## 3 Results
### Modulation of the On-Time  
Modulation of the on-time of the IGBT switches enables some control of the charging voltage per stage. The influence of the on-time of the IGBT switches on the charging voltage has been studied based on the circuit model. Figures 13 and 14 show two simulation results of the charging voltage and the charging current, both derived from the charging input terminal of the generator, with an on-time of 22 \(\upmu\)s and 200 \(\upmu\)s, respectively. The inductive energy, which is initially stored in the charging coil before the beginning of the resonant charging, varies with the on-time. Charging of the stage capacitor is delayed until the solid-state switches open. In the case of a longer on-time of the switches, the stage capacitors are charged to a higher voltage. Hence, the modulation of the on-time can be used for fine-tuning the charging voltage. In the case of an on-time of 22 \(\upmu\)s, the stages are charged to a peak voltage of 1 kV. Thereby, the on-time of 22 \(\upmu\)s is slightly longer than it would be required for pulse generation only. Hence, some additional energy is stored in the charging coil L15, just sufficient to compensate for the losses and to reach exactly twice the source voltage of 500 V. However, when opening the switches, the charging current is still small compared to the pulse current. So, the switches operate almost under soft-switching conditions. For an on-time of 200 \(\upmu\)s, a charging voltage of 1.1 kV per stage is obtained. As long as the switches are closed, the current through L15 rises almost linearly. Figure 15 shows the energy stored in the cores of the leftmost and its neighbouring current-compensated choke and the common-mode currents through both for an on-time of the solid-state switches of 200 \(\upmu\)s. In contrast to both cases with an on-time of 22 \(\upmu\)s, shown in Figures 7 and 12, the common-mode currents and energies in the chokes are almost equal during charging. Nevertheless, the stage capacitor of the leftmost stage is also charged to a slightly higher voltage than the other stage capacitors, as shown in Figure 16. As in the other two cases, this additional charge and, hence, energy is transferred from the cores of the current-compensated chokes after the end of the charging process for the other stages. Figure 12: Energy stored in the cores of two current-compensated chokes (\(W_{\text{Core}}\)) and common-mode current \(\text{I}_{\text{C}}\) through the chokes (Simulation for current-compensated chokes comprising L1, L2 and L3, L4 according to Figure 3, \(\text{R}_{\text{D}}=20\) Ohm, on-time of the solid-state switches: \(\text{t}_{\text{on}}=22\)\(\upmu\)s). Figure 14: Charging voltage \(V_{ch}\) and the charging current \(I_{ch}\) at the charging input terminal of the generator, on-time of the solid-state switches: \(t_{on}\) = 200 \(\mu\)s.  
Figure 13: Charging voltage \(V_{ch}\) and the charging current \(I_{ch}\) at the charging input terminal of the generator, on-time of the solid-state switches: \(t_{on}\) = 22 \(\mu\)s.  
If the on-time of the pulse switches is too short, the stage capacitors are not discharged completely. Figure 17 shows the voltage V\({}_{\rm Ch}\) and the current I\({}_{\rm Ch}\) with an on-time of 10 us, which is not sufficient for a complete discharge of the stage capacitors. As a fraction of the charge remains in the stage capacitors, a smaller voltage swing occurs, and the stage capacitors are charged to the sum of the remaining voltage after the previous pulse and twice the voltage difference to the voltage of the power supply V1. Figure 16: Simulated voltages across the stage capacitors C1, C4, C7, C10, C13, C16, C19, and C22 according to Figure 3 together with the generator’s charging current I\({}_{\rm ch}\) (R\({}_{\rm D}\) = 20 Ohm, on-time of the solid-state switches: t\({}_{\rm on}\) = 200 μs).