# A Simplified Hard-Switching Loss Model for Fast-Switching Three-Level T-Type SiC Bridge-Legs

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

_{oss}, and reverse-recovery charge, Q

_{rr}, only. Additionally, targeting GaN devices, the modeling approach outlined in [13] does not account for reverse-recovery losses, i.e., it is not directly applicable to 3LTT bridge-legs with SiC MOSFETs. The switching-loss model in [13] has only been verified indirectly at the converter level by measuring the total converter losses of a 3LTT undiriectional rectifier adopting 650 V GaN HEMTs and 1200 V SiC Schottky diodes.

## 2. Three-Level T-Type Capacitive Loss Analysis

_{dc}= 800 V. By inserting Equations (2) and (3) in Equation (1) and leveraging Equations (5)–(8), straightforward capacitive loss expressions are obtained:

## 3. Simplified Hard-Switching Loss Model

## 4. Experimental Validation

#### 4.1. No-Load Operation (${I}_{\mathrm{sw}}=0$)

#### 4.2. Operation under Load (${I}_{\mathrm{sw}}>0$, ${I}_{\mathrm{sw}}<0$)

_{j}= 175 °C; the datasheets belonging to the same semiconductor devices in a different, surface-mount TO-263-7L package are used to extract $\tau $ at T

_{j}= 25 °C, enabling a linear interpolation between the $\tau \left({T}_{\mathrm{j}}\right)$ values.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Teichmann, R.; Bernet, S. A Comparison of Three-Level Converters versus Two-Level Converters for Low-Voltage Drives, Traction, and Utility Applications. IEEE Trans. Ind. Appl.
**2005**, 41, 855–865. [Google Scholar] [CrossRef] - Schweizer, M.; Friedli, T.; Kolar, J.W. Comparative Evaluation of Advanced Three-Phase Three-Level Inverter/Converter Topologies against Two-Level Systems. IEEE Trans. Ind. Electron.
**2013**, 60, 5515–5527. [Google Scholar] [CrossRef] - Gurpinar, E.; Castellazzi, A. Single-Phase T-Type Inverter Performance Benchmark Using Si IGBTs, SiC MOSFETs, and GaN HEMTs. IEEE Trans. Power Electron.
**2016**, 31, 7148–7160. [Google Scholar] [CrossRef] - Satpathy, S.; Bhattacharya, S.; Veliadis, V. Comprehensive Loss Analysis of Two-level and Three-Level Inverter for Electric Vehicle Using Drive Cycle Models. In Proceedings of the IECON 2020 the 46th Annual Conference of the IEEE Industrial Electronics Society, Singapore, 18–21 October 2020; pp. 2017–2024. [Google Scholar] [CrossRef]
- Holtz, J. Selbstgeführter Wechselrichter. German Patent 2 339 034 C2, 5 January 1983. (In German). [Google Scholar]
- Cittanti, D.; Guacci, M.; Mirić, S.; Bojoi, R.; Kolar, J.W. Comparative Evaluation of 800V DC-Link Three-Phase Two/Three-Level SiC Inverter Concepts for Next-Generation Variable Speed Drives. In Proceedings of the 2020 23rd International Conference on Electrical Machines and Systems (ICEMS), Hamamatsu, Japan, 24–27 November 2020; pp. 1699–1704. [Google Scholar] [CrossRef]
- Baker, R.H. Bridge Converter Circuit. U.S. Patent 4 270 163 A, 26 May 1981. [Google Scholar]
- Nabae, A.; Takahashi, I.; Akagi, H. A New Neutral-Point-Clamped PWM Inverter. IEEE Trans. Ind. Appl.
**1981**, IA-17, 518–523. [Google Scholar] [CrossRef] - Bruckner, T.; Bemet, S. Loss Balancing in Three-Level Voltage Source Inverters Applying Active NPC Switches. In Proceedings of the 2001 IEEE 32nd Annual Power Electronics Specialists Conference (IEEE Cat. No. 01CH37230), Vancouver, BC, Canada, 17–21 June 2001; Volume 2, pp. 1135–1140. [Google Scholar] [CrossRef]
- Schweizer, M.; Kolar, J.W. Design and Implementation of a Highly Efficient Three-Level T-Type Converter for Low-Voltage Applications. IEEE Trans. Power Electron.
**2013**, 28, 899–907. [Google Scholar] [CrossRef] - Gammeter, C. Multi-Objective Optimization of Power Electronics and Generators of Airborne Wind Turbines. Ph.D. Thesis, ETH Zurich, Zurich, Switzerland, 2017. [Google Scholar] [CrossRef]
- Deboy, G.; Haeberlen, O.; Treu, M. Perspective of Loss Mechanisms for Silicon and Wide Band-Gap Power Devices. CPSS Trans. Power Electron. Appl.
**2017**, 2, 89–100. [Google Scholar] [CrossRef] - Liu, B.; Ren, R.; Jones, E.A.; Gui, H.; Zhang, Z.; Chen, R.; Wang, F.; Costinett, D. Effects of Junction Capacitances and Commutation Loops Associated with Line-Frequency Devices in Three-Level AC/DC Converters. IEEE Trans. Power Electron.
**2019**, 34, 6155–6170. [Google Scholar] [CrossRef] - Kasper, M.; Burkart, R.M.; Deboy, G.; Kolar, J.W. ZVS of Power MOSFETs Revisited. IEEE Trans. Power Electron.
**2016**, 31, 8063–8067. [Google Scholar] [CrossRef] - Lauritzen, P.; Ma, C. A Simple Diode Model with Reverse Recovery. IEEE Trans. Power Electron.
**1991**, 6, 188–191. [Google Scholar] [CrossRef] - Nayak, D.; Yakala, R.K.; Kumar, M.; Pramanick, S. Temperature Dependent Reverse Recovery Characterization of SiC MOSFETs Body Diode for Switching Loss Estimation In a Half-Bridge. IEEE Trans. Power Electron.
**2022**, 37, 5574–5582. [Google Scholar] [CrossRef] - Sochor, P.; Huerner, A.; Hell, M.; Elpelt, R. Understanding the Turn-off Behavior of SiC MOSFET Body Diodes in Fast Switching Applications. In Proceedings of the PCIM Europe Digital Days 2021; International Exhibition and Conference for Power Electronics, Intelligent Motion, Renewable Energy and Energy Management, Online, 3–7 May 2021; pp. 290–297. [Google Scholar]
- Hoffmann, L.; Gautier, C.; Lefebvre, S.; Costa, F. Optimization of the Driver of GaN Power Transistors Through Measurement of Their Thermal Behavior. IEEE Trans. Power Electron.
**2014**, 29, 2359–2366. [Google Scholar] [CrossRef] - Rothmund, D.; Bortis, D.; Kolar, J.W. Accurate Transient Calorimetric Measurement of Soft-Switching Losses of 10-kV SiC MOSFETs and Diodes. IEEE Trans. Power Electron.
**2018**, 33, 5240–5250. [Google Scholar] [CrossRef] - Mantooth, H.A.; Glover, M.D.; Shepherd, P. Wide Bandgap Technologies and Their Implications on Miniaturizing Power Electronic Systems. IEEE Trans. Emerg. Sel. Top. Power Electron.
**2014**, 2, 374–385. [Google Scholar] [CrossRef]

**Figure 1.**Three-level T-type (3LTT) bridge-leg switching transitions involving ${\mathrm{T}}_{1}$ and ${\mathrm{T}}_{2}$. Four different events are identified, depending on the switching sequence ${\mathrm{T}}_{1}\leftrightarrow {\mathrm{T}}_{2}$ and the direction of the bridge-leg output current ${I}_{\mathrm{sw}}$. (

**a**) ${\mathrm{T}}_{1}\leftarrow {\mathrm{T}}_{2}$, ${I}_{\mathrm{sw}}\phantom{\rule{-0.166667em}{0ex}}>\phantom{\rule{-0.166667em}{0ex}}0$ (hard-switching event), (

**b**) ${\mathrm{T}}_{1}\to {\mathrm{T}}_{2}$, ${I}_{\mathrm{sw}}\phantom{\rule{-0.166667em}{0ex}}>\phantom{\rule{-0.166667em}{0ex}}0$ (soft-switching event), (

**c**) ${\mathrm{T}}_{1}\to {\mathrm{T}}_{2}$, ${I}_{\mathrm{sw}}\phantom{\rule{-0.166667em}{0ex}}<\phantom{\rule{-0.166667em}{0ex}}0$ (hard-switching event), (

**d**) ${\mathrm{T}}_{1}\leftarrow {\mathrm{T}}_{2}$, ${I}_{\mathrm{sw}}\phantom{\rule{-0.166667em}{0ex}}<\phantom{\rule{-0.166667em}{0ex}}0$ (soft-switching event). Blue lines represent the charge/discharge current paths of the semiconductor output capacitances, whereas pink lines indicate the diode reverse-recovery current path. The gate signals of ${\mathrm{T}}_{1}$, ${\mathrm{T}}_{2}$, ${\mathrm{T}}_{3}$, and ${\mathrm{T}}_{4}$ are qualitatively shown as ${s}_{1}$, ${s}_{2}$, ${s}_{3}$, and ${s}_{4}$, respectively, and the steady-state, dead time, and transition intervals are indicated.

**Figure 2.**Output charge ${Q}_{\mathrm{oss}}$ dependence on the drain-source voltage ${V}_{\mathrm{DS}}$ of the Wolfspeed C3M0032120K 1200 V 32 mΩ SiC MOSFET, with highlighted capacitive energy components ${E}_{\mathrm{a}}$, ${E}_{\mathrm{b}}$, ${E}_{\mathrm{c}}$, and ${E}_{\mathrm{d}}$, assuming V

_{dc}= 800 V.

**Figure 3.**Overview of the 3LTTC bridge-leg test board and brass heat sink used for calorimetric loss measurements.

**Figure 4.**Comparison between estimated and measured zero output current losses in the 3LTT bridge-leg (${\mathrm{T}}_{1}={\mathrm{T}}_{4}$: C3M0032120K, ${\mathrm{T}}_{2}={\mathrm{T}}_{3}$: C3M0025065K) as a function of the DC-link voltage ${V}_{\mathrm{dc}}$. The results are obtained by switching ${\mathrm{T}}_{1}\leftrightarrow {\mathrm{T}}_{2}$: the additional energy loss related to the charging/discharging of ${C}_{\mathrm{oss},\mathrm{T}4}$ (i.e., ${E}_{\mathrm{c},\mathrm{T}4}+{E}_{\mathrm{d},\mathrm{T}4}$) is indicated in black. The estimated energy losses take into account the measured parasitic capacitance ${C}_{\sigma}\approx 35\text{}\mathrm{pF}$ between the switching node and the DC-link as ${E}_{\sigma}=2\xb7\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.{C}_{\sigma}{V}_{\mathrm{sw}}^{2}$.

**Figure 5.**Comparison between estimated and measured hard-switching losses in the 3LTT bridge-leg (${\mathrm{T}}_{1}={\mathrm{T}}_{4}$: C3M0032120K, ${\mathrm{T}}_{2}={\mathrm{T}}_{3}$: C3M0025065K) as a function of the switched current ${I}_{\mathrm{sw}}$ at ${V}_{\mathrm{dc}}$ = 800 V and ${T}_{\mathrm{j}}$ ≈ 125 °C. The estimated energy losses take into account the measured parasitic capacitance ${C}_{\sigma}\approx 35\text{}\mathrm{pF}+50\text{}\mathrm{pF}$ (between the switching node and the DC-link, and the winding capacitance of the load inductor), as ${E}_{\sigma}=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.{C}_{\sigma}{V}_{\mathrm{sw}}^{2}$. The estimated losses for ${T}_{\mathrm{j}}$ = 25 °C and ${T}_{\mathrm{j}}$ = 175 °C are indicated with dashed lines.

**Table 1.**Comparison between estimated and measured hard-switching losses in the 3LTT bridge-leg as a function of the switched current ${I}_{\mathrm{sw}}$ at ${V}_{\mathrm{dc}}$ = 800 V and ${T}_{\mathrm{j}}$ ≈ 125 °C. The losses are estimated with (15) for ${I}_{\mathrm{sw}}>0$ and with (16) for ${I}_{\mathrm{sw}}<0$.

Switched Current | Measured Loss | Estimated Loss | Error |
---|---|---|---|

−25 A | 155.4 μJ | 128.3 μJ | −17.5% |

−20 A | 140.3 μJ | 116.9 μJ | −16.7% |

−15 A | 123.0 μJ | 105.5 μJ | −14.2% |

−10 A | 107.9 μJ | 94.1 μJ | −12.7% |

−5 A | 90.6 μJ | 82.7 μJ | −8.6% |

+5 A | 96.3 μJ | 85.8 μJ | −10.9% |

+10 A | 116.6 μJ | 100.2 μJ | −14.0% |

+15 A | 137.3 μJ | 114.7 μJ | −16.5% |

+20 A | 154.5 μJ | 129.2 μJ | −16.4% |

+25 A | 174.3 μJ | 143.6 μJ | −17.6% |

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**MDPI and ACS Style**

Cittanti, D.; Gammeter, C.; Huber, J.; Bojoi, R.; Kolar, J.W.
A Simplified Hard-Switching Loss Model for Fast-Switching Three-Level T-Type SiC Bridge-Legs. *Electronics* **2022**, *11*, 1686.
https://doi.org/10.3390/electronics11111686

**AMA Style**

Cittanti D, Gammeter C, Huber J, Bojoi R, Kolar JW.
A Simplified Hard-Switching Loss Model for Fast-Switching Three-Level T-Type SiC Bridge-Legs. *Electronics*. 2022; 11(11):1686.
https://doi.org/10.3390/electronics11111686

**Chicago/Turabian Style**

Cittanti, Davide, Cristoph Gammeter, Jonas Huber, Radu Bojoi, and Johann W. Kolar.
2022. "A Simplified Hard-Switching Loss Model for Fast-Switching Three-Level T-Type SiC Bridge-Legs" *Electronics* 11, no. 11: 1686.
https://doi.org/10.3390/electronics11111686