8.3 Plane waves in lossy media

1
8.3 Plane waves in lossy media
In a source-free lossy medium
(8-42)
where
2
where the complex permittivity
Loss tangent
3

• 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
To solve for a and b

• See problem P.8-9. The equations above are
• general. Well discuss two special cases.

the attenuation constant
Phase const, wave number
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8-3.1 low-loss dielectrics

• 
  
• 
  
• 
  

Np/m (8-48)
(8-50)
rad/m (8-50)
m/s (8-51)
Note at x-ray frequency, copper is no longer a
good conductor!!!
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8-3.2 Good Conductors
0
so,
(8-54)
0
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• 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

• Example 1 Microwave ovens are operating at 2.45
  GHz. The round steak has the permittivity
• ec40(0.1-j0.3)eo(4-j12) eo
• Find the skin depth d.
• Solution
• Is steak a good conductor?

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• The skin depth
• At zd, field decays to e-137 as compared to
  its magnitude on the surface.
• Example 2 Skin depth of copper at 1GHz

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Skin-effect resistance
- the dc resistance
The surface (skin) resistance Rs
Assuming a uniform current
For a conductor wire of radius a, w 2?a
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For an aluminum wire with diameter 2.6 mm find
at 10 MHz, 2 GHz
(a)
(b)