161_1_Class4

161_1_Class4 - EE161 Electromagnetic Waves Spring, 2010...

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Unformatted text preview: EE161 Electromagnetic Waves Spring, 2010 Prof. Y. Ethan Wang Electrical Engineering Dept. UCLA Lesson 4 Waves in Lossy Medium Electromagnetic Power Density Transmission Line Theory Review Wave Propagation in Lossy Media ~ ~ ~ ) ( ~ ~ 2 2 2 2 = = z y x E E E E E ) ( 2 j j + = where j + = The solution is, Considering the wave propagating in z axis with the electric field component in x only, The wave equation for lossy media is, z x z x x e E e E z E or ) ( ~ = : attenuation constant : phase constant z j z x x e e E z E = ) ( ~ Thus ) ( ~ z x x e E z E = 1 = s : Skin depth Amplitudes relate only to the attenuation constant Wave Parameters in Lossy Media 2 2 2 2 ) ( ) ' ' ' ( ) ( j j j + = = + = E H ~ ) ( ~ j + = E H ~ ~ c j = ' ' ' j j c = = Define complex permittivity: For lossy media, Amperes law gives: E H ~ ) ( ~ + = j j c Therefore, the Maxwell equations will have the same form of solution for the lossy and lossless case, assuming the permittivity is a complex number in general The propagation constant: Comparing the real part and imaginary part of the above two yields, 2 / 1 2 1 ' ' ' 1 2 ' + = 2 / 1 2 1 ' ' ' 1 2 ' + + = , f = = 2 2 ' ' Lossy Media Classification Low loss dielectric Good conductor Quasi-conductor ) 10 ( 1 2 ' ' ' < << ) 10 ( 1 2 ' ' ' > >> 2 2 10 10 < < ' '' For low loss dielectric For good conductor 2 2 ' ' = = ' c ) 1 ( ) 1 ( ' ' j f j j c + = + = f = For a lossy medium, the ratio plays an important role in determining...
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161_1_Class4 - EE161 Electromagnetic Waves Spring, 2010...

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