Wiring statistics and printed wiring board thermal conductivity

The thermal conductivity of printed wiring boards depends strongly upon the copper content of the signal and power planes. For boards with continuous power and ground planes, it is adequate to use simple lumped conductivities based on the volume percentage of copper. However, nearly order of magnitude errors can occur when this approach is used with boards with discontinuous or significantly perforated power and ground planes. We describe a statistical approach to modeling the copper connectivity in wired signal planes, based on the probability distribution of wire lengths in the X and Y directions. Using this approach, we have constructed finite element models of six-layer printed wiring boards which approximate functional boards with a wide range of wiring density, via density, and power/ground plane perforations. The finite element results show that the connectivity of the wiring, vias, and power/ground planes plays an important role in establishing the board's average thermal conductivity. Although there is some scatter in the results, due to wiring details, we find that the percentage of copper in the printed wiring board can still be used as an initial indicator of thermal conductivity. We present an empirical fit to the models suitable for design applications.