From statistical model checking to statistical model inference: Characterizing the effect of process variations in analog circuits

This paper studies the effect of parameter variation on the behavior of analog circuits at the transistor (netlist) level. It is well known that variation in key circuit parameters can often adversely impact the correctness and performance of analog circuits during fabrication. An important problem lies in characterizing a safe subset of the parameter space for which the circuit can be guaranteed to satisfy the design specification. Due to the sheer size and complexity of analog circuits, a formal approach to the problem remains out of reach, especially at the transistor level. Therefore, we present a statistical model inference approach that exploits recent advances in statistical verification techniques. Our approach uses extensive circuit simulations to infer polynomials that approximate the behavior of a circuit. A procedure inspired by statistical model checking is then introduced to produce “statistically sound” models that extend the polynomial approximation. The resulting model can be viewed as a statistically guaranteed over-approximation of the circuit behavior. The proposed technique is demonstrated with two case studies in which it identifies subsets of parameters that satisfy the design specifications.