A modeling methodology for thermal analysis of the PCB structure
A modeling methodology is proposed for the thermal analysis of the PCB structure based on integrating both the FVM-based numerical solution and the Fourier-series-based analytical solution of temperature. The heat spreading through tracks and the vertical heat transfer through vias are taken into account in a numerical way and regarded as the additional thermal boundary conditions of insulating layers, which are assumed to be homogeneous from an analytical point of view. A methodology based on the vertex-centered Cartesian-grid Finite Volume Method is also proposed for the electric analysis of PCB tracks in order to take into account the temperature-dependent Joule heating effect, thus the current carrying capacity of tracks can be estimated as well. The necessary and sufficient condition for solving electric distributions in multi-terminal tracks is discussed, described and verified through both the analysis of the equivalent resistor network in a multi-terminal track and the mathematical analysis of a matrix equation, which correlates terminal currents with terminal electric potentials. In addition, the method for analyzing the multilayer structure is also discussed. A thermal solver was developed in MATLAB based on the methodology. Several layouts were modeled in the solver and COMSOL to test the validity of the methodology and to investigate the influence factors of the solution. Based on the analysis and comparisons, mesh density and the number of eigenvalues are the main influence factors. The vertical and horizontal heat transfer contributions of vias were also investigated by modeling the footprint layout of a power mosfet in order to test the modeling assumptions. Finally, the consistency between the modeling results and the reference results was found. Both the advantages and disadvantages of the methodology are discussed throughout the analysis.
fvm finite volume method fem finite element method cfd computational fluid dynamics fr4 flame retardant 4 vcm vertex centered method ep electric potential bga ball grid array fsccm full square cell centered method htc heat transfer coefficient d2pak double decawatt package