### 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) |
---|---|

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 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of the Franklin Institute*,

*279*(2), 83-94.

**Bounds on impedance functions of R, ± L, ± C, T networks.** / Huang, T. S.; Lee, H. B.

Research output: Contribution to journal › Article

*Journal of the Franklin Institute*, vol. 279, no. 2, pp. 83-94.

}

TY - JOUR

T1 - Bounds on impedance functions of R, ± L, ± C, T networks

AU - Huang, T. S.

AU - Lee, H. B.

PY - 1965/2/1

Y1 - 1965/2/1

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=50549198449&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=50549198449&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:50549198449

VL - 279

SP - 83

EP - 94

JO - Journal of the Franklin Institute

JF - Journal of the Franklin Institute

SN - 0016-0032

IS - 2

ER -