Properties of transfer functions of multiloop feedback active filters with identical biquadratic sections

Author

Biernacki, Radoslaw M. ; Styblinska, Bogumila

Volume

Issue

fYear

1980

fDate

5/1/1980 12:00:00 AM

Firstpage

350

Lastpage

357

Abstract

Conditions for realization of an active filter in a multiloop structure with identical biquadratic sections (MIB) are considered in this paper. It is shown that poles (zeros) of a transfer function of a MIB network with biquadratic section $k(s) = (ds^{2} + es +f)/(s^{2} + as + b)$ can be grouped in pairs such that for each pair $s_1$ and $s_2$ , the relation $s_{2}=-(Es_1+ F)/(Gs_1 + E)$ holds where $E=f-bd, F=af-be, G=e-ad$ . A new concept of a characteristic circle of a rational function is introduced. It is shown that its existence is necessary and sufficient for MIB network realization.

Keywords

Active filters; Biquadratic transfer functions; Feedback networks; Active filters; Dynamic range; Feedback; Frequency synthesizers; Hydrogen; Mass production; Network synthesis; Poles and zeros; Prototypes; Transfer functions;

fLanguage

English

Journal_Title

Circuits and Systems, IEEE Transactions on

Publisher

ieee

ISSN

0098-4094

Type

jour

DOI

10.1109/TCS.1980.1084824

Filename

1084824

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1183766