Variability Analysis of Crosstalk Among Differential Vias Using Polynomial-Chaos and Response Surface Methods

The variability of crosstalk due to changes in differential and ground via configurations is studied in this paper. The polynomial-chaos method and the response surface method are adopted to mathematically model the variability. One goal of the work is to exploit the obtained models to locate the optimal response that both meets the performance requirement and remains robust to geometry variations due to manufacturing tolerances. Both methods correlate well with simulations and show great capabilities in practical applications for optimization and sensitivity analysis. The other goal of the work is to compare the two methods in terms of mathematical theories, sampling schemes, postprocessing, accuracy, efficiency, and limitations. Details of the comparison is given through this paper and a summary table is included in Section V.