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Homework12Arrays

Homework12Arrays - direction a The far-field electric...

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ECE 3030: Electromagnetic Fields and Waves Fall 2009 Homework 12 SOLUTIONS for GRADER: Antenna Arrays Reminder: Just one more homework after this one! Date: Tuesday 11/24 1. Problem 17.11: Note the extra statement in the Lecture 34 notes say- ing that a quarter wave of phase progression was provided by the feed network to the 8 COCOs. With this phasing, the 1.8 m spacing, and the 2.1 m above the ground plane, the elevation angle is approximately 40 . 2. Problem 17.15: Half-wave dipole above a reflector. The image dipole has its current going in the same vertical direction. (If the dipole were horizontal, then the image would have its current going in the opposite
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Unformatted text preview: direction. a. The far-field electric field is ~ E( ~ r) = j η I 2 πr e jkr cos ( π 2 cos θ ) sin θ £ e jkh cos θ + e-jkh cos θ / ˆ θ = j η I πr e jkr cos ( π 2 cos θ ) sin θ cos( kh cos θ ) ˆ θ b. Plugging in h = λ/ 2: ~ E( r,θ,φ ) = j η I πr e jkr cos ( π 2 cos θ ) sin θ cos( π cos θ ) ˆ θ p ( θ,φ ) ∼ cos 2 ( π 2 cos θ ) sin 2 θ cos 2 ( π cos θ ) Note that there is no radiation for θ > 90 ◦ , i.e., everything is reflected upward. CORNELL UNIVERSITY c ± WES SWARTZ (09/11/7) 12–1...
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