Global DC-Analysis with the Aid of Standard Network Analysis Programs

  • Tobias Nähring
  • Albrecht Reibiger
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 4)


We present applications of homotopy methods, which make it possible to compute multiple dc-operating points of transistor circuits with standard network analysis programs. It is possible to capture all dc-operating points at least of smaller transistor networks with the help of one- and two-parametric homotopies. Uniqueness criteria of network theory can help to find a parameterization of the homotopy path. As an example for appropriate uniqueness criteria a well known theorem of Nielsen and Willson is applied. Bounds for the parameter space can be found by the no-gain property of transistor circuits.


Param Eter Homotopy Method Feedback Structure Behavioral Equation Homotopy Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Kronenberg, L., Trajković, Lj., and Mathis, W.: Analysis of feedback structures and their effect on multiple dc-operating points. Proc. EGCTD’99, Stresa, Italy, Aug. 1999, pp. 683–686.Google Scholar
  2. 2.
    Widlar, R.J.: Design Techniques for Monolithic Operational Amplifiers. IEEE Journal of Solid-State Circuits, vol. SC-4, No. 4, August 1969Google Scholar
  3. 3.
    Haase, J.: Computation of transfer characteristics of multivalued resistive nonlinear networks. Proc. SSCT82, Part: Short Communications. (1982) 286–272Google Scholar
  4. 4.
    Nielsen, R. O., Willson, A.N.: A Fundamental Result Concerning the Topology of Transistor Circuits with Multiple Equilibria. Proceedings of the IEEE on Circuits and Systems. 68 (1980) 196–208Google Scholar
  5. 5.
    Ushida, A., Chua, L.O.: Tracing solution curves of non-linear equations with sharp turning points. International Journal of Circuit Theory and Applications. 12 (1984) 1–22MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Willson, A.N.: The no-gain property for networks containing three-terminal elements. IEEE Trans. Circuits and Systems. CAS-22 (1975) 678–687Google Scholar
  7. 7.
    Hasler, M., Neirynck, J.: Nonlinear Circuits. Artech House, inc. Norwood, 1986.Google Scholar
  8. 8.
    Reibiger, A., Mathis, W., Nähring, T., Trajkovic, Lj., Kronenberg, L.: Mathematical Foundations of the TC-Method for Computing Multiple DC-Operating Points. XI. ISTET’01 preprints CD-ROM, Linz-Austria, 2001.Google Scholar
  9. 9.
    Nähring, T., Reibiger, A.: Beiträge zur Arbeitspunktberechnung resistiver Netzwerke. Kleinheubacher Berichte, 45 (2001) 262–265Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Tobias Nähring
    • 1
  • Albrecht Reibiger
    • 1
  1. 1.Technische Universität DresdenGermany

Personalised recommendations