ELEG413lec3 - ELEG 413 Lecture #3 Mark Mirotznik, Ph.D....

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Unformatted text preview: ELEG 413 Lecture #3 Mark Mirotznik, Ph.D. Associate Professor The University of Delaware Email: mirotzni@ece.udel.edu SUMMARY m B D J t D H M t B E = = + = - - = m B D J D j H M B j E ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ = = + = -- = ) ~ ~ ( ~ ) ~ ~ ( ~ ) ~ ~ ( ) ~ ~ ( 1 2 1 2 1 2 1 2 =- =- =- =- B B n D D n J H H n E E n s s ) ( ) ( ) ( ) ( 1 2 1 2 1 2 1 2 =- =- =- =- B B n D D n J H H n E E n s s E J H B E D c ~ ~ ~ ~ ~ ~ = = = E J H B E D c = = = 2 ) 1 ( j jX R Z s s s + = + = , ] [ ] 2 1 [ , ] 2 1 [ ) ( 2 2 2 = = = = = = = v d v i i v e v m s s dv E P dv J E P dv E W dv H W ds H E P ~ 2 1 , ] ~ ~ 2 1 [ ] ~ 4 1 [ , ] ~ 4 1 [ ) ~ ~ ( 2 * 2 2 * = = = = = = = v d v i i v e v m s s dv E P dv J E P dv E W dv H W ds H E P Frequency Domain Time Domain Example Problem 2 2 , 1 1 , Two lossless half spaces z j o x inc e E a E 1 ~ - = z j o x r e E a E 1 ~ = z j o x t e TE a E 2 ~ - = Problem: Using Maxwells equations + constituent equations + boundary condition find expressions for 1 , 2 , and T z x y E j H H j E B j E ~ 1 ~ ~ ~ ~ ~ - = - = - = (1) Start by finding H using z j o y z j o z y x t z j o y z j o z y x r z j o y z j o y z j o z y x inc z y x z y x Te E a Te E z y x a a a j H e E a e E z y x a a a j H e E a e E z j a e E z y x a a a j H E E E z y x a a a j H 2 2 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 ~ 1 ~ ) ( 1 1 ~ 1 ~ = - = - = - = = - = - = - =---- H j E E j H D j H ~ 1 ~ ~ ~ ~ ~ = = = (2) See if we can find uisng 1 1 1 1 1 2 2 1 1 1 2 2 1 1 1 2 2 1 1 1 1 1 1 1 1 ) ( 1 1 ~ 1 ~ 1 1 1 1 1 1 = = = = - = = = =------ z j o x z j o x z j o x z j o x z j o z y x z j o x inc z y x z y x e E a e E a e E a e E z j a e E z y x a a a j e E a E H H H z y x a a a j E 2 2 2 = Similarly: Combine the two last results: z j o y t z j o y r z j o y inc Te E a H e E a H e E a H 2 1 1 2 2 1 1 1 1 ~ ~ ~ = - = =- 2 2 2 1 1 1 = = z j o y z j o y t z j o y z j o y r z j o y z j o y z j o y...
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This note was uploaded on 12/13/2011 for the course ELEG 413 taught by Professor Mirotznik during the Spring '11 term at University of Delaware.

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ELEG413lec3 - ELEG 413 Lecture #3 Mark Mirotznik, Ph.D....

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