Feasibility of uncertainty quantification for power distribution network modeling using PCE and a contour integral method

This work presents the modeling of the printed circuit board part of power distribution networks (PDNs) and example results for the uncertainty quantification for the magnitude of the corresponding impedance. Variability is considered for several parameters, including geometry, material properties, and the models of the decoupling capacitors. For the computation of the parallel plate impedance an efficient and accurate two-dimensional contour integral method (CIM) is applied together with models for the wave number for the complete frequency range of interest. Polynomial chaos expansion (PCE) is used in the non-intrusive form of stochastic testing for the uncertainty quantification and Monte Carlo simulations are used for the validation of these results. To our knowledge this combination of methods represents the first application of CIM and PCE to the modeling of PDNs. The PCE is found to be numerically more efficient than Monte Carlo in cases where parameters are varied that have an influence on the parallel plate impedance. It can be less efficient for variation of only the models of decoupling capacitors. It is applicable if not too many parameters are varied at a time and accurate if resonance effects due to low-loss substrate materials and components are not too pronounced at the considered frequency.