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22-Elec-B9 Electromagnetic Field, Transmission Lines, Antennas, and Radiation: May 2013

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

  1. Question 1 Stub-Loaded Line — Frequencies of Short Circuit and of a Matched 50 Ω Termination
  2. Question 2 Distance to the Unit-Conductance Circle on a Mismatched Line
  3. Question 3 Pulse Echoes from Two Shunt Resistors on a Long Line
  4. Question 4 Resonant Frequencies of a 1 × 2 × 3 cm Rectangular Cavity
  5. Question 5 Beam Direction of a Five-Element Phased Array
  6. Question 6 Field of a Short Vertical Element Raised Above Its Ground Plane
  7. Question 7 Radar Return from a Flat Plate at 10 km
  8. Question 8 Phase Shift on Total Internal Reflection

Start with Question 1 →

Paper format. National Exams, May 2013 — 07-Elec-B9, Electromagnetic Field, Transmission Lines, Antennas, and Radiation. Three hours, closed book; an approved Casio or Sharp calculator is permitted. Eight questions are printed and five constitute a complete paper, each of equal value (20 marks); the first five appearing in the answer book are the ones marked. The cover page supplies only two aids, $\varepsilon_0 = 8.85\times 10^{-12}\ \text{F/m}$ and $\mu_0 = 4\pi\times 10^{-7}\ \text{H/m}$, plus a Smith chart on page 4. Candidates are urged to state any interpretation assumptions with their answers. All eight questions are solved below, because this set is a study resource rather than a three-hour sitting.

Reference texts. D. M. Pozar, Microwave Engineering, 4th ed. (transmission lines, the Smith chart, waveguides and cavities); M. N. O. Sadiku, Elements of Electromagnetics, 7th ed. and W. H. Hayt & J. A. Buck, Engineering Electromagnetics, 9th ed. (plane waves, oblique incidence, radiation); C. A. Balanis, Antenna Theory: Analysis and Design, 4th ed. (short elements, arrays, apertures); F. T. Ulaby & U. Ravaioli, Fundamentals of Applied Electromagnetics, 8th ed. (radar equation, ground-plane imaging). SI units throughout; the paper's own $c = 3\times 10^{8}\ \text{m/s}$ and $Z_0 = 377\ \Omega$ are used so that the printed aids reproduce exactly.

Check: reading of the printed data. Some symbols are printed loosely. Question 3 prints “10GH” and “1KWs total energy”; these are read as a 10 GHz carrier and a total pulse energy of $1\ \text{kW}\cdot\text{s} = 1000\ \text{J}$. Question 6 prints “15 MH” (15 MHz) and the aid $R_{\text{rad}} = (2\pi/3)Z_0 (l/\lambda)^2$. Question 7 prints “10GH” (10 GHz) and the aid $\theta_0 = 1.2\lambda/d$. Question 8 prints “an 600 angle” ($60^\circ$).