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Prof. Ji Chen

ECE 3317. Prof. Ji Chen. Spring 2014. Notes 16 Plane Waves in Good Conductors. Good Conductor. Requirement:. Example: copper. Hence. so. Use. Skin Depth. Denote. “skin depth”. Then we have. Skin Depth (cont.). Hence. Skin Depth (cont.). Example: copper.

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Prof. Ji Chen

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  1. ECE 3317 Prof. Ji Chen Spring 2014 Notes 16 Plane Waves in Good Conductors

  2. Good Conductor Requirement: Example: copper Hence so Use

  3. Skin Depth Denote “skin depth” Then we have

  4. Skin Depth (cont.) Hence

  5. Skin Depth (cont.) Example: copper

  6. Skin Depth (cont.) The same penetration principle holds for curved conductors, as long as the radius of curvature is large compared with the skin depth. a a r r The distance z is measured from the boundary of the conductor. c c b b Coax a E H Penetration into inner conductor Penetration into outer conductor

  7. Skin Depth (cont.) a r c a b r c b Coax Regions of strong currents The fields are confined inside the coax if

  8. Surface Impedance x z Equivalent surface current x z

  9. Surface Impedance (cont.) Actual current Surface current model Hence

  10. Surface Impedance (cont.) Define the surface impedance: z

  11. Surface Impedance (cont.) Hence We then have

  12. Surface Impedance (cont.) Define “surface resistance” and “surface reactance” We then have

  13. Skin Depth (cont.) Example: copper

  14. Impedance of Wire - + Find the high-frequency resistance and inductance for a solid wire. V Note: The current mainly flows on the outside surface of the wire!

  15. Impedance of Wire (cont.) Surface-current model: Z=R+ jX= impedance Hence Therefore, we have

  16. Impedance of Wire (cont.) R jX Equivalent circuit:

  17. Impedance of Wire (cont.) Example: copper wire  = 5.8 107 S/m l = 5 cm f = 1.0 GHz Assume:

  18. Impedance of Wire (cont.) Compare with the same wire at DC:  = 5.8 107 S/m l = 5 cm 1.0 GHz DC

  19. Coax We use the surface resistance concept to calculate the resistance per unit length of coax. a r For a length l : c b Resistance per unit length:

  20. Coax (cont.) The skin effect will also contribute to an extra inductance per unit length, called the “internal inductance” per unit length. Internal reactance per unit length: a r c b Internal inductance per unit length: The internal inductance is usually neglected in practice (It is usually small compared with the external inductance, calculated assuming perfect conductors).

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