Cauer Thermal Model
Heat transfer through multiple layers of semiconductor modules.
Description
The Cauer Thermal Model unit represents heat transfer through multiple layers of semiconductor modules. The Cauer Thermal Model consists of several Cauer Thermal Model Element components. The figure below shows an equivalent circuit for a Cauer Thermal Model Element.
The multiple layers of the Cauer Thermal Model include the chip, solder, substrate, and base. Other terms describing Cauer Thermal Model:
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Continuous fractional circuit.
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T-model.
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Ladder network.
The figure below shows the equivalent circuit for the Cauer Thermal Model.
The temperature at the R point is absolute zero.
Equations
The defining equations for each element of the Cauer Thermal Model are
,
,
Where:
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- heat capacity.
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- thermal time constant.
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- thermal resistance.
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- heat flux through the material.
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- temperature difference between layers of material.
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- heat flux through heat capacity.
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- temperature difference through heat capacity.
Parametrization of the Kauer model based on Foster’s coefficients
Technical descriptions of semiconductor devices often use Foster coefficients to define a thermal model. However, Kauer thermal models are more useful because they can be extended with additional thermal components such as heat sinks and radiation or convection elements.
To use the Cauer Thermal Model block based on Foster thermal model data, select the Parameterise Cauer model using Foster coefficient data option.
Ports
Non-directional
A is the primary surface area of an individual semiconductor layer
`heat
A heat port associated with the primary surface of an individual semiconductor layer.
B is the secondary surface of the last layer of the semiconductor
heat
Heat port associated with the secondary surface of the last layer of the semiconductor.
Parameters
Parameterise Cauer model using Foster coefficient data - parameterise Cauer model using Foster coefficients
Off (by default) | On
Select this check box to enable parameterization of the Cauer model using Foster coefficient data.
Thermal resistance data - thermal resistances
1e-3 * [2.6468, 3.8701, 1.2007, 0.8824] K/W (by default).
Thermal resistance vector.
Dependencies
To use this parameter, clear the Parameterise Cauer model using Foster coefficient data parameter checkbox.
Thermal time constant data - thermal time constants
[0.0086, 0.054, 0.3624, 1.651] s (by default).
Vector of thermal time constants.
Dependencies
To use this parameter, uncheck Parameterise Cauer model using Foster coefficient data parameter.
Thermal resistance data (Foster) - thermal resistances parameterised based on Foster coefficients
[0.0016, 0.0043, 0.0013, 0.0014] K/W (by default).
Vector of thermal resistances parameterised based on Foster coefficients.
Dependencies
To use this parameter, select the Parameterise Cauer model using Foster coefficient data checkbox.
Thermal time constant data (Foster) - thermal time constants parameterised based on Foster coefficients
[0.0068, 0.064, 0.32, 2.0] s (by default).
Vector of thermal time constants parameterised on the basis of Foster coefficients.
Dependencies
To use this parameter, select the Parameterise Cauer model using Foster coefficient data checkbox.
Bibliography
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Schütze, T. AN2008-03: Thermal equivalent circuit models. Application Note. V1.0. Germany: Infineon Technologies AG, 2008.
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T. G. Subhash Joshi and V. John, Combined transient thermal impedance estimation for pulse-power applications. 2017 National Power Electronics Conference (NPEC), 2017, pp. 42-47, doi: 10.1109/NPEC.2017.8310432.