A moment method for statistical analysis of high-speed VLSI interconnects

Statistical analysis of VLSI interconnects is important in the manufacturability-driven design of printed circuit boards (PCBs) and multichip modules (MCMs). The conventional Monte-Carlo method for statistical analysis requires highly repetitive circuit simulations. Since interconnects are usually modeled by a network of transmission lines, such statistical analysis is highly CPU intensive.;An efficient approach for statistical analysis based on the statistical moment theory and family of Pearson distributions is presented in this thesis. A high-order sensitivity analysis technique is developed to extend the classical first-order adjoint sensitivity analysis. The technique is used to obtain a high-order response model for the extraction of statistical moment information. Based on statistical moment theory, an explicit analytical relationship between the statistics of the circuit output and that of circuit parameters is derived. The final probability density function of the network responses is then obtained from moment information through a Pearson family of distributions.;This approach is suitable for fast estimation of network statistical analysis; it does not require the Monte-Carlo analysis. The efficiency of the proposed method and the result comparisons between the proposed method and the Monte-Carlo method are validated by several high-speed VLSI interconnect examples.