ECE-305-Lecture20

# ECE-305-Lecture20 - Engineering Electro-Magnetics...

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Engineering Electro-Magnetics Engineering Electro-Magnetics ECE-305, Lecture 20 Dennis McCaughey, Ph.D. 6 April, 2010

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04/06/2010 Dennis McCaughey, ECE305, Spring 2010 2 Homework Homework Due Tues 4/13 Problems 12.8, 12.11, 12.15
04/06/2010 Dennis McCaughey, ECE305, Spring 2010 3 Propagation in Conductors Propagation in Conductors ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ' '' '' ' ' ' '' '' ' ' ' ' ' ' 1 2 and interpret as 3 4 5 tan s s s s s s s s s s s s s ds s ds j j j j j J J j σ σ σ ϖ ε ε ϖε ϖε ϖε ε σ θ ε σ ε ε σ ϖε σ ε ϖ σ ε ϖε ε ϖε = = ∇× = - = + ∇× = + = ∇× = + ∇× = = = = = + = J E H E E E H J E J E H E H J J With finite conductivity the wave loses power through resistive heating of the material We look for an interpretation of the complex permittivity as it relates to conductivity (3) The sum of a conduction and a displacement current (5) Hence the term “loss tangent

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04/06/2010 Dennis McCaughey, ECE305, Spring 2010 4 Small Loss Tangents Small Loss Tangents ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 '' ' '' ' ' ' 2 ' ' 2 ' ' ' 2 ' ' ' ' 1 1 2 1 3 2 1 4 1 8 3 5 1 8 2 1 if 1 Then 8 6 and 7 1 2 jk j j j j ε ε σ ε ϖ σ ϖ με ϖε σ μ α ε σ β ϖ με ϖε μ σ σ η ε ϖε ϖε σ ϖε μ σ β ϖ με η ε ϖε << = = - + - + << + B B B B B 1) Criterion for a small loss tangent which also implies a “good dielectric” 3) and 4) are derived through the use of a Taylor’s series expansion
04/06/2010 Dennis McCaughey, ECE305, Spring 2010 5 Propagation in Good Conductors Propagation in Good Conductors ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 '' ' ' ' ' ' ' 0 0 0 1 1 2 1 3 1 4 5 1 90 1 90 1 45 1 1 2 1 1 2 6 jk j j jk j j jk j j j and j jk j j j f f ε ε σ ϖε ϖ με σ ϖε ϖ με σ ϖε ϖμεσ ϖσμ π μσ α β π μσ = - = - = - - = ∠ - ∠ - = ∠ - = - = - = + = = Interested in losses in a good conductor A good conductor has high conductivity and large conduction currents A good conductor satisfies the high loss criteria (1) High loss tangent (2) High loss tangent applied to a good conductor.

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• Fall '08
• Staff
• Electromagnet, Magnetic Field, Circular polarization, Dennis McCaughey

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