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Question 4 (a) The input impedance of a lossless air-core transmission line with characteristic impedance Ro. phase constant B and length I terminated in an impedance Z, is given by R,+Z, tan( i. Determine the length of an open circuit 50Ω line required to create a 0.1 nH inductor at a frequency of 10 GHz. (6 marks) ii. Determine the input impedance of the line in part () if the open circuit is changed to a short circuit. (3 marks) iii. A 50Ω line is terminated in a 100Ω load. Determine the quarter-wavelength transformer 4 marks) (b) The input impedance of a lossless transmission line with phase constant β (-2m/A) terminated in length and characteristic impedance required to transform the load to 50 Ω at 10 GHz. Note: β-2πΙλ an unknown load Z, with reflection coefficient -:lexpjer,), is given by , where z' is the distance from the load. The voltage standing wave ratio on a 50 Ω line terminated in an unknown impedance is found to be 2.0. The first voltage minimum is located 10 cm from the load and the distance between successive minima is 40 cm. Determine the load voltage reflection coefficient and impedance. (12 marks)
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