This preview shows pages 1–10. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Engineering ElectroMagnetics Engineering ElectroMagnetics ECE305, 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 timevarying 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...
View
Full
Document
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.
 Spring '08
 Staff
 Electromagnet

Click to edit the document details