Is it necessary for a transmitting antenna to be at the same height as that of the receiving antenna for line-of-sight communication? A TV transmitting antenna is 81 m tall. How much service area can it cover if the receiving antenna is at the ground level?

Solution

No. For line of sight communication, the transmitting antenna do not necessarily be of the same height as that of the receiving antenna.

d_{T}^{2} = (R + h)^{2} - R^{2} = R^{2} [{(1 + \frac{h}{R})}^{2} - 1] = R^{2} [1 + \frac{2 h}{R} - 1] = R^{2} . \frac{2 h}{R} d_{T}^{2} = 2 h . R

where d_T is the distance to the horizon,
R is the radius of the earth, and
h_T is the height of the transmitting antenna.

Height of the antenna, h = 81 m

∴ Service area will be,

A = π (d_{T})^{2} = \frac{22}{7} \times (2 hR) = \frac{22}{7} \times 2 \times 81 \times 6.4 \times 10^{6} = 3258 {km}^{2} .

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