Analog circuit sizing based on formal methods using affine arithmetic

Abstract

We present a novel approach to optimization-based variation-tolerant analog circuit sizing. Using formal methods based on affine arithmetic, we calculate guaranteed bounds on the worst-case behavior and deterministically find the global optimum of the sizing problem by means of branch-and-bound optimization. To solve the nonlinear circuit equations with parameter variations, we define a novel affine-arithmetic Newton operator that gives a significant improvement in computational efficiency over an implementation using interval arithmetic. The calculation of guaranteed worst-case bounds and the global optimization are demonstrated by a prototype implementation.

An Introduction to Affine Arithmetic

“…However, the tighter range estimates provided by AA often lead to fewer function evaluations, so the total running time is actually reduced; and this advantage increases as the global error tolerance gets reduced. Indeed, AA has been found to be more efficient than IA in many applications [10,22,34,33,3,25,32,50,6,7,12,15,9]. There are other SV computation models that provide first-order approximations, including E. R. Hansen's generalized interval arithmetic [20] and its centered form variant [41], first-order Taylor arithmetic [41], and the ellipsoidal calculus of Chernousko, Kurzhanski, and Ovseevich [4,31].…”

Verification of Mixed-Signal Systems with Affine Arithmetic Assertions

“…Further, in [33] this methodology found its application in sizing of analog circuits. Using Affine Arithmetic the bounds on the worst case circuit behavior are calculated and the global minimum of sizing problem is determined due to inclusion isotonicity.…”

Fast, accurate static analysis for fixed-point finite-precision effects in DSP designs

“…It has been used in areas such as computer graphics [6], analog circuit sizing [12], and floating point error modeling [2]. In contrast to IA, AA preserves correlations among intervals.…”