Required Heatsink
Rθsa = (Tj,max − Ta) / P − Rθjc − Rθcs
Quick answer
This calculator solves Rθsa = (Tj_max - Ta) / P - Rθjc - Rθcs for Rθsa. With Max Junction Temp 50 °C, Ambient Temp 110 °C, Power 10 W, Rθjc 20 °C/W, Rθcs 44 °C/W, the result is -70 °C/W.
Calculator
Formula
Description
This formula determines the maximum allowable heatsink-to-ambient thermal resistance to keep the junction temperature below its rated maximum. It is the key design equation for selecting heatsinks. After calculating the required Rθsa, find a heatsink with an equal or lower thermal resistance at the expected airflow conditions. If the result is negative, the device cannot be operated at those conditions even with a perfect heatsink, and either the power must be reduced or forced air cooling added.
Variables
- Rθsa — Required sink-to-ambient thermal resistance (°C/W)
- Tj_max — Maximum allowable junction temperature from datasheet (°C)
- Ta — Maximum expected ambient temperature (°C)
- P — Power dissipation (W)
- Rθjc — Junction-to-case thermal resistance (°C/W)
- Rθcs — Case-to-sink thermal resistance (°C/W)
Practical Notes
When the required Rθsa is very low (below 1°C/W), consider switching to a forced-air heatsink, liquid cooling, or reducing the power dissipation by using a more efficient topology. Common TO-220 heatsinks range from 3-20°C/W in natural convection.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| TjMax | Max Junction Temp | °C | °C |
| Ta | Ambient Temp | °C | °C |
| P | Power | W | µW, mW, W, kW |
| Rjc | Rθjc | °C/W | °C/W |
| Rcs | Rθcs | °C/W | °C/W |
Step by step
- 1. What you know: Max Junction Temp 50 °C, Ambient Temp 110 °C, Power 10 W, Rθjc 20 °C/W, Rθcs 44 °C/W
- 2. The relation: Rθsa = (Tj_max - Ta) / P - Rθjc - Rθcs
- 3. Substitute: TjMax = 50 °C, Ta = 110 °C, P = 10 W, Rjc = 20 °C/W, Rcs = 44 °C/W
- 4. Result: Rθsa = -70 °C/W
Worked examples
Minimum range
Given: Max Junction Temp 2.5 °C, Ambient Temp 5.5 °C, Power 10 mW, Rθjc 0.1 °C/W, Rθcs 0.22 °C/W
Result: Rθsa = -300.3 °C/W
Low range
Given: Max Junction Temp 25 °C, Ambient Temp 55 °C, Power 100 mW, Rθjc 1 °C/W, Rθcs 2.2 °C/W
Result: Rθsa = -303.2 °C/W
Typical
Given: Max Junction Temp 50 °C, Ambient Temp 110 °C, Power 10 W, Rθjc 20 °C/W, Rθcs 44 °C/W
Result: Rθsa = -70 °C/W
High range
Given: Max Junction Temp 85 °C, Ambient Temp 187 °C, Power 1 kW, Rθjc 100 °C/W, Rθcs 220 °C/W
Result: Rθsa = -320.1 °C/W
Maximum range
Given: Max Junction Temp 850 °C, Ambient Temp 1870 °C, Power 10 kW, Rθjc 1000 °C/W, Rθcs 2200 °C/W
Result: Rθsa = -3200 °C/W
How Rθsa changes with Max Junction Temp
| Max Junction Temp (input) | Rθsa (result) |
|---|---|
| 5 °C | -74.5 °C/W |
| 12.5 °C | -73.75 °C/W |
| 25 °C | -72.5 °C/W |
| 37.5 °C | -71.25 °C/W |
| 50 °C | -70 °C/W |
| 75 °C | -67.5 °C/W |
| 100 °C | -65 °C/W |
| 200 °C | -55 °C/W |
| 350 °C | -40 °C/W |
| 500 °C | -25 °C/W |
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<p><a href="https://vbatpower.com/formulas/heatsink-required/">Required Heatsink</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Required Heatsink?
Use Rθsa = (Tj_max - Ta) / P - Rθjc - Rθcs. With Max Junction Temp 50 °C, Ambient Temp 110 °C, Power 10 W, Rθjc 20 °C/W, Rθcs 44 °C/W, Rθsa works out to -70 °C/W.
What is the formula for Required Heatsink?
The formula is Rθsa = (Tj_max - Ta) / P - Rθjc - Rθcs. This formula determines the maximum allowable heatsink-to-ambient thermal resistance to keep the junction temperature below its rated maximum.
Related Concepts
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