Towards the Development of Transient Compact Thermal Models of Electronic Packages That Are Consistent With Steady State Limits

Recent progress is presented in the development of a class of transient compact thermal models (CTM’s) that may be used for predicting transient package junction temperatures independently of the boundary conditions imposed on the physical surfaces. The models are traditional RC networks in which the unknown capacitances are extracted by a non-linear optimization process. The resistors of the compact RC network model are values extracted in a traditional steady-state parameter extraction method. Validation results are presented for a canonical transient one-dimensional fin problem with a known analytical solution. Transient CTM’s were formulated for a three layer model exposed to three different BC sets. Using an optimization process based on error minimization of the transient junction temperature, the capacitances networks were extracted at early, middle, and late time intervals. The junction temperature predicted by the dynamic CTM was within 15% of a numerical model. As expected, for a fixed number of parameters, the optimal values of the capacitances are dependent on the time domain. Because the resistances are extracted from the steady state formulations, the dynamic CTM’s asymptote to steady state limits that are consistent with steady state CTM formulations. We hypothesize that the non-uniqueness of the parameter set for this type of reduced order thermal model leads to disparate sets of values that yield similar accuracy.