ECE3010-AU22-Homework2-Solutions

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Ohio State University *

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3010

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Electrical Engineering

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Jan 9, 2024

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1 ECE 3010 – SPRING 2021 HOMEWORK #2 [Covers Lectures 6 to 10] Student Name: ________________________________ Question #1 [20 points / 10 points for (a), 5 points for (b) and (c)] A transmission line of length l connects a load to a sinusoidal voltage source with a frequency f. Assuming that the velocity of wave propagation on the line is 3×10 8 m/sec, explain whether it is reasonable to ignore the presence of the transmission line for each of the following configurations: a) l = 20cm, f = 20kHz b) l = 50km, f = 60Hz c) l = 20cm, f = 600MHz Question #2 [25 points / 5 points each] Indicate whether the following statements are true or false: a) Since copper is a conductor, its conductivity is equal to infinity. True False b) Considering the lumped element model of a transmission line, R’ accounts for the resistance of both of its conductors. True False c) If we only change the dielectric material of a coaxial cable and keep everything else the same, then the value of R’ will change. True False d) The characteristic impedance of a transmission line can be a complex number. True False
2 e) The voltage reflection coefficient of a transmission line is a function of frequency. True False Question #3 [15 points / 5 points each] For a certain transmission line, the line parameters are given by R’=1 Ω/m, L’=167 nH/m, G’=0, and C’=172 pF/m. At the frequency of 1 GHz, calculate its: a) complex propagation constant b) attenuation constant Real part of (a) c) wavenumber Imaginary part of (a) Question #4 [20 points / 10 points each] A 300 Ω lossless air transmission line is connected to a complex load composed of a 600 Ω resistor in series with a 0.02 mH inductor. At 5 MHz, calculate the: a) load impedance b) reflection coefficient at the load in polar coordinates Question #5 [20 points / 10 points each] You are given a transmission line that is 1 m long. The line parameters are: R’ = 1 Ω/m, L’ = 0.5 H/m, G’ = 1 S/m, and C’ = 0.5 F/m.
3 a) Draw the equivalent circuit model of the line across an infinitesimal length Δz. where R’ = 1 Ω/m, L’ = 0.5 H/m, G’ = 1 S/m, and C’ = 0.5 F/m (make sure you show multiplication by Δz for each element) b) If now the wire of this line is replaced with a perfect conductor (R’=0) and if the dielectric is replaced with a lossless material (G’ = 0) draw the equivalent circuit model of the line across an infinitesimal length Δz. where L’ = 0.5 H/m and C’ = 0.5 F/m (make sure you show multiplication by Δz for each element) Question #6 [Your response to this question is optional and will NOT be graded. Responses will be collected and topics that are still unclear will be addressed during the lectures.] What, if anything, is still unclear from Lectures 6 to 10?
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