# 2.5 - Department of Electrical and Computer Engineering...

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Department of Electrical and Computer Engineering ECSE 352 Electromagnetic Waves and Optics 2.5 Waves in good conductors: the skin effect References: Hayt and Buck 12.4 [email protected] 2.5-1 Overview We have already looked at the propagation of waves in low loss and lossy dielectrics, but we have not reallyconsidered conductors in much detail. In this class we will investigate the concep to fth e skin depth ; i.e. the distance which a wave penetrates into a conductive medium. We will see that this results in significant implications for conductor design. ©AGK 2005 ECSE 352 2.5-2 Learning outcomes After taking this class you should be able to: • Define skin depth for a conductor • Explain the impact that it has on the design of onductors conductors • Recognize the implication of the power loss equations ©AGK 2005 ECSE 352 2.5-3 Contents • Power loss estimation • Approximations for low loss dielectrics and good conductors kin depth • Skin depth ©AGK 2005 ECSE 352 2.5-4

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Review: lossy media • In a lossy medium with effective conductivity σ we have a complex propagation constant γ : ' j j = + W ( ) 1 jk γω μ σ ω ε == REVIE 2 '1 ' jj με ωε ⎛⎞ =− ⎜⎟ ⎝⎠ • This is goes into the harmonic wave equation: 2 2 ©AGK 2005 ECSE 352 2.5-5 E γ E = 0 Waves in good conductors In a good conductor: σ/ωε>>1 1 2 ' ωμε ew expression for ttenuation coefficient: New expression for propagation constant γ : •Attenuation coefficient: ©AGK 2005 ECSE 352 2.5-6 Skin depth At and above microwave frequencies, waves do not ©AGK 2005 ECSE 352 2.5-7 really penetrate metals.
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## This note was uploaded on 01/27/2011 for the course ECSE 352 taught by Professor Mi during the Spring '10 term at McGill.

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2.5 - Department of Electrical and Computer Engineering...

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