450fall09hw4

450fall09hw4 - ECE 450 Homework 4 Due: Tue, Sept 22, 2009,...

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ECE 450 Homework 4 Due: Tue, Sept 22, 2009, 5 PM 1. In class notes it is given that the efective length oF a ˆ z -directed halF-wave dipole antenna is ± ( θ )= λ π cos( π 2 cos θ ) sin 2 θ . a) Use l’Hospital’s rule to determine ± (0) . b) Plot ± ( θ ) as a Function oF θ From 0 to 180 degrees. c) Plot ± ( θ )sin θ as a Function oF θ From 0 to 180 degrees. 2. Suppose an antenna has a gain Function G ( θ,φ )= ± D For 0 <θ< π 2 , D sin 2 θ For π 2 <θ<π. Determine D such that the solid angle integral oF G ( θ,φ ) equals 4 π . 3. 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. Show that the radiation ±eld oF the array oF dipoles at an arbitrary location on xy -plane (i.e., θ =90 plane) su²ciently Far away From the origin (so that paraxial approximation can be used) is proportional
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