GATE 2016 EC – Question 63
Two lossless X-band horn antennas are separated by a distance of $200\lambda$. The amplitude reflection coefficients at the terminals of the transmitting and receiving antennas are 0.15 and 0.18, respectively. The maximum directivities of the transmitting and receiving antennas (over the isotropic antenna) are 18 dB and 22 dB, respectively. Assuming that the input power in the lossless transmission line connected to the antenna is 2 W, and that the antennas are perfectly aligned and polarization matched, the power ( in mW) delivered to the load at the receiver is ________
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Correct answer: 2.7 to 3.3
Explanation
Use the Friis transmission formula with mismatch factors: $P_r = P_t G_t G_r \left(\frac{\lambda}{4\pi R}\right)^2 (1 - |\Gamma_t|^2)(1 - |\Gamma_r|^2)$. The gains are $10^{1.8} = 63.1$ and $10^{2.2} = 158.5$, and $\frac{\lambda}{4\pi R} = \frac{1}{4\pi \times 200} = \frac{1}{2513}$. The mismatch factors are $(1 - 0.0225)(1 - 0.0324) = 0.946$. So $P_r = 2 \times 63.1 \times 158.5 \times (1.583 \times 10^{-7}) \times 0.946 = 3.0 \times 10^{-3}$ W, which is 3 mW.