# SiC MOSFET turn-off overvoltage measurement

Mikel Galdeano, Ernesto L Barrios, David Elizondo, Pablo Sanchis

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Mikel Galdeano, Ernesto L Barrios, David Elizondo, Pablo Sanchis. SiC MOSFET turn-off overvoltage measurement. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0261. hal-05085393v2

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# SiC MOSFET turn-off overvoltage measurement

Mikel Galdeano, Ernesto L. Barrios, David Elizondo, Pablo Sanchis

Dept. of Electrical, Electronic and Communications Engineering

Public University of Navarre, Campus Arrosadia, 31006

Pamplona, Spain

mikel.galdeano@unavarra.es, ernesto.barrios@unavarra.es, david.elizondo@unavarra.es,

pablo.sanchis@unavarra.es

**Keywords—**SiC MOSFET, Hard switching, Component for measurements, parasitic elements

**Abstract—** In power electronics, selecting the appropriate measurement system is crucial. This is especially important during MOSFET's turn-off process, where it is essential to measure the voltage rise and accurately capture the peak overvoltage. During turn-off, the interaction between the MOSFET and the parasitic element of the PCB creates a resonance. This phenomenon leads to an overvoltage, which peaks at the resonance frequency and can potentially damage the device. This paper discusses the characteristics of the measurement system needed to capture the peak overvoltage accurately. A step-by-step guide is proposed to ensure the correct selection of the probe and its correct use. This guide is experimentally validated on a three-level converter, where drain-source voltage measurements have been performed with and without a ground reference. The drain to source measurement method proposed in this paper is accurate, capable of minimizing induced noise, and cost-effective.

## I. INTRODUCTION

The adoption of SiC semiconductors has enabled power electronic converters to operate at significantly higher frequencies, improving their performance. However, this also makes the requirements for the measurement system more demanding. The measurement system must be capable of accurately capturing the voltage rise and fall while avoiding the coupling of external noise into the measurement. In SiC MOSFETs, accurate drain-source voltage measurements are particularly important, as the fast turn-off of SiC MOSFETs is associated with an overvoltage caused by the high $di/dt$ that occurs during each turn-off [1]–[12]. SiC MOSFET manufacturers allow these devices to operate close to their breakdown voltage (e.g., 1,000 V for 1,200 V-rated MOSFET). For this reason, the overvoltage can result in operation near or even exceeding the MOSFET breakdown voltage, leading to degradation or failure of the MOSFET and causing the converter to fail [1].

To perform accurate overvoltage measurements caused by MOSFET turn-off, it is necessary to analyze its drain to source voltage waveform. This analysis enables the determination of the required measurement system characteristics, such as bandwidth (BW), maximum voltage, common-mode rejection ratio (CMRR), input impedance and connectors. For wide bandgap (WBG) semiconductors such as SiC and GaN, defining a set of requirements for the measurement system is particularly important, especially the need for a high BW. While some publications analyze the MOSFET turn-off peak overvoltage, they do not specify the type of measurement system used [1]–[4]. The type of probe used is mentioned in [6]–[12] but its selection is not justified. For example, in [6] a 500 MHz fiber optic probe is used, but the accessory to connect it to the test set up is not specified. Similarly, in [8] a 500 MHz high-voltage passive probe is used, but its accessory is also not specified. In [5], [7], [9]–[12] a 200 MHz differential probe with micro grabber tip is used as an accessory. Recently, there has been significant focus in various publications on the capability of probes to reject common-mode signals during floating measurements in semiconductors [13], [14]. However, effective common-mode rejection alone does not ensure accurate measurement of peak overvoltage.

The aim of this paper is to develop a step-by-step guide for selecting the appropriate measurement system to perform accurate drain-source voltage measurements of both ground-referenced and floating MOSFETs. Section II analyzes the MOSFET drain-source voltage waveform. Section III presents the main characteristics of voltage probes and their equivalent circuits, as observed from the test point. This equivalent circuit is subsequently used to analyze the characteristics of the voltage probe and to identify the key considerations required for achieving accurate measurements in power electronics. In Section IV a step-by-step guide for selecting the measurement system characteristics is proposed. Finally, Section V presents experimental results of ground referenced and floating drain-source

<footnote>This work is part of the Projects PID2022-142791OB-I00 and TED2021-132604B-I00 funded by MICIU/AEI/10.13039/501100011033, by ERDF/EU and by the European Union NextGenerationEU/PRTR. It has also been supported by Ingeteam Power Technology.</footnote>
voltage measurements performed on a three-level DC/DC converter.

## II. MOSFET VOLTAGE SWITCHING

Firstly, the waveform to be measured must be analyzed. In this case, the measurements are performed on the MOSFET's drain-source voltage ($V_{DS}$). Fig. 1 shows a ground-referenced $V_{DS}$ measurement, while Fig. 2 presents a floating $V_{DS}$ measurement, both in a DC/DC converter. The $V_{DS}$ waveform is identical for both referenced and floating measurements, except for the presence of a common-mode voltage in floating measurements. In Fig. 3, the temporal $V_{DS}$ waveforms during MOSFET turn-on and turn-off are illustrated. The signal's duty cycle ($\tau$) corresponds to the MOSFET's turn-on duration ($T \cdot \tau$) where $T$ is the switching period. The turn-off duration can be expressed as ($T \cdot (1-\tau)$). The voltage rise time ($t_{vr}$), and the voltage fall time ($t_{vf}$) are also represented in Fig. 3. The parameter $\Delta V_{DS}$ represents the MOSFET turn-off overvoltage.

The different states during MOSFET turn-off have been extensively studied in the literature [15]-[18]. The MOSFET voltage rise time ($t_{vr}$) can be calculated as follows:

$$t_{vr} = V_{DC} \frac{C_{GD} R_{G,total,off}}{V_{Miller} - V_{G,off}}. \quad (1)$$

MOSFET voltage fall time ($t_{vf}$) can be calculated as follows:

$$t_{vf} = V_{DC} \frac{C_{GD} R_{G,total,on}}{V_{G,on} - V_{Miller}}. \quad (2)$$

The Miller voltage ($V_{MILLER}$) varies with the switching current, so the minimum $t_{vr}$ and $t_{vf}$ values must be calculated, as these represent the most restrictive cases for the BW probe selection. To calculate the minimum $t_{vr}$, $V_{MILLER}$ needs to be at its maximum, which corresponds to the maximum switching current. Conversely, to calculate the minimum $t_{vf}$, $V_{MILLER}$ should be at its minimum, which corresponds to the minimum switching current [1].

During MOSFET turn-off, $di/dt$ occurs causing resonance between the MOSFET and the PCB parasitic elements. This resonance occurs at the following frequency [1]

$$f_r = \frac{1}{2\pi\sqrt{L_{TOTAL}C_{OSS,m}(V_{DC})}}, \quad (3)$$

where $L_{TOTAL}$ is the sum of the MOSFET parasitic inductances ($L_{S,m} + L_{D,m} + L_{S,d} + L_{D,d}$), while $L_{PCB}$ represents the inductance of the commutation loop. The parameter $C_{OSS,m}(V_{DC})$ is the MOSFET output capacitance at the voltage $V_{DC}$. This resonance causes the MOSFET overvoltage, which reaches its maximum

at the resonance peak and can potentially destroy the device.

To convert the time-domain values of the $V_{DS}$ signal into frequency-domain values, or in other words, the frequency spectrum of the signal it can be derived as follows [19]:

$$v_{DS}(t) = V_{DC} \frac{\tau}{T} + 2V_{DC} \frac{\tau}{T} \sum_{n=1}^{\infty} \left[ \frac{\sin(n\pi f_o \tau)}{n\pi f_o \tau} \left[ \frac{\sin(n\pi f_o t_{vr})}{n\pi f_o t_{vr}} \right] \cdot \cos[2n\pi f_o t - n\pi f_o (\tau - t_{vr})] \right]. \quad (4)$$

<figure><img src="image_2.png" /><figcaption>Fig. 1. S4 MOSFET referenced $V_{DS}$ measurement diagram.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 2. S2 MOSFET floating $V_{DS}$ measurement diagram</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 3. Simulated MOSFET drain-source temporal values ($V_{DS}$).</figcaption></figure>

In Fig. 4, and as described in (4), the signal frequency spectrum and the voltage frequency envelopes are presented. Frequencies below twice the switching frequency (point 1) exhibit a constant gain
corresponding to the DC voltage. From point 1 to point 2 frequencies decrease at a rate of -20 dB/decade. Beyond point 2, which corresponds to the minimum determined by the voltage rise and fall times, they fall at a rate of -40 dB/decade. The frequency $f_r$, defined in (2), does not appear in (4), as the resonance is not modelled in the equation. However, it can be observed in Fig. 4. as it corresponds to the real Fast Fourier transform (FFT) of the waveform shown in Fig. 3.

<figure><img src="image_5.png" /><figcaption>Fig. 4. Simulated MOSFET drain-source voltage frequency spectrum</figcaption></figure>

### III. VOLTAGE PROBES CHARACTERISTICS AND EQUIVALENT CIRCUIT

#### A. Equivalent circuit

In order to understand the interaction between the measurement system and the circuit under test, it is essential to consider the equivalent circuit of the measurement system as seen from the test point, shown in Fig. 5 [20]-[22].

<figure><img src="image_6.png" /><figcaption>Fig. 5. Measurement system equivalent circuit</figcaption></figure>

This equivalent circuit represents the signal voltage to be measured ($V_{DS}$), the test point voltage ($V_{tp}$) corresponding to the MOSFET drain-source voltage, and the voltage displayed on the oscilloscope ($V_{osc}$). The measurement system includes key elements such as the input capacitance ($C_p$), input resistance ($R_p$) and the connector parasitic inductance ($L_{connector}$). The impedance $Z_{cm}$ is included in the model to represent the grounding characteristics of the probe and oscilloscope system, modelling the impedance of the probe to the flow of common-mode currents (CMRR). The value of

$Z_{cm}$ varies with frequency in active, differential, and optical probes. However, passive probes completely lack common-mode rejection capabilities ($Z_{cm} \approx 0$).

#### B. Characteristics

The types of probes commonly used in power electronics are passive, active, differential, and fiber optic probes. To measure high voltages, such as the MOSFET drain-source voltage, passive, differential, and fiber optic probes are typically employed. The main characteristics to be considered are:

##### 1) Input voltage range

SiC discrete and module MOSFETs have breakdown voltages ranging from 400 V to 3,300 V. To measure the drain-source voltage, it is essential to use probes capable of withstanding these voltage stresses. Low-voltage active probes (single-ended, fiber-optic, and differential) typically support up to 30 V peak voltage [21], [25]. These low-voltage probes will not be analyzed, as their voltage ratings are insufficient for this application. High-voltage passive probes (hereinafter referred to as passive probes) support a wide voltage range, from 2,500 V peak to 20,000 V peak [21], [24] High-voltage differential probes (hereinafter differential probes) can handle up to 6,000 V peak [21], [24]. High-voltage fiber-optic insulated probes (hereinafter referred to as fiber-optic probes) can reach 2,500 V peak voltage [21], [24].

##### 2) Bandwidth (BW)

This characteristic is crucial for accurately measuring the MOSFET turn-off. To understand how the bandwidth (BW) can impact the measurements, the measurement system, from the test point to the voltage displayed on the oscilloscope, can be modeled as a second-order low-pass filter:

$$V_{osc} = V_{tp} \frac{1}{s^2 L_{connector} C_p + \frac{L_{connector}}{R_p} s + 1} \quad (5)$$

The resonance frequency is determined by the parameters $L_{connector}$ and $C_p$ and determines the bandwidth (BW). The value of the input resistance of the probe ($R_p$), determines the damping factor. The lower the value of $R_p$ the greater the damping, which also implies a lower load on the circuit. Real bodes of different types of probes and accessories can be found in [22], [23], where the influence of the connectors on the final BW of an active and differential probe can be seen. Fig. 6 shows the theoretical gain of the measurement system for different bandwidth values. According to (5) selecting an accessory with a high $L_{connector}$ value will cause a decrease in the probe BW [20]-[22]. If the probe gain values shown in Fig. 6 are plotted against the waveform frequency spectrum in Fig. 3, the drain-source voltage measurements for different bandwidths (BW) values can be obtained, as
shown in Fig. 7. As observed, the lower the BW, the greater the loss of information at certain frequencies. This is particularly relevant for measuring peak overvoltage, as the resonance frequency of the MOSFET and PCB parasitic elements is relatively high. In this example, the resonant frequency is 41 MHz with a gain of -3.11 dB. Then, the 50 MHz probe would measure with a gain loss of -7.86 dB, the 200 MHz probe would measure a higher value than the real one (-1.88 dB), and the 500 MHz and 800 MHz probes would measure values close to the real one (-2.92 dB and -3.03 dB, respectively).

When considering commercially available probes, the bandwidth of passive probes ranges from 200-800 MHz [21], [24]. The bandwidth of differential probes is limited, ranging from 50 MHz to a maximum of 200 MHz [21], [24]. Fiber optic BW probes have a wide range, from 200 MHz to 1 GHz [21], [24].

<figure><img src="image_7.png" /><figcaption>Fig. 6. Measurement system percentage gain for different BW values</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 7. Drain-source voltage rise for different BW values.</figcaption></figure>

### 3) Common Mode Rejection Ratio (CMRR)

When floating measurements (e.g., a MOSFET without a ground reference) are made with respect to the

oscilloscope ground reference, common-mode currents flow through the probe, which negatively distort the oscilloscope measurement. To perform this type of measurement, high-voltage differential probes with a high $Z_{cm}$ value are widely used [20]. These probes can handle common-mode voltages of 6 kV with 26 dB CMRR at 100 MHz [26]. Another solution to avoid this effect is the use of fiber optic isolated probes, which have an almost infinite $Z_{cm}$. These probes can withstand common-mode voltages up to 60 kV with a 100 dB CMRR at 100 MHz [27]. In the case of passive high-voltage probes, their $Z_{cm}$ value is low because they lack CMRR, as they only contain passive components. However, it is possible to perform this type of measurement accurately by using two identical passive probes, both referenced to the system ground, as shown in Fig. 2. In this solution, one probe is placed at the MOSFET drain and the other at the source, both having the same ground reference. By subtracting the readings from the two probes, a precise measurement is achieved, and common-mode noise is completely rejected. To ensure accurate measurements, it is necessary that the probes are identical and calibrated at the time of measurement [20].

### 4) Input impedance

The probe input impedance ($R_p, C_p$ and $L_{connector}$) also determines the quality of the measurements. This is because the probe absorbs current from the circuit test point where it is connected, effectively loading the measurement circuit, and potentially altering its operation, which in turn can modify the signal to be measured. The values of $R_p$ and $C_p$ are set by the probe. In passive probes, $C_p$ typically ranges from 2-4 pF and $R_p$ depends on the maximum voltage, with values of 40 MΩ and 100 MΩ for voltages of 2,500V and 40 kV, respectively [24]. In the case of differential probes, $C_p$ value is usually less than 2 pF, with $R_p$ values of 5 MΩ, 10 MΩ and 40 MΩ for voltages of 750 V, 1,500 V and 6,000 V, respectively [26]. Isolated probes have $C_p$ values between 2-3 pF and $R_p$ values of 10 MΩ and 40 MΩ for voltages of 250 V and 2,500 V [27]. Therefore, it can be concluded that the $C_p$ values of the probes are similar and neglectable when having a minimal impact on loading the circuit compared to the MOSFET output capacitance values ($C_{oss,m} \approx 300-600$ pF $>>2-4$ pF).

### 5) Connector parasitic inductance

The $L_{connector}$ value depends on the type of accessory selected for connect the probe to the circuit. For passive probes, the optimal connector is the ground spring, as it allows measurements to be conducted with a short accessory length and without the need to design a specific PCB that includes a specific connector. In the case of differential probes, the measuring cables are long, and an additional accessory is required to connect them to the test point, resulting in higher $L_{connector}$
values. No specific PCB design is needed for the connection. For fiber optic probes, the best accessory is the MMCX connector, as it has virtually no length, minimizing the $L_{connector}$ value to a minimum [20], [22], [27]. However, it is important to design the PCB with careful attention to the placement of these connectors to enable easy soldering later. The requirement for a specific PCB design to perform the measurements can be a disadvantage for manufacturers of industrial electronic power converters, as it necessitates the creation of an additional PCB solely for measurement purposes. Passive and differential probes have accessories that can be easily coupled to the measurement circuit without the need for a specific pre-design. However, for passive, differential, and fiber optic probes with accessories of a certain length, attention must be paid to the interaction between $C_p$ and $L_{connector}$, and $L_{connector}$ independently, as they can cause measurement issues, which are explained below.

**Probe bandwidth limitation:** Is due to the probe's LC circuit response ($C_p$ and $L_{connector}$) to the voltage rise and fall with which it is excited ($V_{DC}$). This resonant frequency can be observed on the oscilloscope if the oscilloscope's bandwidth (BW) is enough to capture the frequency. The higher the $L_{connector}$ value, the lower the parasitic resonance frequency, making this effect more visible on the oscilloscope display. This effect is particularly relevant in differential probes and may also be significant in passive and fiber optic probes if long accessories are used [20], [22].

**Noise induction:** The larger the area formed between the probe tip and the ground reference in the circuit, the higher the $L_{connector}$ value. The probe connection to the measurement circuit acts as an antenna, capable of capturing electromagnetic noise (either generated by the converter itself or externally) and inducing voltages into the probe. These induced voltages are combined with those captured directly from the circuit by the probe, leading to false readings on the oscilloscope. This effect is most noticeable in differential probes, as the area formed by the connectors is significant, even if the connectors are braided. In passive probes with a ground spring connector, this

effect is minimal, and in optical probes with an MMCX connector, the effect is negligible, as there is virtually no area between the probe connection and the measurement circuit [20], [22].

## 6) Cost

In order to quantify the cost of different types of voltage probes and make a comparison, Tektronix is used as the reference manufacturer in the following. Passive probes range in price from €513 to €3,900. Differential probes range from €1,720 to €9,190, and fiber optic probes range from €12,700 to €39,200.

Table I presents a summary of the main characteristics of the different types of voltage probes discussed in this section.

# IV. GUIDE TO PROBE SELECTION AND TURN-OFF OVERVOLTAGE MEASUREMENT

The steps to follow when selecting a probe to measure a specific signal (such as the MOSFET drain-source voltage) proposed in this work are as follows:

## 1) Determine signal characteristics

To measure the MOSFET drain-source voltage, it is necessary to calculate the voltage rise and fall times using equations (1) and (3). The turn-off resonant frequency, as given by equation (2), is obtained through experimental measurement, as determining the value of $L_{PCB}$ is complex.

## 2) Determine maximum voltage

MOSFETs used in high-power electronics must withstand high voltages, so it is necessary to use passive, differential, or high voltage fiber optic probes.

## 3) Bandwidth

For the proper measurement system selection, the system's bandwidth must be at least five times greater than the highest frequency of interest calculated in step 1 [4], [20], [22]. Therefore, to accurately capture the $V_{DS}$ voltage rise and fall edges, as well as the peak overvoltage caused by MOSFET turn-off, the measurement system's bandwidth must meet the following limit:

<table><caption>TABLE I. VOLTAGE PROBE CHARACTERISTICS</caption><thead><tr><th rowspan="3">Voltage probe type</th><th colspan="5">Main characteristics</th></tr><tr><th rowspan="2">Voltage range (V)</th><th rowspan="2">Bandwidth (MHz)</th><th rowspan="2">CMMR (dB @100MHz)</th><th colspan="3">Input impedance</th></tr><tr><th>Cp (pF)</th><th>Rp (MΩ)</th><th>L<sub>connector</sub> length</th><th>Price range (€)</th></tr></thead><tbody><tr><td>Passive probes [24]</td><td>2,500-20,000</td><td>200-800</td><td>-</td><td>2-4</td><td>40 (2,500V)<br>100 (40,000V)</td><td>Low (Spring)</td><td>513-3,900</td></tr><tr><td>Differential probes [26]</td><td>750-6,000</td><td>50-200</td><td>26</td><td>&lt;2</td><td>5 (750V)<br>10 (1,500V)<br>40 (6,000V)</td><td>High (All of them)</td><td>1,720-9,190</td></tr><tr><td>Optical isolated probes [27]</td><td>2,500</td><td>200-1,000</td><td>100</td><td>2-3</td><td>10 (250V)<br>40 (2,500V)</td><td>Very low (MMCX)</td><td>12,700-39,200</td></tr></tbody></table>
$$BW \geq 5 \cdot \max \left( \frac{1}{\pi t_{vf}}, \frac{1}{\pi t_{vr}}, f_r \right). \quad (6)$$

Generally, the resonant frequency is the maximum value in equation (6). This occurs because, in PCB design, the goal is to minimize the $L_{PCB}$ value. When combined with the low $C_{OSS,m}$ values of SiC MOSFETs, this results in high resonant frequency ($f_r$) values. As a result, there are greater demands on the measurement system, including both the probe and oscilloscope.

### 4) Connector selection

Among the accessories that accompany each probe type, always select those recommended by the manufacturer to minimize the value of $L_{connector}$ [20]-[22]. For high voltage passive probes, use the ground spring. In differential probes, ensure the measuring cables are braided to minimize $L_{connector}$. For fiber optic probes, the optimal connector is the MMCX, although it is important to consider its use during the PCB design process. If a longer connector is used, the advantages of the fiber optic probe will be compromised.

### 5) BW probe limitation

It is important to ensure that the probe's self-resonance does not limit its actual bandwidth (BW) and that it does not appear on the oscilloscope measured voltages. To verify this, a simple calculation can be performed to estimate the probe's parasitic self-resonance and check that it is not more than five times below the oscilloscope's bandwidth. For instance, consider a passive voltage probe with 3 pF input capacitance, using either the ground spring (10 nH) or alligator clip (150 nH) as accessories. These systems have self-resonance frequencies of 920 MHz and 240 MHz, respectively. If the oscilloscope's bandwidth (BW) is 500 MHz, the probe with the ground spring will not impact the measured signal, while the probe with the alligator clip will distort the measurement.

Table II shows the measurement system characteristics used in recent studies [5]-[12]. The turn-off resonant frequency ($f_r$) and the MOSFET output capacitance $C_{OSS,m}$ (measured at the operating voltage) were obtained from referenced studies, while the total setup parasitic inductance was calculated (3). The utilized bandwidth ($BW_u$) was then compared to the required bandwidth ($BW_n$) as defined in this paper. In [5], [11], and [12], differential probes are used; however, the required bandwidth (BW) exceeds the BW of the probes utilized, resulting in a loss of accuracy in the peak overvoltage measurement. In [7], [9], and [10], differential probes are also used, and they meet the BW requirements primarily because the total parasitic inductance is high, which results in a lower $f_r$. In [6], a fiber optic probe is employed, while in [8], a high-voltage differential probe is used. Both probes meet the BW requirements, ensuring accurate peak

measurements. It is also important to consider the connector used to attach the probe to the test point. In [6]-[8], [11], and [12], the type of connector is not specified. In [5], [9], and [10], where differential probes are employed, pincer clips are used as connectors. Notably, in [9] and [10], although the bandwidth (BW) requirements are met, the use of this type of connector can result in resonances between the connector inductance ($L_{connector}$) and the probe capacitance ($C_p$). Additionally, it may introduce induced noise due to the area formed by the measurement cables, which could lead to measurement errors.

<table><caption>TABLE II. LITERATURE PAPERS CHARACTERISTICS</caption><thead><tr><th rowspan="2">Ref.</th><th colspan="5">Parameters</th></tr><tr><th>C<sub>OSS,m</sub><br>(nF)</th><th>L<sub>TOTAL</sub><br>(nH)</th><th>f<sub>r</sub><br>(MHz)</th><th>BWn<br>(MHz)</th><th>BWu<br>(MHz)</th></tr></thead><tbody><tr><td>[5]</td><td>0.178</td><td>45</td><td>56</td><td>284</td><td>200</td></tr><tr><td>[6]</td><td>2</td><td>15</td><td>29</td><td>145</td><td>800</td></tr><tr><td>[7]</td><td>0.089</td><td>170</td><td>41</td><td>205</td><td>200</td></tr><tr><td>[8]</td><td>0.055</td><td>70</td><td>81</td><td>405</td><td>500</td></tr><tr><td>[9]</td><td>0.279</td><td>60.5</td><td>39</td><td>195</td><td>200</td></tr><tr><td>[10]</td><td>0.175</td><td>361</td><td>20</td><td>100</td><td>200</td></tr><tr><td>[11]</td><td>0.284</td><td>6.9</td><td>110</td><td>550</td><td>200</td></tr><tr><td>[12]</td><td>0.235</td><td>25</td><td>65</td><td>325</td><td>300</td></tr></tbody></table>

## V. EXPERIMENTAL CASE PROBE SELECTION

For probe type selection, the probes listed in Table I from the manufacturer Tektronix will be used. The measurements were performed on the three-level topology presented in [28], where referenced measurements were made on the S4 MOSFET $V_{DS}$ voltage (Fig. 1), and floating measurements were made on the S2 MOSFET $V_{DS}$ voltage (Fig. 2).

### 1) Determine signal characteristics

The characteristics of the test bench and the semiconductor used (FF17MR12W1M1H_B70) are presented in Table III [29]. The calculations were performed at a temperature of 25 °C. To obtain the Miller voltage for a load current of 30 A, the procedure outlined in [1] was followed. Using equations (1) and (3) for the voltage rise and fall time calculations, 30 ns and 62 ns were obtained, respectively. Converting these time values into frequency values using equation (6) yields 10 MHz and 5 MHz, respectively. The module's parasitic inductance value is provided by the manufacturer (9 nH). However, the PCB routing parasitic inductance value is unknown and difficult to calculate theoretically. Therefore, switching the MOSFET under is necessary. This step can be carried out with any probe (if it complies with the voltage limit), since the focus is on the frequency measurement. The turn-off resonant frequency values obtained were
76 MHz for the S4 MOSFET and 78 MHz for the S2 MOSFET.

<table><caption>TABLE III. TEST BENCH PARAMETERS</caption><thead><tr><th colspan="4">Test bench parameters</th></tr><tr><th>Parameter</th><th>Value</th><th>Parameter</th><th>Value</th></tr></thead><tbody><tr><td>DC input voltage (V<sub>DC</sub>)</td><td>960 V</td><td>Load current (I<sub>LOAD</sub>)</td><td>30 A</td></tr><tr><td>MOSFET equivalent output capacitance (C<sub>oss,eq</sub>)</td><td>0.38 nF</td><td>MOSFET internal gate resistance (R<sub>G,int</sub>)</td><td>2 Ω</td></tr><tr><td>MOSFET drain to gate capacitance (C<sub>GD</sub>)</td><td>67 pF</td><td>MOSFET output capacitance (V<sub>DC</sub>) (C<sub>oss</sub>(V<sub>DC</sub>))</td><td>0.26 nF</td></tr><tr><td>S2 Turn-on external gate resistance (R<sub>G,ext,on</sub>)</td><td>8 Ω</td><td>S2 Turn-off external gate resistance (R<sub>G,ext,off</sub>)</td><td>4 Ω</td></tr><tr><td>S4 Turn-on external gate resistance (R<sub>G,ext,on</sub>)</td><td>12 Ω</td><td>S4 Turn-off external gate resistance (R<sub>G,ext,off</sub>)</td><td>8 Ω</td></tr><tr><td>Miller voltage (V<sub>MILLER</sub>)</td><td>7.75 V</td><td>MOSFET parasitic inductance (L<sub>p</sub>)</td><td>9 nH</td></tr><tr><td>Gate voltage OFF (V<sub>G,off</sub>)</td><td>-3 V</td><td>Gate voltage ON (V<sub>G,on</sub>)</td><td>15V</td></tr></tbody></table>

## 2) Determine maximum voltage

The DC voltage value is 960 V. For grounded-reference measurements, a probe with a maximum input voltage exceeding 500 V is required. Conversely, for non-grounded-reference measurements, a probe with a maximum input voltage higher than 1,000 V is needed. Differential, high-voltage passive, and fiber optic probes listed in Table I offer a wide range of maximum input voltages. To measure both grounded and non-grounded reference voltages, suitable options include differential probes with 1,300 V or 5,600 V ratings, high-voltage passive probes with 2,500 V ratings, or fiber optic probes with 2,500 V ratings.

## 3) Bandwidth

To accurately capture the MOSFET turn-off peak overvoltage from equation (6), a minimum bandwidth of 380 MHz is required for the S4 turn-off and 390 MHz for the S2 turn-off. As a result, differential probes cannot be used due to their more limited bandwidths. While passive and high-voltage fibre optic probes are options, the high cost of fibre optic probes and the need to design a new PCB for the MMCX connector insertion make the high-voltage passive probe the preferred choice for measurements. Therefore, passive high-voltage probes present an affordable, universal solution for conducting measurements. According to Fig. 1, one passive probe is needed for measurements on ground referenced MOSFETs, while two passive probes are required for floating voltage measurements. The Tektronix TPP0850 model has been selected, offering a bandwidth of 800 MHz, an input impedance of 40 MΩ and 1.8 pF, and the ability to handle peak voltages up to 2,500 V. The unit cost is 1,400€.

## 4) Connector selection

Among the accessories included with passive high-voltage probes, the spring has the lowest L<sub>connector</sub> value for performing measurements.

## 5) Ground referenced MOSFET results

The measurements were conducted on the S4 MOSFET shown in Fig. 1. Based on the operation of the three-level converter, the S4 MOSFET conducts current in the first quadrant during turn-off, leading to a hard turn-off, the overvoltage of which can be calculated as described in [1]. The frequency spectrum of the experimental drain-source voltage is shown in Fig. 8. The experimentally obtained on/off times are 38 ns (Fig. 9) and 68 ns (Fig. 10). The peak overvoltage was calculated as described in [1], yielding a value of 30 V. The experimentally measured value is 32 V (Fig. 9).

<figure><img src="image_9.png" /><figcaption>Fig. 8. Experimental S4 MOSFET frequency spectrum</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 9. Experimental S4 MOSFET turn-off</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Fig. 10. Experimental S4 MOSFET turn-on</figcaption></figure>

## 6) Floating MOSFET results

The measurements were conducted on the S2 MOSFET shown in Fig. 2. Before the S2 gate signal turns off, S2 MOSFET conducts current in the third quadrant. After turn-off, the current maintains the same polarity, causing the S2 MOSFET to continue conducting through its body diode. Current stops flowing through the S2 MOSFET when the gate signal of the S1 MOSFET turns on. As a result, the voltage rise of S2 is triggered by the turn-on of S1. In this turn-off scenario, the turn-off intervals of S2 correspond to the turn-on intervals of S1. Thus, the di/dt occurs first between the S1 and S2 MOSFETs, followed by the dv/dt. This behaviour is evident in Fig. 12, where a resonance occurs during the voltage switching process due to the preceding di/dt. Conversely, in Fig. 10, the dv/dt precedes the di/dt, leading to the resonance after the voltage has changed. The measurements were performed using two high-voltage passive probes, as depicted in Fig. 2. The S2 MOSFET voltage was obtained by calculating the difference between the two probes. One of the probes measured voltages ranging from 0 V to 960 V (excluding peak overvoltage), while the other measured between 0 V and 480 V. The frequency spectrum of the experimental drain-source voltage is presented in Fig. 11.

<figure><img src="image_12.png" /><figcaption>Fig. 11. Experimental S2 MOSFET frequency spectrum</figcaption></figure>

Experimentally determined on/off times are 28 ns (Fig. 12) and 25 ns (Fig. 13), with the measured experimental peak overvoltage reaching 54 V (Fig. 12).

<figure><img src="image_13.png" /><figcaption>Fig. 12. Experimental S2 MOSFET turn-off</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 13. Experimental S2 MOSFET turn-on</figcaption></figure>

# VI. CONCLUSIONS

Measuring the drain-source voltage in WBG semiconductors is a challenge. This paper defines the characteristics a probe must have to accurately measure the MOSFET turn-off peak overvoltage. A measurement system with a minimum bandwidth of 500 MHz is required. Additionally, it is important to choose the correct connector to minimize induced noise and prevent the probe's self-resonance. It has been determined that differential probes do not have sufficient bandwidth (BW) to capture this peak overvoltage. Fiber optic probes could be an option, however, their high cost and the need for designing a specific PCB for measurements make them less favourable and many times they are used without appropriate connectors, leading to inaccurate measurements. In contrast, passive high-voltage probes are advantageous due to their high BW, low cost, robustness, ability to measure with or without a ground reference, and effective coupling to the measurement circuit through the ground spring connector. The method proposed in this paper has been demonstrated more accurate, capable of minimizing induced noise, and more cost-effective than the solutions found in the
literature. The study shows that this method is essential for converters with WBG semiconductors due to the high-frequency components of the signal.

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