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prelim2sol (1)

prelim2sol (1) - = 0 367(Note eﬀect of angle f ~ E t =...

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ECE 3030 Prelim 2 Answers 2008/10/28 Problem 1: Plane wave incident in dielectric with ε r = 1 - j 7. a. D ~ S i ( ~ r ) E = 1ˆx W/m 2 . b. ~ E i ( ~ r ) = 27 . 46e - j 20 . 9 x ˆy V/m. (Other directions of E possible.) c. ~ H i ( ~ r ) = 0 . 0728e - j 20 . 9 x ˆ z A/m. (Must be consistent with chosen direction of E.) d. You need to find η t = 107 + j 92 . 9 Ω and T = 0 . 498 + j 0 . 288 -→ | T | 2 = 0 . 33 and noting that k t = k 0 t - jk 00 t = 42 . 07 - j 36 . 49, then D ~ S) t ( ~ r ) E = 0 . 666e - 73 x ˆx W/m 2 . e. SWR = 3 . 75. Problem 2: Wave with ~ k i = k i [ˆx + 2ˆy] / 5 incident on dielctric with ε r = 16. a. Note | ˆx + 2ˆy | / 5 = 1, so k i = ω/c = 20 . 9 m - 1 . b. These should all be drawn on the figure: ~ E i should point out of plane of paper. ~ H i should point to right and down to ~ k i . ~ k r should point to left and up. (It is actually ~ k r = k i [ˆx - 2ˆy] / 5.) ~ E r should point into plane of paper. ~ H r should point to left and down. ~ k t should point to right and very slightly up. ~ E t should point out of plane of paper. ~ H t should point to down and slightly to right to ~ k t . c. ~ E i ( ~ r ) = - 0 . 01e - j 20 . 9 x +2 y 5 ˆ z V/m. d. Get η t = 94 . 25 Ω, θ i = θ r = 26 . 6 , θ t = 6 . 42 , then Γ =
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Unformatted text preview: = 0 . 367. (Note eﬀect of angle!) f. ~ E t =-. 00367e-j 83 . 6[0 . 112 x +0 . 994 y ] ˆ z V/m. g. ~ H t = [3 . 87ˆx-. 44ˆy]-5 e-j [9 . 36 x +83 . 1 y ] ˆ z V/m. Problem 3: Right circular to linear. a. ~ E 1 ( ~ r) = E [ˆx + j ˆ z]e-jk i or just simple ~ E 1 ( ~ r) = E [ˆx + j ˆ z] | y =0 is suﬃcient. b. L = 7 . 5 cm. c. ~ E 1 ( ~ r) = E [ˆx + uz ] | y = L d. η 6 = η , so yes, there will be a reﬂection. Problem 4: Short answers: a. A uniaxial material’s permittivity tensor has all diﬀerent values along the diagonal when aligned with its principle axis. b. A TE or TM (Transverse electric or magnetic wave) impinges on an interface with its electric (or magnetic) ﬁeld perpendicular to the plane of incidence. c. m-1. d. True. (No reason needed.) WES 1...
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