Antenna Polarization Coupling

ANTENNA POLARIZATION COUPLING

Introduction

The polarization of an arbitrary signal can be sensed by two orthogonally polarized, co-located antennas, from measurements of the relative signal strengths and the phase difference between the two antenna outputs. For example, if ev is the signal measured at the terminals of a vertically polarized antenna, eh is the signal received from a horizontally polarized antenna, and φ is the RF phase difference between these h and v components, Table 1 summarizes the expected normalized values for the various prime polarizations. The ratio ev /eh is termed the linear polarization ratio, and the corresponding linear polarization or position angle is α = tan-1(ev /eh).

Table 1 Prime Polarization States

Polarization / ev / eh / φ
Vertical / 1 / 0 / –
Horizontal / 0 / 1 / –
+45 / 1 / 1 / 0
–45 / 1 / 1 / 180
Right-hand circular / 1 / 1 / 90
Left-hand circular / 1 / 1 / -90

1. Polarization Ellipse

A useful graphical representation is the polarization ellipse. This is generated from the path the signal vector tip traces in time, and is demonstrated when ev cos(ωt) is plotted against eh cos(ωt+φ). This ellipse, shown in Figure 1, is characterized by an orientation or tilt angle, τ of the ellipse major axis, and an ellipticity angle ε, being half the angle subtended by the ellipse minor axis from a point at the end of the major axis. The axial ratio, ar, is defined as the ratio of the polarization ellipse major axis to the minor axis and ar = 1/tan(ε). For elliptical polarizations, ar is usually stated in decibels, as |20 log(ar)|. Measurement involves rotating a high fidelity linearly polarized transmitting antenna about its central axis and observing the maximum and minimum powers received by the test antenna. Axial ratio generally varies as a function of test antenna azimuth and this measurement is usually carried out during normal azimuth pattern evaluation. Polarization purity of most antennas is rarely maintained off axis, particularly outside the 3-dB beamwidth.

Figure 1 Polarization ellipse.

2. Poincaré Sphere

Polarization states are often represented graphically as a point on the surface of a sphere, termed the Poincaré sphere (depicted in Figure 2). The six prime polarizations are placed at orthogonal poles of the sphere. The Cartesian coordinates of a point on the sphere’s surface (g1,g2,g3 or Q,U,V) are called Stoke’s parameters and can be represented in terms of either the measured values or the polarization ellipse geometrical parameters (see Table 2). On the sphere surface, polarizations at each end of a diameter are orthogonal and termed cross-polarized.

Figure 2 Poincaré sphere and Stokes parameters

Table 2 Stoke’s Parameters

Stoke’s parameter / Defining data / Polarization ellipse parameters / Comments
g1 or Q / cos2α / cos2τ cos2ε / Tendency to horizontal or vertical
g2 or U / sin2α cosφ / cos2τ sin2ε / Tendency to ±45° linear
g3 or V / sin2α sinφ / sin2τ / Tendency to circular
g0 or I / √(g12+g22+g32)=1 / √(g12+g22+g32)=1 / Poincaré sphere radius, normalized power

Note 1: α = tan-1(ev/eh).

Note 2: Q,U,V and I are terms usual in Radio Astronomy

3. Coupled Power

A signal from a transmitter of polarisation state, (εt,τt) and unit power, induces a complex voltage Vr at the output of a receiving antenna of polarisation, (εr,τr), where,

From this, the equation for calculating the polarization dependent power coupling or polarization loss between transmitting t and receiving r antennas with differing polarizations is

(1)

If the polarisations are matched there is no coupling phase error. In the unmatched case, the phase error is given by,

For all linearly polarised signals and antennas, ε is zero and there is no phase error.

An interesting case occurs for a circularly polarised antenna (τ = 45°) intercepting an elliptically polarised signal, here the phase error is simplified to,

where, using the identities from Table 2,

4. Circular Polarised antenna

A circularly polarised receiving antenna can be synthesised using two identical and co-aligned antennas plus a 90° 3dB coupler as shown in Figure 3. The arrangement is reciprocal in that inputting a signal in the relevant coupler port, transmits RHC or LHC accordingly.

Figure 3 Synthesising a circularly polarised receiving antenna

5. Antenna Cross-Polarisation Performance

Due to mechanical tolerances, electrical match imperfections and geometry, most practical antennas respond to orthogonal polarisations to some degree. In most applications it important to reduce the cross-polarisation response as much as possible. The performance of a typical parabolic reflector antenna using a linear horn feed is shown in Figure 4.

Figure 4 Co- and Cross-polarisation response of a parabolic reflector antenna

The best performance usually occurs on boresight; the ratio degrades off-boresight, and by the first sidelobes, it is not unusual for the levels to be similar. Outside the first sidelobes, co- and cross polarisation sidelobes alternate; either can exceed the other. The effect on the polarisation ellipse representation within the beam is for the major axis to dominate within the beam, but become more elliptical in the sidelobes.

6. Antenna Polarization Applet - POLARISATION.zip

Figure 5 Antenna polarization coupling applet.

The applet in Figure 5 demonstrates antenna polarization concepts and shows how the power coupling between antennas of different polarizations is affected by their polarization parameters. The displays on the left depict the polarization ellipses for both a receiving antenna and a transmitting antenna.

The scrollbars allow the linear polarization angle (α) and the relative phase (φ) between the E-vertical (ev) and E-horizontal (eh) components to be varied to modify the transmitter and receiver antenna polarizations. The corresponding polarization state (Stoke’s parameters) is displayed above the Poincaré sphere on the right. The power coupling loss value, due to any mismatched transmit/receive polarizations, is also displayed. In the default condition, the receive antenna is right-hand circularly polarized and the transmitter is linear-horizontal producing a 3-dB polarization loss. The values listed by Degree of Linear/Circular/45 polarization data are simply measures of the Stoke’s parameters, the largest magnitude value implies the dominant cardinal polarization.

PW East May 2005