Reltaion between transmiting power and receiving power in communication
Answers
When we have a point transmitter (isotropic) in an absorptionless media. Then its power is homogeneously distributed on the outer area of the sphere centered on the the point transmitter. The area of the sphere is give by 4 pi R^2, and accordingly the power per unit area is given by
Pt / (4 pi * R^2),
where Pt is the transmit power. A receiver with an aperture "A" will receive a power of,
Pr = Pt / (4 pi R^2) *A.
In communication systems, you are usually limited by the noise and interference, and you cannot communicate below a certain signal to interference+noise ratio (called the SINR threshold).
You can therefor find form the above relation that the range is proportional to the square root of the transmit power,
Rmax = constant * sqrt (Transmit power)