Worst case analysis for evaluating VLSI circuit performance bounds using an optimization method

Abstract

The process variations are unavoidable in today's VLSI circuits due to the continuing scaled IC technologies, therefore, the likely behaviors of VLSI circuits with process variations may fail to meet the performance specifications. This paper addresses an efficient method to evaluate the performance bounds of VLSI circuits with process variations in time domain. The described approach proceeds by solving a Nonlinear Programming (NLP) problem to find the upper and lower bounds of the interested outputs, either a node voltage or a branch current, constrained by linearlized equations, circuit equations and parameter variations. The preliminary result shows the performance bounds from the proposed method are sufficiently tight comparing with the bounds obtained from intensive Monte Carlo samplings in SPICE.

Exploiting bounds optimization for the semi-formal verification of analog circuits

“…Compared with the methods in [33] and [34] that also employed nonlinear constrained optimization to compute transient performance bounds of analog circuits under process variations, the approach we proposed in this paper has several advantages. Using different approximation methods, the authors in [33] compute the derivations of the linearized analog circuit models and derive the bound of the circuit response in transient domain. Also in [34], a symbolic MNA formulation is applied on a linearized analog circuit model.…”

“…Furthermore, the proposed methods do not consider the sensitivity of their bound analysis to the initial condition. Moreover, the work in [33] and [34] consider the optimization solution for each time step as the stating point of the next time step to speedup the bound analysis at the cost of the accuracy. In contrast, our method directly handles device-level nonlinear models of analog circuits and considers a complete possible set of initial conditions.…”

Performance bound analysis of analog circuits in frequency- and time-domain considering process variations

“…However, the affine interval method can lead to over-conservative results. Recently, Saibua et al [2011] applied an optimization-based method to compute the bounds. Another recent work [Song et al 2013], using reachability analysis, can also efficiently generate variation-induced performance bounds.…”