# Foster Thermal Model

Heat transfer through a semiconductor module

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• Simscape / Electrical / Passive / 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 or ambient 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.

### 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 Variables tab, set Start from steady state to `Off`. The first node temperature corresponds to the temperature in port A.

### Variables

Use the Variables settings to specify the priority and initial target values for the block variables before simulation. For more information, see Set Priority and Initial Target for Block Variables.

Unlike block parameters, variables do not have conditional visibility. The Variables settings include all the existing block variables. If a variable is not used in the set of equations corresponding to the selected block configuration, the values specified for this variable are ignored.

## Ports

### Conserving

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Thermal conserving port associated with the left junction.

Thermal conserving port associated with the right junction.

## Parameters

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Thermal resistance values, Rthermal , of the semiconductor module, specified as a vector.

Thermal time constant values, τ, of the semiconductor module, specified as a vector.

Whether to initialize the block in steady state.

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