Thermal Resistance (Rth) Model
Theory: treating heat flow like a circuit
Overview
A power device datasheet lists θJA and θJC. Which one should I use to calculate the junction temperature?
If it's mounted on a heat sink, use θJC. Thermal resistance is temperature difference divided by heat flow, and resistances add in series and parallel just like electrical ones. But each datasheet value is measured under specific conditions — θJA is on a standardised test board — so using it directly for your own board and enclosure can be badly off. Knowing what each value represents is the first step in thermal resistance modelling.
Basic relations
$L$ is thickness, $k$ conductivity, $A$ area, $h$ heat-transfer coefficient and $P$ power. They hold when heat flows in one direction and each layer can be treated as isothermal.
What datasheet values mean
| Symbol | Meaning | Use |
|---|---|---|
| θJA | Junction to ambient on a standardised test board | Comparing parts |
| θJC | Junction to the case cooling surface (heat-sink side) | Heat-sink design |
| θJB | Junction to board (a point on the board near the part) | Parts cooling through the board |
| ψJT | Junction-to-case-top difference divided by total power (not a resistance) | Estimating junction temperature from case-top temperature in the field |
The key is that ψJT is not called a resistance. Only a small part of the heat actually flows through the case top, yet the difference is divided by total power, so it can't be used as a resistor in the network. It is, however, a handy way to estimate junction temperature accurately from a measured case-top temperature.
How θJA took on a life of its own
θJA was defined so that manufacturers could compare packages fairly: the part is mounted on a test board of set size and copper coverage and measured under set air conditions (the JEDEC JESD51 series). But because it seemed to give junction-to-air resistance for a single part, it came to be used directly as a design value. Real boards differ in copper area and neighbouring parts, and the same device's θJA can change by a factor of two or more. The standards added parameters such as ψJT partly to discourage this misuse.
Worked examples
Example 1: junction temperature and the interface material
With 20 W, 40 °C ambient, $R_{\theta JC} = 0.5$ K/W and a heat sink with $R_{SA} = 2.0$ K/W over a 1 cm² contact, only the material between part and heat sink was changed:
| Interface | Resistance | Junction temperature |
|---|---|---|
| Grease 50 µm (k = 3) | 0.17 K/W | 93 ℃ |
| Pad 0.25 mm (k = 1.5) | 1.67 K/W | 123 ℃ |
| Pad 0.5 mm (k = 1.0) | 5.0 K/W | 190 ℃ |
The thin interface material matters more than the heat sink!
Where large heat flows pass through a small area, even a 0.5 mm layer dominates. Resistance is inversely proportional to area, so in power-device thermal design look first for the smallest area in the path. Real joints also add contact resistance from surface roughness and clamping pressure, so actual values are often higher than the conductivity-only estimate.
Example 2: short pulses and transient impedance
A part with 1 K/W steady-state resistance was represented by a three-stage Foster model ($R$ = 0.1, 0.3, 0.6 K/W; $\tau$ = 1 ms, 20 ms, 1 s), and the temperature rise for 100 W applied for a given time was computed:
| Pulse length | Zth | Rise at 100 W |
|---|---|---|
| 0.1 ms | 0.011 K/W | 1.1 K |
| 1 ms | 0.078 K/W | 7.8 K |
| 10 ms | 0.224 K/W | 22 K |
| 100 ms | 0.455 K/W | 46 K |
| 1 s | 0.779 K/W | 78 K |
| 10 s | 1.000 K/W | 100 K |
For short pulses the heat has not yet spread far, so the same power produces a smaller rise. Momentary heating such as motor start-up currents or short-circuit protection events should be assessed with $Z_{th}(t)$, not the steady resistance. Foster-model nodes do not correspond to physical locations, so to connect it in series with a heat-sink model you need to convert to a Cauer model, which maps onto the physical layer stack.
Practice: resistance networks versus FEM
Which to use
| Situation | Resistance network | FEM / CFD |
|---|---|---|
| Concept estimates | Excellent — fast | Fair |
| Layered stacks with 1D heat flow | ◎ | ○ |
| Spreading from a small source into a wide plate | Fair — needs spreading-resistance formulas | ◎ |
| Mutual heating between parts | △ | ◎ |
| Airflow inside an enclosure | × | Excellent — CFD |
- Extracting per-part resistances from FEM results into a network lets you sweep conditions instantly.
- Large differences between a network and FEM usually come from overlooked spreading resistance — the resistance as heat fans out sideways from a small source.
- Instead of modelling part interiors in detail, use compact thermal models (Delphi/JEDEC) to keep model size down.
“It matches the datasheet but still runs hot”
When a prototype part runs hotter than expected, a common finding is that θJC and the heat sink are fine but the interface is more than twice the design thickness. Pads are specified assuming they compress under clamping; with loose screws they stay thick. Too much grease also leaves a thick layer. Calculating the network's sensitivity to the interface first makes it clear what the assembly process has to control.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Using θJA as a design value | Large errors on the real board | Use θJC/θJB with your own conditions |
| Putting ψJT into the network as a resistance | Temperatures badly wrong | Use it only for estimation |
| Ignoring contact resistance | Junction temperature underestimated | Use measured thickness and pressure |
| Treating pulses as steady | Over-designed cooling | Use $Z_{th}(t)$ |
| Chaining Foster models in series | Unphysical transient response | Convert to Cauer before connecting |
I'd like to try the numbers myself.
Use the heat sink design calculator and the fin array simulator for heat-sink resistance and the LED junction temperature simulator to build up the chain from the part. For more detail see the articles on junction temperature prediction, thermal interface materials and natural versus forced air cooling.
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