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?

Answer – \[3256k{{m}^{2}}\]

There is no physical obstruction between the transmitter and the receiver antennae in case of the line-of-sight communication and hence there is no such requirement that the transmitting and receiving antennae should be at same height.

We are given,

Height of the antenna;  h = 81 m

Radius of earth; R = 6.4 x 10⁶m

We know that the service area of the antenna is given by the relation –

                                      \[A\text{ }=\text{ }\pi {{d}^{2}}\]

Where d is the range given by the formula,  

$d={{\left( 2\pi h \right)}^{\frac{1}{2}}}$

So, the formula of service area becomes –

  $$ A=\pi \left( 2Rh \right) $$

 $$ A=3.14\times 2\times 6.4\times {{10}^{6}}\times 81 $$

 $$ A=3255.55\times {{10}^{6}}{{m}^{2}} $$

 $$ A=3256k{{m}^{2}} $$