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Let’s assume a transmitting antenna having gain 10dB is placed at a distance of 100m from the receiving antenna and radiates a power of 5W. Find the gain of the receiving antenna in dB when the received power is 150μW and transmitter frequency 500MHz?(a) 1.31dB(b) 1.19dB(c) 11.19dB(d) 13.16dBI had been asked this question in an online quiz.My doubt stems from Friis Transmission Equation topic in portion Antenna Parameters of Antennas

Answer»

Right CHOICE is (c) 11.19dB

Explanation: Given Pt=5W, Pr=150μW, f=500MHz, R=100m and Gtin dB=10dB

 Gtin dB=10log10 Gt=10dB

 Gt=10

⇨ \(\lambda = \FRAC{c}{f} = \frac{3×10^8}{500Mhz} = 0.6m\)

From Friss transmission equation, \(\frac{P_r}{P_t} = \frac{G_t G_r \lambda^2}{(4\pi R)^2} \)

⇨ \(G_r=\frac{P_r (4\pi R)^2}{P_t G_t \lambda^2} = \frac{150\mu(4\pi ×100)^2}{5×10×0.6^2}=13.16\)

⇨ GR in dB=10log10 Gr=10log10 13.16=11.19dB


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