## 2 Stated Antenna Design Analysis
### Stated Antenna Design Procedure  
The suggested antenna was designed in four steps, as illustrated in Figure 3. Different square parasitic patches in the patch and inside the ground plane of the antenna were designed to enhance the performance of the stated antenna. The performance of the stated implantable antenna is enhanced stepwise, as shown in the figure below. At a low frequency \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Dimensions (mm)** & **Parameters** & **Dimensions (mm)** \\ \hline \(Lg=L\) & 7 & \(W_{1}\) & 0.5 \\ \(L_{1}\) & 0.50 & \(W_{2}\) & 1.8 \\ \(L_{2}\) & 0.56 & \(W_{3}\) & 1.3 \\ \(L_{3}\) & 0.73 & \(W_{4}\) & 1 \\ \(L_{4}\) & 1 & \(W_{5}\) & 2.1 \\ \(L_{5}\) & 1.5 & \(W_{6}\) & 1.7 \\ \(L_{6}\) & 1.35 & \(W_{7}\) & 2.5 \\ \(L_{7}\) & 1 & \(W_{8}\) & 0.5 \\ \(L_{8}\) & 2.5 & \(W_{9}\) & 1.5 \\ \(L_{9}\) & 3.25 & \(W_{10}\) & 2 \\ \(W_{9}=W\) & 7 & \(W_{11}\) & 4.5 \\ \(W_{22}\) & 3 & \(W_{16}\) & 3 \\ \(W_{13}\) & 0.5 & \(D_{1}\) & 0.8 \\ \(W_{14}\) & 5.5 & \(D_{2}\) & 0.3 \\ \(W_{15}\) & 3 & \(R_{1}\) & 0.55 \\ \(h\) & 0.25 & \(R_{2}\) & 1.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of the parameters of the stated design. Figure 2: Stated design structure; (**a**) front view, (**b**) back view, and (**c**) 3D view. band, the relative permittivity value of the substrate does not change, while it increases with increased frequency. Hence, at intermediate frequencies, the rate of the relative permittivity raises. Equation (1) gives a dielectric constant at the initial stage [6]:  
\[\epsilon_{\text{r\;e\;f\;f}}=\frac{\epsilon_{\text{r}}+1}{2}+\frac{\epsilon_{ \text{r}}-1}{2}\times\left[1+12\times\frac{h}{W}\right]^{-\frac{1}{2}} \tag{1}\]  
The height-to-width ratio equation helps in determining the dimensions of the antenna system. To account for fringing effects, the change in length, width, and height of the antennas' substrate is selected using Equation (2) [9]:  
\[\frac{\Delta L}{h}=0.412\times\frac{(\;\epsilon_{\text{r}}+0.3)\times\left( \frac{W}{h}+0.264\right)}{(\;\epsilon_{\text{r}}-0.258)\times\left(\frac{W}{h} +0.8\right)} \tag{2}\]  
where '\(\epsilon_{\text{r}}\)' stands for relative permittivity of the substrate, '\(h\)' stands for the substrate height, '\(\Delta L\)' stands for the change in patch length, and '\(W\)' stands for patch width. The square-shaped patch antenna's radiating and ground sections are separated into four segments, each with their own set of results. The patch was made of parasitic elements of various sizes. In the first step, two circular slots inside the patch and a horizontal '4'-shaped slot is introduced inside the ground-plane. The return loss value was found to be more than \(-20\) dB at the frequency of 420 MHz (see Figure 4). In the second step, the frequency is shifted from 420 MHz to 780 MHz (360 MHz shift) by creating two square-shaped slots inside the ground plane. In the third step, the frequency of the antenna is again shifted from 780 MHz to 1.15 GHz (370 MHz shift) after again creating a horizontal '4' shaped slot inside the ground plane and creating circular rings in the patch of the second step. As 1.15 GHz is not our required band, to shift the band from 1.15 GHz to 915 MHz (a 235-MHz shift), the feet of the bear-shaped radiator is slotted with rectangular boxes, and rectangular and L-slots are introduced in the ground. Due to this, the antenna's performance is improved, and the desired ISM (915 MHz) band is attained in the fourth step. The rectangular cuts on the patch and the ground are made using various rectangular cuts; the main goal of these cuts is to make the antenna smaller and lighter. The feed is located on the patch's bottom right side. A shorting pin (via) is utilized to keep the stated antenna's dimensions small. As a result, a shorting pin (via) of a radius of 0.5 mm is inserted, starting from the ground and ending in the patch. Figure 4 shows a comparison of the S\({}_{11}\) of the suggested design steps.