Question

Application: Communication in the Atmosphere. A parabolic antenna of radius b [m] transmits at a frequency f to a receiving antenna a distance d [m] away. The receiving antenna is also of radius b [m] and the transmission is parallel to the ground, in the atmosphere, as in Figure 12.25a. Assume that the wave propagates as a plane wave and the beam remains constant in diameter (same diameter as the antennas). Use the following values: b = 1 m, d = 200 km,ɛ = €0 [F/m], µ = µo [H/m] o = 2 × 10¬´ S/m, and f = 300 MHz. (a) Calculate the time-averaged power the transmitting antenna must supply if the receiving antenna must receive a magnetic field intensity of magnitude 1 mA/m. (b) In an attempt to reduce the power required, the transmission is directed to a satellite which contains a perfect reflector, as shown in Figure 12.25b. The waves propagate through the atmosphere, into free space to the satellite and back to the receiving antenna. If the satellite is at a height h [m] and the waves propagate in the atmosphere for a distance q [m] in each direction, what is the power needed in this case for the same reception condition as in(a)? In addition to the values given in Figure 12.25a, h = 36,000 km, q = 20 km, and o = 0 in free space.Compare the result with that in (a).

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