# Implications of Metamaterial on Ultra-Wide Band Microstrip Antenna Performance
## 3 Metamaterials Design
### Circular and Square SRR Design Analysis  
In order to analyze the behavior of SRR unit cell, all structures are designed using the same geometry in [36; 41] and printed on Rogers 5880-LZ substrate with a dielectric constant of \(\varepsilon_{\rm r}=1.96\), with dielectric loss tangent of \(\tan\delta=0.0009\) and substrate thickness of 1.27 mm. Parameters values of circular and square SRRs are shown in Table 3.  
The resonance behavior of the circular SRR, in Figure 12, has resonant frequencies at 3.6246 GHz, 13.5906 GHz and 19.7908 GHz, as displayed in Figure 13. It is noticeable that SRR has a resonance at different frequencies where it has a good transmission. A jumping phenomenon occurs at the resonant frequency where there is a phase change in (S\({}_{11}\)), which confirms some material characteristics such as negative permeability. Figure 14 shows the behavior of the magnetic permeability of the proposed circular SRR. It is clearly shown that the permeability takes negative values at the transmission parameter (S\({}_{21}\)). The surface current density for the circular SRR at the first resonant frequency 3.6246 GHz is shown in Figure 15; it is observed that most the current is concentrated at the inner side of each ring opposite to its gap and the same figure displays the direction of the surface current that flows in the same direction, clockwise, for the two rings.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Circular SRR**} & \multicolumn{2}{c}{**Square SRR**} \\ \hline
**The Unit Cell Parameters** & **Value (mm)** & **The Unit Cell Parameters** & **Value (mm)** \\ \hline Ring width (\(c\)) & 0.7 & Ring width (\(c\)) & 0.5 \\ Ring thickness (\(h\)) & 37 \(\mu\)m & Ring thickness (\(t\)) & 35 \(\mu\)m \\ Inter – ring spacing (\(d\)) & 0.2 & Inter – ring spacing (\(d\)) & 0.2 \\ Split gap (\(g\)) & 0.2 & Split gap (\(g\)) & 0.8 \\ Substrate thickness (\(t\)) & 1.27 & Substrate thickness (\(h\)) & 1.27 \\ Inner ring radius (\(r\)) & 2.2 & Square half side (\(a_{ext}\)) & 2.6 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Circular and square SRR unit cell parameters.  
Figure 12: Circular SRR designed in HFSS.  
The next unit cell to be analyzed is the S-SRR, Figure 16, which has two resonant frequencies at 4.975 GHz and 17.6226 GHz, as displayed in Figure 17. At the transmission parameter \(S_{21}\), the permeability of the square SRR is having a negative value, Figure 18. Metamaterial characteristic is shown clearly in the permeability behavior of changing from positive to negative values at specific frequency. The current concentration is at the inner side of each ring opposite to the gaps at resonant frequency 4.975 GHz, and the flow of the current for the two rings is in the same direction counter-clockwise, Figure 19.  
Figure 14: Real and imaginary effective permeability \(\mu\).  
Figure 15: Surface current density and its vectors for circular SRR.  
Figure 16: Square SRR designed in HFSS.  
Figure 19: Surface current density and its vectors for square SRR.  
Figure 17: S\({}_{11}\) and S\({}_{21}\) for square SRR.  
Figure 18: Real and imaginary effective permeability \(\mu\).