329sum09hw10sol - ECE-329 Summer 2009 Homework 10 —...

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Unformatted text preview: ECE-329 Summer 2009 Homework 10 — Solution July 24, 2009 1. A plane wave field ˜ E i = 10 e- βz ˆ x V m is incident on z = 0 plane (the interface between two media). The region for z < is vacuum ( η 1 = η o ≈ 120 π Ω ) while the region for z > is a perfect dielectric with 2 = 4 o and μ 2 = μ o ( η 2 = 1 2 η o ≈ 60 π Ω ). a) Since, at the interface, the reflection and transmission coefficients are Γ = η 2- η 1 η 2 + η 1 =- 1 3 and τ = 1 + Γ = 2 3 , it can be shown that the reflected and transmitted electric fields are ˜ E r = Γ10 e jβ 1 z ˆ x =- 10 3 e jβ 1 z ˆ x V m and ˜ E t = τ 10 e- jβ 2 z ˆ x = 20 3 e- jβ 2 z ˆ x V m where β 1 = ω √ o μ o = ω c and β 2 = ω √ 4 o μ o = 2 ω c . b) The associated incident, reflected, and transmitted magnetic fields are ˜ H i = 10 η 1 e- jβ 1 z ˆ y = 1 12 π e- jβ 1 z ˆ y A m , ˜ H r =- 10 η 1 Γ e jβ 1 z ˆ y = 1 36 π e jβ 1 z ˆ y A m , and ˜ H t = 10 η 2 τe- jβ 2 z ˆ y = 1 9 π e- jβ 2 z ˆ y...
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This note was uploaded on 09/16/2011 for the course ECE 329 taught by Professor Kim during the Fall '08 term at University of Illinois, Urbana Champaign.

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329sum09hw10sol - ECE-329 Summer 2009 Homework 10 —...

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