# Foster Thermal Model

Heat transfer through a semiconductor module

**Libraries:**

Simscape /
Electrical /
Passive /
Thermal

## Description

**Note**

The Foster Thermal Model block represents an
end-to-end behavioral model for temperature drop across the
T_{j} and T_{c} ports. This block does
not predict the heatflow rate at port **B**. You cannot extend this
model with additional blocks either. To predict the heatflow rate at port B and to
extend the model with additional blocks, use the Cauer Thermal Model block and select the **Parameterize
from Foster coefficients** parameter.

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. *T _{j}* is
the junction temperature and

*T*is the base plate or ambient temperature.

_{c}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 *n*th 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:

*C*is the thermal capacity._{thermal}*τ*is the thermal time constant.*R*is the thermal resistance._{thermal}*Q*is the heat flow through the material._{AB}*T*is the temperature difference between the material layers._{AB}

### Initial Conditions

You can initialize the model in steady state or specify the initial node
temperatures. To initialize the block in steady state, set the **Start from
steady state** parameter to `On`

. To specify
the initial node temperatures and enable the **Initial Targets**
section, set **Start from steady state** to
`Off`

. The first node temperature corresponds to the
temperature in port A.

### Variables

To set the priority and initial target values for the block variables prior to simulation,
use the **Initial Targets** section in the block dialog box or Property
Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model.
Using system scaling based on nominal values increases the simulation robustness. Nominal
values can come from different sources, one of which is the **Nominal
Values** section in the block dialog box or Property Inspector. For more
information, see System Scaling by Nominal Values.

## Examples

## Ports

### Conserving

## Parameters

## References

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

## Extended Capabilities

## Version History

**Introduced in R2016a**