Transmission lines, Antenna and Wave Propagation — DU B. Sc. (Hons) Electronics Previous Year Question Papers

Q1. (a) What are phase matching conditions for oblique incidence? (3) (b) In free space 𝐸(𝑧, 𝑡) = 10 𝑠𝑖𝑛( 𝜔𝑡 + 𝛽𝑧) 𝑎 (c) Show that the input impedance of shorted line with βl<π/2 acts as an inductor. (3) (d) What is waveguide resonator? What is resonating frequency of resonator operating in transverse electric mode? (3) (e) Explain how quarter-wave transformer is used for impedance matching. (3) (f) Define the term- electrostatic field, inductive field and far field region of an antenna. (3) Q2. (a) Derive the expressions for Fresnel’s equations for oblique incidence with electric field intensity vector perpendicular to plane of incidence. (10) (b) Prove Snell’s law for a plane wave at oblique incidence. (8) Q3. (a) What is difference between phase velocity and group velocity of a wave? (6) (b) Find the input impedance and standing wave ratio of – shorted line, open circuited line and matched line. (8) (c) Find the Standing wave ratio of a transmission line with characteristic impedance 75 Ω and load impedance 35 Ω. (4) Q4. (a) Find the expression for input impedance of a lossless transmission line of characteristic impedance Zo and load impedance ZL. (10) (b) Prove that maximum power is delivered to the load when reflection coefficient is zero. (8) Q5. (a) Derive the electric and magnetic field expressions for Transverse Magnetic mode in a rectangular waveguide. (10) (b) Which type of mode is not supported by hollow rectangular waveguide and why. (3) (c) A rectangular waveguide with dimension a = 2.5cm and b = 1cm is to operate below 10.5GHz. How many TE and TM modes can the waveguide transmit if the guide is filled with a medium characterized by 𝜎 = 0, 𝜇𝑟 = 1, 𝜀𝑟 = 4 . Calculate the cut-off frequencies of the modes. Q6. (a) Derive the expression for radiation resistance for Hertzian dipole antenna. (12) (b) Show that the directive gain of the Hertzian dipole is Gd (θ, Φ) = 1.5sin2(θ). (6) Q7. (a) Derive the equation for the power radiated and the radiation resistance of a Half wave dipole antenna. Compare it with that for a quarter wave dipole antenna. (10) (b) An electric field strength of 10 mV/m is to be measured at an observation point = 5 /2, 500 km from a half-wave (resonant) dipole antenna operating in air at 50 MHz i) What is the length of the dipole? ii) Calculate the current that must be fed to the antenna. iii) Find the average power radiated by the antenna. iv) If a transmission line with Zo =75  is connected to the antenna, determine the standing wave ratio. (8)