## 1 Introduction
The capacitance C represents the parallel connection of the generator's stage capacitors. The inductance L forms together with the capacitance C a resonant circuit. The resistance R represents the resistive losses of the circuit. Initially, the capacitance C is uncharged, and there is no current flow through L, i.e., i(0) = 0. So, there is no energy stored in the circuit. Charging ends when the voltage across the capacitance C reaches its peak value. The solution of the differential Equation (9)  
\[v_{\mathbb{C}}(t)+RC\cdot\dot{v}_{\mathbb{C}}(t)+LC\cdot\ddot{v}_{\mathbb{C}}( t)=0 \tag{9}\]  
for the initial conditions \(v_{\mathbb{C}}(0)=0\) and \(\dot{v}_{\mathbb{C}}(0)=\frac{i(0)}{\mathbb{C}}=0\)\(\frac{V}{s}\) describes the time characteristic of the voltage across the paralleled stage capacitors \(C\) for the case of a circuit being initially free of energy. Thereby, depending on the value of the quality factor \(Q\) according to Equation (6), three different cases (\(Q\) < 0.5, \(Q\) = 0.5, and \(Q\) > 0.5) might be considered. However, for efficient charging, the losses represented by R need to be low. Therefore, only the oscillatory case with \(Q\) > 0.5 is of interest. The voltage across the stage capacitors is given by  
\[v_{\mathbb{C}}(t)=V_{0}\left(1-e^{-\frac{R}{2L}\cdot t}\left(\cos(\sqrt{\frac{ 1}{LC}-\frac{R^{2}}{4L^{2}}}\cdot t\right)+\frac{1}{\sqrt{\frac{4L}{R^{2} \mathbb{C}}-1}}\sin(\sqrt{\frac{1}{LC}-\frac{R^{2}}{4L^{2}}}\cdot t)\right)\right) \tag{10}\]  
If the resistance \(R\) is assumed to be zero, the voltage \(v_{\mathbb{C}}(t)\) rises up to a peak value of 2\(\cdot V_{0}\). Hence, for such a design, during repetitive operation, the charging voltage of the stage capacitors may reach approximately twice that of the supplying voltage source. Thereby, the initial condition \(v_{\mathbb{C}}(0)=0\) is guaranteed by a complete discharge of the stage  
\[v_{\text{C}}(t)+RC\cdot\dot{v}_{\text{C}}(t)+LC\cdot\ddot{v}_{\text{C}}(t)=0\]0 Simplified circuit for basic studies on resonant charging. capacitors during the previous pulse. If the initial condition for the current through the inductance \(L\) is modified in such a way, that there is already a significant energy \(W_{L}\) stored in \(L\), which correlates to an initial current  
\[v_{\text{C}}(t)+RC\cdot\dot{v}_{\text{C}}(t)+LC\cdot\ddot{v}_{\text{C}}(t)=0\]1  
The initial condition for \(\dot{v}_{C}(0)\) becomes  
\[v_{\text{C}}(t)+RC\cdot\dot{v}_{\text{C}}(t)+LC\cdot\ddot{v}_{\text{C}}(t)=0\]2  
The initial current of the charging process, \(i(0)\), rises with an extended on-time of the stage switches. As long as these switches are closed, the stage capacitors are shorted, and the current through the inductance \(L\) rises according to  
\[v_{\text{C}}(t)+RC\cdot\dot{v}_{\text{C}}(t)+LC\cdot\ddot{v}_{\text{C}}(t)=0\]3  
However, if the value of the resistance \(R\) is negligibly small, the rise of the current \(i(t)\) can be approximated to be in proportion to the time according to  
\[v_{\text{C}}(t)+RC\cdot\dot{v}_{\text{C}}(t)+LC\cdot\ddot{v}_{\text{C}}(t)=0\]4  
The opening of the switches defines the beginning of the charging process as described above. Thereby, the charging voltage can be fine-tuned by means of a modulation of the on-time of the stage switches. An industrial-scale electroporation device can be designed for an operation around one well-defined operating point. If there is no need for a wide variation of the voltage, the rectified voltage across a DC-link capacitor grounded at its negative pole may serve as a cheap voltage source. An additional transformer may provide the required insulation from the grid. In order to investigate the operation of the resonant charging circuit of a solid-state switched Marx circuit via current-compensated chokes, circuit simulations of an eight-stage Marx circuit have been performed.