Thermal Management

Thermal Resistance

Thermal resistance is way of modelling the thermal behaviour of an object in a way analogous to calculating the current through a resistor by measuring it’s voltage.

The equation is given by:

$$\begin{align} P_D = \frac{\Delta T}{\sum R_\theta} \end{align}$$

where:
$P_D$ = Power dissipated by device ($W$)
$\Delta T$ = Change in temperature between both end-points
$\sum R_{\theta}$ = The sum of thermal resistances over which $\Delta T$ exists

Which is usually expanded (and used) as:

$$\begin{align} P_D = \frac{T_J - T_A}{R_{JC} + R_{CA}} \end{align}$$

If there is a heatsink involved, a new term is added:

$$\begin{align} P_D = \frac{T_J - T_A}{R_{JC} + R_{CH} + R_{HA}} \end{align}$$

A diagram showing how thermal resistance works. Image from http://www.aavid.com/sites/default/files/products/boardlevel/aavid-standard-heatsinks.pdf

An analogy to electrical resistance…

The analogy of thermal resistance to electrical resistance. Image from http://www.vishay.com/docs/28705/mc_pro.pdf

Inaccuracies In The Thermal Resistance Model

• Thermal resistances assume a linear relationship between temperature and heat flow. This is only a first-order approximation.

List Of Component Package Thermal Resistances

See the Component Packages page. This has many of the common component packages and their thermal resistances.

Below is a condensed list of experimentally found internal thermal resistances (junction-to-case).

Experimentally determined values for the internal thermal resistance (junction-to-case) for various sized SMD resistors. Image from http://www.vishay.com/docs/28705/mc_pro.pdf