International Journal of Antennas and Propagation

Volume 2014 (2014), Article ID 302580, 16 pages

http://dx.doi.org/10.1155/2014/302580

## Design of High-Gain and Beam Steering Antennas Using a New Planar Folded-Line Metamaterial Structure

^{1}International Research Institute MICA, HUST-CNRS/UMI-2954-Grenoble INP, Hanoi University of Science and Technology, Hanoi 10000, Vietnam^{2}Department of Instrumentation and Industrial Informatics, School of Electrical Engineering, Hanoi University of Science and Technology, Hanoi 10000, Vietnam^{3}IMEP-LAHC Laboratory, UMR 5130 INPG-UJF-CNRS, Grenoble INP, Grenoble Cedex 1, Grenoble 38400, France

Received 21 April 2014; Revised 7 July 2014; Accepted 8 July 2014; Published 16 September 2014

Academic Editor: Miguel F. Bataller

Copyright © 2014 Minh Thuy Le et al. 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.

#### Abstract

In the last few years, there has been growing interest in employing metamaterials (MTMs) to enhance antenna gain. In this paper we proposed a novel structure of planar folded-line left-handed metamaterial (FL-LHM) and applied it to improve the gain of three 5.8 GHz microstrip antenna types: a circularly polarized patch antenna, an antenna array, and a beam steering antenna. The planar FL-LHM structure was designed based on transmission line analysis. Their scattering parameters were obtained using a numerical model; the negative effective permittivity and permeability were then calculated from these parameters for the assessment of negative refraction index region. The S_{11} and radiation patterns of three fabricated antennas were measured; these results matched well with the simulation. We observed that the gain was increased up to 3 dBi for all the antennas. In addition, we were also able to maintain the circular polarization as well as the steering of the antenna without changing its dimensions.

#### 1. Introduction

Antenna is an important component that affects the performance of wireless communication systems. Antennas with low profile, low manufacturing costs, and high gain are more desirable for the system. To satisfy the requirements, microstrip antenna is a good candidate for the antenna design. However it is difficult to obtain a high gain using a normal microstrip antenna. To resolve this issue, some traditional technologies for enhanced-gain antenna are used such as reflectors, directors, dielectric lenses, superstrates, or array techniques. In recent years, electromagnetic bandgap (EBG) structures and metamaterials have been demonstrated to enhance the antenna gain. This paper will be focused on the high gain antenna using MTM technique.

Metamaterials denote artificial constructed materials that may not be found in nature. Metamaterials has negative permittivity () and/or negative permeability (). The MTM is called double-negative material (DNM) or left-handed material (LHM) when it has double-negative and . With the same incident wave, the reflected wave through a LHM is in opposition to the reflected wave through a positive permittivity and permeability material. LHM acts like lenses to focus wave in the same direction; thus it is usually placed above an antenna to increase its gain. In general, LHM uses a periodic structure and is modeled as an infinite array of MTM unit-cells. Therefore, in this paper, a single LHM unit-cell will be studied instead of the entire array of unit-cells. The dimension of a LHM unit-cell is very small compared to where is the wavelength in free space at the operating frequency. In this paper, we concentrate on the design of a new LHM and its applications in gain enhancement for low-profile antennas.

In the context of improving the antenna gain, two types of MTM are usually found: the left-handed materials or double-negative materials and evanescent materials. LHMs have both negative permittivity and permeability that were mentioned by Veselago in 1968 [1]. His paper introduced the propagation of waves in LHMs that is opposite to the wave vector in the right-handed materials (RHMs); LHMs possess the negative refraction index () and their wave vector is also called the “backward wave.” Evanescent materials are the other type of MTMs with single negative or which were considered by Prendry and his colleagues thirty years later. He found out that thin metallic wire lattices (TMWs) had effectively negative permittivity in [2] and split ring resonators (SRRs) had effectively negative permeability in [3] in specified frequency bands. The first practical LHM unit-cell structure was proposed in [4, 5] by Smith and his colleagues based on SRR of Prendry in [3]. It is constituted of TMW and SRR which have dimension in 3D of (). Ziolkowski then successfully investigated and realized some slabs of planar LHM structures that comprised a substrate Duroid 5880 ( mm) with embedded strip line operating at the band [6]. This one is more compact than the first LHM structure in 3D and suitable for low-profile antenna application. The dimension of these planar LHM unit-cells in 2D is around (). The other LHM structure, the “ shaped,” was first suggested in 1992 by Saadoun and Engheta [7]. In 1997, Simovski et al. presented “” shaped LHM unit-cell in 3D with the dimension of (), application for antenna gain enhancement in [8]. This LHM unit-cell is smaller than the LHM unit-cell of Prendry and Smith. At the same time, they also designed the “” shaped LHM unit-cell in 2D in [9]; then the “” shaped LHM unit-cell in 2D was fabricated in 2008 [10] with the dimension of 6.5 () using Roger Duroid substrate. The new planar “S” shaped LHM unit-cell was investigated by Chen et al. in [11] with the dimension of , but this LHM could not be smaller than 6,5 (see Table 1).

In addition, the negative effective permittivity, permeability, and refraction index can be extracted from average* H*-field and* E*-field of each LHM unit-cell [6, 12–15] or from their reflection and transmission coefficient parameters [16–18]. These methods have been researched and validated by many researchers, especially matched results between the simulation and the experimental parameters which have been demonstrated in [16, 18–20]. For this reason, our new planar “folded-line” LHM (FL-LHM) unit-cell structure will retrieve their effective and from parameters based on the numerical LHM unit-cell model. This FL-LHM unit-cell has a smallest dimension of compared with the published unit-cell structures which are listed in Table 1. In Section 2, we show the methodology to design and to obtain this FL-LHM at defined operating frequency.

The design of novel high gain and beam steering antennas using FL-LHM substrate will be presented more in detail in Section 3. When a LHM substrate covers a reference antenna, it enhances the gain of that antenna and also maintains its performance. This performance can be circular polarization or beam steering. This one is a major advantage of LHM substrate which will be presented in Section 2. As we have reported in our previous work [21, 22], the operating frequency of FL-LHM as well as FL-LHM antenna was defined at 5.8 GHz in order to satisfy the operation-range requirement for reader antenna of electronic-toll-collection (ETC) free-flow system application on the highway in Europe. The ETC free-flow system allows automatic fee payments of vehicles without stopping on the highway. It is composed of a reader and transponders (badges) where the reader is fixed on a gantry of the road and the badge is mounted on a vehicle [22, 23]. Each badge stores all information of each vehicle, such as the class, the owner of vehicle, his address, and his bank account. Reader detects and then communicates with badge to collect all vehicle information when a vehicle enters its operating zone. The fee is offered and then paid based on this collected information between reader and badge. Physical layer of the equipment (the reader and the badge) uses the microwave communication at the spectrum of 5.795 GHz–5.815 GHz or 5.875 GHz–5.905 GHz according to European dedicated short-range communication (DSRC) standard [24, 25]. In this DSRC system, an antenna with higher gain gives a longer distance of communication and hence vehicles can be allowed to pass faster. In addition, an antenna only covers a lane: if a beam steering antenna is used, it could cover multilanes; therefore the price and the size of highway equipment in ETC free-flow system will be reduced. The high gain, low profile, and multibeams are always the requirements for designing of antenna at 5.8 GHz in this system.

#### 2. Theory and Design of New Planar FL-LHM

FL-LHM substrate is created by periodic arrays of FL-LHM unit-cells in and directions. Hence, to design a LHM substrate, we primarily focus on the design of a new planar FL-LHM unit-cell.

##### 2.1. Transmission Line Analysis

LHM substrate is created from periodic LHM unit-cells. Each planar unit-cell consists of two conductor faces etched on a substrate. The shapes of these two conductor faces are the same. Thus, a LHM unit-cell is described by the equivalent circuit using transmission line method as shown in Figure 1.

According to this circuit, the resonant frequency of unit-cell can be estimated using the formula , where and denote total inductance and total capacitance of unit-cell, respectively: The gap between two conductors of two adjacent unit-cells determines their mutual coupling level. The closer the unit-cells are, the larger the current magnitude is; thus the resonant frequency will be increased; refer to (1). We found that these components define resonant frequency like effective permittivity and permeability. For easier understanding and designing, each unit-cell is represented by a symmetrical circuit model as in Figure 2 according to [14, 26], where the total inductance has been split into series () and parallel () components, similarly for the total capacitance .

depends on the total length of conductor line and its value is dominant in series impedance (). On the other hand, depends on area of parallel surface between two conductor faces; its value is dominant in shunt admittance () and depends on the “common” parallel area. As consequence, we can change the total length of line () or the “common” parallel area to achieve desired resonant frequency. This means the higher the or “common” parallel area is, the lower the resonant frequency is. The series impedance and shunt admittance of a unit-cell can be obtained from

The effective permittivity and permeability of unit-cell in this model in Figure 2 can be calculated using the Bloch theorem. We start from the relation of the current and the voltage that passes thought a unit-cell as the following equation: where is the phase crossing through unit-cell : where is the wave vector in the unit-cell and is the dimension of the periodic unit-cell. As in Figure 1, .

Involving the spatial dispersion in these effective parameters, according to [14, 26], the effective permittivity and permeability of a unit-cell can be calculated from the following equations:

The phase crossing through one unit-cell in (4) can be now obtained by (6) with the boundary condition in (7): where , are real numbers; they can be negative or positive depending on the values of , and , as follows:

The wave impedance of LHM unit-cell is

From (5) we can summarize that a LHM unit-cell can be obtained by choosing suitable values of , and , under the condition in (7) combined with (10):

As presented, the total length of the conductor line increases, while the resonant frequency increases. This way, we can tune the FL-LHM to any operating frequency. For convenience, at the frequency of 5.8 GHz of LHM unit-cell , we suppose that and are defined as nH, pF, and pF with . As in Figure 3, the investigated FL-LHM unit-cell consists of two conductor lines etched on Roger 4003 substrate and has the following dimensions.(i)Each conductor face is created by a line with the width of mm and the total length of mm (around ) to satisfy conditions (7) and (10) above to have resonant frequency at 5.8 GHz. This line is folded in one unit-cell with dimensions of mm^{2} () by using meander line structure in direction as in Figures 3(a) and 3(c) to reduce the dimension.(ii)The separation between two unit-cells is of mm.(iii)Two conductor lines are maintained parallel to each other by the substrate dielectric Roger 4003 that has thickness of mm, permittivity of , permeability of , and loss tangent of . The “common” parallel area between these two conductors is defined as in Figure 3(b).

The novel FL-LHM has both negative effective permittivity and permeability which are denoted by and . Their real parts are negative while the imaginary parts are nearly equal to zero at the operating frequency of 5.8 GHz.

##### 2.2. Numerical FL-LHM Model

A quantity of and values can be calculated to have a desired FL-LHM using the transmission line analysis in Section 2.1. However, the mutual inductance and capacitance as well as fringing effect are difficult to evaluate. In addition, this quantification will be more complicated when the incident wave varies. Therefore, a numerical model in Figure 4 is created to simplify the design of a FL-LHM unit-cell and the evaluation of their effective permittivity and permeability likewise.

Figure 4(a) illustrates a FL-LHM antenna model; the FL-LHM substrate is excited by a reference antenna (RA) which could be any type of antennas. In this case, the pattern of RA is equivalent to an incident plane wave at the direction varying from to . The released wave from a FL-LHM is propagating in direction. These waves consist of the forward wave (solid red line) and the wave reflected at the back FL-LHM (dotted blue line). Both waves have the same phase, so that antenna gain is improved.

From this FL-LHM antenna model, we create FL-LHM unit-cell modeling as in Figure 4(b). The FL-LHM unit-cell is excited by an incidence wave in direction. To cover all the types of RA, the excitation of FL-LHM unit-cell is modeled by a plane wave incident in direction of theta (). The released wave from a FL-LHM is propagating in direction. Hence, is set to perfect-matched layer (PML) (open boundary). Due to a geometrical and electrical symmetry of each unit-cell in Figure 2, the sidewall of each unit-cell model can be replaced by periodic boundary conditions. Particularly, the boundaries and and and are set to be periodic boundaries. From this model, the field distribution and the reflection-transmission coefficients of a FL-LHM unit-cell under a normally incident plane wave at any angle are calculated as in Figures 5 and 6 using commercial electromagnetic software CST Microwave Studio 2012. The effective , and refractive index of FL-LHM can be extracted from parameters; this method has been validated and demonstrated a good agreement between simulation and measurement in [16–18]. The retrieval of these effective parameters will be shown in the next section.

##### 2.3. Retrieval of Effective Permittivity and Permeability of the New FL-LHM from S Parameters

Considering our numerical FL-LHM model, the wave propagation through the FL-LHM is shown as in Figure 7.

As we presented in Section 2.2, the reflection and transmission coefficients ( and ) of the FL-LHM unit-cell that are created from Section 2.1, according to [9, 16], are given by these equations: where is the reflection coefficient of an incident wave on the interface between free space and FL-LHM, whereas is the transmission term through the FL-LHM slab: where , are wave impedance and wave number in free space, respectively. The normalized wave impedance and refractive index of the FL-LHM can be expressed in terms of scattering parameters as where is an integer related to the branch index of (principal value of ) and the transmission term as a function of scattering parameters is given by [14]

The effective permittivity and permeability of the FL-LHM are directly calculated from the refractive index and normalized impedance :

The retrieval of effective permittivity and permeability of any metamaterial from the scattering parameters is a sufficiently accurate method which allows characterizing a FL-LHM. Since the FL-LHM is not homogeneous, the improvement based on the determination of two effective boundaries [19] needs to be determined to increase the accuracy. Besides, the measurement/simulation noise of parameters influent on the effective impedance is also considered. This method gives us a theoretical validation of the effective permittivity and permeability of the FL-LHM substrate and its dimension from the parameters results. Because of the periodic structure, we only consider the varying incident angle from 0° to 90°; the results are repeated with . parameters at any angle are shown in Figure 8. We found that parameters are nearly stable when theta squints from 0° to less than 30°; only one resonant frequency at 5.8 GHz is obtained. Varying theta in the range from 30° to 50°, these values are changed, the resonant frequency is increased above 5.8 GHz, and the second resonant frequency at 3.8 GHz has been added. The resonant frequency is shifted as the theta increases. This gives limited condition for RA pattern in FL-LHM antenna, especially in the case of a steering RA.

From the parameters, obtained based on numerical FL-LHM model, combined with the retrieval method according to (11)–(15), the effective parameters of our new FL-LHM are presented in Figures 9–12. Both desired negative and are obtained in the range of 5.5–6.2 GHz (LHM bandwidth) according to Figures 10 and 11 while the effective refraction index is negative in the range of 5.1–6.2 GHz (MTM bandwidth). At this LHM bandwidth, their real parts (solid lines) are negative while imaginary parts (dotted lines) are nearly equal to zero which shows that this FL-LHM works well with the low loss at this range, especially in the range of as in Figures 9 and 10.

#### 3. FL-LHM in Enhanced-Gain for 5.8 Patch and Beam Steering Antenna

In general, the gain of a microstrip patch antenna is around 6-7 dBi. The gain can be increased by using antenna arrays (adding dimensions in , directions), metamaterial technology (only changing dimension in direction), or both of them. The LHM antenna structure is presented in Figure 4(a); it consists of a RA and a FL-LHM substrate to increase the overall gain. Interestingly, this increasing gain is in good agreement with any type of RA such as the circular polarization antenna or beam steering antenna. For experimental verification of the enhanced-gain effect of FL-LHM substrate, we have realized three types of RA: the patch antenna, the antenna arrays of four patches, and the beam steering patch antenna. The Vector Network Analyzer 8510C is used for measurement. The measurement of radiation pattern antenna is performed using the anechoic chamber in our laboratory.

The size of FL-LHM substrate is an important parameter that needs to be defined. According to analysis in Section 2, especially in Figure 4(a), when a RA is covered by a suitable FL-LHM substrate at the height , the RA gain will be improved and the LHM antenna is always well matched at operating frequency. In general, dimensions of FL-LHM substrate () are proportional to the angular width of RA and the air-gap height of between RA and FL-LHM substrate. In addition, suitable FL-LHM substrate dimensions are optimized depending on the dimension of RA as well as the application systems.

##### 3.1. Circularly Polarized Patch Antenna Gain Enhancement

A circularly polarized rectangular patch antenna with dimensions of mm has been created. This RA uses the Roger 4003 substrate with the thickness of 0.8 mm. The circular polarization is obtained by trimming opposite corners of a square patch [27] and exciting at the feed point as in Figure 13(a). A common measure for the quality of the achieved circular polarization is the axial ratio dB. This antenna gain is 6.5 dBi and reflection coefficient at 5.8 GHz is −20 dB and −15 dB in simulation and measurement, respectively.

Our study shows that FL-LHM antenna is well matched with air-gap heights from 28 to 31 mm (Figure 14). In this case, dimensions of fabricated FL-LHM substrate are defined by mm. Figure 15 illustrates the FL-LHM antenna gain versus air-gap height at the frequency of 5.8 GHz. The chosen air-gap height of 30 mm gives the good circular polarization with dB and highest gain (Figure 15) while 20 dB at 5.8 GHz. The simulated gain is increased from 6.6 dBi to 9.8 dBi by using this FL-LHM layer; the measured gain is 9.5 dBi (Figure 16). The reflection coefficients, axial ratios, and radiation pattern of FL-LHM antenna are shown in Figures 17 and 18.

##### 3.2. Antenna Arrays Gain Enhancement

From the patch antenna designed in Section 3.1, an array of patch antennas is created using the 1–4-feed structure as in Figure 19. The antenna arrays gain is 12.7 dBi and 12.1 dBi in simulation and measurement, respectively (see Figure 20).

When this antenna is covered by FL-LHM substrate with the air-gap height mm, the is −12 dB and −14 dB (Figure 21) while the gain is improved to 15.3 dBi and 15.4 dBi (Figure 22) in simulation and measurement, respectively.

##### 3.3. Beam Steering Antenna Gain Enhancement

The reference antenna is used as a beam steering antenna using two passive patches at the right side and the left side of the active patch (driven element) in direction (Figure 23(a)), according to [28]. The active patch is excited by RF source; two patches passive at the right side (patch 2) and at the left side (patch 3) are loaded by the reactive elements and , respectively. The mutual couplings between three patches are proportional to the distance* ds* between them [29]. The current magnitude on the passive radiator is larger when* ds* is smaller so that the gain will be increased.

The phases shifted between antenna elements are turned by changing the reactive load. We denote by the current on the active patch; and are the induced currents on passive patches and , respectively. The array factor is given by [28]

The steering of reference antenna is described in the following three cases (Figures 24 and 25).(i)Case 1: pF; the AF is maximum; the main lobe is located at theta of 0°. Case 1 is noted in red color in all figures.(ii)Case 2: pF and pF; the main lobe is steered at theta of 20°. Case 2 is presented in green color.(iii)Case 3: inversely, if pF and pF, the main lobe is steered at theta of −20°. Case 3 is represented in blue color.

Figures 24 and 25 represent the and radiation pattern of beam steering reference antenna in simulation and measurement, respectively.

Our study found that the beam steering reference antenna is always adaptive in three cases at 5.8 GHz ( dB, dB); the peak of is shifted at the higher frequency in case 2 and case 3. The gain of RA is around 8.2 dBi/8.3 dBi in measurement and simulations for case 1. The gain reduces to 7.7 dBi in simulation and to 7.5 dBi in measurement for cases 2 and 3 (Table 3).

The enhancement gain will be obtained when beam steering antenna is covered by the FL-LHM substrate as in Figure 23(b). The FL-LHM beam steering antenna is well matched at the range of 5.75–5.87 GHz (Figure 26) that covers the DSRC standard. However, the steering angles are reduced to 10° instead of 20° because of FL-LHM effect according to Snell’s law when the waves propagate through FL-LHM substrate.

The reflection coefficient and radiation pattern of FL-LHM beam steering antenna in three cases are shown in Figures 26 and 27. This FL-LHM antenna has dimensions of mm^{3}.

In simulation, the gain of beam steering antenna is improved from 8.2 dBi to 12 dBi for case 1 and from 7.7 dBi to 11 dBi for cases 2 and 3 (Figure 27(a)).

In measurement, the gain obtained is 11.6 dBi for case 1 and 10 dBi for cases 2 and 3 (Figure 27(b)). The difference of FL-LHM antenna gain between case 1 and case 2/case 3 is caused by the limited condition of the FL-LHM substrate that is analyzed in Section 2.2 as well as the effect of capacitor loaded in passive patches.

Table 4 resumes the simulation and measurement results of FL-LHM beam steering antenna in three cases.

#### 4. Conclusion

In this paper, a new planar FL-LHM structure is presented. An equivalent circuit is useful for understanding and designing a FL-LHM substrate for an arbitrary operating frequency. In addition, the FL-LHM modeling is created for easy simulation using electromagnetic software and for enhancement antenna gain. In consequence, the new FL-LHM substrate is used to increase the gain of three types of low-profile antennas which are the circularly polarized rectangular patch antenna, the antenna arrays, and the beam steering antenna. These three low-profile FL-LHM antennas operate at the frequency according to the DSRC standard for ETC free-flow system application. The gains measured are 9.5 dBi, 15.3 dBi, and 11 dBi in measurement. The gain of any RA is increased up to around 2.5–3 dBi by using this planar FL-LHM substrate. The and radiation pattern results in measurement of three FL-LHM antennas are well fit with simulation results.

#### Conflict of Interests

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

#### Acknowledgments

The authors wish to thank A. Gachon (IMEP-LAHC) for his help in fabrication and K. Belmkaddem (CEA-LETI) for her help in the measurement of the prototypes A and B.

#### References

- V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of
*ε*and*μ*,”*Soviet Physics Uspekhi*, vol. 10, no. 4, pp. 509–514, 1968. View at Google Scholar - J. B. Prendry, “Extremely low frequency plasmons in metallic mesostructures,”
*Physical Review Letters*, vol. 76, p. 4773, 1996. View at Publisher · View at Google Scholar - J. B. Prendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,”
*IEEE Transactions on Microwave Theory and Techniques*, vol. 47, no. 11, pp. 2075–2084, 1999. View at Publisher · View at Google Scholar · View at Scopus - D. R. Smith, D. C. Vier, N. Kroll, and S. Schultz, “Direct calculation of permeability and permittivity for a left-handed metamaterial,”
*Applied Physics Letters*, vol. 77, article 2246, no. 14, 2000. View at Publisher · View at Google Scholar · View at Scopus - D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite mediu m with simultaneously negative permeability and permittivity,”
*Physical Review Letters*, vol. 84, no. 18, pp. 4184–4187, 2000. View at Publisher · View at Google Scholar · View at Scopus - R. W. Ziolkowski, “Design, fabrication, and testing of double negative metamaterials,”
*IEEE Transactions on Antennas and Propagation*, vol. 51, no. 7, pp. 1516–1529, 2003. View at Publisher · View at Google Scholar · View at Scopus - M. M. I. Saadoun and N. Engheta, “A reciprocal phase shifter using novel pseudochiral or $\omega $ medium,”
*Microwave and Optical Technology Letters*, vol. 5, no. 4, pp. 184–188, 1992. View at Publisher · View at Google Scholar · View at Scopus - C. R. Simovski, S. A. Tretyakov, A. A. Sochava, B. Sauviac, F. Mariotte, and T. G. Kharina, “Antenna model for conductive omega particles,”
*Journal of Electromagnetic Waves and Applications*, vol. 11, no. 11, pp. 1509–1530, 1997. View at Publisher · View at Google Scholar · View at Scopus - C. R. Simovski, “Plane-wave reflection and transmission by grids of conducting Ω-particles and dispersion of Ω electromagnetic crystals,”
*AEU-International Journal of Electronics and Communications*, vol. 57, no. 5, pp. 358–364, 2003. View at Publisher · View at Google Scholar · View at Scopus - É. Lheurette, G. Houzet, J. Carbonell, F. Zhang, O. Vanbésien, and D. Lippens, “Omega-type balanced composite negative refractive index materials,”
*IEEE Transactions on Antennas and Propagation*, vol. 56, no. 11, pp. 3462–3469, 2008. View at Publisher · View at Google Scholar · View at Scopus - H. Chen, L. Ran, J. Huangfu et al., “Left-handed materials composed of only S-shaped resonators,”
*Physical Review E*, vol. 70, Article ID 057605, 2004. View at Publisher · View at Google Scholar · View at Scopus - D. R. Smith and J. B. Pendry, “Homogenization of metamaterials by field averaging,”
*Journal of the Optical Society of America B*, vol. 23, no. 3, pp. 391–403, 2006. View at Publisher · View at Google Scholar - A. Ramakrishna and J. Pendry, “Non-linear effects in negative magnetive mata-materials,”
*Physical Review*, vol. 4, 2006. View at Google Scholar - R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, “Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory,”
*Physical Review E—Statistical, Nonlinear, and Soft Matter Physics*, vol. 76, Article ID 026606, 2007. View at Publisher · View at Google Scholar · View at Scopus - D. R. Smith, J. Gollub, J. J. Mock, W. J. Padilla, and D. Schurig, “Calculation and measurement of bianisotropy in a split ring resonator metamaterial,”
*Journal of Applied Physics*, vol. 100, no. 2, Article ID 024507, 2006. View at Publisher · View at Google Scholar · View at Scopus - X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco Jr., and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,”
*Physical Review E—Statistical, Nonlinear, and Soft Matter Physics*, vol. 70, Article ID 016608, 2004. View at Publisher · View at Google Scholar · View at Scopus - Y. H. Liu and X. P. Zhao, “Investigation of anisotropic negative permeability medium cover for patch antenna,”
*IET Microwaves, Antennas and Propagation*, vol. 2, no. 7, pp. 737–744, 2008. View at Publisher · View at Google Scholar · View at Scopus - T. Zwick, A. Chandrasekhar, C. W. Baks, U. R. Pfeiffer, S. Brebels, and B. P. Gaucher, “Determination of the complex permittivity of packaging materials at millimeter-wave frequencies,”
*IEEE Transactions on Microwave Theory and Techniques*, vol. 54, no. 3, pp. 1001–1009, 2006. View at Publisher · View at Google Scholar · View at Scopus - P. Markos and C. M. Soukoulis, “Left-handed materials,”
*Physical Review B*, vol. 65, Article ID 033401, 2002. View at Google Scholar - D. McGinnis, “PBAR NOTE 585 Measurement of Ralative permittivity and Permeability using Two Port S-parameter technique,” April 1998, http://lss.fnal.gov/archive/pbarnote/fermilab-pbar-note-585.pdf.
- M. T. Le, Q. C. Nguyen, T. P. Vuong, and C. Defay, “New metamaterial structure for the design of a high gain antenna at 5.8 GHz,” in
*Proceedings of the IEEE International Conference on Wireless Information Technology and Systems (ICWITS ’12)*, pp. 1–4, Maui, Hawaii, USA, November 2012. View at Publisher · View at Google Scholar · View at Scopus - M. T. Le, Q. C. Nguyen, T. T. T. Vu, and T. P. Vuong, “Design of an directive antenna for “free-flow” system application,” in
*Proceedings of the IEEE Conference of Advanced Technologies for Communication*, August 2011. - K. Thales,
*Global Specification for Short Range Communication*, Kapsch, Thales, 2003. - CEN, “DIN EN12253,” 2002.
- CEN, “NF EN ISO 14906,” AFNOR, 2005.
- T. J. Cui, “A symmetrical circuit model describing all kinds of circuit metamaterials,”
*Progress in Electromagnetics Research B*, vol. 5, pp. 63–76, 2008. View at Publisher · View at Google Scholar - A. Balanis,
*Antenna Theory Analysis and Design*, John Wiley & Sons, 3rd edition, 2005. - Y. Yusuf and X. Gong, “A low-cost patch antenna phased array with analog beam steering using mutual coupling and reactive loading,”
*IEEE Antennas and Wireless Propagation Letters*, vol. 7, pp. 81–84, 2008. View at Publisher · View at Google Scholar · View at Scopus - N. G. Alexopoulos and I. E. Rana, “Mutual impedance computation between printed dipoles,”
*IEEE Transactions on Antennas and Propagation*, vol. 29, no. 1, pp. 106–111, 1981. View at Google Scholar · View at Scopus