A Bayesian Deconvolution Application to Calibrate Multi-port RC Network Representation of Electronic Packages

The reliability and thermal issues on electronic components are more and more frequent, complex and crucial for product lifecycle management. Indeed the component temperatures are close to exceed their operating limits. The integration of precise components models at board level simulation is mandatory to analyze their mutual thermal interactions in real concurrent cooling environment. The multi-port RC network approach to model components offers accurate temperature prediction at an affordable simulation time. Nevertheless, establishing a fine representation of the internal structure as well as setting its material properties is required for this approach. This article proposes a way to calibrate the model on a lifelike numerical dataset obtained by different simulations of a perfect numerical model. The study focuses on the deconvolution methods to identify RC ladders network. An iterative Bayesian deconvolution method is preferred to classic Fourier one for this application, thus a fast extraction of a Foster model from discrete time constant spectrum is achieved. Then a Foster-to-Cauer network transformation with many stages of parallel RC ladders is presented with a special attention to performances and limitations of this network conversion. A physical interpretation is possible with this new network model, and its behavior demonstrates a high agreement with the step response impedance of the studied component. This Cauer network finally allows creating the Cumulative Structure Function (CSF) and the Differential Structure Function (DSF) of the component with a great resolution. The spatial superposition of these functions on a numerical dataset of the same component mounted on different configurations of a test board permits to quantify the thermal resistance of vias structures, imperfect report contact and calibrate thermal material properties. This complete calibration procedure permits fixing model discrepancies in order to create a relevant multipath RC network including real manufacturing impact on electronic package and its assembly on PCB. The full process is validated on a usual literature case, and its relevance highlighted on numerical simulations of an electronic component.