Fundamental Parameters of Antennas
2.12 POLARIZATION
2.12.2 Polarization Loss Factor and Efficiency
two, while the minor axis of the ellipse will align with the axis of the field component which is smaller of the two.
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propagation, whose state of polarization has been adjusted for a maximum received power.” This is similar to the PLF and it is expressed as
pe= |e·Einc|2
|e|2|Einc|2 (2-71a) where
e =vector effective length of the antenna Einc =incident electric field
The vector effective length Ge of the antenna has not yet been defined, and it is introduced inSection2.15. It is a vector that describes the polarizationcharacteristics of the antenna. Both the PLF andpe lead to the same answers.
The conjugate (∗) is not used in (2-71) or (2-71a) so that a right-hand circularly polarized incident wave (when viewed in its direction of propagation) is matched to right-hand circularly polarized receiving antenna (when its polarization is determined in the transmitting mode). Similarly, a left-hand circularly polarized wave will be matched to a left-hand circularly polarized antenna.
To illustrate the principle of polarization mismatch, two examples are considered.
Example 2.11
The electric field of a linearly polarized electromagnetic wave given by Ei=ˆaxE0(x, y)e−j kz
is incident upon a linearly polarized antenna whose electric-field polarization is expressed as Ea (ˆax+ˆay)E(r, θ, φ)
Find the polarization loss factor (PLF).
Solution: For the incident wave
ρˆw=ˆax and for the antenna
ρˆa= 1
√2(ˆax+ˆay)
The PLF is thenequal to
PLF= |ρˆw·ρˆa|2= |ˆax· 1
√2(ˆax+ˆay)|2= 12 which indB is equal to
PLF (dB)=10 log10PLF (dimensionless)=10 log10(0.5)= −3
ψ
ψ
p ψp
PLF = (aligned)
w• a2 = 1 PLF =
(orthogonal) w• a2 = 0 PLF =
(rotated)
(a) PLF for transmitting and receiving aperture antennas
w• a2 = cos2 p
ψ PLF =
(aligned)
w• a2 = 1 PLF =
(orthogonal) w• a2 = 0 PLF =
(rotated)
(b) PLF for transmitting and receiving linear wire antennas
w• a2 = cos2 p ψp
ψp
^ ^ ^ ^ ^ ^
^ ^ ^ ^
^ ^
Figure 2.25 Polarization loss factors (PLF) for aperture and linear wire antennas.
Even though in Example 2.11 both the incoming wave and the antenna are linearly polarized, there is a 3-dB loss inextracted power because the polarizationof the incoming wave is not aligned with the polarization of the antenna. If the polarization of the incoming wave is orthogonal to the polarization of the antenna, then there will be no power extracted by the antenna from the incoming wave and the PLF will be zero or−∞dB. InFigures 2.25(a,b) we illustrate the polarizationloss factors (PLF) of two types of antennas: wires and apertures.
We now want to consider an example where the polarization of the antenna and the incoming wave are described in terms of complex polarization vectors.
Example 2.12
A right-hand (clockwise) circularly polarized wave radiated by an antenna, placed at some distance away from the origin of a spherical coordinate system, is traveling in the inward radial directionat anangle(θ, φ)and it is impinging upon a right-hand circularly polarized receiving antenna placed at the origin (see Figures 2.1 and 17.23 for the geometry of the coordinate system). The polarization of the receiving antenna is defined in the transmitting
POLARIZATION 79
mode, as desired by the definition of the IEEE. Assuming the polarization of the incident wave is represented by
Ew=(ˆaθ +jˆaφ)E(r, θ, φ) Determine the polarization loss factor (PLF).
Solution: The polarization of the incident right-hand circularly polarized wave traveling along the−r radial directionis described by the unit vector
ρˆw=
ˆaθ+jˆaφ
√2
while that of the receiving antenna, in the transmitting mode, is represented by the unit vector ρˆa=
ˆaθ −jˆaφ
√2
Therefore the polarizationloss factor is PLF= |ρˆw·ρˆa|2=1
4|1+1|2=1=0 dB
Since the polarization of the incoming wave matches (including the sense of rotation) the polarization of the receiving antenna, there should not be any losses. Obviously the answer matches the expectation.
Based upon the definitions of the wave transmitted and received by an antenna, the polarization of an antenna in the receiving mode is related to that inthetransmitting mode as follows:
1. “In the same plane of polarization, the polarization ellipses have the same axial ratio, the same sense of polarization (rotation) and the same spatial orientation.
2. “Since their senses of polarization and spatial orientation are specified by viewing their polarizationellipses inthe respective directions inwhich they are propa- gating, one should note that:
a. Although their senses of polarization are the same, they would appear to be opposite if both waves were viewed inthe same direction.
b. Their tilt angles are such that they are the negative of one another with respect to a commonreference.”
Since the polarization of an antenna will almost always be defined in its transmitting mode, according to the IEEE Std 145-1983, “the receiving polarization may be used to specify the polarization characteristic of a nonreciprocal antenna which may transmit and receive arbitrarily different polarizations.”
The polarization loss must always be taken into account in the link calculations designof a communicationsystem because insome cases it may be a very critical factor. Link calculations of communication systems for outer space explorations are very stringent because of limitations in spacecraft weight. In such cases, power is a
Figure 2.26 Geometry of elliptically polarized cross-dipole antenna.
limiting consideration. The design must properly take into account all loss factors to ensure a successful operation of the system.
An antenna that is elliptically polarized is that composed of two crossed dipoles, as showninFigure 2.26. The two crossed dipoles provide the two orthogonal field components that are not necessarily of the same field intensity toward all observation angles. If the two dipoles are identical, the field intensity of each along zenith (per- pendicular to the plane of the two dipoles) would be of the same intensity. Also, if the two dipoles were fed with a 90◦ degree time-phase difference (phase quadrature), the polarization along zenith would be circular and elliptical toward other directions.
One way to obtain the 90◦ time-phase difference3φbetweenthe two orthogonal field components, radiated respectively by the two dipoles, is by feeding one of the two dipoles with a transmission line which isλ/4 longer or shorter than that of the other [3φ=k3G=(2π/λ)(λ/4)=π/2]. One of the lengths (longer or shorter) will provide right-hand (CW) rotation while the other will provide left-hand (CCW) rotation.