Electric and Magnetic Fields
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ECE390L16201024.pdf
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COLLEGE OF ENGINEERING School of Electrical Engineering and Computer Science
ECE 390 – Electric & Magnetic Fields L16 – Plane-Wave Propagation (7.1, 7.2)
Fall 2020 T. Weller
School of EECS – ECE 390
Today’s Plan • Time-harmonic fields • Plane-wave propagation in lossless media
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4 Guided EM Waves Unbounded EM Waves
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School of EECS – ECE 390
Maxwell’s Equations
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For sinusoidal time variations: For any vector field:
Hence: and
Consequently, Maxwell’s equations become:
We will use these to derive the wave equation for EM waves.
School of EECS – ECE 390
Complex Permittivity
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School of EECS – ECE 390
Wave Equations
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School of EECS – ECE 390
Wave Equations
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School of EECS – ECE 390
Lossless Media
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If the medium is nonconducting (σ = 0), the wave does not suffer any attenuation as it travels and hence the medium is said to be lossless.
School of EECS – ECE 390
Uniform Plane Wave
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School of EECS – ECE 390
Uniform Plane Wave
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School of EECS – ECE 390
Uniform Plane Wave
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General Form of the Solution:
For a wave travelling along +z only:
Application of yields:
Summary: This is a plane wave with
with
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School of EECS – ECE 390
Uniform Plane Wave
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Summary from previous slide:
Time-Domain Solution
School of EECS – ECE 390
Wave Phase Velocity
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School of EECS – ECE 390
Directional Relation Between E and H
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For Any TEM Wave
School of EECS – ECE 390
Wave Decomposition
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School of EECS – ECE 390
Power Density
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Poynting vector:
Total power intercepted by A:
Time-average power density:
