(a) A 50 m long lossless transmission line with Zo = 50 ohms operating at 50 MHz is terminated with a load ZL = 90 + j 30 ohms. If

the wave velocity is u =0.8 c,where cis the speed of light in vacuum, find: i. The reflection coefficient ii. The input impedance (b) The Direct Broadcast System (DBS) satellite (at a distance of 39000 km)transmits at 13 GHz in the Ku Band, with a transmit power of 200 W, with a transmit antenna gain of 35 dB and with an IF (Intermediate Frequency)bandwidth of 30 MHz. The ground receiving station dish has a gain of 32 d Band sees an average background brightness temperature of Tb = 50 K. The receiver LNB (Low Noise Block) has a noise figure of 1.8 dB. Find: i.The EIRP (Effective Isotropic Radiated Power) ii.The power received at the input of the LNB iii.The signal to Noise ratio at the LNB output iv.Comment on what would happen if both transmit and receive antennas are replaced by typical monopole antennas. (c) A certain two-port network is measured and the following scattering matrix is obtained: [S]=\left[\begin{array}{cc} 0.3 \angle 0^{\circ} & 0.7 \angle 90^{\circ} \\ 0.7 \angle 90^{\circ} & 0.3 \angle 0^{\circ} \end{array}\right] From the data determine: i.If the network is reciprocal ii.If the network is lossless (d) Briefly describe how the following RF systems operate: i.Wilkinson power divider ii.Circulator