# 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?

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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) 13.16dB

My doubt stems from Friis Transmission Equation topic in portion Antenna Parameters of Antennas

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Right choice is (c) 11.19dB

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

Gt  in 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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