ECE-305-Lecture19

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

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Unformatted text preview: Engineering Electro-Magnetics Engineering Electro-Magnetics ECE-305, Lecture 19 Dennis McCaughey, Ph.D. 1 April 2010 04/01/2010 Dennis McCaughey, ECE305, Spring 2010 2 Wave Propagation in Free Space Wave Propagation in Free Space ( 29 ( 29 ( 29 ( 29 1 2 3 4 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 04/01/2010 Dennis McCaughey, ECE305, Spring 2010 3 Example Example 04/01/2010 Dennis McCaughey, ECE305, Spring 2010 4 Example Example 04/01/2010 Dennis McCaughey, ECE305, Spring 2010 5 Uniform Plane Wave Uniform Plane Wave 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 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) 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 04/01/2010 Dennis McCaughey, ECE305, Spring 2010 7 Derivation Derivation 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 04/01/2010 Dennis McCaughey, ECE305, Spring 2010 8 Derivation Derivation 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 04/01/2010 Dennis McCaughey, ECE305, Spring 2010 9 Succinctly Succinctly y x x y x x H E a z t H E a z t μ ε ∂ ∂ = - ∂ ∂ ∂ ∂ = - ∂ ∂ 04/01/2010...
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This note was uploaded on 09/13/2011 for the course ECE 305 taught by Professor Staff during the Spring '08 term at George Mason.

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

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