A satellite in geostationary orbit is used to transmit data via electromagnetic

Question

A satellite in geostationary orbit is used to transmit data via electromagnetic radiation. The satellite is at a heigh of 3.29*10^4 km above the surface of the earth and we assume it has an isotropic power of 23.8 kW.

Part A: Reception devices pick up the variation in the electric field vector of the electromagnetic wave sent out by the satellite. Given the satellite specifications listed in the problem introduction, what is the amplitude of the electric field vector of the satellite broadcast as measured at the surface of the earth? Use E0 for the permittivity of space and 3*10^8 m/s for the speed of light

Answer: E0= 3.63*10^-5 V/m

Part B: Imagine that the satellite described in the problem introduction is used to transmit television signals. You have a satellite TV reciever consisting of a circular dish of radius R which focuses the electromagnetic energy incident from the satellite onto a receiver which has a radius of 3.96×10^-2 m.

How large does the radius E of the dish have to be to achieve an electric field vector amplitude of 5.6×10^-4 V/m , at the receiver?

For simplicity, assume that your house is located directly beneath the satellite (i.e. the situation you calculated in the first part), that the dish reflects all of the incident signal onto the receiver, and that there are no losses associated with the reception process. The dish has a curvature, but the radius R refers to the projection of the dish into the plane perpendicular to the direction of the incoming signal.

Explanation / Answer

Intensity I = power/area = 1000/(4?r^2) w/m^2, where r = 3.5E7 m. I = 6.49612E-14 w/m^2 I = EH = E^2/376.73 (see ref. 1). ? E = sqrt(376.73*I) = 4.947 ?v/m. Note: 376.73 is the value of free-space impedance Z0 in ohms. This number is derived from the electric constant e0 = 8.854187E-12 and magnetic constant ?0 = 1E-7*4?, as Z0 = sqrt(?0/e0) = 376.73 ohms. See ref. 2. Source(s): [1] http://www.osha.gov/SLTC/radiofrequencyr

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