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A method of determining the equivalent Thermal Conductivity of a conductive printed wiring board (PWB) layer with a quasi-random circular hole pattern

The thermal analysis of printed wiring boards (PWB) relies on the accurate mathematical representation of the board constituents and the mounted electronic components. The accuracy of the mathematical model of the PWB thermal properties requires knowledge of the equivalent conductivity associated with each of the copper layers. The Universal Conductivity Curve (UCC) for randomly distributed holes in two dimensional sheets, presented in the literature, is based on Percolation Theory and curve fitting electrical conductivity data for various shaped insulation regions [1]. This paper extends this concept to the case of thermal conductivity in thermally conductive sheets and validates a Universal Thermal Conductivity Curve using finite element analysis results. An application of the Universal Thermal Conductivity Curve allows the analyst to assess the contribution of each copper layer to PWB thermal conductivity. The Universal Thermal Conductivity Curve represents a method of determining the effective in-plane thermal conductivity (K e ) of conducting layers, excluding signal layers, within a PWB. The effective thermal conductivity for each of the conductive layers within a PWB can be determined from the percentage of conductive material associated with the layer. The parallel thermal resistance of each of the conducting layers combines and the PWB equivalent in-plane thermal conductivity is subsequently determined.