Rules: You may consult your own half-page/one-side formula sheet, but nothing else. In particular, the use of any old homework/exam solutions is expressly prohibited. The formula sheet should be limited to equations and must not contain any drawings, problem solutions, or solution algorithms. Staple the signed exam sheet on the top of your paper work with the formula sheet at the bottom of the stack. Write on one side of paper, leaving 1-inch left margins. Calculators may only be used for basic arithmetic operations and use of any calculus/graphing features is not allowed.
Statement: I have read and understood the above Rules. On my honor, I solemnly swear that I have not received unauthorized aid and have not used unauthorized sources during this exam.
A voltage generator with vg(t) = 100sin(2π×109t) [V] and internal impedance Zg = 35Ω is driving a 50-Ω lossless transmission line with air insulation. The line is 36 cm long and is terminated in a load with impedance ZL = 100 − j50Ω. Determine (a) the input impedance (in rectangular form), (b) time-domain load current, and (c) time-average power delivered to the load. Do not use the Smith chart in this problem.
A 50−Ω lossless transmission line operating in a sinusoidal steady state is terminated by a load with unknown impedance ZL. Measurements indicate that the standing wave ratio is 3.0 and that the first and second voltage minima are at 10 cm and 25 cm from the load. Use the Smith chart to find ZL (in rectangular form). [Note: For full credit, mark all important points on the Smith chart as A, B, etc., and on a separate page explain, step by step, your solution procedure.]
A 40 − Ω lossless transmission line with dielectric insulator characterized by is to be matched to an antenna with ZL = 80+j60Ω at the operating frequency of 1 GHz, using a shorted stub. Use the Smith chart to determine the stub length ` and the distance d between the antenna and stub, both in cm [sic]. Choose the design with the smaller d. [Note: For full credit, mark all important points on the Smith chart as A, B, etc., and explain (on a separate page), step by step, your solution procedure.]
A rectangular pulse of an amplitude 15 [V] and a duration 1 [µs] is applied through a series resistance of 25 [Ω] to the input terminals of a 50−Ω, lossless, coaxial-cable transmission line. The line is 400 [m] long and is short-circuited at the far end. The dielectric constant of the insulating material in the cable is 2.25. Draw the bounce diagram and use it to plot the voltage at (a) the input and (b) the midpoint of the line as a function of time up to 8 [µs].
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