Thermal Resistance Jc⚠ unverified
Electrical / Power Electronics · Compute the junction-to-case thermal resistance
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| Tj | Tj | degC | 1.0 | Junction temperature |
| Tc | Tc | degC | 1.0 | Case temperature |
| P | P | W | 1.0 | Power dissipation |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | Rthjc | degC/W | Junction-to-case thermal resistance, in degrees Celsius per watt (degC/W). Returns positive infinity when ``P`` is not positive |
The science & history
Understanding the Parameters
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$T_j$ — the critical reliability temperature of the die. Often inferred from electrical temperature-sensitive parameters or estimated from thermal models; rarely measured directly in application.
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$T_c$ — case temperature at the datasheet reference location (often the tab or a defined top surface). Measurement point must match the definition used for $R_{\theta JC}$.
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$P$ — steady (or average) power dissipated in the device — the sum of conduction, switching, and other losses (see Efficiency Total loss inventory).
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$R_{\theta JC}$ — lower is better packaging from die to case. Full chain to ambient is $R_{\theta JA} \approx R_{\theta JC} + R_{\theta CS} + R_{\theta SA}$ (case-to-sink + sink-to-ambient).
Derivation (Approaching a Proof)
Fourier heat conduction in one dimension gives $\Delta T = P\,R_{th}$ by analogy with Ohm's law ($V = IR$), where thermal resistance $R_{th} = L/(k A)$ for a slab of thickness $L$, conductivity $k$, area $A$. Defining the junction-to-case segment of that chain:
$$R_{\theta JC} \equiv \frac{T_j - T_c}{P}.$$
This is a definition of the effective resistance between those two thermal nodes under the test conditions used to measure it (usually a cold plate on the case). It does not by itself give $T_j$ in free air; you still need the rest of the thermal network and the same $P$.
Rearrangements used in design:
- $T_j = T_c + P\,R_{\theta JC}$ (given case temperature and loss),
- $P_{max} = (T_{j,max} - T_c)/R_{\theta JC}$ (allowed dissipation at a fixed $T_c$).
History
Thermal-resistance networks became standard semiconductor packaging language mid-20th century as power densities rose. JEDEC and manufacturer datasheets still quote $R_{\theta JC}$, $R_{\theta JA}$, and increasingly $\Psi_{JT}$ (junction-to-top characterization) for modern SMT power packages.
Related Concepts: Conduction Loss, Switching Loss, Temperature Rise, Efficiency Total, Diode Forward Loss
Notes: Registry calculator thermal-resistance-jc (unverified). Definitional steady-state model;
transient thermal impedance $Z_{\theta JC}(t)$ is needed for pulses. Registry units use degC /
degC/W (same as Celsius per watt).