## 2 Antenna Design and Optimization  
### Antenna Geometry  
We assume the length and width of the rectangular radiation patch are L and W, respectively, and the radiation patch and GND are displayed in Figure 1a,b. The detailed variable settings and their corresponding values are listed in Table 2. The total size of the antenna is 47.4 mm\({}^{3}\). Its multi-frequency characteristics can be obtained by cutting multiple I-grooves in the right part of the patch. To further increase the bandwidth, the thickness of the substrate can be adjusted appropriately. Its other dimensions and geometry are displayed in Figure 1c. The antenna is energized via a coaxial feed probe with a 0.2 mm radius, located at the right of the ground plane, which enables excellent impedance matching and dual-frequency behavior by adjusting the feed location appropriately. The radiation patch and GND are on the upper and lower surfaces in the dielectric substrate, respectively. This structure protects the radiation patch and prevents it from coming into contact with human tissue. The antenna was implanted in a three-layer body tissue model for simulation analysis, as shown in Figure 1d.  
Figure 1: Design of dual-band antenna (not to scale). (**a**) Patch with slots. (**b**) GND with two crossed, rectangular slots. (**c**) Side view of the antenna. (**d**) Antenna within a three-layer body tissue model.  
The three-layer body tissue model consisted of skin, fat, and muscle. The muscle box measured 80 mm \(\times\) 80 mm \(\times\) 32 mm, the fat box measured 80 mm \(\times\) 80 mm \(\times\) 4 mm and was located above the muscle box, and the skin box measured 80 mm \(\times\) 80 mm \(\times\) 4 mm and was located above the fat box [27]. The electrical behavior of the modeled environment was similar to that of human tissue. The dielectric constants and conductivities of these body tissues at two frequencies are listed in Table 3. For instance, the dielectric constant of skin tissue at 1.4 GHz is 39.6 and the conductivity is 1.036 s/m, but the dielectric constant of skin tissue at 2.4 GHz is 38.0 and the conductivity is 1.464 s/m [28]. Due to differences in the physical characteristics of human tissues at different operating frequencies, the radiation characteristics of implanted antennas will be affected. We assumed that the antenna was located in the middle of the tissue model and implanted at a depth of 20 mm. The S11 and AR simulation results at different frequencies are displayed in Figure 2. The effective AR bandwidth in the WMTS band and the impedance bandwidth in the ISM band cover the design goal very well, as shown in the shaded part of Figure 2a,b.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(W\) & 7.2 & \(L\) & 7.4 & \(W_{1}\) & 7 \\ \(W_{2}\) & 0.6 & \(W_{3}\) & 0.7 & \(W_{4}\) & 2.25 \\ \(W_{5}\) & 3.05 & \(W_{6}\) & 3.9 & \(W_{7}\) & 4.85 \\ \(W_{8}\) & 4.2 & \(W_{9}\) & 4.1 & \(W_{10}\) & 0.4 \\ \(L_{1}\) & 7 & \(L_{2}\) & 6 & \(L_{3}\) & 5.6 \\ \(L_{4}\) & 7.1 & \(L_{5}\) & 7.2 & \(L_{6}\) & 5 \\ \(H_{1}\) & 0.635 & \(H_{2}\) & 0.254 & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Sizes of the antenna’s geometric parameters (unit: mm).  
Figure 2: The S11 and AR simulation results at different operating frequencies: (**a**) at 1.4 GHz; (**b**) at 2.4 GHz.