Extensions of a closed form method for substrate thermal analyzers to include thermal resistances from source-to-substrate and source-to-ambient

An investigation is described of the applicability of Fourier series/integral methods as printed circuit board thermal analyzers. The limitations of a totally uniform heat transfer coefficient for the board surfaces are shown to be somewhat compensated for by using lumped-parameter thermal resistances as board heat removers. The method of employing lumped thermal resistances is extended to permit the incorporation of a thermal interface resistance between a chip package and board as well as between the same package and ambient. The basic theory is verified by comparing enhanced TAMS (Thermal Analyzer for Multilayer Structures) results with both thermal network and finite element model calculations for a problem consisting of four active devices attached to a substrate