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

The Fourier series/integral closed-form method for substrate thermal analyzers has been limited by the specification of heat sources on the substrate surface. A method of complementing the basic substrate boundary value problem with lumped thermal resistances is described. In this manner, the thermal interface resistance between a chip package and board, as well as between the same package and a local ambient can be accommodated. The technique consists of combining the methods of Fourier series solution and lumped parameter thermal resistances. The theory is verified by comparing results with both thermal network and finite element model calculations for a sample problem consisting of four active devices attached to a substrate. The ramifications of a uniform heat flux at the board surface are examined by evaluating an approximate representation of a surface mount chip package. Results are compared with experimental test data for a small printed circuit board with 56 dual in-line resistor packs