IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 50, NO. 1, JANUARY 2002 17 Tilted- and Axial-Beam Formation by a Single-Arm Rectangular Spiral Antenna With Compact Dielectric Substrate and Conducting Plane Hisamatsu Nakano, Fellow, IEEE, Jun Eto, Yosuke Okabe, and Junji Yamauchi, Member, IEEE Abstract—A single-arm rectangular spiral antenna is analyzed using the finite-difference time-domain method. The spiral is printed on a finite-size dielectric substrate backed by a finite-size conducting plane. Both the substrate and conducting planes are square with a side length of less than 0.6 ( : wavelength in free space). The radiation pattern is dependent on the outermost arm peripheral length . The spiral whose peripheral length is within ( : the guided wavelength of the current) radiates a tilted beam of circular polarization. When the peripheral length is decreased to , the spiral radiates an axial beam. The axial beam has a wide half-power beam width of approximately 102 (for ) with a gain of approximately 6.7 dB. The axial beam shows a 15% frequency bandwidth for a 3-dB axial ratio criterion. Over this bandwidth, the voltage standing-wave ratio (VSWR) is less than two, as desired. The experimental results for the radiation pattern, gain, axial ratio, and VSWR are also presented. Index Terms—Beam formation, finite-difference time-domain (FDTD) analysis, printed spiral antenna. I. INTRODUCTION M ANY spiral configurations have been investigated as ra- diation elements [1]–[11]. Among them, the single-arm spiral fed from a coaxial line [9] has the advantage that it does not need balun circuits between the spiral and the feed line. The single-arm spiral in [9] was analyzed under the condition that it is located in free space. The analysis was performed using an in- tegral equation for the antenna current with a free-space Green function [12]. Note that the integral equation was solved by the method of moments (MoM) [13]. The spiral in [9] has a round configuration and is supported by a honeycomb material of relative permittivity (free space). The round spiral is backed by a conducting plane of in- finite extent. In this paper, analysis is focused on a single-arm spiral antenna, which differs from the round spiral [9] in config- uration and support material. The single-arm spiral to be ana- lyzed is rectangular and is printed on a finite-size dielectric sub- strate of , backed by a finite-size conducting plane. Integral equation techniques developed recently [14], [15] can predict the radiation characteristics of an antenna printed on a dielectric substrate backed by a conducting plane. How- ever, these techniques cannot handle the practical case where Manuscript received September 17, 1998, revised March 12, 2001. The authors are with the College of Engineering, Hosei University, Koganei, 184-8584 Tokyo, Japan (e-mail: nakano@k.hosei.ac.jp). Publisher Item Identifier S 0018-926X(02)01723-4. the dielectric substrate and conducting plane are of finite size. These techniques can only handle the antenna on an infinite-size dielectric substrate backed by an infinite-size conducting plane. The single-arm rectangular spiral in this paper, therefore, is analyzed using a different method: the finite-difference time-do- main (FDTD) method [16], [17]. First, the FDTD method is ap- plied to a spiral antenna whose outermost arm peripheral length is within (where is the guided wave- length of the current). The antenna characteristics, including the current distribution, voltage standing-wave ratio (VSWR), radi- ation pattern, gain, and axial ratio, are evaluated on the basis of the electric and magnetic fields obtained in the time domain. It is found that a tilted beam of circular polarization is obtained. Secondly, the FDTD method is applied to a spiral antenna whose outermost arm peripheral length is within . The spiral is constructed with a small-size dielectric substrate and conducting plane for compactness. It is revealed that the spiral radiates an axial beam of circular polarization. Since the axial beam has many applications, the frequency responses of the gain, axial ratio, and VSWR are investigated both theoreti- cally and experimentally. It should be emphasized that the above FDTD analyses show that the single-arm rectangular spiral antenna is a circularly polarized element. The results of these analyses are obviously different from those for an antenna with similar shape—the two-arm rectangular spiral antenna radiating a linearly polar- ized wave [10]. II. CONFIGURATION Fig. 1 shows the configuration of a single-arm rectangular spiral antenna. The horizontal spiral arm of strip width is printed on a square dielectric substrate and connected to a ver- tical arm of wire radius . The antenna is fed by a coaxial line from point . The square dielectric substrate of permittivity has thickness and side length . The dielectric is backed by a conducting plane (ground plane), which is also square and has the same side length as the dielectric. The horizontal spiral arm is composed of multiple filaments, whose lengths are and . The value 4 is regarded as the outermost peripheral length of the spiral arm. 0018-926X/02$17.00 © 2002 IEEE Authorized licensed use limited to: HOSEI UNIVERSITY KOGANEI LIBRARY. Downloaded on October 2, 2009 at 02:10 from IEEE Xplore. Restrictions apply.