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

  • Thao Dang
  • Alexandre Donzé
  • Oded Maler
Conference paper

DOI: 10.1007/978-3-540-30494-4_3

Volume 3312 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Dang T., Donzé A., Maler O. (2004) Verification of Analog and Mixed-Signal Circuits Using Hybrid System Techniques. In: Hu A.J., Martin A.K. (eds) Formal Methods in Computer-Aided Design. FMCAD 2004. Lecture Notes in Computer Science, vol 3312. Springer, Berlin, Heidelberg

Abstract

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 whose dynamic behavior is described by differential algebraic equations. To model and analyze such circuits under all possible input signals and all values of parameters, we build upon two techniques developed in the context of hybrid (discrete-continuous) control systems. First, we extend our algorithm for approximating sets of reachable sets for dense-time continuous systems to deal with differential algebraic equations (DAEs) and apply it to a biquad low-pass filter. To analyze more complex circuits, we resort to bounded horizon verification. We use optimal control techniques to check whether a Δ-Σ modulator, modeled as a discrete-time hybrid automaton, admits an input sequence of bounded length that drives it to saturation.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Thao Dang
    • 1
  • Alexandre Donzé
    • 1
  • Oded Maler
    • 1
  1. 1.VERIMAG, Centre EquationGièresFrance