Symbolic Determinant Decision Diagrams and Their Use for Symbolic Modeling of Linear Analog Integrated Circuits

Abstract

An efficient technique for the symbolic modeling of the frequency behavior of a linearized analog circuit is presented. It uses a compact graph representation based on the Laplace expansion of the system determinant, called determinant decision diagram or DDD. The construction of a circuit's DDD is explained and an analysis of the time and space complexity is given. These DDD's can be used in behavioral modeling by representing the exact numerical transfer function in a compact way. DDD's also enable the generation of symbolic transfer functions, resulting in a symbolic analysis technique with lower computational complexity than techniques not based on DDD's.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    Gielen, G. and Sansen, W., Symbolic Analysis for Automated Design of Analog Integrated Circuits. Kluwer Academic Publishers, 1991.

  2. 2.

    Lin, P. M., Symbolic Network Analysis. Elsevier, 1991.

  3. 3.

    Fernandéz, F. V. F., Rodríguez-Vázquez, A., Huertas, J. L. and Gielen, G., Symbolic Analysis Techniques-Applications to Analog Design Automation. IEEE press, 1998.

  4. 4.

    Gielen, G., Walscharts, H. and Sansen, W., “ISAAC: A symbol5.ic simulator for analog integrated circuits.” IEEE Journal of Solid-State Circuits 24, pp. 1587-1597, December 1989.

    Google Scholar 

  5. 5.

    Seda, S., Degrauwe, M. and Fichtner, W., “Lazy-expansion symbolic expression approximation in SYNAP,” in Proc. IEEE/ACM International Conference on Computer Aided Design, pp. 310-317, 1988.

  6. 6.

    Sommer, R., Hennig, E., Dröge, G. and Horneber, E.-H., “Equation-based symbolic approximation by matrix reduction with quantitative error prediction.” Alta Frequenza-Rivista di Elettronica 6, December 1993.

  7. 7.

    Hassoun, M. and McCarville, K., “Symbolic analysis of largescale networks using a hierarchical signal flowgraph approach.” Analog Integrated Circuits and Signal Processing (3), pp. 31-42, 1993.

  8. 8.

    Fernandéz, F. V. F. and Rodríguez-Vázquez, A., “Interactive AC modeling and characterization of analog circuits via symbolic analysis.” Analog Integrated Circuits and Signal Processing 1, pp. 183-208, November 1991.

    Google Scholar 

  9. 9.

    Pierzchala, M. and Rodanski, B., “Symbolic analysis of largescale networks by circuit reduction to a two-port,” in Proc. Symbolic Methods and Applications in Circuit Design Workshop, Leuven, 1996.

  10. 10.

    Shi, C.-J. and Tan, X., “Symbolic analysis of large analog circuits with determinant decision diagrams,” in Proc. IEEE/ACM International Conference on Computer Aided Design, November 1997.

  11. 11.

    Shi, C.-J. and Tan, X., “Canonical symbolic analysis of large analog circuits with determinant decision diagrams.” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 19(1), pp. 1-18, January 2000.

    Google Scholar 

  12. 12.

    Dobrovolny, P., “Design tool for symbolic analysis based on the matroid intersection theory,” in Proc. IEEE International Symposium on Circuits and Systems, 1998.

  13. 13.

    Bryant, R. E., “Graph-based algorithms for boolean function manipulation.” IEEE Transactions on Computers, pp. 677-691, 1986.

  14. 14.

    Verhaegen, W. and Gielen, G., “Efficient symbolic analysis of analog integrated circuits using determinant decision diagrams,” in Proc. International Conference on Electronic Circuits and Systems, 1998.

  15. 15.

    Vlach, J. and Singhal, K., Computer Methods for Circuit Analysis and Design. Van Nostrand Reinhold Publishers, 1983.

  16. 16.

    Wambacq, P., Gielen, G. and Sansen, W., “A cancellation-free algorithm for the symbolic analysis of large analog circuits,” in Proc. IEEE International Symposium on Circuits and Systems, pp. 1157-1160, 1992.

  17. 17.

    Daems, W., Verhaegen, W., Wambacq, P., Gielen, G. and Sansen, W., “Evaluation of error-control strategies for the linear symbolic analysis of analog integrated circuits.” IEEE Transactions on Circuits and Systems-I 46(5), pp. 594-606, May 1999.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Verhaegen, W., Gielen, G.G.E. Symbolic Determinant Decision Diagrams and Their Use for Symbolic Modeling of Linear Analog Integrated Circuits. Analog Integrated Circuits and Signal Processing 31, 119–130 (2002). https://doi.org/10.1023/A:1015041927036

Download citation

  • linear circuit analysis
  • analog symbolic analysis
  • determinant decision diagrams