Effects of Current Commutation Methods on SiC MOSFET and Si IGBT Based 4-Quadrant Switches

Silicon Carbide (SiC) MOSFETs are promising replacements for Silicon (Si) IGBTs in various power electronic topologies. While extensive research exists on SiC MOSFET based 2-quadrant switches, studies on 4-quadrant switch topologies remain limited. A 4-quadrant switch is typically formed by combining multiple 2-quadrant switches such as MOSFETs, IGBTs, or diodes. Designing such topologies presents challenges, including commutation methods (2-step and 4-step), finite switching speed constraints, variable ON state voltage drops, and quadrant-dependent transition (turn ON/OFF) times. This research systematically investigates these challenges through analysis, simulation, and experimental validation in a controlled FPGA based test environment. The study focuses on selecting an optimal commutation method, analysing the impact of 2-step and 4-step switching on transition times and ON state voltage drops, and evaluating the maximum switching frequency and efficiency of converters utilizing SiC MOSFET based 4-quadrant switches. The findings demonstrate the advantages of these converters in terms of reduced transition times, higher switching frequencies, and improved efficiency, establishing SiC MOSFET based 4-quadrant switches as a viable alternative to Si IGBT based designs.

Nomenclature

$v_{A}$ , $v_{B}$	Instantaneous AC power supply voltage of phases A and B.
$S_{A}$ , $S_{B}$	SiC MOSFET based 4-quadrant switches.
$T_{A}$ , $T_{B}$	Si IGBT based 4-quadrant switches.
$S_{A1}$ , $S_{A2}$ , $S_{B1}$ , $S_{B2}$	SiC MOSFETs of $S_{A}$ and $S_{B}$ .
$T_{A1}$ , $T_{A2}$ , $T_{B1}$ , $T_{B2}$	Si IGBTs of $T_{A}$ and $T_{B}$ .
$V_{4QS}$ , $v_{4QS}$ , $\bar {v}_{4QS}$	DC, instantaneous, and average voltages across 4-quadrant switch.
$v_{4QS,A}$ , $v_{4QS,B}$	Instantaneous voltage across $S_{A}$ /$T_{A}$ and $S_{B}$ /$T_{B}$ , respectively.
$I_{4QS}$ , $i_{4QS}$ , $\bar {i}_{4QS}$	DC, instantaneous, and average currents across 4-quadrant switch.
$i_{4QS,A}$ , $i_{4QS,B}$	Instantaneous currents through $S_{A}$ /$T_{A}$ and $S_{B}$ /$T_{B}$ .
$v_{L}$ , $i_{L}$	Load voltage and current of $2\times 1$ matrix converter.
$v_{GS,A1}$ , $v_{GS,A2}$	Gate-source voltages across $S_{A1}$ and $S_{A2}$ .
$v_{GS,B1}$ , $v_{GS,B2}$	Gate-source voltages across $S_{B1}$ and $S_{B2}$ .
$v_{GE,A1}$ , $v_{GE,A2}$	Gate-emitter voltages across $T_{A1}$ and $T_{A2}$ .
$v_{GE,B1}$ , $v_{GE,B2}$	Gate-source voltages across $T_{B1}$ and $T_{B2}$ .
$I_{rrm}$	Peak reverse recovery current of diode.
$t_{di}$ , $t_{ri}$ , $t_{fv}$	Current delay time, current rise time, and voltage fall time.
$t_{dv}$ , $t_{rv}$ , $t_{fi}$ , $t_{ti}$	Voltage delay time, voltage rise time, Current fall time, and tail time.
$t_{a}$ , $t_{b}$	Time intervals from zero to $I_{rrm}$ and $I_{rrm}$ to zero. turn OFF time of 4-quadrant switch.
$t_{A1}$ , $t_{A2}$ , $t_{B1}$ , $t_{B2}$	Turn ON/OFF times of $S_{A1}$ /$T_{A1}$ , $S_{A2}$ /$T_{A2}$ , $S_{B1}$ /$T_{B1}$ , and $S_{B2}$ /$T_{B2}$ .
$t_{d,4-step}$ , $t_{d,2-step}$	Commutation delays in 4-step and 2-step.
$t_{pdd}$ , $t_{pdi}$ , $t_{pdg}$	Propagation delays of digital lines, digital IC, and gate driver.
$T_{c}$ , $f_{c}$	Clock cycle and clock frequency of FPGA.
$T_{s}$ , $f_{s}$ , $f_{sm}$	Switching time period, switching frequency, and maximum switching frequency of $2\times 1$ matrix converter.
$f_{sm,4-step}$ , $f_{sm,2-step}$	Maximum switching frequencies of $2\times 1$ matrix converter with 4-step and 2-step.
$t_{ON}$ , $t_{OFF}$	Turn ON and turn OFF times.
$t_{ON,A}$ , $t_{ON,B}$	Turn ON times of $S_{A}/T_{A}$ and $S_{B}/T_{B}$ .
$t_{OFF,A}$ , $t_{OFF,B}$	Turn OFF times of $S_{A}/T_{A}$ and $S_{B}/T_{B}$ .
$t_{ON_{Si,4QS}}$ , $t_{ON_{SiC,4QS}}$	Turn ON times of Si IGBT and SiC MOSFET based 4-quadrant switches.
$t_{OFF_{Si,4QS}}$ , $t_{OFF_{SiC,4QS}}$	Turn OFF times of Si IGBT and SiC MOSFET based 4-quadrant switches.
$t_{ON_{First}}$ , $t_{ON_{Second}}$	Turn ON times in first and second quadrants.
$t_{ON_{Third}}$ , $t_{ON_{Fourth}}$	Turn ON times in third and fourth quadrants.
$t_{OFF_{First}}$ , $t_{OFF_{Second}}$	Turn OFF times in first and second quadrants.
$t_{OFF_{Third}}$ , $t_{OFF_{Fourth}}$	Turn OFF times in third and fourth quadrants.
$t_{ON_{min}}$ , $t_{ON_{max}}$	Minimum and maximum turn ON times of 4-quadrant switch.
$t_{OFF_{min}}$ , $t_{OFF_{max}}$	Minimum and maximum turn OFF times of 4-quadrant switch.
$e_{on}$ , $e_{off}$ , $e_{rr}$	Turn ON, turn OFF, and reverse recovery energy losses.
$e_{on,ri}$ , $e_{on,rra}$ , $e_{on,rrb}$	Turn ON energy losses during $t_{ri}$ , $t_{a}$ , and $t_{b}$ .
$e_{sw}$ , $e_{cond}$ , $e_{total}$	Switching, conduction, and total energy losses.
$P_{on}$ , $P_{off}$	Average turn ON and turn OFF power losses.
$P_{rr,BD}$ , $P_{rr,D}$	Average power losses in body diode reverse recovery and diode reverse recovery.
$P_{sw}$ , $P_{cond}$ , $P_{total}$	Average switching, conduction, and total power losses.

SECTION I. Introduction

Silicon Carbide (SiC) MOSFETs have significantly lower turn ON and turn OFF times compared to Silicon (Si) Insulated Gate Bipolar Transistors (IGBTs). This characteristic allows them to switch up to ten times faster than Si IGBTs, resulting in reduced switching losses in power converters [1], [2]. Additionally, their higher switching speed enables increased switching frequencies, which help in reducing the size and weight of passive components such as filters and electric machines [3], [4]. Furthermore, SiC MOSFETs exhibit lower ON state voltage drops [1], higher current density, and improved junction temperature resistance [5], [6] than their Si IGBT counterparts. These advantages contribute to more compact and efficient power converters, as demonstrated by reductions in the size of SiC MOSFET based converters compared to their Si IGBT based equivalents [7]. Moreover, the high blocking voltage capability of SiC MOSFETs has facilitated the development of medium-voltage solid-state transformers (SSTs) [8]. Other notable applications of SiC MOSFETs include electric vehicle (EV) drives [9], EV chargers [7], and traction converters [10].

SiC MOSFETs and Si IGBTs are selected for comparison in this study due to their dominance in power electronics applications, particularly in high-power and high-frequency converters. SiC MOSFETs offer faster switching performance and exhibit lower gate charge properties, which contribute to reduced power dissipation and improved efficiency in high-frequency switching applications [11]. This property, along with smaller input capacitances, further enhances the viability of SiC MOSFETs in next-generation power conversion systems. On the other hand, Si IGBTs provide lower conduction losses at high currents and are often preferred in applications where switching frequency is moderate, and cost is a critical factor. The choice between these two technologies is not straightforward and depends on the trade-off between conduction and switching losses, efficiency, and system cost. Therefore, this study aims to provide a comprehensive comparison to support optimal device selection for converters employing 4-quadrant switches.

Single-stage SSTs often utilize matrix converter topologies [8], which require bidirectional switches — also known as 4-quadrant switches — that can block bipolar voltages and conduct bidirectional currents [12]. The $v-i$ characteristics of a 4-quadrant switch are shown in Fig. 1(a), where $v_{4QS}$ and $i_{4QS}$ represent the instantaneous voltage and current across the switch, respectively. Beyond SSTs, 4-quadrant switches find applications in Vienna rectifiers [13], solid-state circuit breakers [14], and motor drive systems [15]. The ability to control bidirectional power flow makes 4-quadrant switches attractive for various high-performance power electronics applications [16]. Despite their advantages, discrete 4-quadrant switches are not commercially available [17], requiring designers to implement them using 2-quadrant switches, such as Si IGBTs [18] and SiC MOSFETs [19], in combination with power diodes.

FIGURE 1.

4-quadrant switch: (a) Four quadrants of the switch. (b) SiC MOSFETs. (c) Si IGBTs.

Fig. 1(b) illustrates a SiC MOSFET based 4-quadrant switch in a common-source configuration, while Fig. 1(c) presents the common-emitter configuration for a Si IGBT based 4-quadrant switch. A single isolated power supply can drive both 2-quadrant switches in these configurations [20], making them preferable for practical implementations. However, these configurations require current commutation methods to ensure safe operation [12]. Unlike standard H-bridge inverters, which utilize dead-time techniques, converters employing 4-quadrant switches require specialized commutation techniques to prevent source short-circuiting and load open-circuiting. The two primary commutation methods are 2-step and 4-step commutation [12]. The 2-step method involves turning ON one MOSFET/IGBT while turning OFF another, whereas the 4-step method involves turning ON two MOSFETs/IGBTs while turning OFF the other two. While 2-step commutation minimizes delay and enhances waveform quality [21], it does not allow current reversal. In contrast, 4-step commutation permits current reversal but introduces additional delays, limiting maximum switching frequency [22].

Previous studies have primarily focused on 2-step commutation for Si IGBT based 4-quadrant switches due to its lower commutation delay [12], [21]. However, as mentioned earlier, SiC MOSFETs exhibit different characteristics, including faster switching speeds, which can impact the maximum achievable switching frequency. Additionally, gating only one MOSFET in 2-step commutation increases the ON state voltage drop in SiC MOSFET based 4-quadrant switches, leading to higher conduction losses [23]. Conversely, this variation in gating does not significantly affect the conduction losses of Si IGBT based converters [24]. The transition between 4-quadrant switches depends on their operating quadrants (first, second, third, or fourth) [25], with different transition times observed across quadrants [25]. These transition times are influenced by the selected commutation method [22], the switching speed of SiC MOSFETs, and the clock frequency of the FPGA used for implementation [22]. Consequently, the following challenges arise in 4-quadrant switch-based topologies:

• The necessity of commutation methods (2)-step or 4-step).

• Limitations on transition (turn ON/OFF) times due to finite switching speeds of MOSFETs/IGBTs and FPGA constraints.

• Variability in ON state voltage drops depending on the chosen commutation method.

• Quadrant-dependent variations in transition times.

To address these challenges and to facilitate the design of 4-quadrant switch-based topologies using SiC MOSFETs, the following investigations are conducted:

• Impact of commutation method on transition times in different quadrants.

• Effect of commutation method on the maximum switching frequency for SiC MOSFETs and Si IGBTs.

• Influence of commutation method on ON state voltage drops.

• Assessment of commutation method impact on converter efficiency for both SiC MOSFETs and Si IGBTs.

• Identification of the most suitable commutation method for each device type.

Although some prior studies have explored related aspects, they remain insufficient in addressing these key areas. For instance, turn ON/OFF investigations for SiC MOSFET based 4-quadrant switches have been conducted [25], but maximum switching frequencies and efficiency comparisons for 2-step and 4-step commutations are not examined. Additionally, studies analysing maximum switching frequencies in SiC MOSFET based matrix converters using different commutation methods [22] assumed fixed turn ON/OFF times, whereas practical switching times depend on multiple factors such as voltage, current, and gate resistance. Moreover, existing research does not comprehensively evaluate efficiency trends across different switching frequencies [24]. This paper fills these gaps by conducting detailed investigations through analytical modelling, simulations, and experimental validation on laboratory prototypes. The analysis includes mathematical modelling and theoretical waveform generation, while simulations utilize LTspice with selected MOSFET and IGBT models. Experimental validation is performed for both SiC MOSFET and Si IGBT based 4-quadrant switches using developed prototypes. A thorough comparison of analytical, simulated, and experimental results provides insights into the optimal selection of devices and commutation methods for high-performance converters. The key contributions of this paper are as follows:

• Comparative analysis of maximum switching frequency, ON-state voltage drops, and efficiency of SiC MOSFET and Si IGBT based $2\times 1$ matrix converters using 2-step and 4-step commutation.

• Analytical power loss modeling to establish conduction, switching, and total power losses in SiC MOSFET and Si IGBT based converters.

• LTspice simulations to compare efficiency trends across different switching frequencies.

• Experimental validation of switching waveforms, transition times, and power losses for both device types.

• Guidelines for selecting between SiC MOSFETs and Si IGBTs and between 2-step and 4-step commutation for various operating conditions.

The remainder of this paper is organized as follows: Section II presents a literature review, Section III describes SiC MOSFET and Si IGBT characteristics, Section IV formulates the problem, Section V compares the devices in a $2\times 1$ matrix converter, Section VI presents LTspice simulation results, Section VII discusses experimental results, and Section VIII concludes the paper.

SECTION II. Literature Review

SiC MOSFETs have attained massive popularity because of several superior features compared to Si IGBTs. One is lower turn ON/OFF times (high switching speed) [1], [5]. The switching speed of SiC MOSFETs can go up to ten times the switching speed of Si IGBTs [2], consequently reducing the switching loss [26]. The other benefit of a higher switching speed is the increase in switching frequency which reduces the size of the filters [3], the size and weight of electric machines, and the switching harmonics-induced rotor losses in permanent magnet machines [4]. Further, the ON state voltage drop is also reported to be lower than Si IGBTs [1], [27]. SiC MOSFETs have also exhibited high current density and junction temperature resistance [5], [6]. The better temperature characteristics can change the cooling method from liquid to forced-air cooling [4]. Therefore, SiC MOSFET based converters have shown a reduction in size for the same power-rated Si IGBT based converter [7]. Moreover, high blocking voltage of $10-15~kV$ of SiC MOSFETs have been reported in [2] and [8]. It has enabled to develop medium voltage solid state transformers [8] and high power density three-level diode neutral point clamped converter to achieve $6-10~kV$ output [28]. Other applications of SiC MOSFETs are electric vehicle (EV) drives [9], EV chargers [7], traction converters [10], wind turbine converters [3], fuel-cell converters [29], and solar inverters [30].

Among the above applications, EV chargers widely use Vienna rectifiers [13]. It is also used in telecommunication power supplies [15]. This type of converter requires a switch which blocks bipolar voltage and allows bidirectional current. The kind of switch necessary for such an application is a bidirectional or 4-quadrant switch [12]. Other reported applications of the 4-quadrant switch are Swiss rectifiers [31], matrix converters [12], solid-state circuit breakers [14], [32], T-type three-level converters [33], current-source inverters [34], electrical discharge machining [35], PV inverters [15], and motor drive systems [15]. Thus, there are many applications of a 4-quadrant switch because it controls bidirectional power flow by controlling bipolar voltage and bidirectional current [16]. Several monolithic 4-quadrant switches have been reported in the literature based on Si [36], [37], GaN [38], and SiC [39]. The advantages of monolithic 4-quadrant switches mentioned in literature are approximately four times reduction in chip area, reduction in ON state voltage drop, and cost [15], [16]. However, no discrete bidirectional or 4-quadrant switches are available commercially [15], [16], [17]. Therefore, in the past and now, 2-quadrant switches like Si IGBTs [18] and SiC MOSFETs [19], [40], along with power diodes, are being used to achieve the functionality of 4-quadrant switches.

In case of SiC MOSFET, the body diode can be used instead of an external diode to: (1) Reduce the component count and cost; (2) Reduce unwanted circuit parasitics like inductances and capacitances; (3) Reduce design complexity of the converter; and (4) Increase power density of the converter. Although there are concerns regarding the bipolar degradation of body diode of SiC MOSFET [41], the recent literature review suggests that the bipolar degradation of the body diode of SiC MOSFET occurs at very high surge currents [41], [42]. The MOSFET (C2M0080120D) used in this paper is also tested with repetitive surge currents of $70~A$ in [42]. The bipolar degradation of the body diode was not seen in even at very high surge currents ($110~A$ ). In our paper the surge current is well below the $70~A$ mark. The ON state current is also below the rated current ($36~A$ ) of the body diode. The authors in [43] have shown that operating the body diode at rated DC current does not cause bipolar degradation. Moreover, mitigation of bipolar degradation can be done with the help of appropriate gate bias for higher surge currents [44], [45].

The widely used configuration of 2-quadrant switches to create a 4-quadrant switch is common-emitter in the case of Si IGBTs [46] and common-source in the case of SiC MOSFETs [24]. These configurations allow a single isolated power supply to drive the gates of both 2-quadrant switches (Si IGBTs or SiC MOSFETs) [12], [20]. Moreover, the common-source connection of SiC MOSFETs has shown lower turn ON loss and lower input capacitance than the common-drain connection [20]. The 4-quadrant switch constructed from reverse-blocking SiC MOSFETs performs better than the common-source connection [19] but is unavailable commercially. Hence, 4-quadrant switches with common-emitter and common-source connections are used presently and require current commutation methods [12]. The standard current commutation methods are 2-step and 4-step for matrix converters [24], [47]. The input voltage based 1-step commutation method for single-phase matrix converters have also been shown [48]. These commutation techniques change the maximum switching frequency of the converter [22], [25] and efficiency [24], [46], [49]. The turn ON/OFF investigations are done for SiC MOSFET based 4-quadrant switch [25], and efficiency investigations are done for SiC and Si IGBT based matrix converters [24], [46]. Moreover, a comparison of conduction and switching losses is made for SiC MOSFET and SiC MOSFET based 4-quadrant switch [50], which shows higher losses for 4-quadrant switch. Also, power loss in different quadrants of SiC MOSFET based 4-quadrant switch is found [23]. However, the research on the effects of 2-step and 4-step commutations on Si IGBT and SiC MOSFET based 4-quadrant switches is missing in the literature. Therefore, the investigation does detailed research and obtains important findings. It compares the maximum switching frequencies and efficiencies of SiC MOSFET and Si IGBT based $2\times 1$ matrix converters using 2-step and 4-step commutations.

SECTION III. Characteristics of SiC MOSFET and Si IGBT

This section describes the characteristics of the selected Si IGBT and SiC MOSFET. The comparison of the characteristics of Si IGBT and SiC MOSFET helps the reader to easily understand the subsequent sections of the paper. It is the prerequisite for better understanding of Si IGBT and SiC MOSFET based 4-quadrant switches. It further helps in the comparison of Si IGBT and SiC MOSFET based 4-quadrant switches.

The datasheet parameters of the Si IGBT and SiC MOSFET are detailed in Table 1. The SiC MOSFET (C2M0080120D) has the planar-double-diffused-MOSFET (DMOSFET) structure. Although the ON state voltage drop in this structure is high but has lesser electric field stress to the gate-oxide layer compared to the trench-MOSFET structure [51]. The lesser electric field stress gate-oxide layer makes the DMOSFET structure in SiC MOSFETs more reliable in the long run. The Si IGBT (NGTB40N120FL2WG) has a field-stop-trench-gate structure. It has the least ON state voltage drop compared to planar-non-punch-through or planar-field-stop structures [52]. The breakdown voltage of both the devices is $1200~V$ . The maximum continuous current of the SiC MOSFET is $24~A$ and $40~A$ for the Si IGBT at $100~^{o}C$ case temperature. The current derating of Si IGBT with switching frequency and temperature is higher than SiC MOSFET. Therefore, the higher current-rated Si IGBT than SiC MOSFET is selected for comparison in this paper. There is a co-packaged free-wheeling diode with the Si IGBT. In case of SiC MOSFET, the body diode can be used as the free-wheeling diode, which reduces the component count.

TABLE 1 Datasheet Parameters of SiC MOSFET and Si IGBT

A. On State Voltage Drop

The datasheet ON state voltage drops of SiC MOSFET and Si IGBT are shown in Fig. 2. The drain-source voltage, $V_{DS}$ , is the first quadrant ON state voltage drop of the SiC MOSFET. The first quadrant voltage drop of Si IGBT is collector-emitter voltage, $V_{CE}$ . The plots of $V_{DS}$ and $V_{CE}$ are shown in Fig. 2(a). $V_{DS}$ starts from $0~V$ and remains below $V_{CE}$ for ON state currents less than $20.5~A$ . $V_{CE}$ is $1~V$ at $0~A$ and equals $V_{DS}=1.7~V$ at $20.5~A$ , and $V_{DS}$ crosses over $V_{CE}$ after this current. The rise of $V_{DS}$ is steep compared to $V_{CE}$ and goes up to $3.7~V$ at $40~A$ . In contrast, $V_{CE}$ is $1.95~V$ at $40~A$ . From the plot of SiC MOSFET, the approximate voltage-current relationship of SiC MOSFET in first quadrant is given by (1). The curve fitted voltage-current relationship of Si IGBT in first quadrant is given by (2).\begin{align*} V_{DS}& =0.094I \tag {1}\\ V_{CE}& =0.02I+1.179 \tag {2}\end{align*} The ON state voltage drops of the MOSFET’s body diode, $V_{SD}$ , and the co-packaged free-wheeling diode, $V_{EC}$ , are shown in Fig. 2(b). The $V_{EC}$ plot remains significantly below the $V_{SD}$ plot. The $V_{SD}$ plot is $3~V$ initially and becomes $5.6~V$ at $40~A$ , whereas $V_{EC}$ is $0.7~V$ initially and reaches $2.1~V$ at $40~A$ . It suggests that the ON state drop of the MOSFET’s body diode is significantly higher than the free-wheeling diode attached to the IGBT. From the plot of SiC MOSFET’ body diode, the approximate voltage-current relationship of the body diode in third quadrant is given by (3). The curve fitted voltage-current relationship of diode attached to Si IGBT in third quadrant is given by (4).\begin{align*} V_{SD}& =0.062I+3.279 \tag {3}\\ V_{EC}& =0.033I+0.858 \tag {4}\end{align*} Fig. 2(c) shows the ON state voltage drops of the SiC MOSFET conducting in the third quadrant and the free-wheeling diode attached to the Si IGBT. In this case, $V_{SD}=V_{EC}=1.72~V$ at $26~A$ and $V_{SD}$ crosses over $V_{EC}$ after $26~A$ . $V_{SD}=2.65~V$ and $V_{EC}=2.1~V$ at $40~A$ . The ON state voltage drop of SiC MOSFET in the third quadrant is mildly higher than the free-wheeling diode of the IGBT at $40~A$ . From the plot of SiC MOSFET, the approximate voltage-current relationship of SiC MOSFET in third quadrant is given by (5).\begin{equation*} V_{SD}=0.07I \tag {5}\end{equation*}

FIGURE 2.

Datasheet ON state voltage drops of Si IGBT and SiC MOSFET. (a) First quadrant ON state voltage drops. (b) ON state voltage drops of SiC MOSFET’s body diode and Si IGBT’s co-packaged free-wheeling diode. (c) ON state voltage drops of SIC MOSFET in third quadrant and Si IGBT’s co-packaged free-wheeling diode.

B. Switching Characteristics

In Table 1, the input capacitance of SiC MOSFET is $950~pF$ , whereas the input capacitance of Si IGBT is $7385~pF$ . The reverse transfer capacitance of SiC MOSFET is $7.6~pF$ , and it is $140~pF$ for Si IGBT. The lower capacitance values of SiC MOSFET indicate faster switching of the MOSFET. The turn ON and OFF times of SiC MOSFET confirm that the MOSFET’s switching is more rapid than the Si IGBT. The turn ON time is five times higher, and the turn OFF time is nearly ten times higher for the IGBT. This subsection briefly describes the turn OFF and turn ON behaviour differences in the two devices with the help of test circuits and switching waveforms, in Fig. 3.

FIGURE 3.

Switching characteristics of MOSFET and IGBT.

The test circuit in Fig. 3(a) consists of SiC MOSFET, free-wheeling diode-FD, DC supply-$V_{DC}$ , highly inductive load drawing a constant current-$I_{o}$ , gate power supply-$v_{GG}$ , and gate resistance-$R_{G}$ . The parasitic capacitances of the MOSFET are gate-source, $C_{GS}$ , gate-drain, $C_{GD}$ , and drain-source, $C_{DS}$ . Fig. 3(b) presents the gate-source voltage, $v_{GS}$ , drain current, $i_{D}$ , and drain-source voltage, $v_{DS}$ waveforms. In the turn ON process, during current delay time, $t_{di}$ , the rise of $v_{GS}$ occurs due to the charging of $C_{GS}$ and $C_{GD}$ . This interval ends at $v_{GS}=V_{th}$ (gate-threshold voltage). Typically, $V_{th}=2.6~V$ for the selected SiC MOSFET. During $i_{D}$ rise time, $t_{ri}$ , $C_{GS}$ and $C_{GD}$ charges until $v_{GS}=V_{mil}$ and $i_{D}=I_{o}$ . In the $v_{DS}$ fall time, $t_{fv}$ , $v_{DS}$ falls approximately from $V_{DC}$ to the ON state voltage drop of the MOSFET corresponding to the gate bias voltage, $v_{GS}=V_{mil}$ . The discharge of $C_{DS}$ takes place in this interval. After this duration, $v_{GS}$ keeps increasing exponentially up to $V_{GG}$ due to the charging of $C_{GS}$ and $C_{GD}$ . $V_{GG}$ is the maximum gate supply voltage. The approximate expressions for $t_{di}$ , $t_{ri}$ , and $t_{fv}$ are given by (6), (7), and (8), respectively [25], [53]. The transconductance, $g_{m}$ , of the MOSFET, appears in (7). The turn ON time of the MOSFET, $t_{ON}=t_{di}+t_{ri}+t_{fv}$ .\begin{align*} t_{di}& =R_{G}(C_{GS}+C_{GD})\ln {\frac {V_{GG}}{V_{GG}-V_{th}}} \tag {6}\\ t_{ri}& =R_{G}(C_{GS}+C_{GD})\ln {\frac {g_{m}V_{GG}}{g_{m}(V_{GG}-V_{th})-I_{o}}} \tag {7}\\ t_{fv}& =\frac {R_{G}}{V_{GG}-V_{th}}\sum _{i=1}^{n}C_{GD_{i}}\Delta v_{DS} \tag {8}\end{align*} The turn OFF process occurs in the opposite sequence. The delay time, $t_{dv}$ , occurs during the rise of $v_{DS}$ due to the fall of $v_{GS}$ from $V_{GG}$ to $V_{mil}$ . In this interval, discharge of $C_{GS}$ and $C_{GD}$ starts. In the $v_{DS}$ rise interval, $t_{rv}$ , $v_{GS}$ remains constant at $V_{mil}$ , only $C_{GD}$ discharges, $v_{DS}$ rises to $V_{DC}$ , and $i_{D}$ is close to $I_{o}$ . In $i_{D}$ fall time, $t_{fi}$ , $i_{D}$ falls to zero and $I_{o}$ is transferred to FD. $v_{GS}$ becomes $V_{th}$ at the end of this interval and eventually becomes zero. A negative gate bias is preferred to avoid unwanted turn ON of the SiC MOSFET because of the low gate-threshold voltage. The approximate expressions for $t_{dv}$ , $t_{rv}$ , and $t_{fi}$ are given by (9), (10), and (11), respectively [25], [53]. The turn OFF time of the MOSFET, $t_{OFF}=t_{dv}+t_{rv}+t_{fi}$ .\begin{align*} t_{dv}& =R_{G}(C_{GS}+C_{GD})\ln {\frac {g_{m}V_{GG}}{I_{o}+g_{m}V_{th}}} \tag {9}\\ t_{rv}& =\frac {R_{G}}{(I_{o}/g_{m})+V_{th}}\sum _{i=1}^{n}C_{GD_{i}}\Delta v_{DS} \tag {10}\\ t_{fi}& =R_{G}(C_{GS}+C_{GD})\ln {\left ({{1+\frac {I_{o}}{g_{m}V_{th}}}}\right )} \tag {11}\\ t_{ti} & \approx 5\tau _{_{HL}} \tag {12}\end{align*}

The test circuit for Si IGBT in Fig. 3(c) is similar to that of SiC MOSFET. The parasitic capacitances are gate-emitter, $C_{GE}$ , gate-collector, $C_{GC}$ , and collector-emitter, $C_{CE}$ . The turn ON waveforms of Si IGBT in Fig. 3(d) are similar to the SiC MOSFET, but the lengths of $t_{di}$ , $t_{ri}$ , and $t_{fv}$ are higher. The $t_{di}$ and $t_{ri}$ intervals are more significant because the $C_{GE}$ and $C_{GC}$ capacitances are larger than $C_{GS}$ and $C_{GD}$ . The longer $t_{fv}$ interval is affected by larger $C_{GC}$ , and the PNP transistor part of the IGBT moves slower to the ON state from the active state compared to the MOSFET part of the IGBT [52]. The turn OFF waveforms are also similar to that of SiC MOSFET with more significant durations and the addition of collector current, $i_{C}$ , tail time, $t_{ti}$ . The collector-emitter voltage, $v_{CE}$ , is constant at $V_{DC}$ during this interval. Still, the $i_{C}$ decrease is gradual because of the slow recombination process of the excess minority charge carriers (holes) in the N-Base Region and N-Buffer Layer [52]. Therefore, $t_{ti}$ , is a function of excess minority charge carrier lifetime, $\tau _{_{HL}}$ , and $I_{o}$ [52], [54]. The initial tail current part of $i_{C}$ is around 10% of $I_{o}$ [55], [56]. The final $i_{C}$ is ideally zero, but 0.1% of $I_{o}$ is sufficiently small to determine the value of $t_{ti}$ from (12) [57].

The ON state voltage drop comparison suggests a lower ON state voltage drop of SiC MOSFET at smaller currents and a higher voltage drop at higher currents than Si IGBT. The comparison of SiC MOSFET and Si IGBT turn ON and OFF processes also suggests faster SiC MOSFET switching and, consequently, higher SiC MOSFET switching frequency.

SECTION IV. Problem Formulation

This section describes the current commutation in 4-quadrant switches initially. Further, it explains commutation time and datasheet derived ON state drop of Si IGBT and SiC MOSFET 4-quadrant switches. It finds the maximum switching frequencies for SiC MOSFET and Si IGBT based 4-quadrant switches using 4-step and 2-step commutation. It also compares the datasheet derived ON state voltage drops and theoretical switching waveforms of SiC MOSFET and Si IGBT based 4-quadrant switches using commutation. The investigation presented in this Section suggests several dissimilarities between SiC MOSFET and Si IGBT based 4-quadrant switches and motivates detailed investigation.

A. Current Commutation in 4-Quadrant Switch

The current commutation in 4-quadrant switches is crucial for the safety of the switches. The current commutation should be such that the load must not open-circuit and the source must not short-circuit. The concept of dead time is not used for 4-quadrant switches, because there is no free-wheeling path for the load current to flow since all the MOSFETs are OFF. Using dead time commutation for 4-quadrant switches, creates high voltage spike across the MOSFETs due to high speed of current transition, and the MOSFETs may damage. Therefore, there are two standard commutation methods for 4-quadrant switches: 4-step and 2-step [12]. Fig. 4(a) and Fig. 4(b) show $2\times 1$ matrix converter circuits with SiC MOSFETs and Si IGBTs, respectively. The 4-quadrant switches, $S_{A}$ and $S_{B}$ , consist of $S_{A1}$ , $S_{A2}$ , $S_{B1}$ , and $S_{B2}$ SiC MOSFETs. Si IGBTs, $T_{A1}$ and $T_{A2}$ form $T_{A}$ , and Si IGBTs $T_{B1}$ and $T_{B2}$ combination form $T_{B}$ . The circuit also contains voltage sources, $v_{A}$ and $v_{B}$ , and RL load. The direction of the load current, $i_{L}$ , decides the switching sequence of the MOSFETs or the IGBTs during current commutation.

FIGURE 4.

(a) A $2\times 1$ direct matrix converter with SiC MOSFET based 4-quadrant switches. (b) The $2\times 1$ direct matrix converter with Si IGBT based 4-quadrant switches. (c) 4-step commutation. (d) 2-step commutation.

Fig. 4(c) shows 4-step commutation. The ideal commutation between $S_{A}$ /$T_{A}$ and $S_{B}$ /$T_{B}$ occurs instantaneously in Fig. 4(c), but this is not possible in 4-quadrant switches because of the above mentioned safety reasons. If $i_{L}$ is positive and the current commutation takes place from $S_{A}$ /$T_{A}$ to $S_{B}$ /$T_{B}$ , then the following sequence of switching occurs. First step - $S_{A2}$ /$T_{A2}$ turns OFF in $t_{A2}$ duration. Second step - $S_{B1}$ /$T_{B1}$ turns ON in the $t_{B1}$ interval. Third step - $S_{A1}$ /$T_{A1}$ turns OFF in the $t_{A1}$ period, and in the fourth step - $S_{B2}$ /$T_{B2}$ turns ON in $t_{B2}$ duration. This commutation allows current reversal in the 4-quadrant switch. Fig. 4(d) shows 2-step commutation where in the first step - $S_{B1}$ /$T_{B1}$ turns ON in the $t_{B1}$ interval and in the second step - $S_{A1}$ /$T_{A1}$ turns OFF in the $t_{A1}$ period. The authors in [22] have mentioned the commutation delay time expressions for 4-step (13) and 2-step (14) commutations, which show higher commutation delay time for 4-step. The 4-step and 2-step commutations of SiC MOSFET based 4-quadrant switch is explained further for better understanding of commutation methods in SiC MOSFET based 4-quadrant switch.\begin{align*} & t_{d,4-step}=t_{A2}+t_{B1}+t_{A1}+t_{B2} \tag {13}\\ & t_{d,2-step}=t_{B1}+t_{A1} \tag {14}\end{align*}

Fig. 5 shows the 4-step commutation in SiC MOSFET based 4-quadrant switch. Fig. 5(a) shows that MOSFETs, $S_{A1}$ and $S_{A2}$ , conduct before the onset of 4-step commutation when load current, $i_{L}$ , and $v_{AB}$ are positive. In step-I, MOSFET, $S_{A1}$ , and body diode of MOSFET $S_{A2}$ conduct because the gating of $S_{A2}$ is removed, as shown in Fig. 5(b). In step-II, MOSFET, $S_{B1}$ , is ON since it is gated but does not conduct (shown in dotted lines), $S_{A1}$ and body diode of $S_{A2}$ continues current conduction, as shown in Fig. 5(c). In step-III, MOSFET, $S_{B1}$ , and body diode of $S_{B2}$ conduct because the gating of $S_{A1}$ is removed, as shown in Fig. 5(d). In step-IV, MOSFETs, $S_{B1}$ and $S_{B2}$ , conduct since $S_{B2}$ is gated, as shown in Fig. 5(e). It can be observed that body diode of the MOSFET conducts in steps I, II, and III of 4-step commutation. Therefore, the body diode is necessary in 4-step commutation.

FIGURE 5.

4-step commutation in SiC MOSFET based 4-quadrant switch.

Fig. 6 shows the 2-step commutation in SiC MOSFET based 4-quadrant switch. Fig. 6(a) shows that MOSFETs, $S_{A1}$ , and body diode of $S_{A2}$ , conduct before the onset of 2-step commutation when load current, $i_{L}$ , and $v_{AB}$ are positive. In step-I, MOSFET, $S_{B1}$ , is ON since it is gated but does not conduct (shown in dotted lines), $S_{A1}$ and body diode of $S_{A2}$ continues current conduction, as shown in Fig. 6(b). In step-II, MOSFET, $S_{B1}$ , and body diode of MOSFET $S_{B2}$ conduct because the gating of $S_{A1}$ is removed, as shown in Fig. 6(c). It can be observed that the body diode of the MOSFET conducts in all the steps of 2-step commutation. Moreover, if SiC MOSFET is turned ON after 2-step commutation, which is same as Step-IV of 4-step commutation, as shown in Fig. 5(e).

FIGURE 6.

2-step commutation in SiC MOSFET based 4-quadrant switch.

B. Si IGBT Versus SiC MOSFET Based 4-Quadrant Switches

The SiC MOSFET and Si IGBT characteristics in Section III are utilized here to determine the commutation time, maximum switching frequencies for $2\times 1$ matrix converter and ON state voltage drop for Si IGBT and SiC MOSFET 4-quadrant switches.

1) Commutation Delay Time and Maximum Switching Frequency

The delays due to the Field Programmable Gate Array (FPGA) clock cycle, $T_{c}$ , or clock frequency, $f_{c}=1/T_{c}$ , turn ON time, $t_{ON}$ , and turn OFF time, $t_{OFF}$ , of the SiC MOSFET/Si IGBT are included in [22]. Propagation delays of digital lines, $t_{pdd}$ , digital IC, $t_{pdi}$ , and gate driver, $t_{pdg}$ are also included by the authors. The commutation delay time expressions in 4-step (15) and 2-step (16), including the above delays, are also derived in the paper.\begin{align*} t_{d,4-step}& =4/f_{c}+2(t_{ON}+t_{OFF})+4(t_{pdd}+t_{pdg}+t_{pdi}) \tag {15}\\ t_{d,2-step}& =2/f_{c}+t_{ON}+t_{OFF}+2(t_{pdd}+t_{pdg}+t_{pdi}) \tag {16}\end{align*} The maximum switching frequency expressions for the $2\times 1$ matrix converter using 4-step commutation, $f_{sm,4-step}$ , is (17), and using 2-step commutation, $f_{sm,2-step}$ , is (18).\begin{align*} f_{sm,4-step}& =\frac {1}{2\left [{{\frac {4}{f_{c}}+2(t_{ON}+t_{OFF})+4(t_{pdd}+t_{pdg}+t_{pdi}) }}\right ] } \tag {17}\\ f_{sm,2-step}& =\frac {1}{2\left [{{\frac {2}{f_{c}}+t_{ON}+t_{OFF}+2(t_{pdd}+t_{pdg}+t_{pdi}) }}\right ] } \tag {18}\end{align*} The numerical values of $f_{c}=40~MHz$ , $t_{pdd}=2~ns$ , $t_{pdi}=11~ns$ , and $t_{pdg}=500~ns$ [22]. Table 1 shows the turn ON time, $t_{ON}=158~ns$ , and the turn OFF time, $t_{OFF}=407~ns$ for Si IGBT. The $f_{sm,4-step}=152.35~kHz$ and $f_{sm,2-step}=304.70~kHz$ for Si IGBT based $2\times 1$ matrix converter. The turn ON time, $t_{ON}=31~ns$ , and the turn OFF time, $t_{OFF}=42~ns$ , for SiC MOSFET. Therefore, $f_{sm,4-step}=217.58~kHz$ and $f_{sm,2-step}=435.16~kHz$ for SiC MOSFET based $2\times 1$ matrix converter. Usually, Si IGBTs are not operated beyond $50~kHz$ switching frequency owing to higher switching loss. However, this paper finds out the maximum switching frequency possible with Si IGBT based $2\times 1$ matrix converter using 2-step and 4-step commutations. It is done to compare the maximum switching frequencies possible for SiC MOSFET based matrix converter using 2-step and 4-step commutations. The explicit finding of maximum switching frequencies and comparison is missing in the literature.

2) On State Voltage Drop of 4-Quadrant Switch

Fig. 7 shows the plot of the ON state voltage drop of SiC MOSFET and Si IGBT 4-quadrant switches, $V_{4QS}$ , against current, $I_{4QS}$ , derived from the datasheets. Fig. 7(a) presents the plot when only one MOSFET/IGBT is gated. In this condition, $V_{4QS}$ of SiC MOSFET is $3~V$ at $0~A$ and increases as $I_{4QS}$ increases and becomes $9.3~V$ at $40~A$ . The $V_{4QS}$ of Si IGBT starts from $1.7~V$ at $0~A$ and increases to $4~V$ at $40~A$ . The ON state voltage drop of SiC MOSFET 4-quadrant switch is significantly higher than Si IGBT 4-quadrant switch when only one MOSFET/IGBT is gated. Adding (1) and (3), the approximate voltage-current relationship of SiC MOSFET based 4-quadrant switch when only one MOSFET is gated is given by (19). Adding (2) and (4), the approximate voltage-current relationship of Si IGBT based 4-quadrant switch when only one IGBT is gated is given by (20).\begin{align*} V_{4QS}& =0.156I_{4QS}+3.279 \tag {19}\\ V_{4QS}& =0.053I_{4QS}+2.037 \tag {20}\end{align*}

FIGURE 7.

Effect of current commutation on ON state voltage drop across SiC MOSFET and Si IGBT based 4-quadrant switches extracted from datasheets.

Fig. 7(b) presents the plot when only both MOSFETs/IGBTs are gated. In this case, $V_{4QS}$ of SiC MOSFET is $0~V$ at $0~A$ , crosses the IGBT plot at $3.4~V$ at $23~A$ and ends at $4~V$ at $40~A$ . There is no change in the IGBT plot compared to single IGBT gating. Therefore, SiC MOSFET 4-quadrant switch has less ON state voltage drop below $23~A$ compared to Si IGBT 4-quadrant switch when both the MOSFETs/IGBTs are gated. Beyond this point, the ON state voltage drop of the SiC MOSFET 4-quadrant switch is higher. The plots suggest that the ON state voltage drop of the SiC MOSFET 4-quadrant switch is lower when both the MOSFETs are gated, and the voltage drop is even smaller compared to the Si IGBT 4-quadrant switch for a good range of lower values of current. Adding (1) and (5), the approximate voltage-current relationship of SiC MOSFET based 4-quadrant switch when both MOSFETs are gated is given by (21). The approximate voltage-current relationship of Si IGBT based 4-quadrant switch when both IGBTs are gated is also given by (20).\begin{equation*} V_{4QS} =0.164I_{4QS} \tag {21}\end{equation*}

3) Switching Characteristics of 4-Quadrant Switch

The approximate switching characteristics of SiC MOSFET based 4-quadrant switch in all four quadrants are shown in Fig. 8(a)-(d). After turning ON in each quadrant, the current conducting devices are highlighted in red on the top of the switching waveforms. In Fig. 8(a), $S_{A}$ turns ON in first quadrant, and $S_{B}$ turns OFF in fourth quadrant. The $t_{di}$ and $t_{ri}$ intervals are similar to switching waveforms of SiC MOSFET and $S_{A1}$ decides them, but the reverse recovery of the body diode of $S_{B2}$ dominates during $t_{a}$ and $t_{b}$ . $t_{a}$ is the duration when the reverse recovery current of the body diode attains its peak. It is reflected in the currents flowing through $S_{A}$ , $i_{4QS,A}$ , and $S_{B}$ , $i_{4QS,B}$ . $t_{b}$ is the duration when the voltage across $S_{A}$ , $v_{4QS,A}$ , falls completely and the voltage across $S_{B}$ , $v_{4QS,B}$ , rises completely. During $t_{B1}$ , gate-source voltage, $v_{GS,B1}$ of $S_{B1}$ decreases. The approximate switching characteristics of the Si IGBT based 4-quadrant switch in all four quadrants are shown in Fig. 8(e)-(f). The turn ON of $T_{A}$ in first quadrant and turn OFF of $T_{B}$ in fourth quadrant is similar to Fig. 8(a). The turn ON/OFF times of SiC MOSFET based 4-quadrant switch is expected to be lower than Si IGBT based 4-quadrant switch. It is because of the lower values of $t_{di}$ and $t_{ri}$ of SiC MOSFET than Si IGBT, and lower values of $t_{a}$ and $t_{b}$ of SiC body diode than Si diode. The turn ON time of $S_{A}/T_{A}$ , $t_{ON,A}=t_{A1}=t_{di}+t_{ri}+t_{a}+t_{b}$ . The turn OFF time of $S_{B}/T_{B}$ , $t_{OFF,A}=t_{ON,A}+t_{B1}$ .

FIGURE 8.

Turn ON/OFF switching diagram of SiC MOSFET and Si IGBT based 4-quadrant switches using current commutation.

$S_{A}$ turn OFF in first quadrant, and $S_{B}$ turn ON in fourth quadrant of the SiC MOSFET based 4-quadrant switch is shown in Fig. 8(b). In this case, $t_{dv}$ , $t_{rv}$ , and $t_{fi}$ of $S_{A1}$ decide the turn OFF of $S_{A}$ . In the $t_{B1}$ interval, the complete rise of gate-source voltage, $v_{GS,B1}$ , of $S_{B1}$ occurs. Therefore, $t_{OFF,A}=t_{A1}=t_{dv}+t_{rv}+t_{fi}$ and $t_{ON,B}=t_{B1}+t_{OFF,A}$ . The turn OFF of $T_{A}$ in first quadrant and turn ON of $T_{B}$ of Si IGBT based 4-quadrant switch is shown in Fig. 8(f). Due to the presence of tail current in Si IGBTs, $t_{OFF,A}$ in first quadrant and $t_{ON,B}$ in fourth quadrant include $t_{ti}$ . The region shaded in magenta is the $t_{ti}$ interval. Therefore, turn OFF time in first quadrant may become comparable to turn OFF time in fourth quadrant for Si IGBT based 4-quadrant switch discussed above. The $t_{OFF,A}$ and $t_{ON,B}$ of Si IGBT based 4-quadrant switch are higher than SiC MOSFET based 4-quadrant switch because of higher $t_{dv}$ , $t_{rv}$ , $t_{fi}$ , and $t_{B1}$ values.

The turn ON of $S_{B}$ /$T_{B}$ in third quadrant and the turn OFF of $S_{A}$ /$T_{A}$ in second quadrant are shown in Fig. 8(c)/(g). These are identical to the turn ON of $S_{A}$ /$T_{A}$ in first quadrant and turn OFF of $S_{B}$ /$T_{B}$ in fourth quadrant. Similarly, the turn OFF of $S_{B}$ /$T_{B}$ in third quadrant and turn ON of $S_{A}$ /$T_{A}$ in second quadrant shown in Fig. 8(d)/(h) are identical to the turn OFF of $S_{A}$ /$T_{A}$ in first quadrant and turn ON of $S_{B}$ /$T_{B}$ in fourth quadrant.

4) Complexity of Gate Drivers

Optocoupler gate drivers (HCPL-3120) are used for Si IGBT based 4-quadrant switch in this manuscript. This gate driver does not have desaturation protection. Two gate drivers are used for the 4-quadrant switch. The output of the gate drivers has a common terminal connecting to the common emitter terminals of Si IGBT based 4-quadrant switch. Optocoupler gate drivers with desaturation protection like HCPL-316J-000E are also used for Si IGBT based 4-quadrant switch. However, in case of SiC MOSFETs, the Common Mode Transient Immunity (CMTI) requirement is higher for gate drivers as compared to gate drivers for Si IGBTs [58], [59] because of higher switching speed of SiC MOSFETs. Common mode transient occurs between the commons of the power side and the signal side of the gate driver during switching. Current due to common mode transient flows between the power and signal sides, which can disturb the normal operation of the gate driver. Since SiC MOSFETs based 4-quadrant switch being high speed switch CMTI requirement is higher compared to Si IGBT based 4-quadrant switch. Moreover, optocoupler gate driver with desaturation protection with lower CMTI malfunctions in case of SiC MOSFETs [58], [59]. In this manuscript, optocoupler gate driver without desaturation protection (HCPL-3120) is used. Although, the driver is designed to drive Si IGBTs the operation of this driver with SiC MOSFETs is also robust [59].

Gate resistance is used to control the switching speed of the 4-quadrant switch. The value of gate resistances for both MOSFETs in the 4-quadrant switch are same for symmetrical switching times and the gate resistance value ($15~\Omega $ ) is taken from the datasheet of the SiC MOSFET. In first and third quadrants, switching times of the 4-quadrant switch are dominated by the MOSFET carrying the positive current. However, in second and fourth quadrants, both MOSFETs influence the switching times. In case of Si IGBT based 4-quadrant switch, the gate resistance value is also same for the IGBTs. The same value of gate resistance ($15~\Omega $ ) is kept as of SiC MOSFET based 4-quadrant switch for comparison of switching times at the same gate resistance value.

Since SiC MOSFETs can turn ON spuriously when turning OFF because of its very high speed switching and low gate threshold voltage, negative gate bias voltage ($-5~V$ ) is provided during turn OFF for SiC MOSFET based 4-quadrant switch. Negative gate bias voltage is not required for Si IGBT based 4-quadrant switch. However, for comparison of both type of 4-quadrant switches at similar conditions, negative gate bias voltage ($-5~V$ ) is also given to Si IGBT based 4-quadrant switch. Moreover, during PCB design of SiC MOSFET based 4-quadrant switch, gate loop area is kept as small as possible. It reduces the gate parasitic inductance, and thus reduces the oscillations in voltage and current waveforms during switching.

Table 2 compares SiC MOSFET and Si IGBT based 4-quadrant switches using 2-step and 4-step current commutation. The comparison shows dissimilarities in ON state voltage drop, maximum switching frequencies, and turn ON/OFF times operating using 2-step and 4-step commutations. Therefore, further investigation is necessary to establish the apparent differences between SiC MOSFET and Si IGBT based 4-quadrant switches using current commutation.

TABLE 2 Comparison Between SiC MOSFET and Si IGBT Based 4-Quadrant Switches Using Current Commutation

SECTION V. Comparison of SiC MOSFET and Si IGBT Based 4-Quadrant Switches in $2\times 1$ Matrix Converter

This section compares the calculated power loss of SiC MOSFET and Si IGBT based $2\times 1$ matrix converters operating with 2-step and 4-step commutations. The section obtains, discusses, and compares the conduction, turn ON/OFF, switching, reverse recovery, and total power losses at different switching frequencies. The power loss calculation is done for a $2~kW$ load. The power supply line-line voltage is $415~V$ with a fundamental frequency of $50~Hz$ . The duty ratio is fixed at 0.5 for the 4-quadrant switches. Moreover, various energy loss expressions are needed to find the above-mentioned power losses. The turn ON energy loss, $e_{on}$ , consists of:

• Turn ON energy loss during $t_{ri}$ , $e_{on,ri}$ . $t_{ri}$ is obtained from (8).

• Turn ON energy loss during $t_{a}$ , $e_{on,rra}$ . It includes the peak reverse recovery current, $I_{rrm}$ , in the expression. $t_{a}$ is obtained from simulation.

• Turn ON energy loss during $t_{b}$ , $e_{on,rrb}$ . $t_{b}$ is obtained from simulation.

The expressions for $e_{on,ri}$ , $e_{on,rra}$ , $e_{on,rrb}$ , and $e_{on}$ are given by (22), (23), (24), and (25), respectively.\begin{align*} e_{on,ri}& =0.5|\bar {v}_{4QS}||\bar {i}_{4QS}|t_{ri} \tag {22}\\ e_{on,rra}& =|\bar {v}_{4QS}|(|\bar {i}_{4QS}|+0.5|I_{rrm}|)t_{a} \tag {23}\\ e_{on,rrb}& =\bar {v}_{4QS}\left ({{\frac {I_{rrm}}{3}+0.5\bar {i}_{4QS}}}\right )t_{b} \tag {24}\\ e_{on}& =e_{on,ri}+e_{on,rra}+e_{on,rrb} \tag {25}\end{align*} The expressions for reverse recovery energy loss, $e_{rr}$ , turn OFF energy loss, $e_{off}$ , and total switching energy loss, $e_{sw}$ , are given by (26), (27), and (28), respectively. $t_{rv}$ and $t_{fi}$ are obtained from (10) and (11), respectively.\begin{align*} e_{rr}& =|\bar {v}_{4QS}||I_{rrm}|\frac {t_{b}}{6} \tag {26}\\ e_{off}& =0.5|\bar {v}_{4QS}||\bar {i}_{4QS}|(t_{rv}+t_{fi}) \tag {27}\\ e_{sw}& =e_{on}+e_{rr}+e_{off} \tag {28}\end{align*} In one switching period, $T_{s}=1/f_{s}$ , conduction energy loss, $e_{cond}$ , expression becomes (29). This expression can cause significant error in the calculation at low frequencies like $1~kHz$ because of the high magnitude of ripples in $v_{4QS}$ and $i_{4QS}$ . The total energy loss, $e_{total}$ , is given by (30).\begin{align*} e_{cond}& =|\bar {v}_{4QS}||\bar {i}_{4QS}|(T_{s}-(t_{ri}+t_{a}+t_{b}+t_{rv}+t_{fi})) \tag {29}\\ e_{total}& =e_{sw}+e_{cond} \tag {30}\end{align*} Further, various average power losses are calculated by averaging the above energy losses over one fundamental cycle. The subsections discuss the variation of various average power losses of SiC MOSFET and Si IGBT based $2\times 1$ matrix converters operating with 2-step and 4-step commutations.

A. SiC MOSFET Based Matrix Converter Using 2-Step Commutation

Fig. 9 shows the plots of different power losses for SiC MOSFET based $2\times 1$ matrix converter, operating with 2-step commutation, at different switching frequencies, $f_{s}$ . The switching power loss, $P_{sw}$ , consists of turn ON power loss, $P_{on}$ , turn OFF power loss, $P_{off}$ , and reverse recovery power loss of the body diode, $P_{rr,BD}$ . Therefore, $P_{sw}=P_{on}+P_{off}+P_{rr,BD}$ . $P_{cond}$ represents the conduction power loss, and $P_{total}$ represents the total power loss. $P_{on}$ , $P_{off}$ , $P_{rr,BD}$ , and $P_{sw}$ increase linearly with $f_{s}=1-435~kHz$ . $P_{on}$ is similar to $P_{off}$ for all frequencies, and the contribution of $P_{rr,BD}$ to power loss is insignificant. $P_{cond}$ remains nearly constant around $110~W$ for all $f_{s}$ , and $P_{sw}$ overtakes it around $400~kHz$ . $P_{total}$ is about $111~W$ at $1~kHz$ , increasing to $225~W$ at $435~kHz$ .

FIGURE 9.

Calculated power loss in SiC MOSFET based $2\times 1$ matrix converter using 2-step commutation.

B. SiC MOSFET Based Matrix Converter Using 4-Step Commutation

Fig. 10 shows the plots of $P_{on}$ , $P_{off}$ , $P_{rr,BD}$ , $P_{sw}$ , $P_{cond}$ , and $P_{total}$ at $f_{s}=1-217~kHz$ , for SiC MOSFET based $2\times 1$ matrix converter, operating with 4-step commutation. The trends and values of $P_{on}$ , $P_{off}$ , $P_{rr,BD}$ , and $P_{sw}$ match with SiC MOSFET based $2\times 1$ matrix converter operating with 2-step commutation. However, $P_{cond}$ is almost $55~W$ at all frequencies, 50% of the $2\times 1$ matrix converter operating with 2-step commutation. It reduces $P_{total}$ by $55~W$ at every $f_{s}$ . Therefore, $P_{total}$ is around $55~W$ at $1~kHz$ , increasing to $111~W$ at $217~kHz$ . $P_{sw}$ overtakes $P_{cond}$ around $200~kHz$ .

FIGURE 10.

Calculated power loss in SiC MOSFET based $2\times 1$ matrix converter using 4-step commutation.

C. Si IGBT Based Matrix Converter Using 2-Step Commutation

Fig. 11 presents the plots of $P_{on}$ , $P_{off}$ , $P_{rr,D}$ (diode power loss during reverse recovery), $P_{sw}$ , $P_{cond}$ , and $P_{total}$ at $f_{s}=1-304~kHz$ , for Si IGBT based $2\times 1$ matrix converter, operating with 2-step commutation. $P_{on}$ , $P_{off}$ , $P_{rr,D}$ , and $P_{sw}$ increase with increasing $f_{s}$ . $P_{on}$ is higher than $P_{off}$ and $P_{rr,D}$ is negligible at all frequencies. $P_{cond}$ remains reasonably constant around $55~W$ at all $f_{s}$ and $P_{sw}$ crosses it around $35~kHz$ . $P_{total}$ is around $58~W$ at $1~kHz$ , increasing to $547~W$ at $304~kHz$ .

FIGURE 11.

Calculated power loss in Si IGBTT based $2\times 1$ matrix converter using 2-step commutation.

D. Si IGBT Based Matrix Converter Using 4-Step Commutation

Fig. 12 presents the plots of $P_{on}$ , $P_{off}$ , $P_{rr,D}$ , $P_{sw}$ , $P_{cond}$ , and $P_{total}$ at $f_{s}=1-152~kHz$ , for Si IGBT based $2\times 1$ matrix converter operating with 4-step commutation. The trends and values of all the plots match the plots of Si IGBT based $2\times 1$ matrix converter operating with 2-step commutation till $152~kHz$ . $P_{total}$ is around $58~W$ at $1~kHz$ , increasing to $297~W$ at $150~kHz$ .

FIGURE 12.

Calculated power loss in Si IGBTT based $2\times 1$ matrix converter using 4-step commutation.

E. Loss Comparison of Si IGBT and SiC MOSFET Based $2\times 1$ Matrix Converters

Fig. 13 shows the power loss comparison of SiC MOSFET and Si IGBT based $2\times 1$ matrix converters using 2-step and 4-step commutations. Fig. 13(a) compares the conduction losses. Fig. 13(b) compares the switching losses. Fig. 13(c) compares the total losses. The comparisons are for $f_{s} \le 50~kHz$ . Fig. 13(d) compares the total losses for $f_{s} \le 200~kHz$ . Efficiency comparisons up to $50~kHz$ are done in Fig. 14(a) and up to $200~kHz$ are done in Fig. 14(b). The comparisons are listed below:

• $P_{cond}$ of SiC MOSFET based matrix converter using 4-step and Si IGBT based matrix converter using 2-step and 4-step is approximately 50% less than SiC MOSFET based matrix converter using 2-step. This percentage change is nearly constant at all frequencies.

• The $P_{sw}$ of SiC MOSFET based matrix converter is approximately 84% less than Si IGBT based matrix converter.

• $P_{total}$ of SiC MOSFET based matrix converter using 4-step is approximately $5-50\%$ less than Si IGBT based matrix converter using 2-step and 4-step, in $f_{s}=1-50~kHz$ range. At $f_{s}=200~kHz$ , the $P_{total}$ of SiC MOSFET based matrix converter using 4-step commutation is 72% less than Si IGBT based matrix converter using 2-step.

• $P_{total}$ of SiC MOSFET based matrix converter using 4-step is approximately $51-46\%$ less than SiC MOSFET based matrix converter using 2-step, in $f_{s}=1-50~kHz$ range. At $f_{s}=200~kHz$ , the $P_{total}$ difference is 35%.

• $P_{total}$ of SiC MOSFET based matrix converter using 2-step is approximately $48-1\%$ more than Si IGBT based matrix converter using 2-step and 4-step, in $f_{s}=1-40~kHz$ range. After $f_{s}=40~kHz$ and up to $200~kHz$ , the $P_{total}$ of SiC MOSFET based matrix converter using 2-step decreases and becomes $0-57\%$ less than Si IGBT based matrix converter using 2-step and 4-step.

• The efficiency of SiC MOSFET based matrix converter using 4-step is approximately $97.6-95.4\%$ , in $f_{s}=1-200~kHz$ range. The efficiency of SiC MOSFET based matrix converter using 2-step is approximately $95.2-93.1\%$ , in $f_{s}=1-200~kHz$ range.

• The efficiency of Si IGBT based matrix converter using 2-step and 4-step is approximately $97.4-85.3\%$ , in $f_{s}=1-200~kHz$ range. These plots fall and cross the SiC MOSFET based matrix converter using 2-step plot around $f_{s}=42~kHz$ .

Table 3 presents the power loss and efficiency comparison of SiC MOSFET and Si IGBT based matrix converters using 2-step and 4-step commutations.

TABLE 3 Calculated Power Loss and Efficiency Comparisons between SiC MOSFET and Si IGBT Based $2\times 1$ Matrix Converters Using 2-Step And 4-Step Commutations

FIGURE 13.

Calculated power loss comparison. (a) Conduction loss. (b) Switching loss. (c) Total loss upto $50~kHz$ to show clear comparisons at lower $f_{s}$ . (d) Total loss upto $200~kHz$ to show comparisons at higher $f_{s}$ .

FIGURE 14.

Calculated efficiency comparison.

F. Thermal Stress on 4-Quadrant Switch During Switching

In each switching event of a 4-quadrant switch, only one of the MOSFETs or IGBTs contributes significantly to the switching loss. Therefore, analyzing the thermal stress of this specific MOSFET or IGBT during switching operation is essential. Due to the short turn ON and turn OFF times of these devices, heat generated during switching cannot be effectively dissipated from the chip to the package via the heatsink. As a result, adiabatic heating occurs, leading to an increase in the junction temperature of the MOSFET or IGBT [51]. The resulting temperature rise during switching is given by following equations:\begin{align*} dT_{j}& =\frac {p_{d}(t)dt}{AWC_{v}} \tag {31}\\ dT_{j}& =\frac {p_{d}(t)dt}{AWC_{s}\rho } \tag {32}\\ T_{j,on}& =T_{j,o}+\frac {e_{on}}{AWC_{s}\rho } \tag {33}\\ T_{j,off}& =T_{j,o}+\frac {e_{off}}{AWC_{s}\rho } \tag {34}\\ T_{j,rr}& =T_{j,o}+\frac {e_{rr}}{AWC_{s}\rho } \tag {35}\end{align*} where;

$p_{d}(t)=$	Instantaneous power loss
$A=$	Area of the chip
$W=$	Thickness of the chip
$C_{v}=$	Volumetric specific heat
$C_{s}=$	Specific heat capacity
$\rho =$	Density of the material
$T_{j,on}=$	Junction temperature during turn ON
$T_{j,off}=$	Junction temperature during turn OFF
$T_{j,rr}=$	Junction temperature during reverse recovery
$T_{j,o}=$	Initial junction temperature

$T_{j,on}$ and $T_{j,off}$ occur in the first and third quadrants, while $T_{j,rr}$ appears in the second and fourth quadrants. During turn-on in the fourth quadrant, the power loss in the device is negligible. Consequently, there is no significant increase in the junction temperature of the device in this quadrant.

1) Thermal Stress on SiC MOSFET Based 4-Quadrant Switch

The manufacturer of the selected SiC MOSFET does not provide numerical values for A and W. To estimate these parameters, values were taken from the bare die SiC MOSFET (CPM2-1200-0080A) of the same ratings from the same manufacturer. Since the body diode of the MOSFET is used, A and W are identical. The parameters $C_{s}$ and $\rho $ for silicon carbide are readily available. Consequently, the numerical values obtained for the SiC MOSFET are:

For SC MOSFET:

A $=11.16 \times 10^{-6}~m^{2}$

$W=180 \times 10^{-6}$ m

$C_{s}=750~Jkg^{-1}K^{-1}$ )

$\rho$ = $3.1 \times 10^{3}~kgm^{-3}$

For a particular $T_{j,o}$ , the change in junction temperature, $\Delta T_{j}$ , for different switching events for SiC MOSFET based 4-quadrant switch are:\begin{align*} \Delta T_{j,on}& =214.11e_{on} \tag {36}\\ \Delta T_{j,off}& =214.11e_{off} \tag {37}\\ \Delta T_{j,rr}& =214.11e_{rr} \tag {38}\end{align*} The maximum change in junction temperature, $(\Delta T_{j})_{max}$ , for different switching events for are obtained by finding the maximum $e_{on}$ , $e_{off}$ , and $e_{rr}$ . $(\Delta T_{j})_{max}$ , for different switching events are shown below:\begin{align*} (\Delta T_{j,on})_{max}& =214.11(e_{on})_{max}=0.056~K \tag {39}\\ (\Delta T_{j,off})_{max}& =214.11(e_{off})_{max}=0.055~K \tag {40}\\ (\Delta T_{j,rr})_{max}& =214.11(e_{rr})_{max}=0.003~K \tag {41}\end{align*} The maximum thermal stress on SiC MOSFET based 4-quadrant switch is similar during turn ON and turn OFF. However, maximum thermal stress during turn ON and turn OFF are higher than reverse recovery.

2) Thermal Stress on Si IGBT Based 4-Quadrant Switch

The manufacturer of the selected Si IGBT does not provide numerical values for A and W. To estimate these parameters, values were taken from the bare die Si IGBT (NGTD30T120F2) of the same ratings from the same manufacturer. Since the anti-parallel diode is co-packaged with the IGBT, it has a separate chip. The values of A and W for the diode are assumed to be the same as those of the IGBT, given that their voltage and current ratings are identical. The parameters $C_{s}$ and $\rho $ for silicon are readily available. Consequently, the numerical values obtained for the Si IGBT are:

A $=29.58 \times 10^{-6}~m^{2}$

$W=127 \times 10^{-6}$ m

$C_{s}=710~Jkg^{-1}K^{-1}$ )

$\rho$ = $2.33 \times 10^{3}~kgm^{-3}$

For a particular $T_{j,o}$ , the change in junction temperature, $\Delta T_{j}$ , for different switching events for Si IGBT based 4-quadrant switch are:\begin{align*} \Delta T_{j,on}& =160.91e_{on} \tag {42}\\ \Delta T_{j,off}& =160.91e_{off} \tag {43}\\ \Delta T_{j,rr}& =160.91e_{rr} \tag {44}\end{align*} $(\Delta T_{j})_{max}$ , for different switching events are shown below:\begin{align*} (\Delta T_{j,on})_{max}& =160.9(e_{on})_{max}=0.386~K \tag {45}\\ (\Delta T_{j,off})_{max}& =160.9(e_{off})_{max}=0.119~K \tag {46}\\ (\Delta T_{j,rr})_{max}& =160.9(e_{rr})_{max}=0.001~K \tag {47}\end{align*} The maximum thermal stress on Si IGBT based 4-quadrant switch is higher during turn ON compared to turn OFF and reverse recovery. Moreover, the maximum thermal stress during turn ON and turn OFF are higher than SiC MOSFET based 4-quadrant switch. However, maximum thermal stress during reverse recovery is lower than SiC MOSFET based 4-quadrant switch. Table 4 presents the Maximum thermal stress comparison of SiC MOSFET and Si IGBT based 4-quadrant switches during switching events.

TABLE 4 Maximum Thermal Stress Comparison of SiC MOSFET and Si IGBT Based 4-Quadrant Switches During Switching Events

SECTION VI. LTspice Simulation Results of SiC MOSFET and Si IGBT Based 4-Quadrant Switches

This section describes the LTspice simulation results of SiC MOSFET and Si IGBT based 4-quadrant switches using 2-step and 4-step commutations. The simulation results contain the ON state drop, switching waveforms, turn ON/OFF times, and power loss. The comparison of results gives essential findings.

A. On State Voltage Drop

Fig. 15 shows the test circuit to find the ON state voltage drop of SiC MOSFET and Si IGBT based 4-quadrant switches. $R_{ov}$ is varied and $V_{4QS}$ is obtained at various $I_{4QS}$ . $V_{DC}$ is kept constant at $120~V$ and $R_{ov}$ is varied to get $I_{4QS}=5-25~A$ . Figure 16 shows the plots of the ON state voltage drops of SiC MOSFET and Si IGBT 4-quadrant switches using 2-step and 4-step commutations, and the comparisons are discussed below.

FIGURE 15.

(a) Test circuit for ON state voltage drop of SiC MOSFET based 4-quadrant switch. (b) Test circuit for ON state voltage drop of Si IGBT 4-quadrant switch.

FIGURE 16.

Comparison of simulated ON state voltage drop of SiC MOSFET and Si IGBT 4-quadrant switches.

1) 2-Step Commutation

Fig. 16(a) shows the plots of the ON state voltage drop of SiC MOSFET and Si IGBT 4-quadrant switches when only one MOSFET/IGBT is gated. This condition occurs in 2-step commutation. The ON state voltage drop, $V_{4QS}=4.18-7.36~V$ , for $I_{4QS}=5-25~A$ , for SiC MOSFET based 4-quadrant switch. The ON state voltage drop for Si IGBT based 4-quadrant switch, $V_{4QS}=2.22-3.09~V$ for $I_{4QS}=5-25~A$ . The comparison shows that the ON state voltage drop for Si IGBT using 2-step commutation is $46.9-58\%$ lower than SiC MOSFET using 2-step commutation.

2) 4-Step Commutation

Fig. 16(b) shows the plots of the ON state drop of SiC MOSFET and Si IGBT 4-quadrant switches when both MOSFETs/IGBTs are gated. This condition occurs in 4-step commutation. $V_{4QS}=0.72-4.39~V$ , for $I_{4QS}=5-25~A$ , for SiC MOSFET based 4-quadrant switch. $V_{4QS}=2.22-3.09~V$ , for $I_{4QS}=5-25~A$ , for Si IGBT based 4-quadrant switch. The ON state voltage drop for SiC MOSFET using 4-step commutation is $67.6-14.9\%$ lower in $5-15~A$ range and $10.4-42.1\%$ higher in $20-25~A$ than Si IGBT using 2-step and 4-step commutations. The ON state voltage drop for SiC MOSFET using 4-step commutation is $82.3-40.4\%$ lower than SiC MOSFET using 2-step commutation.

B. Switching Characteristics

This subsection compares the simulated switching waveforms of SiC MOSFET and Si IGBT 4-quadrant switches in first and fourth quadrants. The subsection also compares the turn ON/OFF times of SiC MOSFET and Si IGBT 4-quadrant switches in all quadrants. The waveforms in third and second quadrants are similar to the first and fourth quadrants. Therefore, the waveforms in third and second quadrants are not discussed explicitly. The waveforms are obtained for $v_{4QS}=120~V$ , $i_{4QS}=20~A$ , and gate resistance of $15~\Omega $ . The turn ON/OFF time plots against $|i_{4QS}|$ are also obtained at fixed $v_{4QS}=120~V$ . Test circuit for switching characteristics of SiC MOSFET based 4-quadrant switch is shown in Figure 17(a). Test circuit for switching characteristics of Si IGBT based 4-quadrant switch is shown in Figure 17(b). The test circuit is run as half-bridge inverter using sinusoidal pulse width modulation for under-modulation condition.

FIGURE 17.

(a) Test circuit for switching characteristics of SiC MOSFET based 4-quadrant switch. (b) Test circuit for switching characteristics of Si IGBT based 4-quadrant switch.

1) Switching Waveforms

Fig. 18(a) shows the turn ON of the SiC MOSFET based 4-quadrant switch, $S_{A}$ , in first quadrant and the turn OFF of SiC MOSFET based 4-quadrant switch, $S_{B}$ , in fourth quadrant. Similarly, Fig. 18(b) shows the turn ON of Si IGBT based 4-quadrant switch, $T_{A}$ , in first quadrant and turn OFF of Si IGBT based 4-quadrant switch, $T_{B}$ , in fourth quadrant. The turn ON time of $S_{A}$ , $t_{ON,A}=145~ns$ and the turn OFF time of $S_{B}$ , $t_{OFF,B}=500~ns$ . In comparison, the turn ON time of $T_{A}$ , $t_{ON,A}=320~ns$ and the turn OFF time of $T_{B}$ , $t_{OFF,B}=772~ns$ . The reverse recovery current is visible in the turn OFF of $S_{B}$ /$T_{B}$ in fourth quadrant. The peak reverse recovery current is $40~A$ in $T_{B}$ and $20~A$ in $S_{B}$ .

FIGURE 18.

Simulated turn ON in first quadrant and turn OFF in fourth quadrant of SiC MOSFET and Si IGBT based 4-quadrant switches.

Fig. 19(a)/ Fig. 19(b) shows the turn OFF of $S_{A}$ /$T_{A}$ in first quadrant and the turn ON of $S_{B}$ /$T_{B}$ in fourth quadrant. $t_{OFF,A}=78~ns$ for $S_{A}$ and $t_{ON,B}=430~ns$ for $S_{B}$ but $t_{OFF,A}=430~ns$ for $T_{A}$ and $t_{ON,B}=777~ns$ for $T_{B}$ . The comparison shows that the turn ON/OFF times are higher for Si IGBT based 4-quadrant switch. There is no reverse recovery current in first quadrant for both SiC MOSFET and Si IGBT based 4-quadrant switches. However, a tail current period is present in the fall of $i_{4QS,A}$ of $T_{A}$ , shown in Fig. 19(b).

FIGURE 19.

Simulated turn OFF in first quadrant and turn ON in fourth quadrant of SiC MOSFET and Si IGBT based 4-quadrant switches.

2) Turn on/off Time

Fig. 20 shows the turn ON/OFF time plots against $|i_{4QS}|$ of SiC MOSFET based 4-quadrant switch. Fig. 21 shows the turn ON/OFF time plots against $|i_{4QS}|$ of Si IGBT based 4-quadrant switch. The trends of $t_{ON}$ in all quadrants for Si IGBT based 4-quadrant switch (Fig. 21(a)) are similar to SiC MOSFET based 4-quadrant switch (Fig. 20(a)). In first and third quadrants, $t_{ON}$ is increasing, because from (7) $t_{ri}$ and reverse recovery period ($t_{a}$ and tb) increase with current. In second and fourth quadrants, $t_{ON}$ is decreasing, because $t_{ON}$ is directly related to decreasing $t_{OFF}$ in first and third quadrants, which is seen from 20(b) and 21(b). Since the net effect of current on the sum of $t_{dv}$ , $t_{rv}$ , and $t_{fi}$ is decreasing [25], $t_{OFF}$ is decreasing in nature for SiC MOSFET. Although, the effect of $t_{ti}$ on turn OFF time of Si IGBT is directly related to current, the net turn OFF time is still decreasing in Si IGBT in the simulation results. $t_{ON}$ for Si IGBT based 4-quadrant switch is roughly 100% more than SiC MOSFET based 4-quadrant switch in all quadrants.

FIGURE 20.

Simulated turn ON/OFF time of SiC MOSFET based 4-quadrant switch. (a) $t_{ON}$ . (b) $t_{OFF}$ .

FIGURE 21.

Simulated turn ON/OFF time of Si IGBT based 4-quadrant switch. (a) $t_{ON}$ . (b) $t_{OFF}$ .

The trends of $t_{OFF}$ in all quadrants for Si IGBT based 4-quadrant switch (Fig. 21(b)) are similar to SiC MOSFET based 4-quadrant switch (Fig. 20(b)). In first and third quadrants, $t_{OFF}$ is decreasing; the reason is discussed above. In second and fourth quadrants, $t_{OFF}$ is constant, as a fixed and the maximum value of $t_{OFF}$ for the given current range is chosen for safe commutation. $t_{OFF}$ of the Si IGBT based 4-quadrant switch is approximately $330-473\%$ greater than SiC MOSFET based 4-quadrant switch in first and third quadrants. However, $t_{OFF}$ is only 55% higher in second and fourth quadrants. $t_{OFF}$ in all quadrants for Si IGBT based 4-quadrant switch is more comparable than $t_{OFF}$ in all quadrants for SiC MOSFET based 4-quadrant switch.

C. Efficiency of SiC MOSFET and Si IGBT Based $2\times 1$ Matrix Converters

The circuit simulation of SiC MOSFET and Si IGBT based $2\times 1$ matrix converters for $2~kW$ output load using 2-step and 4-step commutations gives the efficiency of the converters. Fig. 22(a) compares efficiency plots for $f_{s} \le 50~kHz$ . The efficiency of SiC MOSFET based $2\times 1$ matrix converter using 4-step starts at 96.1% at $1~kHz$ . It has the highest efficiency of 96.9% at $20~kHz$ , then reduces to 96.5% at $50~kHz$ . Si IGBT based matrix converter using 2-step and 4-step commutations follows a similar trend with an efficiency of around $96~\%$ at $1~kHz$ , decreasing to 94.2% at $50~kHz$ . However, the efficiency of SiC MOSFET based matrix converter using 2-step stays nearly constant at about 94%. Therefore, SiC MOSFET based matrix converter using 4-step is the most preferred for $f_{s} \le 50~kHz$ . SiC MOSFET based matrix converter using 2-step is the least preferred for $f_{s} \le 50~kHz$ . Fig. 22(b) shows the efficiency plots from $1~kHz$ to their maximum switching frequencies. The comparison indicates that SiC MOSFET based matrix converter using 4-step is the most preferred for $f_{s}\gt 50~kHz$ . Si IGBT based matrix converter using 2-step and 4-step is the least preferred for $f_{s}\gt 50~kHz$ .

FIGURE 22.

Simulated efficiency comparison of SiC MOSFET and Si IGBT based $2\times 1$ matrix converter. (a) Till $50~kHz$ switching frequency. (b) Till maximum switching frequencies.

The efficiency plots nearly follow the trends (decrease with frequency as switching losses increase) observed in Section V. At $20~kHz$ , the efficiency has increased for SiC MOSFET based matrix converter using 4-step and Si IGBT based matrix converter using 2-step and 4-step commutations. The probable reason for such a trend is that; With higher switching frequency lower order harmonics reduce in the load current waveform. However, this effect is overcome by the higher switching loss at switching frequencies above $20~kHz$ . In contrast, SiC MOSFET based matrix converter using 2-step remained fairly constant, as the above effect does not seem to dominate because of lower efficiency ($94~\%$ ). Table 5 compares simulated results of SiC MOSFET and Si IGBT based 4-quadrant switches using 2-step and 4-step commutations. The representation of minimum and maximum turn ON/OFF times are $t_{ON,min}$ , $t_{ON,max}$ , $t_{OFF,min}$ , and $t_{OFF,max}$ . These times are used to calculate the maximum switching frequency, $f_{sm}$ , for SiC MOSFET and Si IGBT based $2\times 1$ matrix converters using 2-step and 4-step commutations. Equations (17) and (18) are modified to give expressions (48) and (49) for $f_{sm}$ .\begin{align*} f_{sm,4-step} & = \frac {1}{\frac {8}{f_{c}}+2(t_{ON,min}+t_{OFF,min})+t_{ON,max}} \\ & \quad + t_{OFF,max}+8(t_{pdd}+t_{pdg}+t_{pdi}) \tag {48}\\ f_{sm,2-step} & = \frac {1}{\frac {4}{f_{c}}+t_{ON,max}+t_{OFF,max}} \\ & \quad +4(t_{pdd}+t_{pdg}+t_{pdi}) \tag {49}\end{align*}

TABLE 5 Simulation Result Comparison of SiC MOSFET and Si IGBT Based 4-Quadrant Switches Using Current Commutation

D. Effect of Delay Time on Efficiency of SiC MOSFET and Si IGBT Based $2\times 1$ Matrix Converters

In both 4-step and 2-step commutation methods, a delay time is allotted for each MOSFET/IGBT to turn ON/OFF in each step, as shown in Fig. 4(c)-(d). The longer delay time reduces the maximum switching frequency and distorts the load waveforms. The delay time should only be increased if the turn ON time of the IGBT, $t_{ON}$ , or the turn OFF time of the IGBT, $t_{OFF}$ , or both increase. The efficiency decreases if $t_{ON}$ , or $t_{OFF}$ , or both increase. In this paper, a fixed delay time of $500~ns$ is kept for Si IGBT based matrix converter considering the maximum $t_{ON}$ , $t_{OFF}$ , and safety factor. However, keeping $t_{ON}$ and $t_{OFF}$ unchanged, and the delay time is increased, then the efficiency of Si IGBT based matrix converter does not change. It happens so because the conduction period of the diode remains same, and thus the conduction loss is unchanged. Moreover, the type of commutation - 2-step or 4-step, also does not affect the efficiency because one diode always conducts in both the commutation methods.

A fixed delay time of $250~ns$ is kept for SiC MOSFETT based matrix converter considering the maximum $t_{ON}$ , $t_{OFF}$ , and safety factor. The longer delay time does not affect the efficiency of SiC MOSFET based matrix converter using 2-step commutation. It happens so because the conduction period of the body diode does not change, and thus the conduction loss is unchanged.

However, the longer delay time reduces the efficiency of the SiC MOSFET based matrix converter using 4-step. The reduction is because the conduction period of the body diode increases which consequently increases the conduction loss. The doubling of delay time from $250~ns$ to $500~ns$ reduces the efficiency by $0-0.6\%$ only, in $1-100~kHz$ range, as shown in Fig. 23. The reduction in efficiency can be considered insignificant. The quadrupling of delay time from $250~ns$ to $1000~ns$ reduces the efficiency by $0.02-0.9\%$ only, in $1-80~kHz$ range, as shown in Fig. 23. In this condition also, the reduction in efficiency is not so significant.

FIGURE 23.

Effect of delay time on the efficiency of SiC MOSFET based matrix converter using 4-step commutation.

SECTION VII. Experimental Verification

This section describes the experimental set up, experimental procedure, reproducibility considerations, and sources of error. It also explains the experimental results and overall inferences obtained. It discusses the practical application impacts and technical prospects of the results, and the influence on future device selection and design. It also mentions the limitations of the study and unresolved issues, as well as their potential impact on the research findings.

A. Experimental Set up

Fig. 24 shows the experimental setup for comparing SiC MOSFET and Si IGBT based 4-quadrant switches. It consists of a power board, a sensing board, a sbRIO-9636 FPGA board, a resistive load, and an inductive load. The power board contains SiC MOSFETs/Si IGBTs connected in common-source/common-emitter configuration to create 4-quadrant switches. SiC MOSFETs/Si IGBTs are on the bottom layer of the board with heat sinks, and the ambient temperature is kept at $25~^{o}C$ . Separate power boards are used for SiC MOSFET and Si IGBT based 4-quadrant switches. The power board also works as the $2\times 1$ matrix converter because it has multiple 4-quadrant switches. The Hall effect current sensor on the sensing board senses the load current. The sensing board conditions the sensed signal and makes it useful for the FPGA board. The current commutation control programming is created in LabVIEW. The interface circuit on the sensing board boosts the digital signals from the FPGA board for gate drivers. Mixed domain oscilloscope (MDO3000) of $1~GHz$ bandwidth is used to capture the experimental results. Differential probe (P5200A) of $100~MHz$ bandwidth is used for switch and load voltage measurements. For gate voltage measurements differential probes (HZ 100) of $40~MHz$ bandwidth and low voltage rating are used. For input voltage measurements differential probes (HZ 100) of $40~MHz$ bandwidth and high voltage rating are used. Current probe (TCP312A) of $100~MHz$ bandwidth and amplifier (TCPA300) are used to measure switch, load and input currents. The setup does not operate at its maximum voltage and current limits for its safe operation. Instruments are well calibrated before measurement. Efforts are taken to minimize systematic and random errors, and avoid gross errors. All the measurements are taken at $25^{o}C$ ambient temperature.

FIGURE 24.

Experimental setup for $2\times 1$ matrix converter.

B. On State Voltage Drop

Fig. 15 is used to get the ON state voltage drops for 4-quadrant switches. The procedure for measurement is already mentioned in Section VI-A. The results are taken by differential probes and verified by multimeter measurements to avoid errors.

1) 2-Step Commutation

Fig. 25 shows the experimental results for the ON state voltage drop of SiC MOSFET and Si IGBT based 4-quadrant switches when only one MOSFET/IGBT is gated (2)-step commutation). The ON state voltage drop, $V_{4QS}=3-6.99~V$ , for $I_{4QS}=0-25~A$ , for SiC MOSFET based 4-quadrant switch, in Fig. 25(a). The ON state voltage drop for Si IGBT based 4-quadrant switch, $V_{4QS}=1.7-3.09~V$ , for $I_{4QS}=0-25~A$ . The ON state voltage drop for Si IGBT based 4-quadrant switch using 2-step commutation is $43.3-55.8\%$ lower than SiC MOSFET based 4-quadrant switch using 2-step commutation. The voltage drop across the SiC MOSFET $S_{1}$ , $V_{S1}$ , is smaller than that across the Si IGBT $T_{1}$ , $V_{T1}$ , for $I_{4QS}\lt 20~A$ , in Fig. 25(b). However, the voltage drop across the SiC MOSFET $S_{2}$ , $V_{S2}$ , is larger than that across the Si IGBT $T_{2}$ , $V_{T2}$ , for all $I_{4QS}$ , in Fig. 25(c). $V_{S2}$ becomes the major contributor of $V_{4QS}$ of SiC MOSFET based 4-quadrant switch. It is expected because the body diode of $S_{2}$ conducts, due to non-gating, has a higher voltage drop than the Si diode of $T_{2}$ .

FIGURE 25.

Experimental ON state voltage drop comparison of Si IGBT and SiC MOSFET based 4-quadrant switches when only one MOSFET/IGBT is gated.

2) 4-Step Commutation

Fig. 26 shows the experimental results for ON state voltage drop of SiC MOSFET and Si IGBT based 4-quadrant switches when both MOSFETs/IGBTs are gated (4)-step commutation). The ON state voltage drop, $V_{4QS}=0-3.68~V$ , for $I_{4QS}=0-25~A$ , for SiC MOSFET based 4-quadrant switch, in Fig. 26(a). The ON state voltage drop for Si IGBT based 4-quadrant switch, $V_{4QS}=1.7-3.09~V$ , for $I_{4QS}=0-25~A$ . The ON state voltage drop for SiC MOSFET based 4-quadrant switch using 4-step commutation is $100-20.5\%$ lower than Si IGBT based 4-quadrant switch using 4-step commutation, for $I_{4QS}=0-15~A$ . $V_{S1}$ and $V_{S2}$ are smaller than $V_{T1}$ and $V_{T2}$ , for $I_{4QS}\lt 20~A$ , Fig. 26(b)-(c). It is expected because $S_{2}$ conducts in third quadrant because of gating and has a lower voltage drop than the Si diode of $T_{2}$ for $I_{4QS}\lt 20~A$ . However, the ON state voltage drop for SiC MOSFET based 4-quadrant switch using 4-step commutation is $0-19.1\%$ higher than Si IGBT based 4-quadrant switch using 4-step commutation, for $I_{4QS}=20-25~A$ . The ON state voltage drop for SiC MOSFET based 4-quadrant switch using 4-step commutation is $100-47.3\%$ smaller than SiC MOSFET based 4-quadrant switch using 2-step commutation, for $I_{4QS}=0-25~A$ .

FIGURE 26.

Experimental ON state voltage drop comparison of Si IGBT and SiC MOSFET based 4-quadrant switches when both MOSFETs/IGBTs are gated.

C. Switching Characteristics

This subsection discusses the experimental switching waveforms in first quadrant and turn ON/OFF times in all quadrants of SiC MOSFET and Si IGBT 4-quadrant switches. Fig. 15 is used to get the switching waveforms for 4-quadrant switches. The procedure for measurement is already mentioned in Section VI-B. The results are taken by differential and current probes. Since the rise and fall times are different for differential probes and current probe, a few nanoseconds of delay occurs among the voltage and current waveforms. However, the aim of the experiment is to match the trends obtained in LTspice simulations without bothering much about the accuracy. Moreover, the miller plateau is not visible in the gate voltage waveforms due to lower CMRR ($\gt 50~DB$ ) of differential probes. These miller plateau is clearly observed with the help of very high CMRR optical probes which are unavailable in the laboratory. Moreover, small random circuit parasitics may also alter the waveforms, however, the effects are negligible. The experiments are repeated thrice at the same operating point, and found that no significant deviation occurred among the results. The waveforms are obtained for $v_{4QS}=120~V$ , $i_{4QS}=10~A$ , and gate resistance of $15~\Omega $ . The turn ON/OFF time plots against $|i_{4QS}|$ are also obtained at fixed $v_{4QS}=120~V$ .

1) Switching Waveforms

Fig. 27(a) shows the turn ON of the SiC MOSFET based 4-quadrant switch, $S_{A}$ , in first quadrant. Similarly, Fig. 27(b) shows the turn ON of the Si IGBT based 4-quadrant switch, $T_{A}$ , in first quadrant. The turn ON time of $S_{A}$ , $t_{ON,A}=108~ns$ , and the turn OFF time of $S_{B}$ , $t_{OFF,B}=350~ns$ . In comparison, the turn ON time of $T_{A}$ , $t_{ON,A}=290~ns$ , and the turn OFF time of $t_{B}$ , $t_{OFF,B}=430~ns$ . The oscillations in $i_{4QS}$ is seen in the results of Si IGBT, which is negligible for SiC MOSFET. The oscillations are due to higher value of reverse recovery current of Si diode and circuit parasitics. In case of SiC MOSFET, reverse recovery current of body diode is small.

FIGURE 27.

Experimental turn ON in first quadrant of SiC MOSFET and Si IGBT based 4-quadrant switches.

Fig. 28(a)/ Fig. 28(b) shows the turn OFF of $S_{A}$ /$T_{A}$ in first quadrant. $t_{OFF,A}=154~ns$ for $S_{A}$ and $t_{ON,B}=410~ns$ for $S_{B}$ , but $t_{OFF,A}=412~ns$ for $T_{A}$ and $t_{ON,B}=656~ns$ for $T_{B}$ . The comparison shows that the turn ON/OFF times are higher for Si IGBT based 4-quadrant switch. The oscillations in $v_{4QS}$ is seen in the results, which is the result of parasitic inductances and decoupling capacitances used in the circuit. Other results are similar to the simulation results and theory.

FIGURE 28.

Experimental turn OFF in first quadrant of SiC MOSFET and Si IGBT based 4-quadrant switches.

2) Turn on/off Time

Fig. 29 shows the turn ON/OFF time plots against $|i_{4QS}|$ for SiC MOSFET based 4-quadrant switch. Fig. 30 shows the turn ON/OFF time plots against $|i_{4QS}|$ for Si IGBT based 4-quadrant switch. The trends of $t_{ON}$ in all quadrants for the Si IGBT based 4-quadrant switch, in Fig. 30(a), are similar to the SiC MOSFET based 4-quadrant switch, in Fig. 29(a). In first and third quadrants, $t_{ON}$ increases; in second and fourth quadrants, $t_{ON}$ decreases. The reasons for the trends are discussed in the simulation section. $t_{ON}$ for Si IGBT based 4-quadrant switch is $240-78\%$ more than SiC MOSFET based 4-quadrant switch in first and third quadrants and $t_{ON}$ is $103-41\%$ greater in second and fourth quadrants.

FIGURE 29.

Experimental turn ON and turn OFF time of SiC MOSFET based 4-quadrant switch.

FIGURE 30.

Experimental turn ON and turn OFF time of Si IGBT based 4-quadrant switch.

The trends of $t_{OFF}$ in all quadrants for Si IGBT based 4-quadrant switch (Fig. 30(b)) are similar to SiC MOSFET based 4-quadrant switch (Fig. 29(b)). In first and third quadrants, $t_{OFF}$ decreases; in second and fourth quadrants, $t_{OFF}$ is constant. The reasons for the trends are discussed in the simulation section. $t_{OFF}$ of Si IGBT based 4-quadrant switch is approximately $240-162\%$ greater than SiC MOSFET based 4-quadrant switch in first and third quadrants. However, $t_{OFF}$ is only 20% higher in second and fourth quadrants. $t_{OFF}$ in all quadrants for Si IGBT based 4-quadrant switch is comparable.

The reasons for discrepancy between the IGBT turn-off time simulated in Fig. 21(b) and the experimental data obtained in Fig. 30(b) are explained below. The simulation and experimental turn OFF time, $t_{OFF}$ , in first and third quadrants are comparable, which can be seen from Fig. 21(b) and Fig. 30(b). $t_{OFF}$ is in the range of $400-500~ns$ for simulation. Whereas, $t_{OFF}$ is in the range of $350-600~ns$ for experiment. The reasons behind some difference in the range are:

• The inaccurate LTspice model of IGBT and gate driver causes longer time for $v_{GE}$ fall in the simulation compared to experiment. The difference can be observed from the simulation waveform of $v_{GE,A1}$ in Fig. 18(b) and the experimental waveform of $v_{GE,A1}$ in Fig. 27(b). The fall of $v_{GE,A1}$ in simulation takes more than $400~ns$ whereas, the fall of $v_{GE,A1}$ in experiment takes around $200~ns$ . The difference due to this reason is more visible as current increases.

• It is impossible to include the unknown parasitic inductances and capacitances of the experimental setup in the LTspice simulation. The unknown parasitics also cause differences in the simulation and experimental results.

The difference in simulation and experimental $t_{OFF}$ in second and fourth quadrants is around $350~ns$ , which can be seen from Fig. 21(b) and Fig. 30(b). This is mainly because of the inaccurate LTspice model of IGBT and gate driver. The difference can be observed from the simulation waveform of $v_{GE,B1}$ in Fig. 18(b) and the experimental waveform of $v_{GE,B1}$ in Fig. 27(b). The fall of $v_{GE,B1}$ in simulation takes more than $400~ns$ whereas, the fall of $v_{GE,B1}$ in experiment takes around $200~ns$ .

D. Efficiency of SiC MOSFET and Si IGBT Based $2\times 1$ Matrix Converters

1) Load Voltage and Current Waveforms

Fig. 31(a) shows the experimental $250~W$ load voltage, $v_{L}$ , and load current, $i_{L}$ , of SiC MOSFET based $2\times 1$ matrix converter using 4-step commutation. The switching frequency $f_{s}=1~kHz$ . The switching waveforms are more clearly visible at $f_{s}=1~kHz$ than at higher switching frequencies. The fundamental frequency of the input supply and $i_{L}$ is $50~Hz$ . The peak $v_{L}=170~V$ , and the peak $i_{L}=10~A$ . Fig. 31(b) shows the experimental waveforms of $v_{L}$ and $i_{L}$ at $100~kHz$ switching frequency. The efficiency calculation uses the experimental data of $v_{L}$ , $i_{L}$ , input currents, and input voltages for $f_{s}=1-100~kHz$ . The data is captured with the help of digital oscilloscope in MS Excel sheets. Efficiency is calculated for $50~Hz$ fundamental frequency. Similarly, the efficiency calculation for SiC MOSFET based matrix converter using 2-step and Si IGBT based matrix converter using 2-step and 4-step, for $f_{s}=1-100~kHz$ , is done. The maximum switching frequency is limited to $100~kHz$ because of the maximum sampling rate of $200~kHz$ of the FPGA board’s inbuilt analog-digital converter (ADC). Since ADC samples the sensed $i_{L}$ for current commutation, the $200~kHz$ sampling rate for more than $100~kHz$ switching frequency will cause more erroneous switching sequences near the zero-crossing of $i_{L}$ .

FIGURE 31.

$250~W$ load voltage, $v_{L}$ , and load current, $i_{L}$ , of SiC MOSFET based $2\times 1$ matrix converter. The fundamental frequency of the input supply and $i_{L}$ is $50~Hz$ . (a) At $1~kHz$ switching frequency.(b) At $100~kHz$ switching frequency.

2) Efficiency Plots

Fig. 32 shows the comparison of experimental efficiencies. The efficiency trends in Fig. 32(a) are similar to those obtained from the simulation, except that the peak efficiency occurs at $10~kHz$ rather than $20~kHz$ . The efficiency decreases for all at higher switching frequencies. The efficiency of the Si IGBT based matrix converter using 2-step or 4-step commutation are lower than the SiC MOSFET based matrix converter using 4-step. This trend matches with the simulation trend. However, the efficiency of the Si IGBT based matrix converter using 2-step or 4-step is lower than the SiC MOSFET based matrix converter using 2-step at all switching frequencies. This trend does not match with the simulation trend. The possible reasons for the mismatch are:

• The experimental turn ON/OFF time of the Si IGBT based 4-quadrant switch is nearly double compared to the simulation (Fig. 21) in first and third quadrants. However, the comparison of Fig. 29 and Fig. 20 shows this does not occur in SiC MOSFET based 4-quadrant switch.

• The higher turn ON loss than expected due to the significant ringing in the Si IGBT based 4-quadrant switch current, $i_{4QS}$ , during turn ON. The ringing is visible in the experiment (Fig. 27(b)) but absent in the simulation (Fig. 18(b)). However, for SiC MOSFET based 4-quadrant switch, the $i_{4QS}$ ringing during turn ON is insignificant (Fig. 27(a)).

Fig. 32(b), at $100~kHz$ , the efficiency of the Si IGBT based matrix converter is drastically low (78.1%) compared to SiC MOSFET based matrix converter using 4-step (93.2%) and 2-step (88.3%).

FIGURE 32.

Comparison of experimental efficiency of SiC MOSFET and Si IGBT based $2\times 1$ matrix converter using 2-step and 4-step commutations. (a) Till $50~kHz$ switching frequency. (b) Till $100~kHz$ switching frequency.

E. Discussion

Table 6 compares SiC MOSFET and Si IGBT based 4-quadrant switches based on experimental results. The below points discuss comparing SiC MOSFET and Si IGBT based 4-quadrant switches.

• The ON state voltage drop of Si IGBT based 4-quadrant switch using 2-step commutation is $43.3-55.8\%$ lower than SiC MOSFET based 4-quadrant switch using 2-step commutation.

• The ON state voltage drop of SiC MOSFET based 4-quadrant switch using 4-step commutation is $100-20.5\%$ lower than Si IGBT based 4-quadrant switch using 2-step commutation in $0-15~A$ range.

• The ON state voltage drop of SiC MOSFET based 4-quadrant switch using 4-step commutation is $0-19.1\%$ higher than Si IGBT based 4-quadrant switch using 2-step commutation in $20-25~A$ range.

• The ON state voltage drop of SiC MOSFET based 4-quadrant switch using 4-step commutation is $82.3-40.4\%$ lower than SiC MOSFET based 4-quadrant switch using 2-step commutation.

• The turn ON/OFF times trends are similar for SiC MOSFET and Si IGBT based 4-quadrant switches.

• The turn ON time of Si IGBT based 4-quadrant switch is $240-78\%$ higher than SiC MOSFET based 4-quadrant switch in first and third quadrants.

• The turn ON time of Si IGBT based 4-quadrant switch is $103-41\%$ higher than SiC MOSFET based 4-quadrant switch in second and fourth quadrants.

• The turn OFF time of Si IGBT based 4-quadrant switch is $240-162\%$ higher than SiC MOSFET based 4-quadrant switch in first and third quadrants.

• The turn OFF time of Si IGBT based 4-quadrant switch is 20% higher than SiC MOSFET based 4-quadrant switch in second and fourth quadrants.

• The turn OFF time of Si IGBT based 4-quadrant switch is comparable in all quadrants.

• The turn ON/OFF times of SiC MOSFET based 4-quadrant switch is significantly lower. Hence, SiC MOSFET based $2\times 1$ matrix converter using 2-step commutation has the highest maximum switching frequency of $351~kHz$ , calculated from (49).

• The efficiency of SiC MOSFET based matrix converter using 2-step commutation is around $92-88.3\%$ for $f_{s} \le 50~kHz$ .

• Above $50~kHz$ , the efficiency of SiC MOSFET based matrix converter using 2-step commutation is significantly better than Si IGBT based matrix converter.

• Therefore, SiC MOSFET based matrix converter using 2-step commutation is more suited than Si IGBT based matrix converter for higher switching frequencies.

• The maximum switching frequency of Si IGBT based $2\times 1$ matrix converter using 2-step commutation is $304~kHz$ , calculated from (49).

• For $f_{s} \le 50~kHz$ , the efficiency of Si IGBT based $2\times 1$ matrix converter using 2-step commutation is $91.1-86.2\%$ , and suited up to $50~kHz$ .

• The maximum switching frequency of Si IGBT based $2\times 1$ matrix converter using 4-step commutation is $152~kHz$ , calculated from (48) and suited up to $50~kHz$ .

• The efficiency of Si IGBT based $2\times 1$ matrix converter using 4-step commutation is $91.1-86.2\%$ for $f_{s} \le 50~kHz$ , and also suited up to $50~kHz$ .

• The maximum switching frequency of SiC MOSFET based $2\times 1$ matrix converter using 4-step commutation is $187~kHz$ , calculated from (48).

• The efficiency of SiC MOSFET based $2\times 1$ matrix converter using 4-step commutation is $98-93.2\%$ and, is the highest among all.

TABLE 6 Experimental Result Comparison of SiC MOSFET and Si IGBT Based 4-Quadrant Switches Using Current Commutation

1) Practical Applications and Future Impacts

• SiC MOSFET based 4-quadrant switch with 4-step commutation must be preferred for applications like grid interface circuits and motor drive systems, as the switch count is large and efficiency becomes a major factor for the selection of device and commutation method. Converters like current source rectifier, dual active bridge (DAB), and single stage solid-state transformer (SST), current source inverter, and matrix converter come under these applications.

• SiC MOSFET based 4-quadrant switch with 2-step commutation must be preferred for applications like electric vehicle charger (Vienna rectifier and T-type rectifier) and electrical discharge machining, as size becomes a constraint. Since maximum switching frequency can be obtained using SiC MOSFET and 2-step commutation. Moreover, the switch count is small in these applications causing lesser impact on efficiency.

• Si IGBT must be preferred in applications where switching frequency is low and cost is the essential factor for design. Such applications can be grid interface circuits and motor drives.

2) Applicability to Other Devices and Converters

• The above findings are expected to be reasonable for any Si IGBT and SiC MOSFET with same physical structure (Planar-DMOSFET and Field-stop-trench-gate IGBT).

• The qualitative findings remain intact with some variation in quantitative findings for Si IGBT and SiC MOSFET with different physical structure and similar voltage-current ratings.

• The findings are expected to be reasonable and similar to Si IGBT for Si MOSFET (APT28M120L) with similar rating to Si IGBT. The Si MOSFET has similar input, reverse transfer, and output capacitances to Si IGBT. Efficiencies of Si MOSFET based $2\times 1$ matrix converter with 2-step and 4-step commutation will remain same. However, the efficiencies of Si MOSFET based matrix converter will be lower than Si IGBT based matrix converter due to high ON state resistance.

• The findings are expected to be reasonable and similar to SiC MOSFET for GaN FET (TP120H058WS) with similar ratings to SiC MOSFET. GaN FET has similar input, reverse transfer, and output capacitances to SiC MOSFET. The efficiency of the GaN FET matrix converter using 4-step will be higher than GaN FET matrix converter using 2-step because of the lower ON state voltage drop when GaN FET is gated during reverse conduction. The efficiency of the GaN FET based matrix converter will be higher than SiC MOSFET based matrix converter because the ON state resistance and reverse voltage drop of GaN FET are lower than SiC MOSFET.

• If the 4 quadrant switch is implemented on any other topology like $3\times 1$ matrix converter, $3\times 3$ matrix converter, cyclo-converter, AC-AC DAB converter, Vienna rectifier, T-type converter, etc., the conclusion must remain reasonable for 4-quadrant switch. However, the converters’ maximum switching frequency and efficiency may vary from converter to converter as maximum switching frequency and efficiency can also depend on the topology, modulation, etc.

3) Limitations and Unresolved Issues

• Effect of variation of 4-quadrant switch voltage on turn ON and turn OFF times, and eventually on maximum switching frequency is not determined in this study. 4-quadrant switch voltage variation have an impact on the $t_{fv}$ and $t_{rv}$ as seen from (8) and (10), which impacts the maximum switching frequency of the switch.

• Different modulation strategies also impact the efficiency of the converter, which is missing in the study. Proper modulation strategy can enhance the efficiency of the converter.

• Effect of variable commutation delay on maximum switching frequency are missing in this study. Variable delay can also reduce the harmonic content and enhance the efficiency.

Study on above parameters can be done in future work.

F. Overall Inferences

The overall inferences from the analysis in Section IV, power loss calculation in Section V, simulation results in Section VI, and experimental results in this section are:

1. The ON state voltage drop of SiC MOSFET based 4-quadrant switch using 4-step is less than SiC MOSFET based 4-quadrant switch using 2-step commutation. It is also less than Si IGBT based 4-quadrant switch using both 2-step and 4-step commutations (till $20~A$ ). However, the ON state voltage drop of Si IGBT based 4-quadrant switch using both 2-step and 4-step is less than SiC MOSFET based 4-quadrant switch using 2-step commutation.

2. The turn ON/OFF times trends are similar for SiC MOSFET and Si IGBT based 4-quadrant switches in all quadrants. However, the turn ON/OFF times of Si IGBT based 4-quadrant switches are up to 240% higher than SiC MOSFET based 4-quadrant switches.

3. The maximum switching frequency of SiC MOSFET based $2\times 1$ matrix converter using 2-step commutation is $351~kHz$ ; using 4-step commutation, it is $187~kHz$ . The maximum switching frequency of Si IGBT based $2\times 1$ matrix converter using 2-step commutation is $304~kHz$ ; using 4-step commutation, it is $152~kHz$ .

4. The efficiency of SiC MOSFET based $2\times 1$ matrix converter using 4-step commutation is found to be the best. Preferred applications are grid interface circuits and motor drive systems. SiC MOSFET based $2\times 1$ matrix converter using 2-step commutation has the second-best efficiency. Preferred applications are electrical vehicle chargers and electrical discharge machining.

5. Si IGBT based $2\times 1$ matrix converter using 2-step and 4-step commutations have the worst efficiencies beyond $50~kHz$ switching frequencies. But efficiencies are comparable to SiC MOSFET based $2\times 1$ matrix converter using 2-step commutation in $1-50~kHz$ range. However, Si IGBTs may be preferred for low switching frequency and low cost applications.

6. The longer delay time reduces the efficiency of SiC MOSFET based converter using 4-step only. However, the reduction is below 1%, as shown in Section VI-D. This inference is only valid if the maximum turn ON/OFF times of the SiC MOSFET/IGBT are not altered.

SECTION VIII. Conclusion

SiC MOSFET based 4-quadrant switches show significant advantages in many performance aspects and are expected to become a strong alternative to Si IGBT based 4-quadrant switches in various applications. Design of converters based on SiC MOSFET 4-quadrant switches suffer problems related to commutation, quadrant and commutation dependent transition times, and commutation dependent ON state voltage drops. The paper does detailed investigations on the problems through analysis, simulation, and experiment on developed prototypes. Investigation of several trends of SiC MOSFET and Si IGBT based 4-quadrant switches reveals several key findings, which are useful for the design of converters based on 4-quadrant switches.

The ON state voltage drop of SiC MOSFET based 4-quadrant switch using 4-step is less than SiC MOSFET based 4-quadrant switch using 2-step commutation. It is also less than Si IGBT based 4-quadrant switch using 2-step and 4-step commutations. However, the ON state voltage drop of Si IGBT based 4-quadrant switch using 2-step or 4-step is less than SiC MOSFET based 4-quadrant switch using 2-step. The turn ON/OFF times of Si IGBT based 4-quadrant switches are up to 240% higher than SiC MOSFET based 4-quadrant switches. The maximum switching frequency of the SiC MOSFET based $2\times 1$ matrix converter is higher than the Si IGBT based $2\times 1$ matrix converter. The maximum switching frequency of SiC MOSFET based $2\times 1$ matrix converter using 2-step commutation is higher than using 4-step commutation. The efficiency of SiC MOSFET based $2\times 1$ matrix converter using 4-step commutation is the best, and preferred applications are grid interface circuits and motor drive systems for to efficiency enhancements. SiC MOSFET based $2\times 1$ matrix converter using 2-step commutation has the second-best efficiency, and preferred applications are electrical vehicle chargers and electrical discharge machining due to compact size. Beyond $50~kHz$ , Si IGBT-based $2\times 1$ matrix converters have the lowest efficiency among the studied cases. However, efficiencies are comparable to SiC MOSFET based $2\times 1$ matrix converter using 2-step commutation in $1-50~kHz$ range. Si IGBTs may be preferred for low switching frequency and low cost applications. Future research should explore how variable commutation delay, switch voltage variation, and modulation strategies impact switching frequency and efficiency.