sp08hw5sol1

sp08hw5sol1 - HW5 ECE329 Spring20008 for E1 = 2 cos(ωt −...

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Unformatted text preview: HW5 ECE329 Spring20008 for E1 = 2 cos(ωt − βz )ˆ x a)H1 = η20 cos(ωt − βz )ˆ y 4 2 z b) P = E × H = η0 cos (ωt)ˆ In the xy plane, P · dS = η40 cos2 (ωt)in units W ˜ ˜ c) E1 = 2e−jβz x and H1 = η20 e−jβz y ˆ ˆ d)Time average power through the surface = η20 in units W e) The electric eld is linearly polarized in the x direction. ˆ for E2 = E0 cos(ωt − βz )ˆ − E0 sin(ωt − βz )ˆ x y a)H2 = η10 E0 cos(ωt − βz )ˆ + η10 E0 sin(ωt − βz )ˆ y x 2 b)P = E × H = η20 E0 z ˆ 2 In the xy plane, P · dS = η20 E0 in units W 0 ˜ ˜ c)E2 = E0 e−jβz (ˆ + j y ) and H2 = E0 e−jβz (−j x + y ) x ˆ ˆˆ η 2 2 d)Time average power through the surface = η0 E0 in units W e)Left circularly polarized for H3 = cos(ωt + βz + π )ˆ + sin(ωt + βz − π )ˆ 3x 6y ˆ H3 = cos(ωt + βz + π )(ˆ − y ) 3x a)E3 = η0 cos(ωt + βz + π )(ˆ + y ) xˆ 3 b)P = E × H = −2η0 cos2 (ωt + βz + π )ˆ 3z In the xy plane, P · dS = −2η0 cos2 (ωt + π ) in units W 3 π π ˜ ˜ xˆ xˆ c)E3 = η0 ejβz ej 3 (ˆ + y ) and H3 = ejβz ej 3 (ˆ − y ) ¯ ˜ ˜ ˆ d)P = 1 Re(E × H∗ ) = −η0 z . The time average power through the surface is −η0 . 2 e)Eis linearly polarized along the (ˆ + y ) direction. xˆ 1 ...
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