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329sum11hw9 - ECE 329 Homework 9 Due Fri 5PM 1 For each of...

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ECE 329 Homework 9 Due: Fri, July 15, 2011, 5PM 1. For each of the four plane TEM waves (in free space) described by a) E 1 = 2 cos( ω t - β z x V/m b) E 2 = E o cos( ω t - β z x - E o sin( ω t - β z y V/m c) H 3 = cos( ω t + β z + π 3 x + sin( ω t + β z - π 6 y A/m d) H 4 = cos( ω t - β x z + sin( ω t - β x y A/m: i. Determine the corresponding E and H field phasors. ii. Determine the time-averaged Poynting vector S , that is S E × H , by utilizing the phasor cross product ˜ E × ˜ H * appropriately. iii. Determine the time-averaged power that crosses a 1 m 2 area in the xy -plane from - z to + z by using the results of (ii). 2. We have on x = 0 plane a pulse of sheet current J s ( t ) = ˆ y 2 t rect ( t τ ) A/m, where τ = 2 μ 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 μ s. d) Determine the TEM wave energy radiated per unit area (in J/m 2 units) by the current pulse J s ( t ) .
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