Thermal Runaway Stability Check
Stable if dP/dT < 1/Rth_ja
Quick answer
This calculator solves Stability condition: dP/dT < 1/Rth_ja for Stable if dP/dT < 1/Rth_ja. With Power Temp Coefficient 0.5, Junction-to-Ambient Rth 20 °C/W, the result is -0.45.
Calculator
Formula
Description
Thermal runaway occurs when a component power dissipation increases with temperature faster than the cooling system can remove heat, creating a positive feedback loop that leads to destruction. The stability condition requires that the rate of power increase with temperature (dP/dT) must be less than the cooling capability (1/Rth_ja). The forward result shows the stability margin: positive means stable, negative means thermal runaway risk. This is critical for BJTs (which have positive temperature coefficient of current), MOSFETs in linear mode, and voltage regulators at high power.
Variables
- dP/dT — Rate of power increase with temperature (W/°C)
- Rth_ja — Junction-to-ambient thermal resistance (°C/W)
Practical Notes
A positive result indicates stability margin. A negative result means the thermal design is unstable — either improve cooling (lower Rth) or reduce the power-temperature sensitivity. BJTs are particularly susceptible because collector current increases with temperature (about 7%/°C), which increases power dissipation. MOSFETs have a negative temperature coefficient in saturation mode, providing inherent stability, but a positive coefficient in linear (ohmic) mode.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| dPdT | Power Temp Coefficient | — | — |
| Rth | Junction-to-Ambient Rth | °C/W | °C/W |
Step by step
- 1. What you know: Power Temp Coefficient 0.5, Junction-to-Ambient Rth 20 °C/W
- 2. The relation: Stability condition: dP/dT < 1/Rth_ja
- 3. Substitute: dPdT = 0.5, Rth = 20 °C/W
- 4. Result: Stable if dP/dT < 1/Rth_ja = -0.45
Worked examples
Minimum range
Given: Power Temp Coefficient 0.025, Junction-to-Ambient Rth 0.1 °C/W
Result: Stable if dP/dT < 1/Rth_ja = 9.975
Low range
Given: Power Temp Coefficient 0.25, Junction-to-Ambient Rth 1 °C/W
Result: Stable if dP/dT < 1/Rth_ja = 0.75
Typical
Given: Power Temp Coefficient 0.5, Junction-to-Ambient Rth 20 °C/W
Result: Stable if dP/dT < 1/Rth_ja = -0.45
High range
Given: Power Temp Coefficient 0.8, Junction-to-Ambient Rth 100 °C/W
Result: Stable if dP/dT < 1/Rth_ja = -0.79
Maximum range
Given: Power Temp Coefficient 8, Junction-to-Ambient Rth 1000 °C/W
Result: Stable if dP/dT < 1/Rth_ja = -7.999
How Stable if dP/dT < 1/Rth_ja changes with Power Temp Coefficient
| Power Temp Coefficient (input) | Stable if dP/dT < 1/Rth_ja (result) |
|---|---|
| 0.125 | -0.075 |
| 0.25 | -0.2 |
| 0.375 | -0.325 |
| 0.5 | -0.45 |
| 0.75 | -0.7 |
| 1 | -0.95 |
| 2 | -1.95 |
| 3.5 | -3.45 |
| 5 | -4.95 |
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<p><a href="https://vbatpower.com/formulas/thermal-runaway-check/">Thermal Runaway Stability Check</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Thermal Runaway Stability Check?
Use Stability condition: dP/dT < 1/Rth_ja. With Power Temp Coefficient 0.5, Junction-to-Ambient Rth 20 °C/W, Stable if dP/dT < 1/Rth_ja works out to -0.45.
What is the formula for Thermal Runaway Stability Check?
The formula is Stability condition: dP/dT < 1/Rth_ja. Thermal runaway occurs when a component power dissipation increases with temperature faster than the cooling system can remove heat, creating a positive feedback loop that leads to destruction.
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