Global Positioning System Reference
In-Depth Information
If the receiving antenna has a unit gain, the effective area is ( 16 )
λ 2
4 π
A eff
=
( 3 . 44 )
where λ is the wavelength of the receiving signal.
The received power is equal to the power density multiplied by the effective
area of the receiving antenna. The power density is equal to the radiating power
divided by the surface of the sphere. The receiving power can be written as
λ 2
4 π
P t λ 2
( 4 πR su ) 2
P t A eff
4 πR su =
P t
4 πR su
P r
=
=
( 3 . 45 )
where R su is the distance from the satellite to the user. Assume R su = 25785 ×
10 3 m, which is the farthest distance as shown in Figure 3.1. Using 478.63 W
as the transmitting antenna and the wavelength λ = 0 . 19 m, the receiving power
P r calculated from the above equation is 1 . 65 × 10 16 w(or 157.8 dBw). If
the loss through the atmosphere is taken into consideration, the received power
is close to the minimum required value of 160 dBw.
The power level at the receiver is shown in Figure 3.10. It is a function of
the elevation angle. ( 1 ) At zenith and horizon, the powers are at 160 dBw. The
maximum power level is 158 dBw, which occurs at about 40 degrees. If the
receiving antenna is taken into consideration, the received power will be modified
by its antenna pattern.
3.14 SUMMARY
This chapter discusses the orbits of the GPS satellite. The orbit is elliptical but
it is very close to a circle. Thus, the circular orbit is used to figure the power
difference to the receiver and the Doppler frequency shift. This information is
important for tracking the satellite. In order to find the position of a satellite the
FIGURE 3.10 Power level versus elevation angle.
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