329fall09hw10sol - ECE 329 Fall 2009 Homework10 Solution...

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Unformatted text preview: ECE 329 Fall 2009 Homework10 Solution Due: Nov. 10, 2009 1. a) ∵ η 1 = r μ , η 2 = r μ 4 = 1 2 η 1 . ∴ Γ = 1 2- 1 1 2 + 1 =- 1 3 , τ = 1 2 · 1 1 2 + 1 = 2 3 . b) ˜ E i = 5 e- j ( βy + π 2 ) ˆ x. At y = 0 , ( ˜ E r = Γ ˜ E i =- 5 3 e- j π 2 ˆ x ˜ E t = τ ˜ E i = 10 3 e- j π 2 ˆ x . Therefore, for arbitrary y we have ( ˜ E r =- 5 3 e j ( βy- π 2 ) ˆ x ˜ E t = 10 3 e- j ( β 2 y + π 2 ) ˆ x = 10 3 e- j ( 2 βy + π 2 ) ˆ x , where β 2 = ω √ μ · 4 = 2 ω √ μ 0 0 = 2 β. c) The magnetic eld of a plane wave is related to the corresponding electric eld by ˜ H = 1 η ˆ β × ˜ E . where ˆ β is the unit vector in the wave propagation direction. Therefore, ˜ H i = 1 η 1 ˆ y × 5 e- j ( βy + π 2 ) ˆ x =- 5 η 1 e- j ( βy + π 2 ) ˆ z ˜ H r = 1 η 1 (- ˆ y ) × h- 5 3 e j ( βy- π 2 ) ˆ x i =- 5 3 η 1 e j ( βy- π 2 ) ˆ z ˜ H t = 1 η 2 ˆ y × 10 3 e- j ( β 2 y + π 2 ) ˆ x =- 10 3 η 2 e- j ( β 2 y + π 2 ) ˆ z =- 20...
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This note was uploaded on 04/06/2010 for the course ECE 329 taught by Professor Franke during the Fall '08 term at University of Illinois at Urbana–Champaign.

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329fall09hw10sol - ECE 329 Fall 2009 Homework10 Solution...

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