CIRCUIT DESIGN

Thermal Management

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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:

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

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:

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

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

$$P_D = \frac{T_J - T_A}{R_{JC} + R_{CH} + R_{HA}}$$
A diagram showing how thermal resistance works. Image from http://www.aavid.com/sites/default/files/products/boardlevel/aavid-standard-heatsinks.pdf.

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.

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.

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.


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