Electric and Magnetic Fields
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ECE390L17201024.pdf
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COLLEGE OF ENGINEERING School of Electrical Engineering and Computer Science
ECE 390 – Electric & Magnetic Fields L17 – Wave Reflection and Transmission (8.1-8.2)
Fall 2020 T. Weller
School of EECS – ECE 390
Today’s Topics
• Wave reflection and transmission at normal incidence
• Snell’s law
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Signal Refraction at Boundaries
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Radiation by antenna (Chapter 9)
Wave propagation in lossless medium (Chapter 7)
Wave propagation in lossy medium (Chapter 7)
Antenna reception (Chapter 9)
Wave refraction across a boundary (this chapter)
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Normal and Oblique Incidence
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Normal Incidence
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We can use all the transmission‐line concepts and techniques of Chapter 2 to analyze plane wave reflection and transmission at interfaces between dissimilar media
School of EECS – ECE 390
Modeling Normal Incidence
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Individual Waves
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Note ‒ sign
Note + sign
Note ‒ sign
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Boundary Conditions
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Total fields
At the boundary z = 0:
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Boundary Conditions
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Solution gives:
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Reflection and Transmission Coefficients
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Similar form as for transmission lines
Lossless and non‐magnetic material
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With Lossy Material • If Medium 2 is lossy (i.e. > 0) then it will have a
complex wave impedance • Consequently, the reflection coefficient will be a
complex number • If is
– Negative, then the reflected wave is 180 degrees out of phase with the incident wave
– Positive, then the reflected wave is in phase with the incident wave
– Complex, then the reflected wave is out of phase with the incident wave somewhere between 0 and +/- 180 degrees
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Power Transfer
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Medium 1
Medium 2
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Example 8‐3 (cont.)
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Example 8-3 (cont.)
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Snell’s Laws
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Angles of Incidence, Reflection & Refraction
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Nonmagnetic Media
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Index of refraction n:
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Refraction
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When the refraction angle is 90 degrees, the corresponding incidence angle is called the critical angle.
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