# Flexible Hilbert-Curve Loop Antenna Having a Triple-Band and Omnidirectional Pattern for WLAN/WiMAX Applications

Authors: Dang-Oh Kim; Che-Young Kim; Dae-Geun Yang
Journal: International Journal of Antennas and Propagation
 (2012)

---

## Abstract

A triple-band flexible loop antenna is proposed for WLAN/WiMAX applications in this paper. The proposed antenna is formed by the third-order Hilbert-curve and bending type structure which provides flexible characteristics. Even though the radius of the curvature for bending antennas is changed, a triple-band feature still remains in the proposed antenna. Moreover, the antenna exhibits the characteristics of omnidirectional radiation pattern and circular polarization. To verify the receiving performance of antenna, a simulation on the antenna factor was conducted by an EM simulator. Based on these results, the suggested antenna makes a noteworthy performance over typical loop antennas.


---

## Body

## 1. Introduction

Recently, the proliferation of radio devices in diverse shapes and rapid progress in flexible technology require the antennas mounted on wireless devices to be manufactured in various shapes. Furthermore, vibrant studies of wearable systems, RFID tags, and flexible displays have spurred on much attention to the flexible antenna technology. Especially, there are increasing requirements of flexible antennas with low-profile, compact size, and multiband including the wireless local area network (WLAN) band 2.4/5.2/5.8 GHz and the world interoperability for microwave access (WiMAX) band 3.5 GHz due to the explosive growth of demand for wireless data communication. The antennas operating for wearable systems and RFID tags are prone to the proximity effect by the material itself so that they usually suffer from degrading performance due to the resonating currents on the ground plane and their compact size. Particularly, these weaknesses mainly occur in the antennas used for data communications. Once encountered, to mitigate the performance degradation, a loop antenna has been an alternative since the current induced on the ground surface becomes small in magnitude [1–3]. Consequently, the loop antenna is regarded as a reference antenna in this paper.This paper presents a flexible Hilbert curve loop antenna endorsing the Hilbert curve over the typical rectangular loop, which is aimed for WLAN/WiMAX applications. The suggested antenna possesses the flexible bending structure and shows triple-band characteristics at 2.4/3.5/5.5 GHz operating bands. In addition, the antenna exhibits the omnidirectional pattern without null in comparison to a traditional loop antenna. In order to check the receiving performance of antenna, the antenna factorK is examined with an EM simulator. The structure of our proposed antenna is different from conventional flexible antennas such as spiral curve-shaped monopole antenna [4], conventional patch-shaped antenna [5], meander line antenna [6, 7], comb-shaped monopole antenna [8], inverted-F-shaped antenna [9], ultra-wideband (UWB) antenna [10], the zeroth-order resonant (ZOR) antenna [11–13], coplanar waveguide- (CPW-) fed monopole antenna [14], and folded slot dipole antenna [15]. Moreover, this is the first time the Hilbert-curve geometry to a loop antenna has been applied to such an application.


## 2. Description of the Antenna

In this study, the Hilbert curve, first proposed by Hilbert in 1891, was used as the space-filling curve structure. The Hilbert-curve geometry in antenna design has been explored to reduce the antenna size and to make it operate at multiple frequencies [16–22]. In addition, recent research has shown the use of this curve in the designs of the circular polarized antennas, metamaterial resonators, and high impedance frequency-selective structures (FSSs) [23–26]. The issue on the Hilbert-curve geometry is to find the most effective way to fill the lines in the fixed space. The Hilbert antenna has shown to be an effective structure to obtain small antennas [27]. The performance of the meander line is similar to the Hilbert curve. But unlike the meander line, the Hilbert-curve takes the advantage of tagging the iteration order number associated with geometries and providing other performances such as circular polarization. Figure 1 shows the first few iterations order of Hilbert curve geometry. It is self-evident that as the iteration order increases, the total length of the line segment is increased thereafter. The sum of line segment S is given by [18, 24]
(1)S=(22n-1)d=(2n+1)L,d=L2n-1,
where L is the side dimension of the Hilbert curve, d is the length of each line segment, and n indicates the order of iteration. Namely, as the iteration order is increased, the total length of the line segment is increased while its footprint size is kept fixed. From the electrical resonance length point of view, this property is what allows the Hilbert curve to possess a relatively low resonant frequency, which could lead to the miniaturization of structure. In this paper, the Hilbert curve with the third-order (n=3) iteration was fit into a loop antenna forming a closed-loop configuration. Figure 2 shows the configuration and dimensions of the flat Hilbert curve loop antenna in a flat shape without bending. The proposed antenna consists of only a copper film without the dielectric substrate. The top part of the antenna is the third-order Hilbert curve where the bottom part of antenna reaches to the feeding point as shown in Figure 1(c). The matching plane to tune the input impedance of the antenna is embedded in the feeding part. With adjustment of the length g and s sizing the matching plane, the impedance matching is accomplished. Also, the aggregated structure maintains its symmetry about the center line. All of the geometrical parameters of the antenna were optimized by Microwave Studio of CST. Figure 3 shows the radius of curvature of the bending structure and the geometry bent to the flexible Hilbert-curve loop antenna as shown in Figure 2. The antenna of the bending structure with the fixed width W has the radius of curvature r with a corresponding bending level. The degree of bending is measured by the radius of curvature by
(2)r=180⋅Wπθ.The Hilbert curves with increasing iteration order numbern. (a) First order, (b) Second order, and (c) Third order.
(a)(b)(c)Figure 2
Geometry and dimensions of the proposed Hilbert-curve loop antenna.Figure 3
Geometry of the flexible Hilbert-curve loop antenna and radius of its curvature.


## 3. Results and Discussion

Figure4 shows the simulated S11 plots of the finalized flexible Hilbert-curve loop antenna with 55 mm radius of curvature. As depicted by the simulation result, this loop antenna operates at a frequency of WLAN band 2.45 GHz, WiMAX band 3.35 GHz. Moreover, the antenna covers the entire 5 GHz WLAN bands. In here, the side dimension L of the Hilbert curve can be put to about 0.2λ(at 2.45 GHz), 0.3 λ (at 3.45 GHz), and 0.5 λ (at 5.5 GHz). The simulated S11 plots of the antennas bent with different radii of curvature are shown in Figure 5. This figure reveals that the return loss result of the antenna is changed by the adjustment of the bending level of the proposed antenna. Although the resonant frequencies were marginally shifted to adjacent frequency owing to antenna bending, the operating frequencies of the antenna were still maintained in the targeted band within the limit of the partial radius of curvature. From this result, the proposed antenna can be adaptable to bending structures and finds its way to flexible applications.Figure 4
S11 results of the flexible Hilbert-curve loop antenna.Figure 5
S11 results of the proposed antenna in terms of the radius of curvature.Figure6 shows the simulated omnidirectional radiation pattern of the proposed flexible Hilbert-curve loop antenna. The radiation pattern in Figure 6 is suitable for the conventional WLAN/WiMAX communication system requiring the omnidirectional pattern. In addition, its most notable distinction of radiation pattern is a uniform pattern without nulling. The maximum gains and radiation efficiencies of antenna are 3.96 dBi (0.88) at 2.45 GHz, 2.88 dBi (0.96) at 3.35 GHz, and 3.84 dBi (0.92) at 5.5 GHz (parenthesis designates the radiation efficiency). Figure 7 shows the simulated surface current distributions at each resonance frequency. The applied power to each antenna is 1 Watt. The large current distribution is indicated in dark color, and the small one is in light color. It is seen that the resonant surface currents concentrated on the Hilbert curve at 2.4 GHz and 3.5 GHz are higher than the case of 5.5 GHz. This means that many segments of the Hilbert curve at 5.5 GHz could not contribute effectively to the working role of the individual antenna segment.Simulated radiation patterns of the proposed antenna at 2.45/3.35/5.5 GHz. (a)xz-plane, (b) yz-plane, and (c) xy-plane.
(a)(b)(c)Surface current distribution of the proposed antenna at resonance frequencies. (a) 2.45 GHz, (b) 3.35 GHz, and (c) 5.5 GHz.
(a)(b)(c)To demonstrate the superiority of the radiation pattern and receiving performance of the proposed antenna, the conventional rectangular loop antennas operating at each triple band were introduced as a reference antenna in this study. This was rooted in the idea that the operation mechanism and characteristics of the rectangular loop antenna are similar to that of classical circular loop antenna; thus, this rectangular antenna could be a representative of the whole loop antenna group. Further, the rectangular loop antenna can be analogized with the primitive structure of the proposed Hilbert-curve loop antenna. The geometry and dimensions of the imposed rectangular loop antennas are shown in Figure8 and tabulated in Table 1. The feeding structure of this antenna is the same as one of the Hilbert-curve loop antennas. For fair comparison between the flexible Hilbert-curve loop antenna and the rectangular loop antenna, three rectangular loop antennas corresponding to each operating band 2.45/3.35/5.5 GHz were designed since the rectangular loop antenna has generally a single operating frequency. The simulated return loss results of the designed rectangular loop antennas are plotted in Figure 9. Note that the size of the Hilbert-curve loop is only 26.6 mm⋆26.6 mm compared to 48.8 mm⋆26 mm of the rectangular loop, that is, a reduction of two times the area. Figure 10 shows the radiation pattern of the rectangular loop antenna at 2.45 GHz. This pattern is the general radiation pattern of a loop antenna, so other bands such as 3.35 GHz and 5.5 GHz are similar to the pattern of Figure 10. In comparing Figures 6 and 10, in this regard, it is observed that the proposed flexible Hilbert-curve loop antenna achieved an even radiation pattern without null, which indicates that the pattern of the proposed antenna is superior to the pattern of the conventional loop antenna.Table 1
Dimensions of the reference rectangular loop antenna.
DimensionABCSize (mm) for 2.45 GHz48.8262.5Size (mm) for 3.35 GHz3719.12.5Size (mm) for 5.5 GHz2211.81.5Figure 8
Geometry of the reference rectangular loop antenna.Figure 9
S11 results of the rectangular loop antennas with each operating band.Figure 10
Simulated radiation patterns of the reference rectangular loop antenna at 2.45 GHz.To confirm the omnidirectional receiving performance of the proposed antenna, the antenna factorK was used in this paper. The antenna factor is an important antenna parameter to determine the receiving sensitivity of a radio communication system, which becomes one of the significant parameters directly affecting the performance of the WLAN/WiMAX communication system. To calculate the antenna factor, a load resistor of 50 Ω was connected to the feeding point of the proposed Hilbert loop antenna and rectangular loop antenna. Then, the induced voltage across a load resistor was developed for the incident plane wave. With the obtained voltage, the antenna factor K was calculated through the following equation [28]:
(3)K=EiVA[m-1],
where VA is the voltage induced on the loaded loop antenna and Ei is the amplitude of the electric field of the incident plane wave. Based on the aforementioned simulation, the resultant antenna factor for the various directions of the incident plane wave could be obtained for the proposed antenna and rectangular loop antenna. Figure 11 depicts the simulation configuration of the antenna factor. The amplitude of the incident electric field is the stationary 1 [V/m], and an incident plane wave is propagating toward the center of the antenna. The incident angle of plane wave has two cases: one with ϕ=0° (xz-plane) and the other with ϕ=90° (yz-plane) for all of the rotated angle θ in this simulation. The polarization of the incident wave kept its direction as shown in Figure 11. The simulation in Figure 11 was performed for the proposed flexible Hilbert-curve loop antenna at each operating band and for the three rectangular loop antennas. The outcomes are indicated in Figures 12 and 13.Figure 11
Simulation setup of the incident plane wave to obtain the antenna factorK.Variation of the antenna factorK at ϕ = 0° (xz-plane) for the proposed flexible Hilbert-curve loop antenna and rectangular loop antenna. (a) 2.45 GHz, (b) 3.35 GHz, and (c) 5.5 GHz.
(a)(b)(c)Variation of the antenna factorK at ϕ=90°(yz-plane) for the proposed flexible Hilbert-curve loop antenna and rectangular loop antenna. (a) 2.45 GHz, (b) 3.35 GHz, and (c) 5.5 GHz.
(a)(b)(c)The relative variation of the antenna factor is given in Figures12 and 13 because the proposed and the reference antenna do have their own physical length for respective resonances. As seen in Figure 12, the deviations of the antenna factor of the proposed flexible Hilbert-curve antenna for ϕ=0° (xz-plane) and all operating bands are within 10~20 [dB/m], whereas the rectangular loop antennas are in range of 40~50 [dB/m]. It was observed that the shape of the curve in Figure 12 was also in good agreement with the radiation pattern of the antenna in Figures 6 and 10. In other words, the peaking angles of the antenna factor observed at θ=90° and θ=270° correspond to that of the null angle appeared in the radiation pattern. Moreover, the antenna factor at ϕ=90° (yz-plane) of the proposed antenna was 2.8~3.3 [dB/m], while the rectangular loop antennas were 4.4~4.7 [dB/m] as shown in Figure 13. As seen in Figures 12 and 13, a big difference in the antenna factor between the two antennas was observed at ϕ=0° whereas a small difference was observed at ϕ=90°. To sum up, the proposed antenna reveals more omnidirectional characteristics than the conventional loop antenna. This feature values the proposed antenna for wireless communication applications. We have addressed the usefulness of the antenna factor together with the radiation pattern to evaluate the receiving performance. However, most papers treating similar topics only adhere to the radiation pattern rarely mentioning the antenna factor.Figure14 represents a degree of circular polarization in terms of axial ratio (AR) with respect to the angle θ at ϕ=0° for the proposed and the reference antenna. In general, the conventional loop antennas have a linear polarization with a very high value of axial ratio. However, the proposed flexible Hilbert-curve loop antenna reveals a circular polarization performance (AR < 4 dB) as shown in Figure 14. This circular polarization property was observed at 2.45 GHz and 3.35 GHz bands since all the segments of the Hilbert curve were cooperative in their phases and magnitudes in these bands. This phenomenon agrees with the result in Figure 7. In recent years, there has been some research on generating the circular polarization from the Hilbert-curve antennas [23, 29]. Though not appeared toward a boresight, the observed circular polarization may find its usefulness in some applications.Figure 14
Axial ratio of the proposed flexible Hilbert-curve loop antenna and rectangular loop antenna atϕ=0°.


## 4. Conclusion

In this paper, the Hilbert-curve loop antenna with an omnidirectional radiation pattern was proposed, and the simulation results are discussed focusing on the flexibility. The finalized antenna possesses the triple-band performance for the WLAN/WiMAX communication system. To compare with the proposed antenna performance, the rectangular loop antenna was used as a reference antenna. On the basis of the far-field characteristics and the result of antenna factor, it was seen that the proposed antenna achieved good omnidirectional radiation pattern and circular polarization performance. The presented results in this paper will be helpful for designing and constructing a flexible Hilbert-curve loop antenna. Furthermore, the proposed antenna could be suitable for the application in WLAN/WiMAX communication systems.



---

*Source: 687256-2012-03-26.xml*