TY - JOUR

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

AU - Huang, T. S.

AU - Lee, H. B.

N1 - Funding Information:
This work was supported in part by the U. S. Army, Navy, and Air Force under Contract DA 36-039-AMC-03200 (E); in part by the National Science Foundation (Grant GP-2495), the National Institutes of Health (Grant MH-04737-04), and the National Aeronautics and Space Administration (Grant NsG-496).

PY - 1965/2

Y1 - 1965/2

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).

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U2 - 10.1016/0016-0032(65)90208-5

DO - 10.1016/0016-0032(65)90208-5

M3 - Article

AN - SCOPUS:50549198449

SN - 0016-0032

VL - 279

SP - 83

EP - 94

JO - Journal of the Franklin Institute

JF - Journal of the Franklin Institute

IS - 2

ER -