# Comparison of the electrical and thermal method for determining the power losses of a QDPAK-MOSFET

Marcus Praast, Christopher Zeidler, Thomas Komma

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Marcus Praast, Christopher Zeidler, Thomas Komma. Comparison of the electrical and thermal method for determining the power losses of a QDPAK-MOSFET. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0021 . hal-05074020

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# Comparison of the electrical and thermal method for determining the power losses of a QDPAK-MOSFET

Marcus Praast, Christopher Zeidler, Thomas Komma

FTZ Leipzig e.V., at Leipzig University of Applied Sciences

Karl-Liebknecht-Strasse 132

04277 Leipzig, Germany

+49 / (0) - 341 3076 1101

marcus.praast@htwk-leipzig.de, christopher.zeidler@htwk-leipzig.de

https://ftz-leipzig.de/

## Acknowledgements

This article is funded by the German Federal Ministry for Economic Affairs and Climate Action within the program elektro-mobil as a part of the project noLIMIT.

M. Praast and C. Zeidler contributed equally to this work.

## Keywords

«Power losses», «Switching and conduction losses», «MOSFET», «Double pulse test», «Measurements».

## Abstract

Due to increasingly higher switching speeds, the electrical determination of power losses in power electronics is more challenging. In this paper, a double-pulse test is performed to determine the switching losses of a MOSFET. Additionally, it presents an approach for the thermal determination of power losses in semiconductors, which significantly reduces measurement duration from minutes to seconds. The accuracy of the thermal method is demonstrated, with a deviation of 0.16% between the measurement results and those obtained with a power analyzer. Beyond its high accuracy, the thermal method offers high resolution, enabling the detection of even the smallest differences in power losses. Furthermore, a comparison between electrical and thermal power loss determination is provided.

## Introduction

The introduction of new semiconductor generations, higher switching frequencies and shorter switching times are becoming more common in power electronic systems, making it more challenging to determine the switching losses in semiconductors.

Traditional measurements using the double-pulse test (DPT) are becoming increasingly complex as shown in [1]. Current and voltage sensors require very high bandwidths and proper compensation. Additionally, these sensors introduce parasitic elements into the setup, which affect the signal waveforms of the switching process [2, 3]. Furthermore, the steep switching slopes cause oscillations that complicate the measurement of current and voltage. The manual selection of the interval limits for the switching process adds another source of error [4]. Operating converters at switching frequencies of several hundred kilohertz magnifies these measurement errors, thereby increasing the overall error.

Alternatively, power losses can be determined using calorimetric methods. According to [5], there are numerous measurement systems that can determine the total power loss of power electronics. Many of these calorimeters are only suitable for power losses greater than 10 W, and they often require measurement durations of several hours.

To determine the power losses in modern power semiconductors, this paper uses the approach from [6], which has also been applied in studies by [4, 7-9]. This method is combined with an infrared camera (IR-camera), which measures the temperature rise at the case instead of the heatsink like in [4, 7-9]. This combination reduces the measurement duration from minutes to seconds and allows power losses in semiconductors to be measured independently of switching speed, current and voltage measurement.

The following paper presents a comparison between electrical measurement and the thermal approach for determining power losses of a MOSFET. This MOSFET is operating in an exemplary buck converter with a maximum output power of 2.5 kW and switching frequencies up to 300 kHz.
# Theory of determining power losses

## Electrical method

Power losses in semiconductor switches can be divided into switching losses and conduction losses. The electrical determination of switching losses in hard-switching topologies known as DPT is a standard test procedure today [7]. The test circuit used in this paper contains a MOSFET as switch and is shown in Fig. 1.

<figure><img src="image_2.png" /><figcaption>Fig. 1: Double-pulse test (DPT) circuit, current measurement with resistor</figcaption></figure>

To determine the energy loss across the switch, the drain-source voltage $v_{DS}$ and the drain current $i_D$ are detected. Equations (1) and (2) can be used to calculate the energy losses for turn-on $E_{on}$ and turn-off $E_{off}$ of the device.

Both the turn-on and the turn-off process are defined as shown in Fig. 2 und Fig. 3.

$$E_{on} = \int_{t_1}^{t_2} i_D \cdot v_{DS} dt \quad (1)$$

$$E_{off} = \int_{t_3}^{t_4} i_D \cdot v_{DS} dt \quad (2)$$

<figure><img src="image_3.png" /><figcaption>Fig. 2: Definition of switching intervals for turn-on</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 3: Definition of switching intervals for turn-off</figcaption></figure>

By multiplying the calculated switching loss energies for one switching operation by the desired switching frequency $f_{switch}$, the expected power loss for turn-on $P_{on}$ and turn-off $P_{off}$ is obtained, as shown in equations (3) and (4).

$$P_{on} = E_{on} \cdot f_{switch} \quad (3)$$

$$P_{off} = E_{off} \cdot f_{switch} \quad (4)$$

A conduction loss $P_{RDS(on)}$ occurs during the conduction phase ($t_2$ to $t_3$) of the switch. According to the equation (5), it can be determined from the RMS value of the drain current $I_{D,RMS}$ and the drain-source on-state resistance $R_{DS(on)}$.

$$P_{RDS(on)} = I_{D,RMS}^2 \cdot R_{DS(on)} \quad (5)$$

Losses during the switch off-time are neglected. The total losses $P_{total}$ in the switch consist of the sum of turn-on, turn-off and conduction losses as shown in (6).

$$P_{total} = P_{on} + P_{off} + P_{RDS(on)} \quad (6)$$

## Thermal method

In contrast to the conventional calorimetric method [5], this paper measures power losses based on the temperature rise rates of the device under test (DUT), a technique first implemented by [6] and subsequently utilized in studies by [4, 7–9]. In this paper the DUT is a MOSFET.

The theory of this thermal method is based on the equivalent circuit of Foster and equation (7), which describes the behaviour of the temperature $T$ at the junction when a power loss $P_{loss}$ is applied. The time-constant $\tau_n$ is defined by the thermal resistance $R_{th,n}$ and capacitance $C_{th,n}$ per equation (8).
$$T(t) = P_{\text{loss}} \sum_{n=1}^{m} R_{\text{th},n} \cdot \left(1 - e^{-\frac{t}{\tau_n}}\right) \quad (7)$$

$$\tau_n = R_{\text{th},n} \cdot C_{\text{th},n} \quad (8)$$

Differentiating equation (7) with respect to time equates (9). According to the circuit of Foster, the temperature heating curve follows a sum of e-functions in which a constant temperature rise $\frac{\Delta T}{\Delta t}$ can be assumed at the beginning ($t = 0$).

By setting $t = 0$, we obtain equation (10), which demonstrates that the rate of temperature rise $\frac{\Delta T}{\Delta t}$ is directly proportional to the equivalent thermal capacity $C_{\text{th}}$ and the power loss $P_{\text{loss}}$.

$$\frac{dT}{dt} = P_{\text{loss}} \sum_{n=1}^{m} \frac{1}{C_{\text{th},n}} \cdot e^{-\frac{t}{\tau_n}} \quad (9)$$

$$\frac{\Delta T}{\Delta t} = P_{\text{loss}} \sum_{n=1}^{m} \frac{1}{C_{\text{th},n}} = \frac{P_{\text{loss}}}{C_{\text{th}}} \quad (10)$$

This paper focuses on determining the power losses of a MOSFET. It is important to note that the temperature heating curve can only be considered linear at the beginning if the measurement is conducted at the junction. Instead, the measurements are taken at the case of the MOSFET, as the junction is located within the MOSFETs package and therefore would need to be exposed. Measuring at the case causes a delay in the heating curve, which occurs due to the thermal RC-network within the MOSFET. The linear range begins, as soon as the delay ends, as shown in Fig. 4. Therefore, an interval of the curve must be determined where the approximately linear range is.

<figure><img src="image_5.png" /><figcaption>Fig. 4: Exemplary temperature heating curve of a DUT induced by an applied power loss</figcaption></figure>

To determine an unknown power loss $P_{\text{loss}}$ of a DUT, a reference measurement is first carried out in the estimated power loss range. For the

reference measurement a known power loss is forced through the MOSFET. The temperature rise rate of the reference $\frac{\Delta T}{\Delta t_{\text{ref}}}$ on the one hand and the reference power loss $P_{\text{ref}}$ on the other are recorded. After that the unknown power loss $P_{\text{loss}}$ must be induced, and the measurement of the temperature rise rate $\frac{\Delta T}{\Delta t_{\text{loss}}}$ must be taken.

According to (11) and (12) the power losses also depend on their $C_{\text{th}}$.

$$P_{\text{ref}} = C_{\text{th,ref}} \cdot \frac{\Delta T}{\Delta t_{\text{ref}}} \quad (11)$$

$$P_{\text{loss}} = C_{\text{th,loss}} \cdot \frac{\Delta T}{\Delta t_{\text{loss}}} \quad (12)$$

As stated in equation (13), the thermal capacity $C_{\text{th}}$ depends on the temperature.

$$C_{\text{th}} = f(T) \quad (13)$$

However, according to the law of Dulong and Petit, the heat capacity of solids remains nearly constant for temperatures above 300 K, provided the amount of substance is constant [10]. In order to capitalise on this property, the investigations concentrate on a narrow temperature range of just a few Kelvin, thereby ensuring that $C_{\text{th}}$ remains almost constant.

In both the reference measurement and the loss measurement with the unknown power loss $P_{\text{loss}}$, this paper ensures the same initial temperature and determines the rise rate within the same temperature range $\Delta T$. This approach guarantees that the thermal capacity of the DUT can be treated as a constant in both cases.

Therefore, (11) and (12) can be set in relation to each other, allowing $C_{\text{th}}$ to be removed from the equation. With that, the unknown power losses $P_{\text{loss}}$ of the DUT can be easily calculated with (14).

$$\frac{P_{\text{loss}}}{P_{\text{ref}}} = \frac{\frac{\Delta T}{\Delta t_{\text{loss}}}}{\frac{\Delta T}{\Delta t_{\text{ref}}}} \quad (14)$$

Additionally, for reference and loss measurement, the same conditions must be ensured, i.e. no changes to measurement setup or DUT.
Dependency of power losses

To determine power losses, it is crucial to
consider their temperature dependence. As the
R<sub>DS(on)</sub> is a thermally sensitive resistor, the
dissipated power will also change with
temperature.

In order to compare the electrical and thermal
methods, it is essential that the junction
temperatures are within the same temperature
range. In the double pulse test, the junction
temperature can be considered constant because
the energy dissipation caused by the double pulse
results in virtually no heating.

In the thermal measurement, however, the
unknown power dissipation is impressed and
causes the junction to heat up. Since the
evaluation takes place in a brief time range, the
temperature change within this range is only a
few Kelvin. The R<sub>DS(on)</sub> can therefore be
considered as almost constant for the evaluation.

Measurement setup

Electrical method

A hard-switching buck converter with an output
power of 2.5 kW was designed for the
comparison of the measurements presented.
Fig. 5 shows the circuit diagram of the converter.
By short-circuiting the output capacitor C<sub>out</sub> and
inserting a current sensing resistor R<sub>sense</sub> in series
with the switch S, the measurement can be
conducted in the DPT as shown in Fig. 1. All
measurements presented in this paper are carried
out using the consistent experimental setup. This
approach ensures that all tests are performed
under nearly identical conditions, including the
gate drive circuit and power loop inductance.

<figure><img src="image_6.png" /><figcaption>Fig. 5: Schematic of the buck converter</figcaption></figure>

The planned maximum switching frequency of
the converter should be 300 kHz. As shown in
[11] and [12], parasitic stray inductances and
capacitances have a significant influence on the

transistor switching speed. For this reason, a
switch in a SMD package with top-side cooled
technology (TSC) is chosen. SMD packages have
a lower intrinsic stray inductance than through-
hole devices and offer reduced manufacturing
costs [13]. TSC technology allows the thermal
and electrical path to be decoupled [14]. The
elimination of large areas for heat dissipation on
the printed circuit board (PCB) and the careful
layout of the board allow the stray inductance of
the power loop to be reduced to a minimum.
Fig. 6 shows the developed converter, for which
an IPDQ60R045CFD7 (Infineon CoolMOS,
650 V, 52 A) in a QDPAK package is chosen.
The freewheeling diode was an
IDDD16G65C6XT (Infineon, SiC Schottky,
650 V, 16 A) in a DDPAK package. The study is
conducted under an input voltage of V<sub>in</sub> = 400 V
and a gate drive signal with a duty cycle of 50%
to provide an output current of 10 A. The
inductance used was 180 µH. A driver
1ED3124MC12H with R<sub>gate(on)</sub> = 8.2 Ω and
R<sub>gate(off)</sub> = 12 Ω is used to drive the switch via its
Kelvin source connection. The turn-on gate
voltage is set to 15.5 V.

<figure><img src="image_7.png" /><figcaption>Fig. 6: Converter for loss measurement with top-side cooled (TSC) semiconductor on the backside, load inductance, input and output capacitors and drive circuit</figcaption></figure>

The measurement system used comprises an
RTA4004 oscilloscope with a bandwidth of
1 GHz. The drain current of the switch is captured
in the DPT using a coaxial measurement resistor
SSDN-015, which has a bandwidth of 1.2 GHz. A
passive voltage probe RT-ZP10 (1:10 attenuation
ratio, bandwidth 500 MHz) is employed to
measure the drain-source voltage. This passive
probe is inserted into a corresponding PCB
adapter located right next to the switch. Fig. 7
shows the DPT hardware setup used to determine
power losses.
<figure><img src="image_8.png" /><figcaption>Fig. 7: Double-pulse test hardware setup</figcaption></figure>

## Thermal method

The thermal measurement setup is shown in Fig. 8. It consists of a measurement chamber, an IR-camera, a power analyzer, an electronic source, a sink and the buck converter. The source is used to apply a constant DC-current $I_{ref}$ in the reference measurement and to function as a voltage source in buck converter operation. The sink ensures that the same output current is drawn at all switching frequencies in buck converter operation. The measurement chamber is designed to maintain a stable ambient temperature $T_A$ for the DUT. Additionally, the reference and the loss measurement are intended to start at the same ambient temperature $T_A$.

<figure><img src="image_9.png" /><figcaption>Fig. 8: Measurement setup for the thermal method of determining power losses</figcaption></figure>

During the reference measurement, a constant DC-current $I_{ref}$ is applied to the MOSFET. The resulting power loss is recorded using the power

analyzer Yokogawa WT5000, which has an overall DC-measurement accuracy of ±0.03%. Both the current $I_{ref}$ through the MOSFET and the voltage $v_{DS}$ across the MOSFET are measured. Due to the nonlinear and temperature-dependent behaviour of $R_{DS(on)}$, the reference power $P_{ref}$ varies. The measurement is therefore sampled and averaged every 10 ms, taking into account only those power losses that occur within the specified temperature range for evaluation.

The chosen IR-camera is the infratec 8300hp, which features a frame rate of 1000 Hz in quarter-frame mode. The high frame rate is crucial due to the relatively small thermal capacity of the MOSFET case, which causes high temperature rise rates. The temperature rise of the case can be measured through a pre-planned hole in the PCB, which is shown in Fig. 9. The MOSFET of the buck converter is placed in the centre of the bottom-side of this hole.

In the studies described in [4, 7–9], the temperature rise rates were measured at the heatsink of the DUT. Due to the high thermal capacitance of these heatsinks, these methods require measurement times of several minutes. The measurement time of the proposed method, however, decreases to seconds due to the much smaller thermal capacitance of the case.

<figure><img src="image_10.png" /><figcaption>Fig. 9: Setup for measuring *T* of DUT</figcaption></figure>

## Demonstration of the accuracy of the thermal measurement setup

The following measurement is intended to demonstrate the accuracy of the thermal measurement setup.

Two constant DC-currents will be applied to the DUT. In both cases, the power loss is determined using the power analyzer. Simultaneously, the rise rates of the induced power losses are measured with the IR-camera. After that the measurement difference between the power analyzer and the thermal method can then be determined.
As DUT the MOSFET of the buck converter was used. First, a constant DC-current $I_1$ = 12.5 A was applied to the DUT. The second measurement was conducted with a constant DC-current $I_2$ = 13 A. In Fig. 10, the upper graph shows the recorded heating curves for both currents. In addition, the lower graph displays the curves within the temperature range for evaluation which was set between 26°C and 28°C. Within the temperature range, the temperature rise rate for the current $I_1$ is $\frac{\Delta T}{\Delta t_1}$ = 4.31 K/s and for $I_2$ it is $\frac{\Delta T}{\Delta t_2}$ = 4.67 K/s.

<figure><img src="image_11.png" /><figcaption>Fig. 10: Temperature heating curves for the demonstration of the accuracy of the thermal setup</figcaption></figure>

The losses for $I_1$ = 12.5 A and $I_2$ = 13 A, as measured by the power analyzer, are shown in Fig. 11. To calculate the power losses using the thermal method, equation (14) is used. The power loss for $I_2$ can be calculated by the thermal method with the power loss of $I_1$ as reference. This corresponds to a difference of 0.15% between the averaged measurements of the power analyzer and the thermal method. Conversely, determining the power loss of $I_1$ using the power loss of $I_2$ as reference, corresponds to a difference of 0.16% compared to the power analyzer.

<figure><img src="image_12.png" /><figcaption>Fig. 11: Measured power losses for both currents with the thermal method and the power analyzer</figcaption></figure>

## Results and Comparison

In this section, a comparison of the electrical and thermal power loss determination methods for a hard-switching MOSFET in a buck converter providing an output current of 10 A is presented. To demonstrate the applicability of the thermal measurement method, the experiment was carried out at switching frequencies of 100, 200 and 300 kHz.

A DPT is performed to determine the switching losses. The signal waveforms of the switching events are shown in Fig. 12 and Fig. 13. In addition, the power losses and the energy losses for the switching events have been calculated and plotted. The waveforms shown were recorded at an ambient temperature $T_A$ of 25°C.

<figure><img src="image_13.png" /><figcaption>Fig. 12: Switching waveforms at turn-on</figcaption></figure>

According to the established definitions of the switching intervals, the energy loss for the turn-on process $E_{on}$ is determined to 36.6 µWs, while
the corresponding value for the turn-off process $E_{\text{off}}$ is 13.5 µWs.

<figure><img src="image_14.png" /><figcaption>Fig. 13: Switching waveforms at turn-off</figcaption></figure>

To determine the conduction losses of the MOSFET in the presented setup, a DC-current of 10 A was applied to the switch. The $R_{\text{DS(on)}}$ was measured to be 38 mΩ.

The RMS value of the drain current has been calculated for each switching frequency with respect to the actual measured waveform, which is nearly trapezoidal. For a switching frequency of 100 kHz, the determined RMS value $I_{\text{D,RMS}}$ is 7.18 A, while it is 7.20 A for 200 kHz, and 7.36 A for 300 kHz.

Equations (1) and (6) can be used to determine the expected losses at different switching frequencies. Fig. 15 illustrates the electrically determined power losses, represented by the light blue, dark blue and lilac bars.

Furthermore, the determination of the MOSFET power loss using the thermal method is described below. Temperature heating curves were recorded for switching frequencies of 100, 200, and 300 kHz in buck converter operation. Additionally, corresponding reference measurements were conducted. It is ensured that the reference and the buck converter operation measurements have the same conditions.

Fig. 14 shows the measured heating curves of the MOSFET in buck converter operation and the reference measurements. The temperature ranges used for the evaluation are displayed.

<figure><img src="image_15.png" /><figcaption>Fig. 14: Temperature heating curves of the buck converter for different switching frequencies and the corresponding reference measurements</figcaption></figure>

With the given temperature rise rates, the reference power losses and equation (14), the power losses in buck converter operation can be calculated. The results for the different switching frequencies are shown in Fig. 15. The determined power losses of the thermal method are displayed by the orange bars.
<figure><img src="image_16.png" /><figcaption>Fig. 15: Comparison of electrical and thermal determined losses</figcaption></figure>

After evaluating both methods, it was observed that the thermal method determined higher power losses. Due to the prior determination of the measurement accuracy of the setup, it can be assumed that the losses in buck converter operation correspond to those determined by the thermal method. This confirms that electrical determination of power losses becomes increasingly complex with higher MOSFET switching speeds, particularly noticeable in the measurement of switching losses. In contrast to the electrical determination of switching losses, the thermal method is independent of current and voltage measurements.

It is important to note that the evaluation of power losses using the thermal method was performed at temperatures above those in the double pulse. This discrepancy can be attributed to the thermal measurement of the MOSFET case, which introduces a delay in the heating curve. As a result, it becomes challenging to compare different measurements at identical temperatures, as the linear region of the heating curve occurs within different temperature ranges.

This results in higher power losses in comparison with the electrical method, due to the thermo-sensitive $R_{DS(on)}$. Nevertheless, given that the evaluated temperature range is merely a few Kelvin above that of the ambient temperature in the double pulse, the resulting differences in losses are negligible.

Further, it is noteworthy that the evaluation of the temperature range in the thermal method occurs within the first 1-2 seconds, thus limiting the measurement duration to a few seconds.

## Conclusion

This paper presents an approach for the thermal determination of power losses in semiconductor devices. The method is based on the recording of the temperature rise rates for a reference measurement and a loss measurement using an IR-camera. By performing the loss measurement at the case of the MOSFET, its duration could be reduced to seconds per measurement instead of minutes.

As part of the research, the measurement method was successfully applied to a buck converter operating at a high switching frequency. A measurement with a double-pulse test leads to lower values for the occurring power losses. It is therefore assumed that losses occur in the MOSFET, which are difficult to measure using the electrical method. Moreover, a complicated measurement setup and high-quality voltage and current probes are required to obtain accurate results.

The advantage of the thermal method, on the other hand, is its independence of the switching speed, current and voltage measurements. Furthermore, the accuracy of the thermal method was demonstrated, with a deviation of 0.16% between the measurement results and those obtained with a power analyzer. In addition to high accuracy, the thermal method also provides high resolution of power losses. This means that even the smallest differences in power loss can be detected. As a result, the thermal method is well suited to determining losses that would be difficult to measure using conventional electrical methods.

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