Broadband Reflectarray Antenna Using Subwavelength ... - IEEE Xplore

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 64, NO. 1, JANUARY 2016

[8] X. Chen, C. Gu, Z. Li, and Z. Niu, “Sparsified multilevel adaptive cross approximation,” in Proc. 3rd IEEE Asia-Pac. Conf. Antennas Propag. (APCAP’14), Jul. 2014, pp. 971–973. [9] X. Chen, C. Gu, J. Ding, Z. Li, and Z. Niu, “Multilevel fast adaptive cross-approximation algorithm with characteristic basis functions,” IEEE Trans. Antennas Propag., vol. 63, no. 9, pp. 3994–4002, Sep. 2015. [10] W. C. Gibson, The Method of Moments in Electromagnetics. Boca Raton, FL, USA: CRC Press, 2007. [11] E. Michielssen and A. Boag, “A multilevel matrix decomposition algorithm for analyzing scattering from large structures,” IEEE Trans. Antennas Propag., vol. 44, no. 8, pp. 1086–1093, Aug. 1996. [12] G. H. Golub and C. F. Van Loan. Matrix Computations. Baltimore, MD, USA: The Johns Hopkins Univ. Press, 1996.

Broadband Reflectarray Antenna Using Subwavelength Elements Based on Double Square Meander-Line Rings Pei-Yuan Qin, Y. Jay Guo, and Andrew R. Weily

Abstract—A linearly polarized broadband reflectarray is presented employing a novel single layer subwavelength phase shifting element. The size of the element is a fifth of a wavelength at the center frequency of 10 GHz and the element consists of double concentric square rings of meander lines. By changing the length of the meander line, a 420◦ phase variation range is achieved at the center frequency. This characteristic makes the proposed configuration unique, as most of the reported subwavelength reflectarray elements can only realize a phase range far less than 360◦ . In addition, the slope of the phase response remains almost constant from 9 to 11 GHz, demonstrating a broadband property. A 48 × 48-element reflectarray antenna is simulated, fabricated, and measured. Good agreement is obtained between simulated and measured results. A measured 1.5-dB gain bandwidth of 18% and 56.5% aperture efficiency is achieved. Index Terms—Double square ring, reflectarray antenna, subwavelength.

meander

line,

microstrip,

I. I NTRODUCTION A reflectarray antenna consists of an array of phase shifting elements on a flat surface that provide an appropriate phase response to form a focused beam or a contoured beam when illuminated by a feed [1]–[5]. Due to their advantages of low profile, light weight, and ease of transportation, reflectarray antennas have become attractive for satellite communication systems. Compared to their parabolic reflector counterparts, however, reflectarrays tend to have narrower bandwidth that limits their practical applications. This is partly due to the inherent narrow band property of most phase shifting elements. In order to overcome this drawback, several techniques have been proposed such as using stacked phase shifting elements [6] or patches aperture Manuscript received April 25, 2015; revised November 06, 2015; accepted November 18, 2015. Date of publication November 23, 2015; date of current version December 31, 2015. P.-Y. Qin and Y. J. Guo are with the Faculty of Engineering and Information Technology, University of Technology, Sydney, N.S.W. 2007, Australia. A. R. Weily is with the Data61, CSIRO, Sydney, N.S.W. 1710, Australia. Color versions of one or more of the figures in this communication are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2015.2502978

coupled to true-time delay lines [7]. In order to reduce the manufacturing cost and mitigate the alignment errors that occur in multilayer reflectarrays, single-layer broadband reflectarrays have been proposed, which employ multiresonant elements, such as double circular/square rings [8], [9] or circular rings with open-circuited stubs [10]. Recently, in contrast to the aforementioned reflectarray elements with a cell size of half a wavelength, subwavelength coupled-resonant elements were introduced [11]–[15], where the resonance is a result of the coupling between the elements instead of the self resonance of the elements. The reflectarray made from subwavelength elements can achieve a higher gain compared to its counterparts with halfwavelength elements [12]. However, there are some limitations for the currently reported subwavelength elements. First, the achievable phase range is usually much smaller than 360◦ partly due to the etching tolerance on the small gaps between the elements and it decreases significantly with the cell size. Take, e.g., a normal chemical etching process with a tolerance of 0.1–0.2 mm, a single-layer rectangular patch element with an element size of λ/3 has a phase range around 300◦ [12], [13]. As a result, there is always an unattainable phase range that will result in phase errors and reduce the antenna gain. Such drawbacks are more severe for subwavelength elements with a size smaller than λ/3. Second, when calculating the phase response of a reflectarray cell element, the mutual coupling effects are generally taken into account by assuming all its surrounding elements are the same in an infinite periodic environment. However, for subwavelength variable-sized elements, such an approach may lead to inaccuracies. In this communication, a single-layer phase shifting element with a cell size of λ/5 at 10 GHz based on double square meander-line microstrip rings is proposed. By varying the length of the meander line, a phase variation range of around 420◦ can be obtained. In addition, as the size variation range of the proposed element is much smaller than other reported subwavelength elements, the mutual coupling effects can be analyzed more accurately. A 48 × 48-element reflectarray operating at 10 GHz is designed to validate the performance of the proposed element. The 1.5-dB gain bandwidth is found to be 18% and the 3-dB bandwidth is greater than 32%. The proposed wideband reflectarray is suitable for satellite communications, such as DBS systems, with appropriate scaling of the operating frequency. Compared to our previous design on a phase shifting element using similar double square meander-line rings, which could only realize a 340◦ phase range, this communication extends the work reported in [16] significantly and the main contribution is as follows. First, a new single-layer subwavelength cell element is proposed that can satisfy the 360◦ phase range requirement and has wideband performance. Second, the operating mechanism of the phase shifting element and the design method are described. Third, the simulated and measured results for a complete reflectarray antenna are shown, which validates the feasibility of the proposed cell element. This communication is organized as follows. In Section II, the configuration of the proposed phase shifting element is described and the simulated phase responses are provided. Its operating mechanism is investigated in Section III by using parametric studies. Then, the design of the reflectarray is presented in Section IV. Finally, the conclusion is given in Section V. II. P HASE S HIFTING E LEMENT Fig. 1 shows the configuration of the reflectarray element. It is composed of two concentric square meander-line microstrip rings and is designed on a 3.175-mm-thick RO5880 substrate (dielectric constant

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379

Fig. 2. Simulated reflection phase versus the meander line length. Fig. 1. Configuration of the reflectarray phase shifting element.

2.2, tanδ = 0.0009). For the outer ring, 8 meander-line units are inserted on each side. For the inner ring, 6 meander-line units are inserted into both the top and bottom sides and 2 meander-line units are etched on both the right and left sides due to the limited space. The cell size P (element spacing) is 6 mm (λ/5 at 10 GHz). The length of the outer (L1 ) and inner (L2 ) square rings are 4 and 3.52 mm, respectively, with a gap of 0.12 mm. The width of the meander line and the gap between them are all 0.12 mm. The length of the meander line L0 can be changed from 0 to 0.9 mm. Therefore, the variation range of the size of the element is from 4 to 5.8 mm, which is less than λ/16. Varying the length of the meander line leads to different reflection phases when a wave is incident on the element. Full-wave simulations of the reflection phase versus the length of the meander line were calculated using the frequency domain solver of CST Microwave Studio [17]. Periodic boundary conditions were employed under a plane wave incidence to include the mutual coupling between the adjacent identical elements. Under normal wave incidence, the element is analyzed in a rectangular waveguide where the top and bottom surfaces of the waveguide are electric conducting walls and the right and left surfaces are magnetic conducting walls. In this analysis, a y-polarized TEM wave impinges on the reflectarray element. Fig. 2 shows the computed phase response of the proposed element at 8.5, 9, 10, 11, and 11.5 GHz versus the meander-line length. It should be noted that the length of all the meander lines are changed simultaneously. It can be seen that a 420◦ phase variation range is achieved at 10 GHz when the meander-line length varies from 0 to 0.9 mm. In addition, it is observed that an approximately constant phase slope is achieved for different operating frequencies, which enables the reflectarray element to have a large bandwidth. Fig. 3 shows the simulated magnitude of the input reflection coefficient. It is observed that the losses are very small for different meander-line lengths across the 9–11 GHz range. The accuracy of the simulation has been validated by measuring the elements in a WR-90 waveguide [16]. Therefore, the validation process is not repeated in this communication. The element phase shifting response has also been examined for oblique incidence. The results shown in Fig. 4 give the phase performance with the angle of incidence of θ = 30◦ for both the principal plane (ϕ = 0◦ ) and off principal plane (ϕ = 30◦ ). Also, the phase performance with the angle of incidence of θ = 15◦ and ϕ = 30◦ is given. It can be seen that the variation between the normal and oblique incidence up to 30◦ is small in both planes.

Fig. 3. Simulated magnitude of the input reflection coefficient versus frequency for different meander line lengths.

Fig. 4. Simulated phase response versus meander line length for different angles of incidence at 10 GHz. The substrate thickness is 3.175 mm.

In addition, although the reflection phase response shown in Fig. 2 is obtained by using a y-polarized TEM wave impinging on the element, the results do not change very much for an x-polarized TEM wave, which is not shown here due to the limited space.

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Fig. 5. (a) Structure of the proposed element with the length of the meander line equal to zero. (b) Structure of the proposed element with 6 and 4 meander-line units on the outer and inner rings, respectively. (c) Structure of the proposed element with 4 and 2 meander-line units on the outer and inner rings, respectively.

III. D ESIGN P RINCIPLE AND PARAMETRIC S TUDY

Fig. 6. Simulated phase response of a double-square ring element at 10 GHz.

This section presents the design principle of the proposed phase shifting element and the study of the effects of its key parameters on the phase response. For the proposed phase shifting element, the reflection phase range is the phase difference between a double square ring element with the length of meander lines equal to zero (initial phase) and the element with the longest meander line (final phase), given as follows: Φ (phase range) = ΦI (initial phase) − ΦF (final phase).

(1)

In this work, the final unwrapped phase is a value below zero. A greater value of the initial phase or a lower value of the final phase will lead to a greater phase range. As the phase of the above two elements is related to the length of the outer square ring L1 , the value of L1 should be chosen first. Once the operating frequency is given, the cell element size P is calculated. Here, we take an operating frequency of 10 GHz as an example, thereby making P equal to 6 mm (λ/5). In this way, the model shown in Fig. 1 is redrawn with the meander-line length equal to zero, which produces a double-square ring. Its structure is shown in Fig. 5(a). Other parameters including the substrate thickness, the width of the two rings, and the gap between the rings are exactly the same as the proposed element given in Section II. Regarding the initial phase of the proposed element, a parametric study of L1 on the reflection phase at 10 GHz is conducted and the result is shown in Fig. 6. The same periodic boundary conditions are used as that presented in Section II. The length of the outer ring L1 is varied from 1 to 5.88 mm, resulting in a minimum gap between two adjacent cell elements of 0.12 mm (6–5.88 mm). The length of the inner ring L2 varies with L1 since L2 = L1 − 4 × 0.12. It can be seen from Fig. 6 that the initial phase ΦI is increased when L1 is decreased. According to (1), L1 should be as small as possible in order to have a large phase range if the final phase ΦF is fixed. However, as discussed in the next paragraph, L1 also has an influence on ΦF . Hence, a decision on L1 cannot be made until that effect is taken into account. It should be pointed out that the double-square ring alone can be used as a phase shifting element for the reflectarray design. But, it is shown in Fig. 6 that with a cell size variation of about λ/5, a simple double-square ring can realize a phase changing range of about 300◦ , which does not meet the 360◦ phase requirement. In addition, in a reflectarray design, it is not advisable to use elements with a large size variation ratio since the mutual coupling effects are normally considered by assuming all their surrounding elements are of the same size. A large size ratio between elements would lead to increased inaccuracies. In order to have a phase variation of at least 360◦ for a cell size of

Fig. 7. Simulated phase response for the proposed element with different number of meander-line units at 10 GHz (L1 = 4 mm).

λ/5, an effective approach is to replace straight microstrip lines with meander lines to increase the length of the rings. There are two factors affecting the final phase (ΦF ) of the proposed element. The first is the length of the meander line. As shown in Fig. 2, the final phase decreases when the length of the meander line increases. Therefore, a longer meander-line length can lead to a greater reflection phase range. The second is the number of the meander-line units on each side of the rings. A parametric study of the effects of the number of the meander-line units of the rings on the phase range was conducted. In the analysis, only the number of the meander-line units is changed and the other parameters remain the same as the structure shown in Fig. 1. Fig. 5(b) and (c) shows the structure of the elements with a reduced number of meander-line units compared to that shown in Fig. 1. The number of the units at each side of the outer and inner rings is reduced in steps of two. However, as there are only two units along the y-axis of the inner ring, these two units are kept for the three elements under comparison. The result of the phase comparison is shown in Fig. 7. It is clear from Fig. 7 that more meander-line units will produce a larger phase range. Unfortunately, the length of the outer ring L1 has an opposite effect on the two factors aforementioned. For example, a longer outer ring, such as 5 mm, will accommodate more meander-line units but leaves less room for the meander line to change. On the other hand, a short outer ring, such as 3 mm, cannot accommodate sufficient meanderline units, although it leads to a larger meander-line changing range.


381

Fig. 9. Photograph of the antenna.

elements has been designed and fabricated using the phase characteristics obtained in the previous simulations. The reflectarray is designed to produce a beam in the broadside direction. The focal length F from the surface of the reflectarray to the phase centre of the feed horn is chosen to be equal to the reflectarray aperture size D = 288 mm, giving an F/D ratio equal to 1. A photograph of the fabricated antenna prototype is shown in Fig. 9. Considering a reflectarray on the x–y plane illuminated by a feed horn, the required phase distribution for each element to collimate a beam in the (θ0 , ϕ0 ) direction is calculated using the following equation [1], [19]: Φm,n = k0 (di − (xi cosϕ0 + yi sinϕ0 ) × sinθ0 ) Fig. 8. Simulated reflection phase versus the meander-line length when (a) L1 = 5, the number of the meander-line units are 10 and 8 for the outer and inner rings, respectively; (b) L1 = 3, the number of the meander line units are 6 and 4 for the outer and inner rings, respectively.

Therefore, a compromise needs to be made. The simulated reflection phases versus meander-line length for L1 = 5 mm and L1 = 3 mm are shown in Fig. 8(a) and (b), respectively. It should be noted that the number of the meander-line units changes for the phase shifting element with different values of L1 . When L1 is equal to 5 mm, the numbers of the units at the outer ring and inner ring are 10 and 8, respectively. They become 6 and 4 when L1 is equal to 3 mm, respectively. As seen from Fig. 8, the phase variation ranges are 370◦ and 315◦ for L1 = 5 mm and L1 = 3 mm at 10 GHz, respectively, which are much less than that when L1 is equal to 4 mm. In addition, the linearity become worse for L1 = 5 mm. Therefore, in this work, L1 = 4 mm is selected. After the length of the outer ring L1 is chosen, several other parameters need to be decided. For our design, in order to accommodate as many meander-line units as possible, the length of the inner square ring L2 is set to be as long as possible, which is 3.76 mm. This makes the gap between two rings be equal to 0.12 mm that can be easily fabricated. For similar reasons, the widths of the two square rings, the widths of the meander lines, and the gap between them are all set to be 0.12 mm.

IV. R EFLECTARRAY D ESIGN AND R ESULTS In order to validate the feasibility of the proposed phase element, a square prime-focus feed reflectarray composed of 48 × 48 such

(2)

where k0 is the propagation constant in a vacuum and di is the distance from the phase center of the feed horn to the cell element i of the array. The required physical length of the variable meander line for each phase shifting element is obtained from the characteristic at 10 GHz shown in Fig. 2. The half subtended angle of the aperture is 26.5◦ (tan−1 (D/2F)). A commercial pyramid horn antenna (SH19015 Fairview Microwave Inc) [20] having a −3−dB beamwidth of approximately 30◦ is used to illuminate the reflectarray, giving an edge taper of approximately −10 dB. Far-field radiation patterns were measured in a 12-m indoor farfield anechoic chamber located at CSIRO, Australia. A horn antenna (Flann Model DP240-AA) was used as the transmitting antenna and the reflectarray was used as the receiving antenna. The reflectarray antenna with the feed horn was simulated by the time domain solver of CST Microwave Studio. Fig. 10(a) presents the simulated and measured E-plane (y–z plane) copolarized radiation patterns at 10 GHz. The corresponding H-plane (x–z plane) results are given in Fig. 10(b). It can be seen from Fig. 10 that the simulated results agree well with the measured ones. The small differences between the measured and simulated radiation patterns are most likely due to phase discrepancies in the fabricated prototype caused by manufacturing tolerances in the reflectarray PCB and slight misalignment of the feed horn. For the Eand H-plane results, the radiation patterns have the main beams at the desired direction of 0◦ . The measured 3-dB beamwidth is around 6◦ at 10 GHz in both E- and H-planes. In addition, both the E- and H-plane radiation patterns remain approximately constant over the whole frequency bands. The results for other frequency points are omitted here due to limited space. Fig. 11 shows the measured cross-polarized radiation patterns of E- and H-planes at 10 GHz, respectively. As seen in Fig. 11, the cross polarization levels are all below −30 dB for both planes.

382


Fig. 12. Simulated and measured realized gain of the reflectarray.

Fig. 10. Simulated and measured co-polarized radiation patterns of the reflectarray at 10 GHz. (a) E-plane. (b) H-plane.

The simulated and measured realized gains of the reflectarray are shown in Fig. 12. Reasonably good agreement has been achieved. The simulated and measured maximum realized gains occur at 10.1 GHz which is 28.5 and 28.2 dBi, respectively. The measured 1.5 and 3 dB gain bandwidths are 18% (9–10.8 GHz) and 32% (8.4–11.6 GHz), respectively. It is seen from Fig. 12 that there are some ripples on the simulated and measured gain curves, particularly for higher frequency band, which are due to the multiple reflections between the feed horn and the reflectarray surface and the errors of the measurement system. The gain bandwidth will most likely increase if an offset feed is used to reduce the multiple reflections. In this work, a prime-focus feed is used instead of an offset feed with the aim of making the reflectarray symmetric about both the x- and y-axes. This simplifies both the design and analysis, as we only need to calculate and model a quarter of the entire reflectarray elements. The antenna aperture efficiency, calculated by comparing the measured realized gain with the directivity based on the physical aperture area, is 56.5% at 10.1 GHz.

V. C ONCLUSION A broadband single-layer reflectarray using a subwavelength phase shifting element has been described. The element is composed of double square rings loaded with meander lines and its cell size is λ/5 at 10 GHz. A 420◦ phase range is realized at 10 GHz. This is a significant improvement compared to other reported subwavelength elements (λ/3 element spacing) whose phase variation range is typically much less than 360◦ . In addition, a single-layer reflectarray prototype using the proposed phase shifting element was designed, simulated, and fabricated. The measured results have demonstrated a 1.5-dB bandwidth of 18% that confirms the wideband operation of the reflectarray.

ACKNOWLEDGMENT

Fig. 11. Measured cross-polarized radiation patterns of the reflectarray at 10 GHz.

The authors would like to thank K. Smart for helping with the measurement and I. Kekic for assisting with the fabrication of the mounting fixture. They would also like to express appreciation to Dr. F. Demming-Janssen and F. Wolfheimer from Computer Simulation Technology (CST) for assisting with the simulation.


R EFERENCES [1] J. Huang and J. A. Encinar, Reflectarray Antennas. Piscataway, NJ, USA: IEEE Press/Wiley, 2008. [2] Y. J. Guo and S. K. Barton, “Phase efficiency of the reflective array antenna,” IEE Proc. Microw. Antennas Propag., vol. 142, no. 2, pp. 115– 120, Apr. 1995. [3] L. Li et al., “Frequency selective reflectarray using crossed-dipole elements with square loops for wireless communication applications,” IEEE Trans. Antennas Propag., vol. 59, no. 1, pp. 89–99, Jan. 2011. [4] L. Li et al., “Novel broadband planar reflectarray with parasitic dipoles for wireless communication applications,” IEEE Antennas Wireless Propag. Lett., vol. 8, pp. 881–885, Jul. 2009. [5] Y. Li and L. Li, “Broadband microstrip beam deflector based on dual-resonance conformal loops array,” IEEE Trans. Antennas Propag., vol. 62, no. 6, pp. 3028–3034, Jun. 2014. [6] J. A. Encinar, “Design of two-layer printed reflectarrays using patches of variable size,” IEEE Trans. Antennas Propag., vol. 49, no. 10, pp. 1403– 1410, Oct. 2001. [7] E. Carrasco, J. A. Encinar, and M. Barba, “Bandwidth improvement in large reflectarrays by using true-time delay,” IEEE Trans. Antennas Propag., vol. 56, no. 8, pp. 2496–2503, Aug. 2008. [8] M. E. Bialkowski and K. H. Sayidmarie, “Investigations into phase characteristics of a single-layer reflectarray employing patch or ring elements of variable size,” IEEE Trans. Antennas Propag., vol. 56, no. 11, pp. 3366–3372, Nov. 2008. [9] M. R. Chaharmir, J. Shaker, M. Cuhaci, and A. Ittipiboon, “A broadband reflectarray antenna with double square rings,” Microw. Opt. Technol. Lett., vol. 48, no. 7, pp. 1317–1320, Jul. 2006. [10] Y. Li, M. E. Bialkowski, and A. M. Abbosh, “Single layer reflectarray with circular rings and open-circuited stubs for wideband operation,” IEEE Trans. Antennas Propag., vol. 60, no. 9, pp. 1–7, Sep. 2012. [11] J. Ethier, M. R. Chaharmir, J. Shaker, and D. Lee, “Development of novel low-cost reflectarray,” IEEE Antennas Propag. Mag., vol. 54, no. 3, pp. 277–287, Jun. 2012. [12] D. M. Pozar, “Wideband reflectarrays using artificial impedance surfaces,” Electron. Lett., vol. 43, no. 3, pp. 148–149, Feb. 2007. [13] P. Nayeri, F. Yang, and A. Z. Elsherbeni, “A broadband microstrip reflectarray using sub-wavelength patch elements,” in Proc. IEEE Antennas Propag. Soc. Int. Symp., 2009, pp. 1–4. [14] G. Zhao, Y.-C. Jiao, F. Zhang, and F.-S. Zhang, “A subwavelength element for broadband circularly polarized reflectarrays,” IEEE Antennas Wireless Propag. Lett., vol. 9, pp. 330–333, Apr. 2010. [15] J. Ethier, M. R. Chaharmir, and J. Shaker, “Reflectarray design comprised of sub-wavelength coupled-resonant square loop elements,” Electron. Lett., vol. 47, no. 22, pp. 1215–1217, Oct. 2011. [16] P.-Y. Qin, Y. J. Guo, and A. R. Weily, “A sub-wavelength reflectarray element based on double square rings loaded with meander lines,” in Proc. Eur. Conf. Antennas Propag. (EuCAP’14), Apr. 2014, pp. 1–3. [17] CST Studio Suit 2013, Computer Simulation Technology, Darmstadt, Germany. [18] S. D. Targonski and D. M. Pozar, “Analysis and design of a microstrip reflectarray using patches of variable size,” in Proc. IEEE Antennas Propag. Soc. Int. Symp., Jun. 1994, pp. 1820–1823. [19] D. M. Pozar, S. D. Targonski, and H. D. Syrigos, “Design of millimeter wave microstrip reflectarrays,” IEEE Trans. Antennas Propag., vol. 45, no. 2, pp. 287–296, Feb. 1997. [20] Fairview Microwave Inc. [Online]. Available: http://www.fairview microwave.com/

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Wideband Monopole Antenna With Less Nonground Portion For Octa-Band WWAN/LTE Mobile Phones Yan Wang and Zhengwei Du

Abstract—An octa-band WWAN/LTE monopole antenna with a size of 80 mm × 8 mm × 5.8 mm for 5.7-inch mobile phones is proposed and studied. The proposed antenna consists of a folded metal plate with a lumped-element high-pass matching circuit. The working mechanism is analyzed based on the S-parameters and the surface current distributions. The 0.25-wavelength, 0.5-wavelength, and 1-wavelength modes of the monopole antenna are excited and used. The attractive merit of the proposed antenna is that the height of the nonground portion is only 8 mm. A prototype is fabricated and measured. Its measured −6 dB impedance bandwidths are 290 MHz (0.69–0.98 GHz) and 1.11 GHz (1.63–2.74 GHz) which cover the LTE700, GSM850, GSM900, GSM1800, GSM1900, UMTS, LTE2300, and LTE2500 bands. Within the two frequency bands, good radiation performances are obtained. Index Terms—Mobile antenna, mobile phone, nonground portion, small size, wideband/multiband.

I. I NTRODUCTION In recent years, numerous wireless communication standards with different working frequencies and communication protocols have been developed and deployed worldwide. To provide all these services simultaneously, the antenna in mobile phones should cover multiple frequency bands or a wide frequency band. In addition, since a large display with a narrow frame has become the mainstream of the modern mobile phones, the space for the antennas is very limited. So, designing a multiband/wideband mobile antenna with a small size is not only an essential requirement but also a major technological challenge [1], [2]. The main types of modern mobile antenna are the monopole antenna [3]–[13], the loop antenna [14]–[18], and the slot antenna [12], [13], [19]–[21]. The common working modes of the monopole antenna are the 0.25-wavelength monopole mode and the 0.75-wavelength higher order monopole mode [3]–[13]. For the loop antenna, it could work at the 2 × 0.25-wavelength monopole mode, the 2 × 0.5-wavelength dipole mode, the 2 × 0.75-wavelength higher order monopole mode, and the 4 × 0.5-wavelength higher order dipole mode [14]–[18]. For the slot antenna, apart from the 0.25-wavelength slot mode and the 0.75-wavelength higher order slot mode, the 0.5-wavelength slot mode could also be adopted [12], [13], [19]–[21]. With the multiple modes of the monopole/loop/slot antenna, the multiple resonant paths of a single mode of the monopole/loop/slot antenna, and the combination of the monopole/loop/slot antenna modes, multiple frequency bands or a wide frequency band could be covered simultaneously. Apart from the resonant monopole/loop/slot antenna, nonresonant antenna [22] or the combination of the resonant and nonresonant antennas [7] is also applied recently. In addition, the coupled-fed matching method [3]–[5], [8], [15], the lumped-element Manuscript received May 29, 2015; revised November 02, 2015; accepted November 23, 2015. Date of publication November 25, 2015; date of current version December 31, 2015. This work was supported in part by Beijing Natural Science Foundation under Grant 4152025 and in part by Guangdong Provincial Science and Technology Plan Projects under Grant 2013B010401025. The authors are with the State Key Laboratory on Microwave and Digital Communications, Tsinghua National Laboratory for Information Science and Technology, Department of Electronic Engineering, Tsinghua University, Beijing 100084, China (e-mail: [email protected]). Color versions of one or more of the figures in this communication are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2015.2503730

0018-926X © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.