Verification of Analog and Mixed-Signal Circuits Using Hybrid System Techniques

In this paper we demonstrate a potential extension of formal verification methodology in order to deal with time-domain properties of analog and mixed-signal circuits. The dynamic behavior of an analog circuit can be described by a system of differential algebraic equations. To model and analyse such circuits under all possible input signals and all values of parameters, we apply various techniques developed in the context of hybrid (discrete-continuous) control systems. Two methodologies are investigated: First, we extend dense-time reachability analysis to differential algebraic equations (DAEs) and apply it to a biquad lowpass filter. Then, an optimal control technique, for discrete-time hybrid, similar in spirit to bounded model-checking, is used to check stability of a ∆-Σ modulator.