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Prof. D. R. Wilton

ECE 3317. Prof. D. R. Wilton. Notes 16 Plane Waves in Good Conductors. Good Conductor. Use. Hence. Skin Depth. “skin depth” or “penetration depth”. Denote. Then we have. Skin Depth (cont.). Hence. Skin Depth (cont.). Example: copper. Skin Depth (cont.).

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Prof. D. R. Wilton

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  1. ECE 3317 Prof. D. R. Wilton Notes 16 Plane Waves in Good Conductors

  2. Good Conductor Use Hence

  3. Skin Depth “skin depth” or “penetration depth” Denote 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 r c (PEC) b E         a H PEC coax Penetration into conductor Regions of strong currents

  7. Surface Impedance x z Equivalent surface current x z

  8. Surface Impedance (cont.) actual current through cross section surface current model Hence

  9. Surface Impedance (cont.) Define the surface impedance:

  10. Surface Impedance (cont.) Hence (“good conductor” approximation) We then have

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

  12. Skin Depth (cont.) Example: copper

  13. 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!

  14. Impedance of Wire (cont.) Surface-current model: Z = R + j X = impedance Hence where

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

  16. Impedance of Wire (cont.) Example a= 0.01 mm l= 5 cm f= 1.0 GHz Assume:

  17. Impedance of Wire (cont.) Compare with the same wire at DC:

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

  19. Two-conductor lines w a b The surface resistance concept may be used to calculate the resistance per unit length of two conductor lines. Arbitrary cross section lines Microstrip line or integrated circuit traces Two-wire line • Skin depth assumed small with respect to conductor thickness and curvature • Conductor currents are (approx.) uniformly distributed

  20. Material Propagation Parameter Summary

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