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# 329lect22 - 22 Imperfect dielectrics good conductors...

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22 Imperfect dielectrics, good conductors Condition β α | η | τ λ = 2 π β δ = 1 α Perfect dielectric σ = 0 ω μ 0 μ 0 2 π ω μ Imperfect dielectric σ ω 1 ω μ β 1 2 σ ω = σ 2 μ μ σ 2 ω 2 π ω μ 2 σ μ Good conductor σ ω 1 π σ π σ ω μ σ 45 2 π π σ 1 π σ Perfect conductor σ = 0 - 0 0 The table above summarizes TEM wave parameters in homogeneous conducting media where the propagation velocity x -polarized phasor ˜ E = ˆ xE o e α z e j β z accompanied by ˜ H = ± ˆ y E o η e α z e j β z . v p = ω β (note that it can be frequency dependent) and field phasors can be expressed in formats similar to that shown in the margin, keeping in mind that propagation direction coincides with vector ˜ S ˜ E × ˜ H * such that S = E × H = 1 2 Re { ˜ S } is the average energy flux per unit area (time-average Poynting vector). 1

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Example 1: Consider the plane TEM wave ˜ E = ˆ y 2 e - α z e - j β z V m , in an imperfect dielectric . Determine ˜ H and time-average Poynting vector S . Compute S at z = 0 and z = 10 m, if = 4 o , μ = μ o , σ = 10 - 3 S/m, and ω = 2 π · 10
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329lect22 - 22 Imperfect dielectrics good conductors...

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