Combination of thermal subsystems modeled by rapid circuit transformation

This paper will deal with the modeling-problem of combining thermal subsystems (e.g. a semiconductor module or package with a cooling radiator) making use of reduced models. The subsystem models consist of a set of Foster-type thermal equivalent circuits, which are only behavioral models. A fast algorithm is presented for transforming the Foster-type circuits in Cauer-circuits which have physical behavior and therefore allow for the construction of the thermal model of the complete system. Then the set of Cauer-circuits for the complete system is transformed back into Foster-circuits to give a simple mathematical representation and applicability. The transformation algorithms are derived in concise form by use of recursive relations. The method is exemplified by modeling and measurements on a single chip IGBT package mounted on a closed water cooled radiator. The thermal impedance of the complete system is constructed from the impedances of the subsystems, IGBT-package and radiator, and also the impedance of the package can be inferred from the measured impedance of the complete system.