# A Split Ring Resonator-Based Metamaterial for Microwave Impedance Matching with Biological Tissue
## 3 Design
The metamaterial considered in this paper consists of an array of complementary broadside coupled split square-rings. The lattice of this inhomogeneous structure is shorter than the guided wavelength of antenna radiation, so the composite behaves as an effective homogeneous medium. The design and optimization of the metamaterial lens has been numerically performed via CST Microwave Studio(r). After several simulations, in which the SRR geometry and cell size have been parametrically changed, the optimized geometric parameters are listed in Table 2. The optimized SRR metamaterial exhibits resonant frequency range overlapping the operating frequency range of the SIW cavity-backed patch antenna. Figure 4 shows the 3D view (a) and plan front view (b) of the unit cell of the SRR, respectively. The metamaterial lens used as superstrate of the SIW cavity-backed patch antenna is shown in Figure 5. \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Dimension (mm)** & **Description** \\ \hline \(\Delta x\) & 3.20 & Length of the unit cell in the \(x\) direction \\ \(\Delta y\) & 3.20 & Length of the unit cell in the \(y\) direction \\ \(l_{x1}\) & 2.45 & Length of the external SRR in the \(x\) direction \\ \(l_{y1}\) & 2.45 & Length of the external SRR in the \(y\) direction \\ \(l_{x2}\) & 2.00 & Length of the internal SRR in the \(x\) direction \\ \(l_{y2}\) & 2.00 & Length of the internal SRR in the \(y\) direction \\ \(s\) & 0.11 & Split gap of the SRR \\ \(w\) & 0.11 & Width of the SRR \\ \(g\) & 0.11 & Distance between the complementary SRRs in the \(xy\) plane \\ \(t\) & 3.04 & Distance between the broadside coupled SRRs in the \(z\) direction \\ \(d\) & 6.90 & Distance between the SIW antenna and the metamaterial lens \\ \(L_{x}\) & 22.40 & Length of the metamaterial lens in the \(x\) direction \\ \(l_{y}\) & 36.00 & Length of the metamaterial lens in the \(y\) direction \\ \hline \end{tabular}
\end{table} 
Table 2: List of the geometric parameters of the SRR Unit Cell of Figures 2, 4 and 5. Figure 4: 3D model of complementary broadside coupled SRR unit cell designed in CST Microwave Studio®. (a) 3D view and (b) top view. The \(S_{11}\) parameter of the microwave applicator placed at distance \(D\) from a model of human tissue is simulated to evaluate the lens metamaterial behavior as impedance matching layer. Figure 6 shows the sideview of the layout of SIW cavity-backed patch antenna covered by the metamaterial lens and at distance \(D\) from the biological tissue. The biological tissue considered in the simulation is a slab of skin-fat-muscle, whose electromagnetic parameters at the \(f=11\) GHz frequency are listed in Table 3[35]. The scattering parameter modulus \(|S_{11}|\) of the SIW cavity-backed patch antenna with SRR superstrate has been simulated for different distances from the biological tissue, and the obtained results are compared in Figure 7a. It is apparent that the metamaterial placed at distance \(D=10\) mm allows the best impedance matching with the biological tissue. It is worthwhile noting that even if Figure 7a shows a narrow dip at \(f=10.9\) GHz, the overall operating bandwidth is typically defined at \(|S_{11}|=-10\) dB level. Therefore, a very large frequency range of about 2 GHz can be exploited. Figure 5: Layout of the SRR metamaterial placed as the patch antenna superstrate. Figure 6: Sideview of SIW cavity-backed patch antenna with SRR superstrate placed at distance \(D\) from human tissue. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Biological Tissue** & **El. Conductivity (\(\sigma\)) (S-m\({}^{-1}\))** & **Permittivity (\(\varepsilon\))** \\ \hline Skin & 9.1658 & 30.313 \\ Fat & 0.6567 & 4.5278 \\ Muscle & 12.083 & 41.419 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Electromagnetic parameters human tissue at \(f=11\) GHz.