homework12

homework12 - School of Electrical and Computer Engineering...

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1 School of Electrical and Computer Engineering, Cornell University ECE 303: Electromagnetic Fields and Waves Fall 2005 Homework 12 Due on Dec. 02, 2005 by 5:00 PM Reading Assignments: i) Review the lecture notes. ii) Review sections 9.1-9.5, 9.7, 9.8 of the paperback book Electromagnetic Waves . Problem 12.1: (Receiving and transmitting antenna system) Consider the following setup for a mobile wireless receiver Assume that: GHz 0 . 1 cm 15 km 1 150 30 2 1 2 1 = = = = = = f d d L o o θ The antennas are always assumed to be matched to their respective circuits (But I can give you the unmatched case in the final exam – be sure to ask your recitation instructors how to handle that case). a) Find the ratio in out P P assuming that the antennas do not dissipate power (i.e. 0 = diss R ). b) Find the ratio in out P P assuming that each antenna has a 25 impedance contribution due to internal dissipation (i.e. = 25 diss R ). P in d 1 P out d 2 1 2 L Base station Mobile receiver
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2 Problem 12.2: (N-turn small wire loop antenna) Consider the N -turn small wire loop antenna shown below. In this problem you will verify the antenna theorem: () () φ θ π λ , 4 , 2 G A = for the small wire loop antenna in the same way as was done in the lecture notes for a short-dipole antenna. Since the expression for gain has already been derived in the lecture notes, you will need to calculate the antenna effective area directly and then verify the above relation. Consider plane wave radiation with Poynting vector magnitude P incident from the direction. You will need to find the power received P rec by a matched circuit connected to the antenna. a) Find the magnitude | H | of the H-field for the incident plane wave given its Poynting vector magnitude P . b) Using Faraday’s law, find the voltage phasor V generated across the open-circuited ends of the loop when a plane wave with magnetic field phasor H passes through the loop. Assume that the plane wave is incident from the direction and the H-field is polarized in the ˆ -direction (as shown in the figure above). Hint: don’t forget the angular dependence here. Note that when angle is 0-degrees no magnetic flux passes through the loop and when the angle is 90-degrees maximum magnetic flux passes through the loop. c) From you result in part (b), find the maximum power
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