Volume Evaluation of a PWM Inverter with
Wide Band-Gap Devices for Motor Drive System
Jun-ichi Itoh

Takahiro Araki

Dept. of Electrical, Electronics and Information Engineering
Nagaoka University of Technology
Nagaoka, Niigata, Japan
itoh@vos.nagaokaut.ac.jp

Dept. of Electrical, Electronics and Information Engineering
Nagaoka University of Technology
Nagaoka, Niigata, Japanarakit@stn.nagaokaut.ac.jp

Abstract—This paper investigates a PWM inverter for an
adjustable speed drive using wide band-gap devices. First, therelationship between the carrier frequency of the PWM inverter
and the volume of an EMC filter is clarified by simulation,
besides the relationship between the carrier frequency and thevolume of a cooling system. As a result, the total volume of theinverter system that contains an EMC filter and a cooling system
will be reduced by 81.6% at the carrier frequency of 300 kHz. In
addition, the conduction noise is measured from a prototype of
the PWM inverter that is constructed by GaN-FET. Furthermore,
the total volume of EMC filter for GaN-FET inverter system isreduced by 70% with a 300-kHz carrier frequency compared to a
10-kHz carrier frequency.

considered for minimizing the volume of the EMC filter undera high frequency switching operation.

Keywords—Wide Band-Gap Devices; PWM inverter; HighFrequency switching; EMC filter

I.

INTRODUCTION

Recently, attentions are focused on miniaturization of
PWM inverters for adjustable speed drive systems such asindustrial motor drive and electric vehicle. PWM inverter cancontrol the output voltage and output frequency by using
switching devices. However, the noise is occurred at theswitching because the voltage and current are change quickly.
The noise may cause a false operation of other control system.
Hence, it is limited by some regulations such as CISPR(Special international committee on radio interference). To
suppress the noise which is emitted from the inverter, the EMC
filter that is constructed by passive components such as
inductor and capacitor is added to the input and output of
inverter. In addition, the PWM inverter is become smaller
depending on the high performance switching device anddevelopment of cooling technique. Meanwhile, EMC filters
accounts for a large portion in a motor drive system. Therefore,
the volume of EMC filter must be considered in order tominiaturize the motor drive system.
The volume of an EMC filter is determined by theattenuation rate of the noise. The EMC filter consists of normal
mode filters and common mode filters. The normal mode filtersin the EMC filter is miniaturized by a high frequency switching.
In contrast, the switching loss of PWM inverter is increased by
the high frequency switching. Consequently, the coolingsystem such as the heat sinks and fans become larger.
Therefore, the volume of the cooling system must be

In order to achieve a high frequency switching operation,
the inverter needs to implement with fast-switching devices,because slow-switching is cause of large switching loss anddead time error. However, silicon based switching devices suchas Si-MOSFETs and Si-IGBTs, are difficult to achieve asignificant performance improvement because those devices
performance is almost reaching the limit that the derived fromthe physical properties of silicon. On the other hand, theswitching devices that are composed of a wide band-gap
semiconductor such as gallium nitride (GaN) or silicon carbide(SiC) has been studied in recent years [1-10]. Those wideband-gap devices can perform fast-switching and features low
on-voltage drop compared with the normal silicon devices
under the high temperature operation. The wide band-gap
device has been studied to achieve the high efficiency in a hightemperature operation. However, the performance and theminiaturization effect have not been discussed in previous
studies when wide band-gap semiconductors are applied to the
PWM inverter for a motor drive system.
In this paper, the relationship between the carrier frequency
and the total volume of the inverter system is discussed basedon simulation and experiments using GaN-FET inverter. At
first, the loss and the volume estimation method of the inverter
system is mentioned. Secondary, the design method of thesingle stage EMC filter is clarified. Then, the relationshipbetween the carrier frequency of the PWM inverter and thevolume of an EMC filter is clarified by simulation, besides therelationship between the carrier frequency and the volume of acooling system. At last, a prototype of GaN-FET inverter isdemonstrated by experiments. Output current waveforms,
output current harmonics components, output current THD and
conducted emission are shown. In addition, the total volume of
the EMC filter for GaN-FET inverter system is calculated
based on the experimental results. Moreover, the total volumeof the GaN-FET inverter system that is constructed by multistage EMC filter is calculated. As the result, it is confirmed thatthe total volume of GaN-FET inverter system can be reduced to
64.8% compared to the case of a single stage EMC filter byusing a two stage EMC filter.

II.

INVERTER LOSS AND VOLUNE ESTIMATION

A. Power Loss of Switching device
Fig. 1 shows the circuit configuration of the PWM inverter
for adjustable speed drive systems. The switching loss of eachdevice PSW is calculated by (1) [11].


PSW 

VDC I meon  eoff  f SW 
4VDCd I md

composed by a single stage LC filter, which is constructedfrom market products. In this paper, the reactor volume isfocused, because it is changed significantly by the parameter ofthe component. There are several ways to select the core for thereactor. In this paper, the reactor is designed by the Area
Product concept [13] using a window area and a cross-sectional
area. Then volume of the reactor volL is given by (4).



3

 2W  4 
vol L  K v 
 K u Bm J where fSW is the carrier frequency, VDC is DC link voltage,
Im is the maximum output current, eon is the turn on energy ofeach switching, eoff is the turn off energy of each switching,
VDCd and Imd are voltage and current at the switching time.
Table 1 shows the parameters that are used for design the
EMC filter and cooling system. The switching loss increases inproportional to the carrier frequency form (1). On the other
hand, the conduction loss is generated by on-state resistance of
the FET. The total loss generated in the switching devices Ploss
which be composed of the conduction loss and the switching
loss, is calculated by (2).

where Kv is the constant value depending on the shape ofcores, W is the maximum energy of the reactor, Ku is theoccupancy of the window, Bm is the maximum flux density of
the core, and J is the current density of the wire.
From (6), the volume of reactor is proportional to the power
From EMC filter

To motor2

Ploss  PSW 

Im
RON 
2



VDC



where RON is the on-state resistance of the FET.
B. Volume of Cooling System
The switching devices that used for PWM inverter is heatedby the switching loss and the conduction loss. Significant risein temperature could be a cause of a breaking the switching
devices. Hence, the PWM inverter requires the cooling systemsuch as heat sinks and fans. Generally, a thermal resistance isused to evaluate the cooling system performance. However, it
is not enough because the evaluation based on the thermal
resistance does not consider the volume of the cooling system.
In this paper, CSPI (Cooling System Performance Index),
which is a reciprocal of the product of the volume and thethermal resistance, is introduced to estimate the volume ofcooling system. The CSPI indicates the cooling performance
per unit volume of the cooling system. It means that a highperformance cooling system shows high CSPI. Therefore, thecooling system is miniaturized when CSPI become higher. The
volume of the cooling system volcooling is given by (3) from therelationship between the power loss and the rise in temperature[12].


vol cooling 

1
Ploss


Rth  CSPI
T j  Ta  CSPI







PWM Rectifier

Table1. Simulation Parameters.
Input voltage Vin
200V
Input current Iin
12.5A
Input frequency fin
50Hz
Output voltage Vout
200V
Output current Iout
12.5A
Output frequency fout
50Hz
0.85
Power factor cos
DC voltage Vdc
400V
CSPI
5
50ns
Turn on time ton
50ns
Turn off time toff
Ambient temperature Ta
20℃
Junction temperature Tj
100℃
Ripple current Iripple
0.5A
Load factor k
0.2
Lead angle 
5/180rad
On-resistance RON
50m
Leakage current Ileak
100mA
From gridwhere Rth is the thermal resistance of the cooling system, Tj
is the junction temperature of the switching device, Ta is theambient temperature, Ploss is the power loss of the switching
device.
C. Volume of EMC Filter
Fig. 2 shows a circuit schematic of a single stage EMC
filter. In order to compare the volume, the EMC filter is

PWM Inverter

Fig. 1. PWM rectifier and inverter
for an adjustable speed drive system.

LC

To rectifier
LD

CX
CY

Fig. 2. Circuit schematic of a single stage EMC filter.

of 3/4 of the maximum energy of the reactor.
DESIGN METHOD OF EMC FILTER

Fig. 3 shows the measurement circuit diagram ofconduction noise [14]. The EMC filter is connected to the inputof the inverter.
A. Differential Mode Reactor
The differential mode reactor is used to smooth the input
current ripple of the PWM rectifier. Therefore, the inductanceof differential mode reactor LD is given by (5) using acceptablecurrent ripple Iripple.


LD 

VDC

2 f SW I ripplewhere Iripple is the maximum current ripple in a carrier
period.
B. Differential Mode Capacitor
X capacitors suppresses the fluctuations of the input voltage.
However, it reduces the power factor at the light load.
Therefore, the capacitance of the differential mode capacitor
CX is given by (6) using an allowable lead angle of input
current at a light load.


3kI in

CX 
Vin



where k is the load factor (output power/maximum power),Iin is the input current,  is the maximum lead angle of the input
current,  is the input frequency, and Vin is the input voltage.
C. Common Mode Capacitor
A common mode current is bypassed to the frame ground(FG) by the Y capacitors that are connected between eachphase and FG. The common mode reactor is miniaturized when
the capacitance of the Y capacitors is large, but also leakage
current corresponds to the input voltage frequency flows to FG.
The capacitance of the Y capacitors CY is designed by (7) basedon the acceptable leakage current, so the ground faultinterrupter does not work by this leakage current.


CY 

IV.

D. Common Mode Reactor
The EMC filter components are designed by (5)-(7) except
the common mode reactor. Therefore, the common mode
reactor is designed by the attenuation rate of the EMC filter Att
to suppress the conduction noise below the limit of CISPR.
Hence, the inductance of common mode reactor LC is given by(8) based on the simulation results of conduction noise without
the common mode reactor.



SIMULATION RESULTS OF INVERTER VOLUME

A. Volume of reactor
Fig. 4 shows a relationship between the carrier frequency
and the differential mode reactor. First, the inductance of thedifferential mode reactor decreases in inverse proportion to thecarrier frequency because the current ripple is reduced by theshort switching period at high frequency. Additionally, thevolume of differential mode reactor is decreased at high carrier
frequency because it is proportional to the power of 3/4 of theinductance.
Fig. 5 shows a relationship between the carrier frequency
and the common mode reactor. Over 150 kHz, the inductanceof the common mode reactor is decreased when the carrier
frequency getting higher. If the carrier frequency is less than
150 kHz, the EMC filter has to suppress the conduction noisethat is harmonics of carrier frequency. However, if the carrier
frequency is more than 150 kHz, the EMC filter has to suppress
the conduction noise that is fundamental harmonic of carrier
frequency. Therefore, the inductance of common mode reactor
Vin

RL load
LISN

EMC
filterRectifier

PWM
inverter

Stray capacitanceFig. 3. Conduction noise measurement system for
GaN-FET inverter system.
1

where Ileak is the acceptable leakage current.

1Volume of Reactor:VLD
Inductance:LD

0.1

0.01

LD:1 p.u.=9.9 mH at 10 kHz
VLD:1 p.u.=7.25×10-3 m3 at 10 kHz
0

200
400
Carrier frequency[kHz]0.1

Volume of Reactor[p.u]3I leakVin1

C 2CY Att

E. Modeling of Stray CapacitanceThe differential mode noise and the common mode noise
are generated by stray capacitances. Hence, it must be modeled
in order to estimate the conduction noise in simulations.
Therefore, the capacitors of 100 pF are added between theswitching devices and FG, and the capacitor of 1 nF is added
between output voltage midpoint and FG in order to model thestray capacitances of a general inverter. In this paper, modeled
LISN and a spectrum analyzer is used to estimate theconduction noise by the simulation [15].

Inductance[p.u.]

III.

LC 



0.01
600

Fig. 4. Value and volume of Differential mode reactor
in EMC filter by carrier frequency.

is reduced at high carrier frequency.

B. Volume of cooling system

102

10

Fig. 9 shows a relationship between the carrier frequency
and the total volume of the inverter system volinverter. The total
volume of the inverter system is given by (9) that is sum of thevolume of cooling system and the volume of reactors that
construct the EMC filter volEMC.

vol inverter  vol cooling f SW   vol EMC  f SW  

1
1p.u.=7.27×10-3 m3 at 10 kHz

0.75
0.5
0.25
0

0

Fig. 10 shows the volume of the cooling system that iscompared conventional system with GaN-FET inverter system.
The rated power of the system is assumed 3.7 kW that is same
condition to estimating the conduction noise by simulation. As
a result, the total loss of conventional system is 102 W when
the carrier frequency is 10 kHz and the total loss of GaN-FET
inverter system is 308 W when the carrier frequency is 300
kHz. According to this result, the conduction loss accounts forlarge portion in a total loss. Therefore, the carrier frequency
does not so affect to the total loss and the volume of coolingsystem. As a consequence, the volume of the cooling system is0.26 little when the carrier frequency is 10 kHz and 0.77 little
when the carrier frequency is 300 kHz.

600

60

Switching Loss[p.u.]

According to Fig.9, the inverter system is miniaturized at ahigh carrier frequency because the volume of the differential
mode reactor is decreased sharply. On the other hand, thecooling system is getting larger when the carrier frequency ishigher than 300 kHz because switching loss becomes large. As
a result, the total volume of inverter system can be smallest at
the carrier frequency of 300 kHz. Where the total volume ofinverter system is 1.38×10-3 m3 , the power density is 2680
W/litter. That means the power density is increased 5.4 times
larger than the conventional inverter system.

200
400
Carrier frequency[kHz]Fig. 6. Volume of total reactor
in EMC filter by carrier frequency.
1.5
Conducion Loss:Pcon40

1

Switching Loss:PSW

20

0.5

Pcon:1 p.u.=94.7 W at 10 kHz
PSW:1 p.u.=7.11 W at 10 kHz
0

0

200
400
Carrier frequency[kHz]0600

Fig. 7. Relationship between carrier frequency andpower loss of power devices.
5

Volume of coolingsystem[p.u.]

dt

1
600

Conduction Loss[p.u.]

dt

200
400
Carrier frequency[kHz]vol inverter  d vol cooling f SW   d vol EMC  f SW   0  
dt

0Fig. 5. Value and volume of Common mode reactor
in EMC filter by carrier frequency.

Therefore, the carrier frequency that achieve the minimum
volume of inverter system can be calculated by solving the (10)

10Inductance:LC

1

Volume of total Reactor[p.u.]

C. Total volume of inverter

102
Volume of Reactor:VLC

Fig. 7 shows a relationship between the carrier frequency
and power loss. The conduction loss is approximately 13 times
larger than the switching loss at the carrier frequency of 10 kHz.
However, the switching loss accounts for a large portion of thetotal loss when the carrier frequency is higher than 130 kHz
because it increases in proportional to the carrier frequency.
Fig. 8 shows a relationship between the carrier frequency
and the volume of the cooling system. The volume of thecooling system is increased in proportion to the carrier
frequency.

103

LC:1 p.u.=0.03 mH at 10 kHz
VLC:1 p.u.=1.85×10-5 m3 at 10 kHz

Volume of Reactor[p.u.]

Fig. 6 shows a relationship between the carrier frequency
and the total volume of the reactors. The total volume of thereactors is decreased at high carrier frequency because thedifferential mode reactor is larger than the common mode
reactor.

Inductance[p.u.]

103

4
3
2
1
0

volcooling:1 p.u.=0.26×10-3 m3 at 10 kHz
0

200
400
Carrier frequency[kHz]Fig.8 . Relationship between carrier frequency andvolume of cooling system.

600

Fig. 11 shows the total volume of the conventional systemthat is compared with GaN-FET inverter system. From theresults, the EMC filter accounts for large portion in aconventional system. Therefore, the total volume of GaN-FET
inverter system can be smaller by using high frequency carrierat this condition. As a result, the total volume of GaN-FET
inverter system is reduced by 81.6% with a 300-kHz carrier
frequency compared to a 10-kHz carrier frequency

C1

n

2
Cooling system
0

From grid
LCn

LDn

CXn

CXn

CYn
1

To rectifier
LDn

LCn

2

3

0.2

CYn
n

Carrier frequency fcarrier=300kHz

0.15
0.1

Cooling system

0.5
EMC filter

0.25

0
0
0

EMC filter

Fig. 12. Circuit schematics of multi stage EMC filter

Total volume [l]Volume of Inverter system[p.u.]

10kHz
300kHzCarrier frequency

Fig. 11. Total volume of GaN-FET inverter system
calcurated by experimental results.

1

0.5

81.6%

4



1 p.u.=7.64×10-3 m3 at 10 kHz

10kHz
300kHzCarrier frequency

6

1

0.75

0.26 [l]0.28Therefore, the inductance of common mode reactors andthe differential mode reactors are designed by (12) that using
an attenuation of each LC filter.

Fig. 13 shows the total volume of GaN-FET inverter
system that is constructed by multi stage EMC filter under the
carrier frequency of 300 kHz. It is noted that, the total volumeof X capacitors and Y capacitors is assumed as same regardlessof the number of EMC filter stages because the total
capacitance of each filter is same. As a result, the total volumeof GaN-FET inverter system can be reduced to 64.8%
compared to the case of a single stage EMC filter by using a
two stage EMC filter. Especially, the multi stage EMC filter isvery effective because this system generate large noise at highfrequency region. However, the total volume of GaN-FET

0.4

conventional system (10 kHz)with GaN-FET inverter system (300 kHz)

where n is number of filter stage, and C1 is capacitance ofX capacitor or Y capacitor in case of single stage EMC filter.



0.6

Fig. 10. Volume of the cooling system that is compared




n
1
 
Ln   2 n n  Cn Att 

0.77 [l]0.80Total volume [l]

Cn 



Volume of cooling system [l]Fig. 12 shows the circuit schematics of multi stage EMC
filter. Generally, the attenuation of LC filter can be improved
using a multi stage filter at a high frequency region, the multistage EMC filter is very effective in case of a high carrier
frequency inverter. In this paper, the multi stage EMC filter isconstructed by connecting the single stage EMC filter in series.
Each filter that has different number of stages is designed to geta same attenuation. In addition, the capacitance C of X
capacitors and Y capacitors are divided equally for all stages
that are given by (11).

1.0

200
400
Carrier frequency[kHz]Fig. 9. Relationship between carrier frequency
and volume of inverter system.

600

1
2
3
Number of EMC filter stages

Fig. 13. Total volume of GaN-FET inverter systemconstructed by multi stage EMC filter.

inverter system cannot be smaller even if the number of filter
stages is increased more than two, because the volume of Y
capacitor becomes a large part of the EMC filter. Moreover, thePCB board that is used for make an EMC filter, will becomelarger in the actual circuit compared to the theoreticalconsideration in according to the increasing of the number ofthe stage of EMC filter.
V.

EXPERIMENTAL RESULTS USING GaN-FETThe GaN-FETs (VDSmax=600V ， IDmax=10A， RON=100m)are used for the PWM inverter to achieve the 300-kHz
switching, and the Si-diodes are used as a rectifier part toevaluate the conduction noise generated by the inverter unit.
The PWM inverter is controlled by an open-loop control. The
PWM signals are generated by comparing the triangle wave
and the output voltage command. The conduction noise
generated by control circuit is deducted to evaluate theconduction noise of inverter. Table 2 shows the circuit
parameters at the experimental condition.

Therefore, the volume of EMC filter is reduced by 70% with
300-kHz carrier compared to 10-kHz carrier.
VI.

In this paper, the relationship between the carrier frequency
and the total volume of the inverter for a motor drive systemusing wide band-gap device, is analyzed by simulation. As aresult, the total volume of the inverter system that contains an
EMC filter and a cooling system will be reduced by 81.6% at
the carrier frequency of 300 kHz. The conduction noise andefficiency are measured from a prototype of PWM inverter thatis constructed by GaN-FET. As a result, it is confirmed that theTable 2. Circuit parameters.
Input voltage Vin
100V
Input frequency fin
50Hz
Output current Iout
1A
Output frequency fout
50Hz
0.99
Power factor cos
Modulation factor a
0.4
Carrier frequency fcarrier
300kHzDead time TD
100ns
Differential-mode reactor LD
500H
X capacitor CX
6F
Y capacitor CY
3F
Common-mode reactor LC
100H

Fig. 14 shows the photograph of experimental platform.
The Si-diode bridge rectifier and the GaN-FET inverter are
mounted on another heat sink. Both heat sinks are notconnected to the earth. Two GaN-FETs are connected in series
and mounted on a PCB board. Three boards are used toconstruct the three phase PWM inverter.

300mm

Fig. 15 shows three phase output current waveform. The
low distorted sinusoidal waveforms are obtained from allphases under the carrier frequency of GaN-FET inverter is 300
kHz.

Fig. 17 shows conduction noise in the prototype circuit of
PWM inverter. Red line is the limit of CISPR. In order toconfirm the validity of design method for the EMC filter, thesingle stage EMC filter is designed based on the chapter III.
And then, the conduction noise of PWM inverter that isconstructed by GaN-FET, is measured by experiments. It isnoted that the carrier frequency is 300 kHz. As a result, it isconfirmed that the experimental result agrees with simulation
results. Especially, the conduction noise is suppressed below
the limit of CISPR. Therefore, the proposed design method for
EMC filters is valid in the experiment.
Fig. 18 shows the volume of each component that becomposed of the EMC filter. The volume of the EMC filter is
0.61 litters with 300-kHz carrier frequency. By contrast, thevolume of differential mode reactor is 0.47 litters with 10-kHz
carrier frequency which is 12.8 times larger than its volume
with 300-kHz carrier frequency. Also, the volume of common
mode reactor is 4.28 ml with 10-kHz carrier, which is 0.4 times
smaller than its volume with 300-kHz carrier frequency.

Input
Si-diode bridge
Heat sink

GaN-FET board

250mm

Fig. 16 shows the results of harmonics analysis on the
output current from the experimental results. From Fig. 12 (a),it can be confirmed that the low order harmonic components inthe output current are low and the output current THD is 1.67%.
From Fig. 12 (b), main peaks occur at the carrier frequency andits harmonics components. Therefore, it is confirmed that the
prototype of GaN-FET inverter works with 300-kHz carrier
frequency.

CONCLUSION

To control circuit

OutputFig. 14. Photo of experimental platform.
U phase current iu [A]2[A/div]

V phase current iv [A]2[A/div]

W phase current iw [A]2[A/div]

0004[ms/div]

Fig. 15. Output current waveform of GaN-FET inverter that is working under
the carrier frequency is 300 kHz.

conduction noise is lower than the limit of CISPR by using thedesigned EMC filter. Furthermore, the total volume of EMC
filter for GaN-FET inverter system is reduced by 70% with a
300-kHz carrier frequency compared to a 10-kHz carrier
frequency. In addition, the total volume of GaN-FET inverter
system can be reduced to 64.8% compared to the case of asingle stage EMC filter by using a 2 stage EMC filter. In the
future work, the total volume of GaN-FET inverter system with
PWM rectifier will be evaluated.

Output current iO [p.u.]1

THD:1.76% (from 50 Hz to 2 kHz)

10-1
10-2
10-3
10-4

50

400

800
1.2k
Frequency [Hz]

1.6k

2k

(a) From 50 Hz to 2 kHz

REFERENCES

Carrier frequency fcarrier=300kHz[1]

2fcarrier

10-2

3fcarrierfcarrier

10-4
10-6
50

250k

500k
750k
Frequency [Hz]1M(b) From 50 Hz to 1.25 MHz
Fig. 16. Harmonics components in the output current
of GaN-FET inverter with 300 kHz carrier.

Conduction noise [dBV]

80
60
40
20
0
0.15

0.3 0.51
2
5Frequency [MHz]1030

Fig. 17. Conduction noise of the GaN-FET inverter
using 300 kHz carrier with designed EMC filter.
0.8
0.6

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Output current iO [p.u.]

1

0.4

70%

0.2
0

10kHz
300kHzCarrier frequency

X capacitor
Common mode reactor
Y capacitor
Differential mode reactor

Fig. 18. Volume of EMC filter components based on theexperimental results of conducted emission.