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

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ELEG 413 Lecture #5 Mark Mirotznik, Ph.D. Associate Professor The University of Delaware Email: [email protected]
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Polarization
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Polarization
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Polarization
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Polarization
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Polarization
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Polarization
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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 + =
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Uniform Plane Waves: Propagation in Any Arbitrary Direction 0 ) ( ~ = = - 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 ϖμ με ϖ ϖμ β β β β ϖμ β ϖμ β ϖμ β ϖμ ϖμ ϖμ ϖμ 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
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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 = × = = = = + - = × = + - = = - 0 0 0 0 ) 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
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Reflection and Transmission
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Reflection and Transmission
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Reflection and Transmission
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Reflection and Transmission
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Reflection and Transmission
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Reflection and Transmission
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Reflection and Transmission
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Reflection and Transmission
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Reflection and Transmission
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Angle of Incidence, Degrees Reflection Coefficient Example: Reflection from an Ocean Interface
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