161_1_Class8

161_1_Class8 - EE161 Electromagnetic Waves Spring 2010 Prof...

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EE161 Electromagnetic Waves Spring, 2010 Prof. Y. Ethan Wang Electrical Engineering Dept. UCLA
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Lesson 8 Introduction to Waveguide General Plane Wave Solutions General Waveguide Solutions TEM, TE, TM Waves
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History of Waveguides 1893 - Heaviside considered the possibility of wave propagation inside a hollow tube, soon he denied himself 1897 - Lord Rayleigh (Cambridge) proved wave propagation inside a hollow tube is possible, for both circular and rectangular cross- sections 1932 - Rediscovered and experimentally validated by G.C. Southworth (AT&T) & W. L. Barrow (MIT) independently 1950s - Development of planar lines (stripline, microstrip….) . .
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Waveguides Definition: Guiding structures for Electromagnetics Waves Features: Infinitely long, transverse cross-sections are the same Methodology of Analysis: -Assuming longitudinal variation of the field is known as exponential and solve for the transverse variation of the field for given B.C. -Separate different field components and solve for one of them (longitudinal one) first -Solve for other field components based on transverse-longitudinal relationship
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Waveguide Solutions General waveguide field solutions are propagating in z direction can be written as: [ ] [] z j z z j z e y x h z y x z y x e y x e z y x z y x β + = + = ) , ( ˆ ) , ( ) , , ( ~ ) , ( ˆ ) , ( ) , , ( ~ t t h H e E transverse component longitudinal component longitudinal variation transverse variation TEM waves: 0 = = z z H E TE waves: 0 , 0 = z z H E TM waves: 0 , 0 = z z H E Other hybrid waves
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TEM Waves (1) , μεω β = = k 0 TEM waves is defined for the possibility of solution that satisfies: = = z z H E One can either guess or prove that 0 ) , ( 2 = y x t t e (Laplace’s equations, classical electrostatic problems) 0 ) , ( 2 = y x t t h Conclusion: The field distribution of TEM waves imitate those (1)
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This note was uploaded on 05/10/2010 for the course EE 190776201 taught by Professor Yuanxunethanwang during the Spring '10 term at UCLA.

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161_1_Class8 - EE161 Electromagnetic Waves Spring 2010 Prof...

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