161_1_Class6

161_1_Class6 - EE161 Electromagnetic Waves Spring 2010 Prof...

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Unformatted text preview: EE161 Electromagnetic Waves Spring, 2010 Prof. Y. Ethan Wang Electrical Engineering Dept. UCLA Lesson 6 • Oblique Incidence • Parallel Polarization • Special Angles • Applications Example 1 A plane wave radiated by a distant antenna is incident in air upon a plane soil surface at z=0. The electric field of the incident wave is given by, ) 73 . 1 cos( 100 ˆ z x t y i π π ω − − = E and the soil medium may be assumed to be a lossless dielectric with a relative permittivity of 4. (a) Determine k 1 , k 2 and the incidence angle θ i . (b) Obtain expressions for the total electric fields in air and in the soil medium (c) Determine the average power density carried by the wave traveling in the soil medium Solution: ) 73 . 1 cos( 100 ˆ z x t y i π π ω − − = E i x jk z j x j i e y e y 1 100 ˆ 100 ˆ ~ 73 . 1 − − − = = π π E i i i z k x k z x x k Therefore, θ θ π π cos sin 73 . 1 1 1 1 + = + = (a) π θ π θ 73 . 1 cos sin 1 1 = = i i k k Method 1: through rotation of axis , o i θ k 30 73 . 1 tan (rad/m) 2 ) 73 . 1 ( 1 2 2 1 = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = = + = − π π π π π The wavelength in medium 1 (air) is thus given by, The phasor is i i i z x x θ θ cos sin + = m 1 2 1 1 = = k π λ The wavelength in medium 2 (soil) is m 5 . 4 1 2 2 = = = r ε λ λ Method 2: ) ( 73 . 1 1 1 100 ˆ 100 ˆ ~ z k x k j z j x j i z x e y e y + − − − = = π π E o z x i z x k k θ k k k 30 73 . 1 tan tan 2 ) 73 . 1 ( 1 1 1 1 2 2 2 1 2 1 1 = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = = + = + = − − π π π π π General plane wave solution gives, π λ π 4 2 2 2 = = k frequency 300MHz Solution: (b) o i θ 30 = is the incident angle,...
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161_1_Class6 - EE161 Electromagnetic Waves Spring 2010 Prof...

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