A Method to Display Complicated Polarization of An Arbitrary Antenna

Abstract

Antenna polarization is a very important consideration when choosing and designing an antenna. The far field energy radiated by any antenna is contained in a transverse electromagnetic wave that is comprised of an electric and a magnetic field. These fields, like a plane wave, are always orthogonal to one another and orthogonal to the direction of propagation. In a specified direction from an antenna and at a point in its far field, the polarization of the local plane wave defines the polarization of an antenna in a specified direction [1]. The polarization of a plane wave is defined according to the locus of the tip of its electric field vector, [2] with the ratio of the magnitude of the major and minor axes of the ellipse determining the type of polarization. In general, all electromagnetic waves are elliptically polarized. Axial ratio, tilt angle and the sense of polarization are frequently used terms to describe the state of polarization. The Axial Ratio (AR) is the ratio of the major axis to the minor axis of the polarization ellipse. Two special cases of elliptical polarization are linear and circular polarization. When the minor axis tends towards zero, the ellipse changes into a line segment that is orientated along the major axis. This is effectively called linear polarization and the axial ratio is ∞. If the major axis and minor axis are identical, the polarization ellipse becomes a circle and its axial ratio would be±1. The sign indicates the sense of the rotation, Left Hand Circular Polarization or Right Hand Circular Polarization. The tilt angle is the angle measured clockwise from the reference line to the major axis [1]. Generally, the type and the orientation of polarization varies with different values of θ and φ. (angles that define the observation position) Therefore, in order to completely describe the polarization of an antenna, four parameters (θ, φ, axial ratio and tilt angle) are needed. There are various methods to display the polarization of an antenna. The Poincaré sphere is a frequently used tool to represent polarization. However, the directional information cannot be displayed on this sphere. Wolfgang-Martin Boerner et al. projected the surface of the Poincaré sphere onto a complex plane, so the entire sphere could be displayed and mapped onto the same plane [3]. Harry Mieras used equal area projection of the Poincaré sphere to display polarization [4]. Georges A. Deschamps and P. Edward Mast improved the Poincaré sphere representation by introducing points inside the sphere to represent partially polarized states [5]. George H. Knittle introduced polarization charts, which are stereographic projections of a Poincaré sphere [6], to investigate polarization. Thus, although the Poincaré sphere and its projection can describe the polarization at a certain set of observation parameters precisely, it is unable to display global polarization information of antenna in all directions. Furthermore, some projections are not very easily understood. Comparing the traces of Eθ and Eφ (the orthogonal components of the electric far field) can also provide information about polarization. None of the previous methods has been able to display all four parameters at same time. It is inconvenient to judge the complicated polarization of an arbitrary antenna, because the axial ratio and the tilt angle will vary with observation angle. Most manufacturers specify the axial ratio at the antenna boresight or as a maximum value over a range of angles, generally chosen to represent the main beam of the antenna. From different observation angles, we can obtain different ARs, hence, different polarizations. The method described in this paper can visually display the polarization characteristics of an antenna at different observation angles, which is necessary to understand the overall polarization characteristics of the antenna.