# A New Observation in Spiral and Curl Antenna Configurations above the Ground Plane
## 1 Introduction  
Circularly polarized (CP) elements, such as patch and cross slot antennas, have been found in many applications [1, 2]. The patch and cross slot are resonant antennas, and usually require two feeds with the same amplitude and a phase difference of 90\({}^{\circ}\) for CP radiation. To incorporate the two feeds into one, we often use perturbation segments [3] and slots of slightly different lengths [4].  
Spiral [5] and curl [6] antennas are also known as CP elements [7, 8]. These are non-resonant antennas, and are excited with a single feed. This paper focuses on the spiral and curl antennas because of their simple feed systems.  
Backing the spiral antenna with a ground plane is a simple method used to form a unidirectional radiation beam. The spiral antenna and ground plane spacing is conventionally chosen to be one-quarter wavelength [9, 10]. This spacing (antenna height) has been reduced using several techniques: water dielectric [11] and magnetodielectric [12] substrates, and a ring-shaped absorber [13].  
This paper aims to reduce spiral antenna height above the ground plane without any particular substrate or absorber. The spiral configuration parameters are appropriately selected so that the antenna radiates a CP wave. The change in radiation characteristics with decreasing antenna height (down to 0.15 wavelengths) are discussed using simulated results based on the moment method [14].  
We also analyze a curl antenna above the ground plane, considering that the antenna is regarded as a simplified version of a single-arm spiral antenna. The analysis enables one to understand the relationship between the spiral and curl antennas. Furthermore, the analysis leads to the realization of a low-profile curl antenna (with a height of 0.10 wavelengths).  
It is necessary to clarify the difference between the present paper and the authors' preliminary conference paper [15]. The preliminary paper shows only simulated CP wave bandwidths of non-resonant spiral and curl antennas to supplement resonant loop bandwidths. In contrast, the present paper further investigates the input impedance of thespiral and curl antennas and impedance matching. An electromagnetic coupling feed is adopted to a resultant low-profile curl antenna, and the radiation characteristics, including the VSWR, radiation patterns, and gain, are presented alongside experimental work. This paper also demonstrates that adjacent arm distance and straight part length (\(d\) and \(L_{\mathrm{f}}\) in Figure 1) are critical for reducing the antenna height, which was not discussed in the preliminary paper.  
To date, spiral and curl antennas have only been individually investigated, and the abovementioned preliminary study [15] is the only one to explore the relationship between the two antennas. This relationship is further examined in this paper, the results of which aid in understanding and designing spiral and curl antennas. In other words, the novelty of this paper is that it examines both spiral and curl antennas and notices essentially the same configurations of the two antennas, for the first time. Therefore, this paper serves as the groundwork for new ideas in antenna design, including spiral and curl antennas, in the future.