450fall09hw5 - ECE 450 Homework 5 Due Tue 5 PM 1 Consider...

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ECE 450 Homework 5 Due: Tue, Sept 29, 2009, 5 PM 1. Consider an array of four identical ˆ z -polarized short dipoles with input currents I o = 1 0 A at locations ( x, y, z ) = ( d, 0 , 0) and (0 , d, 0) and I o = 1 180 A at locations ( x, y, z ) = ( - d, 0 , 0) and (0 , - d, 0) . a) Determine the smallest possible non-zero value of d in wavelengths λ , so that the array radiation pattern has a “far-field” null along the positive x -axis (i.e., for φ = 0 and θ = 90 ). Justify your answer without deriving the expression for the array factor (A.F.) — instead use symmetry and interference arguments pertinent to the region where paraxial approximation is well justified (far-field). b) For d found in part (a) determine the A.F. and then the values of φ for which the A.F. has a global maximum on the θ = 90 plane. c) Determine the smallest possible non-zero value of d in wavelengths λ , so that the array radiation pattern has a far-field null along x = y in θ = 90 plane. What is the corresponding A.F. for an arbitrary φ ?
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