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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?

User Neonit
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1 Answer

6 votes

Answer:

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

User Furniture
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