329sum09hw8sol - ECE-329 Summer 2009 Homework 8 —...

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Unformatted text preview: ECE-329 Summer 2009 Homework 8 — Solution July 15, 2009 1. A y-polarized plane TEM wave propagates in vacuum in- ˆ x direction. If the wave field varies at x = 0 according to E y (0 ,t ) = 12Δ ( t τ ) V / m , where Δ ( t τ ) is the unit triangle function with width τ = 4 μ s , we can find that a) The wave’s electric field is given by E ( x,t ) = 12Δ( t + x/c τ ) ˆ y V m , where c ≈ 3 × 10 8 m / s is the wave propagation velocity in vacuum. b) The associated wave’s magnetic field is H ( x,t ) =- 12 η o Δ( t + x/c τ ) ˆ z A m , where η o ≈ 120 π Ω is the intrinsic impedance of vacuum. c) The Poynting vector is E × H =- 144 η o Δ 2 ( t + x/c τ ) ˆ x W m 2 and its pick value is max( | E × H | ) = 144 η o ≈ 6 5 π W m 2 . d) The location of the peak of E × H evolves according to t + x/c τ = 0 → x =- ct. e) Plotting E y vs t at x =- 1500 m . Time [ μ s] E y ( x,t ) h V m i 2 4 6 8 10 2 4 6 8 10 12 x =- 1500 m 1 ECE-329 Summer 2009 f) Plotting H z vs x...
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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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329sum09hw8sol - ECE-329 Summer 2009 Homework 8 —...

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