Hyperbolic polynomial chaos expansion (HPCE) and its application to statistical analysis of nonlinear circuits

摘要

In this paper a novel improvement to the polynomial chaos (PC) approach for the uncertainty analysis of high speed circuits is presented. The key feature of this work is the development of an alternative hyperbolic truncation scheme to replace the conventional linear truncation scheme used in generation of PC expansions. This hyperbolic truncation scheme results in a sparse PC expansion for marginal loss of accuracy. The computational effort required to evaluate the coefficients of the resultant sparse expansion is only a small fraction of that required for full-blown PC expansions. A greedy adaptive methodology to determine the number of basis terms and evaluate the corresponding coefficients for the sparse expansion is also presented. This approach is validated on a nonlinear radio-frequency (RF) circuit against conventional full-blown PC methods.