350sp11hw5 - ECE 450 Homework 5 Due Tue 5 PM 1 Three identical z-directed short dipoles are located at(x y z =(d 0 0(0 0 0 and(d 0 0 and have input

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ECE 450 Homework 5 Due: Tue, Feb 22, 2011, 5 PM 1. Three identical ˆ z -directed short dipoles are located at ( x, y, z )=( - d, 0 , 0) , (0 , 0 , 0) ,and( d, 0 , 0) and have input current phasors of 1 0 A, 2 0 A, and 1 0 A, respectively. a) Show that the radiation Feld of the array of dipoles at an arbitrary location on xy -plane (i.e., θ =90 plane) su±ciently far away from the origin (so that paraxial approximation can be used) is proportional to ( e j 1 2 kd cos φ + e - j 1 2 kd cos φ ) 2 cos 2 ( 1 2 kd cos φ ) . b) Calculate the distance d in wavelengths that will result in a null in the radiation Feld of the array on the xy -plane along ± x . 2. ²or the same antenna array , assume, next, that the input current phasors for the dipoles at ( - d, 0 , 0) and ( d, 0 , 0) are, respectively, 1 ψ Aand 1 - ψ A, while the input current phasor for the dipole at the origin remains unchanged. a) How is the answer to part (a) of Problem 1 modiFed after introducing the input current phase
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This note was uploaded on 08/25/2011 for the course ECE 350 taught by Professor Kudeki during the Spring '11 term at University of Illinois at Urbana–Champaign.

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