A Wide-Band Circularly Polarized Wide-Gap Antenna Loaded with a Y-Shaped Metal Strip for L-Band Application

Abstract

A wide-band circularly polarized wide-gap antenna loaded with a Y-shaped metal strip applied to L-band is proposed in this paper. The Y-shaped metal strip coupling motivates the wide gap to achieve wide-band circularly polarized radiation. Both the simulated results by CST Microwave Studio and the measured results indicate that the antenna impedance bandwidth (reflection coefficient less than -10 dB) and axial ratio bandwidth (AR < 3 dB) are 35.9% (1.1-1.71 GHz). The antenna produces a dual circularly polarized radiation with gain of 0.8-3.2 dBic. The equivalent current array model of the antenna is also presented, which well explains the radiation characteristics of the antenna. The introduction of the metal reflecting plate makes the antenna a directional one, whose gain is above 4 dBic within the band. This design enables the satellite communication for most frequency bands with high gain, which has a vast potential for future development.

Chun-Ying Kang 1 and Shu Lin 2, 3 and Hua Zong 3 and Zhi-Hua Zhao 3 and Xue-Ying Zhang 3

Academic Editor:Vincenzo Galdi

1, School of Information Science and Technology, Heilongjiang University, Harbin 150080, China
2, Control Science and Engineering Post-Doctoral Research Center, Harbin Institute of Technology, Harbin 150080, China
3, School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin 150080, China

Received 16 January 2015; Revised 14 April 2015; Accepted 28 April 2015; 18 May 2015

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

In mobile and satellite communications, in order to suppress the interference produced by the rain, fog, or multi-path effects, circularly polarized microstrip antennas are widely adopted for their advantages of small size, light weight, and low profile. The presently proposed implementations of circularly polarized microstrip antenna mainly including three methods, which refer to single feed point method [1, 2], multiple feed point method [3], and multi-element method [4, 5], respectively. Single feed point method generally introduces a micro perturbation, which results in two orthogonal polarized degenerate modes to achieve the circular polarization. With no extra phase shifter and power divider, the structure is simple and easy to realize miniaturization, so it has been widely used though the bandwidth is not broad. In order to adapt to the multi-mode satellite communications, antennas must be capable of achieving wide-band circular polarization. Currently, wide-gap microstrip antennas are widely used to achieve wide band [6, 7], and the circular polarization is realized by introducing a micro perturbation at the edge of inside gap [8] or the feeding part [9]. Moreover, the circular polarization of antenna element with poor axial ratio mode can be improved by forming an array [10, 11], though this would introduce a more complex feed network.

In this paper, a wide-gap antenna loaded with a Y-shaped metal strip for L-band is proposed in order to achieve wide-band circular polarization. The antenna is fed by the composition of the microstrip line and coplanar waveguide. The central strip of the coplanar waveguide is stretched into the inside of the wide gap and bent twice to form a U shape. Then a metal strip is loaded at the bottom of the U-shaped strip to finally form a loaded Y-shaped metal strip. The antenna is simulated by CST Microwave Studio and measured in an anechoic chamber. The proposed antenna has a wide impedance bandwidth with [figure omitted; refer to PDF] dB within the band of 1.1-1.71 GHz and a broad axial ratio bandwidth with AR < 3 dB within the band of 1-1.8 GHz. However, such antennas have bidirectional radiation which leads to a low gain. In order to achieve the directional radiation, a metal reflecting plate is loaded to finally obtain a directional antenna with a gain more than 4 dBic within the band. In addition, in the analysis of the radiation mechanism, the antenna is equivalent to an array of eight currents according to the simulation result of the surface current. The paper is divided into the following parts: (1) Introduction; (2) Antenna Structure; (3) The Influence of Main Antenna Parameters over the Bandwidth and Axial Ratio; (4) Antenna Radiation Mechanism; (5) Simulated and Measured Results; (6) Directional Antenna with a Reflecting Plate; (7) Conclusion.

2. Antenna Structure

The antenna is a double-sided printed circuit as shown in Figure 1. Metal is printed on both sides of an FR-4 epoxy board whose relative permittivity is 4.4 and thickness is 1.5 mm. The top view of the antenna is a square gap structure as shown in the dark area (copper area) of Figure 1. The size of the wide gap is [figure omitted; refer to PDF] , and the Y-shaped strip which is coupled with the wide gap to motivate is stretched into the center of the square gap. The antenna is fed by the combination of a 50 Ω microstrip line and an asymmetric coplanar waveguide. The feed method is the same as the one in [10], but the Y-shaped coupling motivation metal strip introduced in the paper can improve the axial ratio of the antenna in a wide band, which helps realize the wide-band circular polarization. The dimensions in Figure 1 are as follows: [figure omitted; refer to PDF] mm, [figure omitted; refer to PDF] mm, [figure omitted; refer to PDF] mm, [figure omitted; refer to PDF] mm, [figure omitted; refer to PDF] mm, [figure omitted; refer to PDF] mm, [figure omitted; refer to PDF] mm, [figure omitted; refer to PDF] mm, [figure omitted; refer to PDF] 2 mm, [figure omitted; refer to PDF] mm, and [figure omitted; refer to PDF] mm.

Figure 1: Wide-gap antenna loaded with Y-shaped metal strip.

[figure omitted; refer to PDF]

3. The Influence of Main Antenna Parameters over the Bandwidth and Axial Ratio

3.1. The Influence of Parameters [figure omitted; refer to PDF] over the Bandwidth and Axial Ratio

Maintaining other set antenna parameter unchanged, the influence of parameters [figure omitted; refer to PDF] over the antenna performance is studied firstly. As shown in Figure 2, the simulations for [figure omitted; refer to PDF] mm, 35 mm, and 38 mm are completed. The simulation results of the reflection coefficient indicate that the lower limit of antenna working frequency moves towards a lower frequency band, which correspondingly affects the working bandwidth. The simulation result of axial ratio also indicates that the change of [figure omitted; refer to PDF] has a larger impact on the circular polarization bandwidth. When [figure omitted; refer to PDF] mm and 35 mm, the antenna axial ratios are both lower than 5 dB within the band 1.2-1.7 GHz, while when [figure omitted; refer to PDF] mm, the antenna axial ratio is lower than 5 dB within the band 1.2-1.65 GHz. It is thus clear that [figure omitted; refer to PDF] is able to affect the coupling strength between the feed element and gap resulting to affect the antenna bandwidth; additionally, this parameter can also change the radiation current phase and thereby affect the antenna axial ratio. As a result, take [figure omitted; refer to PDF] mm.

Figure 2: The influence of parameters [figure omitted; refer to PDF] over the antenna performance.

(a) The influence over reflection coefficient

[figure omitted; refer to PDF]

(b) The influence over axial ratio

[figure omitted; refer to PDF]

3.2. The Influence of Parameters [figure omitted; refer to PDF] over the Bandwidth and Axial Ratio

Maintaining other set antenna parameter unchanged, the influence of parameters [figure omitted; refer to PDF] over the antenna performance is studied secondly. As shown in Figure 3, the simulations for [figure omitted; refer to PDF] mm, 23 mm, and 25 mm are completed. The simulation result indicates that the antenna performance has little changes with the increase of parameter [figure omitted; refer to PDF] . When [figure omitted; refer to PDF] is too large or too small, the axial ratios within the frequency range 1.2-1.7 GHz exceed 5.5 dB without exception, while when [figure omitted; refer to PDF] mm, they are lower than 5 dB. It is evident that the loaded branches have little influence on the feed element and coupling strength but much on the axial ratio, which is mainly caused by the influence of these branches over the amplitude and phase of the radiation currents on the feed elements.

Figure 3: The influence of parameters [figure omitted; refer to PDF] over the antenna performance.

(a) The influence over reflection coefficient

[figure omitted; refer to PDF]

(b) The influence over axial ratio

[figure omitted; refer to PDF]

4. Antenna Radiation Mechanisms

The antenna can achieve a wide-band circular polarization, which mainly depends on two factors. One is the wide-gap coupling feed and the other is the shape of the feeder and the introduced micro perturbation. The wide-gap coupling feed has a lower impedance bandwidth relative to narrow gap, making it possess a flatter input impedance changing pattern to achieve a wider bandwidth. Wide-gap coupling feed can improve the strength of the coupling between the feed element and radiation element in order to broaden the antenna bandwidth. The micro perturbation introduced in the power feeding structure together with the feeding structure can produce two orthogonal radiation fields in order to obtain the polarization characteristics. The simulated results of the antenna surface current are shown in Figure 4. The surface current at the main frequency points within the antenna operating band is guided by the microstrip line and then forms two orthogonal line current distributions which can produce two orthogonal radiation fields in far field. When the current goes through the long microstrip line, it will produce a great phase lag. According to the antenna structure in this paper, the current phase in the horizontal direction lagging behind the one in the vertical direction can produce a circularly polarized radiation field in far field. Similarly, the annular current on the edge of the gap can also produce an orthogonal radiation field with a phase difference in far field. This is the radiation mechanism of circular polarization. The micro perturbation introduced in the paper is to improve the effect of circular polarization radiation. The simulated results show that the introduction of the micro perturbation can achieve the circular polarization radiation in a wider band.

Figure 4: Simulated results of surface current.

(a) 1.228 GHz

[figure omitted; refer to PDF]

(b) 1.575 GHz

[figure omitted; refer to PDF]

As shown in Figure 4, the feed structure shows a Y-shape, whose main part is an L-shaped metal strip, and two vertical metal strips are loaded afterwards. L-shaped metal strip realizes the fundamental element of circular polarization, that is, the orthotropic radiation amplitude and phase difference, and on this basis, two vertical metal strips realize the fine-tuning of the current amplitude and phase in order to achieve the circular polarization finally.

Quantitative analysis results in Figure 5 show that at the frequency of 1.228 GHz there are 8 current parts which can produce radiation, distributed at the edge of the square gap and the metal strips, respectively. Thus, the radiation field of the designed antenna is obtained by superposing these 8 current parts. The amplitudes and phases of these 8 current parts are shown in Figures 6(a)-6(h).

Figure 5: Schematic diagram of each current part.

[figure omitted; refer to PDF]

Figure 6: Amplitude and phase of each current part.

(a) Amplitude and phase of [figure omitted; refer to PDF]

[figure omitted; refer to PDF]

(b) Amplitude and phase of [figure omitted; refer to PDF]

[figure omitted; refer to PDF]

(c) Amplitude and phase of [figure omitted; refer to PDF]

[figure omitted; refer to PDF]

(d) Amplitude and phase of [figure omitted; refer to PDF]

[figure omitted; refer to PDF]

(e) Amplitude and phase of [figure omitted; refer to PDF]

[figure omitted; refer to PDF]

(f) Amplitude and phase of [figure omitted; refer to PDF]

[figure omitted; refer to PDF]

(g) Amplitude and phase of [figure omitted; refer to PDF]

[figure omitted; refer to PDF]

(h) Amplitude and phase of [figure omitted; refer to PDF]

[figure omitted; refer to PDF]

The annular current at the edge of the gap is composed of [figure omitted; refer to PDF] ~ [figure omitted; refer to PDF] , and the simulated results of the current phases show that these 4 currents totally present the distribution of a traveling wave which travels along the edge of the wide gap. The information of these currents is tabulated in Table 1. In addition, the simulated results of the current phases show that [figure omitted; refer to PDF] and [figure omitted; refer to PDF] , which are orthogonal in orientation, are also traveling wave currents which are listed in Table 1, too.

Table 1: Surface current ( [figure omitted; refer to PDF] ~ [figure omitted; refer to PDF] ) at 1.228 GHz.

Current name	Direction	Average relative amplitude value [figure omitted; refer to PDF] (based on input current)	Average value of phase difference [figure omitted; refer to PDF] (°) compared to [figure omitted; refer to PDF]	Electrical length of electric streamline [figure omitted; refer to PDF]	Slow wave factor of traveling wave current [figure omitted; refer to PDF]
[figure omitted; refer to PDF]	[figure omitted; refer to PDF]	1.00	0	0.287	1.42
[figure omitted; refer to PDF]	[figure omitted; refer to PDF]	0.37	-124.6	0.287	1.03
[figure omitted; refer to PDF]	[figure omitted; refer to PDF]	0.22	-232.7	0.287	1.19
[figure omitted; refer to PDF]	[figure omitted; refer to PDF]	0.21	-321.3	0.287	1.31
[figure omitted; refer to PDF]	[figure omitted; refer to PDF]	0.6	-156.4	0.09	1.77
[figure omitted; refer to PDF]	[figure omitted; refer to PDF]	0.75	-218.2	0.10	1.03

According to the uniform transmission line theory, the current distribution along the conductor can be expressed by Formula (1), where [figure omitted; refer to PDF] is the current amplitude at [figure omitted; refer to PDF] . Formula (2) refers to the slow-wave coefficient, where [figure omitted; refer to PDF] is the speed of light and [figure omitted; refer to PDF] is the phase velocity of current wave along the conductor. Formula (1) shows that the current presents a traveling wave distribution along the conductor and propagates along the [figure omitted; refer to PDF] direction at a phase velocity of [figure omitted; refer to PDF] without attenuation: [figure omitted; refer to PDF]

According to Table 1 and Formula (3), the radiation field inspired by the traveling wave currents [figure omitted; refer to PDF] ~ [figure omitted; refer to PDF] can be calculated as follows: [figure omitted; refer to PDF]

According to Formula (3) and Table 1, the radiation fields on [figure omitted; refer to PDF] -plane and [figure omitted; refer to PDF] -plane which are inspired by [figure omitted; refer to PDF] and the array of [figure omitted; refer to PDF] and [figure omitted; refer to PDF] are computed. The same operation is done to compute the radiation fields on [figure omitted; refer to PDF] -plane and [figure omitted; refer to PDF] -plane inspired by [figure omitted; refer to PDF] and the array of [figure omitted; refer to PDF] and [figure omitted; refer to PDF] . All these calculating results are expressed by (4)~(11). Equations (4)~(5) express the field component of [figure omitted; refer to PDF] direction on [figure omitted; refer to PDF] -plane and (6)~(7) express the field component of [figure omitted; refer to PDF] direction on [figure omitted; refer to PDF] -plane. Equations (8)~(9) express the field component of [figure omitted; refer to PDF] direction on [figure omitted; refer to PDF] -plane and (10)~(11) express the field component of [figure omitted; refer to PDF] direction on [figure omitted; refer to PDF] -plane: [figure omitted; refer to PDF]

By Formulas (4)~(11), the radiation pattern (1228 MHz) of the designed antenna is calculated and compared with the simulated results in Figure 7. The equivalent model is proved effective since the calculated results are approximately the same as the simulated ones.

Figure 7: Simulated and calculated radiation pattern.

(a) [figure omitted; refer to PDF] -plane

[figure omitted; refer to PDF]

(b) [figure omitted; refer to PDF] -plane

[figure omitted; refer to PDF]

The introduction of the micro perturbation also brings current onto the metal strips. The simulated results show that these currents present a distribution of standing wave. In order to calculate them easily, the information is tabulated in Table 2.

Table 2: Surface current ( [figure omitted; refer to PDF] ~ [figure omitted; refer to PDF] ) at 1228 MHz.

Current name	Direction	Average relative amplitude value (based on input current)	Value of phase difference (°) compared to [figure omitted; refer to PDF]	Electrical length of electric streamline
[figure omitted; refer to PDF]	[figure omitted; refer to PDF]	0.31	0	0.09
[figure omitted; refer to PDF]	[figure omitted; refer to PDF]	0.40	50.8	0.09

The radiation field inspired by [figure omitted; refer to PDF] and [figure omitted; refer to PDF] can be calculated according to the following formula: [figure omitted; refer to PDF]

The total radiation field is obtained by superposing the radiation field inspired by the traveling wave currents [figure omitted; refer to PDF] ~ [figure omitted; refer to PDF] and the radiation field inspired by the standing wave currents [figure omitted; refer to PDF] ~ [figure omitted; refer to PDF] . Since the two standing wave currents are of opposite direction and close to each other (0.07λ ) with approximately the same amplitude and phase, the total radiation field is nearly equal to zero. Finally, an elliptic polarized field is formed.

The calculated axial ratio near the maximum radiation direction and the simulated results are shown in Table 3, which agree with each other well.

Table 3: Calculated and simulated results of axial ratio near the maximum radiation direction.

Angle	[figure omitted; refer to PDF] - 30°	[figure omitted; refer to PDF] - 15°	[figure omitted; refer to PDF]	[figure omitted; refer to PDF] + 15°	[figure omitted; refer to PDF] + 30°
Calculated value of AR (dB)	4.6	4.6	5.1	5.8	5.9
Simulated value of AR (dB)	5.0	4.7	4.7	4.8	5.3

In Section 4, an equivalent traveling wave current array model is proposed to explain the antenna radiation mechanism. The results of software simulation and model calculation show that the model can well explain the radiation of the antenna. This approach can also explain the radiation of other wire antennas (slot antennas).

5. Simulated and Measured Results

The simulated results of reflection coefficient, axial ratio, and gain are shown in Figures 8 and 9, respectively. The [figure omitted; refer to PDF] is below -10 dB in the band of 1.1-1.71 GHz, meaning the impedance bandwidth is 43.4%. The AR is below 6 dB in the band of 1-1.8 GHz, meaning the axial ratio bandwidth is 57.1%. The average gain in 1.1-1.8 GHz is 4.3 dBic. Figure 10 shows the radiation patterns at two frequencies (1.228 GHz and 1.575 GHz), which indicates that the antenna has a bidirectional radiation characteristic.

Figure 8: Simulated results of reflection coefficient.

[figure omitted; refer to PDF]

Figure 9: Simulated results of gain and axial ratio.

[figure omitted; refer to PDF]

Figure 10: Simulated results of radiation pattern.

(a) [figure omitted; refer to PDF] -plane, 1.228 GHz

[figure omitted; refer to PDF]

(b) [figure omitted; refer to PDF] -plane, 1.228 GHz

[figure omitted; refer to PDF]

(c) [figure omitted; refer to PDF] -plane, 1.575 GHz

[figure omitted; refer to PDF]

(d) [figure omitted; refer to PDF] -plane, 1.575 GHz

[figure omitted; refer to PDF]

As shown in Figure 11, a prototype is fabricated according to the simulated results. The reflection coefficient, radiation patterns, gain, and axial ratio are measured in an anechoic chamber. The main utilized instrument is the Agilent E8363B vector network analyzer. The measured results of radiation patterns and the axial ratios are obtained by combining the results of two linear polarization gains measured in the orthogonal planes. The measured results are shown in Figures 12~14.

Figure 11: Prototype of antenna.

(a) Top view

[figure omitted; refer to PDF]

(b) Bottom view

[figure omitted; refer to PDF]

Figure 12: Comparison between measured and simulated results of reflection coefficient.

[figure omitted; refer to PDF]

The measured results shown in Figure 12 indicate that the reflection coefficient in the band of 1.19-1.71 GHz is below -10 dB and the relative bandwidth is 35.9%, which is a little smaller than the simulated results (43.4%). The measured and simulated results of the axial ratio and the gain are shown in Figure 13. It can be seen that the antenna has a circular polarization bandwidth of 48.3%, which is in good agreement with the simulated results, while the measured gain is 2 dB lower than the simulated one. The circular polarization patterns at 1.228 GHz and 1.575 GHz are shown in Figure 14. The measured results and the simulated ones are also in good agreement, which indicates that the antenna can work in these frequency bands for the GPS system. In addition, the antenna shows a characteristic of right-handed circular polarization in the + [figure omitted; refer to PDF] direction and left-handed in the - [figure omitted; refer to PDF] direction.

Figure 13: Comparison between measured and simulated results of gain and axial ratio.

[figure omitted; refer to PDF]

Figure 14: Comparison between measured and simulated results of radiation pattern.

(a) [figure omitted; refer to PDF] -plane, 1.228 GHz

[figure omitted; refer to PDF]

(b) [figure omitted; refer to PDF] -plane, 1.228 GHz

[figure omitted; refer to PDF]

(c) [figure omitted; refer to PDF] -plane, 1.575 GHz

[figure omitted; refer to PDF]

(d) [figure omitted; refer to PDF] -plane, 1.575 GHz

[figure omitted; refer to PDF]

Causes for the differences between the experimental results and the simulated results are mainly as follows.

(1) The parameters of material set in simulation software differ from the ones in the real test. For the experiment, except for the nonuniform relative permittivity of dielectric material, the loss and inhomogeneity of material are also the main reasons to affect the test result of reflection coefficient for antenna. Such effect is of discreteness.

(2) The loss characteristic of materials is an essential reason to produce the difference between the measured antenna gain and simulated results, which generally causes measured gain lower than the simulated results.

(3) The loss characteristic and the discreteness of relative permittivity of materials are the essential reasons to influence the axial ratio performance, because the loss will lead an additional phase shift which is discrete and also affect the radiation current phase, thereby having a significant impact on the antenna axial ratio.

(4) When testing, the fixture used to fix antenna will affect the radiation pattern. Due to the discreteness of fixture material and antenna material, there will still exist difference between the simulated result with fixture and experimental result. Thus, in this paper, the authors only focus on the difference of main lobe for directional antenna between the simulated result and test result. According to the result, it can be concluded that the difference is very small.

(5) The welding spots made during the fabrication of antenna prototype will also affect the reflection coefficient, which is also of greater discreteness.

6. Directional Antenna with a Reflecting Plate

In order to restrain the backward radiation and obtain a higher gain, a metal reflecting plate is added to the antenna. The principles of choosing the reflecting plate are mainly as follows. The side length of the plate and the distance to the antenna are as small as possible. The impacts on the reflection coefficient and the axial ratio are reduced as much as possible. In this paper, a square plate of 120 mm × 120 mm is chosen and placed 80 mm away from the antenna. The plate is supported by a piece of polyfoam (relative permittivity [figure omitted; refer to PDF] ), as shown in Figure 15. The measured results of the antenna with and without the reflecting plate are shown in Figures 16 and 17, respectively. According to the measured results of the reflection coefficient, the band moved slightly to the lower frequency band after adding the reflecting plate. In Tables 4~5, the measured and simulated results of the axial ratio and the gain with and without the reflecting plate are listed. The circularly polarized radiation patterns at 1.228 GHz and 1.575 GHz are shown in Figure 17. The measured gains with the reflecting plate at these two frequencies are 5.6 dBic and 4.1 dBic, increasing 3.3 dB and 0.9 dB, respectively. Moreover, the front-to-back ratio of the radiation patterns is improved markedly. The front-to-back ratio is, respectively, 8.6 dB and 9.4 dB larger than that without a reflecting plate.

Table 4: Comparison of measured results of axial ratio and gain.

Parameter	AR (dB)	Gain (dBic)
Frequency (GHz)	1.228	1.575	1.228	1.575
Without baffle-board	0.8	0.9	2.3	3.2
With baffle-board	0.5	2	5.6	4.1

Table 5: Comparison of simulated results of axial ratio and gain.

Frequency (GHz)	1.1	1.228	1.3	1.575	1.616	1.8
Without baffle-board	AR (dB)	4.4	4.6	4.5	1.1	1.2	6.3
Gain (dBic)	3.5	3.7	3.9	4	4.4	4.3
With baffle-board	AR (dB)	8.2	5.3	3.6	2.9	5.2	8.9
Gain (dBic)	7.3	7	6.8	6	6.5	5.9

Figure 15: Prototype of antenna with reflecting plate.

[figure omitted; refer to PDF]

Figure 16: Comparison of measured results of reflection coefficient with and without the reflecting plate.

[figure omitted; refer to PDF]

Figure 17: Measured and simulated results of radiation pattern after adding the reflecting plate.

(a) [figure omitted; refer to PDF] -plane, 1.228 GHz

[figure omitted; refer to PDF]

(b) [figure omitted; refer to PDF] -plane, 1.228 GHz

[figure omitted; refer to PDF]

(c) [figure omitted; refer to PDF] -plane, 1.575 GHz

[figure omitted; refer to PDF]

(d) [figure omitted; refer to PDF] -plane, 1.575 GHz

[figure omitted; refer to PDF]

7. Conclusion

A wide-band circularly polarized wide-gap antenna loaded with a Y-shaped metal strip for L-band is provided in this paper. The wide-band circular polarization is achieved by the micro perturbation produced by the coupling effect from the introduction of the Y-shaped metal strip and the gap. The measured results show that the impedance bandwidth and axial ratio bandwidth of the antenna are 35.9%, so it can work at two frequency bands of GPS system. The circularly polarized gain of the antenna is 0.8-3.2 dBic within the operating band, and the antenna can produce a bidirectional circularly polarized radiation. If a reflecting plate is added on one side of the antenna, the antenna becomes a wide-band circularly polarized antenna with directional radiation, and the antenna gain can reach 4 dBic or more within the operating band.

The antenna radiation field can be equivalent to the circularly polarized radiation field produced by the surface traveling wave current. The calculated and simulated results of the pattern and axial ratio of the equivalent model agree with each other well, which indicates the correctness of the equivalent model. In addition, the simulated results show that the antenna surface current is a traveling wave current, which leads to the wide-band characteristic of the antenna.

Acknowledgments

The authors would like to express their sincere gratitude to the funds supported by Postdoctoral Science-Research Developmental Foundation of Heilongjiang province (Grant no. LBH-Q12112) and the National Natural Science Foundation of China (no. 61301203). The authors would also like to thank CST Ltd., Germany, for providing the CST Training Center (Northeast China Region) at their university with a free package of CST MWS software.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

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