# Compact Design and Impact Ionization: Utilizing Small-Sized Thyristors in a 4-Stage Marx Generator
## 2 Materials and Methods
### Capacitive Probe  
During the testing of the pulse generator, we encountered significant challenges with our measuring equipment, particularly with the standard high-voltage (HV) and high-frequency (HF) attenuators that we utilized. These devices began to experience breakdowns when subject to output voltages surpassing 6 kV, as explained in [34]. To address this issue cost-effectively, we transitioned to an alternative method--namely, capacitive probes--to measure the output voltages. This adjustment provided a more robust measurement configuration. This adjustment provided a more robust measurement configuration by mitigating escalating voltage levels and ensuring the oscilloscope and attenuator were protected from excessive voltage exposure, as capacitive probes can withstand higher thresholds. Figure 8: Simulated voltage reflections on the different stages (SiC MOSFETs and TP1 to 4) in the controlled impedance case. Figure 9: Simulated current reflections on the SiC MOSFETs in the fixed (20\(\Omega\)) impedance (dotted, blue) and controlled impedance (continuous, yellow) cases. Capacitive probes offer the advantage of non-contact voltage measurements, thereby preserving the integrity of the oscilloscope and attenuator by reducing the voltage that reaches these sensitive instruments [35]. Their application is well-established within the pulsed power community for testing high-voltage, fast pulses [36], and they have been successfully developed in laboratories utilizing printed circuit board (PCB) techniques [37]. Integrating capacitive sensor plates into the existing PCB design eliminates the need for additional components, leveraging the intrinsic capacitance between the probe and the test point. This non-contact approach significantly reduces the risk of arcing and damage to delicate components, thereby ensuring a safer measurement environment. The 2 mm capacitive probe is positioned beneath the much larger target signal plane, allowing for effective voltage measurement without direct electrical contact. We recognized that the accuracy of our capacitive probe measurements could be influenced by both the voltage amplitude and the frequency of the signal due to the frequency-dependent limitations of FR4, as documented in recent studies ([38; 39; 40]). To mitigate these concerns, we maintained consistent geometrical dimensions for the capacitive probe and its associated high-voltage island, following the recommendations from the aforementioned literature ([38; 39; 40]) to ensure reliable calibration. In our setup, the capacitive probe functions as a first-order high-pass filter. The choice of FR4 as the PCB material could potentially limit high-frequency measurements as the choice of material affects the upper-frequency limit due to dielectric losses. We conducted comparative measurements of the driver output using both our current FR4 PCB and a high-frequency PCB material (RO4350B) [41] (Figure 10). The results indicated no significant improvement in rise time (FR4: 680 ps; RO4350B: 768 ps), leading us to continue using FR4 for further measurements as it meets our requirements without imposing limitations on the bandwidth of the capacitive probe while having the added advantage of being more economically priced. The final PCB setup, illustrated in Figure 11, features a 2 mm diameter pad connected to an SMA plug for the measurement cable connection, with copper shielding included to enhance signal accuracy. Figure 10: Driver output measurement. Comparison between FR4 and RO4350B PCB materials. To evaluate the accuracy and reliability of the capacitive probe, we conducted a series of tests comparing the probe's measurements with those obtained using a standard coaxial cable (RG58) connected to a 50 \(\Omega\) attenuator. Due to the attenuator's voltage rating limitations, measurements were performed such that the resulting output signals reached a maximum of 2.7 kV. Both measurement methods were employed simultaneously to assess performance.