# Research on a Novel Nanosecond Marx Generator and Its Efficiency Analysis
## 4 Experiments  
To verify the energy efficiency of the novel generator, a 3 \(\times\) 5-stage Marx generator based on the avalanche BJTs (circuit I) is built, as shown in Figure 7. It mainly consists of an FPGA controller, a full-bridge circuit, a rectifying circuit, and a 3 \(\times\) 5-stage Marx generator. The DC source is a Hanshenpuyuan-5000 (HS-5000). The input voltage and power can be read directly from the DC source. The switches of the full-bridge circuit are IXYX120N120C3, the resonant inductor \(L_{\rm r}\) is about 5 \(\mu\)H, the resonant capacitor \(C_{\rm r}\) is about 1.5 \(\mu\)F, the turns ratio of the booster transformer TX is about 60, the model of the diodes from D1 to D12 is DSEP12-12A, the BJTs are C1815 GR, the energy-storage capacitors are 1 nF ceramic capacitors, the isolation resistors \(R_{\rm C}\) are 5 k\(\Omega\) cement resistors, and the load resistor \(R_{\rm L}\) is 50 \(\Omega\). Because of series resonant charging, the voltage of the storage capacitors will increase until the avalanche voltage is reached. When the voltage is higher than the breakdown voltage of the Collector and Emitter, the avalanche BJTs will automatically turn on. When \(V_{\rm dc}\) is 40 V, and \(f_{\rm s}\) is 25 kHz, the voltage waveform of the load is shown in Figure 8. The nanosecond output pulses with a repetitive frequency of 50 kHz, a pulse FWHM width of 12.68 ns, and an amplitude of 2.9 kV are obtained over a resistive load. According to Equation (21), \(P_{\rm o}\) is about 80.27 W.  
The voltage waveform of the energy-storage capacitors and the waveform of the resonant current \(i_{\rm r}\) are shown in Figure 9. It can be seen that a resonant current charges the capacitors in the circuit. When the resonant current is zero, the voltage of the capacitors remains unchanged. The peak voltage of the capacitors is about 750 V in a charging period (\(V_{\rm dc}\) is 40 V, n is about 60, and the theoretical maximum voltage of \(C_{1-5}\) is about 2400 V). However, due to the series BJTs, when the capacitor voltage is about 750 V, the Marx generator will enter the discharge period. At this time, the avalanche breakdown voltage of the three BJT connected in series is about 750 V which is much lower than 2400 V, the series-resonant power supply will always charge the capacitors with a constant average current. According to Equation (17), \(P_{\rm c}\) is about 70.31 W. The power stored in the capacitors  
Figure 8: The voltage waveform of the load (circuit I): (**a**) discharge waveform with a repeatable frequency of 50 kHz; (**b**) enlarged view of load voltage. Figure 7: A photograph of the 3 \(\times\) 5 stage Marx generator based on the avalanche BJTs. is even lower than the power of the load 80.27 W, because the series-resonant power supply still operates during the discharge period and releases energy to the resistive load, which further improves the energy efficiency. The input power can be read from the parameters of HS-5000 (here, \(P_{\text{in}}\) is about 105.04 W). According to Equation (16), \(\eta_{\text{c}}\) is calculated to be 66.94% and \(\eta\) is 76.42%. The improved nanosecond Marx generator using isolating inductors build the circuit as shown in Figure 5. When \(V_{\text{dc}}\) is 40 V, and \(f_{\text{s}}\) is 25 kHz, the voltage waveform of the load is shown in Figure 10. The nanosecond output pulses with a repetitive frequency of 50 kHz (as shown in Figure 10a), a pulse width of 8.45 ns, and an amplitude of 4.0 kV are obtained on a resistive load. According to Equation (21), \(P_{\text{o}}\) is about 101.81 W. Moreover, the discharge frequency \(f\) can be continuously adjusted in a particular range by changing the switching frequency \(f_{\text{s}}\). The discharge voltage on the load is very stable and will not be affected by the switching frequency, as shown in Figure 10b. The voltage waveform of the energy storage capacitors and the waveform of the resonant current \(i_{\text{r}}\) are shown in Figure 11. The maximum voltage of the capacitors is about 850 V in a charging period.