# Cauer Thermal Model

Heat transfer through multiple layers of a semiconductor module

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• Simscape / Electrical / Passive / Thermal

## Description

The Cauer Thermal Model block represents heat transfer through multiple layers of a semiconductor module. A Cauer Thermal Model contains multiple Cauer Thermal Model Element components. The figure shows an equivalent circuit for a Cauer Thermal Model Element.

The multiple layers of a Cauer thermal model include chip, solder, substrate, solder, and base. Other terms that describe a Cauer thermal model are:

• Continued fraction circuit

• T model

This figure shows an equivalent circuit for a Cauer Thermal Model.

R is the absolute reference port. If you set the Show absolute reference port parameter to Off, this is equal to the absolute zero temperature. To modify the absolute reference, set Show absolute reference port to On and connect the R port to a temperature source with your desired reference temperature.

### Equations

The defining equations for each Cauer thermal model element are

${C}_{thermal}=\frac{\tau }{{R}_{thermal}},$

${Q}_{AB}=\frac{{T}_{AB}}{{R}_{thermal}},$

and

${Q}_{AR}={C}_{thermal}\frac{d{T}_{AR}}{dt},$

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.

• QAR is the heat flow through the thermal capacity.

• TAR is the temperature drop across the thermal capacity.

### 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.

To specify the initial temperatures of each thermal capacity, set the value of the Vector of thermal mass temperatures variable. The length of this vector must be equal to the number of Cauer thermal model elements. It corresponds to the temperature drop across each thermal capacity in the model.

## Ports

### Conserving

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Thermal conserving port associated with the first surface of the individual layer of the semiconductor.

Thermal conserving port associated with the chosen thermal reference.

#### Dependencies

To enable this port, set Show absolute reference port to On.

Thermal conserving port associated with the second surface of the last layer of the semiconductor.

## Parameters

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Vector of thermal resistances.

Vector of thermal time constants.

Whether to enable absolute reference port.

## References

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