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

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Formal Methods in Computer-Aided Design (FMCAD 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3312))

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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.

This work was partially supported by the European Community projects IST-2001-33520 CC (Control and Computation) and IST-2003-507219 PROSYD (Property-based System Design) and by the US Army Research Office (ARO) contract no. DAAD19-01-1-0485.

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References

  1. Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T.A., Ho, P.-H., Nicollin, X., Olivero, A., Sifakis, J., Yovine, S.: The algorithmic analysis of hybrid systems. Theoretical Computer Science 138, 3–34 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  2. Alur, R., Pappas, G.J. (eds.): HSCC 2004. LNCS, vol. 2993. Springer, Heidelberg (2004)

    MATH  Google Scholar 

  3. Asarin, E., Dang, T.: Abstraction by projection. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 32–47. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  4. Asarin, E., Dang, T., Girard, A.: Reachability analysis of nonlinear systems using conservative approximation. In: Maler, O., Pnueli, A. (eds.) HSCC 2003. LNCS, vol. 2623, pp. 20–35. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  5. Asarin, E., Bournez, O., Dang, T., Maler, O.: Reachability analysis of piecewiselinear dynamical systems. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 20–31. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  6. Asarin, E., Dang, T., Maler, O.: The d/dt tool for verification of hybrid systems. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 365–370. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  7. Ascher, U.M., Petzold, L.R.: Stability of computational methods for constrained dynamics systems. SIAM Journal on Scientific Computing 14, 95–120 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  8. Bemporad, A., Morari, M.: Control of systems integrating logic, dynamics, and constraints. Automatica 35, 407–427 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  9. Brenan, K.E., Campell, S.L., Petzold, L.R.: Numerical Solution of Initial Value Problems in Ordinary Differential-Algebraic Equations. North Holland, Amsterdam (1989)

    Google Scholar 

  10. Chutinan, A., Krogh, B.H.: Verification of polyhedral invariant hybrid automata using polygonal flow pipe approximations. In: Vaandrager, F.W., van Schuppen, J.H. (eds.) HSCC 1999. LNCS, vol. 1569, pp. 76–90. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  11. Lubich, C., Hairer, E., Wanner, G.: Geometric Numerical Integration. In: Structure-Preserving Algorithms for Ordinary Differential Equations. Series in Comput. Mathematics, vol. 31. Springer, Heidelberg (2003)

    Google Scholar 

  12. Pérez-Verdú, B., Medeiro, F., Rodríguez-Vázquez, A.: Top-Down Design of High-Performance Sigma-Delta Modulators, ch. 2. Kluwer Academic Publishers, Dordrecht (2001)

    Google Scholar 

  13. Feldmann, U., Günther, M.: The DAE-index in electric circuit simulation. In: Proc. IMACS, Symposium on Mathematical Modelling, vol. 4, pp. 695–702 (1994)

    Google Scholar 

  14. Floberg, H.: Symbolic Analysis in Analog Integrated Circuit Design. Kluwer, Dordrecht (1997)

    MATH  Google Scholar 

  15. Ghosh, A., Verumi, R.: Formal verification of synthesized analog circuits. Int. Conf. on Computer Design 4, 40–45 (1999)

    Google Scholar 

  16. Goodson, M., Schreier, R., Zhang, B.: An algorithm for computing convex positively invariant sets for delta-sigma modulators. IEEE Transactions on Circuits and Systems I 44, 38–44 (1997)

    Article  Google Scholar 

  17. Tomlin, C.J., Greenstreet, M.R. (eds.): HSCC 2002. LNCS, vol. 2289. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  18. Gupta, S., Krogh, B.H., Rutenbar, R.A.: Towards formal verification of analog designs. In: Proc. ICCAD (2004) (to appear)

    Google Scholar 

  19. Hartong, W., Hedrich, L., Barke, E.: On discrete modelling and model checking for nonlinear analog systems. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 401–413. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  20. Hein, S., Zakhor, A.: On the stability of sigma delta modulators. IEEE Transactions on Signal Processing 41 (1993)

    Google Scholar 

  21. Kouramas, K., Rakovic, S.V., Kerrigan, E.C., Mayne, D.Q.: Approximation of the minimal robustly positively invariant set for discrete-time LTI systems with persistent state disturbances. In: 42nd IEEE Conference on Decision and Control (2003)

    Google Scholar 

  22. Kurshan, R.P., McMillan, K.L.: Analysis of digital circuits through symbolic reduction. IEEE Trans. on Computer-Aided Design 10, 1350–1371 (1991)

    Google Scholar 

  23. Maler, O.: On optimal and sub-optimal control in the presence of adversaries. In: Workshop on Discrete Event Systems, (WODES) (2004) (to appear)

    Google Scholar 

  24. Maler, O., Nickovic, D.: Monitoring temporal properties of continuous signals. In: Proc. FORMATS/FTRTFT (2004) (to appear)

    Google Scholar 

  25. Maler, O., Pnueli, A. (eds.): HSCC 2003. LNCS, vol. 2623. Springer, Heidelberg (2003)

    MATH  Google Scholar 

  26. MOSEK ApS. The Mosek Optimization Toolbox for Matlab version 3.0 (revision 19) user’s guide and reference manual (November 2003)

    Google Scholar 

  27. Salem, A.: Semi-formal verification of VHDL-AMS descriptors. IEEE Int Symposium on Circuits and Systems 5, V-333–V336 (2002)

    Google Scholar 

  28. Schreier, R.: The delta-sigma toolbox version 6.0 (January 2003)

    Google Scholar 

  29. Sorensen, H.V., Aziz, P.M., Spiegel, J.V.D.: An overview of sigma-delta converters. IEEE Signal Processing Magazine, 61–84 (January 1996)

    Google Scholar 

  30. Varaiya, P.: Reach set computation using optimal control. In: Proc. KIT Workshop, Verimag, Grenoble (1998)

    Google Scholar 

  31. Wichmann, T.: Computer aided generation of approximate DAE systems for symbolic analog circuit design. In: Proc. Annual Meeting GAMM (2000)

    Google Scholar 

  32. Wichmann, T., Popp, R., Hartong, W., Hedrich, L.: On the simplification of nonlinear DAE systems in analog circuit design. In: Computer Algebra in Scientific Computing. Springer, Heidelberg (1999)

    Google Scholar 

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Author information

Authors and Affiliations

  1. VERIMAG, Centre Equation, 2 avenue de Vignate, 38610, Gières, France

    Thao Dang, Alexandre Donzé & Oded Maler

Authors
  1. Thao Dang
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  2. Alexandre Donzé
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  3. Oded Maler
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Editor information

Editors and Affiliations

  1. Computer Science Department, University of British Columbia,  

    Alan J. Hu

  2. IBM Austin Research Laboratory, 11400 Burnet Rd, MS 904-6H004, TX 78758-3493, Austin, USA

    Andrew K. Martin

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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. https://doi.org/10.1007/978-3-540-30494-4_3

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  • DOI: https://doi.org/10.1007/978-3-540-30494-4_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23738-9

  • Online ISBN: 978-3-540-30494-4

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