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ELEG413lec5 - ELEG 413 Lecture#5 Mark Mirotznik Ph.D...

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Unformatted text preview: ELEG 413 Lecture #5 Mark Mirotznik, Ph.D. Associate Professor The University of Delaware Email: [email protected] Polarization Polarization Polarization Polarization Polarization Polarization Uniform Plane Waves: Propagation in Any Arbitrary Direction E H y x z z z y y x x o z y x z z y y x x r j o E a E a E a E z a y a x a r a a a e E r E ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ) ( ~ + + = + + = + + = = ⋅- β β β β β 2 2 2 z y x β β β εμ ϖ β + + = = θ φ 2 2 2 2 2 ) sin( z y x y x β β β β β φ + + + = 2 2 ) cos( y x y β β β θ + = Uniform Plane Waves: Propagation in Any Arbitrary Direction ) ( ~ = ⋅ = ⋅- o r j o E e E r E β β E H y x z θ φ Since E and β are at right angles from each other. [ ] [ ] [ ] [ ] [ ] [ ] E a E a E a E E e E E e j j E e j e E j E j H r j o o r j o r j r j o × = × = × = × = × = × = × = × ∇ = × ∇ = × ∇ = ⋅- ⋅- ⋅- ⋅- β β β β β β β η ϖ μ με ϖ ϖ μ β β β β ϖ μ β ϖ μ β ϖ μ β ϖ μ ϖ μ ϖ μ ϖ μ ˆ 1 ˆ ˆ 1 1 1 1 1 1 ~ 1 ~ where ε μ η = 2 2 2 ˆ ˆ ˆ ˆ z y x z z y y x x a a a a β β β β β β β β β + + + + = = and Uniform Plane Waves: Propagation in Any Arbitrary Direction [ ] β β β β β β β β ϖ η η β ϖ a a a a a H a a E a E r t E t r H E a r H a E r t E t r E e E r E H E H o E o H o o o E o o r j o = × = ⋅ = ⋅ = ⋅ = ⋅ ∠ + ⋅- = × = ∠ + ⋅- = = ⋅- ) cos( ) , ( 1 ) ( ~ ) cos( ) , ( ) ( ~ Observation 1. E, H and β vectors are pointing in orthogonal directions. Summary and Observations: Frequency Domain Time Domain Observation 2. E and H are in phase with each other, however, H’s magnitude is smaller by the amount of the wave impedance Reflection and Transmission Reflection and Transmission Reflection and Transmission...
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ELEG413lec5 - ELEG 413 Lecture#5 Mark Mirotznik Ph.D...

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