
=
≈
(8.8)
Consequently, the angular cross section of the beam is
λ
2
A
e
θ
3
φ
3
≈
-----
(8.9)
Eq. (8.9) indicates that the antenna beamwidth decreases as increases. It
follows that, in surveillance operations, the number of beam positions an
antenna will take on to cover a volume
A
e
V
is
V
θ
3
φ
3
N
Beams
>
-----------
(8.10)
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