Question

Why a signal transmitted from a TV lower cannot be received beyond a certain distance? Write the expression for the optimum separation between the receiving and the transmitting antenna.

Answer 1

Waves travel in straight line from transmitting antenna to the receiving antenna. The signal transmitted from a TV tower cannot be received beyond a certain distance because of the surface of the Earth is curved.

Waves transmitted from transmitter 2 gets absorbed or blocked by the curvature of Earth and are not received. The optimum separation between the receiving antenna and transmitting antenna is

d = 2√2R_ch

Consider following figure, where T is a transmitter of height h_T, R is a receiver of height h_R, Re is the radius of the Earth, d_m is the distance between transmitter and receiver, d_T is the distance between the transmitter and the horizon.

When we consider transmitter:

R_e + h_T = R_e² + d_T² ⇒ R_e² + h_T² + 2R_e h_T = R_e² + d_T² 

We know that

Similarly, when we consider for receiver: