Question

A 3 GHz line-of-sight microwave communication link consists of two lossless parabolic dish antennas, each1 m in diameter. If the receive antenna requires 10 nW of receive power for good reception and the distance between the antennas is 40 km, how much power should be transmitted?

Answer 1

0.25938 W

Step-by-step explanation:

c = Speed of light =
`3* 10^8\ m/s`

`\\u` = Frequency = 3 GHz

d = Diameter of lossless antenna = 1 m

r = Radius =
`(d)/(2)=(1)/(2)=0.5\ m`

`A_t` = Area of transmitter

`A_r` = Area of receiver

R = Distance between the antennae = 40 km

`P_r` = Power of receiver =
`10* 10^(-9)\ W`

`P_t` = Power of Transmitter

Wavelength

`\lambda=(c)/(\\u)\\\Rightarrow \lambda=(3* 10^8)/(3* 10^9)\\\Rightarrow \lambda=0.1\ m`

From Friis transmission formula we have

`(P_t)/(P_r)=(\lambda^2R^2)/(A_tA_r)\\\Rightarrow P_t=P_r(\lambda^2R^2)/(A_tA_r)\\\Rightarrow P_t=10* 10^(-9)(0.1^2* (40* 10^3)^2)/(\pi 0.5^2* \pi 0.5^2)\\\Rightarrow P_t=0.25938\ W`

The power that should be transmitted is 0.25938 W