2.1. Design of the Conventional Patch Antenna
The top plane of the designed conventional antenna in HFSS is depicted in Figure 1. It consists of ground, substrate and patch respectively. The ground is below the substrate and the patch is on the substrate. The inset cuts on the both sides of the microstrip transmission feedline give the impedance matching between antenna and transmission feedline. The materials of patch as well as ground are copper and the substrate is taken as FR4. The permittivity and the thickness are 4.4 and 1.6 mm respectively. The length and width of the microstrip feedline has a length of 6.5 mm and width 1.
The length and width of patch and substrate are calculated using following Eqs. (1)(6) as described in [4]. The dimensions are shown in Table 1
\(\text{W}=\frac{{\upsilon }_{0} }{2{f}_{r} }\sqrt{\frac{2}{{ϵ}_{r}+1}}\) (1)
\(L=\frac{{\upsilon }_{0}}{2{f}_{r}\sqrt{{ϵ}_{reff}} }2\varDelta L\) (2)
$${ϵ}_{reff}=\frac{{ϵ}_{r}+1}{2}+ \frac{{ϵ}_{r}1}{2}{\left[1+12\frac{h}{w} \right]}^{\frac{1}{2}}$$
3
$$\varDelta L=h0.412\frac{\left({ϵ}_{reff} + 0.3\right) \left(\frac{W}{h} + 0.264\right)}{\left({ϵ}_{reff } 0.258\right) \left(\frac{W}{h} + 0.8\right)}$$
4
\(\text{W}\) is the width of the patch
\(\varDelta L\) is extension of length of the patch
\(L\) is the length of the patch
\({f}_{r}\) is the resonant frequency
υ0 is the speed of light
\(h\) is the thickness of dielectric substrate
\({ϵ}_{r}\) is the dielectric constant of substrate
\({ϵ}_{reff}\) is the effective dielectric constant
Table 1
Dimensions of microstrip patch antenna
Parameters

Dimensions (In mm)

\(\text{W}\)

9.15

\(L\)

6.4

\({W}_{s}\)

18.75

\({L}_{s}\)

16

2.2 Design of The Unit Cell
The unit cell is designed with FR4 substrate with relative permittivity 4.4. The length and width of substrate are 2.5 mm and 2.5 mm respectively. The length outermost square is 2.5 mm and the length of inner most square is 1.5 mm as shown in Fig. 2.2. The line width of each ring is 0.2 mm. The gap between two rings is 1.5 mm. The split in each ring is 0.3 mm and they are opposite to each other. The perfect electric plane and the perfect magnetic plane are assigned to Z and Y axes and the excitation is given to X axis as shown in Fig. 2.1. The dimensions of the unit cell are shown in Fig. 2.2. A wire is also place below the substrate for metamaterial properties extractions.
2.3 Extraction of Metamaterial Properties
Figure 2.3 shows transmission and reflection coefficient of unit cell. The unit cell resonates at 9.4 GHz and the S11 and S12 curves intersect each other at 9.9 GHz. The unit cell has permeability negative properties in the range of 9.8 GHZ to 11.6 GHz as shown in Fig. 2.5. The imaginary value of permittivity of unit cell is negative from 9.5 GHz to 1.5 GHz as show in Fig. 2.6. The effective refractive index is also near to zero as shown in Fig. 2.4. All the parameter mentioned blow are calculated using the following Eqs. (7)(10) as described in [5].
$${n}_{eff}=j.ln\left\{\frac{{s}_{21}}{1{s}_{11}\left(\frac{z1}{z+1}\right)}\right\}\frac{1}{{k}_{0}d}$$
7
$${z}_{eff}=\pm \sqrt{\frac{{\left(1+{s}_{11}\right)}^{2}{{s}^{2}}_{21}}{{\left(1{s}_{11}\right)}^{2}{{s}^{2}}_{21}}}$$
8
$${\mu }_{eff}={n}_{eff}.{z}_{eff}$$
9
$${ϵ}_{eff}=\frac{{n}_{eff}}{{z}_{eff}}$$
10
\({n}_{eff}\) is the effective refractive index
\({k}_{0}\) is the number of wave
\(d\) is thickness of unit cell
\({z}_{eff}\) is the effective impedance
\({\mu }_{eff}\) is the effective permeability
\({ϵ}_{eff}\) is the effective permittivity
2.4 Design of Metamaterial Antenna
An additional dielectric layer called superstrate consisting of array of rectangular split ring resonator on the top layer is inserted at a height of 16 mm above the conventional patch antenna. The height is varied and the height of 16 mm gives best results and this height is taken for fabrications of proposed antenna. The material of the superstrate is FR4 epoxy dielectric whose relative permittivity is 4.4 with a thickness measuring 1.6 mm. The width and length of the superstrate are 18.75 mm and 16 mm respectively as shown in Fig. 2.7. An array of (5x5) of 2 rectangular split ring is placed on the superstrate. These rings show the metamaterial properties and as the metamaterial superstrate has negative permeability characteristics, it suppresses the unwanted surface wave and thus results into a significant antenna performance.