final_fa08

final_fa08 - ECE 3030 Electromagnetic Fields and Waves Fall...

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Unformatted text preview: ECE 3030: Electromagnetic Fields and Waves Fall 2008 Your Name: FINAL EXAM December 15 Instructions: Do all problems. Show your work, giving appropriate units with numerical answers. Correct solutions to bonus questions offset lost points. No points will be deducted for wrong answers to bonus questions. Your CIT ID: (e.g., wes5). Exam Number: Academic integrity is expected of all students of Cornell University at all times, whether in the presence or absence of the faculty. Understanding this, I declare I shall not give, use or receive unauthorized aid in this work, nor will I discuss this exam in the presence of anyone who has not yet taken the exam (just in case there is a makeup). Your Signature: 1 CORNELL UNIVERSITY c circlecopyrt WES SWARTZ (08/11/29w) EX–1 ECE 3030: Electromagnetic Fields and Waves Fall 2008 Your Name: FINAL EXAM December 15 Reminder: Do your own work! Problem Score Regrade Bonus 1 /25 /25 None 2 /30 /30 5 3 /20 /20 5 4 /15 /15 None 5 /10 /10 None Total /100 /100 μ = 4 π × 10 − 7 H/m ε = 8 . 85 × 10 − 12 F/m η = 377 Ω c = 3 × 10 8 m/s ω = 2 πf k = k ′ − jk ′′ ε = ε ′ − jε ′′ η = radicalbigg μ ε k = ω √ με n = radicalbigg ε ε Γ = V − V + = Z L − Z Z L + Z SWR = | V max | | V min | = 1 + | Γ | 1 − | Γ | n i sin θ i = n t sin θ t k 2 x + k 2 y + k 2 z = ω 2 μ ε = parenleftBig mπ a parenrightBig 2 + parenleftBig nπ b parenrightBig 2 + k 2 z vector A( vector r) = integraldisplay integraldisplay integraldisplay μ vector J( vector r ) 4 π | vector r − vector r ′ | e − jk | vector r − vector r ′ | d V ′ vector J( vector r) = Idδ 3 ( vector r ) vector A( vector r ) = μ o Id 4 πr e − jk ( r − ˆ r · vector h ) ˆ z vector E ff ( vector r ) = j η kId 4 πr sin θ e − jkr e jk ˆ r · vector h ˆ θ vector H ff ( vector r) = j kId 4 πr sin θ e − jkr e jk ˆ r · vector h ˆ φ vector S( vector r) = vector E × vector H ∗ < vector S( vector r) > = 1 2 ℜ braceleftBig vector E × vector H ∗ bracerightBig = η 2 vextendsingle vextendsingle vextendsingle vextendsingle kId 4 πr vextendsingle vextendsingle vextendsingle vextendsingle 2 sin 2 θ vector r = sin θ cos φ ˆx+sin θ sin φ ˆy+cos θ ˆ z G ( θ, φ ) = 3 2 sin 2 θ = ⇒ p ( θ, φ ) = G ( θ, φ ) G max = sin 2 θ vector S( vector r ) = η I 2 8 π 2 r 2 · cos 2 ( π 2 cos θ ) sin 2 θ ˆ r = ⇒ p ( θ, φ ) = cos 2 ( π 2 cos θ ) sin 2 θ | F 1 ( θ, φ ) | 2 = vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle N − 1 summationdisplay m =0 ( e jkd cos θ + α ) m vextendsingle vextendsingle vextendsingle...
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This note was uploaded on 01/16/2010 for the course ECE 3030 at Cornell.

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final_fa08 - ECE 3030 Electromagnetic Fields and Waves Fall...

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