Question

Two lossless X- band horn antenna 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 antannas (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 2W, and that the antennas are perfectly aligned and polarization matched, the power (in mW) delivered to the load at the reciver is

• A. 3

Answer 1

The correct option is A 3



$\left|{\Gamma }_t\right|=0.15\left|{\Gamma }_r\right|=0.18$

18dB 22 dB

$P_t=2W{P}_r=?$

$G_t={10}^{1.8},G_r={10}^{2.2}$

$P_r=\frac{(1-{\left|{\Gamma }_t\right|}^2)(1-{\left|{\Gamma }_r\right|}^2)G_t{G}_r}{{\left(\frac{4\pi d}{\lambda }\right)}^2}\cdot P_t$

= $\frac{(1-{\left|0.15\right|}^2)(1-{\left|0.18\right|}^2){10}^{1.8}\cdot {10}^{2.2}}{{\left(\frac{4\pi 200\lambda }{\lambda }\right)}^2}\times 2$

= 2.995 mW = 3mW