The Physics: Thermal Resistivity vs. Thermal Resistance
Before we start bolting aluminum to silicon, we need to clear up a terminology trap that burns hobbyists and junior engineers alike. Thermal resistivity and thermal resistance are not the same thing, even though forum posts use them interchangeably.
Thermal resistivity (often denoted as ρth or rθ) is an intrinsic material property. It tells you how well a specific substance opposes heat flow, measured in °C·m/W (or K·m/W). Copper has a low thermal resistivity; FR4 fiberglass has a high one. It doesn't care about the shape or size of the object.
Thermal resistance (Rθ), on the other hand, is the extrinsic property of a specific physical component or interface, measured in °C/W. It accounts for the material's thermal resistivity plus its geometry (thickness and cross-sectional area). When you are sizing a heatsink or reading a datasheet, you are almost always working with thermal resistance. We will use thermal resistance for our system math, but keep thermal resistivity in mind when selecting PCB substrates and thermal interface materials (TIMs).
The Math: Junction-to-Ambient Thermal Path Calculation
Heat flows from the silicon junction to the ambient air exactly like current flows from a voltage source to ground. Temperature is our voltage, power dissipation is our current, and thermal resistance is our electrical resistance. This is the foundation of all thermal management.
The governing equation for the total thermal path is:
Tj = Ta + Pd × (RθJC + RθCS + RθSA)
| Variable | Description | Typical Source |
|---|---|---|
| Tj | Junction Temperature (°C) | The silicon die itself (what we want to protect) |
| Ta | Ambient Temperature (°C) | The air inside your enclosure (not the room!) |
| Pd | Power Dissipation (Watts) | Calculated from your circuit (e.g., Vdrop × I) |
| RθJC | Junction-to-Case Resistance (°C/W) | Silicon die to the metal tab (from the datasheet) |
| RθCS | Case-to-Sink Resistance (°C/W) | The thermal paste or mica pad interface |
| RθSA | Sink-to-Ambient Resistance (°C/W) | The heatsink's efficiency (what we need to solve for) |
Worked Example: Sizing a Heatsink for an LM7805
Let's say you are dropping 12V down to 5V to power a 1A microcontroller circuit using a standard TO-220 LM7805 linear regulator.
- Power Dissipation (Pd): (12V - 5V) × 1A = 7W.
- Ambient Temp (Ta): It's inside a plastic enclosure on a workbench. Assume 40°C.
- Target Junction Temp (Tj): The datasheet says absolute max is 125°C, but we want reliability. Let's target 100°C.
- RθJC: The LM7805 datasheet lists this as 5°C/W.
- RθCS: Using a standard silicone-based thermal paste (like Arctic Silver Ceramique), assume 0.5°C/W.
Rearranging the formula to solve for the required heatsink (RθSA):
RθSA = [(Tj - Ta) / Pd] - RθJC - RθCS
RθSA = [(100 - 40) / 7] - 5 - 0.5
RθSA = 8.57 - 5.5 = 3.07°C/W
You need a heatsink with a thermal resistance of 3.07°C/W or lower. For a deep dive into the underlying physics of these interfaces, All About Circuits provides an excellent primer on thermal resistance networks.
Reading the Datasheet: Derating Curves and 'How Hot is Too Hot'
How hot is too hot for this part? The absolute maximum junction temperature (Tj(max)) for most commercial silicon is 150°C. If you hit 151°C, the silicon doesn't instantly melt, but the semiconductor physics break down—leakage currents spike, and the part may latch up or destroy itself.
However, operating at 140°C is a terrible idea. The Arrhenius equation dictates that for every 10°C rise in operating temperature, the expected lifespan of an electronic component is roughly halved. For a 24/7 IoT node or a power supply, you should design for a maximum Tj of 85°C to 100°C to ensure a 5-to-10-year operational life.
Interpreting the Power Derating Curve
Every power datasheet includes a power derating curve. It looks like a linear slope starting at 100% power at 25°C and dropping to 0W at Tj(max) (usually 150°C).
If your TO-220 part is rated for 15W at 25°C, but your ambient enclosure temperature is 75°C, you cannot draw 15W. You must look at the curve: at 75°C, the allowable power is derated to roughly 60% of maximum, meaning you can only safely dissipate 9W before requiring active cooling or a redesign. Always check the derating curve before finalizing your BOM.
If you push components past their thermal limits, they rarely just 'stop working' cleanly. Look for these physical failure signatures on your bench:
- Electromigration: High temps cause metal atoms in the silicon traces to physically migrate, eventually creating open circuits or shorting adjacent lines.
- Thermal Runaway: Common in BJTs and some MOSFETs. As the die heats up, its on-resistance drops (or leakage increases), causing it to draw more current, which creates more heat, until catastrophic failure.
- Solder Joint Fatigue: Repeated thermal cycling (heating up under load, cooling down at idle) causes the solder to 'creep' and crack due to the coefficient of thermal expansion (CTE) mismatch between the silicon, the copper leadframe, and the PCB.
- Package Delamination: The epoxy resin of the IC package absorbs moisture. Rapid heating turns that moisture to steam, cracking the plastic from the inside (the 'popcorn effect').
Airflow, Enclosures, and Heatsink Selection
Returning to our LM7805 example, we need a TO-220 heatsink rated for ≤ 3.07°C/W. A great off-the-shelf choice is the Wakefield-Vette 641K. It's an extruded aluminum TO-220 heatsink with a natural convection RθSA of roughly 2.8°C/W. At 7W, our junction temp will settle around 96°C—safely under our 100°C target.
What Airflow and Enclosure Changes Buy You
If you need to drop the temperature further without buying a massive chunk of metal, you manipulate the boundary layer of air around the fins.
- Forced Air (Fans): Slapping a standard 40mm x 10mm 12V brushless fan (like a Noctua NF-A4x10) against the Wakefield 641K drops its effective RθSA from 2.8°C/W down to approximately 1.2°C/W. This drastically drops Tj and allows for a much smaller physical footprint.
- Enclosure Venting: A sealed plastic box traps heat, raising Ta. Adding passive louvered vents at the bottom and top of the enclosure creates a chimney effect. For every 10°C you lower the internal Ta, you directly lower Tj by the same amount, regardless of the heatsink.
- Chassis Mounting: If your enclosure is aluminum, bolt the TO-220 directly to the chassis using the enclosure wall as an infinite heatsink. Use a shoulder washer to isolate the tab if it's not ground-referenced. For more on practical mechanical thermal design, check out this SparkFun guide to thermal management.
FAQ: Thermal Resistivity in Practical Applications
How does thermal resistivity differ from thermal resistance in PCB design?
In PCB design, thermal resistivity is the material constant you use to calculate the thermal resistance of a specific copper pour or via array. For example, the thermal resistivity of pure copper is roughly 0.0025 °C·m/W. If you are designing a thermal via farm under a QFN package, you use the copper's thermal resistivity, the thickness of the PCB (length), and the total cross-sectional area of your vias to calculate the effective thermal resistance (°C/W) of that via array to the ground plane.
What is the thermal resistivity of standard FR4 vs aluminum core PCBs?
This is where material selection dictates your power limits. Standard FR4 fiberglass has a terrible thermal resistivity of approximately 3.5 to 4.0 °C·m/W, making it a fantastic electrical insulator but a thermal blanket. In contrast, an Aluminum Core PCB (MCPCB or Metal Core PCB) uses a dielectric layer with a thermal resistivity around 0.05 to 0.1 °C·m/W, bonded to an aluminum base (approx 0.004 °C·m/W). If you are driving 1W or 3W high-power LEDs or MOSFETs, FR4 will choke the heat; you must switch to an MCPCB to keep the junction temps in check.
How do I calculate thermal resistivity for a custom 3D printed enclosure?
You generally don't calculate the resistivity of the plastic itself; you treat the entire enclosure as a thermal barrier. PLA and PETG have high thermal resistivities (around 4.0 to 5.0 °C·m/W) and very low glass transition temperatures (PLA softens at 60°C). Instead of calculating the material's resistivity, measure the internal ambient temperature (Ta) with a thermocouple while the circuit is under load. If the internal air is 20°C hotter than the room, your enclosure's effective thermal resistance to the room is too high. Fix it by increasing the surface area (adding printed fins), switching to a higher-temp filament like ABS or Polycarbonate, or adding forced ventilation.
