# Compact Design and Impact Ionization: Utilizing Small-Sized Thyristors in a 4-Stage Marx Generator
## 2 Materials and Methods  
To achieve ultra-fast thyristor triggering in industrial thyristors, we developed a small thyristor stack generator utilizing thyristors rated at 2.4 kV [29]. These thyristors show a parasitic capacitance of 220 pF while functioning at a bias voltage of 1.4 kV, and they possess a static breakdown voltage of 3 kV. As previously stated in Section 1, the peak voltage required for impact ionization in these thyristors is 6 kV. Therefore, to achieve effective ionization, our triggering generator must provide a voltage of 4.6 kV after accounting for the 1.4 kV biasing voltage. Therefore, the generator must meet the following operating parameters:  
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The first stage of the Marx generator utilizes a single 1.2 kV rated thyristor (VS-16 TTS12-M3, [30]). For these thyristors to enter impact-ionization mode, the triggering voltage must far exceed their breakdown thresholds--reaching at least twice their standard values. This triggering signal is derived from the output of six parallel SiC MOSFETs, as shown in Figure 3, supplemented by the voltage stored in \(C3_{1}\) to enable impact ionization. The increasing number of thyristors in the subsequent stages of the Marx generator is used to manage the rising voltage levels as the pulse propagates through the stages. Each capacitor at the beginning of each stage (\(C3_{1}\) to \(C3_{4}\)) adds the corresponding voltage (\(HV_{i}\)) to the pulse. Each additional thyristor helps distribute voltage stress within the stage. Small leakage currents in thyristors increase with the voltage across them, facilitating voltage redistribution. This phenomenon occurs as the leakage current through each thyristor adjusts the voltage stress across its junction, thereby maintaining a stable voltage division [31]. To enhance this balancing effort, voltage-sharing resistors (\(Rs3_{1}\) to \(Rs3_{9}\)) connected in parallel with each thyristor have been incorporated to even out voltage differences [31]. At a maximum charging voltage of 1.3 kV, these resistors ensure a balancing current of about 13 \(\upmu\)A, significantly exceeding the typical leakage current of 1 \(\upmu\)A at this voltage. These resistors, however, have been omitted from the schematic in Figure 4 to improve its clarity and readability. In our design, we intentionally introduced an impedance mismatch between the six SiC MOSFET stages and the individual Marx stages to generate a positive reflection at the output, facilitating the initial triggering of the thyristor in impact-ionization mode. The primary mismatch occurs in the thyristor before it turns on. At the output of the six SiC MOSFET stages, the circuit can deliver a very high current (370 A) due to its voltage and impedance characteristics, as detailed in our previous publication [23]. However, the thyristor from the following Marx stage, in its off-state, has a parasitic capacitance of 14 pF, which only draws a small portion of this current (1 kV/ns \(\cdot\) 14 pF \(=\) 14 A). In this state, the thyristor can be approximately considered an open circuit, causing nearly  
Figure 4: The thyristor Marx generator schematic. Figure 3: The parallel SiC MOSFET configuration that triggers the thyristor Marx generator. double the voltage to reflect back onto it. As detailed in the same publication, this reflection enhances the voltage pulse at the input of the first stage, contributing to the sharp rise time and increased amplitude available for triggering. This reflection is significantly more pronounced than the impedance mismatch between stages. To address this, we employed impedance grading, where the impedance of the higher-voltage stage was adjusted to maintain current continuity. After benefiting from this initial reflection, we progressively increased the impedance in subsequent stages (Table 1). This impedance transition reduces signal reflections at the output and prevents undesired high-voltage spikes, which could otherwise cause excessive stress on the thyristors.