161_1_Class5

# 161_1_Class5 - EE161 Electromagnetic Waves Spring, 2010...

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Unformatted text preview: EE161 Electromagnetic Waves Spring, 2010 Prof. Y. Ethan Wang Electrical Engineering Dept. UCLA Lesson 5 • Wav Reflection & Transmission at Normal Incidence • Transmission Line Analogue • Power Reflection & Transmission • Oblique Incidence Wave Reflection and Transmission rocedures to solve the wave incidence problems: 1. Write down the general wave solutions with unknown coefficients for each region 2. Derive the expressions of total field in each region 3. Enforce boundary conditions and match the total field expressions on the boundary to derive the unknown coefficients Field Solution for Normal Incidence (1) Incident wave: Reflected wave: Transmitted wave: ⎪ ⎩ ⎪ ⎨ ⎧ = × = = − − z jk i i i z jk i i e E y z z z e E x z 1 1 1 1 ˆ ) ( ~ ˆ ) ( ~ ˆ ) ( ~ η η E H E ⎪ ⎩ ⎪ ⎨ ⎧ − = × − = = z jk r r r z jk r r e E y z z z e E x z 1 1 1 1 ˆ ) ( ~ ) ˆ ( ) ( ~ ˆ ) ( ~ η η E H E ⎪ ⎩ ⎪ ⎨ ⎧ = × = = − − z jk t t t z jk t t e E y z z z e E x z 2 2 2 2 ˆ ) ( ~ ˆ ) ( ~ ˆ ) ( ~ η η E H E t r E E , i E 2 1 2 1 , , , Unknown field strength Known field strength η η k k Known parameters Field Solution for Normal Incidence (2) Total field for Medium 1: ⎪ ⎩ ⎪ ⎨ ⎧ ⋅ − = + = + = + = − − 1 1 1 1 ) ( ˆ ) ( ~ ) ( ~ ) ( ~ ) ( ˆ ) ( ~ ) ( ~ ) ( ~ 1 1 1 1 η z jk r z jk i r i z jk r z jk i r i e E e E y z z z e E e E x z z z H H H E E E Total field for Medium 2: ⎪ ⎩ ⎪ ⎨ ⎧ = = = = − − 2 2 2 2 2 ˆ ) ( ~ ) ( ~ ˆ ) ( ~ ) ( ~ η z jk t t z jk t t e E y z z e E x z z H H E E Apply the boundary conditions on the boundary (z=0), ⎪ ⎩ ⎪ ⎨ ⎧ = = ) ( ~ ) ( ~ ) ( ~ ) ( ~ 2 1 2 1 H H E E No perfect conducting medium ! 2 1 1 η η η t r i t r i E E E E E E = − = + Can be solved jointly!!! Reflection and Transmission Coefficients Simultaneous solutions for and in terms of give, r E i E E t i i t i i r E E E E E E 1 2 2 1 2 1 2 2 τ η η η η η η η = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + = Γ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + −...
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## This note was uploaded on 05/10/2010 for the course EE 190776201 taught by Professor Yuanxunethanwang during the Spring '10 term at UCLA.

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161_1_Class5 - EE161 Electromagnetic Waves Spring, 2010...

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