Modeling and Experimental Investigation of Electromagnetic Interference (EMI) for SiC-Based Motor Drive

Abstract

The motor drive has been widely adopted in modern power applications. With the emergency of the next generation wide bandgap semiconductor device, such as silicon carbide (SiC) MOSFET, performance of the motor drive can be improved in terms of efficiency, power density, and reliability. However, the fast switching transient and serious switching ringing of the SiC MOSFET can cause unwanted high-frequency (HF) electromagnetic interference (EMI), which may significantly reduce the reliability of the motor drive in many aspects. In order to comprehensively reveal the mechanism of the EMI previously used in motor drives using SiC MOSFET, this paper plans to analyze the influences of both HF impedance of the motor and switching characteristics of the SiC MOSFET. A simulation model for motor drives has been proposed, which contains the HF circuit model of the motor as well as a semi-behavioral analytical model of the SiC MOSFET. Since the model shows a good agreement with the experimentally measured results on spectra of drain-source voltage of the SiC MOSFET ($v_{ds}$), phase to ground voltage of the motor ($v_{phase}$), CM voltage ($v_{cm}$), phase current of the motor ($i_{dm}$), and CM current ($i_{cm}$), it can be adopted to quantitatively investigate the influence of the motor impedance on EMI through frequency-domain analysis. Additionally, the impacts of switching characteristics of SiC MOSFET on EMI are also well studied according to relative experiment results in terms of switching speed, switching frequency, and switching ringing. Based on the analysis above, the relationship between motor impedance, switching characteristics of the SiC MOSFET, and HF EMI can be figured out, which is able to provide much helpful assistance for application of the motor drive.

1. Introduction

The motor drive has been recognized as the heart component in modern power applications, such as electric aircraft, maritime, railway transportation as well as new energy vehicles. With the enhanced demands in efficiency and power density, a more effective power converter is required for the motor drive. However, most power converters adopt traditional silicon (Si) insulated gate bipolar transistors (IGBT) and metal oxide semiconductor field effect transistors (MOSFET), which can not guarantee larger efficiency and higher power density due to the limitation of the Si material [1]. In order to improve efficiency and power density of the motor drive, the next generation semiconductor device, such as silicon carbide (SiC) MOSFET, should be considered for applications [2].

Compared with Si IGBT and MOSFET, SiC MOSFET is mainly characterized by faster switching speed, lower switching loss, and higher available operation temperature, which contribute to its greater efficiency, higher power density, and improved reliability for motor drives [3,4,5,6]. However, the high-frequency (HF) electromagnetic interference (EMI) previously used in the motor drive becomes more serious because of the rapid switching speed and obvious switching ringing caused by SiC MOSFET. Moreover, the SiC MOSFET enables higher switching frequency, which also intensifies the HF EMI dramatically [7,8]. As a consequence, the HF EMI should be paid much more attention when applying motor drives based on SiC MOSFET.

The EMI previously used in motor drives can always be represented by common mode (CM) voltage and CM current. The CM voltage can be considered as the origination of the bearing voltage [9,10]. Once the bearing voltage reaches its threshold value, it can cause electric discharge (ED) current that may damage the motor [10,11]. The CM current can flow into other electric equipment through grounding lines, which may significantly reduce reliability of the whole system. Meanwhile, the HF components of the CM current can reach the bearing through HF parasitic effect, which may induce premature bearing failure. In addition, the impedance mismatches between cable and motor accompanied with rapid switching speed of the SiC MOSFET, serious voltage surge can also be observed on motor terminals, which may lead to severe electric insulation issue of the motor [12,13].

Recently, many researches have been focused on the prediction of bearing voltage, CM voltage, CM current, and overvoltage phenomenon with HF modeling of the motor. Equivalent circuit models for evaluating bearing voltage [10,11], CM voltage [14,15], CM current [14,15,16], and overvoltage on motor terminals [12,13,15] have been proposed. However, these works have not properly considered the impact of switching behavior of the semiconductor device, which is widely considered as the source of the EMI [17]. For instance, the switching transients of the semiconductor device are approximated as ideal step waveform in [13,15]. Meanwhile, the CM and differential mode (DM) impedances of the motor, especially at middle frequency range (100 kHz∼1 MHz), can not be well represented by these models [10,11,13,14,15,16], which is responsible for deviations between calculated and experimental measured results.

In [18], the authors indicated that the level of EMI can be effectively estimated through analyzing the spectrum of switching waveform of the semiconductor device. Based on the statement above, the works in [8,19] have investigated the relationship between switching characteristics of the SiC MOSFET and EMI with spectrum analysis. However, the influence of motor impedance has been neglected in [8,19], which is considered as propagation path of the EMI. A comprehensive modeling of the motor drive has been proposed in [20]. In this work, the HF impedance characteristics of the motor and switching behavior of the semiconductor device are modeled and simulated by SPICE for EMI prediction. However, the HF modeling of the motor is based on curve fitting method, which can not be used to reveal the mechanism of the EMI previously used in motor drives due to the lack of physical meanings. Additionally, the driving strategy of the motor, such as space vector modulation (SVM), can not be realized by SPICE. As a result, the simulation is implemented by switching one of the six semiconductor devices in the converter. Generally, there are few publications that have focused on analysis of both motor impedance and switching characteristics of the SiC MOSFET for EMI investigation in motor drive.

In this paper, we have comprehensively analyzed the EMI previously used in motor drives based on modeling and experimental investigation. Compared with other existing works, the main contributions of this paper can be summarized as:

• A simulation model of the motor drive is proposed, which contains an improved HF circuit model of the motor and simplified behavior model of the SiC MOSFET. Meanwhile, the simulation can be carried out by Simulink, which is able to easily realize the SVM driving strategy of the motor. The simulated results show a good agreement with the measured ones because the modeling of the motor impedance and switching behavior of the SiC MOSFET exhibit sufficient accuracy.
• Influence of motor impedance on EMI can be well demonstrated through frequency-domain analysis based on simulation results including the spectra of drain-source voltage of the SiC MOSFET ($v_{ds}$), phase to ground voltage of the motor ($v_{phase}$), CM voltage ($v_{cm}$), phase current of the motor ($i_{dm}$), and CM current ($i_{cm}$). Moreover, impacts of switching characteristics of the SiC MOSFET on EMI are also well investigated with relative experimental results in terms of switching speed, switching frequency, and switching ringing.

The rest of the paper is organized as follows. In Section 2, the characteristics of motor drives, including motor impedance and switching behavior of the SiC MOSFET, have been analyzed. Then, the modeling of the motor drive is elaborated in Section 3, which contains HF modeling of the motor and simplified modeling of the switching behavior of SiC MOSFET. Simulation and experiment results are presented and analyzed in Section 4. Influence of motor impedance on EMI are demonstrated through frequency-domain analysis with simulation in Section 5. Meanwhile, impacts of switching characteristics of the SiC MOSFET on EMI in motor drives are elaborated with relative experiment results in Section 6. Finally, the conclusions are summarized in Section 7.

2. Characteristics of the Motor Drive Based on SiC MOSFET

The scheme of a typical motor drive is shown in Figure 1. The power converter is constituted by three half-bridges, and each half-bridge contains two SiC MOSFETs. The cables are replaced by copper wires ($L_c$), which connect between motor terminals and output nodes of the converter. Different from the cables, the impedance characteristic of the wire can be considered as inductive in a wide frequency range. The the CM propagation path is formed by connecting motor frame to the neutral point (o) with a grounding line ($L_g$). Meanwhile, the CM coupling path between MOSFET and heat sink can be removed by using the separated heat sinks [21]. $L_{loop}$ is the lumped stray inductance in the power circuit of the converter, which mainly contributes to the HF ringings on $v_{ds}$ during switching transients. Consequently, based on the above descriptions, the CM equivalent circuit of the motor drive can be obtained (see Figure 2).

According to Figure 2, the CM current can be expressed as:

$$i_{cm}=\frac{v_0}{Z_C+Z_{cm}}$$

(1)

where, $Z_c$ means the CM impedance of the dc-link capacitors ($C=C_1+C_2$), and $Z_{cm}$ represents the CM impedance of the motor plus connection wire and grounding line. The $v_0$ is the source of CM EMI, and can be written as:

$$v_0=\frac{1}{3}\left(v_{uo}+v_{vo}+v_{wo}\right)$$

(2)

in which, $v_{uo}$, $v_{vo}$, $v_{wo}$ represent converter output to ground voltage, which can be viewed as drain-source voltage of the SiC MOSFET because $v_{uo}=v_{ds2}-v_{dc}/\phantom{v_{dc}2}2$. The $v_{ds2}$ means the drain-source voltage of the low-side SiC MOSFET of the power converter, such as $M_2$, illustrated in Figure 1.

Based on (1) and (2), it can be observed that the HF impedance of the motor plus connection wire and grounding line provides propagation path, which impacts the CM current flows through the system. The switching behavior of the SiC MOSFET is the source of EMI, which determines $v_{phase}$ and $v_{cm}$. In order to comprehensively reveal the mechanism of the EMI in motor drives, influences of motor impedance and switching performance of the SiC MOSFET should be considered together.

2.1. HF Impedance of the Motor

The HF impedance of the motor can be obtained with impedance analyzer. In this study, WK 6500B is adopted to measure the impedance of the motor from 100 Hz to 10 MHz. The measurement of CM and DM impedances of the motor is given in Figure 3. The CM impedance is measured between motor terminals connected together and motor frame, and the DM impedance is measured between the terminal of one phase and the terminals of the other two phases connected together [22]. And the measurement results of CM and DM impedances are shown in Figure 4. Figure 4a illustrates the CM impedance of the motor with and without connection wire and grounding line. With the influence of the wires and parasitic capacitors of the motor ($C_g$ presented in Figure 1), the CM resonance is formed around 4 MHz. Similarly, the DM impedance of the motor ($Z_{dm}$) with and without connection wire and grounding line is shown in Figure 4b. The DM resonance which appears at approximately 8 MHz is also attributed to the equivalent inductance of the wires ($L_s$ and $L_g$ shown in Figure 1) and $C_g$. Both CM and DM resonances deserve much more consideration because they have played significant roles in determining $v_{phase}$ and $v_{cm}$, which closely relate to the level of EMI.

2.2. Switching Behavior of the SiC MOSFET

Generally, the analytical switching waveform of the drain-source voltage of the SiC MOSFET can be approximated as asymmetric trapezoid wave plus decayed sine wave (see Figure 5). With the Fourier Transformation, the spectrum of $v_{ds}$ can be derived in (3)∼(5) [23].

$$\begin{array}{c}{a}_n=\underset{Asymmetrical-trapezoidal-waveform}{\underbrace{\frac{V_{dc}T}{4n^2{\pi }^2}\left(\begin{array}{c}\frac{1}{t_f}\left(1-e^{-jn\frac{2\pi }{T}{t}_f}\right)e^{-jn\frac{2\pi }{T}\left(t_t+t_d\right)}\hfill \\ -\frac{1}{t_r}\left(1-e^{-jn\frac{2\pi }{T}{t}_r}\right)\hfill \end{array}\right)}}\hfill \\ +\underset{Turn-off-oscillation}{\underbrace{\frac{K_1{\omega }_1}{T\left(C_1^2+{{\omega }_1}^2\right)}{e}^{-jn\frac{2\pi }{T}{t}_r}\left(\begin{array}{c}1-cos\left({\omega }_1{t}_d\right)e^{-C_1{t}_d}\hfill \\ -\frac{C_{1}sin\left({\omega }_1{t}_d\right)}{{\omega }_1}{e}^{-C_1{t}_d}\hfill \end{array}\right)}}\hfill \\ -\underset{Turn-on-oscillation}{\underbrace{\frac{K_2{\omega }_2}{T\left(C_2^2+{{\omega }_2}^2\right)}{e}^{-jn\frac{2\pi }{T}{t}_0}\left(\begin{array}{c}1-cos\left({\omega }_2\left(T-t_0\right)\right)e^{-C_2\left(T-t_0\right)}\hfill \\ -\frac{C_{2}sin\left({\omega }_2\left(T-t_0\right)\right)}{{\omega }_2}{e}^{-C_2\left(T-t_0\right)}\hfill \end{array}\right)}}\hfill \end{array}$$

(3)

$$\left\{\begin{array}{c}{C}_1={\alpha }_1+jn\frac{2\pi }{T}\hfill \\ C_2={\alpha }_2+jn\frac{2\pi }{T}\hfill \\ t_0=t_r+t_f+t_d\hfill \end{array}\right..$$

(4)

$$S\left(n\right)=\left|2a_n\delta (f-n{f}_0)\right|,(f_0=1/\phantom{1T}T).$$

(5)

According to (3)∼(5), it can be figured out that the voltage commutation transient (including duration of $t_r$ and $t_f$) interprets attenuation rate of the spectrum [8], and the switching ringings are responsible for the spikes at HF range (tens of mega hearts) [23]. Additionally, the switching frequency is closely related to the amplitude of the spectrum, and can be considered as another critical factor that significantly impacts the EMI in motor drives.

3. Modeling of the SiC-Based Motor Drive

3.1. HF Modeling of the Motor

The impedance characteristics of the motor can be depicted through HF modeling. In this case, based on impedance curves and wingding configurations of the motor, an equivalent circuit (see Figure 6) is proposed to illustrate the impedance characteristics of the motor.

According to Figure 6, the winding of the motor is mainly composed by three parts. The part I winding is mainly responsible for describing CM impedance at the whole frequency range (100 Hz∼10 MHz), while it also impacts DM impedance in the middle frequency range (0.01∼1 MHz). The part II winding mainly determines the DM impedance at low frequency range (100 Hz∼10 kHz), and the part III winding impacts the DM impedance from 10 kHz∼1 MHz. The series $L_{j1i}$-$R_{j1i}$-$C_{j1i}$ ($i=1,2$) and $L_{j2}$-$R_{j2}$-$C_{j2}$ branches reflect interturn effects of the Part I and II windings, respectively. The series $L_T$-$R_T$-$C_T$ branch represents the leakage effect occurs on first few turns of the part I winding, which largely impacts both CM and DM impedance at the middle frequency range. The $C_{gi}$ (i = 1, 2, 3, 4) are parasitic capacitances between winding and frame of the motor, and the $R_g$ can be considered as the terminal resistance of the motor. Additionally, the EMF block reflects the generated electromotive force when motor is operating.

The values of the electric parameters described above can be determined (see

Table 1. Values of electric parameters of the model.

Parameter	Value	Parameter	Value	Parameter	Value
$C_{g1}$	0.25 nF	$R_{22}$	189 $\mathsf{\Omega }$	$L_{11}$	9 mH
$C_{g2}$	0.98 nF	$R_{23}$	350 $\mathsf{\Omega }$	$L_{21}$	9.6 mH
$C_{g3}$	30 pF	$R_{24}$	630 $\mathsf{\Omega }$	$L_{22}$	5.3 mH
$C_{g4}$	30 pF	$R_{25}$	1.12 k$\mathsf{\Omega }$	$L_{23}$	4.9 mH
$C_{j11}$	14.4 pF	$R_{31}$	100 k$\mathsf{\Omega }$	$L_{24}$	4.2 mH
$C_{j12}$	37.4 pF	$R_g$	4.2 $\mathsf{\Omega }$	$L_{25}$	4.0 mH
$C_{j2}$	1.86 nF	$R_{j11}$	650 $\mathsf{\Omega }$	$L_{j11}$	0.21 mH
$C_T$	0.19 nF	$R_{j12}$	260 $\mathsf{\Omega }$	$L_{j12}$	17.4 $\mathsf{\mu }$H
$R_{11}$	5.3 k$\mathsf{\Omega }$	$R_{j2}$	9.47 k$\mathsf{\Omega }$	$L_{j2}$	6.9 mH
$R_{21}$	120 $\mathsf{\Omega }$	$R_T$	3.23 k$\mathsf{\Omega }$	$L_T$	1.9 mH

) based on the method elaborated in our previous works [22]. Figure 7 compares the calculated and measured impedance of the motor. The calculated CM and DM impedances of the motor are in nice accordance with the ones measured by impedance analyzer. It is obvious that the proposed HF model can describe impedance of the motor with sufficient accuracy, especially in the middle frequency range (100 kHz∼1 MHz), compared with the ones in [10,11,13,14,15,16].

3.2. Simplified Modeling of the SiC MOSFET

According to operation mechanism of the SiC MOSFET, the voltage commutation is mainly determined by gate resistance, drain and source inductances, and junction capacitances ($C_{gs}$, $C_{gd}$, and $C_{ds}$) [24,25]. The switching ringing can be attributed to the resonance between output capacitance ($C_{oss}$ = $C_{gd}$ + $C_{ds}$) and summation of stray inductance in the circuit [23]. Analytical modeling presented in [23,24,25] can accurately illustrate the switching behavior of the SiC MOSFET. In general, these models are suitable for several micro-seconds level system simulation.

Since the operation frequency of motor is no more than several tens hertz, the simulation time for motor drives should be no less than several hundreds milliseconds, which makes the aforementioned analytical models time consuming, and not suitable for system simulation of the motor drive. As a result, simplified modeling should be proposed to improve the calculation efficiency.

The voltage rise and fall stages during switching transient are linearized for simplification in this case. Therefore, the voltage commutation can be realized by a controlled voltage source. Meanwhile, the second order $L-R-C$ circuit is adopted to represent the switching ringing on $v_{ds}$. The simplified behavior model of the SiC MOSFET is shown in Figure 8. Since most of physical mechanisms during switching transient are ignored, the calculation speed of the model can be enhanced significantly. However, the accuracy of the model will be reduced. Obviously, the trade-off between calculation speed and accuracy of the model should be well balanced.

Figure 9 illustrates the comparisons between calculated and measured waveforms of $v_{ds}$ during switching transient of the SiC MOSFET. According to operation principles of the SiC MOSFET, the slew rate of $v_{ds}$ is determined by $L_p·\frac{d{i}_d}{dt}$ during current commutation, and the charging and discharging rate of the gate-drain capacitance $C_{gd}$ is attributed to slew rate of $v_{ds}$ during voltage commutation. Since the $d{v}_{ds}$/$dt$ is approximated as a constant value, the voltage rise and fall stages can not be accurately illustrated in the modeling. However, based on statement in [8], the spectrum envelop is mainly determined by rise and fall time ($t_r$ and $t_f$) of the $v_{ds}$, which indicates that the model can correctly reflect the spectrum of $v_{ds}$ because the calculated $t_r$ and $t_f$ are the same with the measured ones.

4. Simulation and Experiment Results

The simulation model of the motor drive is realized by Simulink (see Figure 10), which contains simplified model of switching action for SiC MOSFET, and HF model of the motor, connection wire, ground line. Furthermore, the SVM algorithm is also implemented with Simulink. The waveforms of $v_{ds}$, $v_{phase}$, $v_{cm}$, $i_{dm}$, and $i_{cm}$ are obtained in the simulation.

A three-phase permanent magnet synchronous motor (see Figure 11a) is selected in this study. The detailed parameters of the motor are listed in

Table 2. Parameters of the motor in the test.

Parameters	Values
Rated Power	3 kW
Rated Voltage	380 V
Maximum current	6.2 A
Pole Pairs	2
Rotor Configuration	Surface Mounted
Winding Connection	Star

. The main circuit board of the motor drive is shown in Figure 11b, which contains three phase-legs. Each phase-leg is constituted by two SiC MOSFETs (C2M0080120D from Wolfspeed). Six isolated gate drivers, designed with ACPL-W346 from Avago, are used to drive the SiC MOSFETs, and three groups of dc-link capacitors are adopted to limit dc-bus voltage variation. The output nodes of the inverter (u, v, and w) are connected to the motor terminals (a, b, and c) with copper wires, and the motor frame is connected to the neutral point o with grounding line. Six separated heat-sinks are attached on the top of the MOSFETs. HF parasitic effect between MOSFET and heat-sink can be neglected once the heat sink is floating in the system. STM32F103 is adopted as the core of the control unit, which is responsible for driving the motor with SVM algorithm. The dc power supply is 200 V in the experiment. The switching frequency of the power inverter is set as 80 kHz, and the motor is operating at 600 rpm. The voltage and current waveforms of the motor drive are obtained with Lecroy’s Wave-Runner 8404-M. Three high-voltage and high-bandwidth differential probes HVD3106 (1.5 kV, 120 MHz) are utilized to measure the phase to ground voltage including $v_{ao}$, $v_{bo}$, and $v_{co}$. The CM and line current of the motor are measured with a high-bandwidth current probe TCP312A (30 A, 100 MHz).

4.1. Calculated and Measured Spectra of $v_{ds}$, $v_{phase}$, and $v_{cm}$

Figure 12a illustrates the calculated and measured spectra of $v_{ds}$. Since the calculated waveform of $v_{ds}$ is in nice accordance with the measured ones (see Figure 5), the calculated spectra of $v_{ds}$ can also fit well with the measured ones.

Figure 12b shows the comparison between calculated and measured spectra of $v_{phase}$. It can be observed that the measured spectrum of $v_{phase}$ is less than that of the calculated ones from 5 to 10 MHz. This is mainly due to the ignorance of contact impedances of the connectors between inverter output nodes and copper wires in the model. Such contact impedance can induce some voltage drops at this frequency range (5∼10 MHz) in the measurement.

Figure 12c depicts the calculated and measured spectra of $v_{cm}$. The calculated spectrum of $v_{cm}$ is in nice accordance with the measured ones below 5 MHz. However, the calculated and measured results cannot fit well with each other from 5 to 30 MHz. Unlike the measured spectrum of $v_{cm}$, the spike cannot be observed on the calculated result around 8 MHz.

We should notice that $v_{cm}$ is synthesized by $v_{phase}$, and can be expressed as the following equation.

$$v_{cm}=\frac{1}{3}\left(v_{ao}+v_{bo}+v_{co}\right).$$

(6)

Therefore, influence of the contact impedance on $v_{phase}$ ($v_{ao}$, $v_{bo}$, and $v_{co}$) mentioned above is responsible for such deviations. It should also be found that unlike simulation, propagation delay indeed exists in each voltage probe, which can cause asymmetric phase angle between the measured $v_{ao}$, $v_{bo}$, and $v_{co}$ during experiment. As a consequence, the voltage components around 8 MHz can not be canceled completely during synthesizing.

4.2. Calculated and Measured Spectra of $i_{dm}$ and $i_{cm}$

Figure 13 shows the calculated and measured spectra of $i_{dm}$ and $i_{cm}$. The calculated $i_{dm}$ and $i_{cm}$ are fitted well with the measured ones, and the spectra peaks around 4 and 8 MHz can also be well reflected by the model. Therefore, it can be confirmed that the model can effectively predict the line current and CM current in motor drives.

In addition, it can be observed that $v_{phase}$, $v_{cm}$, and impedance of the motor are responsible for $i_{dm}$ and $i_{cm}$ according to (7). In other words, the accuracy of the calculated $v_{phase}$ and $v_{cm}$ can also be verified due to the nice accordance in the calculated and measured amplitude of $i_{dm}$, $i_{cm}$ and motor impedance (including $Z_{dm}$ and $Z_{cm}$).

$$\left\{\begin{array}{c}{i}_{dm}=v_{phase}/\phantom{v_{phase}{Z}_{dm}}{Z}_{dm}\hfill \\ i_{cm}=v_{cm}/\phantom{v_{cm}{Z}_{cm}}{Z}_{cm}\hfill \end{array}\right..$$

(7)

5. Impacts of the Impedance Characteristics on EMI in Motor Drive

Since the effectiveness of the proposed model has been verified, we plan to analysis the relations between $v_{ds}$, $v_{phase}$, $v_{cm}$, $i_{dm}$, $i_{cm}$ as well as motor impedance to demonstrate impacts of impedance characteristics on EMI in motor drives with the model in this section.

5.1. Comparison between $v_{ds}$ and $v_{phase}$

In order to elaborate the relationship between $v_{ds}$ and $v_{phase}$, the following assumptions should be made at first.

• $M_1$ is turning on, $M_2$ is turning off, $M_3$ and $M_5$ are turned off, $M_4$ and $M_6$ are turned on (see Figure 1).
• The voltage drops on SiC MOSFETs and its body diodes are neglected in this condition.

Therefore, the DM propagation path of the HF components can be plotted (see Figure 14). The motor winding can be considered as open circuit in this case because the HF components (above 1 MHz) can not penetrate the winding deeply [26,27]. Then, the DM equivalent circuit of the motor drive can be obtained accordingly (see Figure 15).

Three $L-R-C$ resonance loops ($L_1$, $L_2$, and $L_3$) can be observed in Figure 15, which mainly contribute to resonances shown in Figure 16. It can be observed that the LF resonances (less than 10 MHz) attribute to interactions between copper wire ($L_c$), grounding line ($L_g$), and parasitic capacitance of the motor ($C_{g1}$), and the HF resonance (around 45 MHz) owes to stray inductance in power circuit ($L_{loop}$) and output capacitance of the SiC MOSFET ($C_{oss}$).

Figure 17 illustrates the calculated time-domain waveforms and spectra of $v_{ds}$ and $v_{phase}$. It is obvious that the additional ringings and spikes on $v_{phase}$ are attributed to LF resonances described above. It can be also observed that the increased impedances of $L_c$ and $L_g$ cause non-negligible voltage drops, which contribute to the slower slew rate and reduced amplitude in time- and frequency-domain waveforms of $v_{phase}$ at a higher frequency range (above 10 MHz).

5.2. Comparison between $v_{ds}$ and $v_{cm}$

In order to elaborate the relationship between $v_{ds}$ and $v_{cm}$, the following assumptions should be made initially.

• $M_1$ is turning off, $M_2$ is turning on, $M_3$ and $M_5$ are turned off, $M_4$ and $M_6$ are turned on (see Figure 1).
• The voltage drops on SiC MOSFETs and its body diodes are neglected in this condition.

Therefore, the CM propagation path of the HF components can be plotted (see Figure 18). Similarly, the CM equivalent circuit of the motor drive can be obtained accordingly (see Figure 19).

Two $L-R-C$ resonance loops ($L_1$ and $L_2$) can be observed in Figure 19, which lead to resonances shown in Figure 20. It can be observed that the LF resonance (around 4 MHz) owes to impacts of copper wire ($L_c$), grounding line ($L_g$), and parasitic capacitance of the motor ($C_{g1}$), and the HF ones (around 45 MHz) is attributed to stray inductance in power circuit ($L_{loop}$) and output capacitance of the SiC MOSFET ($C_{oss}$).

Figure 21 compares the calculated spectra of $v_{ds}$ and $v_{cm}$. The added peak component on spectrum of $v_{cm}$ can be attributed to the resonance around 4 MHz. From 5 to 10 MHz, the spectrum of $v_{cm}$ drops because harmonics in this frequency range can be canceled during synthesizing process described in (6). The amplitude of $v_{cm}$ spectrum is also less than that of $v_{ds}$ at higher frequency range (above 10 MHz) due to the voltage drops between inverter output nodes and motor terminals.

5.3. Comparison between $v_{phase}$ and $v_{cm}$

Figure 22 depicts the calculated waveforms of $v_{phase}$ and $v_{cm}$ in the time- and frequency-domain. It can be clearly observed that the ringing and spike around 8 MHz on $v_{cm}$ have been removed. According Figure 16 and Figure 20, only two resonances can be observed on frequency-domain characteristics of the CM circuit because the $L_3$ loop previously used in the DM circuit is bypassed during CM analysis. It can be also considered that the 8 MHz ringing on $v_{cm}$ can be canceled during synthesizing process depicted in (6).

5.4. Comparison between $i_{dm}$ and $i_{cm}$

Figure 23 shows the calculated spectra of $i_{dm}$ and $i_{cm}$. At lower frequency range (100 kHz∼5 MHz), CM impedance of the motor is far less than that of DM impedance (see Figure 24). Since the spectrum amplitude of $v_{cm}$ is nearly the same with that of $v_{phase}$ (see Figure 22b), the spectrum amplitude of $i_{cm}$ is larger than that of $i_{dm}$ in this frequency range. The peak component of $v_{cm}$ (≃4 MHz) and lower CM impedance contribute to the spectrum spike of $i_{cm}$ (≃4 MHz). The current spike on spectrum of $i_{dm}$ is much lower due to the larger DM impedance. According to Figure 24, $Z_{dm}$ is almost 5–6 times $Z_{cm}$ from 100 to 5 MHz.

At higher frequency range (above 5 MHz), the spectrum of $v_{cm}$ drops dramatically, and the deviation between spectrum amplitude of $v_{cm}$ and $v_{phase}$ is about 10 dBuV (see Figure 22b). Accordingly, the spectrum amplitude of $i_{cm}$ attenuates faster. The peak component of $i_{dm}$ (≃ 8 MHz) can be clearly observed due to the spectrum spike on $v_{phase}$. Although $Z_{cm}$ is still lower than $Z_{dm}$, there is no spectrum spike on $i_{cm}$ because spectrum amplitude of $v_{cm}$ around 8 MHz is much lower than that of $v_{phase}$.

5.5. Influence of the Motor Impedance on EMI

Influence of the motor impedance on EMI has been summarized in Figure 25. The switching behavior of the SiC MOSFET is considered as the source of EMI. With the resonances between copper wires, grounding line and parasitic capacitors, the HF harmonics of $v_{ds}$ have been changed, which contributes to the formation of $v_{phase}$ and $v_{cm}$. Then, with the influence of motor impedance, $i_{phase}$ and $i_{cm}$ can be determined accordingly. Thus, it can be confirmed that the resonances caused by copper wires, grounding line and parasitic capacitors as well as motor impedance significantly impact the level of EMI below 10 MHz. It is obvious that the LF (less than 10 MHz) EMI is expected to be reduced with an added filter, which can modify impedance characteristics of the resonances between $L_c$, $L_g$ and $C_g$. In some cases, integrated motor drives have been adopted to minimize the level of EMI, which can improve impedance of the motor drive around resonance frequency [3].

6. Impact of the Switching Characteristics of the SiC MOSFET on EMI in Motor Drive

In this section, $v_{cm}$ and $i_{cm}$ are selected as investigation objective to analyze impact of switching characteristics of the SiC MOSFET, including switching speed, switching frequency ($f_s$), and switching ringing, on EMI in motor drives. Relative experiment results are given in Figure 26 and Figure 27.

6.1. Impact of Switching Speed

Variation of parasitic capacitances and inductances can impact switching characteristics of the SiC MOSFET significantly [24]. However, these parasitic parameters must be maintained in small values to guarantee sufficient reliability of the SiC MOSFETs in practical applications. Therefore, regulating the gate resistor ($R_{g\left(ex\right)}$) can be considered as an effective method to flexibly change the switching characteristics of the SiC MOSFET. Figure 26a compares the spectra of $v_{ds}$ when $R_{g\left(ex\right)}$ equals to 10 and 47 $\mathsf{\Omega }$. In this study, the motor speed is 600 rpm, power supply voltage $v_{dc}$ = 200 V, switching frequency $f_s$ = 80 kHz, and gate resistance $R_{g\left(ex\right)}$ = 10 and 47 $\mathsf{\Omega }$. The amplitude at HF range (above 20 MHz) is reduced with the increased $R_g$. Additionally, the spectrum spike around 45 MHz is also attenuated once $R_{g\left(ex\right)}$ is selected as 47 $\mathsf{\Omega }$ due to the enlarged damping ratio of the second $L-R-C$ circuit. As a result, the spectrum amplitude of $v_{phase}$ become lower at the frequency range above 20 MHz, and the HF spectrum spikes on $v_{cm}$ around 45 MHz is also reduced when $R_{g\left(ex\right)}$ equals to 47 $\mathsf{\Omega }$ (see Figure 27b). But the $i_{cm}$ is nearly not affected by the variation of the $R_{g\left(ex\right)}$.

The spectrum envelop of the drain-source voltage of the SiC MOSFET ($v_{ds}$) mentioned in [8] is shown in Figure 28. Obviously, the spectrum envelop of the $v_{ds}$ is determined by corner frequencies ($f_{c1}$, $f_{c2}$, and $f_{c3}$), which depends largely on switching characteristics of the SiC MOSFET. Relationships between switching characteristics of the MOSFET and corner frequencies of the spectrum envelop can be expressed as [8]:

$$\left\{\begin{array}{c}{f}_{c1}=\frac{1}{\pi min(t_r,t_f)}\hfill \\ f_{c2}=\frac{1}{\pi max(t_r,t_f)}\hfill \\ f_{c3}=\frac{2f_s}{\left|e^{-j\pi \left(2t_d+t_r-t_f\right)/\phantom{j\pi \left(2t_d+t_r-t_f\right)T_s}{T}_s}-1\right|}\hfill \end{array}\right.$$

(8)

in which, $t_r$, $t_f$, $t_d$ are rise-time, fall-time and off-time of the SiC MOSFET. $f_s$ is the switching frequency of the SiC MOSFET, and $T_s$=$1/f_s$.

We should admit that the switching response speed can be reduced with the increased $R_{g\left(ex\right)}$ as well as the corner frequencies ($f_{c1}$ and $f_{c2}$), but the values of $f_{c1}$ and $f_{c2}$ are still above 10 MHz when $R_g$ increased to 47 $\mathsf{\Omega }$. As a result, the LF spectra of $v_{cm}$ and $i_{cm}$ are nearly not affected by the increase of $R_{g\left(ex\right)}$ in this case. With continuous increase of the $R_{g\left(ex\right)}$, the $f_{c1}$ and $f_{c2}$ will decrease below 10 MHz, and the amplitude of $v_{cm}$ and $i_{cm}$ spectra at the lower frequency range (below 10 MHz) would be weaken. However, the switching loss will be increased dramatically, which may adversely affect efficiency of the motor drive. This view point has been emphasized in [28]. Moreover, slower response speed causes larger preset dead-time zone, which may largely reduce the accuracy of control algorithm.

Consequently, to regulate the gate resistor in a reasonable range can alleviate the HF EMI (above 20 MHz) with slightly increased switching loss, and ensure the accuracy of control algorithm. But for LF EMI (below 10 MHz) mitigation, this method seems less effective.

6.2. Impact of Switching Frequency

Switching frequency of the SiC MOSFET can impact the spectrum of $v_{ds}$ in the whole frequency range. According to (3), the lower switching frequency means the reduced spectrum amplitude of $v_{ds}$. This view point has also been confirmed in [8]. In this study, the motor speed is 600 rpm, power supply voltage $v_{dc}$ = 200 V, gate resistance $R_{g\left(ex\right)}$ = 10 $\mathsf{\Omega }$, and switching frequency $f_s$ = 20 and 80 kHz.

Figure 26b compares the spectra of $v_{ds}$ with different switching frequencies ($f_s$ = 20 and 80 kHz). It can be observed that the spectrum amplitude is largely reduced with the lower switching frequency. As a result, the spectra amplitude of $v_{cm}$ and $i_{cm}$ are reduced remarkably when $f_s$ is set as 20 kHz (see Figure 27b). According to Figure 28 and (8), it can be clearly figured out that corner frequency ($f_{c3}$) will be reduced with lower switching frequency as well as spectrum envelop. The average deviations between thees two cases are more than 10 dBuV. Obviously, the EMI previously used in motor drives can be effectively suppressed with lower switching frequency. However, lower switching frequency can not ensure higher power density, and also reduces controllability as well as robustness of the motor drive. As a result, to make the trade-off between EMI, power density, controllability, and robustness of the motor drive, optimized switching frequency of the SiC MOSFET is recommended.

6.3. Impact of Switching Ringing

Adding RC snubber can effectively suppress the switching ringing on $v_{ds}$. Therefore, the spikes on spectrum of $v_{ds}$ at a higher frequency range (above 30 MHz in this case) would be mitigated based on (3). In this study, the motor speed is 600 rpm, power supply voltage $v_{dc}$ = 200 V, gate resistance $R_{g\left(ex\right)}$ = 10 $\mathsf{\Omega }$, switching frequency $f_s$ = 80 kHz, snubber capacitor $C_s$ = 10 nF, and snubber resistor $R_s$ = 10 $\mathsf{\Omega }$.

Figure 26c compares the spectrum of $v_{ds}$ with and without RC snubber. It is obvious that the added RC snubber can effectively mitigate the HF switching ringing, and alleviate the amplitude of the spectrum at HF range (above 30 MHz). As a result, the spectrum peak around 45 MHz on $v_{cm}$ is disappeared with the added RC snubber (see Figure 27c).

It should be noticed that the RC snubber is designed to suppress the HF ringing caused by resonance between $L_{loop}$ and $C_{oss}$, it has limited effect on LF ringing suppression caused by resonance between $L_c$, $L_g$, and $C_{g1}$. The RC snubber can not change the switching speed of the SiC MOSFET [23], as a result, the corner frequencies ($f_{c1}$ and $f_{c2}$) of the spectrum envelop are also unchanged with the added RC snubber. Therefore, the amplitude of $v_{cm}$ spectrum drops dramatically above 30 MHz with the added RC snubbers, while the amplitude of $v_{cm}$ and $i_{cm}$ spectra below 20 MHz is nearly not affected (see Figure 27c). Apparently, the RC snubbers are very helpful to attenuate EMI at HF range.

7. Conclusions

This paper has investigated EMI in SiC-based motor drives based on modeling and experiment. To quantitatively analyze mechanism of the EMI in motor drive, a simulation model is proposed with sufficient consideration of switching action of the SiC MOSFET and motor impedance, which can be recognized as the key factors on EMI. The effectiveness of the model has been verified through comparisons between model-calculated and experiment-measured results. Then, based on the model, the influence of the motor impedance on EMI has been well investigated with frequency-domain analysis of $v_{ds}$, $v_{phase}$, $v_{cm}$, $i_{dm}$, $i_{cm}$. Additionally, impacts of the switching characteristics of SiC MOSFET on EMI have also been discussed in detail with relative experiment results. It can be figured out that:

• The switching behavior of the SiC MOSFET is considered as the source of EMI. With the impacts of the resonances between copper wires, grounding line and parasitic capacitors, the HF harmonics of $v_{ds}$ are changed, which leads to $v_{phase}$ and $v_{cm}$. Then, with the influence of motor impedance, $i_{cm}$ and $i_{dm}$ can be determined accordingly. As a result, it can be confirmed that the resonances caused by copper wires, grounding line and parasitic capacitors, and motor impedance largely impact the level of EMI below 10 MHz in the motor drive.
• To reduce the spectra spikes in the frequency range above 20 MHz, changing the switching characteristics of the SiC MOSFET is considered as an effective method. With properly selected $R_g$ as well as RC snubber, the HF spectrum peak can be mitigated dramatically. However, in order to reduce the spectra spikes in the frequency range form 1 to 10 MHz, the method described above seems ineffectiveness. The LF (1 to 10 MHz) do not change with the variation of the switching speed and ringing. The spectrum amplitude can be suppressed with the reduced switching frequency at the expense of power density, controllability, and robustness of the motor drive. Thus, in this situation, properly designed EMI filter should be considered to change the CM and DM impedances characteristics around the resonance frequencies (4 and 8 MHz), which can effectively mitigate the spectrum peaks in the LF ranges.

The summaries described above are expected to give much valuable guidance to cope with EMI issues in SiC-based motor drives.