Analyzing via impedance variations with a stochastic collation method

In this paper, we describe a systematic approach to optimize and analyze the equivalent characteristic impedance of practical via structures. The procedure consists of (a) optimizing via structures for impedance matching using a Genetic algorithm, and (b) numerically characterize, by stochastic collocation method, the sensitivity of the equivalent characteristic impedance to the manufacturing uncertainties in the various geometrical parameters of a via structure. Such procedure naturally leads to a rigorous methodology for EM design/control in the presence of multiple sources of uncertainty.