STATE- SPACE APPROACH TO NETWORK SYNTHESIS

Abstract

The state-space approach to network analysis and synthesis has aroused considerable interest during the recent years, primarily, to develop computer-aided analysis and design techniques. This thesis is concerned with the application of this approach to various aspects of network synthesis problem. In particular, state-space interpretation of classical synthesis methods is sought and new techniques for network realization from state-variable or input-output characterization are discussed with a view to evolve improved procedures. The classical synthesis methods for linear, timeinvariant networks are well known. An interesting problem concerning the use of state variables for network synthesis would be interpretation, in state-space terms, of common synthesis procedures such as Foster, Cauer, Brune etc. Tnirs problem along with the interpretation of some of the proper ties of network functions in state-space terms is briefly discussed first. State-space techniques for the determination of impedance matrix from its given even part and a direct method for determining the transfer-function matrix from the given state-space specifications are proposed. In modern synthesis, many a time, the given information is in terms of state-variable characterization -viiirather than the input-output characterization. In this case, the natural approach to network synthesis is by state models. Before developing new synthesis procedures, generalized state models for RLC networks have been discussed. ks regards synthesis procedures,, js realization technique was given by Yarlagadda [86j for state model belonging to n-port LC networks. An improved method for this class has been evolved which is suitable for computerization. The proposed computer algorithm exploits the results reported by Anderson and NewcombJ,6j and is free from many problems faced while using Yarlagadda and Tokad[86J procedure. Further, a synthesis procedure is proposed for a class of n-port RLC networks^in which there are no cut-sets of inductors only, no loops of capacitors only and there is no coupling between the link resistances and tree-branch conductances. A synthesis procedure for a similar class of LC time-varying networks is also suggested. A procedure fcr the realization of A-matrix (portless networks) for a mere general class of RLC networks in which there is nc coupling between link resistances and tree-branch conductances is also given. It may be noted that starting from minimal state model these procedures result in minimal realizations and in case the given set of timeinvariant state equations is not minimal, procedures exist for obtaining a minimal sot[50J. In this context, for synthesis from a given set of non-minimal time-varying state equations, an interesting algorithm for removing uncontroll able (unobservable) states is proposed.