lecture16

# lecture16 - 1 ECE 303 – Fall 2005 – Farhan Rana –...

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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 µ ω − = × ∇ ( ) ( ) ( ) r E j r J r H o r r v r r r ε ω + = × ∇ Faraday’s Law: Ampere’s Law: Complex Wave Equation: Assume: ( ) ( ) = = r r J r v r ρ ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 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 ε µ ω ε µ ω ε µ ω µ ω 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 . ˆ − = ( ) ( ) r k j o o e E n k r H r r r r . ˆ ˆ − × = η E H k r Ω ≈ = 377 o o o ε µ η c k o o ω ε µ ω = = 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 . ˆ − = traveling in an infinite dielectric medium with permittivity ε E H ε What is different from wave propagation in free space? ( ) ( ) r H j r E o r r r r µ ω − = × ∇ ( ) ( ) ( ) r E j r J r H r r v r r r ε ω + = × ∇ Faraday’s Law: Ampere’s Law: Complex Wave Equation: Assume: ( ) ( ) = = r r J r v r ρ ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 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 ε µ ω ε µ ω ε µ ω µ ω 2 2 2 2 2 . − = ∇ ⇒ = ∇ − ∇ ∇ ⇒ = × ∇ − = × ∇ × ∇ compare with the complex wave equation in free space ( ) ( ) r E r E o o r r r r ε µ ω 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 . ˆ − = E H ε Substitute the plane wave solution: in the complex wave equation: ( ) ( ) r E r E o r r r r ε µ ω 2 2 − = ∇ To get: ( ) ( ) ( ) ( ) ε µ ω ε µ ω ε µ ω 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 ε µ ω o k = ⇒ Define refractive index “ n ” of a dielectric medium as: Refractive Index: o n ε ε = o o k ε µ ω = 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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## This note was uploaded on 02/02/2008 for the course ECE 3030 taught by Professor Rana during the Fall '06 term at Cornell.

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

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