## 2 Four Channels Generator
### Marx Modulator Design  
The specifications for the generator include the possibility to produce pulse burst of 6500 V, 65 A from 100 ns to 100 \(\upmu\)s, with a maximum frequency of 5 MHz, on each channel, with a maximum 100 W average output power for the all generator. In addition, the possibility to set in each pulse burst, a time sequence with different pulse widths and amplitudes, for each channel independently. Considering the above, each Marx modulator was assembled with 8 stages, for an U\({}_{\text{dc}}\) up to about 820 V. For the S\({}_{\text{pi}}\) and S\({}_{\text{ni}}\) switches TO-263-7 C3M0280090J SiC Creek MOSFETs (i.e., 900 V, 22 A pulsed current and 280 m\(\Omega\)) were chosen. Considering the required pulse current of 65 A, two MOSFETs were placed in parallel in each switch S\({}_{\text{pi}}\) and S\({}_{\text{ci}}\). Although the current presented on the datasheet is lower, the MOSFETs were tested up to 35 A each, at vgs \(\approx\) 17.5 V, with good performance and no observed derating. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**\# MM0** & **Pause (ns)** & **Pulse (ns)** & **Mask** & **Stages on** \\ \hline
1 & 200 & 200 & 510 & 8 \\
2 & 200 & 400 & 2 & 1 \\
3 & 400 & 600 & 30 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Example of command line of a pulse sequence for MM 0, for three pulses. Figure 5: Example of pulse burst sequence defined from Table 1, with train number 3 and frequency \(f\). The pulse and charging switches were designed alike, since more than one channel can work simultaneously. Hence, is possible to have several operating conditions, depending on how the load is connected between the outputs, were one MM could be in pulse mode and another is charge mode, sinking the current from the first one. This operation is presented in the Results section, for bipolar operation, with the load connect to HV+ of two channels. For each Marx modulator, the stage \(\mathrm{C_{i}}\) capacitors, in Figure 2 circuit, has a capacitance of 0.75 \(\mathrm{\upmu F}\), comprising five 0.15 \(\mathrm{\upmu F}\)/1000 V capacitors in parallel, reference B32653A0154 from TDK. The maximum energy stored inside each MM, \(\mathrm{W_{g}}\), for an input \(\mathrm{U_{dc}}\) of about 820 V, is about 2 J, from:  
\[\mathrm{W_{g}}=(n/2)\;\mathrm{C_{i}}\;(\mathrm{U_{dc}})^{2}, \tag{1}\]  
where \(n=8\). Considering the energy stored inside the MM, \(\mathrm{W_{g}}\), the maximum pulse energy, \(\mathrm{W_{p}}\), should be less than 5 times, 0.4 J, to have a maximum 10% pulse voltage droop, from:  
\[\mathrm{W_{p}}=n\;\mathrm{U_{dc}}\;\mathrm{I_{p}}\;\mathrm{t_{on}}, \tag{2}\]  
where \(n\) is the number of stages that participate in the pulse, \(\mathrm{U_{dc}}\) is the CCPS voltage, \(\mathrm{I_{p}}\) the pulse current and \(\mathrm{t_{on}}\) the pulse width. This means that for a pulse of 650 V and 65 A, having 10% voltage droop (i.e., 650 V), the maximum pulse width would be about 946 ns. In addition, the operating frequency in single or burst series mode is limited by the HVPS 100 W, such that the time between pulses must be sufficient in order that the Marx capacitors are charged to the set voltage. Considering that the pulse duty cycle is normally less than 1%. A simple way to estimate the maximum pulse frequency is by:  
\[\mathrm{f}=P/W_{g}, \tag{3}\]  
where \(P\) is the CCPS power, 100 W. Hence, for the example given above, the maximum pulse frequency would be 250 Hz. In relation to the signal transmission, the TLP2367 series photocoupler was used, with 50-Mbps in small SO6 package, internal Faraday shield that provides a guaranteed common-mode transient immunity of \(\pm\)25 kV/us, and 3750 V\(\mathrm{V_{rms}}\) isolation voltage, with just 12 ns propagation delay time (i.e., the delay D used in Figure 4c are also of 12 ns). A critical aspect with the pulse generator is current protection, as the load is biological, in order to protect the hardware and to keep the load from undesirable operating conditions that may lead to its destruction.