161_1_Lecture_2

161_1_Lecture_2 - EE161 El EE161 Electromagnetic Waves...

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EE161 Electromagnetic Waves all 2010 Fall, 2010 Instructor: Dr. Shenheng Xu Electrical Engineering Dept., UCLA gg p , © Prof. Y. Ethan Wang
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ecture 2 Lecture 2 • Boundary Conditions for Dielectrics nd PEC and PEC omplex Variable & Phasor Notation • Complex Variable & Phasor Notation ime- armonic Maxwell’s Equations Time Harmonic Maxwell s Equations • Wave Equations
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ummary of Boundary Conditions Summary of Boundary Conditions 0 ) ( E E i ) ( ) ( 2 1 2 1 D D i J H H i S n n 1 boundary In vector forms 0 ) ( 2 1 2 1 B B i n S n n i Unit normal to the surface 2 scalar forms 0 2 1 t t E E In scalar forms 2 1 2 1 S n n S t t ρ D D J H H 0 2 1 n n B B Applications of boundary conditions are essential in solving Maxwell’s equations in differential form.
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oundary Conditions on Dielectrics Boundary Conditions on Dielectrics oundary n i 1 boundary 0 2 1 2 1 S t t t t J H H E E 1 2 Unit normal to the surface 2 0 2 1 S n n B B ρ D D 2 1 n n 0 , 0 , 2 1 S S ρ J finite 2 1 t t E E he conclusion is: 2 1 n n D D 2 1 t t H H The conclusion is: 2 1 n n B B
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Boundary Conditions on PEC 1 boundary 0 E E 1 n i Unit normal to 2 2 1 2 1 S t t t t J H H EC: 2 the surface 0 2 1 2 1 n n S n n B B ρ D D 0 D B H E (inside PEC) PEC: Perfect Electric Conductor 2 2 2 2 2 S n J H i 1 2 0 2 1 t t E E 2 S n D 1 2 0 2 1 n n B B
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Maxwell’s Equations and Boundary Conditions in One Glance Integral Form Differential Form Boundary Conditions d S C d dt d S B l E t B E D 0 2 1 t t E E 0 ) ( 2 1 E E i n or
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161_1_Lecture_2 - EE161 El EE161 Electromagnetic Waves...

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