3-D thermal models calibration by parametric dynamic compact thermal models

Detailed 3-D thermal models of electronic systems require the calibration of unknown parameters to accurately describe the experimental data, which is usually obtained by a least square optimization of the measured transient thermal response to a given set of power inputs. This paper presents an extremely efficient technique to perform the identification of boundary conditions, material thermal properties, and geometrical sizes, which is based on the adoption of the trust region algorithm in combination with parametric dynamic compact thermal models. The calibration of parameters of a Package-on-Package system is performed by a simulated experiment procedure to validate the applicability and accuracy of the proposed approach. It is shown that using parametric compact models allows for a significant reduction in computational effort in comparison to conventional brute-force optimization. The calibration robustness with respect to input degradation is examined by observing the variation in the extracted parameters at different levels of noise.