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ProblemSet1_Solutions

# ProblemSet1_Solutions - and determines that it takes 70...

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ECE 3025 Problem Set #1 (1) A coaxial cable is made of polystyrene ( e = e 0 e r = 2.6 e 0 , where e 0 =8.854 x 10 -12 F/m). The cable is 2.5 meters long. (a) What is the time-of-flight for an electrical signal to pass through this cable? If a sinusoidal signal is applied to the cable, what is the phase shift along the cable if the frequency is (b) 10 kHz, (c) 1 MHz, and (d) 100 MHz? (2) A bankrupt student discovers a 15-meter long piece of coaxial cable in the stairway with connectors on each end, so that it is not possible to see the center conductor. Another student bets her \$60 that she can’t figure out the outside diameter of the inner conductor, or the nature of the insulating material between the conductors without cutting the cable open. The student takes the bet. First she holds the piece of cable up to a magnet, and discovers that since it is not attracted, it contains no magnetic materials (i.e. m = m 0 =1.256 x 10 -6 H/m). Second, she uses a dual trace oscilloscope to measure the time it takes a pulse to travel down the line,

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Unformatted text preview: and determines that it takes 70 nanoseconds. Third, she uses the capacitance meter on her digital voltmeter to determine the total capacitance of the 15-meter long cable to be 3 nanofarads. Finally, by measuring the outer diameter of the cable and guessing the thickness of the outer conductor, she estimates the inside radius of the outer conductor to be b=6 mm. a) What is the phase velocity on this transmission line? b) What is the relative dielectric constant of the insulating material between the two conductors? (Note that e =8.854 x 10-12 F/m). c) What is the capacitance per unit length of this cable? d) What is the diameter of the center conductor? e) What is the characteristic impedance of this transmission line? (3) Problem 3.2 at the end of Lecture Note #3 (4) Problem 3.3 at the end of Lecture Note #3...
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ProblemSet1_Solutions - and determines that it takes 70...

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