Black-box modeling of passive systems by rational function approximation

Rong Gao, Yidnekachew S. Mekonnen, Wendemagegnehu T. Beyene, Jose E. Schutt-Ainé

Research output: Contribution to journalArticlepeer-review


In this paper, a rational interpolation approach is used to approximate the transfer function of passive systems characterized by sampled data. Orthogonal polynomials are used to improve the numerical stability of the ill-conditioned Vandermonde-like interpolation matrix associated with the ordinary power series. First, the poles of the system are obtained by efficiently and accurately transforming the coefficients of the orthogonal polynomials to the ordinary power series using Clenshaw's recurrence algorithm. Then, the residues are solved in real or in complex conjugate pairs to insure a physically realizable system. Finally, the passivity of the system is enforced by applying certain constraints on the poles and residues of the system. The performances of the three most common orthogonal polynomials, Legendre and Chebyshev of the first and second kinds, are also compared to that of the power series.

Original languageEnglish (US)
Pages (from-to)209-215
Number of pages7
JournalIEEE Transactions on Advanced Packaging
Issue number2
StatePublished - May 2005


  • Chebyshev polynomials
  • Legendre
  • Orthogonal polynomials
  • Power series
  • Rational interpolation
  • Transfer function
  • Vandermonde matrix

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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