Junction Temperature Prediction
Theory: steady and transient thermal resistance
Overview
A motor-drive MOSFET averages 10 W loss and should have margin by thermal resistance, yet it failed. Why?
Perhaps because the loss came in pulses rather than steadily. The die is small with little heat capacity, so it heats sharply while current flows and cools between pulses. Average loss times thermal resistance gives only roughly the middle of that swing. What matters is the peak, and the lower the pulse frequency, the longer each pulse and the bigger the swing. Transient thermal impedance lets you compute the peak.
Transient thermal impedance
Transient thermal impedance $Z_{th}$ is the temperature rise time $t$ after applying constant power, divided by that power. Datasheets often give it as pairs of resistance $R_i$ and time constant $\tau_i$ (a Foster network). After long enough, it equals the steady resistance.
Peak temperature under repetitive pulses
The steady-periodic peak rise when on-time $t_{on}$ and off-time $t_{off}$ repeat, found by superposing each time constant.
Semiconductor life set by temperature
Many semiconductor failures come from chemical and physical degradation that accelerates with temperature. Since the 1960s a rule of thumb has held that failure rate roughly doubles per 10 °C rise (from the Arrhenius equation). In power semiconductors, each temperature swing also strains the die against solder and bond wires through expansion mismatch, and repetition lifts wire bonds. So estimating both peak temperature and temperature swing, not just the average, is the basis of lifetime design.
Worked example: MOSFET temperature
Junction-to-case Foster network (0.05 K/W · 0.1 ms, 0.15 · 1 ms, 0.30 · 10 ms, 0.50 · 100 ms; total 1.0 K/W) plus case-to-ambient (with heat sink) 1.0 K/W · 60 s. Ambient 40 °C:
| Operation | Resistance / impedance | Rise | Junction temperature |
|---|---|---|---|
| Steady 20 W | 2.0 K/W | 40.0 K | 80.0 °C |
| Single 100 W, 1 ms | 0.178 K/W | 17.8 K | 57.8 °C |
| Single 100 W, 10 ms | 0.437 K/W | 43.7 K | 83.7 °C |
| 100 W, 10%, 1 kHz (avg 10 W) | — | 23.6 K | 63.6 °C |
| 100 W, 10%, 10 Hz (avg 10 W) | — | 56.5 K | 96.5 °C |
Same 10 W average, yet at low frequency the rise more than doubles.
Both average-power estimates are 20 K, but at 1 kHz each pulse lasts just 0.1 ms, ending before the die heats fully, so the swing is small at 23.6 K. At 10 Hz each pulse lasts 10 ms — comparable to the die's time constants of around 10 ms — so it heats substantially, peaking at 56.5 K. Low-frequency intermittent operation, such as repeated motor starts and stops, is harsh on the die, and the swing also feeds directly into solder and wire-bond fatigue life.
Prediction workflow
- Derive the loss waveform (conduction and switching) from the operating profile.
- Obtain Zth or Foster constants from datasheets or thermal analysis.
- Add case-to-ambient resistance and time constants (interface material, heat sink).
- Find peak temperature and swing by superposition.
- Compare peak with the rating and estimate power-cycling life from the swing.
“Plenty of margin on average”
On a forklift motor-drive board, junction temperature from average loss was about 100 °C, well within the 150 °C rating, yet MOSFETs failed in service. Large current flowed only during the few seconds of a lift, with loss more than five times average. Recomputing with transient thermal impedance showed junction temperature exceeding the rating by the end of the lift. Thermal calculations must look at the harshest few to tens of seconds of operation, not the average.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Average power for pulses | Peak underestimated | Superpose with Zth |
| Using θJA directly | Board conditions differ | Analyse actual mounting |
| Estimating from case with θJC | Overestimate from top temperature | Use ΨJT |
| Ignoring worst-case operation | Short-term overheating | Worst few to tens of seconds |
| Ignoring swing | Fatigue life missed | Power-cycling assessment |
I'd like to learn related topics.
Try the cooling side with the heat sink designer. Related pages include thermal resistance, heat sink design, power module cooling, compact thermal models and thermal interface materials.