Extension of Brune's Energy Function Approach to the Study of LLF Networks

Abstract

An effective analytic approach to the study of the fundamental properties of driving point and transfer functions of RLC networks (also designated LLFPB networks) is based upon expressing the network functions in terms of energy functions associated with the network. Using this approach, Brune deduced the well-known necessary conditions on driving point and transfer functions of LLFPB networks. It is the aim of this paper to extend this approach to a class of active non-bilateral PLC networks (designated as LLF networks) generated by augmenting RLC networks through the addition of resistive, capacitive, and inductive multiterminal-pair devices which are not required to be passive or bilateral. In order to derive effectively the properties of LLF networks using the energy function approach, it is desirable to be able to analyze networks whose elements are multiterminal-pair devices. Such a method of analysis is suggested here as a generalization of a method due to Guillemin. Using the energy function approach, necessary conditions are derived for driving point and transfer functions of several classes of LLF networks. In addition, some of these conditions are shown to be sufficient. Networks are considered which consist of resistors, inductors, and capacitors, both positive and negative, in addition to gyrators and generalized versions of gyrators (to an inductive and capacitive nature).