Circuits, Systems and Signal Processing

, Volume 2, Issue 2, pp 239–253 | Cite as

Realization of a multivariable positive real function with polynomial derivative being a reactance function

  • V. Ramachandran
  • M. O. Ahmad
Article
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Revised:

Abstract

Multivariable positive real functions whose polynomial derivatives are reactance functions — a characteristic not possible in the case of single-variable positive real functions — are discussed. It is shown that the input impedances of certain cascaded multivariable networks belong to this class. Necessary and sufficient conditions for a multivariable positive real function with unity degree in each variable to be the input impedance of a resistively-terminated cascade of two lossless two-ports in mutually exclusive variables and separated by a series inductor or a shunt capacitor in another variable are discussed.

Keywords

Real Function Input Impedance Reactance Function Series Inductor Shunt Capacitor 
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References

  1. 1.
    F. M. Reza, “Use of the Derivative in Electrical Network Problems,” Research Lab. of Electronics, M.I.T., Cambridge, Mass., Quarterly Research Report, Pt. 3, pp. 78–82, July 15, 1953.Google Scholar
  2. 2.
    F. M. Reza, “A Generalization of Foster's and Cauer's Theorems,” IRE Convention Record, Vol. 3, Pt. 2. pp. 22–26, 1955.Google Scholar
  3. 3.
    A. Talbot, “Some Theorems on Positive Real Functions,” IEEE Trans. Circuit Theory, Vol. CT-12, No. 4, pp. 607–608, December 1965.Google Scholar
  4. 4.
    R. E. Vowels, “A Note on Positive Real Functions,” IEEE Trans. Circuit Theory, Vol. CT-18, No. 3, pp. 383–386, May 1971.Google Scholar
  5. 5.
    E. G. Ansell, “On Certain Two-Variable Generalizations of Circuit Theory with Applications to Networks of Transmission Lines and Lumped Reactances,” IEEE Trans. Circuit Theory, Vol. CT-11, pp. 214–223, June 1964.Google Scholar
  6. 6.
    T. Koga, “Synthesis of Finite Passive n-ports with Prescribed Two-Variable Reactance Matrices,” IEEE Trans. Circuit Theory, Vol. CT-13, No. 1, pp. 31–52, March 1966.Google Scholar
  7. 7.
    T. Koga, “Synthesis of Finite Passive n-ports with Prescribed Positive Real Matrices of Several Variables,” IEEE Trans. Circuit Theory, Vol. CT-15, No. 1, pp. 2–23, March 1968.Google Scholar
  8. 8.
    V. Ramachandran, A. S. Rao, and P. K. Verma, “Some Theorems on Multivariable Positive Real Functions,” Archiv für Elektronik und übertragungstechnik, Vol. 28, No. 12, pp. 509–511, December 1974.Google Scholar
  9. 9.
    V. Ramachandran and M. O. Ahmad, “On a Dissimilarity of Polynomial Derivatives of Single- and Multi-Variable Positive Real Functions,” Proc. IEEE, Vol. 70, No. 10, pp. 1233–1234, October 1982.Google Scholar
  10. 10.
    H. Ozaki and T. Kasami, “Positive Real Functions of Several Variables and Their Applications to Variable Networks,” IRE Trans. Circuit Theory, Vol. CT-7, No. 3, pp. 251–260, September 1960.Google Scholar
  11. 11.
    M. O. Ahmad, H. C. Reddy, V. Ramachandran, and M. N. S. Swamy, “Cascade Synthesis of a Class of Multivariable Positive Real Functions,” IEEE Trans. Circuits and Systems, Vol. CAS-25, No. 10, pp. 871–878, October 1978.Google Scholar
  12. 12.
    Y. Kamp and V. Belevitch, “A Class of Multivariable Positive Real Functions Realizable by the Bott-Duffin Method,” Philips Research Report, Vol. 26, No. 6, pp. 433–442, December 1971.Google Scholar

Copyright information

© Birkhäuser Boston, Inc. 1983

Authors and Affiliations

  • V. Ramachandran
    • 1
  • M. O. Ahmad
    • 1
  1. 1.Department of Electrical EngineeringConcordia UniversityMontrealCanada

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