ECE 1100 Introduction to Electrical and Computer Engineering

1
ECE 6340 Intermediate EM Waves
Fall 2008
Prof. David R. Jackson Dept. of ECE
Notes 16
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Polarization of Waves
Consider a plane wave with both x and y
components
Assume
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Polarization of Waves (cont.)
Time Domain
Depending on b and b, three different cases arise.
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Linear Polarization
b 0 or ?
At z 0
(shown for b 0)
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Circular Polarization
b a AND b ?? p/2
At z 0
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Circular Polarization (cont.)
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Circular Polarization (cont.)
y
IEEE convention
b p/2
a
LHCP
f
x
b -p/2
RHCP
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Circular Polarization (cont.)
RHCP
RHCP
(opposite rotation in space and time)
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Unit Rotation Vectors
RHCP
LHCP
Add
Subtract
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General Wave Representation
Note any polarization can be written as
combination of RHCP and LHCP waves.
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Elliptical Polarization
Includes all other cases
(b ??0 or ? and b ??? p/2) or (b ?? p/2 and
b? a)
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Elliptical Polarization (cont.)
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Proof of Ellipse Property
so
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Proof of Ellipse Property (cont.)
General quadratic form
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Proof of Ellipse Property (cont.)
so
Hence, this is an ellipse
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Rotation Property
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Rotation Property (cont.)
Take the derivative
so
(proof complete)
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Phasor Picture
Rule The electric field vector rotates from
the leading axis to the lagging axis
y
x
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Phasor Picture (cont.)
Rule The electric field vector rotates from
the leading axis to the lagging axis
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Example
y
What is this waves polarization?
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Example (cont.)
In time, the wave rotates from the z axis to the
x axis.
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Example (cont.)
LHEP or LHCP
Note and
(so this is not LHCP)
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Example (cont.)
LHEP
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Axial Ratio (AR) and Tilt Angle (?)
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Axial Ratio (AR) and Tilt Angle (?)
Note The tilt angle ? is ambiguous to the
addition of ? 90o.
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Axial Ratio (AR) and Tilt Angle (?)
Tilt Angle