# State-space analysis and synthesis of active RLC networks

## Abstract

"This dissertation provides theoretical foundations for the state-space analysis and synthesis of linear active RLC networks containing all four types of controlled sources. The analysis portion is concerned with an explicit representation of the state model and the order of complexity of a general linear active RLC network. The problem considered in the synthesis portion is the realization of a given A-matrix with an active nondegenerate RLC-ladder network or an active RLC network without any particular structure.

The general active RLC network state model representations are explicitly expressed in terms of the fundamental circuit submatrices, the network element submatrices, and the dependency submatrices. The branch-capacitor voltages and the chord-inductor currents are uniformly chosen as the state variables. The controlled sources are controlled by the variables of the passive elements and the independent sources. The topological relationships of the network elements and controlled sources appear explicitly in the various submatrices of the state model representations. Such a formulation is helpful in providing an in-depth investigation of the qualitative properties of linear active networks.

An algorithm using a unified procedure for evaluating the least upper bound of the order of complexity of a general linear active network is presented. Derivation of this algorithm is based upon the transformation of the original network into an equivalent network containing only resistors, inductors, capacitors, and controlled sources. The algorithm is simple and easy to apply and does not require finding a particular tree or making complicated calculations.

The realization of a given A-matrix with an active nondegenerate RLC-ladder network is accomplished by factoring the A-matrix into three matrices. From these matrices, the values of the reactive elements, the topological structure of the passive elements, and the types, locations, and controlling functions of the controlled sources in the realized network are determined.

The approach to the realization of a given A-matrix with an active RLC network without any particular structure is to examine the A-matrix for certain properties, identify them, and then synthesize a network from the given A-matrix. Within the general class of active RLC networks, two special classes are considered. Also the sufficient conditions for decomposition of a paramount matrix of order three are established"--Abstract, pages ii-iii.

Fowler, Eddie R.

## Committee Member(s)

Bourquin, Jack J.
Bertnolli, Edward C.
Penico, Anthony J., 1923-2011
Fannin, D. Ronald

## Department(s)

Electrical and Computer Engineering

## Degree Name

Ph. D. in Electrical Engineering

Chinese Air Force (Chinese Military Defense Program)

## Publisher

University of Missouri--Rolla

1974

## Pagination

xx, 230 pages

Includes bibliographical references (pages 199-202).

## Document Type

Dissertation - Open Access

text

## Language

English

Electric network synthesis
State-space methods
Electric circuits

T 3029

6013083

## Electronic OCLC #

913221948

http://merlin.lib.umsystem.edu/record=b1067260~S5

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