Global Positioning System Reference
In-Depth Information
beam width of the antenna, the distance from the satellite to the user, and the
effective area of the receiving antenna. The power amplifier of the transmitter is
50 w
(
8
)
(or 17 dBw). The input to the transmitting antenna is 14.3 dBw.
(
8
)
The
difference might be due to impedance mismatch or circuit loss.
The gain of the transmitting antenna can be estimated from the beam width
(or solid angle) of the antenna. The solid angle is denoted as
θ
, which is 21.3
degrees. The area on the surface of a sphere covered by the angle
θ
can be
obtained from Figure 3.9 as
θ
=
2
πr
2
θ
0
Area
=
2
π(r
sin
θ)rdθ
sin
θdθ
0
=
2
πr
2
(
θ
0
=
2
πr
2
(
1
−
cos
θ)
−
cos
θ)
|
(3.42)
The ratio of this area to the area of the sphere can be considered as the gain of
the transmitting antenna, which can be written as
4
πr
2
2
πr
2
(
1
−
cos
θ)
2
0
.
683
≈
29
.
28
≈
14
.
7dB
G
=
≈
(
3
.
43
)
|
21
.
3
0
Using 14.3 dBw as the input to the antenna, the output of the antenna should
be 29 dBw (14
.
3
14
.
7). However, the transmitting power level is listed as
478.63 w,
(
14
,
15
)
which corresponds to 26.8 dBw. This difference between the
power levels might be due to efficiency of the antenna and the accuracy of the
solid angle of the antenna because the power cannot be cut off sharply at a
desired angle.
+
FIGURE 3.9
Area facing solid angle
θ
.
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