Estimating TJ: Calculation Example Using Transient Thermal Resistance

Up until now, examples of calculations to estimate T_J when power consumption is constant have been presented. Here, however, a method of calculation and example are described for conditions in which there is a transient increase in power consumption.

Example of Transient Fluctuation

As a result of transient fluctuation of the input voltage, the power consumption also fluctuates in a transient manner, and consequently it can easily be imagined that T_J will fluctuate as well. In such cases, the transient thermal resistance is used to calculate T_J by adding the transient temperature rise to the steady-state T_J.

About Transient Thermal Resistance

Strictly speaking, T_J rises (heat is generated) from the time power is input, and stabilizes after a certain time. The normal thermal resistance θ_JA is the value obtained by dividing the steady-state heat generation by the power consumption. On the other hand, the transient thermal resistance has a time-based parameter. In the example of Fig. 1, the transient thermal resistance is the value obtained by dividing the heat generation when V_IN has changed from 13.5 V to 35 V and 3 seconds have elapsed by the changed power consumption.

Fig. 2 shows a transient thermal resistance example. From the graph, the longer the time in the transient state (the longer the pulse width), the greater is the transient thermal resistance Z_TH, and we see that when about 300 seconds have elapsed, the thermal resistance becomes constant.

An Example of Calculation to Estimate T_J Using Transient Thermal Resistance

As stated above, T_J is determined by adding the transient temperature rise calculated using the transient thermal resistance to the steady-state T_J. As the procedure used, first the steady-state and the transient power consumption values are calculated, and then the thermal resistance in each case is used to calculate the temperature rise (heat generation) for each. Then T_A is added to the sum of the heat generation values for the steady state and for the transient state to determine the transient T_J. Let’s try performing the calculations.

We calculate the power consumption P1 for steady-state V_IN=13.5 V, V_OUT=5.0 V, I_OUT=90 mA, and I_CC=40 μA (typ).

The power consumption P2 in the transient state with V_IN=35 V is calculated. Keep in mind that P2 is a value that includes the steady-state power consumption P1=0.77 W.

Using the steady-state thermal resistance θ_JA=40℃/W and the transient thermal resistance Z_TH (3s)=21℃/W for 3 seconds/5% duty, the respective T_J temperature increases are calculated. The transient temperature rise is calculated from the power consumption resulting by subtracting the steady-state power consumption P1 from P2.

Steady-state temperature increase 

Transient temperature rise 

These temperature increases are added to find the overall temperature increase.

Overall temperature increase 

Finally, the ambient temperature T_A in the transient state is added to determine T_J. Here T_A is assumed to be 65°C.

In the transient state: 

With this, we can find the maximum T_J under the condition that V_IN of 13.5V transiently rises to 35V for 3s in a 60s period. Fig. 3 illustrates the temperature rise for the transient change in V_IN. The temperature increase waveform is the V_IN integrated waveform because the transient thermal resistance characteristic shown in Fig. 2 has a time-based parameter.

The purpose of the T_J calculations up to this point are to facilitate an understanding of the T_J peak when there is a transient increase in power consumption. Apart from this, there is also the approach of approximating T_J from the average power consumption. The following is a calculation example for the same conditions as those used above. As the thermal resistance, the steady-state thermal resistance θ_JA=40°C/W is employed.

Average power consumption  ※0.05 is from Duty＝5%.
Average temperature rise 

In the above calculations, the temperature rise during transient behavior is 71.3°C, and so we see that in this case, calculation using an average power consumption is not appropriate.

The most important thing to confirm in thermal calculations is whether or not T_J exceeds the absolute maximum rating T_{J MAX}. A surge above the absolute maximum rating is not allowed, even for a moment, and so the transient peak temperature must be determined.

If the transient state is sufficiently long (setting aside whether it should then be called “transient”), for example in the example of Fig. 2 in which the pulse width exceeds 300 seconds, the transient thermal resistance equals the steady-state thermal resistance. Hence it is sufficient to simply determine T_J under maximum power consumption for the steady-state thermal resistance, and confirm that this is less than T_{J MAX}.