# Brain Implantable End-Fire Antenna with Enhanced Gain and Bandwidth
## 2 Antenna Design  
Figure 2 provides an overview of the proposed skull-embedded Vivaldi antenna. It was vertically installed against the dura matter below the skull. The antenna was sandwiched  
Figure 1: Conceptual illustrations of the brain-implanted antenna placement: (**a**) conventional horizontal placement and (**b**) proposed vertical placement. inside a Taconic RF-35, a biocompatible insulator with relative permittivity (\(\epsilon_{\mathrm{r}}\)) and loss tangent (tan\(\delta\)) of 3.5 and 0.002, respectively. Its low tan\(\delta\) value at the antenna design frequency (i.e., 3-5 GHz) is beneficial for improving the antenna gain [11]. In addition, the RF-35 is mechanically durable (tensile strength of 27,000 psi and dimensional stability of 0.00004 mm/mm) and has a low moisture absorption of 0.02%. The height of the insulator was fixed to 7 mm, corresponding to a typical height of an adult human skull. The thickness and width of the insulator were 0.5 mm and 12 mm, respectively (see Figure 2). The width of 12 mm matched half of the guided wavelength (\(\lambda_{\mathrm{g}}\)) at the center frequency (4 GHz). The geometry of the insulated Vivaldi antenna was optimized using full-wave electromagnetic simulation software (Ansys HFSS). The goal was to achieve a good impedance matching condition (reflection coefficient, \(S_{\mathrm{11}}<-10\) dB) and high end-fire gain (\(\mathrm{\sim}\)15 dB) over a wide bandwidth (3-5 GHz) even in the lossy brain environment. It consisted of seven different layers of brain tissues; their material properties and thicknesses assigned in the simulation model are listed in Table 1[20]. The material properties of each layer are presented in the center frequency 4 GHz of the target bandwidth (3-5 GHz). The geometry of the Vivaldi antenna is depicted in Figure 3. The tapered slot at the middle gradually opened up to support a smooth impedance transition and to generate end-fire radiations over a broad bandwidth. Simulation results showed that an ordinary Vivaldi antenna modeled in the given area of 7 \(\times\) 12 mm\({}^{2}\) resonated around 6 GHz, which is higher than the desirable 4 GHz (i.e., the center frequency of 3-5 GHz). Therefore, an antenna miniaturization technique was required to reduce the antenna footprint. One way \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Layer** & **Relative Permittivity (\(\epsilon_{\mathrm{r}}\))** & **Loss Tangent (tan\(\delta\))** & **Thickness (mm)** \\ \hline Skin & 40.84 & 0.297 & 1 \\ Fat & 5.12 & 0.160 & 2 \\ Skull & 10.53 & 0.310 & 7 \\ Dura & 40.10 & 0.308 & 1.5 \\ CSF & 63.73 & 0.366 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material properties of brain tissues at 4 GHz. Figure 2: The proposed Vivaldi antenna surrounded by insulators and embedded in the skull. to miniaturize a Vivaldi antenna is to add horizontal slots along the side edges [21; 22; 23]. The horizontal slots act as a choke to lessen undesirable currents flowing at the side edges, which can improve the impedance-matching condition. However, this method accompanies the decrease of end-fire gain. The substrate size along the longitudinal direction was extended [24] and driving elements between the tapered slots were added to recover the end-fire gain [22]. Instead of horizontal slots, the proposed Vivaldi implemented comb-shaped vertical slots to miniaturize the Vivaldi antenna. We found that the method effectively improved the end-fire gain by concentrating more currents along the tapered slot in the middle. Figure 4 shows the surface current densities at 3, 4, and 5 GHz for the conventional Vivaldi without slots and proposed Vivaldi with slots. The conventional design exhibited excessive currents at the bottom edge where the antenna feed was located. Stronger currents were observed at the lower frequency of 3 GHz, which has a longer wavelength.