**2. Directivity and bandwidth enhancement of proximity-coupled microstrip antenna**

Directive patch antennas are very popular in electromagnetic community. Their attractive features, such as low profile, light weight, low cost and compatibility with Microwave Monolithic Integrated Circuits (MMICs), do not exist in other antennas.

Two distinctive types of directive antennas are parabolic antennas and large array antennas. Bulk and curved surface of parabolic antennas limits their use in many commercial applications. Also, complex feeding mechanism and loss in the feeding network are two major disadvantages associated with microstrip array antennas.

One solution to these problems is to use metamaterial cover over the patch antenna (Alu et al., 2006; Xu et al., 2008; Zhu et al., 2005; Huang et al., 2009). One of the first works was done by B. Temelkuaran in 2000, (Temelkuaran et al., 2000). In 2002, S. Enoch proposed a kind of metamaterial for directive emission, (Enoch et al., 2002). Another problem associated with microstrip antennas is their narrow bandwidth. The previous works so far (Xu et al., 2008; Zhu et al., 2005; Huang et al., 2009) have dealt only with the enhancement of the antenna directivity using metamaterial cover, but the effect of this cover on the antenna input impedance has not been investigated.

Recently, a new metamaterial cover has been proposed to enhance both the antenna bandwidth and directivity, (Ju et al., 2009). But, its directivity is significantly lower compared to the primary metamaterial cover, (Xu et al., 2008; Zhu et al., 2005; Huang et al., 2009).

In this section, it is demonstrated that both the impedance and directivity bandwidths of the proximity-coupled patch antenna can be enhanced using the metamaterial cover. It is known that proximity-coupled patch antennas are sensitive to the transverse feed point location. In the case at hand, a parasitic microstrip line has been used on the opposite side of the feed line to mitigate this drawback (Jafargholi et al., 2011). The dimensions of the analyzed metamaterial cover are:

$$P = 0.41 \lambda\_{\text{6GHz}} \text{ t} = 0.01 \,\lambda\_{\text{6GHz}} \text{ L} = 0.31 \lambda\_{\text{6GHz}} \text{ l} = 0.49 \lambda\_{\text{6GHz}} \tag{2}$$

Where *λ6GHz* (50mm) denotes the free space wavelength at 6GHz, P is the periodicity, t is the thickness of the metallic grids, *L* is the edge of the square holes and h is the distance between the two sheets which is the same as the distance between the patch antenna and the first sheet.

In the FDTD simulations, a uniform 0.01*λ6GHz* grid size is used. The resulting transmission curve is plotted in Fig.3. As can be seen, this structure has three microwave plasma frequencies at about 5GHz, 5.81GHz and 8.1GHz which make it suitable for the antenna applications. When the aforementioned metamaterial cover is placed over the conventional proximity-coupled patch antenna, the final metamaterial antenna can be approximated by a homogenous medium terminated in a ground plane.

This approximation is similar to that used for the transmission coefficient calculations. It is a simple matter to obtain the surface impedance of this grounded slab as a function of metamaterial parameters. A surface impedance of the grounded slab of thickness *h* is:

Theory and Applications of Metamaterial Covers 281

cover Patch

(a)

Parasitic line

h

h

antenna

(b) Fig. 4. Geometry of a metamaterial proximity-coupled patch antenna, (a) top view and (b)

Reflection coefficient of the proposed metamaterial patch antenna has been simulated and was compared to the one obtained for the conventional proximity-coupled patch antenna in Fig. 5. As revealed in the figure, the antenna return loss is significantly improved compared

The impedance bandwidth of the patch antenna is increased from 2.9% to 5.23% (ranging from 5.649GHz to 5.952GHz). Using the usual formulas mentioned in (Garg et al., 2001), the conventional proximity-coupled patch antenna discussed here has a *TM01* mode resonant frequency of approximately 5.9GHz. The second resonant frequency of the metamaterial patch antenna is obviously due to the *TM01* mode of the conventional patch antenna. (See

Since the metamaterial superstrate disturbs the current distribution of the *TM01* mode, this resonant frequency slightly shifts down to a lower frequency. An interested reader is recommended to refer to (Zhong et al., 1994) for more details. The first resonant frequency is the result of reactive cancellation between the capacitive feeding structure and the inductive

On the other hand, the first resonant frequency is close to the second resonant frequency, which results in broadband operation. The simulation results of Fig. 5 are in good agreement with the theoretical predictions discussed above, which serve to justify the approximations used to model the metamaterial patch antenna as a grounded homogenous

to the reference patch antenna without the metamaterial cover.

cross view.

Main microstrip line

> Foam Substrate

Metamaterial

Fig.5)

medium.

metamaterial cover.

$$Z\_s = j\eta \tan\left(2\pi\hbar \text{ / } \mathcal{X}\right) \tag{3}$$

where *η* and *λ* are the wave impedance and wavelength in the slab, respectively. For the extremely low values of *εeff*, the surface impedance is inductive. In addition, the inductive reactance is *Xl*=*jωL*.

For equivalence we can equate them, leading to the following equation:

$$\text{j\u0L} = \text{j\eta}\tan\left(2\pi\text{h} \mid \text{\u0}\right) \tag{4}$$

Since *εeff*<<1 we can apply the small-angle approximation, so that above equation then becomes *L*=*µ0h*. Consequently, the operation mechanism of this metamaterial based cover can be explained using this equivalent inductance.

In addition, coupling between the feed line and the patch antenna is totally capacitive. And thus, one can expect another resonant frequency due to the reactive cancellation between the capacitive feeding structure and the inductive metamaterial cover. Consequently, an appropriate selection of the coupling capacitor value can result in a broadband operation. To this aim, the metamaterial cover described above is placed over the conventional proximity-coupled patch antenna.

A schematic of proposed metamaterial patch antenna is shown in Fig. 4. In general, the two dielectrics can be of different thicknesses and relative permittivity, but here both dielectrics are 0.762mm Duroid with, *εr*= 2.2. For the case discussed here, the patch of the antenna is rectangular with 12.45mm width and 16mm length.

The distance between the main microstrip line and the parasitic line is also 7mm. Each metamaterial cover composed of 9×9 unit cells, as shown in Fig.4. Consequently, the total size of the dielectric substrate and the metamaterial cover is 184.5mm×184.5mm. Furthermore, the working frequency of the conventional patch antenna is selected at 5.9GHz.

Fig. 3. FDTD simulated transmission of metamaterial cover.

280 Trends in Electromagnetism – From Fundamentals to Applications

where *η* and *λ* are the wave impedance and wavelength in the slab, respectively. For the extremely low values of *εeff*, the surface impedance is inductive. In addition, the inductive

 tan 2 / ( ) π λ

> πλ

(3)

= tan 2 / ( ) (4)

*Zj h <sup>s</sup>* = η

*jL j h*

Since *εeff*<<1 we can apply the small-angle approximation, so that above equation then becomes *L*=*µ0h*. Consequently, the operation mechanism of this metamaterial based cover

In addition, coupling between the feed line and the patch antenna is totally capacitive. And thus, one can expect another resonant frequency due to the reactive cancellation between the capacitive feeding structure and the inductive metamaterial cover. Consequently, an appropriate selection of the coupling capacitor value can result in a broadband operation. To this aim, the metamaterial cover described above is placed over the conventional

A schematic of proposed metamaterial patch antenna is shown in Fig. 4. In general, the two dielectrics can be of different thicknesses and relative permittivity, but here both dielectrics are 0.762mm Duroid with, *εr*= 2.2. For the case discussed here, the patch of the antenna is

The distance between the main microstrip line and the parasitic line is also 7mm. Each metamaterial cover composed of 9×9 unit cells, as shown in Fig.4. Consequently, the total size of the dielectric substrate and the metamaterial cover is 184.5mm×184.5mm. Furthermore, the working frequency of the conventional patch antenna is selected at

<sup>4</sup> 4.5 <sup>5</sup> 5.5 <sup>6</sup> 6.5 <sup>7</sup> 7.5 <sup>8</sup> 8.5 <sup>9</sup> 9.5 <sup>0</sup>

**Frequency[GHz]**

 η

For equivalence we can equate them, leading to the following equation:

can be explained using this equivalent inductance.

rectangular with 12.45mm width and 16mm length.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Fig. 3. FDTD simulated transmission of metamaterial cover.

**Transmission**

proximity-coupled patch antenna.

5.9GHz.

ω

reactance is *Xl*=*jωL*.

Fig. 4. Geometry of a metamaterial proximity-coupled patch antenna, (a) top view and (b) cross view.

Reflection coefficient of the proposed metamaterial patch antenna has been simulated and was compared to the one obtained for the conventional proximity-coupled patch antenna in Fig. 5. As revealed in the figure, the antenna return loss is significantly improved compared to the reference patch antenna without the metamaterial cover.

The impedance bandwidth of the patch antenna is increased from 2.9% to 5.23% (ranging from 5.649GHz to 5.952GHz). Using the usual formulas mentioned in (Garg et al., 2001), the conventional proximity-coupled patch antenna discussed here has a *TM01* mode resonant frequency of approximately 5.9GHz. The second resonant frequency of the metamaterial patch antenna is obviously due to the *TM01* mode of the conventional patch antenna. (See Fig.5)

Since the metamaterial superstrate disturbs the current distribution of the *TM01* mode, this resonant frequency slightly shifts down to a lower frequency. An interested reader is recommended to refer to (Zhong et al., 1994) for more details. The first resonant frequency is the result of reactive cancellation between the capacitive feeding structure and the inductive metamaterial cover.

On the other hand, the first resonant frequency is close to the second resonant frequency, which results in broadband operation. The simulation results of Fig. 5 are in good agreement with the theoretical predictions discussed above, which serve to justify the approximations used to model the metamaterial patch antenna as a grounded homogenous medium.

Theory and Applications of Metamaterial Covers 283

Metamaterial antenna Conventional antenna

4.8 5 5.2 5.4 5.6 5.8 6

Frequency [GHz]


Metamaterial antenna at f=5.6GHz Metamaterial antenna at f=5.7GHz Metamaterial antenna at f=5.8GHz

Conventional antenna

θ [degree]

(a)

2






Directivity [dB]

0

5

10

15

20

Fig. 6. Simulated broadside directivity versus frequency.

4

6

8

10

Directivity [dB]

12

14

16

18

It is necessary to mention that the parasitic line section, used on the opposite side of the feed line, stabilizes the antenna performance at its resonant frequency at the expense of an additional resonance frequency at about 6.24GHz (Jafargholi et al., 2011). By using the metamaterial cover over the patch antenna, the antenna radiation patterns in E- and Hplanes are concentrated in a direction perpendicular to the patch antenna (*θ*=0).

The simulated broadside directivity versus frequency is shown in Fig. 6. As can be seen, the maximum directivity of the patch antenna is increased from 6.25dB to16.16dB using metamaterial cover. The 3dB directivity bandwidth of the metamaterial antenna is also between 5.685GHz and 5.91GHz, or 3.88%.

Fig. 5. Simulated reflection coefficient versus frequency.

The antenna radiation patterns within its bandwidth are also investigated. The E-plane and H-plane patterns of the metamaterial patch antenna at three frequencies (5.7GHz, 5.8GHz and 5.9GHz) have been simulated and were compared to the one obtained for the conventional antenna, at 5.9GHz, in Fig. 7.

Although the radiation pattern of the metamaterial antenna changes a bit at each frequency, the main lobe of the metamaterial antenna at all frequencies (ranging from 5.65 to 5.95GHz) is in the broadside direction and maximum directivity is reasonably good. The variation of the radiation pattern is mainly attributed to the nature of metamaterial cover.

The maximum directivities of the metamaterial antenna at 5.7GHz and 5.9GHz are 13.24dB and 14dB, respectively. The maximum directivity of an aperture antenna is calculated by *Dmax*=4*πA*/*λ*2. In the present case, the area of the aperture is A=and λ=c0/f0= 51.724mm, so that maximum directivity then becomes *Dmax*= 22dB.

The maximum directivity of the metamaterial patch antenna, occurring at 5.81GHz, (16.16dB) has approached the maximal directivity obtained, theoretically, with the same aperture size.

282 Trends in Electromagnetism – From Fundamentals to Applications

It is necessary to mention that the parasitic line section, used on the opposite side of the feed line, stabilizes the antenna performance at its resonant frequency at the expense of an additional resonance frequency at about 6.24GHz (Jafargholi et al., 2011). By using the metamaterial cover over the patch antenna, the antenna radiation patterns in E- and H-

The simulated broadside directivity versus frequency is shown in Fig. 6. As can be seen, the maximum directivity of the patch antenna is increased from 6.25dB to16.16dB using metamaterial cover. The 3dB directivity bandwidth of the metamaterial antenna is also

The antenna radiation patterns within its bandwidth are also investigated. The E-plane and H-plane patterns of the metamaterial patch antenna at three frequencies (5.7GHz, 5.8GHz and 5.9GHz) have been simulated and were compared to the one obtained for the

5 5.2 5.4 5.6 5.8 6 6.2 6.4

 **Frequency[GHz]**

X: 5.952 Y: -10.02

> Second resonant frequency

Although the radiation pattern of the metamaterial antenna changes a bit at each frequency, the main lobe of the metamaterial antenna at all frequencies (ranging from 5.65 to 5.95GHz) is in the broadside direction and maximum directivity is reasonably good. The variation of

The maximum directivities of the metamaterial antenna at 5.7GHz and 5.9GHz are 13.24dB and 14dB, respectively. The maximum directivity of an aperture antenna is calculated by *Dmax*=4*πA*/*λ*2. In the present case, the area of the aperture is A=and λ=c0/f0= 51.724mm, so

The maximum directivity of the metamaterial patch antenna, occurring at 5.81GHz, (16.16dB) has approached the maximal directivity obtained, theoretically, with the same

the radiation pattern is mainly attributed to the nature of metamaterial cover.

planes are concentrated in a direction perpendicular to the patch antenna (*θ*=0).

X: 5.649 Y: -10.01

Conv. Ant MTM Ant First resonant frequency

between 5.685GHz and 5.91GHz, or 3.88%.

Fig. 5. Simulated reflection coefficient versus frequency.

that maximum directivity then becomes *Dmax*= 22dB.

aperture size.

conventional antenna, at 5.9GHz, in Fig. 7.




 **|S11|[dB]**



0

Fig. 6. Simulated broadside directivity versus frequency.

Theory and Applications of Metamaterial Covers 285

top of the one-layer metamaterial cover. In this section, instead of using meander line or metallic wire polarizer, the geometry of the metamaterial cover is changed to provide circular polarization. Consequently, the second layer (polarizer layer) can be replaced with

Moreover, in contrast to the previous directive circularly polarized antennas (Iriarte et al., 2006; Diblanc et al., 2005; Arnaud et al., 2007), polarization state of the directive antennas using our proposed metamaterial cover can be mechanically changed regardless of the feed

In this section, a useful guideline has been established as how to use the magnitude and phase of the transmission coefficient to identify the operational frequency band of the directive circularly polarized antennas based on polarization dependent metamaterial

As revealed in the previous sections, when a plane wave normally impinges upon a metamaterial cover, the phase and magnitude of the transmitted wave change with frequency. In order to illustrate the polarization feature of the PDMTM cover, we assume

*<sup>i</sup> jkz jkz E a e ja e x y* − − = +

where *k* is the free-space wavenumber, is normally impinged upon a director placed in *X*-*Y* plane. The field transmitted through the director can be easily calculated from the following

> ( ) ( ) *y x <sup>x</sup> <sup>j</sup> <sup>t</sup> jkz j E e e a ja e x y* <sup>−</sup> θ

<sup>−</sup> <sup>=</sup> +

*jy x jy x <sup>t</sup> jkz j x <sup>r</sup> <sup>l</sup> e e Ee e e e* θ θ

> ( ) <sup>2</sup> , *x y*

*a ja*

− − <sup>−</sup> − + = +

*<sup>e</sup>* <sup>=</sup> <sup>+</sup> ( )

and *θx* and *θy* denote the transmission phases for the *x*- and *y*-polarized waves, respectively. For a traditional metamaterial cover (*θy*- *θx*=0), the transmitted wave is purely LHCP and thus the polarization does not change. In order to change the polarization state of the antenna, the PDMTM cover can be used as a director. At a certain frequency where phase difference is 180° and transmission is considerable, the transmitted wave is purely right-

The left-hand circularly polarized incident wave can be also converted to the linearly polarized (LP) wave where the phase difference is 90° and the transmission is also considerable. One can follow the same procedure for the linearly polarized incident wave,

The above field can be decomposed into two circularly polarized components

θ

*l*

θ θ

() () 1 1 [ ( ) ( )] 2 2

2 *x y <sup>r</sup> <sup>a</sup> ja e* <sup>−</sup> <sup>=</sup> 

(5)

θ θ

(6)

another metamaterial cover layer, which in turn results in higher directivity.

that a left-hand circularly polarized (LHCP) wave, namely,

mechanism.

covers.

equation:

Where

hand circularly polarized (RHCP).

, *<sup>i</sup> jkz jkz E ae ae x y* − − = +

Fig. 7. CST simulated radiation patterns at different frequencies over the operating bandwidth, (a) E-plane, and (b) H-plane.
