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Foster and Cauer equivalent networks

version (27.9 KB) by Bartlomiej Ufnalski
Continued fraction formula is used to calculate parameters of the equivalent Cauer-type RC ladder.


Updated 06 Oct 2014

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You will need only basic matrix operations to construct the Cauer-type RC ladder equivalent to the Foster-type RC chain. The algorithm is often being embedded into thermal modelling tools; therefore, usually you don't have to perform this transformation externally. My submission is then purely for educational purposes. You will also need Control System Toolbox xor Symbolic Math Toolbox to perform some initial transfer function manipulations. However, it is also possible to provide numerator and denominator coefficients explicitly. To run the illustrative non-parametrized model, you will need the free PLECS Viewer ( The full parametrized version of the PLECS-based model is also included.

Cite As

Bartlomiej Ufnalski (2020). Foster and Cauer equivalent networks (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (7)

Armin Ebrahimian

Tosin Babarinde

Thanks to the Bartlomiej for sharing this.

One (general) question: I set the ambient temperature above 0degC (or V) in a SPICE simulation. The Foster model could depict correctly this ambient but the Cauer model can not. The two plots do eventually show the transients though but not the right ambient temperature (or voltage) level.

Any idea what could be the issue?

PS- literature suggests that Cauer gives the better representation of the thermal curve. But this doesn't seem to agree with my simulation as related to ambient temperature above 0degC

Haoran Wang




Jennifer Lindenfels

Marek Michalczuk

MATLAB Release Compatibility
Created with R2013a
Compatible with any release
Platform Compatibility
Windows macOS Linux

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