MIT6_013S09_pset11

# MIT6_013S09_pset11 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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30 ο metal roof antenna y x z D MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.013 – Electromagnetics and Applications Problem Set 11 (five problems) Suggested Reading: Course notes, Sections 10.3.3-10.3.4; 4.2, 10.4.2, 10.4.5, 11.3.1-11.3.3; 11.1; 10.4.5, 11.3.4 Problem 11.0 To transmitter (a) Some homeowners have flat metal roofs sloped at 30 o directly toward the transmitter, as illustrated, and use a single half-wave dipole antenna mounted a distance D from the roof (see figure). If the transmitted signal is horizontally polarized and arrives from the horizon, what should D be in order to optimize reception, and how should the antenna be oriented? Assume the surface of the earth is absorbing. (b) Repeat (a) for a vertically polarized transmitter. This is tricky but not computationally difficult. You might want to think of the antenna as transmitting toward the horizon. (c) What is the increase or decrease R in receiver antenna gain G (dB) toward the transmitter relative to the gain for (b) if the roof were removed and the dipole antenna were reoriented in an optimum manner? A power ratio R in dB is 10 log 10 R. Problem 11.1 (a) What is the maximum Thevenin open-circuit voltage V produced in a short dipole antenna of length L = 1 m by a 1-kW 1-MHz transmitter at distance r = 1 km away?

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