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Homework11Hertzian

Homework11Hertzian - R rad = 6 π k‘ 2 = 2 π 3 ±...

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ECE 3030: Electromagnetic Fields and Waves Fall 2009 Homework 11 SOLUTIONS for GRADER: Hertzian Dipole Antennas Reminder: Prelim 3 November 19 at 7:30. Date: Tuesday 11/17 1. Problem 17.1 Pattern produced by two Hertzian dipole antennas. The Poynting flux in the far field is: ~ S( ~ r ) fl fl fl θ = π 2 = η 0 fl fl fl fl kId 4 πr fl fl fl fl 2 fl fl fl e e jk h 2 cos φ + e - jk h 2 cos φ fl fl fl 2 = p ( θ = π 2 , φ ) = 1 + cos [ kh cos φ + α ] 2 With α = π/ 2 and kh = π : p ( θ = π 2 , φ ) = 1 + cos £ π cos φ + π 2 / 2 Figure 1: Polar and rectangular plots of the pattern in the x - y plane. 2. Problem 17.12: The (corrected) radiation resistance of this Hertzian dipole is
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Unformatted text preview: R rad = η 6 π ( k‘ ) 2 = 2 η π 3 ± ‘ λ ¶ 2 = 2 · 377 π 3 (0 . 01) 2 = 0 . 079 Ω With such a small radiation resistance, this antenna is not very efficient. 3. Problem 17.23 Wireless link between a half-wave dipole and a loop. Since the H-field for a half-wave dipole in the far-field is polarized in the φ direction, it does not couple into the loop antenna oriented as shown in the figure. Hence: P out P in = 0 CORNELL UNIVERSITY c ± WES SWARTZ (09/8/12) 11–1...
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