Unformatted text preview: ECE 450 Homework 3 Due: Tue, Sept 15, 2009, 5 PM 1. Consider a circular wire loop of radius a carrying a timeharmonic current I = I o cos ( ωt ) and radiating in a homogeneous medium of electric permittivity ε and magnetic permeability μ . The loop is placed on the xyplane of the reference coordinate system, with its center at the origin. The current flow in the loop is in the counterclockwise direction when looking down on xyplane in ˆ z direction. It can be shown 1 that if the loop is small enough (i.e., in the limit as a → ) the retarded vector potential phasor is given by ˜ A ( r, θ ) = ˆ φ μI o πa 2 4 πr e jkr jk + 1 r sin θ where k = ω √ μ . a) Calculate the magnetic and electric field phasors ˜ H and ˜ E of the small loop antenna starting with ˜ B = μ ˜ H = ∇× ˜ A , and also using ∇× ˜ H = ˜ J + jω ˜ E where ˜ J = 0 . b) Using the expressions derived above in the limit as r λ , show that the radiation fields of the loop antenna are given by...
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This note was uploaded on 02/22/2010 for the course ECE 450 taught by Professor Franke during the Fall '09 term at University of Illinois at Urbana–Champaign.
 Fall '09
 FRANKE

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