SiSMA: a statistical simulator for mismatch analysis of MOS ICs

Abstract

This paper preenta a simulator for the statistical analysis of MOS integrated circuita affected hy mismatch effect. The tool is based on a rigorous formulation of circuit equations including random current murces to take into account technological toleran-. The simulator requires a simulation time of several orders of magnitude lower than that required by Montecarlo analysis, while ensuring a good accuracy. K e y w O r d sDevice mismatch, stochastic simulation, MNA, MOS ICs, nonMontecarlo analysis.

Piecewise linear second moment statistical simulation of ICs affected by non‐linear statistical effects

“…Although previous works [13,14] have addressed the problem of solving Equation (8), the approach used is based on the assumptions: (i) the magnitude of g is sufficiently small to consider the solution of Equation (9) as linear in the range of variability of g or (ii) the non-linearities in Equation (9) are so smooth that they might be considered as linear even for a wide range of g. The above hypothesis makes it possible to linearize Equation (8) by the first-order Taylor expansion, so that the resulting linear equation can easily be solved.…”

“…In order to make the problem manageable, we exploit the arbitrariness of f ( ), or that of f ( ), which is the same since g and j are related by the transformation of Equation (13).…”

Stochastic Analysis of Deep-Submicrometer CMOS Process for Reliable Circuits Designs

“…We will interpret (14) as an Ito system of stochastic differential equations. Now rewriting (14) in the more natural differential form (15) where we substituted with a vector of Wiener process . If the functions and are measurable and bounded on the time interval of interest, there exists a unique solution for every initial value [29].…”

“…Since the magnitude of the noise content in a signal is much smaller in comparison to the magnitude of the signal itself in any functional circuit, a system of nonlinear stochastic differential equations described in (13) can be piecewise-linearized under similar assumptions as noted in the previous section. Now, including the noise content description, (9) can be expressed in general form as (14) where . We will interpret (14) as an Ito system of stochastic differential equations.…”