Fields and Waves
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Fields and Waves. Lesson 5.3. PLANE WAVE PROPAGATION Lossy Media. Wave Equations for a Conducting Medium. Homogenous wave equation for . Homogenous wave equation for . ; propagation constant is complex. Propagation Constant. Phase constant. Attenuation constant. [Np/m].

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Fields and Waves

Lesson 5.3


Lossy Media

Lale T. Ergene

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Wave Equations for a Conducting Medium

Homogenous wave equation for

Homogenous wave equation for

; propagation constant is complex

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Propagation Constant

Phase constant

Attenuation constant


(for a lossy medium)


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Solution of the Wave Equation

The Electric Field in phasor form (only x component)

General solution of the differential equation for a lossy medium

backward traveling in -z direction

forward traveling in +z direction

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Intrinsic Impedance, ηc

The relationship between electric and magnetic field phasors is the same but the intrinsic impedance of lossy medium, ηc is different

If +z is the direction of the propagation

intrinsic impedance

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Skin Depth, δs

shows how well an electromagnetic wave can penetrate into a conducting medium

Skin Depth


Perfect dielectric:

σ=0 α=0 δs=∞

Perfect Conductor:

σ=∞ α=∞ δs=0

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Low-Loss Dielectric

defined when ε’’/ε’<<1

practically if ε’’/ε’<10-2, the medium can be considered as a low-loss dielectric




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Good Conductor

defined when ε’’/ε’>>1

practically if ε’’/ε’>100 , the medium can be considered as a good conductor




  • When 10-2≤ ε’’/ε’ ≤100, the medium is considered as a “Quasi-Conductor”.

  • Do Problem 1

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Average Power Density

Average power density


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Average Power Density

If ηc is written in polar form

Average power density



Do Problem 2