# Foster Thermal Model

Heat transfer through a semiconductor module

## Library

Semiconductors / Fundamental Components / Thermal

## Description

The Foster Thermal Model block represents heat transfer through a semiconductor module. The figure shows an equivalent circuit for a fourth-order Foster Thermal Model block. Tj is the junction temperature and Tc is the base plate temperature.

A Foster thermal model contains one or more instances of Foster thermal model elements. The figure shows an equivalent circuit for a Foster thermal model element.

The number of thermal elements is equal to the order of representation. For a first order model, use scalar block parameters. For an nth order model, use row vectors of length n. Other terms that describe a Foster thermal model are:

• Partial fraction circuit

• Pi model

The defining equations for a first-order Foster thermal model element are:

`${C}_{thermal}=\frac{\tau }{{R}_{thermal}}$`
and
`${Q}_{AB}=\frac{{T}_{AB}}{{R}_{thermal}}+{C}_{thermal}\frac{d{T}_{AB}}{dt},$`
where:

• Cthermal is the thermal capacity.

• τ is the thermal time constant.

• Rthermal is the thermal resistance.

• QAB is the heat flow through the material.

• TAB is the temperature difference between the material layers.

## Parameters

Thermal resistance data

Thermal resistance values, Rthermal , of the semiconductor module, specified as a vector. The default value is `[ 0.0016 0.0043 0.0013 0.0014 ]` `K/W`.

Thermal time constant data

Thermal time constant values, τ, of the semiconductor module, specified as a vector. The default value is `[ 0.0068 0.064 0.32 2 ]` `s`.

## Ports

The block has the following ports:

A

Thermal conserving port associated with the semiconductor junction.

B

Thermal conserving port associated with the base plate junction.

## References

[1] Schütze, T. AN2008-03: Thermal equivalent circuit models. Application Note. V1.0. Germany: Infineon Technologies AG, 2008.