NNSE508_EM-L5_Electrodynamics-2

NNSE508_EM-L5_Electrodynamics-2 - 1 Lecture contents...

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NNSE 508 EM Lecture #5 1 Lecture contents Macroscopic Electrodynamics -2 Skin effect Boundary conditions, wave propagation through interface Wave packet, group velocity, dispersion Circuits
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NNSE 508 EM Lecture #5 2 Medium with losses After some long algebra: The impedance becomes complex: For good dielectrics: 12 2 1 1 1 0 2              2 1 1 1 0 2 22 Ei i H         2 1 1 For good conductors: 2 1 1 2   2 1 1 8  2 31 1 82 i                2   i  1 p v  2 p v 
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NNSE 508 EM Lecture #5 3 Skin depth In a good conductor (metal) the attenuation of the wave is determined by attenuation constant a : The skin depth of material is the depth to which a uniform plane wave can penetrate before it is attenuated by a factor of 1/e . For planar surfaces, skin depth is given as: Penetration depends on frequency ( f -1/2 ), conductivity and permeability. The skin effect is the result of induction: time-varying magnetic field is accompanied by a time varying electric field time varying current secondary fields Skin-effect implies dissipation of the wave power by the current 2   12 skin 
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NNSE 508 EM Lecture #5 4 Skin effect Another result of skin effect is non- uniform distribution of current in conductors at high frequencies Current density drops into the metal at high frequencies due to screening of the EM field by the induced current Usually in engineering disciplines it is modeled as if all current flowed in -thick outer layer of conductor As a result, resistance of a thick conductor increase with frequency. If a wire radius a >> , Skin layer thickness in Cu: 12 skin   , 0, , z>0 zz i xx J z J e e    From Neff, 1991 2 l R a  
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NNSE 508 EM Lecture #5 5 Example of Boundary Condition: Normal Component of D Consider electric field normal to the boundary Consider a cylinder with cross-sectional area D s and height D h lying half in medium 1 and half in medium 2: Applying Gauss’s law to the cylinder 1 2 D s h/2 h/2 x x x x x x s ˆ n a 11 ED 22 f SV D ds q dv
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NNSE508_EM-L5_Electrodynamics-2 - 1 Lecture contents...

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