Answer:
0.25938 W
Explanation:
c = Speed of light = [tex]3\times 10^8\ m/s[/tex]
[tex]\nu[/tex] = Frequency = 3 GHz
d = Diameter of lossless antenna = 1 m
r = Radius = [tex]\frac{d}{2}=\frac{1}{2}=0.5\ m[/tex]
[tex]A_t[/tex] = Area of transmitter
[tex]A_r[/tex] = Area of receiver
R = Distance between the antennae = 40 km
[tex]P_r[/tex] = Power of receiver = [tex]10\times 10^{-9}\ W[/tex]
[tex]P_t[/tex] = Power of Transmitter
Wavelength
[tex]\lambda=\frac{c}{\nu}\\\Rightarrow \lambda=\frac{3\times 10^8}{3\times 10^9}\\\Rightarrow \lambda=0.1\ m[/tex]
From Friis transmission formula we have
[tex]\frac{P_t}{P_r}=\frac{\lambda^2R^2}{A_tA_r}\\\Rightarrow P_t=P_r\frac{\lambda^2R^2}{A_tA_r}\\\Rightarrow P_t=10\times 10^{-9}\frac{0.1^2\times (40\times 10^3)^2}{\pi 0.5^2\times \pi 0.5^2}\\\Rightarrow P_t=0.25938\ W[/tex]
The power that should be transmitted is 0.25938 W
