lecture16 - 1 ECE 303 Fall 2005 Farhan Rana Cornell...

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Unformatted text preview: 1 ECE 303 Fall 2005 Farhan Rana Cornell University Lecture 16 Waves in Isotropic Media: Dielectrics and Conductors In this lecture you will learn: Wave propagation in dielectric media Waves propagation in conductive media ECE 303 Fall 2005 Farhan Rana Cornell University Review: Plane Waves in Free Space ( ) ( ) r H j r E o r r r r = ( ) ( ) ( ) r E j r J r H o r r v r r r + = Faradays Law: Amperes Law: Complex Wave Equation: Assume: ( ) ( ) = = r r J r v r ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) r E r E r E r E r E r E r H j r E o o o o o o o r r r r r r r r r r r r r r r r 2 2 2 2 2 . = = = = For a plane wave in free space we know the E-field and H-field phasors to be: ( ) r k j o e E n r E r r r r . = ( ) ( ) r k j o o e E n k r H r r r r . = E H k r = 377 o o o c k o o = = 2 ECE 303 Fall 2005 Farhan Rana Cornell University Waves in a Dielectric Medium Wave Equation Suppose we have a plane wave of the form, ( ) r k j o e E n r E r r r r . = traveling in an infinite dielectric medium with permittivity E H What is different from wave propagation in free space? ( ) ( ) r H j r E o r r r r = ( ) ( ) ( ) r E j r J r H r r v r r r + = Faradays Law: Amperes Law: Complex Wave Equation: Assume: ( ) ( ) = = r r J r v r ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) r E r E r E r E r E r E r H j r E o o o o r r r r r r r r r r r r r r r r 2 2 2 2 2 . = = = = compare with the complex wave equation in free space ( ) ( ) r E r E o o r r r r 2 2 = ECE 303 Fall 2005 Farhan Rana Cornell University Waves in a Dielectric Medium Dispersion Relation ( ) r k j o e E n r E r r r r . = E H Substitute the plane wave solution: in the complex wave equation: ( ) ( ) r E r E o r r r r 2 2 = To get: ( ) ( ) ( ) ( ) o o o k r E r E k k r E r E 2 2 2 2 2 . = = = r r r r r r r r r r compare with for waves in free space o k = Define refractive index n of a dielectric medium as: Refractive Index: o n = o o k = 3 ECE 303 Fall 2005 Farhan Rana Cornell University Waves in a Dielectric Medium Velocity ( ) r k j o e E n r E r r r r ....
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lecture16 - 1 ECE 303 Fall 2005 Farhan Rana Cornell...

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