# A Split Ring Resonator-Based Metamaterial for Microwave Impedance Matching with Biological Tissue
## 3 Design  
The considered microwave applicator, depicted in Figure 2, is an SIW cavity-backed patch antenna, designed and optimized for Ku-Band applications (10.7-12.7 GHz). It consists of a stack structure: a microstrip patch antenna coupled with a circular resonant cavity based on SIW technology: The substrate Rogers Duroid 5880 with low dielectric constant \(\varepsilon_{r}=2.2\) and low losses \(\tan\delta=0.0009\) has been considered for both layers. This antenna combines the attractive features of both SIW cavity-backed and patch antennas with truncated corners. The design has been performed by varying the size of the cavity, the hole diameters, the hole pitch, and the patch geometry. All the details  
Figure 1: Scheme of the normal wave propagation through the two layers sandwiched between two semi-infinite media. The split ring resonator (SRR) metamaterial layer is placed to distance \(t_{2}\) from the medium to be matched. pertaining to designs of this kind of antenna are reported in [22]; they are not reported for shortness. The two cuts on the sides of the rectangular patch were designed to provide a wider frequency band and a frequency downshift. This allows a more compact size. The metallized cavity further broadens the bandwidth and improves the gain of the antenna; furthermore, the SIW technology offers the typical advantages of the standard PCB processes, such as easiness of fabrication, low cost, compact size and high integration with the planar circuits. Figure 3 shows the layout of an SIW cavity-backed patch antenna, the geometric parameters of which are listed in Table 1.  
The metamaterial theory reported in Section 2 has been applied to roughly identify the geometric parameters of the metamaterial operating at the Ku-Band applications. The analytical model for simple split ring resonators has been employed in order to obtain simple and preliminary line guides for the actual design, which is numerically performed via CST Microwave Studio(r). The employed dielectric substrate is Rogers RO4350B with dielectric constant \(\varepsilon_{r}=3.48\) and dissipation factor of \(\tan\delta=0.004\) \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Dimension** & **Description** \\ \hline \(a\) & 8.00 mm & Length of the patch \\ \(b\) & 2.86 mm & Length of the lateral cuts \\ \(c\) & 1.50 mm & Width of the lateral cuts \\ \(r\) & 6.72 mm & Radius of the SIW cavity \\ \(v\) & 1.24 mm & Diameter of the vias \\ \(\alpha\) & \(15^{\circ}\) & Angular distance between the consecutive vias \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of the geometric parameters of the SIW cavity-backed patch antenna. Figure 3: Layout of SIW cavity-backed patch antenna. (**a**) Top view of the patch antenna and (**b**) top view of the SIW circular resonant cavity. Figure 2: Layout 3D view of the microwave applicator with the split ring resonator-based metamaterial superstrate placed on the substrate integrated waveguide (SIW) cavity-backed patch antenna at a distance \(d\). The geometry of the SRR unit cell has been suitably modified and scaled with respect to the literature [14] in order to operate at the resonance frequency of the SIW microwave applicator. Moreover, with respect to [14], the unit cell of the proposed SRR presents a further double ring with splits placed on the opposite side and operates at a different frequency. A complementary configuration, i.e., a couples of coplanar rings written symmetrically with respect to the common center, has been considered to obtain a resonance frequency close to that of a single ring with the same dimensions, but with a larger magnetic moment due to higher current density. Since they are written on both sides of a dielectric substrate, they are broadside coupled. The analytical model of a single (not complementary) broadside coupled SRR satisfactorily approximates the complementary configuration when the couple of rings are very close each other.