The Resistance and Temperature Equation: Why Heat Breeds Heat
The fundamental resistance and temperature equation for conductive materials is:R(T) = R0 [1 + α (T - T0)]
Where:- R(T) is the resistance at the operating temperature.
- R0 is the baseline resistance at T0 (usually 25°C).
- α (alpha) is the temperature coefficient of resistance.
How Hot is Too Hot?
Most power MOSFET datasheets list a maximum junction temperature ($T_{j(max)}$) of 150°C or 175°C. However, operating at the absolute maximum is a fast track to failure. The practical ceiling for reliable, long-life operation is 100°C to 110°C. Pushing past 110°C accelerates electromigration in the metallization layers and degrades the gate oxide, drastically shortening the component's lifespan.
Thermal Path Math: From Junction to Ambient
To keep the junction under 110°C, we use the thermal equivalent of Ohm's Law. Heat flows from the silicon junction to the ambient air, encountering thermal resistance ($R_{\theta}$) along the way.Tj = Ta + Pd × (RθJC + RθCS + RθSA)
| Parameter | Symbol | Description | Typical Value (TO-220) |
|---|---|---|---|
| Junction-to-Case | RθJC | Internal resistance from silicon die to metal tab | 0.75 °C/W |
| Case-to-Sink | RθCS | Resistance of the thermal interface material (TIM) | 0.50 °C/W (Silpad) |
| Sink-to-Ambient | RθSA | Resistance of the heatsink to the surrounding air | Varies by heatsink |
| Power Dissipation | Pd | Heat generated (I² × R(T)) | Calculated |
- Elevated RDS(on) = 8mΩ × 1.6 = 12.8mΩ (0.0128Ω)
- Power Dissipation (Pd) = I² × R = 20² × 0.0128 = 5.12W
Reading the Derating Curve and Failure Signatures
Every power semiconductor datasheet includes a power derating curve. This graph shows a linear drop-off in allowable power dissipation starting from 25°C up to $T_{j(max)}$. If a part is rated for 200W at 25°C, and the derating slope is 1.33 W/°C, its allowable dissipation at 100°C case temperature drops to exactly 100W.What Airflow and Enclosure Changes Buy You
Your ambient temperature ($T_a$) is not the room temperature; it is the air temperature immediately surrounding the heatsink inside your enclosure. A sealed NEMA enclosure can easily trap heat, raising local $T_a$ by 15°C to 20°C above room temp. Adding a single 40mm exhaust fan (moving ~10 CFM) across a finned heatsink will typically drop the $R_{\theta SA}$ by 50% to 70%, effectively doubling the heatsink's capacity without increasing its physical footprint.
Failure Signatures of Thermal Stress
When the resistance and temperature equation drives a part into thermal runaway, the physical failure signatures are distinct:
- Solder Creep / Cracking: Repeated thermal cycling causes the silicon and the PCB copper to expand at different rates (Coefficient of Thermal Expansion mismatch), cracking the drain/source solder joints.
- Desiccated Thermal Pads: Cheap silicone thermal pads dry out, turn chalky, and lose their thermal conductivity, spiking $R_{\theta CS}$.
- Epoxy Bulging: The plastic TO-220 or D2PAK package physically swells or cracks near the tab due to internal vaporization of moisture (the "popcorn effect").
- Catastrophic Short: The silicon die melts, permanently shorting the drain to the source, often taking the gate driver down with it.
Heatsink Selection: A Real-World Sizing Example
Let us size a heatsink for our 20A IRF3205 example. Our Constraints:- Target Max Junction Temp ($T_j$): 105°C
- Worst-case Ambient inside Enclosure ($T_a$): 45°C
- Calculated Power ($P_d$): 5.12W
- Known Resistances: $R_{\theta JC}$ (0.75) + $R_{\theta CS}$ (0.50) = 1.25 °C/W
105 = 45 + 5.12 × (1.25 + RθSA)
60 = 5.12 × (1.25 + RθSA)
11.71 = 1.25 + RθSA
RθSA = 10.46 °C/W
We need a heatsink with a thermal resistance of 10.46 °C/W or lower in natural convection. Looking at standard extruded aluminum profiles, the Wakefield-Vette 641K-100 (a standard TO-220 board-level heatsink) has a natural convection $R_{\theta SA}$ of roughly 9.5 °C/W. This provides a comfortable 10% margin. If you place this inside a sealed box and the ambient spikes to 55°C, your junction temp will rise to 110.2°C—still safely below the 150°C silicon limit, proving the math holds up in the real world.Decision Tree: Sizing Your Thermal Management
Use this decision path to finalize your thermal design without guessing. Follow the logic from top to bottom to arrive at your physical implementation.| Condition / Measurement | Action / Next Step | Concrete Hardware Pick |
|---|---|---|
| Calculated Pd at 100°C is < 1.5W | Rely on PCB copper pour as a heatsink. Use 2oz copper, 1 sq. inch pad with thermal vias. | No external heatsink. Use D2PAK or DPAK footprint. |
| Calculated Pd at 100°C is 1.5W to 8W | Calculate required RθSA. Select a stamped or small extruded board-level heatsink. | Wakefield-Vette 641K series (approx. 9.5 °C/W). |
| Calculated Pd at 100°C is 8W to 25W | Requires large extruded profile. Ensure enclosure has ventilation slots directly below and above the fins for chimney effect. | Aavid Thermalloy 593202B03500G (approx. 4.5 °C/W natural). |
| Required RθSA is < 3.0 °C/W in a sealed box | Natural convection is physically impossible without a massive chassis. You must add forced air. | Add a Noctua NF-A4x10 40mm fan. Recalculate RθSA using forced convection curves. |
| Operating in high-vibration environment (automotive/industrial) | Do not use spring clips. They fatigue and lose tension, spiking RθCS over time. | Use screw-mount with Bergquist Sil-Pad 2000S40 and nylon shoulder washers. |
By anchoring your design in the resistance and temperature equation rather than trusting the 25°C datasheet highlights, you eliminate the guesswork. Calculate the hot resistance, map the thermal path, and select the exact heatsink profile required to keep your silicon alive.






