Compact thermal models of packages used in conduction cooled applications

Results of an extensive study aimed at developing boundary condition independent compact steady-state thermal models of a variety of electronic packages used in conduction cooled applications are presented. Formal mathematical principles were used to establish a nonredundant set of thermal boundary conditions representing board edge and backside cooling with variable board and underfill conductivity. A Design of Experiments approach was employed to reduce the total number of boundary conditions to four, allowing the generation of boundary condition independent CTM´s. Two general network topologies, incorporating both simple star-shaped and more complex, shunted networks were developed. To extract the CTM parameters, the thermal networks were optimized using a genetic algorithm-based approach allowing constrained nonlinear global optimization in a standard spreadsheet environment. Comparisons of the accuracy of models from simple to complex are presented for two types of generic parts. It was found that optimized star-shaped CTM´s accurately predict junction temperatures, but usually give insufficient accuracy for the heat flows leaving via the package prime lumped surfaces. The inclusion of a floating node allows sufficient degree of freedom to correctly redistribute the heat flows between the “outlet” nodes of the networks. Using the optimization technique, CTM´s were derived for thirty parts representing thirteen package families. For most of the packages only network topologies that included a floating node and surface-to-surface links provided satisfactory accuracy. With three different network configurations, for which examples are presented, it was possible to capture the thermal behavior of all the package families investigated