Thermal compact models for electronic systems

Compact thermal models have been constructed for different levels in electronic systems with a variable degree of success. Many of these models suffer from the need to make ad-hoc assumptions about the number of nodes to be used in the model and require a pre-defined set of boundary conditions that are used to generate the compact model. In this work first steps towards a method that is firmly based on physical understanding and mathematical rigor are presented for linear compact models. The method gives general constraints on the form of compact models that will ensure an adequate description of thermal systems. Furthermore, the method allows reduction of the generating set of boundary conditions to an absolute minimum while at the same time providing information about the errors that are inevitable in the predictions of a compact model. Using these error estimates it is possible to determine the optimal number of nodes to be used in the compact model for a desired accuracy. The method will be applied to the benchmark defined in [1] for this purpose.