Foster Thermal Model
Heat transfer through a semiconductor module.
Description
| The Foster Thermal Model block is a continuous dynamic model of temperature drop on ports from to . This block does not determine the specific heat flux at port B. This model cannot be extended with additional blocks. To determine the specific heat flux at port B and extend the model with additional blocks, use the Cauer Thermal Model block and select the Parameterise Cauer model using Foster coefficient data option. |
The Foster Thermal Model block represents the heat transfer through the semiconductor module. The figure below shows a fourth order equivalent circuit for the Foster Thermal Model, where is the transition temperature in the semiconductor, is the substrate or ambient temperature.
The Foster thermal model contains one or more thermal elements. The figure shows an equivalent circuit for one element of the Foster thermal model.
The number of thermal elements is equal to the modelling order. For the first order model scalar block parameters are used. For the -th order model, string vectors of length . are used. Other terms describing Foster’s thermal model are:
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Fractional Scheme
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Pi model
The defining equations for the first order element of Foster’s 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.
Initial conditions
You can initialise the model in steady state or set the initial temperatures of the nodes. To initialise the block in steady state, set Start from steady state to on. To set initial node temperatures and enable the Initial Targets section, set Start from steady state to off. The temperature of the first node corresponds to the temperature at port A.
Parameters
Thermal resistance data - values of thermal resistances
[0.0016, 0.0043, 0.0013, 0.0014] K/W (by default)
Values of thermal resistances of semiconductor module specified as a vector.
Thermal time constant data - thermal time constants
[0.0068, 0.064, 0.32, 2.0] s (by default).
Values of thermal time constants of semiconductor module, specified as a vector.
Start from steady state - initialisation of the model in steady state mode
on (by default) | off
Specify whether the block should be initialised in steady state mode.