## 3 Antenna Sensor Simulation and Parameter Optimization
### The Antenna Performance after Optimization and Measurement  
The above simulations show that the resonant points of the antenna and its VSWR are both influenced by the feed position and dielectric layer thickness, and the antenna possesses four resonant points when the probe is located at the \(X\)-axis. Thanks to the optimetrics of the simulation software, this study changes the probe position at \(X\)-axis and dielectric layer thickness to examine antenna parameters. The probe position is varied from 0 mm to 103 mm along the \(X\)-axis with a step of 1 mm, and the thickness is set from 0 mm to 5 mm with a step of 0.1 mm. With each change in position or thickness, a different VSWR will be obtained. Finally based on these VSWR values, the optimal parameter combination could be determined. The final design parameters are shown at in Table 3.  
Figure 8 shows the final simulated VSWR of the antenna sensor after parameter optimization. The simulation results show that the antenna sensor possesses four resonant points, with the lowest resonant point being 441 MHz, which is slightly different from the 403 MHz results obtained by the theoretical estimation. On the one hand, structural differences exist between the snowflake patch and circular patch. On the other hand, for the circular patch antenna, a certain difference is observed between the practical radius and the theoretical radius [19]. Considering these two factors, the practical resonant frequency is slightly higher than the theoretical resonant frequency. The other three resonant points at the low-frequency band are 672, 734, and 933 MHz. The VSWR of the four resonant points are \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Thickness (mm)** & **Resonance Frequency (MHz)** & **VSWR** \\ \hline \multirow{4}{*}{\(1\)} & 1 & 450 & 1.126 \\  & 2 & 644 & 1.344 \\  & 3 & 711 & 1.383 \\  & 4 & 940 & 3.167 \\ \hline \multirow{4}{*}{\(2\)} & 1 & 453 & 1.685 \\  & 2 & 654 & 2.515 \\  & 3 & 723 & 1.389 \\  & 4 & 940 & 1.906 \\ \hline \multirow{4}{*}{\(3\)} & 1 & 452 & 2.240 \\  & 2 & 660 & 3.494 \\  & 3 & 728 & 1.964 \\  & 4 & 934 & 1.523 \\ \hline \multirow{4}{*}{\(4\)} & 1 & 453 & 2.660 \\  & 2 & 666 & 4.158 \\  & 3 & 730 & 2.491 \\  & 4 & 929 & 1.402 \\ \hline \multirow{4}{*}{\(5\)} & 1 & 454 & 2.977 \\  & 2 & 674 & 4.559 \\ \cline{1-1}  & 3 & 728 & 2.887 \\ \cline{1-1}  & 4 & 922 & 1.308 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Resonance points and their VSWR under different dielectric layer thickness. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Length (mm)** & **Width (mm)** & **Base Koch Curve (mm)** & **Thickness (mm)** & **Probe Position (mm)** \\ \hline
280 & 240 & 180 & 5 & (83, 0) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Final design parameters. 1.988, 2.102, 1.507, and 1.205, which indicates that the antenna possesses a good impedance matching degree. The results also show that the antenna presents good multi-frequency performance in the high-frequency range, and it can further enhance the PD detection ability of the sensor. The ability to receive signals from different directions is important for the built-in antenna sensor, because the antenna sensor is tightly attached to the inner wall of the high-voltage switchgear. Therefore, the radiation direction of the four resonant points is analyzed in this study. Figure 9 shows the E-plane and H-plane antenna radiation patterns for four resonance frequencies. When the frequency is 441 MHz, the optimal signal receiving direction is perpendicular to the radiation surface inside the switchgear, which shields external signals to some extent. That is to say, the capability of the antenna against external low-frequency interference is strengthened. Comparing the radiation patterns at different resonant frequencies of 441, 672, 734, and 933 MHz, it can  
Figure 8: The simulated VSWR of the antenna. Figure 9: The antenna simulated radiation pattern in resonance points.