### Abstract

It is shown that if Z_{ij}(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 Z_{ij}(jw) satisfies the inequality | Z _{ij}(jw) - R_{ijo} + R_{ijs} 2 | ≤ (R_{ijo} - R_{ijs}) 2 (R_{jjo} - R_{jjs}) 2 (i,j = 1,2) for all real ω, where. R_{ijo} = the impedance Z_{ij} of N when all reactive elements are open circuited, and. R_{ijs} = the impedance Z_{ij} 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 Z_{ij}(jw).

Original language | English (US) |
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Pages (from-to) | 83-94 |

Number of pages | 12 |

Journal | Journal of the Franklin Institute |

Volume | 279 |

Issue number | 2 |

State | Published - Feb 1 1965 |

### ASJC Scopus subject areas

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

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## Cite this

Huang, T. S., & Lee, H. B. (1965). Bounds on impedance functions of R, ± L, ± C, T networks.

*Journal of the Franklin Institute*,*279*(2), 83-94.