Question

If the whole earth is to be connected by $LOS$ communication using space waves (no restriction of antenna size or tower height), what is the minimum number of antennas required? Calculate the tower height of these antennas in terms of earth's radius?

Answer 1

Key concept: Distance or range of transmission tower, $dT=\sqrt{2R{h}_T}$

where,

$R$ is the radius of the earth (approximately 6400 km).

$h_T$ is the height of transmission tower, .

$dT$ is also called the radio horizon of the transmitting antenna.

Let us consider the figure given below to solve this problem.

Assume the height of transmitting antenna or receiving antenna in order to cover the entire surface of earth through communication is h1, i.e. $h_T=h_R$ and radius of earth is R.

If dM is the line-of-sight distance between the transmission and receiving antennas, then maximum distance

Assume the height of transmitting antenna or receiving antenna in order to cover the entire surface of earth through communication is ht i.e.$h_T=h_R$ and radius of earth is. R.

If dM is the line - of-sight distance between the transmission and receiving antennas, then maximum distance

$d_m^2=2(R+h_T{)}^2$

$8R{h}_T=2(R+h_T{)}^2$

$4R{h}_T=R^2+h_T^2+2R{h}_T$

$(R-h_T{)}^2=0$

$R=h_T$

Since space wave frequency is used, $l<<hT$, hence only tower height is taken to consideration. In three dimensions, 6 antenna towers of hr = R would do.