1. EEE340Lecture 331 8.3 Plane waves in lossy media In a source-free lossy medium where (8-42)

2. EEE340Lecture 332 where the complex permittivity Loss tangent

3. EEE340Lecture 333 The complex propagation constant Since a complex can be split into real and imaginary, where  is the attenuation constant, and  is the phase constant. (8-43) (8-44)

4. EEE340Lecture 334 See problem P.8-9. The equations above are general. We’ll discuss two special cases. the attenuation constant Phase const, wave number To solve for  and  :

5. EEE340Lecture 335 Np/m (8-48) (8-50) rad/m (8-50) m/s (8-51) 8-3.1 low-loss dielectrics Note at x-ray frequency, copper is no longer a good conductor!!!

6. EEE340Lecture 336 0 so, 0 (8-54) 8-3.2 Good Conductors

7. EEE340Lecture 337 The time domain fields are: Physically, the H field is perpendicular to the E field, and H is 45 degree lacking. By setting the decay to 36.79%, we define the skin depth. Skin depth (8-57)

8. EEE340Lecture 338 Example 1: Microwave ovens are operating at 2.45 GHz. The round steak has the permittivity  c =40(0.1-j0.3)  o =(4-j12)  o Find the skin depth  Solution: Is steak a good conductor?

9. EEE340Lecture 339 The skin depth At z= , field decays to e -1 =37% as compared to its magnitude on the surface. Example 2 Skin depth of copper at 1GHz

10. EEE340Lecture 3310 - the dc resistance The surface (skin) resistance R s Assuming a uniform current For a conductor wire of radius a, w = 2  a Skin-effect resistance

11. EEE340Lecture 3311 For an aluminum wire with diameter 2.6 mm find at 10 MHz, 2 GHz (a) (b)