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 no of antennas required ? Calculate the tower height of these antennas in terms of earth's radius?

Answer 1

Given :

i) No restriction on antenna size or tower height.

Find :

i) The minimum no. of antennas required

ii) The tower height of these antennas in terms of earth's radius

Solution :

i) For line of sight transmission/communication, six antennas are required i.e transmitting and receiving antenna to cover whole three dimensional earth.

ii) Let Ht and Hr be the height of transmitting and receiving tower respectively.

• R be the radius of the earth i.e R = 6400 km

• We know that,

d = √2×R×Ht + √2×R×Hr ..... 1

Also from diagram given above,

d^2 = (R + Ht)^2 + (R + Hr)^2 ..... 2

• For covering whole earth, Ht should be equal to Hr

°•° d = 2√2×R×Ht ..... 3

And d^2 = 2(R + Ht)^2 ..... 4

• Substitute value of d from 3 in 4

8R×Ht = 2(R + Ht)^2

R^2 - 2R×Ht + Ht^2 = 0

(R - Ht)^2 = 0

• Ht = Hr = R