# Using IGBT thermal calculations to optimize power designs

Calculating the junction temperature for most semiconductor devices is a well known process. Typically, the case or lead temperature is known. The power dissipation of the die is measured and multiplied by the theta for the die to package to calculate the temperature rise from the case to the junction. This method applies to all single die packages including BJTs, MOSFETS, diodes and thyristors. For multiple die IGBTs, however it proves to be insufficient.

Some IGBTs are single die devices, either with a monolithic diode or no diode; however, the majority of them come with a co-packaged diode. Most manufacturers provide a single theta for the junction-to-case thermal resistance calculation. This is a simplified approach to calculating the die temperature and will lead to incorrect analysis of the two junction temperatures involved.

For multiple die devices, the thetas are typically different and the power dissipation of the two dice is also different, requiring a separate calculation for each. In addition, each die provides thermal energy to the other, so the interaction must also be considered.

**Figure 1: IGBT & Diode Mounted on Lead Frame of a TO-247 Package**

**Power Calculations**

The voltage and current waveforms must be multiplied and then integrated to measure the power. Although the simple multiplication of the voltage and current will give the instantaneous power, it is not simple to derive the average power from this, so the integral is used to convert this to energy. The sum of the energies of the various losses can then be used to calculate the average power across the waveform.

It is important to define the boundaries of the turn-on, conduction and turn-off losses before starting as it would create errors in the measurement if some areas of the waveform were left out or alternately if some areas were duplicated. For this analysis we will use the 10% points; however, although this is a common method of doing this, other levels such as 5% or 20% can be used, as long as they are applied to all of the components of the losses.

Normally the waveforms are taken at the peak of the sine wave that is being formed. This is the peak power dissipation. The average power is 50% of this value (factored by 2 for the voltage and 2 for the current).

In general, at the peak of the voltage waveform, the IGBTs will be conducting and not the diodes. To measure the diode losses, a reactive load, such as a motor is required and the waveform needs to be captured when the current is in the reactive state i.e. being fed back into the source.

**Figure 2: IGBT Turn on Waveforms**

At turn-on, the losses should be measured, beginning at the 10% IC level and ending at the 10% VCE point. These levels are fairly standard although somewhat arbitrary. Other points may be used if desired. Regardless of the levels chosen to measure the various intervals, it is important to be consistent so that data taken for various devices can be compared based on the same criteria. The power is calculated from the oscilloscope waveforms. Since it is not constant, and the average power is required, the integral of the power waveform must be calculated. This is shown at the bottom of the trace and is 674.3 Ws (or Joules) in this case.

**Figure 3: IGBT Turn-off Waveforms**

Similarly, turn-off losses are measured as shown below.

**Figure 4: IGBT Conduction Loss Waveforms**

The conduction losses are measured in a similar manner. They should start at the end point of the turn-on losses and end at the beginning of the turn-off losses. This can be difficult to measure exactly, since the time scale for the conduction losses is much longer than that for the switching losses.

**Figure 5: Diode Turn-off Waveforms**

Diode turn-on loss data must be taken during a portion of the cycle at which the current is in a reactive mode so that the diode is conducting. It is normally measured from the 10% points of the peak, negative, reverse conduction current.

**Figure 6: Diode Conduction Loss Waveforms**

The diode conduction losses are the last loss component required to calculate the total losses in the IGBT packages. When all of the losses have been measured, they need to be applied to the overall waveform based on the duration of that mode of operation. This is described in detail in the ON Semiconductor application note AND9140. When the energies are added and factored, they can be added together and multiplied by the switching frequency to obtain the power losses for the diode and IGBT.

**Die Temperature Calculations**

In order to accurately calculate the temperatures of the two dice in the package, it is important to consider the self-heating thermal interaction between the two. This requires three constants: The diode theta, the IGBT theta and the die interaction Psi. Some manufacturers publish a single theta for the package, in which case the die temperatures are only an estimate and in practice accuracy can vary greatly.

The charts for the IGBT and diode thetas are included in the datasheets for ON Semiconductor devices. The steady-state thetas are given on the charts shown in Figures 7 and 8. These are 0.470 °C/W for the IGBT and 1.06 °C/W for the diode. There is one other thermal coefficient required for the calculations, and that is the Psi which is the thermal interaction constant between the two dice. Testing has shown that for the TO-247, TO-220 and similar packages, it is about 0.15 °C/W, which is what will be used in the following example.

**Figure 7: IGBT Transient Thermal Impedance**

**Figure 8: IGBT Transient Thermal Impedance**

The die temperature for the IGBT can be calculated from the following equation:

TJ-IGBT = (PIGBT RIGBT) + (PDIODE Psi ) + TCASE

Assuming the following conditions:

TC = 82°C

RJC-IGBT = 0.470°C/W

PD-IGBT = 65 W

PD-DIODE = 35 W

Psi-interaction = 0.15°C/W

The temperature for the IGBT die is:

TJ-IGBT = (65 W 0.470°C/W)+(35 W 0.15°C/W ) + 82°C

TJ-IGBT = 118°C

Diode Die Temperture

RJC-diode = 1.06°C/W

TJ-DIODE = (PDIODE RDIODE) + (PIGBT Psi) + TCASE

Likewise, the temperature for the diode die is:

TJ-DIODE = (35 W 1.06°C/W ) + (65 W 0.15°C/W ) + 82°C

TJ-DIODE = 129°C

**Peak Die Temperatures**

The temperatures calculated in the above analysis are for the average die temperature. This varies throughout the cycle and the peak die temperatures can be calculated by using the thermal transient curves in Figures 7 and 8. For this, it is necessary to read the transient information from the curves. If the line frequency is 60 Hz, one half cycle would have a period of 8.3 ms. So, using the 50% duty cycle curve for an 8.3 ms period, the Psi values are:

IGBT 0.36 °C/W

Diode 0.70°C/W

TJpk-IGBT = TJ-IGBT + (PIGBT RIGBT)

The peak temperature for the IGBT die would be:

TJpk-IGBT =118°C+ (65 W 0.36°C/W )

TJpk-IGBT = 141°C

And the peak diode die temperature would be:

TJpk-DIODE = TJ-DIODE + (PDIODE RDIODE)

TJpk-DIODE =129°C+ (35 W 0.70°C/W )

TJpk-DIODE =154°C

**Conclusion**

Evaluating the temperature of the semiconductor dice in a multi-die package requires additional analytical techniques compared to those applicable for single die devices. It is necessary to have both DC and transient thermal information available from both dice to accurately calculate the die temperatures.

It is also necessary to measure the power dissipation in both devices and analyze those losses across the entire half sine waveform. This analysis will add confidence that the semiconductors in the system will be operating at a safe and reliable temperature for optimal system performance.