The Hilbert Monopole Revisited I. Sanz 1 , J.Anguera 1,2 , A.Andújar 1 , C.Puente 1,3 , C. Borja 1 1 Technology and Intellectual Property Rights Dept. Fractus, Alcalde Barnils 64, Edificio Testa, Sant Cugat del Vallés, 08190 Barcelona, Spain (ivan.sanz@fractus.com, jaume.anguera@fractus.com) 2 Electronics and Telecommunications Dept. Universitat Ramon LLull, Barcelona, Spain 3 Signal Theory and Communications Dept. Universitat Politècnica de Catalunya, Barcelona, Spain Abstract— A comparison between the resonant performance of the third iteration Hilbert monopole and a spiral shaped one of the same size and resonant frequency is presented. Quality factor, bandwidth, efficiency and radiation patterns are investigated. Although the Hilbert monopole total wire length is longer, it shows nearly the same radiation efficiency yet a lower quality factor. Hence the higher compression efficiency of the spiral shaped monopole does not provide any advantage in the antenna electromagnetic performance. Differences in radiation pattern are also observed. It is demonstrated that antenna resonance performance depends on its geometry, and not only on its size or wire length. I. INTRODUCTION The suitability of fractal geometries in the design of small wire resonant antennas has been broadly investigated. Small antennas like the Koch and the Hilbert monopole are described in the literature [1-3]. It has been demonstrated [2] that the Hilbert monopole becomes electrically smaller as the fractal iteration increases, being possible to reduce, in terms of resonance frequency, the electrical size of a classical λ/4 monopole up to factors of 11. Extensive research on the behaviour of antennas with geometries based on the Hilbert curve has been developed [2- 8]. The antenna performance properties of the Hilbert monopole have been compared with other geometries [9-11]. Total wire length, resonant frequency, quality factor, 2:1 SWR bandwidth and efficiency are explored. In these comparative studies, there is no mention about the radiation pattern properties which may vary from one geometry to another. The resonant performance of the third iteration Hilbert monopole and the one of a spiral-shaped monopole is compared in [9]. Both antennas show the same resonant frequency and occupy the same planar area. Total wire length, resonant frequency, resonant resistance, radiation resistance, quality factor, 2:1 SWR bandwidth and efficiency are considered. In the present paper the comparison of the resonant performance of the third iteration Hilbert monopole and the one of a spiral shaped monopole is revisited. A fully comparison is performed, exploring some antenna parameters that have not been considered before, such as for instance the radiation pattern, together with an additional discussion on bandwidth and quality factor. It will be demonstrated that the geometry of the antenna affects to its resonant performance. This paper is divided as follows. Section II describes the geometries of the third iteration Hilbert and the spiral shaped monopoles and also investigates their compression efficiency. The compression efficiency is defined as the ratio between the total wire length of the antenna and the wire length that would have a straight vertical monopole resonating at the same frequency [2]. This parameter is related to the coupling effects associated to the antenna geometry. Section III shows the performance of the antennas. Discussion on quality factor, bandwidth, efficiency and radiation pattern is presented. Finally, Section IV contains the main conclusions drawn from this research. II. ANTENNA DESCRIPTION The third iteration Hilbert monopole and the spiral-shaped monopole have a planar area of 156.8x156.8 mm 2 and antenna height is 227 mm in both cases (Fig.1). Both antennas are made of copper and they are placed over and infinite groundplane. The width of the copper strip is 1 mm and its thickness is 0.035 mm. The value of copper conductivity is set to 5.8x10 7 S·m -1 . The spiral shaped monopole wire length is selected so that its first resonance frequency matches the corresponding resonance of the third iteration Hilbert monopole. Performance properties of these antenna designs are calculated with Zeland IE3D simulation software based on MoM. Fig. 1. Third iteration Hilbert monopole and spiral shaped monopole Both antennas present the same first resonant frequency: 84.5 MHz. The Hilbert monopole shows lower compression efficiency, it needs 54% more wire to achieve the same resonant frequency than the spiral shaped monopole (Table I). The question is how this may impact the electromagnetic performance of the antenna. TABLE I COMPRESSION EFFICIENCY COMPARED TO A λ/4 STRAIGHT MONOPOLE Antenna Resonant Frequency (MHz) Wire Length (mm) Compression Efficiency (%) Hilbert 84.5 1141.2 62.9 Spiral 84.5 916.8 96.8