ECE 450Homework 4Due: Tue, Sept 22, 2009, 5 PM1. In class notes it is given that the effective length of aˆz-directed half-wave dipole antenna is(θ) =λπcos(π2cosθ)sin2θ.a) Use l’Hospital’s rule to determine(0).b) Plot(θ)as a function ofθfrom 0 to 180 degrees.c) Plot(θ) sinθas a function ofθfrom 0 to 180 degrees.2. Suppose an antenna has a gain functionG(θ,φ) =Dfor0<θ<π2,Dsin2θforπ2<θ<π.DetermineDsuch that the solid angle integral ofG(θ,φ)equals4π.3. Three identicalˆz-directed short dipoles are located at(x, y, z) = (-d,0,0),(0,0,0), and (d,0,0)andhave input current phasors of1∠0◦A,2∠0◦A, and1∠0◦A, respectively.Show that the radiation field of the array of dipoles at an arbitrary location onxy-plane (i.e.,θ= 90◦plane) sufficiently far away from the origin (so that paraxial approximation can be used) is proportional
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180 degrees, antenna array, Dipole antenna, input current phasors, kd cos