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प्रश्न
Derive an expression for the maximum line of sight distance between two antennas for space wave propagation.
उत्तर
Maximum line of sight distance:
The transmitting and receiving antennae are shown below.
Consider only the transmitter antenna. From the geometry of the figure, we get
`(R+h_r)^2=R^2+d_r^2`
`:.R^2+2h_rR +h_r^2=R^2 +d_r^2`
But, we know that `h_r^2 "<< "2h_rR`
∴ `R^2+2h_rR=R^2+d_r^2`
`:.d_r^2=2h_rR`
`:.d_r=sqrt(2h_rR)`
This is the distance between the transmitter and horizon.
Similarly, for the receiver, we have `d_r=sqrt(2h_rR)`
Hence, the maximum line-of-sight distance between the transmitter and the receiver is
`d=d_r+d_R=sqrt(2Rh_r)+sqrt(2Rh_R)`
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