University of KwaZulu-Natal

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University of KwaZulu-Natal School of Engineering Electrical, Electronic & Computer Engineering Instructions to Candidates: UNIVERSITY EXAMINATIONS DECEMBER 2016 ENEL3EM: EM THEORY Time allowed: 2

1 University of KwaZulu-Natal School of Engineering Electrical, Electronic & Computer Engineering Instructions to Candidates: UNIVERSITY EXAMINATIONS DECEMBER 2016 ENEL3EM: EM THEORY Time allowed: 2 hours 1. This paper contains 4 questions 2. Answer any THREE questions. 3. All questions carry equal marks. The marks for each question/section are indicated. 4. Answers should show sufficient working steps to indicate the solution method used. 5. Any additional examination material is to be placed in the answer book and must indicate clearly the question number and the Student Registration number The following materials are provided: 1. Smith Chart 2. Mathematical Tables & Formula Sheet Examiners Dr. Akintunde A. Alonge Prof. Thomas J.O. Afullo Dr. Pradeep Kumar Durban, December 2016 ENEL3EM EM THEORY EXAMINATIONS DECEMBER 2016 Page 1

2 QUESTION ONE (25 MARKS) a) A generic transmission line is described by the following primary constants: series resistance, R Ω/m, series inductance L, H/m, shunt conductance G, S/m, and shunt capacitance C, F/m. Show that general solutions for line current, I, and line voltage, V, at any arbitrary distance,, along the transmission line with respect to the source are given by: Where (9 marks) b) A transmission line operating at 10 KHz has the listed primary constants: R=40 Ω/m, L= 10 mh/m, G= 2 S/m and C= 250 μf/m. Determine the following design parameters of the line: i) The characteristic impedance ii) The propagation constant iii) The attenuation constant and phase constant iv) The wavelength, and, v) Phase velocity of the line (9 Marks) c) Polyethylene has a dielectric constant of 6 and a loss tangent of 2x10-4. Determine, for a plane wave propagating through the material at 10 GHz: i) The attenuation constant ii) The intrinsic impedance iii) The phase velocity (7 marks) ENEL3EM EM THEORY EXAMINATIONS DECEMBER 2016 Page 2

3 QUESTION TWO (25 MARKS) a) Consider a circuit consisting of generator with voltage,, and generator impedance of connected to a transmission line of length,, with characteristic impedance,. If at the end of the transmission line, a load of impedance,, is used to terminate the line. Show that as time approaches infinity ( and recursive transients within the circuit become more negligible, the following mathematical expression is valid: Assume as the initial input voltage at the time, (8 marks) b) A generator circuit with VG = 20 V and ZG = 100 Ω was used to excite a 75-Ω lossless line of 100 m. If the line was terminated in a load ZL = 125 Ω. i) Find the voltage at the load and generator for transient bound between (Assume m/s) ii) Hence, using the bounce diagram profile for this transient period, deduce the asymptotic voltage as (9 marks) c) Show from fundamental Maxwell s equations of electromagnetism that the ratio of electric field, in the x-plane and magnetic field, in the y-plane propagating in free space in the direction of z is approximately given by: Where is the intrinsic impedance in free space. (8 marks) ENEL3EM EM THEORY EXAMINATIONS DECEMBER 2016 Page 3

4 QUESTION THREE (25 MARKS) a) An antenna with impedance of is set to be matched with a transmission line of characteristic impedance,. If a quarter-wave transformer is proposed as a matching line between the antenna and the transmission line. Show that this quarter-wave line has a characteristic impedance given by: Hence, compute the characteristic impedance of quarter-wave transformer is required to match a 120-Ω load to a 75-Ω line. (7 marks) b) A 75-Ω lossless line is to be matched to a j80-ω load with a shorted stub. Using a Smith chart, determine the following: i) The necessary stub admittance ii) The stub position from the load iii) The stub length (8 marks) c) Give qualitative descriptions regarding the following areas of Electromagnetic Compatibility and Electromagnetic Interference: i) Electromagnetic Compatibility (EMC) and Electromagnetic Interference (EMI). ii) Explain two solutions applied in resolving interference issues under EMI/EMC problems iii) Describe three (3) applications of EMC in Engineering practice (10 marks) ENEL3EM EM THEORY EXAMINATIONS DECEMBER 2016 Page 4

5 QUESTION FOUR (25 MARKS) a) State the electromagnetic conditions governing the propagation of plane waves in the following media: i) Lossy dielectric, ii) Lossless dielectric, iii) Good conductor, and, iv) Free space (8 marks) b) A uniform plane wave propagating in a medium has an electric field given by: If the medium is characterized by = 1, = 20, and σ = 6 S/m, find: i) The loss tangent ii) The attenuation constant, α iii) The phase constant, β iv) The wave impedance v) The equivalent field (10 marks) c) In free space ( ), a plane wave is incident normally on a lossless medium ( =2, µ=8µo) in region. Determine the reflected wave, and the transmitted wave,, if, (7 marks) ENEL3EM EM THEORY EXAMINATIONS DECEMBER 2016 Page 5

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University of KwaZulu-Natal

University of KwaZulu-Natal School of Engineering Electrical, Electronic & Computer Engineering UNIVERSITY EXAMINATIONS NOVEMBER 2015 ENEL3EM: EM THEORY Time allowed: 2 hours Instructions to Candidates: