ECE-305-Lecture19 - Engineering Electro-Magnetics...

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Engineering Electro-Magnetics Engineering Electro-Magnetics ECE-305, Lecture 19 Dennis McCaughey, Ph.D. 1 April 2010
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04/01/2010 Dennis McCaughey, ECE305, Spring 2010 2 Wave Propagation in Free Space Wave Propagation in Free Space ( 29 ( 29 ( 29 ( 29 0 0 0 1 2 3 0 4 0 v t t ρ ε μ = = ∇× = ∇× = - ∇• = ∇• = J E H H E E H Eq. 1 states if E is changing with time, then H has curl at that point and will change with time Eq. 2 states that if H varies with time it generates a time-varying E This field is at a small distance from the point at which H varies What is the speed? Requires a more details investigation of Maxwell’s equations
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04/01/2010 Dennis McCaughey, ECE305, Spring 2010 3 Example Example
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04/01/2010 Dennis McCaughey, ECE305, Spring 2010 4 Example Example
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04/01/2010 Dennis McCaughey, ECE305, Spring 2010 5 Uniform Plane Wave Uniform Plane Wave 0 0 Assume the electric field is polarized in the direction Further assume the wave travel is in the z direction Then The direction of the curl of determines the direc x x y x y y x E a H E a a z t t μ μ = ∇× = = - = - E H E E tion of Thus in a uniform plane wave, the directions of and and the direction of travel are mutually orthogonal. Using the - magnetic filed and the fact that it only varies with z y y directed H a z ∇× = H E H H 0 0 x x x E a t t ε ε = = E E and H lie in the transverse plane The plane normal to the direction of propagation Both fields are of constant magnitude in the transverse plane This wave is sometimes called a transverse electromagnetic wave (TEM)
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04/01/2010 Dennis McCaughey, ECE305, Spring 2010 6 Plane Wave Illustration (Sinusoid) Plane Wave Illustration (Sinusoid) Note that E and H are in phase at any point in time
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04/01/2010 Dennis McCaughey, ECE305, Spring 2010 7 Derivation Derivation 0 0 0 0 0 0 x y z x x x y x x y x y x y y a a a E E E a a x y z z y E H E a a t t H a t μ μ μ ∇× = = = ∇× = - = - ∇× = - H E
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04/01/2010 Dennis McCaughey, ECE305, Spring 2010 8 Derivation Derivation 0 0 0 0 0 0 x y z y y y x y y x y y x x a a a H H H a a x y z z x H E H a t t E a t ε ε ε ∇× = = = ∇× = = ∇× = E H
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04/01/2010 Dennis McCaughey, ECE305, Spring 2010 9 Succinctly Succinctly 0 0 y x x y x x H E a z t H E a z t μ ε = - = -
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04/01/2010 Dennis McCaughey, ECE305, Spring 2010 10 Uniform Plane Wave Continued
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