Experimental Loss Separation of Mega-hertz
Inverter for WPT System using Calorimetric Power
Loss Measurement
Masamichi Yamaguchi
Dept. of Science of Technology
Innovation
Nagaoka University of Technology
Nagaoka, Niigata, Japanm_yamaguchi@stn.nagaokaut.ac.jp

Keisuke Kusaka
Dept. of Electrical, Electronics andInformation Engineering
Nagaoka University of Technology
Nagaoka, Niigata, Japan
kusaka@vos.nagaokaut.ac.jp

Abstract— This paper discusses a power loss, which occurs
in a load-resonant inverter operating at megahertz for wirelesspower transfer (WPT) systems. A calorimetric method isapplied to measure the power losses in the mega-hertz operation
accurately. The loss is measured using a single chamber withtemperature control of the internal chamber using a Peltier
device. The loss can be measured within 10% error when theloss is less than 23 W with a prototype chamber in experiment.
A drive circuit loss, conduction loss of GaN devices, and PCB
pattern loss are measured using the measurement site.
Moreover, the total loss of the inverter with 6.78-MHz operationis measured under the zero voltage switching (ZVS) condition.
The losses on the inverter are separated by a combination ofeach measurement result. As a result, the loss, which is related
to the mega-hertz operation under the ZVS condition, is 9.9 W
when the output power is 417 W at 6.78-MHz operation.
Keywords— high-frequency inverter, calorimetric power loss
measurement

I. INTRODUCTION
In recent years, battery chargers for electric vehicles (EVs)have been installed rapidly by increasing the interest in EVs.
Notably, wireless power transfer (WPT) systems for battery
chargers have been actively studied from the safety andconvenience perspective in this decade. Especially, rapid
charging is required for EVs to reduce the charging time
because the charger using the WPT system takes a long time
to charge the onboard batteries. Thus, increasing the power
density of the WPT system is urgent.
A transmission frequency of 85 kHz is used in thestandardization of WPT systems. However, the 85 kHz system
is bulky and heavy because the WPT system has a ferrite intransmission coils. A heavy system on the vehicle directly
causes an increase in power consumption during the running.
Employing mega-hertz order switching frequency is one of thesolutions to achieve high power density and a light system.
Thus, the mega-hertz operation in a WPT system has been
actively studied [1-2].
An inverter circuit for the mega-hertz operation requires
nano-second order switching. GaN-transistors, which canswitch in a few nano-second, are used for these highfrequency WPT systems. A surface-mounted device (SMD)
package is commonly adopted to the GaN-transistor because
the SMD allows decreasing a parasitic inductance on thedevices. Although, SMD has a small heat spreader because the978-1-6654-3448-5/21/$31.00 ©2021 IEEE

Jun-ichi Itoh
Dept. of Electrical, Electronics andInformation Engineering
Nagaoka University of Technology
Nagaoka, Niigata, Japan
itoh@vos.nagaokaut.ac.jp

package size is small. Thus, the design of heat dissipation ofdevices is a critical issue for mega-hertz operation.
The accurate calculation of thermal resistance andestimation of the loss of devices is essential for thermal design.
However, accurate measurement of devices loss based on thevoltage and current is difficult in mega-hertz operation
because the difficulty of accurate measurement with megahertz voltage and current is still high. It prevents an accurate
thermal design and decreases power density.
A loss measurement based on the thermal measurement
has been conducted in recent studies[3-18]. Ref. 3 shows theloss measurement of the full-bridge converter, which employs
a GaN-transistor. The calculation and measurement resultshows good agreement, although the converter is operated at
160 kHz. Ref. 4 investigates a calorimetric method for loss
measurement of the SiC-MOSFET. However, the switchingfrequencies higher than 1 MHz have not been investigated.
In this paper, the breakdown of power loss caused by themega-hertz resonant inverter is experimentally analyzed withthe calorimetric method. The calorimetric method is based on
the thermal measurement without sensing voltage and currentof the main circuit. Thus, the loss can be measure accurately
even though the circuit as the device under test (DUT) is
operated in megahertz. The losses are experimentally
separated into a drive circuit loss, a conduction loss of theGaN-devices, and a conduction loss of a PCB pattern. As aresult, the loss, which is related to the mega-hertz operation
under the ZVS condition, is clarified by a combination of theresult of each measurement.
II. CALORIMETRIC LOSS MEASUREMENT
A. Load-resonant Inverter as DUT
Figure 1 shows the circuit configuration of the mega-hertz
resonant inverter as a DUT in loss measurement. The GaNtransistors (PGA26E07BA: 600 V, 26 A, Panasonic) are used
for the mega-hertz switching (6.78MHz). The resonant load isconnected to the output side as the primary side of a WPTsystem. The ZVS should be achieved to reduce the switchingloss on the transistor. Thus, the resonant frequency of theresonant load is selected to the 6.34 MHz because the phaseof the load current should be lag to achieve the ZVS condition.
Figure 2 shows the voltage waveforms of the inverter
output at 6.78 MHz. The DC link voltage is 150 V. The ZVS
condition is achieved at the output voltage. The RMS value ofthe voltage at load resistor vload is 91.4 V. The load resistance

PCB
FET1

CY
100 pF
Cf1 Cf1 Cf1
Cf2
Cf2
1 mF
0.47 mF

VDC

Cf3
Cf3
470 pF

CY

FET3

Rf
1

Lr
Cr
3 mH 205 pF

Rf

Cf4
100 pF

Cf2 Cf2 Cf3 Cf3

Cf4

FET2

vinv
Lr

FET4

RL
20 
Cr

vload

Resonant load

Fig. 1. Mega-hertz resonant inverter.
20 ns/div

100 V/div0

Isolated DC-DC

vinv

0

vload

100 V/div

Fig. 2. Voltage of inverter output and load resistor.

GaN devices(Placed on bottom side)

is 20 . Thus the calculated output current is 4.6 A in thisoperation. Figure 3 (a) shows a thermal picture of the inverter
circuit with 75 W output, and figure 3(b) shows the outlook of
the circuit. The main thermal sources are GaN-transistors in
the main circuit and isolated DC/DC converter ICs in a gate
drive circuit.
B. Calorimetric Method with Single Chamber
The calorimetric method is used to measure the power loss
based on a thermal measurement of the DUT. Figure 4 showsa configuration of the measurement system applying acalorimetric method with a single chamber[5]. The DUT is
operated in the chamber, which has a Peltier device as a heatexchanger to control an internal temperature constantly. The
power loss of the DUT can be calculated by the endotherm of
the Peltier device when the internal temperature is kept
constant. The endotherm of the Peltier device is expressed by

Isolated DC-DC(a) Heat distribution on circuit.
Isolated DC-DC

GaN devices(Placed on bottom side)

Isolated DC-DC

T −T 1Ploss = S pTc I p − h c − rp I p 2 .............................. (1),Rp
2where Sp is the Seebeck coefficient, Tc is the temperature of
the cold side, Th is the temperature of the hot side, Rp is thethermal resistance, rp is electric resistance, Ip is the current of
the Peltier device. The chamber has a fan motor to make an air
circulation in the chamber. Thus, the loss value of the DUT is
expressed by
T −T 1Ploss = S pTc I p − h c − rp I p 2 − PFC ....................... (2),Rp
2(b) Outlook of circuit.
Fig. 3. Load-resonant inverter as DUT.
Fan motor
Hot side
heat sinkTh
Cold sideheat sink
Fan motor

Peltier device
Tc

where PFC is the power loss of the internal fan motor.
Figure 5 shows the PI controller for the internal
temperature control. In this investigation, the internal
temperature is controlled to the same as the ambient
temperature because the thermal flow, which throughpolystyrene wall, cannot be ignored if the temperature
difference is large.

Chamber

PLoss
DUT

Tin

Tamb

Fig. 4. Calorimetric power loss measurement with single chamber.

PlossTc_p.u.
Thermalcommand1
Ti s + 1

Tc_p.u.*-Ti s + 1
Ti s

Kp

+

Command filter

Vp.u.

ZOH

Vn

Voltage
Amp.

PI-controller
Tm_p.u.

1
Tn

Tm

Gain

V

ADC

ZOH

×

V2

1
Rpe

+

1
sC

-

Peltier device

ChamberSp

VthermoController

T

Thermocouple

Fig. 5. Thermal control system for calorimetric power loss measurement.

Figure 6 shows a prototype of the measurement site basedon the calorimetric method with the single chamber. The
chamber is made from expanded polystyrene with a thicknessof 20 mm. The mega-hertz resonant inverter is operated in thischamber as the DUT. The resonant load is placed outside of
the chamber and connected to the inverter circuit by cable.
Table 1 shows the parameter of the prototype of themeasurement site.

III. EXPERIMENTAL LOSS BREAKDOWN
The loss of a device should be clarified although the total
loss value in the chamber can be measured by the calorimetricmethod. This is because the loss of the device is the mostimportant point in the thermal design. Thus, the loss of othercomponents, drive circuit, and the PCB pattern, are separated
by a combination of some measurements result.
Moreover, the loss on the transistor consists of the
conduction loss and the switching loss. Especially, theswitching loss, which is related to the switching frequency,
should be revealed in the mega-hertz operation. Thus, the loss
measurement flow in order to separate the cause of losses is asfollows.
A. Drive circuit loss
First, a drive circuit loss is measured without applying DClink voltage. The drive circuit loss is caused by a gate current,
which conducts from the drive circuit to the input capacitanceof transistors Ciss when transistors switch. The drive loss
increases with the switching frequency. Thus, the drive loss ismeasured from DC to 6.78 MHz in 1.695 MHz increments.
The drive loss changes with DC-link voltage VDC because
the Ciss changes with the vds. However, the variation of the Cissis relatively small (Ciss = 550 pF at vds = 0 V, Ciss = 405 pF at
vds = 400 V). Thus, the measured loss value at mega-hertz
operation without DC-link voltage is considered as the drive
loss.
Figure 7 shows the measurement result of the drive circuit
loss based on (1). The drive circuit loss is 4.6 W at 6.78-MHz
operation, and the loss at 0 Hz (DC) is 3.5 W. The drive circuit
loss consists of a proportional term to the switching frequency
and constant term, which is dominant in the drive circuit loss.
The main cause of the constant loss is considered as the power
consumption of isolated DC/DC ICs on the drive circuit.

Resonant
Capacitor

Chamber

Resonant
inductor

Data loger

Fig. 6. Loss measurement site.
Table 1. Parameter of measurement site.
Peltier device
ThermopowerSp

0.0564 V/K

Thermal resistance of Peltier deviceRp

1.58 K/W

Resistance of Peltier device

rp3

Respons frequency

fr0.002 Hz

Attenuation coefficient

0.5

Thermal capacitance in ChamberC

31.5 J/K

PI controller

5.0
4.0
Drive loss Pdrive W

The accuracy of the measurement site with the temperature
control is validated using a known resistor with DC-current on
the DUT. The accuracy of the loss measurement is 3.6% at 5.1
W and 7.3% at 23.0 W. Thus, the accuracy of the measurementsite is sufficient to measure the circuit losses.

Hot side heat sink
Load resistor

3.0

2.0
1.0

0.0

0

1.695

3.39
Frequency f MHz

5.085

6.78

Fig. 7. Drive circuit loss of inverter.

FET1 FET3CY
100 pF
Rf
1
Cf1
Cf2
Cf3
1 mF 0.47 mF 470 pF Cf4×3×2×4 100 pF

IDC
CY

×2

FET2 FET4

Fig. 8. Circuit connection at conduction loss measurement.

Figure 9 shows the measured conduction losses of GaNdevices with the DC-current. The conduction loss with 1.6 A
cannot be measured because the loss value is very small. The
theoretical conduction loss is about 0.3 W based on an onresistance of the GaN-transistor at 1.6 A (at junction
temperature Tj = 25℃). The measured loss at 3.2 A shows

4.0

Conduction loss of GaN-transistor
Pcond_GaN[W]B. Conduction loss of GaN-transistor
Second, a conduction loss of GaN-transistors is measured
with DC-current. Figure 8 shows the circuit connection at the
conduction loss measurement of the GaN-transistors. The
input side of the DC-link is connected to a constant current
supply, and the output terminal of the inverter is shorted. DCcurrent is conducted to two GaN-transistors, which are
implemented to an opposite side of each arm in the H-bridge.
The DC-current value is selected to be the same as the RMS
value in the mega-hertz operation. The current of 1.6 A, 3.2A,
and 4.6A are selected as the DC-current value. The
measurement result involves the conduction loss of the GaNtransistor and the drive loss, which is measured in the section
A. Thus, the drive loss at the DC is subtracted from themeasured value to compensate for the conduction loss.

Measured loss

3.0
Theoretical loss at Tj = 75

2.0
1.0
Theoretical loss at Tj = 25

0

0

1.6

FET1
CY
100 pF

FET3

Rf
1

Cf1
1 mF
×3

Cf2
Cf3
0.47 mF 470 pF
×2
×4

IAC

Cf4
100 pF

CY

×2

FET2

FET4

Fig. 10. Circuit connection at loss measurement of PCB pattern.

Output terminal

C. Conduction loss of PCB pattern
The conduction loss on a current path is increased by a skineffect in mega-hertz operation. The skin depth  is expressedas:1....................................................... (3), f m0 2
where f is frequency and 2 is the conductivity of a material.
The skin depth is about 25 mm in 6.78 MHz. The top and thebottom layer have 70 mm thickness in the inverter circuit. Thus,
the skin effect should be considered in the measurement ofconduction loss of the PCB pattern.

=

Figure 10 shows the circuit connection at the conduction
loss measurement of the PCB pattern. The path of the megahertz current, DC-link capacitor and two GaN-transistors, areshorted. The output terminal of the inverter is connected to themega-hertz current supply. The pattern loss is measured withthe mega-hertz current to include the influence of the skineffect. Figure 11(a) shows the thermal picture with a currentof 4.6 A, and figure 11(b) shows the circuit photo from thesame angle. The pattern, especially near the output terminal,
has been heated. This is because the pattern width near the
output terminal is narrow due to the limitation of the board
layout.
Figure 12(a) shows the conduction losses of the PCB
pattern with a current of 3.2 A and 4.6 A. The conduction loss
increases as the switching frequency in each current condition.

4.8

Fig. 9. Conduction loss of GaN-transistors.

good agreement with the theoretical loss at Tj = 25℃.
On the contrary, the measured loss at 4.6 A has adifference of about 2.3 W from the theoretical loss at Tj = 25℃.
The reason for the loss difference is considered as thedifference in junction temperature. The theoretical loss at 4.6
A with Tj = 75 ℃ shows good agreement. Although thedifference based on the junction temperature occurs in themeasured result, the difference can be ignored in the following
consideration because the difference value is relatively small
compared to the total loss value.

3.2
DC current IDC A(a) Heat emission from PCB pattern.

Output terminal

Pattern of DC-link C(Shorted)(b) Circuit connection.
Fig. 11. Loss measurement of PCB pattern.

PPCB = 0.224I 2 + 0.552I ........................................ (4).

The quadratic term is considered as the pattern resistanceat 6.78 MHz. The proportional term is considered as theincreases of RPCB by the heating. The measurement result
implies that the PCB pattern should be designed on the
viewpoint about parasitic resistance, which is considered of
the skin effect, and the heat dissipation of the pattern.
D. Total loss at mega-hertz operation
Finally, a total loss of the inverter at the mega-hertz
operation is measured. The RMS value of the output current
is 1.6 A, 3.2 A, and 4.6 A when the DC-link voltage is 50 V,
100 V, and 150 V. The output power at load resistor is 417 W
when the DC-link voltage is 150 V. The inverter is operated
by the ZVS condition at 6.78 MHz. In general, the switchingloss is zero under ZVS conditions on switching devices. In thisinvestigation, the drive loss, the conduction loss of the GaNtransistor, and the PCB are subtracted from the total loss inorder to clarify the loss, which is related to the switchingfrequency.

4.0

2.0
0.0

This work was supported by Council for Science,
Technology and Innovation (CSTI), Cross-ministerial
Strategic Innovation Promotion Program (SIP), “Energy
systems of an Internet of Energy (IoE) society” (Funding
agency: JST).

3.39

5.085
Frequency f MHz

6.78(a) Difference of switching frequency.
5.0

4.0
3.0
2.0

1.0
0.0

0

1.6

3.2
AC current IAC A

4.8(b) Loss measurement with 6.78 MHz.
Fig. 12. Conduction loss of PCB pattern.

Measured loss[W]25

IV. CONCLUSIONSACKNOWLEDGMENT

3.2 A

6.0

Figure 13 shows the loss measurement result with a 6.78MHz operation. The total loss is 24.6 W when VDC is 150 V.
Then, loss excluding the drive and conduction loss from thetotal loss is defined as another loss. Another loss is about 9.9W when VDC is 150 V. Another loss is caused by the megahertz operation. The causes of another loss can be consideredas the increasing parasitic resistance on the GaN-transistor by
the skin effect, and snubber loss in the mega-hertz operation.
This paper investigates a power loss of the load-resonant
inverter in the mega-hertz operation. The calorimetric method
is applied to measure the loss in mega-hertz operation
accurately. The measurement error of the losses achieves
within 10% using a single chamber with a Peltier device. The
drive loss, the conduction loss of the GaN-transistor,
conduction loss of the PCB pattern, and total loss aremeasured respectively by the calorimetric method.
Particularly, the total loss of the inverter with 6.78-MHz
operation is measured under the ZVS condition. The losses on
the inverter are separated by a combination of eachmeasurement result. Measurement results show that the loss,
which is caused by the mega-hertz operation, exists in the loadresonant inverter at the mega-hertz operation under the ZVS
condition. The consideration of the influence of the junction
temperature and loss of the passive components like a snubber
circuit are future works.

4.6 A

Conduction loss of PCB pattern
PPCB W

Figure 12(b) shows the conduction loss of the PCB patternat 6.78MHz. The measured result is approximated to thequadratic equation as

8.0

Conduction loss of PCB pattern
PPCB W

The cause of the loss increment is considered as the influenceof the skin effect.

Another loss

20

Conduction loss of PCB pattern

15
Conduction loss of GaN-devices
10

Drive circuit loss
5
0

0

50
100
DC-link voltage VDC V

150

Fig. 13. Total loss of inverter circuit with 6.78 MHz operation.

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