329sum09hw8 - for the medium. b) Determine the propagation...

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ECE 329 Homework 8 Due: July 16, 2009, 5PM 1. A y -polarized plane TEM wave is propagating in vacuum (i.e., v = c 3 × 10 8 m/s and η = η o 120 π Ω ) in - x direction. If in the wave Feld varies at x =0 with time according to E y (0 ,t ) = 12 ± ( t τ ) V/m, where τ =4 μ s and ± ( t τ ) is the unit triangle function with width τ , a) Determine the vector waveFeld E ( x, t ) written explicitly in terms of all space and time variables x and t , b) Determine the accompanying waveFeld H ( x, t ) in A/m units, c) Determine the maximum value of Poynting vector E × H . d) What trajectory function x = x ( t ) describes instantaneous locations of the peak of E × H . e) Plot E y ( x, t ) vs t at x = - 1500 m. f) Plot H z ( x, t ) vs x at t = 12 μ s. 2. In a homogeneous lossess dielectric with ± = ± r ± o and μ = μ r μ o a plane TEM wave with the following components is observed: E yu ( t - z c/ 2 ) + ˆ xg ( t - z c/ 2 ) V m and H y 10( t - z c/ 2 ) - ˆ x 1 120 π u ( t - z c/ 2 ) A m , where u ( t ) denotes the unit-step function and c is the speed of light in free space. Using the above information, a) Determine the intrinsic impedance η
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Unformatted text preview: for the medium. b) Determine the propagation velocity v . c) Determine r and r . d) unction g ( t ) . 3. We have on x = 0 plane a pulse of sheet current J s ( t ) = y 2 t rect ( t ) A/m, where = 2 s. Regions adjacent to the current sheet are vacuum. a) Determine and plot E y ( x, t ) and H z ( x, t ) vs t for x = 1200 m. b) Repeat (a) for x =-1200 m. c) Determine and plot E y ( x, t ) and H z ( x, t ) vs x for t = 5 s. d) Determine the TEM wave energy radiated per unit area (in J/m 2 units) by the current pulse J s ( t ) = y 2 t rect ( t ) A/m. Hint: integrate the power injected per unit area,-J s E , over the duration of pulse J s ( t ) . 4. Given a uniform TEM plane wave with H = cos( t + z ) y A m , Fnd the corresponding E if = 2 3 c and = 2 . 25 o . 1...
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