# Research on a Novel Nanosecond Marx Generator and Its Efficiency Analysis
## 5 Discussion  
As shown in Table 1, compared with the energy efficiency below 30% in the generators in references [6,8], the energy efficiency of the proposed nanosecond Marx generator in this paper is greatly improved to 76% and 94%.  
As shown in Figure 12, considering the effect of switching frequency on discharge frequency and amplitude of the pulse, the discharge frequency can be adjusted continuously from 10 to 60 kHz. When the discharge frequency is below 50 kHz, the output voltage amplitude \(U_{\text{m}}\) is about 4 kV. The voltage amplitude declines when the discharge frequency is higher than 50 kHz, as shown by the red line in Figure 12 demonstrating the effect of switching frequency on discharge frequency and amplitude of the pulse. With the increase in discharging frequency, the generator's input power and output power increase, as shown in Figure 13. When the frequency is greater than 50 kHz, the input power reaches the maximum power of HS-5000, and the pulse amplitude will decrease as the discharge frequency of the generator continues to increase to maintain the output power. The energy efficiency of the generator remains very high with different discharging frequencies as shown in Figure 14. The comparison of theoretical and practical energy efficiency values is very close, and the error rate is less than 5%, which verifies the reliability of the calculation. According to the analysis above, the maximum energy efficiency of the generator is 94.24%.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Reference [6]** & **Reference [8]** & **Circuit I** & **Circuit II** \\ \hline \(\eta/\%\) & 21.55 & 26.67 & 76.42 & 94.24 \\ \(\eta_{c}/\%\) & 52.38 & 61.52 & 66.94 & 83.60 \\ \hline \hline \end{tabular} Reference [6], a traditional nanosecond pulse generator with avalanche BITs charged by a DC source. Reference [8], an improved Marx generator with avalanche BITs using an isolation BIT.  
\end{table}
Table 1: Efficiency comparison of nanosecond Marx generators based on avalanche BITs.  
Figure 11: The waveform of the energy-storage capacitors \(U_{\text{c}}\) and the resonant current \(i_{\text{r}}\) (circuit II).  
Figure 12: The effect of switching frequency on discharge frequency and amplitude of the pulse.  
Figure 13: The power with a different output pulse frequency.  
In fact, in addition to the energy efficiency used in this paper, some researchers also use voltage efficiency \(\eta_{\text{voltage}}\) to compare the performance between circuits, as shown in References [19,20]. The equation of voltage efficiency is shown in Equation (23). The key parameters are summarized in Table 2. The new generator proposed in this paper significantly improves the voltage efficiency of the circuit from 50% to 90%. Compared with the traditional structure, the number of BJTs required to achieve the 4 kV repetition output is significantly reduced to 16. In addition to substantially improving voltage efficiency, the proposed generator in this paper also achieves a high repetition frequency which is adjustable from 10 to 60 kHz.  
\[\eta_{\text{voltage}}\ =\ \frac{V_{\text{peak}}}{N_{\text{c}}\cdot u_{\text{c}}} \times 100\% \tag{23}\]  
where \(V_{\text{peak}}\) is the peak voltage of the output pulses, \(N_{\text{c}}\) is the number of energy storage capacitors, and \(u_{\text{c}}\) is the voltage of the energy-storage capacitors.