# A Metamaterial Inspired AMC Backed Dual Band Antenna for ISM and RFID Applications
## 2 Materials and Methods
### Design Principle of Proposed Antenna  
Computer Simulation Technology (CST) software is being widely employed to interrogate and simulate the prototype antenna. The antenna design was developed upon a substrate of FR4 material with 4.3 dielectric constant with thickness H\({}_{\rm{t}}\), 1.6 mm. Thus, the size of the proposed monopole antenna was formed with dimensions of 70 mm \(\times\) 31 mm. The width of the microstrip transmission line was f\({}_{\rm{w}}\) = 3 mm. The dimensional characteristics of the proposed monopole antenna are depicted in Figure 4. The antenna front view and the rear view are shown in Figure 4a,b. The prototype fabricated antenna is illustrated in Figure 4c,d. Figure 3: Results of antenna iterations. Figure 2: Antenna Iterations, (**a**) iteration 1, (**b**) iteration 2, (**c**) iteration 3, (**d**) iteration 4. The specifications of the designed antenna parameters are listed in Table 1. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Dimension (mm)** \\ \hline L & 70 \\ W & 31 \\ H\({}_{\text{t}}\) & 1.6 \\ f\({}_{\text{w}}\) & 3 \\ W\({}_{1}\) & 15 \\ W\({}_{2}\) & 3 \\ W\({}_{3}\) & 16 \\ W\({}_{4}\) & 3 \\ L\({}_{1}\) & 51 \\ L\({}_{2}\) & 40 \\ L\({}_{3}\) & 15 \\ L\({}_{4}\) & 6 \\ L\({}_{5}\) & 3.9 \\ L\({}_{6}\) & 3 \\ I\({}_{8}\) & 33.5 \\ w\({}_{6}\) & 3 \\ L\({}_{0}\) & 8 \\ L\({}_{i}\) & 7.2 \\ g & 0.3 \\ d & 0.5 \\ a & 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter Specifications of Proposed Antenna. Figure 4: Designed Antenna (**a**,**b**), Fabricated Antenna (**c**,**d**), (**a**,**c**) Front view, (**b**,**d**) Rear view. On both sides of the feed line a metamaterial was positioned. Metamaterials are designed with the two squared split ring resonators. A gap of 0.4 mm separated the outer and inner split resonators. A diagonal metal strip connected the inner split resonator from one end to the other. The length of the outer rectangle of the metamaterial L0 = 8 mm. L1 = 7.2 mm is the inner rectangle of the metamaterial, while lg = 33.5 mm specified the partial ground length, and wg = 31 mm specified the ground width. Split ring resonators on both sides of feed line consisted of two square-shaped concentric metal rings separated by a gap and splits on either side of the two square-shaped rings. The gap between the inner and outer rings along with the splits at the rings induce Magnetic Resonance. For the lower band, the design used an outer square metallic strip forcing the patch to radiate an equivalent magnetic-current loop. For the upper band, another magnetic current loop was created by adding a metamaterial structure near the feed line on the patch. By placing split ring resonators, antenna exhibits narrow dual band frequency characteristics. This design was selected as it was compact in size, low cost and achieved desired bandwidth accurately. Depending upon the fundamental equations, the mathematical formulae [29] to design the antenna can be derived as follows:  
The operating wavelength of the antenna \(\lambda_{0}\) is calculated by  
\[\lambda_{0}=c/f_{r} \tag{1}\]  
where \(f_{r}\) is the resonant frequency; \(c\) is the value of the velocity of light in free space. Wavelength is calculated by the formula  
\[\lambda_{d}=\frac{\lambda_{0}}{\sqrt{\varepsilon_{r}}} \tag{2}\]  
where \(\varepsilon_{r}\) is the dielectric constant.