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 Cauer model using Foster coefficient data 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_c 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:

$C_{t h e r m a l} = \frac{τ}{R_{t h e r m a l}}$

and

$Q_{A B} = \frac{T_{A B}}{R_{t h e r m a l}} + C_{t h e r m a l} \frac{d T_{A B}}{d t},$

where:

C_thermal is the thermal capacity.
τ is the thermal time constant.
R_thermal is the thermal resistance.
Q_AB is the heat flow through the material.
T_AB 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 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

Quantifying IGBT Thermal Losses

The generation of a temperature profile based on switching and conduction losses in an insulated-gate bipolar transistor (IGBT). There are two buck converters. For one converter, the IGBT attaches to a Foster thermal model. For the other converter, the IGBT attaches to a Cauer thermal model. The parameters for the thermal models are tuned to give roughly equivalent results. At a simulation time of 50ms, the driving frequency changes from 40kHz to 20kHz, which increases the conduction losses and decreases the switching losses. The change in the losses results in a corresponding change in the temperature of the IGBT.

Open Model

Ports

Conserving

expand all

A — Left junction
thermal

Thermal conserving port associated with the left junction.

B — Right junction
thermal

Thermal conserving port associated with the right junction.

Parameters

expand all

Thermal resistance data — Thermal resistance values
`[ 0.0016 0.0043 0.0013 0.0014 ]` `K/W` (default)

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

Thermal time constant data — Thermal time constant data
`[ 0.0068 0.064 0.32 2 ]` `s` (default)

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

Start from steady state — Thermal time constant data
`On` (default) | `Off`

Whether to initialize the block in steady state.

References

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2016a

Foster Thermal Model