On the upper bounds of the equivalent oscillator and notch-filter circuits: a non-commutative group theoretic approach

Author

Raadhakrishnan, P. ; Yagle, Andrew E. ; Rao, B.V. ; Dorband, John E.

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., Michigan Univ., Ann Arbor, MI, USA

Volume

39

Issue

9

fYear

1992

fDate

9/1/1992 12:00:00 AM

Firstpage

756

Lastpage

759

Abstract

It is shown that the problem of synthesizing equivalent oscillators and notch filters from the knowledge of a given parent circuit is identical to that of finding the isomorphisms of a noncommutative group. It is also shown that many of the results established by earlier methods can easily be explained using the theory developed. The results derived show that earlier results do not lead to the best possible upper bound. The corrected upper bound is derived by counting the numbers of the noncommutative group. A well-known family of circuits is used to illustrate the theory developed

Keywords

active filters; group theory; notch filters; oscillators; RC oscillators; circuit synthesis; equivalent oscillators; family of circuits; isomorphisms; noncommutative group; noncommutative group theory; notch-filter circuits; upper bounds; Circuit synthesis; Equivalent circuits; Frequency; Impedance; Network synthesis; Operational amplifiers; Oscillators; Passive networks; Upper bound; Voltage;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.250166

Filename

250166