10 IEEETRANSACTIONSONANTENNASANDPROPAGATION, zyxw VOL. zyxw Ap-33, NO. zy 1, JANUARY 1985 z ' Polarization Properties of the Axial Mode Helix Antenna RODNEY G. VAUGFMN, MEMBER, IEEE, zyxwvut AND J. BACH ANDERSEN, SENIOR MEMBER, IEEE Abstract-The helix is considered as a surface wave antenna. A network model of the infinite structure provides a simple vehicle to view the fields behavior. The far-field polarization properties are examined in detail, and it is shown how they depend on the surface wave structure and the open and feed end configurations. By suitably arranging the antenna ends, perfect endfire polarization purity can he produced independent of antenna length (i.e., number of turns). Inclnsion of a dielectric core decreases the cross polarizedradiationin off-axis directions.Theoreticalandexperimental patterns illustrate these results. I. INTRODUCTION P OLARIZATION purity is an important aspect of modem feed elementsforfrequency reuse systems. Here,the axial mode helix with dielectric core is investigated with a view to using it as a reflector antenna feed. The helix antenna is a sound choice, since its surface wave antenna character and inherent circular polarization make it a flexible element without the need for a polarizer. However, little is known about the polarization properties in off-axis directions, which is the subject of this paper. Thesurface wave theory accounts for the helix asasurface wave device, where the cylindrical modes are considered on the infinite structure. The contributions from these individual modes to the total polarization can be used to explain experimental pat- tern characteristics. The theoretical and numerical difficulties in analyzing the feed and open end forbid an exact theory for the finite antenna and its general polarization properties.However, the effects of the(antenna)ends are discussed in some detail, since it is these effects which limit the accuracy of the radiation pattern calculation and contribute unwanted polarization zyxwvut [ 11 . Section I1 gives a brief account of previous approaches to the helix. These fall into two areas: surface wave propagation along the infinite structure and treatment of the finite structure as an antenna.Althoughsome useful design criteria can bededuced from the infinite structure analysis, the helix antenna design equations have stemmed from the quasi-empirical approach to the finite antenna structure. Some of the equations were derived from studying actual radiation patterns whichconsist of both the contribution from the helix surface wave structure and that from thefeedendandopenend. These equations,then, should be sensitive to the helix end configurations, a conclusion reached in this paper. In Section I11 the finite helix is discussed as a surface wave an- tenna, where the radiation contribution from the helix structure is separated from that caused by the terminations. The discrete spectrum of the periodic structure offers theoretical limits for the polarization purity independent of antenna length, while the con- Manuscript received October 18, 1983; revised June 1, 1984. R. G. Vaughan is with the Institute of Electronic Systems, Aalborg University, Strandvejen 19,9000 Aalborg, Denmark, on leave from the Physics and Engineering Laboratory, Department of Scientific and Industrial Research, Lower Hutt, New Zealand. J. B. Andersen is with the Institute of Electronic Systems, Aalborg, University, Strandvejen 19, 9OOO Aalborg, Deumark. tinuous spectrum of the end effects provide practical limits. The source independent modes on the helixexistas Fourier expan- sions called supermodes since they consist of an infinite number of modes usually with one mode dominant. The existence of the supermodes is a result of modal coupling due to the finite width of the helix conductor. A network model for an individual mode is used for field cal- culations. An infinite number of networks (one for each mode)is required to describe a single supermode existing on the helix. For the radiation calculations of Section IV, only the first few terms (modes) of the Fourier expansion have been used. The fields due to the individual modes are used to calculate the radiation pattern due to the helix structure alone, with the direct feed radiation and open end scattering being ignored. Under these conditions and assuming modal purity, a helix with perfect polarization in all directions can be conceived [2]. In practice, however, the feed and open end effects seriously degrade the performance, and must be considered in the design. Experimental patterns provide an investigation of the continu- ous spectrum radiation, where the experimental parameters are the structure terminations. The radiation due to the helix structure alone has much better forward direction polarization properties than is seen in typical radiation patterns. It is shown that by con- trolling the feed radiation and suppressing open end reflections, the endfire cross polarization can be made arbitrarily small and independent of the helix length. This result is consistent with the surface wave antenna theory. 11. BACKGROUND The Quasi-EmpiricalApproach The classic work by Kraus collected in [3] provides design formulas for main beam shape, gain, input impedance, bandwidth, and endfire axial ratio. The equations for bandwidth, pattern shape, and input impedance (and thence directivity) were ascer- tained by taking a large number of pattern measurements. The formulas do not take into account sidelobes, although their pres- ence and form can be predicted from the linear array considera- tions used to investigate the antenna pattern. The gain formula is thus often optimistic by one or two dB, as reported by Harris [4] . The formula for axial ratio does not provide information for off axis directions. Atendfire,the axial ratio is lengthdependent given by 2n+ 1 AR= - 2n for an n turn helix. It is worth noting here that the surface wave an- tenna theory (Section 111) gives the polarization as independent of antenna length. This is an important difference between the two results. The above formula is derived using a quasi-empirical method, where the helix phase velocity is assumed unidirectional and to always satisfy the Hansen-Woodyard condition for in- creased directivity. Although it turns out that the phase velocity of the forward direction current on the helix follows an approxi- 0018-926X/85/0100-0010$01.00 zyxwv 0 1985 IEEE