Variability analysis of via crosstalk using polynomial chaos expansion

Abstract

In this work we use the method of polynomial chaos expansion (PCE) for statistical analysis of a via interconnect in a printed circuit board (PCB) in presence of geometrical uncertainties. A physics-based via (PBV) model is applied to the case of two signal vias surrounded by ground vias. This model consist of a near-field part and a far-field part. Here, the focus is on the far-field part modeled by the contour integral method (CIM). In order to account for variability in the geometry, namely a variation of the pitch, PCE is applied to the CIM in an intrusive manner. The system matrix of the deterministic case is replaced by an augmented version. The method is validated with Monte Carlo Sampling (MC) and shows excellent agreement for a simple geometry. We observe the same agreement in more complicated geometric configurations- A t least for frequencies below the first resonance.