Is it necessary for the transmitting antenna and receiving antenna to be of the same height for line of sight communication? Find an expression for maximum line of sight distance d_M between these two antennas of heights h_T and h_R.

Solution

No. It is not necessary that the transmitting antenna and receiving antenna should be of the same height.

For transmitting antenna of height h_t, we have

(h_{t} + R_{e})^{2} = x^{2} + {R_{e}}^{2}

∵

h_{t} < < R_{e}

where, h_t is the height of the transmitting antenna and
R_e is the radius of the earth.

∴

x = d_{t}

This implies,

(h_{t} + R_{e})^{2} = d_{t}^{2} + R_{e}^{2}

= d_{t}^{2} + R_{e}^{2}

({h_{t}}^{2} is negligible)

\Rightarrow

d_{t} = \sqrt{2 R_{e} h_{t}}

where, d_t is called the radio horizon of the transmitting antenna.

The maximum line of sight distance dx between the two antennas is given by,

d_{m} = \sqrt{2 R_{e} h_{t}} + \sqrt{2 R_{e} h_{R}}

where h_R is the height of receiving antenna.

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