Heat Sink Formulas: Junction Temperature

Heat sink formulas: junction temperature from thermal resistances, the heat sink resistance needed for a maximum junction temperature, with a worked example.

The formulas

P is the power dissipated in the device in watts, Ta the ambient air temperature in °C and the three resistances are in K/W (the same as °C/W): junction to case, case to sink (the thermal pad or paste) and sink to ambient. The method is the thermal equivalent of Ohm’s law, with temperature as voltage and power as current. Take Rθjc from the device data sheet and Rθsa from the heat sink data at your airflow. Leave a margin below the maximum junction temperature.

Worked example: junction temperature

P = 15 W, Ta = 40 °C, Rθjc = 1.5 K/W, Rθcs = 0.5 K/W and Rθsa = 3 K/W.

1. Rθ = 1.5 + 0.5 + 3 = 5 K/W
2. Tj = 40 + 15 × 5 = 115 °C
3. The case is at 40 + 15 × (0.5 + 3) = 92.5 °C

Worked example: heat sink for a 125 °C limit

1. Rθsa = (125 − 40) / 15 − 1.5 − 0.5 = 3.667 K/W or lower

Junction temperature and the heat sink needed

Frequently asked questions

What is thermal resistance?

It is the temperature rise per watt of heat flowing through a path, in K/W. A lower value conducts heat better.

Should I design to the maximum junction temperature?

No. A lower temperature extends the life, so many designs keep a margin of 20 °C or more, or derate to a lower limit.

Does a bigger heat sink always help?

Up to a point. The case-to-sink resistance and the device resistance stay the same, and the sink needs airflow or a large surface in still air.

Which ambient temperature do I use?

The highest air temperature around the heat sink in service, inside the enclosure and not the room, because other parts also heat the air.

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