Analysis of via impedance variations with a Polynomial Chaos method

In this paper, we propose a systematic framework for the optimization and analysis of the equivalent characteristic impedance of practical via structures. The framework consists of (a) optimizing via structures for impedance matching using a Genetic algorithm, and (b) numerically characterize, by Polynomial Chaos (PC) method, the sensitivity of the equivalent characteristic impedance to the manufacturing uncertainties in the various geometrical parameters of a via structure. The PC method can be effectively used to compute important statistical information, such as moments, probabilities and sensitivities with respect to the design variables. The PC method is straightforward to implement, and can be orders of magnitude faster than the traditional Monte Carlo (MC) method. The proposed framework naturally leads to a rigorous methodology for EM design/control in the presence of multiple sources of uncertainty.