Dr. S. Cruz-Pol, INEL 4152Electromagnetics
Polarization
Polarization:
• In general, plane wave has 2 components; in x & y
Why do we care??
• Antenna applications –
– Antenna can only TX or RX a polarization it is designed to support. Straight
wires, square waveguides, and similar rectangular systems support linear
waves (polarized in one direction, often) Round waveguides, helical or flat
spiral antennas produce circular or elliptical waves.
• Remote Sensing and Radar Applications –
– Many targets will reflect or absorb EM waves differently for different
polarizations. Using multiple polarizations can give different information
and improve results.
• Absorption applications –
– Human body, for instance, will absorb waves with E oriented from head to
toe better than side-to-side, esp. in grounded cases. Also, the frequency at
which maximum absorption occurs is different for these two polarizations.
This has ramifications in safety guidelines and studies.
E ( z ) = xˆE x + yˆE y
• And y-component might be out of phase wrt to x-component, δ is
the phase difference between x and y.
E x = Eo e − jβ z
Ex
x
y
Ey
y
Cruz-Pol,ECE Dept. UPRM
Front View
Cruz-Pol,ECE Dept. UPRM
Several Cases
• Linear polarization: δ=δy-δx =0o or ±180on
• Circular polarization: δy-δx =±90o & Eox=Eoy
• Elliptical polarization: δy-δx=±90o & Eox≠Eoy, or
δ=≠0o or ≠180on even if Eox=Eoy
• Unpolarized- natural radiation
x
E y = Eo e − jβ z +δ
Linear polarization
Front View
• δ =0
x
E x = Eo e − jβ z
E y = Eo e
Ex
− jβ z
y
Ey
• @z=0 in time domain
E x = E xo cos(ωt)
E y = E yo cos(ωt)
Back View:
x
y
Cruz-Pol,ECE Dept. UPRM
Cruz-Pol,ECE Dept. UPRM
Circular polarization
Elliptical polarization
• Both components have
same amplitude Eox=Eoy,
• δ =δ y-δ x= -90o = Right
circular polarized (RCP)
• δ =+90o = LCP
E x = E xo cos(ωt)
E y = E yo cos(ωt − 90 o )
in phasor :
E = xˆE xo + yˆ E yo e − j 90 = xˆE xo − jE yo yˆ
• X and Y components have different amplitudes
Eox≠Eoy, and δ =±90o
• Or δ ≠±90o and Eox=Eoy,
Cruz-Pol,ECE Dept. UPRM
Electrical Engineering, UPRM
Cruz-Pol,ECE Dept. UPRM
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Dr. S. Cruz-Pol, INEL 4152Electromagnetics
Parámetros de la elipse
AR = axial ratio = oa / ob
tan 2τ = tan 2γ cosδ
sin 2ε = sin 2γ sin δ
Polarization Loss Factor PLF
y
Eyo
r
E
ρˆ =
E
a
b
cot ε = AR
o
Eyo
E 
γ = tan −1  yo 
 E xo 
Cruz-Pol,ECE Dept. UPRM
x
PLF = ρˆ i • ρˆ a*
2
PLF = ρˆ t • ρˆ r*
2
Cruz-Pol,ECE Dept. UPRM
Poincaré Sphere
• Plots any possible state of polarization
Cruz-Pol,ECE Dept. UPRM
Electrical Engineering, UPRM
Cruz-Pol,ECE Dept. UPRM
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