Bounds on impedance functions of R, ± L, ± C, T networks

T. S. Huang, H. B. Lee

Research output: Contribution to journalArticle


It is shown that if Zij(s) is an open circuit impedance of a two-port network N containing positive resistances, positive and negative inductances, positive and negative capacitances, and ideal transformers, then Zij(jw) satisfies the inequality | Z ij(jw) - Rijo + Rijs 2 | ≤ (Rijo - Rijs) 2 (Rjjo - Rjjs) 2 (i,j = 1,2) for all real ω, where. Rijo = the impedance Zij of N when all reactive elements are open circuited, and. Rijs = the impedance Zij of N when all reactive elements are short circuited. The inequality is useful for finding bounds on the magnitude, the phase angle, and the real and the imaginary parts of the Zij(jw).

Original languageEnglish (US)
Pages (from-to)83-94
Number of pages12
JournalJournal of the Franklin Institute
Issue number2
StatePublished - Feb 1 1965
Externally publishedYes


ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Computer Networks and Communications
  • Applied Mathematics

Cite this