Some invariant properties of linear electrical circuits

• Main Author: Rollett, John Mortimer
• Published: University of Surrey 1971
• Subjects: 621.3
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.751773

Linear n-ports are examined, at a single frequency, in the light of a method based on invariance principles, with regard to various physical properties including activity, non-reciprocity, transfer activity and absolute stability. For each particular property, the method leads to characteristic invariants, which form the basis for appropriate equivalent circuits. The method rests on the construction of an equivalence class of n-ports, which are all equivalent with respect to the physical property chosen for consideration. Provided the physical operations (2n-port imbeddings) inter-relating the n-ports form a group, invariants of the n-port descriptions can be determined. If the invariants form a necessary and sufficient set for equivalence, then they will represent measures, discrete or continuous, of the physical properties held in common by the n-ports. The chosen property will therefore be describable in terms of one or more of the invariants. The use of the method allows n-ports to be partitioned into separate equivalence sub-classes by arithmetic invariants, and ordered within the classes by algebraic invariants. It is thus shown that activity and nonreciprocity are essentially discontinuous properties, while transfer activity and absolute stability admit continuous measures. Other properties of lesser engineering interest are treated briefly. The general results are applied specifically to two-ports, and a systematic account of two-port invariants is given, illustrated by logic diagrams. Necessary and sufficient conditions for the equivalence of two-ports under lossless reciprocal imbedding are found, corresponding to transfer activity, and canonical equivalent circuits are discussed. A similar treatment is given for absolute stability, and the invariant absolute stability factor is derived in a generalized form. Measurement methods for the more important two-port invariants are described, and applied to high-frequency transistors. The work as a whole shows that the invariance method is a valuable technique in the fundamental study of n-ports.