# Investigation of the Opposite-Electrode Effect on the Planar Solid-State Pulse-Forming Line
## 6 Discussion  
In this study, we found that the ground electrode structure affects the edge capacitance of the planar solid-state PFL, which in turn affects the withstand voltage and temperature performance of the PFL. It can be theoretically inferred that as the width of the ground electrode increases, the edge capacitance of the planar solid-state PFL also increases; however, this trend will weaken as the thickness of the dielectric plate increases. Therefore, the full-electrode PFL with the ground electrode covering the entire plane has a lower characteristic impedance; however, this also manifests in some unexpected problems. According to the relationship between capacitance, voltage, and charge, as the planar solid-state PFL edge capacitance increases, the edge charge density of the high-voltage electrode will also increase. According to [PERSON]'s law, a higher charge density at the high-voltage edge of the electrode will result in a larger electric field at the edge of the high-voltage electrode. Areas with a higher electric field strength will generate more heat during continuous operation; therefore, the full-electrode PFL may cause localized overheating after continuous operation. Using the FEM, we simulated the capacitance per unit length of the PFL under different ground electrode widths and high-voltage electrode widths. The simulation results show that as the width of the ground electrode increases, the edge capacitance per unit length of the PFL also increases (Figure 3). Upon further analysis, it can be observed that the additional capacitance resulting from the increased width of the ground electrode is \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Full-Electrode PFL** & **Opposite-Electrode PFL** \\ \hline Withstand voltage/kV & 23 & 33 \\ Average temperature & 31.3 & 30.2 \\ (10,000 times)/\({}^{\circ}\)C & 35.7 & 33.3 \\ Average temperature & 34.3 & 31.9 \\ Peak temperature & 40.8 & 37.6 \\ (20,000 times)/\({}^{\circ}\)C & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter comparison of the full-electrode PFL and the opposite-electrode PFL. relatively independent and has a marginal effect. Based on the simulation results of the edge electric field and electrode width relationship (Figure 4), it can be observed that when the width of the high-voltage electrode and the grounding electrode is consistent, the edge electric field of the electrode is smaller. These simulation results confirm the correctness of the theoretical analysis presented above and also guided us in designing the opposite-electrode PFL with ground electrodes and high-voltage electrodes structurally consistent and positioned directly opposite each other. The electrostatic simulation results indicate that the edge electric field of the full-electrode PFL's high-voltage electrode consistently exceeds that of the opposite-electrode PFL's high-voltage electrode along the entire length of the electric field monitoring lines (Figure 6). The opposite-electrode PFL achieves a reduction in the PFL edge capacitance by making the width of the ground electrode equal to that of the high-voltage electrode at all points, thereby reducing the edge electric field of the electrodes. Therefore, in theory, an opposite-electrode PFL would have higher insulation and temperature performance than a full-electrode PFL. The results of the withstand voltage test show that the opposite-electrode PFL has a higher withstand voltage than the full-electrode PFL (Figure 9). When only the ground electrode structure is changed, the characteristic impedance of the opposite-electrode PFL is slightly larger than that of the full-electrode PFL; however, its withstand voltage increases by 43% (from 23 kV to 33 kV). Furthermore, the gain in higher withstand voltage of the opposite-electrode PFL outweighs the disadvantage of increased characteristic impedance, meaning that the energy density of the opposite-electrode PFL is improved compared to the full-electrode PFL.