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

Authors: Minh Thuy Le; Quoc Cuong Nguyen; Tan Phu Vuong
Journal: International Journal of Antennas and Propagation
 (2014)

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## 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 S11 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.


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## Body

## 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 (ε<0) and/or negative permeability (μ<0). The MTM is called double-negative material (DNM) or left-handed material (LHM) when it has double-negative ε and μ. 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 λ0 where λ0 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 (n) and their wave vector k is also called the “backward wave.” Evanescent materials are the other type of MTMs with single negative ε<0 or μ<0 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 d=λ0/7.5 (dx×dy×dz). Ziolkowski then successfully investigated and realized some slabs of planar LHM structures that comprised a substrate Duroid 5880 (hsub=0.8 mm) with embedded strip line operating at the X 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 d=λ0/6 (dx×dy×hsub). The other LHM structure, the “Ω shaped,” was first suggested in 1992 by Saadoun and Engheta [7]. In 1997, Simovski et al. presented “Ω” shaped LHM unit-cell in 3D with the dimension of d=λ0/9 (dx×dy×dz), 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 “Ω” shaped LHM unit-cell in 2D in [9]; then the “Ω” shaped LHM unit-cell in 2D was fabricated in 2008 [10] with the dimension of d=λ0/6.5 (dx×dy×hsub) using Roger Duroid substrate. The new planar “S” shaped LHM unit-cell was investigated by Chen et al. in [11] with the dimension of λ/5×λ/9.7×hsub, but this LHM could not be smaller than λ0/6,5 (see Table 1).Table 1
Review of LHM structures.
LHM structure (3D)
Planar LHM structure (2D)
SSRR-TMW LHM [4, 5]
SSRR-TMW LHM [6]
f = 5 GHz
f = 9.6 GHz
Size: 8 × 8 × 8 mm3~λ0/7.5
Size: 4.55 × 5.05 mm2~λ0/6
Ω  shaped LHM [8]
Ω  shaped LHM [10]
f = 8.35 GHz
f = 13 GHz
Size: 4 × 4 × 4 mm3~λ0/9
Size: 3.3 × 4.1 mm2~λ0/6.5
S shaped LHM [11]
f = 11 GHz
Size: 5.2 × 2.8 mm2~λ0/5×λ0/9.7
Our FL-LHM
f = 5.8 GHz
Size: 4.3 × 4.3 mm2~λ0/9.5Table 2
Parameters of new FL-LHM in Figures1 and 3.
Symbol
Value
w
0.25 (mm)
l
28.25 (mm)
g
0.25 (mm)
s
2 (mm) (gap between two folded lines)
A
x
4.3 (mm)
A
y
4.3 (mm)
d
x
5.3 (mm) (dimension of a unit-cell inx direction)
d
y
5.3 (mm) (dimension of a unit-cell iny direction)
ε
r
3.55 permittivity of substrate (3.55 +j0.0027)
μ
r
Permeability of substrateIn addition, the negative effective permittivity, permeability, and refraction index can be extracted from averageH-field andE-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 S 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 ε and μ from S parameters based on the numerical LHM unit-cell model. This FL-LHM unit-cell has a smallest dimension of λ0/9.5 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 Section3. 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 ofNx×Ny FL-LHM unit-cells in x and y 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 Figure1.Figure 1
LHM substrate is created by periodic arrays of LHM unit-cells (left) and the equivalent circuit of a unit-cell (right); excitation waves (from the reference antenna) are coming to LHM substrate inz direction.According to this circuit, the resonant frequency of unit-cell can be estimated using the formulaf=1/2πLtCt, where Lt and Ct denote total inductance and total capacitance of unit-cell, respectively:
(1)Lt=Lself+2Lmutual,Ct=Cself+Cmutual2.
The gap s 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 Lt has been split into series (Ls) and parallel (Lp) components, similarly for the total capacitance Ct.Figure 2
LHM unit-cell is described by symmetrical circuit model.L
s depends on the total length of conductor line l and its value is dominant in series impedance (Zs). On the other hand, Cp depends on area of parallel surface between two conductor faces; its value is dominant in shunt admittance (Yp) and depends on the “common” parallel area. As consequence, we can change the total length of line (l) or the “common” parallel area to achieve desired resonant frequency. This means the higher the l 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
(2)Zs=-jωLs-1jωCs,YP=-jωCp-1jωLp.The effective permittivity and permeability of unit-cell in this model in Figure2 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:
(3)In+1=Inejβ,Vn+1=Vnejβ,
where β is the phase crossing through unit-cell n:
(4)β=kp,where  k is the wave vector in the unit-cell and p is the dimension of the periodic unit-cell. As in Figure 1, p=dx=dy=d.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:
(5)μeff=ωLs-(1/ωCs)2ωpβtan(β/2),εeff=2βtan(β/2)(ωLs-(1/ωCs))ωp.The phase crossing through one unit-cellβ in (4) can be now obtained by (6) with the boundary condition in (7):
(6)sin2(β2)=Zs′Yp′4,(7)0≤Zs′Yp′4≤1⟺0≤Zs′Yp′≤4,
where Zs′, Yp′ are real numbers; they can be negative or positive depending on the values of Ls, Cs and Lp, Cp as follows:
(8)Zs′=ωLs-1ωCs,Yp′=ωCp-1ωLp.The wave impedance of LHM unit-cell is(9)Z=VnIn=12Zs′tan(β/2).From (5) we can summarize that a LHM unit-cell can be obtained by choosing suitable values of Ls, Cs and Lp, Cp under the condition in (7) combined with (10):
(10)ωLs<1ωCs.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-cell5.8×109=1/2πLtCt, we suppose that Lt and Ct are defined as Ls=32.73 nH, Cs=0.018 pF, and Cp=0.95 pF with ωCp<1/ωLp. 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 ofw=0.25mm and the total length of l=28.25 mm (around λ0/2) 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 4.3×4.3 mm2 (λ0/9.5) by using meander line structure in y direction as in Figures 3(a) and 3(c) to reduce the dimension.(ii)
The separation between two unit-cells is ofs=2mm.(iii)
Two conductor lines are maintained parallel to each other by the substrate dielectric Roger 4003 that has thickness ofhsub=0.8mm, permittivity of εr=3.5, permeability of μr=1, and loss tangent of tanδ=0.0027. The “common” parallel area between these two conductors is defined as in Figure 3(b).New FL-LHM unit-cell structure for resonant frequency at 5.8 GHz: (a) front view of FL-LHM unit-cell; (b) “common” parallel area of unit-cell; (c) back view; (d) side view. The details of parameters are summarized in Table2.
(a)
(b)
(c)
(d)The novel FL-LHM has both negative effective permittivity and permeability which are denoted byεeff and μeff. 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 ofL and C 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.(a) FL-LHM antenna model which improves the antenna gain by FL-LHM substrate. The reference antenna makes excitation for FL-LHM substrate. The solid red line represents the forward wave and the dotted blue line indicates the wave reflected at the back FL-LHM. (b) Numerical FL-LHM unit-cell model for simulation.
(a)
(b)Figure4(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 -θ to θ. The released wave from a FL-LHM is propagating in +z 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 Figure4(b). The FL-LHM unit-cell is excited by an incidence wave in z 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 (-90°<θ<90°). The released wave from a FL-LHM is propagating in +z direction. Hence, zmax⁡ 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 x=xmin⁡ and x=xmax⁡ and y=ymin⁡ and y=ymax⁡ 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 θ are calculated as in Figures 5 and 6 using commercial electromagnetic software CST Microwave Studio 2012. The effective εeff, μeff and refractive index n of FL-LHM can be extracted from S 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.Electric and magnetic field distribution in FL-LHM unit-cell.
(a)
(b)Figure 6
Reflection and transmission coefficient in dB of FL-LHM unit-cell under an incident wave at angle of 0° and 45°.


### 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 Figure7.Figure 7
Wave propagation of an infinite slab FL-LHM in free space.As we presented in Section2.2, the reflection and transmission coefficients (S11 and S21) of the FL-LHM unit-cell that are created from Section 2.1, according to [9, 16], are given by these equations:
(11)S11=b1a1=(1-T2)R1-R2T2,S21=a2a1=(1-R2)T1-R2T2,
where R is the reflection coefficient of an incident wave on the interface between free space and FL-LHM, whereas T is the transmission term through the FL-LHM slab:
(12)R=Z-Z0Z+Z0=z-1z+1,T=e-jk0nd,
where Z0, k0 are wave impedance and wave number in free space, respectively. The normalized wave impedance z=Z/Z0 and refractive index n of the FL-LHM can be expressed in terms of scattering parameters as
(13)z=±(1+S11)2-S212(1-S11)2-S212,n=-1k0d{[[ln⁡⁡(T)]′′+2mπ]-j[ln⁡⁡(R)]′},
where m is an integer related to the branch index of n′ (principal value of m=0) and the transmission term as a function of scattering parameters is given by [14]
(14)T=1-S112+S2122S21±j1-(1-S112+S2122S21)2.The effective permittivity and permeability of the FL-LHM are directly calculated from the refractive indexn and normalized impedance z:
(15)εeff=nz;μeff=nz.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 S 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 S parameters results. Because of the periodic structure, we only consider the varying incident angle from 0° to 90°; the results are repeated with -90°<θ<0°. S parameters at any angle are shown in Figure 8. We found that S 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 S 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.Figure 8
Reflection and transmission coefficients of FL-LHM unit-cell under incident wave at any direction from 0° to 90°.From theS 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 εeff and μeff 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 -45°≤θ≤45° as in Figures 9 and 10.Effective permittivity (a) and permeability (b) of FL-LHM unit-cell under an incident wave of 45° extracted fromS parameters correspondent.
(a)
(b)Effective refraction index (a) and normalized impedance (b) of FL-LHM unit-cell under an incident wave of 45° extracted correspondent.
(a)
(b)Figure 11
Effective permittivity values are obtained with varying incident wave.Effective permeability (a) and refraction index (b) values are obtained with varying incident wave.
(a)
(b)


## 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 Figure1.Figure 1
LHM substrate is created by periodic arrays of LHM unit-cells (left) and the equivalent circuit of a unit-cell (right); excitation waves (from the reference antenna) are coming to LHM substrate inz direction.According to this circuit, the resonant frequency of unit-cell can be estimated using the formulaf=1/2πLtCt, where Lt and Ct denote total inductance and total capacitance of unit-cell, respectively:
(1)Lt=Lself+2Lmutual,Ct=Cself+Cmutual2.
The gap s 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 Lt has been split into series (Ls) and parallel (Lp) components, similarly for the total capacitance Ct.Figure 2
LHM unit-cell is described by symmetrical circuit model.L
s depends on the total length of conductor line l and its value is dominant in series impedance (Zs). On the other hand, Cp depends on area of parallel surface between two conductor faces; its value is dominant in shunt admittance (Yp) and depends on the “common” parallel area. As consequence, we can change the total length of line (l) or the “common” parallel area to achieve desired resonant frequency. This means the higher the l 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
(2)Zs=-jωLs-1jωCs,YP=-jωCp-1jωLp.The effective permittivity and permeability of unit-cell in this model in Figure2 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:
(3)In+1=Inejβ,Vn+1=Vnejβ,
where β is the phase crossing through unit-cell n:
(4)β=kp,where  k is the wave vector in the unit-cell and p is the dimension of the periodic unit-cell. As in Figure 1, p=dx=dy=d.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:
(5)μeff=ωLs-(1/ωCs)2ωpβtan(β/2),εeff=2βtan(β/2)(ωLs-(1/ωCs))ωp.The phase crossing through one unit-cellβ in (4) can be now obtained by (6) with the boundary condition in (7):
(6)sin2(β2)=Zs′Yp′4,(7)0≤Zs′Yp′4≤1⟺0≤Zs′Yp′≤4,
where Zs′, Yp′ are real numbers; they can be negative or positive depending on the values of Ls, Cs and Lp, Cp as follows:
(8)Zs′=ωLs-1ωCs,Yp′=ωCp-1ωLp.The wave impedance of LHM unit-cell is(9)Z=VnIn=12Zs′tan(β/2).From (5) we can summarize that a LHM unit-cell can be obtained by choosing suitable values of Ls, Cs and Lp, Cp under the condition in (7) combined with (10):
(10)ωLs<1ωCs.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-cell5.8×109=1/2πLtCt, we suppose that Lt and Ct are defined as Ls=32.73 nH, Cs=0.018 pF, and Cp=0.95 pF with ωCp<1/ωLp. 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 ofw=0.25mm and the total length of l=28.25 mm (around λ0/2) 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 4.3×4.3 mm2 (λ0/9.5) by using meander line structure in y direction as in Figures 3(a) and 3(c) to reduce the dimension.(ii)
The separation between two unit-cells is ofs=2mm.(iii)
Two conductor lines are maintained parallel to each other by the substrate dielectric Roger 4003 that has thickness ofhsub=0.8mm, permittivity of εr=3.5, permeability of μr=1, and loss tangent of tanδ=0.0027. The “common” parallel area between these two conductors is defined as in Figure 3(b).New FL-LHM unit-cell structure for resonant frequency at 5.8 GHz: (a) front view of FL-LHM unit-cell; (b) “common” parallel area of unit-cell; (c) back view; (d) side view. The details of parameters are summarized in Table2.
(a)
(b)
(c)
(d)The novel FL-LHM has both negative effective permittivity and permeability which are denoted byεeff and μeff. 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 ofL and C 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.(a) FL-LHM antenna model which improves the antenna gain by FL-LHM substrate. The reference antenna makes excitation for FL-LHM substrate. The solid red line represents the forward wave and the dotted blue line indicates the wave reflected at the back FL-LHM. (b) Numerical FL-LHM unit-cell model for simulation.
(a)
(b)Figure4(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 -θ to θ. The released wave from a FL-LHM is propagating in +z 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 Figure4(b). The FL-LHM unit-cell is excited by an incidence wave in z 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 (-90°<θ<90°). The released wave from a FL-LHM is propagating in +z direction. Hence, zmax⁡ 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 x=xmin⁡ and x=xmax⁡ and y=ymin⁡ and y=ymax⁡ 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 θ are calculated as in Figures 5 and 6 using commercial electromagnetic software CST Microwave Studio 2012. The effective εeff, μeff and refractive index n of FL-LHM can be extracted from S 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.Electric and magnetic field distribution in FL-LHM unit-cell.
(a)
(b)Figure 6
Reflection and transmission coefficient in dB of FL-LHM unit-cell under an incident wave at angle of 0° and 45°.


## 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 Figure7.Figure 7
Wave propagation of an infinite slab FL-LHM in free space.As we presented in Section2.2, the reflection and transmission coefficients (S11 and S21) of the FL-LHM unit-cell that are created from Section 2.1, according to [9, 16], are given by these equations:
(11)S11=b1a1=(1-T2)R1-R2T2,S21=a2a1=(1-R2)T1-R2T2,
where R is the reflection coefficient of an incident wave on the interface between free space and FL-LHM, whereas T is the transmission term through the FL-LHM slab:
(12)R=Z-Z0Z+Z0=z-1z+1,T=e-jk0nd,
where Z0, k0 are wave impedance and wave number in free space, respectively. The normalized wave impedance z=Z/Z0 and refractive index n of the FL-LHM can be expressed in terms of scattering parameters as
(13)z=±(1+S11)2-S212(1-S11)2-S212,n=-1k0d{[[ln⁡⁡(T)]′′+2mπ]-j[ln⁡⁡(R)]′},
where m is an integer related to the branch index of n′ (principal value of m=0) and the transmission term as a function of scattering parameters is given by [14]
(14)T=1-S112+S2122S21±j1-(1-S112+S2122S21)2.The effective permittivity and permeability of the FL-LHM are directly calculated from the refractive indexn and normalized impedance z:
(15)εeff=nz;μeff=nz.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 S 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 S parameters results. Because of the periodic structure, we only consider the varying incident angle from 0° to 90°; the results are repeated with -90°<θ<0°. S parameters at any angle are shown in Figure 8. We found that S 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 S 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.Figure 8
Reflection and transmission coefficients of FL-LHM unit-cell under incident wave at any direction from 0° to 90°.From theS 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 εeff and μeff 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 -45°≤θ≤45° as in Figures 9 and 10.Effective permittivity (a) and permeability (b) of FL-LHM unit-cell under an incident wave of 45° extracted fromS parameters correspondent.
(a)
(b)Effective refraction index (a) and normalized impedance (b) of FL-LHM unit-cell under an incident wave of 45° extracted correspondent.
(a)
(b)Figure 11
Effective permittivity values are obtained with varying incident wave.Effective permeability (a) and refraction index (b) values are obtained with varying incident wave.
(a)
(b)


## 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 inx, y directions), metamaterial technology (only changing dimension in z 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 S11 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 Section2, especially in Figure 4(a), when a RA is covered by a suitable FL-LHM substrate at the height h=λ0/2, the RA gain will be improved and the LHM antenna is always well matched at operating frequency. In general, dimensions of FL-LHM substrate (Lx,Ly) are proportional to the angular width of RA and the air-gap height of h 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 of46×46×0.8 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 ARRA=Emax⁡/Emin⁡=-0.08dB. This antenna gain is 6.5 dBi and reflection coefficient S11 at 5.8 GHz is −20 dB and −15 dB in simulation and measurement, respectively.Prototype of FL-LHM antenna: (a) circularly polarized patch reference antenna; (b) prototype of FL-LHM antenna.
(a)
(b)Our study shows that FL-LHM antenna is well matched with air-gap heights from 28 to 31 mm (Figure14). In this case, dimensions of fabricated FL-LHM substrate are defined by Lx=Ly=46 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 ARLHM-A=-0.12dB and highest gain (Figure 15) while S11<-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.Figure 14
Reflection coefficients of antenna with varying air-gap height.Figure 15
Gain versus air-gap height at 5.8 GHz.Figure 16
Reflection coefficients of FL-LHM antenna withh=30 mm in simulation and measurement.Figure 17
Axial ratio of reference antenna and FL-LHM antenna.Figure 18
Radiation pattern of fabricated FL-LHM antenna in simulation and measurement.


### 3.2. Antenna Arrays Gain Enhancement

From the patch antenna designed in Section3.1, an array of 2×2 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).Figure 19
Structure of FL-LHM antenna arrays using 1–4-feed structure.Figure 20
Prototype of FL-LHM antenna arrays with dimensions of90×90×30 mm3.When this antenna is covered by FL-LHM substrate with the air-gap heighth=30 mm, the S11 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.Figure 21
Reflection coefficients of FL-LHM antenna arrays withh=30 mm in simulation and measurement.Figure 22
Radiation pattern of fabricated FL-LHM antenna arrays in simulation and measurement.


### 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) inx 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 C2 and C3, respectively. The mutual couplings between three patches are proportional to the distanceds between them [29]. The current magnitude on the passive radiator is larger whends is smaller so that the gain will be increased.Structure of FL-LHM beam steering antenna: (a) beam steering reference antenna; (b) FL-LHM beam steering antenna withh=30 mm.
(a)
(b)The phases shifted between antenna elements are turned by changing the reactive load. We denote byI1 the current on the active patch; I2 and I3 are the induced currents on passive patches P2 and P3, respectively. The array factor is given by [28]
(16)AF=∑i=13|IiI1|ej(k*dx*sinθ+ang(Ii/I1)).The steering of reference antenna is described in the following three cases (Figures24 and 25).(i)
Case  1:C2=C3=0.2 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:C2=2 pF and C3=0.2 pF; the main lobe is steered at theta of 20°. Case  2 is presented in green color.(iii)
Case  3: inversely, ifC2=0.2 pF and C3=2 pF, the main lobe is steered at theta of −20°. Case  3 is represented in blue color.(a) Reflection coefficients of beam steering reference antenna in simulation. (b) Reflection coefficients of beam steering reference antenna in measurement.
(a)
(b)(a) Radiation pattern of beam steering RA in simulation. Beam steering horizontally; steering angles: −20° (case 2), 0° (case 1), and 20° (case 3). (b) Radiation pattern of beam steering RA in measurement. Beam steering horizontally; steering angles: −20° (case 2), 0° (case 1), and 20° (case 3).
(a)
(b)Figures24 and 25 represent the S11 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 (S11simulation=-15 dB, S11measurement=-20 dB); the peak of S11 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).Table 3
Parameters of LHM beam steering antenna at 5.8 GHz as in Figure23.
Symbol
Value
W
1
=
L
1
14 (mm)
ds
3 (mm) (gap between two patches)
y
e
5 (mm)
x
f
0.5 (mm)
W
2
1.7 (mm)
l
2 (mm)
h
30 (mm)
x
sub
30 (mm) (substrate Roger 4003)
y
sub
90 (mm)The enhancement gain will be obtained when beam steering antenna is covered by the FL-LHM substrate as in Figure23(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.(a) Reflection coefficients of FL-LHM beam steering antenna withh=30 mm in simulation. (b) Reflection coefficients of FL-LHM beam steering antenna with h=30 mm in measurement.
(a)
(b)The reflection coefficientS11 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 30×90×30 mm3.(a) Radiation pattern of FL-LHM beam steering antenna withh=30 mm in simulation. Beam steering horizontally; steering angles: −10° (case 2), 0° (case 1), and 10° (case 3). (b) Radiation pattern of FL-LHM beam steering antenna with h=30 mm in measurement. Beam steering horizontally; steering angles: −10° (case 2), 0° (case 1), and 10° (case 3).
(a)
(b)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 (Figure27(a)).In measurement, the gain obtained is 11.6 dBi for case 1 and 10 dBi for cases 2 and 3 (Figure27(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.Table4 resumes the simulation and measurement results of FL-LHM beam steering antenna in three cases.Table 4
Simulation and measurement results of LHM beam steering antenna.
f = 5.8 GHz
LHM beam steering antenna(30 × 90 × 30 mm3)
Case 1
Case 2
Case 3
Sim.
Meas.
Sim.
Meas.
Sim.
Meas.
S
11 (dB)
−20
−15
−11
−27
−10
−24
BW(MHz)
277
250
179
120
194
140
Peak gain (dBi)
12
11.6
11.1
10
11
9.8
Δ
G (dBi)
3.8
3.3
3.4
2.5
3.2
2.3
Sim.: simulation.
Meas.: measurement.
BW: bandwidth.
Δ
G: increased gain by using FL-LHM substrate (compared with RA).


## 3.1.  Circularly Polarized Patch Antenna Gain Enhancement

A circularly polarized rectangular patch antenna with dimensions of46×46×0.8 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 ARRA=Emax⁡/Emin⁡=-0.08dB. This antenna gain is 6.5 dBi and reflection coefficient S11 at 5.8 GHz is −20 dB and −15 dB in simulation and measurement, respectively.Prototype of FL-LHM antenna: (a) circularly polarized patch reference antenna; (b) prototype of FL-LHM antenna.
(a)
(b)Our study shows that FL-LHM antenna is well matched with air-gap heights from 28 to 31 mm (Figure14). In this case, dimensions of fabricated FL-LHM substrate are defined by Lx=Ly=46 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 ARLHM-A=-0.12dB and highest gain (Figure 15) while S11<-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.Figure 14
Reflection coefficients of antenna with varying air-gap height.Figure 15
Gain versus air-gap height at 5.8 GHz.Figure 16
Reflection coefficients of FL-LHM antenna withh=30 mm in simulation and measurement.Figure 17
Axial ratio of reference antenna and FL-LHM antenna.Figure 18
Radiation pattern of fabricated FL-LHM antenna in simulation and measurement.


## 3.2. Antenna Arrays Gain Enhancement

From the patch antenna designed in Section3.1, an array of 2×2 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).Figure 19
Structure of FL-LHM antenna arrays using 1–4-feed structure.Figure 20
Prototype of FL-LHM antenna arrays with dimensions of90×90×30 mm3.When this antenna is covered by FL-LHM substrate with the air-gap heighth=30 mm, the S11 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.Figure 21
Reflection coefficients of FL-LHM antenna arrays withh=30 mm in simulation and measurement.Figure 22
Radiation pattern of fabricated FL-LHM antenna arrays in simulation and measurement.


## 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) inx 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 C2 and C3, respectively. The mutual couplings between three patches are proportional to the distanceds between them [29]. The current magnitude on the passive radiator is larger whends is smaller so that the gain will be increased.Structure of FL-LHM beam steering antenna: (a) beam steering reference antenna; (b) FL-LHM beam steering antenna withh=30 mm.
(a)
(b)The phases shifted between antenna elements are turned by changing the reactive load. We denote byI1 the current on the active patch; I2 and I3 are the induced currents on passive patches P2 and P3, respectively. The array factor is given by [28]
(16)AF=∑i=13|IiI1|ej(k*dx*sinθ+ang(Ii/I1)).The steering of reference antenna is described in the following three cases (Figures24 and 25).(i)
Case  1:C2=C3=0.2 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:C2=2 pF and C3=0.2 pF; the main lobe is steered at theta of 20°. Case  2 is presented in green color.(iii)
Case  3: inversely, ifC2=0.2 pF and C3=2 pF, the main lobe is steered at theta of −20°. Case  3 is represented in blue color.(a) Reflection coefficients of beam steering reference antenna in simulation. (b) Reflection coefficients of beam steering reference antenna in measurement.
(a)
(b)(a) Radiation pattern of beam steering RA in simulation. Beam steering horizontally; steering angles: −20° (case 2), 0° (case 1), and 20° (case 3). (b) Radiation pattern of beam steering RA in measurement. Beam steering horizontally; steering angles: −20° (case 2), 0° (case 1), and 20° (case 3).
(a)
(b)Figures24 and 25 represent the S11 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 (S11simulation=-15 dB, S11measurement=-20 dB); the peak of S11 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).Table 3
Parameters of LHM beam steering antenna at 5.8 GHz as in Figure23.
Symbol
Value
W
1
=
L
1
14 (mm)
ds
3 (mm) (gap between two patches)
y
e
5 (mm)
x
f
0.5 (mm)
W
2
1.7 (mm)
l
2 (mm)
h
30 (mm)
x
sub
30 (mm) (substrate Roger 4003)
y
sub
90 (mm)The enhancement gain will be obtained when beam steering antenna is covered by the FL-LHM substrate as in Figure23(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.(a) Reflection coefficients of FL-LHM beam steering antenna withh=30 mm in simulation. (b) Reflection coefficients of FL-LHM beam steering antenna with h=30 mm in measurement.
(a)
(b)The reflection coefficientS11 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 30×90×30 mm3.(a) Radiation pattern of FL-LHM beam steering antenna withh=30 mm in simulation. Beam steering horizontally; steering angles: −10° (case 2), 0° (case 1), and 10° (case 3). (b) Radiation pattern of FL-LHM beam steering antenna with h=30 mm in measurement. Beam steering horizontally; steering angles: −10° (case 2), 0° (case 1), and 10° (case 3).
(a)
(b)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 (Figure27(a)).In measurement, the gain obtained is 11.6 dBi for case 1 and 10 dBi for cases 2 and 3 (Figure27(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.Table4 resumes the simulation and measurement results of FL-LHM beam steering antenna in three cases.Table 4
Simulation and measurement results of LHM beam steering antenna.
f = 5.8 GHz
LHM beam steering antenna(30 × 90 × 30 mm3)
Case 1
Case 2
Case 3
Sim.
Meas.
Sim.
Meas.
Sim.
Meas.
S
11 (dB)
−20
−15
−11
−27
−10
−24
BW(MHz)
277
250
179
120
194
140
Peak gain (dBi)
12
11.6
11.1
10
11
9.8
Δ
G (dBi)
3.8
3.3
3.4
2.5
3.2
2.3
Sim.: simulation.
Meas.: measurement.
BW: bandwidth.
Δ
G: increased gain by using FL-LHM substrate (compared with RA).


## 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. TheS11 and radiation pattern results in measurement of three FL-LHM antennas are well fit with simulation results.



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*Source: 302580-2014-09-16.xml*