© 2016 IEEE

Proceedings of the 7th International Symposium on Power Electronics for Distributed Generation Systems (PEDG 2016),Vancouver, Canada, June 27-30, 2016

Accurate Transient Calorimetric Measurement of Soft-Switching Losses of 10kV SiC MOSFETs

D. RothmundD. BortisJ. W. Kolar

This material is published in order to provide access to research results of the Power Electronic Systems Laboratory / D-ITET / ETH Zurich. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the copyright holder. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.

Accurate Transient Calorimetric Measurement ofSoft-Switching Losses of 10kV SiC MOSFETs

Daniel Rothmund, Dominik Bortis and Johann W. KolarPower Electronic Systems Laboratory, ETH Zurich

Email: rothmund@lem.ee.ethz.ch

Abstract—The characterization of soft-switching losses of mod-ern high-voltage SiC MOSFETs is a difficult but necessary taskin order to accurately model converter systems such as medium-voltage-connected Solid-State Transformers (SSTs), where soft-switching techniques are employed for an increased efficiency.Usually, switching losses in general are measured with the well-known double pulse method. However, in case of soft-switchingloss measurements, this method is very sensitive to severaleffects such as probe skew and limited measurement accuracy,among others, and thus unsuitable for the characterization offast switching high-voltage MOSFETs. This paper presents anaccurate and reliable calorimetric method for the measurement ofsoft-switching losses using the example of 10 kV SiC MOSFETs.Finally, measured soft-switching loss curves of these 10 kV SiCMOSFETs are presented for different DC-link voltages, currentsand gate resistors.

I. INTRODUCTION

Soft-switching techniques are widely utilized in powerelectronic converters for the reduction of switching losses,especially in DC/DC applications [1]–[3] and also in TCMoperated AC/DC applications [4], [5]. Although Wide Band-Gap (WBG) devices such as SiC MOSFETs offer superiorswitching behaviour compared to Silicon devices [6]–[9], thesoft-switching losses of these devices (especially in case ofhigh blocking voltage devices in the range of 10 kV) are notnegligible, as will be shown in this paper. Therefore, it is veryimportant to consider the soft-switching losses during the designprocess. However, most of the device datasheets only providemeasurement data for hard-switching losses which means thatit is necessary to measure the soft-switching losses of theparticular devices. Since soft-switching losses are typicallysmall compared to hard-switching and conduction losses, itis challenging to measure soft-switching losses accuratelyunder different operating conditions such as different chiptemperatures and independently of external factors such asthe PCB-layout and parasitic inductances of e.g the DC-linkcapacitors.

There are basically two types of switching loss measure-ment methods, namely electrical measurement methods andcalorimetric measurement methods. Electrical methods, suchas the well-known double pulse test, feature the advantagethat the measurement time is rather short, since only pulsemeasurements have to be performed. Furthermore, with thesame measurement setup both, the hard- and soft-switchinglosses can be directly determined at different chip temperaturesby electrically measuring the device voltage and current duringa turn-on and turn-off transient. However, due to the fastswitching transients, the accuracy of the measured waveformsand thus the measured switching losses suffers e.g. fromimproper deskew and jitter between the current and voltage

probes, from signal offsets and amplitude errors, from limitedbandwidths of the passive or active probes, or from any othermeasurement distortion such as common mode. In addition,also the post-processing of the measured waveforms is verycrucial, e.g. the selection of the proper interval in which themeasured power has to be integrated in order to extract thecorrect loss energy. In contrast to electrical measurements, witha calorimetric measurement setup the semiconductor losses, i.e.the sum of the switching and conduction losses, are determinedby measuring the dissipated heat of the device under test(DUT) in continuous operation and, since no fast switchingtransients have to be measured, typically a higher measurementaccuracy can be achieved. Unfortunately, due to the largethermal time constants, calorimetric measurements consumea considerable amount of time until the thermal equilibriumis reached. Furthermore, in order to obtain the pure switchinglosses, the conduction losses have to be subtracted from thetotal measured semiconductor losses after the data acquisition.The conduction losses can be calculated based on the DUT’s on-state resistance RDS,on given in the manufacturer’s datasheet.The on-state resistance of the examined 10 kV SiC MOSFETs,however, is strongly depending on the device current, thechip temperature, the current direction (above approximately10 A, the anti-parallel diode chip starts to conduct due tothe flatter characteristic compared to the MOSFET) and evendeviates from device to device for more than 20 % because theMOSFETs at hand are prototype devices.

As can be noticed, both types of measurement methodsshow certain disadvantages in terms of accuracy and separationof switching and conduction losses. However, there is noquantitative comparison of the measurement accuracy ofdifferent measurement methods so far. Therefore, in Section IIof this paper, a short overview of electrical and calorimetricmeasurement methods is given. Based on the performed erroranalysis it becomes clear that electrical measurement methodsknown up to now could lead to tremendously wrong resultsand thus are not suited for soft-switching loss measurements.On the other hand, the accuracy achieved with calorimetricmeasurements strongly depends on the accurate determinationof the conduction losses. Therefore, in Section III a novelcalorimetric measurement method is presented, which alsoeliminates the problem of the switching and conductionloss separation and thus results in a superior measurementaccuracy. In section IV, this method is applied to 10 kV SiCMOSFETs. The obtained soft-switching losses for differentDC-link voltages, currents and gate resistors are presented andcan be utilized for the design of medium-voltage converterssuch as DC/DC stages in Solid-State Transformers [10], amongothers. Section V finally provides a conclusion and an outlook.

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II. EXISTING SWITCHING LOSS MEASUREMENT METHODS

A. Electrical measurement methods

A commonly used electrical method for the measurementof switching losses is the double pulse test which is origi-nally intended for the measurement of hard-switching losses.However, by adapting the modulation scheme, this circuit canalso be used for the measurement of soft-switching losses.Fig. 1 (a) shows the double pulse test circuit which consistsof a half bridge, a split DC-link and an inductor. Furthermore,in Fig. 1 (b) the inductor current iL, as well as the low-side MOSFET’s drain current iS2 and its drain-source voltageuS2 are shown for a single measurement pulse obtained withthe adapted modulation scheme. There, S2 performs a softturn-off for a positive inductor current and a soft (i.e. underzero voltage) turn-on for a negative inductor current. For agiven DC-link voltage UDC and inductance value L1, the pulsetimings and the dead time are adjusted such that the switchedcurrent reaches its desired value and the conduction time of thebody diodes are minimized. In order to obtain the switchingenergies, the drain-source voltage and the drain current ofS2 are multiplied and integrated over the particular switchingtransitions, leading to Eoff and Eon, as indicated in Fig. 1(b). The net switching energy loss (per transition) is finallyobtained via ESW = Eoff + Eon due to the fact that in eachswitching transition, one of the two MOSFETs stores Eoff

while the other feeds Eon back to the DC-link, because Eon

is negative. Since there are two transitions per cycle, each ofthe MOSFETs dissipates the net energy ESW per cycle, suchthat the corresponding switching losses per switch are obtainedvia PSW = ESW · fSW, where fSW denotes the switchingfrequency.

However, this method is subject to large measurement errorsdue to the fact that the soft-switching losses only consist of asmall portion of Eon and Eoff , e.g. for this particular type ofMOSFET (10 kV, 30 A from Wolfspeed), ESW is in the rangeof 10 % of the returned energy |Eon|, i.e. ESW ≈ 0.1 · |Eon|.This means that small errors in the measurement of Eoff andEon can lead to large errors in ESW, as the following exampleshows. Assuming that Eoff ≈ 1.1 · |Eon| and both, Eon andEoff contain a measurement error of ±5 % (which would bealready very accurate, having in mind that Eon and Eoff arisefrom the integration of a multiplication of a voltage and acurrent measurement), the measured worst case switching lossenergy would result in ESW,meas = 1.05 ·Eoff −0.95 · |Eon| ≈

1.05·(1.1 · |Eon|)−0.95·|Eon| = 0.205·|Eon| which comparedto the assumed 0.1 · |Eon| is a relative error of +105 %, i.e.factor two higher switching losses. In the other case, if Eoff ismeasured 5 % too small and |Eon| is measured 5 % too large,the relative error is −105 %, i.e. energy would be generated ineach switching cycle which clearly is not the case. This showsthat already small measurement errors can lead to tremendouslywrong results, thus the double pulse method and probably alsoother electrical measurement methods are not suitable for themeasurement of soft-switching losses of these 10 kV devices.In order to have a quantitative statement of the achievableaccuracy, a detailed error analysis is performed in the following.

Error analysis for electrical soft-switching loss measurementmethods

Figs. 2 (a) & (b) show measurements of the drain-sourcevoltage uS2 and the drain current iS2 of MOSFET S2 inFig. 1 (a) for 8 kV, 10 A soft turn-off and soft turn-on transi-tions, respectively. In order to analyze the influence of the probeskew on the measurement accuracy, the originally measuredcurrent waveform iS2 is delayed for tsk, exemplary 8 ns inthe figure for better visualization. Below the waveforms, thepower and the cumulated energy in S2 are shown for both,the original and the skewed measurements. It can be seen thatthe skewed turn-off energy Eoff,sk is larger than the originalenergy whereas the absolute value of the skewed turn-on energy|Eon,sk| is smaller than the original one. In this case, moreenergy seems to be dissipated in the turning-off switch whereasless energy seems to be regained from the turning-on switch,leading to an increase of the net switching losses. If the delay isnegative, the overlap of voltage and current decreases comparedto its original value, resulting in too low net switching losses.Fig. 2 (c) shows the relative error of the net switching lossesin dependency of the skew for different DC-link voltages and aswitched current of iSwitched = 10 A (since the effect is almostindependent of the switched current). It can be noted that askew of only 2 % of the switching transition’s rise/fall time canlead to a switching loss error of 30...40 %, depending on thevoltage. In this particular case, where uS2 is in the kV-range,the skew of the 20 kV voltage probe (PHV 4002 from PMK incombination with a 12-bit oscilloscope) is mainly a problemdue to the lack of a reference voltage which is necessary forthe deskewing of the probe.

As already mentioned, further sources for measurement er-rors are possible DC offsets and amplitude errors in the voltageand current measurements during the switching transitions.Thereby, especially the 20 kV voltage probe is again causingproblems, because it is not possible to accurately compensatethe probe to a proper low-frequency gain, high-frequency gain(responsible for overshoots) and zero voltage offset at thesame time. Therefore, a compromise between these factors isnecessary which means that in a certain extent these effectsare always present.

Hence, a similar error analysis to the one in Fig. 2 can beperformed concerning DC offsets and amplitude errors, assum-ing a certain DC offset difference or amplitude difference inthe voltage measurement between the Eoff and Eon transitions.Accordingly, if the voltage uS2 is offset free during the turn-ontransition but shows a slight positive offset during the turn-offtransition (which could arise from a non-ideal compensation of

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drain-source voltage measurements for the determination of Eoff and Eon.(b) Relative switching loss error due to a voltage amplitude difference in theuS2 drain-source voltage measurements.

the voltage probe), the integration will lead to an increased turn-off energy Eoff , whereas the turn-on energy Eon is assumed tobe measured correctly for this analysis. Since the net switchingloss energy is again only in the range of 10 % of Eon, theerror in the measurement of Eon and Eoff is strongly amplifiedwhich leads to large switching loss errors in ESW as shownin Fig. 3 (a). Depending on the switched current, an offsetdifference of only 1 % of the DC-link voltage can lead to a

switching loss error of more than 30 %.Similarly, in Fig. 3 (b) the resulting relative switching loss

error caused by an amplitude difference between the voltagemeasurements during the turn-off and turn-on transitions isgiven. As an example, if for the measurement of the soft-switching losses for 7 kV, 2 A, the amplitude of the risingvoltage edge is measured 2 % too large whereas the fallingedge is assumed to be measured correctly, this leads to aswitching loss error of 25 %.

Another source of measurement error can be found in thelimited bandwidth of active and passive probes, since frequencyharmonics which are contained in the original signal and arelocated above the probe’s cut-off frequency, are filterd outand thus could lead to wrongly measured waveforms withe.g. decreased voltage and current slopes. Assuming that thetransfer functions of the probes show first order low-passcharacteristics, the original signal can be reconstructed bytransforming the measured signal into the frequency domain,multiplying it with the inverse of the probe’s low-pass transferfunction and transforming the result back into the time domain.For a voltage probe bandwidth of 100 MHz (according to thedatasheet), it turns out that the measured and reconstructedwaveforms (voltage rise times in the range of 100 ns) arevirtually identical apart from a slight skew which has tobe compensated experimentally in order not to cause largeswitching loss measurement errors, as explained above. Asidefrom the skew, the bandwidths of the utilized voltage probe andcurrent transformer (with a bandwidth > 100 MHz) seem to behigh enough for this application. However, if the measurementbandwidth is reduced, for the measurements at hand the signalquality starts to suffer if the bandwidth falls below 70 MHzwhich in this case is considered as the lower bandwidth limit.The reader should note that for the switching loss measurementof e.g. 600 V GaN switches which can reach voltage risetimes between 10 ns and 20 ns, the probe (and oscilloscope)

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bandwidths have to be higher than 350 MHz to 700 MHz fora sufficient accuracy, respectively.

Besides the described measurement errors, further errorscan be introduced in the post-processing of the measured data.For example the proper selection of the time interval in whichthe switching losses are integrated is aggravated by possibleringing, which in consequence results in wrong turn-on andturn-off switching energies. This is also shown in Figs. 2 (a)& (b), where the current iS2 exhibits certain oscillations atthe end of each switching transient. In case of the turn-ontransition, these current oscillations are, in order to obtain thepower PS2, multiplied with uS2 which has already decayedto zero at that time. Hence, these oscillations vanish in thepower calculation, resulting in a smooth waveform and it isclear where to set the integration limits. However, for theturn-off transition, the current oscillations are multiplied withthe full DC-link voltage, leading also to large oscillations inthe calculated power waveform and thus making the properselection of the integration time more difficult. As an example,Fig. 4 shows a 7 kV, 15 A turn-off transition together with thecalculated power and the resulting switching energy, wheret0 denotes the beginning of the integration interval. As canbe noted, due to the appearing oscillations in the powercalculation, the determination of the integration interval’s endis not clear any more. There are basically two reasonablepossibilities to select this integration limit as denoted withtA and tB. tA corresponds to the first zero crossing of thecurrent and tB is selected such that both, the HF and the LFoscillations have decayed. Accordingly, the obtained turn-offenergies are Eoff,A = 2.83 mJ and Eoff,B = 3.19 mJ, whereasthe corresponding turn-on energy is Eon = −2.45 mJ. Theassociated soft-switching losses are thus ESW,A = 380 µJ and

ESW,B = 740 µJ which results in a relative soft-switchingloss error of 48.6 % or 94.7 %, depending on which value isconsidered as the reference. Hence, the post-processing withthe selection of the integration limits is very crucial and canlead to similar errors as obtained during the measurementprocedure.

Since the impact of the skew, the offset/amplitude difference,the probe bandwidths and the selection of the integration limitson the measurement error is large and might all in all lead toswitching loss errors which are higher than 200 % (although theassumed skew, offset and amplitude difference values are verysmall and fairly realistic), it is concluded that the double pulsemeasurement method is unsuitable for the measurement ofsoft-switching losses. Therefore, other measurement methodswith improved accuracy have been developed in the recentyears as will be shortly described in the following.

In [11], for example, the switching losses are measuredelectrically based on the energy conservation principle duringone switching cycle. It is claimed that, in a buck-type circuit,the switching losses equal the difference between the energysupplied by the DC-link capacitor and the energy stored inthe load inductor, i.e. input power minus output power ofthe bridge-leg. Thus, in contrast to the double pulse method,where a transient MOSFET current is multiplied with a transientMOSFET voltage, with the method proposed in [11], the inputpower is found by multiplying the MOSFET current with theconstant DC-link voltage and the output power is calculatedby multiplying the drain-source voltage of the MOSFET withthe constant output current. Consequently, the skew betweenthe measured MOSFET voltage and current transients is nolonger a problem. Nevertheless, the remaining measurementerrors as well as the integration problem still exist. Furthermore,the output current is only constant if hard-switching lossesare measured; for the measurement of soft-switching losses, atriangular current waveform as shown in Fig. 1 (b) is needed.

In [12] and [13], switching losses have been measuredbased on the opposition method, where in contrast to thedescribed pulsed measurements, a full-bridge is operatedcontinuously with an inductive load. Similar to [11], thesemiconductor losses are obtained by electrically measuringthe DC input power and subtracting the calculated ohmiclosses of the inductor based on the inductor’s AC-resistanceand the measured inductor current. Thus, the AC-resistanceof the inductor has to be well-characterized in terms of itsfrequency and temperature dependency in order to achieve asufficiently accurate measurement of the semiconductor losses.Beneficially, the inductor is realized as an air core inductor(without magnetic material) in order to not include additionalerrors due to core losses into the measurement. Furthermore, thepure switching losses are obtained by subtracting the conductionlosses (calculated based on the on-state resistance RDS,on) fromthe measured total semiconductor losses. However, as alreadymentioned, since the RDS,on shows a certain dependency onthe temperature, current and current direction - especially forthe examined 10 kV SiC MOSFETs - significant measurementerrors can be introduced. Thus this method is not suitable forthe underlying application.

For the sake of completeness, as a combination of electricaland calorimetric switching loss measurement methods, theinductor losses in the opposition method can also be measured

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calorimetrically [14]. On the one hand, this leads to moreaccurate results and on the other hand, a magnetic core materialcan be used. Nevertheless, the switching and conduction lossesstill have to be separated.

B. Calorimetric measurement methodsInstead of measuring the input and output power in a circuit, a

more direct way of measuring switching losses is to exclusivelymeasure the power dissipation of the switches in a calorimetricmanner.

In [15], a half-bridge as part of a synchronous buck converteris operated continuously, whereby the two switches, theirgate drivers and the DC-link capacitor are enclosed in acalorimeter in order to measure the power dissipation. Inthis method, the power dissipation of the gate drives (whichare additionally measured electrically) have to be subtractedfrom the total power in the calorimeter in order to obtain thesemiconductor losses. In [16], a similar calorimetric method ispresented. Thereby, a metal block is attached to the switchesof a half-bridge circuit which is continuously operated. Themetal block acts as a thermal capacitance CTh which is heatedup by the dissipated power of the switches resulting in acertain temperature increase ∆ϑ. Based on the given thermalcapacitance CTh in combination with the time required to heatup the metal block, the dissipated power can be calculated. Theadvantage of this method is that the gate driver losses etc. donot influence the measurement due to the thermal decoupling.Still, the challenge for these methods is the separation of theconduction and switching losses.

In order to separate these losses directly in the measurementinstead of calculating the conduction losses (with error-prone RDS,on values) and subtracting them from the totalsemiconductor losses, a novel calorimetric soft-switching lossmeasurement method featuring a high accuracy is proposed inthe following section.

III. FUNCTIONAL PRINCIPLE OF THE PROPOSEDMEASUREMENT METHOD

The basic idea of the proposed method for the measurementof soft-switching losses is on the one hand to measure thesemiconductor losses calorimetrically and on the other hand tomeasure switching and conduction losses separately. Therefore,as shown in Fig. 5 (a), a third MOSFET S0 has to be insertedin series to either the low-side switch S2 or the high-side

switch S1. In the following it is assumed that S0 is connectedin series to the high-side switch S1, since the cooling pad isconnected to the drain potential of the MOSFET and thus inthis configuration is fixed to a stable voltage. Furthermore, theMOSFET module S0 is mounted on top of a 50×50×100 mmbrass block, which absorbs the dissipated semiconductor lossesand acts as a thermal capacitance CTh. Brass is selected as heatsink material due to its high thermal capacitance per volume.In addition, the brass block is isolated with thermal insulationmaterial in order to minimize the heat transfer to the ambient.Consequently, assuming a constant power dissipation in thesemiconductor device S0 (DUT), the temperature of the brassblock linearly increases with time, whereas the temperatureslope is proportional to the dissipated power of S0. Hence, thepower dissipation of S0 can be calculated as

P =CTh ·∆ϑ

∆τ, (1)

where ∆ϑ denotes the temperature difference and ∆τ equalsthe measurement time. Based on (1), the dissipated powerof S0 can be determined now by measuring the time whichis required to heat the insulated brass block from e.g. 30 Cto 40 C while the system is continuously operated with atriangular inductor current, as already shown in Fig. 1 (b). Apicture of the corresponding 10 kV SiC hardware setup withthe thermally insulated MOSFET is shown in Fig. 6 (a). Thereader should note that the MOSFETs S1 and S2 are alsomounted on separate brass blocks instead of heat sinks in ordernot to influence the measured temperature of the insulatedbrass block with any air stream.

Now, in order to separate the switching and conductionlosses, two different measurements M1 and M2 have to beperformed at the same operating point, i.e. the same switchedcurrent. In the first measurement M1, S0 and S2 are switchingwith a 50 % duty-cycle, while S1 is always turned on. Inthis case, S0 generates both, switching and conduction losses(PS0 = PCond + PSW), which is measured calorimetricallyas described above. After the system has cooled down, inthe second measurement M2 the MOSFETs S0 and S1 swaptheir roles such that S0 is now permanently on and S1 isswitching together with S2 at exactly the same conditions asin the first measurement, i.e. equal switching frequency, deadtime, inductance value and DC-link voltage. In this case, S0

generates conduction losses only, namely exactly the same

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Fig. 6: (a): 10 kV SiC half-bridge with the additional MOSFET S0 on a thermally insulated brass block. (b)-(e): Thermal calibration measurements at constantDC power levels, (b) 10 W, (c) 20 W, (d) 40 W, and (e) 60 W. Each temperature profile is linearized around the measurement temperature range and thecorresponding thermal capacitance is calculated for the given slope. A high linearity can be achieved in the temperature range from 30 C to 40 C and thepower range from 20 W to 40 W. Thus, all the switching loss measurements are carried out in this power and temperature range.

amount as before, if the dead time interval is neglected forthe moment (i.e. PS0 = PCond). Subtracting the two measuredpowers from each other and dividing the difference by theswitching frequency results in the net soft-switching lossesof one switch. It should be noted that effects such as thedependency of the RDS,on on the drain current and the currentdirection don’t influence the measured results due to the factthat both measurements are performed at the same conditions,i.e. exactly equal current waveforms, and thus cancel out whenthe two powers are subtracted. The only parameter which isslightly different in the two measurements is the average chiptemperature. Although in both measurements the temperaturerange from 30 C to 40 C is equal, the thermal resistance RJB

between junction and brass block causes a slight difference ofthe chip temperature, because the power is not the same in thetwo measurements. However, assuming a thermal resistance ofRJB = 0.5 K/W (obtained from a finite element simulation)and a maximum power difference of around 20 W, the worstcase chip temperature difference is 10 K which has a negligibleeffect on the conduction and the switching losses [17]–[19].In order to keep this error small for all measured operatingpoints, the power difference is limited to 20 W by adaptingthe switching frequency and the inductance value as well asutilizing a modified modulation scheme, as described below.

The problem of measuring only conduction losses is thatfor small switched currents the conduction losses are in therange of 1...2 W, whereby the optimum power range for thebuilt setup is between 20 W and 40 W in order to keep theinfluence of the heat transfer to the ambient to a minimum andthus to still obtain a linear increase in temperature. In Figs. 6(b)-(e), the temperature profiles of the insulated brass block fordifferent thermal calibration measurements at different powerratings are shown. For these calibration measurements, thesame hardware configuration (including the copper busbar tothe DC-link, the gate drive, etc.) is used and constant DC-power

is fed into the MOSFET module, which is permanently turned-on, by driving a controlled current through the MOSFET suchthat the constant power levels of 10 W, 20 W, 40 W and 60 Ware reached. It can be seen that the measurements for 20 Wand 40 W are nicely linear between 30 C and 40 C, whereasfor the 10 W measurement, the heat transfer to the ambienthas a significant effect on the temperature profile because thesteady state temperature of the thermally insulated brass blockdecreases with decreasing power dissipation which causes thetemperature slope to flatten already at around 35 C. On theother hand, the 60 W measurement suffers from a nonlinearbehaviour in the lower temperature range due to certain effectsof the heat propagation. Thus, all measurements are performedin the range of 20 W to 40 W. Furthermore, as indicated in thefigure, the linearized thermal capacitance CTh is not constantfor the selected power range. Therefore, the thermal capacitanceis interpolated iteratively from the calibration measurementsfor the purpose of obtaining the correct power dissipation.

In order to overcome the problem that the measurement M2,in which only the conduction losses are measured, generates toolow thermal power feed-in for the brass block to be operatedin its linear region, the modulation scheme is modified asindicated in Fig. 5 (b). Instead of permanently turning on S0

in this measurement, S0 and S1 share the switching lossesamong each other. The share of the switching cycles which areactively switched by S0 is defined as the switching cycle sharek. A value of k = 1 means that S0 is switching continuouslywhile S1 is permanently turned on. As an example, in Fig. 5 (b),k is equal to 0.5 which means that both, S0 and S1 are activelyswitching 50 % of the switching cycles and are turned on for theother 50 % of the switching cycles. For practical reasons in thecase of the 10 kV SiC MOSFETs, S0 and S1 are alternatinglyswitched for 100 cycles. Hence, with this modulation scheme,the dissipated power of S0 can be brought into the mentionedpower range of 20 W to 40 W resulting in a linear temperature

uS1 uS2

iLiS2

iS0 = iS1

uS0

UDC

0

0

isw

-isw

0 t1 t3 t4 T+t1T

s0s1s2 t

t

t

S0

S1

S2

PDT1

PSW,on

PSW,off

PCond

PCond

0

PDT2

PSW,off

PSW,on PCond

0

0

PDT1

PSW,on

PSW,off t

s(t)

Vol

tage

Cur

rent

Los

ses

(a)

C1

C2

S1

S2

L1

iS0

iS1

iS2

S0

iL

uS1

uS0

uS2

C1

C2

S1

S2

L1

iS0

iS1

iS2

S0

iL

uS1

uS0

uS2

[0, t1] [t1, t3]

[t3, t4] [t4, T ]

(b)

t2 t5

C1

C2

S1

S2

L1

iS0

iS1

iS2

S0

iL

uS1

uS0

uS2

C1

C2

S1

S2

L1

iS0

iS1

iS2

S0

iL

uS1

uS0

uS2

Fig. 7: (a) Current and voltage waveforms as well as the gate signals of the three switches and the corresponding share of losses in each time interval. (b)Schematic diagrams showing the current path during the specific time intervals. Shaded symbols do not conduct current.

profile. In Fig. 5 (c), measured temperature profiles at UDC =8 kV and a switched current of 7.5 A (cf. Fig. 1 (b)) are shownfor different values of k. As can be noticed, the measurementsfollow a linear characteristic which means that the thermalsetup is operated in its linear region as desired. Furthermore, inFig. 7 (a) the ideal (simulated) waveforms of the three switches,together with their gate signals and the power dissipationduring the different time intervals are given. The shown sectioncorresponds to a moment in time in which S0 is turned onpermanently whereas S1 and S2 are switching alternatingly.The switched current is chosen rather small in order to illustratethat the dead time interval, in which the output capacitancesof the switches have to be charged/discharged, can occupy asignificant share of a switching period. Actually, since S0 isconnected in series to S1, S0 should only generate conductionlosses during the on-state interval of S1. However, as shownin Fig. 7 (b) during the dead time intervals [0, t1] and [t3, t4],the switched current of S1, which flows through the nonlinearoutput capacitance of S1, also flows through the MOSFETchannel of S0, generating additional conduction losses PDT1

and PDT2 in S0. Due to the symmetric current excitation, thelosses in both dead times are equal (PDT1 = PDT2). As soonas S0 and S1 swap their roles, i.e. when S0 is switching and S1

is turned on, the current through both switches stays exactly thesame with the difference that the switched current now flowsthrough the nonlinear capacitance of S0 instead of flowingthrough the MOSFET channel, generating switching lossesPSW,on and PSW,off , respectively. Averaging these losses overtime and considering the switching cycle share k, the dissipatedpower of the MOSFET S0 can be calculated as

PS0 = k (PSW + PCond) + (1− k) (PDT + PCond)

= k · PSW + PCond + (1− k)PDT, (2)where PSW = PSW,on +PSW,off and PDT = PDT1 +PDT2. Inthe first measurement M1 where k = 1, the power dissipatedin S0 is

PM1 = PS0 (k = 1) = PSW + PCond. (3)In the second measurement M2 where k < 1, the dissipated

power in MOSFET S0 is given asPM2 = k · PSW + PCond + (1− k)PDT

= k · PM1 + (1− k) (PCond + PDT) , (4)whereby PSW = PM1 − PCond is used. Since with k > 0 onlytwo linear independent measurements M1 and M2 but threeunknowns (PSW, PCond and PDT) exist, a further relationbetween PCond and PDT is required in order to solve thesystem of equations consisting of (3) and (4). Therefore, itis assumed that the conduction losses during the dead timeinterval [0, t1] and the conduction interval [t1, t2] (within onehalf-cycle (HC) [0, t2]) arise from an ohmic behaviour of theMOSFET and can be described by Pohm = RDS,on · i2 if thedependency of the RDS,on on the value and direction of thedrain current is neglected at the moment (the resulting erroris negligible as will be shown in the error analysis, since thecurrent exhibits a similar and quasi triangular shape with equalpeak value in both time intervals). Hence, based on the averageconduction losses during the dead time and the conductioninterval referred to one half-cycle, (cf. (5) and (6), respectively),the proportionality factor hP of both contributions is introducedas additional equation, cf. (7).

PDT,HC =PDT

2=

2

T·

t1∫0

RDS,on · i2S0 · dt (5)

PCond,HC =PCond

2=

2

T·

t2∫t1

RDS,on · i2S0 · dt (6)

hP =PDT,HC

PCond,HC=

t1∫0

i2S0 · dt

t2∫t1

i2S0 · dt

=PDT

PCond(7)

Due to the symmetry of the current iS0 within one switchingcycle, the proportionality factor of one switching cycle remainsthe same as the one of a half-cycle, as indicated in (7). SincehP is independent of the RDS,on of the device, hP can be

obtained by measuring the drain current and by solving thegiven integrals in (7). The system of equations can now besolved, whereby the conduction losses are given by

PCond =PM2 − k · PM1

1− k + (1− k) · hP, (8)

and the dead time losses as well as the switching losses arecalculated as

PDT = hP · PCond and (9)PSW = PM1 − PCond, (10)

respectively. Finally, the switching energy per MOSFET canbe determined as

ESW = PSW/fSW. (11)It should be mentioned that for the soft-switching loss measure-ments of the 10 kV SiC MOSFETs, a switching cycle shareof k = 0.5 has been chosen for the second and k = 0.75for a third (verification) measurement, leading to stable andreproducible results.

IV. DISCUSSION AND EXPERIMENTAL RESULTS

The following section analyzes the accuracy of the proposedsoft-switching loss measurement method and discusses possiblelimitations and sources of measurement errors. Finally, themeasured soft-switching losses are presented and discussed.

A. Error analysis for the proposed soft-switching loss measure-ment method

Although calorimetric measurements are probably the mostdirect and accurate way of measuring power dissipations, thereare several effects that have to be considered in order toobtain accurate results. First of all, an accurate and EMI robusttemperature measurement is required. Depending on the devicepackage, the cooling terminal might be on drain potential ofthe MOSFET (which is the case for the 10 kV SiC MOSFETsat hand) such that the metal block including the temperaturesensor is on (floating) potential and is possibly exposed to highdu/dt values which could disturb the temperature measurement.Furthermore, the position of the temperature sensor on themetal block must not change between the calibration andthe switching loss measurements. Otherwise, measurementerrors could arise due to a possibly inhomogeneous temperaturedistribution within the metal block. Generally important for thismeasurement method is the thermal decoupling of the DUTand its brass block from the ambient (by applying thermalinsulation material to the brass block) and especially fromother heat sources contained in the hardware setup (such asthe other switches) in order to prevent undesired heat transfersto the brass block. This is easily possible for the 10 kV SiCMOSFETs at hand due to the specific package design andthe anyway required distances between the switch and otherparts of the circuit for the reason of electrical isolation. Forother device packages and especially lower voltage devices,however, the thermal decoupling of the DUT might be aproblem since a thermal decoupling goes hand in hand with anincrease of the commutation loop inductance which could leadto voltage overshoots and ringing. For the employed 10 kVdevices operated with DC-link voltages in the kV-range, thevoltage overshoot caused by the additional inductance of thethird switch is negligible and not even measurable.

Since the measurement method includes a measurement ofa rather small temperature difference ∆ϑ of e.g. 10 K, as inthis case, the accuracy of the temperature measurement isthe most critical parameter. Assuming a measurement errorof ∆ϑ = ±0.1 K (which corresponds to a relative error of±1 %), a ±2 % error in the thermal capacitance CTh and aperfect time measurement (since time can be measured veryprecisely), the worst case error of a single power measurementis ±3 % (cf. (1), 102% · 101% ≈ 103%). Hence, as a worstcase estimation, if PM1 is measured 3 % too high and PM2 ismeasured 3 % too low, the relative errors in the switching lossesare 5.8 % for the 7 kV, 2.5 A case and 15.5 % for the 7 kV,15 A case, whereby measured values for PM1, PM2 and hP (cf.TABLE I) are inserted into equations (8) and (10) for the erroranalysis in order to give practical examples. Compared to thepreviously analyzed double pulse method, a 10 to 20 timeshigher accuracy can be achieved with the proposed calorimetricmethod. Furthermore, in all of the performed measurements,the k = 0.5 and the k = 0.75 (reference) measurements matchwithin 5 % error which demonstrates that the worst case isnot very likely to occur if the measurements are carried outcarefully and indicates that the accuracy of the method is veryhigh.

As can be noticed, the measurement error increases withincreasing switched currents, thus the switching losses shouldhold the largest share of the overall measured power dissipationin order to keep the measurement accuracy high. This canbe managed by choosing a rather high switching frequency,which however is limited by certain constraints such as thegate drive power capability, the total generated losses onthe metal block (which might be too high and result in anonlinear temperature profile at some point) or the fact that withhigher switching frequencies the dead time interval consumesa major part of the overall switching cycle. Another (limited)possibility to increase the measurement accuracy is to increasethe temperature difference ∆ϑ. However, the temperaturedependency of the MOSFET properties might start playing arole for higher values of ∆ϑ. Furthermore, in the derivation ofthe switching losses from the two measurements M1 and M2,in equations (5)-(7) it is assumed that the on-state resistanceRDS,on is constant. As already mentioned, this is not true forthe 10 kV SiC MOSFETs at hand since there is a dependencyof the RDS,on on temperature as well as on the direction andthe value of the drain current. Hence, the RDS,on doesn’t cancelout in equation (7) and leads to a certain calculation error ofhP. However, the sensitivity of the soft-switching losses oncalculation errors of hP is very low. On the one hand, for lowswitched currents, the switching frequency is selected ratherhigh (cf. TABLE I) in order to increase the switching lossesuntil a total power dissipation between 20 W and 40 W isachieved on the brass block for the mentioned reasons. In thiscase, the dead time consumes a major part of the switchingcycle (hP ≈ 1), thus the corresponding losses PDT are similarto the conduction losses PCond (cf. TABLE I). Due to the highswitching frequency and the low current rating, however, theswitching losses PSW are orders of magnitudes higher thanPDT or PCond. Consequently, calculation errors of hP hardlyinfluence the switching losses. E.g. with the values given forthe 7 kV, 2.5 A measurement in TABLE I, the switching losserror stays below 0.012 %, if for the determination of hP a

TABLE I: Measured and calculated values for the case of low switched current(7 kV, 2.5 A) and high switched current (7 kV, 15 A).

Parameter Value for 7 kV, 2.5 A Value for 7 kV, 15 A

PM1 37.50 W 38.54 W

PM2 18.84 W 26.99 W

hP 1.1883 0.0731

PCond 0.09 W 14.38 W

PSW 37.41 W 24.16 W

PDT 0.10 W 1.05 W

fSW 200 kHz 100 kHz

calculation error of ±10% is assumed. On the other hand,for high switched currents, the charging/discharging of theMOSFET’s output capacitances occurs much faster such thatthe dead time interval is short, i.e. hP ≈ 0. Hence, errors in thecalculation of hP have an negligible impact on the switchinglosses. Assuming again an error of ±10% in hP, for the caseof 7 kV, 15 A (cf. TABLE I), the switching loss error is below0.41 %. This demonstrates the superior numerical conditioningof the described measurement method and shows that the effectof errors in hP on the switching loss measurement error isinsignificant.

B. Measurement results

In order to cover a wide range of applications in which theanalyzed 10 kV SiC MOSFETs could be utilized, soft-switchingloss measurements have been performed for different DC-linkvoltages, currents and gate resistors.

Fig. 8 shows the net measured switching losses of the10 kV SiC MOSFETs for DC-link voltages between 4 kVand 8 kV and switched currents between 2.5 A and 15 A.Unless otherwise noted, the gate resistors are Ron = 20 Ω andRoff = 10 Ω. It is clearly visible that the soft-switching lossesare mainly depending on the DC-link voltage. The dependencyof the soft-switching losses on the switched current is quasilinear with a rather flat and voltage-independent slope. It is alsointeresting that the switching loss curves would not cross theorigin if they were extrapolated towards zero current. Instead,

Sw

itch

ing

Los

ses

[µJ]

Current [A]0 2 4 6 8 10 12 14 16

0

50

100

150

200

250

300

350

400

4 kV

5 kV

6 kV

7 kV

8 kV

7 kV, 5Ω Roff

7 kV, 15Ω Roff

Fig. 8: Calorimetrically measured soft-switching losses of the 10 kV SiCMOSFETs for different DC-link voltages, switched currents and gate resistors.Unless otherwise noted, the turn-off gate resistor is Roff = 10 Ω.

0

2

4

6

8

10

12

14

Time [ns]-100 0 100 200 300 400

0

1

2

3

4

5

6

7

Cur

rent

[A

]

Vol

tage

[kV

]

5 Ω10 Ω15 Ω

RoffiD

vDS

(a)

(b)

Cur

rent

[A

]0

5

10

15

0

2.5

5

7.5

Vol

tage

[kV

]

iD vDS

5 Ω10 Ω15 Ω

Roff

7

Fig. 9: Comparison of switching transitions for different turn-off gate resistorsat UDC = 7 kV for (a) iSwitched = 10 A and (b) iSwitched = 15 A.

the curves would show an offset even for very low currentswhich means that there are voltage-dependent residual soft-switching losses which cannot be avoided. Future work willanalyze the source of these residual soft-switching losses inmore detail in order to gain a better understanding of theunderlying loss mechanisms. Compared to the hard-switchingoperation of these 10 kV SiC MOSFETs, cf. [20], factor 100lower switching losses can be achieved by applying soft-switching techniques which allows for much higher switchingfrequencies, efficiencies and power densities. Comparing thethree 7 kV curves with different turn-off gate resistors Roff inFig. 8, it is evident that a turn-off resistor of Roff = 10 Ω leadsto the lowest soft-switching losses. The reader should notethat the turn-on resistor does not or hardly influence the soft-switching losses. For the case of Roff = 15 Ω, the dependencyon the switched current shows a clear trend towards higherlosses for higher switched currents which is an indication forincreased channel losses due to a larger overlapping of thevoltage and current transients during turn-off. This behaviourcan be explained by analyzing the switching transitions givenin Fig. 9 (a) for 7 kV, 10 A and in Fig. 9 (b) for 7 kV, 15 A.While at 10 A all turn-off gate resistance values Roff result inthe same voltage slope, the turn-off transition at 15 A is clearlyslowed down in the beginning if a turn-off gate resistanceof Roff = 15 Ω is used. Hence, at higher switched currents,the higher gate resistor leads to a stronger overlapping of theMOSFET voltage and channel current transients and thus tohigher switching losses. On the other hand, a low turn-offgate resistance of 5 Ω results in stronger oscillations in thedrain current due to parasitic inductances introduced by the

semiconductor packaging and thus cause higher soft-switchinglosses. Consequently, for the 10 kV SiC MOSFETs at hand, theoptimal turn-off gate resistance is Roff = 10 Ω, which couldbe probably slightly decreased if another package with lowerparasitic inductances and/or with Kelvin source connection isused. However, even though the packaging can be improved,a substantial reduction of the soft-switching losses is notexpected.

V. CONCLUSION

In this paper, an accurate calorimetric method for themeasurement of soft-switching losses of 10 kV SiC MOSFETsis presented. It is shown that electrical measurement methodssuch as the double pulse test can lead to large measurementerrors and thus are unsuitable for the characterization ofthe utilized 10 kV SiC MOSFETs and other fast-switchingdevices. On the other hand, with calorimetric measurementmethods, the total semiconductor losses can be measuredaccurately. However, the calorimetric methods known up tonow are not able to separate the switching losses from theconduction losses without calculations which could result againin certain measurement errors. Therefore, in this paper anovel calorimetric measurement method is proposed whicheliminates this disadvantage. The proposed method introducesan additional switch into the well-known double pulse circuitwhich in combination with a novel modulation scheme enablesto measure the conduction and switching losses separatelywith a high accuracy. The error analysis for the proposedmeasurement method shows that the worst case error is 15 %which is a factor 10 to 20 times more accurate than theaccuracy obtained with the double pulse method. Based on theproposed measurement method, the soft-switching losses of theexamined 10 kV SiC MOSFETs for different DC-link voltages,switched currents and gate resistors are presented and analyzed.Compared to the hard-switching losses of these 10 kV SiCMOSFETs, the soft-switching losses are around 100 times lowerwhich allows for a higher system performance. However, thesoft-switching losses are still relevant and have to be consideredin the converter design, especially for applications utilizinghigh switching frequencies. In future work, the soft-switchinglosses of the 10 kV SiC MOSFETs will be analyzed further inorder to figure out the underlying loss mechanisms.

ACKNOWLEDGEMENT

The authors would like to acknowledge Wolfspeed, aCree Company, for granting access to prototype 10 kV SiCMOSFETs.

This research project is part of the National ResearchProgramme ”Energy Turnaround” (NRP 70) of the Swiss Na-tional Science Foundation (SNSF). Further information on theNational Research Programme can be found at www.nrp70.ch.

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