On the Treatment of Circuit Boards as Thermal Two-Ports

It is shown that a thin circuit board with a single heat source may be treated as a “two-port,” a concept borrowed from electrical network theory. In situations where a circuit board may be approximated by varying regions of roughly axisymmetric geometry, a cascaded two-port model may be easily constructed and solved analytically. Each axisymmetric segment of the model is a two-port (in thermal terms, a circular fin lacking the traditional adiabatic boundary condition at the outer radius), hence an arbitrarily complex (axisymmetric) board model is represented by a cascaded two-port network. The overall network is driven by a heat source at its inner radius, and some outer radius boundary condition; the two-port concept naturally separates the interior conduction and surface convection properties from the temperature and heat flux boundary conditions. Thus, using this scheme, temperature and heat flow may be easily determined at every position within the model, thus providing necessary information on the interactions between locations within the model — permitting yet more complex analyses of a circuit board as a multiple heat source system. Application of the axisymmetric two-port method is made to thermal characterization of semiconductor devices, including the relationship between so called “min pad” and “1-inch pad” device characteristics. The model is also compared to other experimental data, where the “best fit” of the model parameters shows a reasonable correlation with the expected physical values of the experiment.