Microwave Systems (10EC74) AssignmentSet -8 Instruction to students: Write in A4 Sheet with necessary margin. Answer All the Questions 1. a. It is found that the attenuation on a 50 Ω distortion less transmission line is 0.01 (dB/m). The line has a capacitance of 0.1 (pF/m). i. Find the resistance, inductance, and conductance per meter of the line. ii. Find the velocity of wave propagation. iii. Determine the percentage to which the amplitude of a voltage travelling wave decreases in 1 (km) and in 5 (km). b. A signal generator having an internal resistance 1 Ω and an open circuit voltage vg ( t )=0.3cos 2 π 108 t ( V ) is connected to a 50 Ω lossless transmission line. The line is 4 m long and the velocity of wave propagation on the line is 2.5 x 108 (m/s). For a matched load, find (a) the instantaneous expressions for the voltage and current at an arbitrary location on .the line, (b) the instantaneous expressions for the voltage and current at the load, and (c) the average power transmitted to the load. 2. a. Obtain approximate expressions for y and Z, for a lossy transmission line at very low frequencies such that ωL << R and ωC << G. b. The following characteristics have been measured on a lossy transmission line at 100 MHz: Z0 = 50 + j0 Ω α = 0.01 dB/m β = 0.8 π rad/m. Determine R,L,G and C for the line. 3. Calculate and compare the values of β, vp, vg, λg and ZTE10 for a 2.5 (cm) x 1.5 (cm) rectangular waveguide operating at 7.5 GHz a. If the waveguide is hollow b. If the waveguide is filled with dielectric medium characterized by εr= 2, μr=1 and σ = 0 c. Find the maximum amount of 10-(GHz) average power that can be transmitted through an air-filled rectangular waveguide a = 2.25 (cm), b = 1 .00 (cm)-at the TE10 mode without a breakdown. 4. a. Estimate the directivity of an antenna with θHP = 2°, φHP = 1°, and (b) find the gain of this antenna if efficiency k = 0.5. What is the maximum effective aperture of a microwave antenna with a directivity of 900? 8. assuming the source impedance is Z0. derive expressions for the resistors R1. R2.5 km over a freespace 1 GHz circuit consisting of a transmitting antenna with a 25 dB gain and a receiving antenna with a 20 dB gain? The gain is with respect to a lossless isotropic source. a loss resistance of 2 ohms. . and R3.34 dB are connected as shown below. a. Consider the general resistive divider shown below. What is the maximum power received at a distance of 0. Determine the power radiated by the antenna 7. and a reactance of 50 ohms is connected to a generator with open-circuit voltage of 10 V and internal impedance of 50 ohms via a λ/4-long transmission line with characteristic impedance of 100 ohms. 6. relative to port 1. and the output characteristic impedances Zo2 and Zo3 so that all ports are matched. Two identical 90◦ couplers with C = 8. For an arbitrary power division ratio α = P2/P3. Determine the power supplied by the generator c.b. 5. The transmitting antenna input is 150 W. Find the resulting phase and amplitudes at ports 2’ and 3’. Draw the equivalent circuit b. An antenna with a radiation resistance of 48 ohms. 3 dB (over isotropic) at 10 GHz. Assuming that the input power is 200 mW.2–12. Two X-band (8. and the antennas are polarization-matched.4 cm and each with a gain of 16. the VSWR of each is 1. the conduction-dielectric efficiency is 100%.9.4 GHz) rectangular horns.1. with aperture dimensions of 5. find the maximum received power when the horns are separated in air by (a) 5 m (b) 50 m (c) 500 m 10.5 cm and 7. are used as transmitting and receiving antennas. Briefly explained about Smart Antennas with neat construction diagram .