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: 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 Prof. Thomas J.O. Afullo Prof. Vrinjay Srivastava Durban, November 2015 ENEL3EM EM THEORY EXAMINATIONS NOVEMBER 2015 Page 1
Question 1 (25 Marks) a) Given a transmission line along the z-axis, with the following primary constants: Series resistance, R /m, series inductance L, H/m, shunt conductance G, S/m, and shunt capacitance C, F/m, show that the standard equations relating the line voltage, V, and current, I, can be reduced to: 2 d V 2 V 2 dz 2 d I 2 I 2 dz where R jlg jc (8 marks) b) A transmission line has the following parameters: L=0.4x10-6 H/m; C=40x10-12 F/m; R=20 mg=0.08 S/m. If the line operates at 95.5 MHz, determine: i) The propagation constant ii) iii) iv) The attenuation constant and phase constant The guide wavelength The phase velocity v) The characteristic impedance (10 marks) c) Copper has a conductivity of 5.8x10 7 mhos/m and is considered an ideal material for electromagnetic shielding. A shield is made of copper with a thickness of 1 mm. If a uniform plane wave is normally incident upon the copper shield, determine, at a frequency of 500 MHz: i) The attenuation constant ii) The intrinsic impedance iii) The surface resistance iv) The absorption loss in the copper shield (7 marks) ENEL3EM EM THEORY EXAMINATIONS NOVEMBER 2015 Page 2
Question 2 (25 Marks) a) Show that for an unbounded plane electromagnetic wave propagating in a lowloss dielectric material with electric permittivity, magnetic permeability, and electric conductivity, and operating at radian frequency, the propagation constant is given by: j 1 1 j 2 8 2 (6 Marks) b) Sea water has a conductivity of 5.0 S/m and a dielectric constant r=70. A submarine antenna operating 3 meters under the sea surface receives an electromagnetic wave. If a uniform plane wave at 1 MHz is vertically incident upon the antenna from the top, determine: i) The loss angle ii) iii) The attenuation constant The absorption loss in the sea, in db (7 Marks) c) A plane wave propagating through a medium with r=8 and r=2 has an electric field given by: Determine: E e z / 3 sin 10 8 t zxˆ i) The attenuation constant, ii) iii) iv) The wave number, The loss tangent The wave impedance (12 Marks) ENEL3EM EM THEORY EXAMINATIONS NOVEMBER 2015 Page 3
Question 3 (25 Marks) a) Travelling E and H waves in free space (region 1) are normally incident on the interface with a perfect dielectric (region 2) for which r=3.0. Determine the magnitudes of the incident, reflected, and transmitted E and H waves at the interface. (8 Marks) b) A 50- transmission line having a transit time =50 nanoseconds connects a pulse generator to a 150- load resistance. The internal resistance of the pulse generator is 60, and its voltage magnitude is 10 V at no load. Determine the variation of the voltage at the mid-point of the line for a duration of 5 if the pulse width is 1 nanosecond. (7 Marks) c) Answer the following pertaining to Electromagnetic Compatibility and Electromagnetic Interference: i) Explain in your own words the meaning of Electromagnetic Compatibility (EMC) and Electromagnetic Interference (EMI). ii) iii) Explain the coupling path classifications encountered in an EMC/EMI problem. Briefly explain typical biological effects of EMI. (10 Marks) ENEL3EM EM THEORY EXAMINATIONS NOVEMBER 2015 Page 4
Question 4 (25 Marks) a) In a Smith chart, use sketches to identify and explain the locus of the following circles: i) Constant resistance circles ii) Constant reactance circles iii) Constant standing wave ratio circles (6 Marks) b) A lossless transmission line with a characteristic impedance of 50 is connected to a load ZL=100-j150. It is required to design a single stub tuner to match the load impedance to the line. Using the Smith Chart, determine: i) The shortest distance between the antenna and the point where the stub is placed. ii) iii) The susceptance contributed by the stub. The length of the stub (11 Marks) c) Consider again the above transmission line with a characteristic impedance of 50 is connected to a load ZL=100-j150. If it is required to a quarter-wavelength transformer to match the load impedance to the line. With the aid of the Smith chart, determine: iv) The shortest distance between the antenna and the point where the transformer is placed. v) The input impedance Zin seen by the quarter-wave transformer. vi) The characteristic impedance of the matching transformer. (8 Marks) *******************************END OF PAPER***************************** ENEL3EM EM THEORY EXAMINATIONS NOVEMBER 2015 Page 5
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