A fast analog mismatch analysis by an incremental and stochastic trajectory piecewise linear macromodel

To cope with an increasing complexity when analyzing analog mismatch in sub-90nm designs, this paper presents a fast non-Monte-Carlo method to calculate mismatch in time domain. The local random mismatch is described by a noise source with an explicit dependence on geometric parameters, and is further expanded by stochastic orthogonal polynomials (SOPs). This forms a stochastic differential-algebra-equation (SDAE). To deal with large-scale problems, the SDAE is linearized at a number of snapshots along the nominal transient trajectory, and hence is naturally embedded into a trajectory-piecewise-linear (TPWL) macromodeling. The TPWL is improved with a novel incremental aggregation of subspaces identified at those snapshots. Experiments show that the proposed method, isTPWL, is hundreds of times faster than Monte-Carlo method with a similar accuracy. In addition, our macromodel further reduces runtime by up to 25X, and is faster to build and more accurate to simulate compared to existing approaches.