# 10 kV SiC MOSFET Evaluation for Dielectric Barrier Discharge Transformerless Power Supply

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. DBD Load Properties and Modeling

_{diel}and the capacitance of the gas by C

_{gas}. Generally, C

_{gas}<< C

_{diel}. In the OFF state, the DBD is equivalent to the series C

_{eq}capacitance, approximately equal to C

_{gas}. When the discharge is in the ON state, we consider that the gas voltage does not change and remains at the breakdown level, ±V

_{th}(the sign depends on the direction of the current). This assumption is valid when the discharge is a Townsend or glow discharge. It concerns a macroscopic point of view and does not take local phenomena into account, but it is largely sufficient to consider the electrical non-linearity of the plasma. As shown in Figure 1b, the discharge is modeled by a (V

_{gas}, I

_{gas}) dipole, that reflects the breakdown mechanism; this dipole is parallel to the gas capacitance C

_{gas}.

#### 2.2. Operating Principle of the Transformerless Topology

_{dbd}current flowing through the DBD must be controlled. Because of the capacitive behavior of the device, this current must have an average value of zero. An inductor is placed in series with the DBD and the direction of the current is controlled with the states of the switches. The inductance forms a resonant tank with the DBD and directly controls the current injected into the discharge. On the basis of the switches’ electrical constraints (voltage and current waveforms) described in the following part, the static and dynamic characteristics of both semiconductors can be shown to be those of thyristors. There are no thyristors on the market in the range of the target frequencies (tens of kHz), therefore, this function is synthesized by combining a MOSFET and a diode in series (see Figure 2b) [25].

_{gas}, Figure 3a, during a time interval, ∆t

_{off}. As the DBD is initially negatively charged, V

_{dbd}and V

_{gas}increase until the discharge is ignited with a positive current (when V

_{gas}reaches V

_{th}the breakdown level). From this time, during time interval ∆t

_{on}, the V

_{gas}voltage remains constant at +V

_{th}, while the V

_{dbd}voltage and the I

_{dbd}current are governed by the LC

_{diel}circuit, Figure 3b, until the I

_{dbd}current drops to zero. This event causes Th1’s diode to turn OFF. The discharge extinguishes (Sequence (c)) and its voltage does not change until Th2 is initiated.

_{gas}when the discharge is OFF, Figure 3d, and LC

_{diel}when it is ON, Figure 3e. The waveforms of V

_{gas}and I

_{dbd}are symmetrical with respect to those obtained in the first half period. Because of the half bridge configuration, V

_{dbd}voltage is not symmetrical.

#### 2.3. Semiconductor Selection: Analytic Study of the Operation and Sizing Equations

^{+}

_{dbd}. Then, the inductor voltage V

_{L}is zero because no current flows through it, hence, the DBD voltage is seen by Th2. According to the Equation (1), Th1 supports (E − V

^{+}

_{dbd}); this negative voltage is denoted V

^{−}

_{dbd}and is held by the diode D1 of Th1, until the end of the half period.

^{−}

_{dbd}. The thyristor Th1, then, supports the voltage (E − V

^{−}

_{dbd}). This positive voltage is V

^{+}

_{dbd}and is supported by the MOSFET (MOS1) of Th1. To resume, each MOSFET supports a maximum voltage equal to V

^{+}

_{dbd}and each diode a negative voltage equal to V

^{−}

_{dbd}. The current through the semiconductors is equal to the current of the DBD. In our case, it is not a limiting parameter.

_{pulse}. It defines the minimal duration of the half switching period of the MOSFETs as:

_{pulse}mainly depends on the inductance, L, and the capacitance of the DBD. Therefore, knowing the DBD’s capacitance enables the inductance, L, to be sized with respect to Equation (3), using the formula given in Table 1b. A second advantage of this topology is that the magnitude of the discharge current pulse is also controlled by the value of the inductance. Moreover, the MOSFET’s switching frequency can directly control the power transferred to the discharge (Equation (4)).

#### 2.4. High-Voltage Switch Opportunities

_{pulse}is chosen, and therefore defines the moment when the diode spontaneously turns OFF. Then, the turn-OFF control order of the MOSFET is sent 1 µs after ∆t

_{pulse}(and always before T/2). With this condition, we are sure that the MOSFET is turned off when there is zero current (ZCS operation). This minimizes the switching losses and requires the discontinuous mode translated by Equation (3).

^{+}

_{dbd}, while the diodes must hold V

^{−}

_{dbd}. Preliminary SiC power DMOSFETs from company CREE with a 10 kV maximum drain to source voltage are used [28]. Series connected low-voltage MOSFETs [29] have been considered as well, but this solution, which is not presented in this paper, requires static and dynamic voltages balancing. For the diodes, preliminary SiC diodes from CREE, holding up to 10 kV, are used. To limit the parasitic effects that alter the operation described in the previous section, diodes with low parasitic capacitance are favored.

#### 2.5. Experimental Setup and Measurement

_{th}= 1310 V. This breakdown voltage is not the voltage applied across the terminals of the bulb, it is only the voltage across the gas gap. The applied voltage sums this gas voltage and the dielectrics voltages. To calculate V

_{th}, we use measurements of the electric signals applied to the DBD (V

_{DBD}and I

_{DBD}) and the electrical model of the DBD presented in Figure 1. The electrical parameters of the bulb are summarized in Table 2. Measurements and calculations of these data are taken as per the approach set out in [23,24]. In the Discussion Section 4 we compare the performance of the whole system, using this long lamp and a short one (with same tubes diameters), as presented in Figure 5b.

## 3. Results

#### 3.1. Electrical Waveforms

_{dbd}and a slight drop in V

_{dbd}. Synthesized thyristors have a positive voltage of 5030 V (voltage at the MOSFET terminals) and a negative voltage of −1350V (voltage held by the diodes).

#### 3.2. Influence of the Parasitic Capacitance of the SiC MOSFET

_{diode}

_{1}, C

_{diode}

_{2}, C

_{oss}

_{1}, C

_{oss}

_{2}and C

_{eq}(Figure 7c). As shown in Figure 6, when the DC HV supply does not impose the voltage on the open thyristor, oscillations appear. They cause over-voltage across the semiconductors.

_{oss}for the MOSFETs and diodes are taken from CREE data sheets and arranged in tables indexed by semiconductor voltage. C

_{para}is the parasitic capacitance of the high-voltage connection to the DBD apparatus with respect to the ground; it is experimentally measured when the discharge is OFF.

_{dbd}current when the discharge is ignited. We now consider that this model accurately depicts the actual device. If the capacitance of the semiconductors is removed from the simulation, no oscillation occurs (data not shown). Therefore, the semiconductors are definitely responsible for this oscillation. In this topology, if the half period is close to the discharge current conduction (meaning that ∆T

_{blank}as seen in Figure 2. is almost null), oscillation is minimized. Therefore, an accurate modification of the switching frequency could be a solution for reducing the oscillations associated with the semiconductor parasitic capacitance.

#### 3.3. Power Balance

_{dbd}= 2.6 kV, the discharge is never ignited, therefore, all the power is dissipated in the MOSFETs. The voltage across the switches is measured just before turn ON and the switching losses are calculated, with the energy stored in the C

_{OSS}, using the capacitance value that is given by the constructor (232 pF), via the following formula: Switching losses = f.C

_{OSS}.V

^{2}

_{MOSFET.}

## 4. Discussion

_{gas}and C

_{diel}are modified. The surface in contact with the discharge being lower, current and power transferred to the lamp are lower. In Figure 10, we show the comparison between the small and the long lamp, concerning the transferred power and MOSFETs’ losses.

_{oss}. For a given switch, they depend only on V

^{+}

_{dbd}, the voltage applied across the switch at turn ON, which rises with the applied voltage E.

_{th}) and a large area. Here, we work with the lamp having the largest area for a cylindrical configuration, available in our laboratory.

_{oss}, a simulation of the whole system (static converter + DBD device) is performed. It shows that the conduction losses are negligible (less than 1 W). The results of this simulation are consistent with the experiment presented above. As shown in Figure 11, the MOSFET losses directly depend on the intrinsic capacitance of these semiconductors. In addition, according to the selected topology, these turn-ON losses are also proportional to the switching frequency, P

_{turnON}= k.f.Coss.E

^{2}. In the study previously presented in [27], we showed that all the parasitic capacitances (inductance, voltage probes, diodes, and MOSFET) modified the theoretical value of the transferred power, and that taking advantage of the latter to improve the performances was a possible option. Nevertheless, this was a marginal optimization and power balance point of view needed to be considered. Our present experimental results demonstrate that only the intrinsic capacitance of the MOSFET directly affects the efficiency. The other parasitic capacitances only change the voltage waveform as the frequency and the amplitude of the oscillations, when the discharge turn OFF.

_{OSS}capacitance. Consequently, turn-ON losses caused by the energy stored in the C

_{OSS}intrinsic capacitance would be reduced.

_{oss}intrinsic capacitance must be reduced. Several solutions are possible for this purpose. The first one is do design a 10 kV MOSFET with a lower C

_{oss}, as explained above. This kind of component is unfortunately currently unavailable, and we can assume that the high-voltage/low-current applications (as DBD) are not numerous enough to envisage an industrial development of such a device. A more realistic possibility is to connect MOSFETs in series, as it is done in a commercial switch [18]. Figure 11 shows the calculated losses with one 10 kV SiC MOSFET and also losses with two 10 kV SiC MOSFET in series. However, in a series connection, the voltage is distributed between the whole components set. MOSFETs with a lower voltage rating and a lower C

_{oss}could be used [27]. It is important to note that this solution implies an efficient voltage balance of the MOSFETs.

## 5. Conclusions

_{oss}, due to the energy stored there before turn ON, causes significant losses in the MOSFETs.

_{oss}, and thus reducing the losses, have shown to be advantageous for the improvement of the system’s efficiency. Moreover, this solution allows the system to sustain a higher voltage. Secondly, the selected SiC MOSFETs can profitably be considered, provided the power transmitted to the DBD is sufficiently high. It implies generally to consider a DBD with a large surface.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Lamp model—blue background, and (

**b**) proposed current-controlled source to supply the dielectric barrier discharge (DBD)—green background.

**Figure 2.**(

**a**) Theoretical I

_{dbd,}current and V

_{dbd}, V

_{diel}, and V

_{gas}voltages; (

**b**) Synthesized thyristors.

**Figure 3.**The six operating stages—to be observed on the waveforms of Figure 2a. + positive current pulse. (

**a**) Th1 is turned ON (plasma being OFF); (

**b**) V

_{gas}voltage has reached V

_{th}and the plasma is ON; (

**c**) End of the positive current pulse. I

_{dbd,}has reached the 0 level and Th1 has spontaneously turned OFF. + negative current pulse, (

**d**) Th2 is turned ON (plasma being OFF); (

**e**) V

_{gas}voltage has reached, V

_{th}and the plasma is ON; (

**f**) End of the positive current pulse. I

_{dbd,}has reached the 0 level and Th2 has spontaneously turned OFF. Background colors of Figure 3 are directly linked to the corresponding colors/periods of Figure 2. (a): blue, when the current pulses have started, but the plasma is still OFF (

**a**and

**d**), pink, during the time the plasma is ON (

**b**and

**e**), green during the idle time (plasma is OFF and there is no current pulse,

**c**and

**f**).

**Figure 5.**Experimental setups. (

**a**) Schematic of the setup with voltage and current probes, the photo is the long DBD lamp when plasma is ignited (250 W); (

**b**) Picture of the experimental setup connected to the short DBD lamp in the rear part and MOSFET board in the front part. The solid lines correspond to the power wires, the dashed lines to the measurement wires.

**Figure 6.**Experimental measurements, showing the effect of the MOSFET parasitic capacitances, E = 3.5 kV, f = 60 kHz.

**Figure 7.**Operating conditions with parasitic capacitances. (

**a**) Before the breakdown (current flows through diode1 and MOSFET 1); (

**b**) During the discharge (gas voltage is equal to V

_{th}); (

**c**) After the discharge and after Th1 opening (current flows through the parasitic capacitance of diode 1 and MOSFET 1).

**Figure 8.**Simulation model. (

**a**) Experimental and measured waveforms, E = 4 kV, f = 30 kHz; (

**b**) Switch and DBD voltage on the top plot, DBD current on the bottom plot.

**Figure 9.**Discharge power and loss in one MOSFET, versus the high voltage (HV) DC supply’s voltage E, f = 60 kHz.

**Figure 11.**Simulated losses for one MOSFET versus C

_{oss}. Operating conditions, E = 3 kV and f = 30 kHz.

Op. Stage | Switches States | Gas State | Stage Duration ^{1} | V_{dbd} Voltage Peak Value |
---|---|---|---|---|

(a) | Th1 ON, Th2 OFF | OFF | $\u2206{t}_{off}=\sqrt{L\xb7{C}_{eq}}\xb7\left(\pi -arcos\left(\frac{4{V}_{th}\left(1+r\right)\left({V}_{th}-E\right)+{E}^{2}}{4{V}_{th}^{2}\left(1+r\right)-{E}^{2}}\right)\right)$ | ${V}_{dbd}^{+}=\frac{4{V}_{th}^{2}\left(1+r\right)-{E}^{2}}{4{V}_{th}-2E}$ and ${V}_{dbd}^{-}=E-{V}_{dbd}^{+}$ |

(b) | Th1 ON, Th2 OFF | ON | $\u2206{t}_{on}=\sqrt{L\xb7{C}_{diel}}\xb7arcos\left(\frac{4{V}_{th}\left(1+r\right)\left({V}_{th}-E\right)+{E}^{2}}{4{V}_{th}^{2}\left(1+r\right)-E\left(4{V}_{th}-E\right)}\right)$ |

^{1}With: $r=\frac{{C}_{gas}}{{C}_{diel}}$, E being the DC voltage source magnitude.

V_{th} | C_{diel} | C_{gas} | Supply | ||
---|---|---|---|---|---|

Long bulb (60 cm) | 1310 V | 373 pF | 123 pF | L | f |

Short bulb (15 cm) | 1310 V | 85 pF | 30 pF | 4 mH | 10–70 kHz |

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**MDPI and ACS Style**

Diop, M.A.; Belinger, A.; Piquet, H.
10 kV SiC MOSFET Evaluation for Dielectric Barrier Discharge Transformerless Power Supply. *Plasma* **2020**, *3*, 103-116.
https://doi.org/10.3390/plasma3030009

**AMA Style**

Diop MA, Belinger A, Piquet H.
10 kV SiC MOSFET Evaluation for Dielectric Barrier Discharge Transformerless Power Supply. *Plasma*. 2020; 3(3):103-116.
https://doi.org/10.3390/plasma3030009

**Chicago/Turabian Style**

Diop, Mame Andallah, Antoine Belinger, and Hubert Piquet.
2020. "10 kV SiC MOSFET Evaluation for Dielectric Barrier Discharge Transformerless Power Supply" *Plasma* 3, no. 3: 103-116.
https://doi.org/10.3390/plasma3030009