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Some topologico‐dynamical properties of linear passive reciprocal networks
Author(s) -
Milić M. M.
Publication year - 1977
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490050413
Subject(s) - reciprocal , mathematics , algebraic number , topology (electrical circuits) , transformer , representation (politics) , algebraic structure , state space representation , polynomial , discrete mathematics , pure mathematics , combinatorics , algorithm , mathematical analysis , philosophy , linguistics , physics , voltage , quantum mechanics , politics , political science , law
The paper considers the complete solvability and the order of complexity of passive RLCT (T = multiwinding ideal transformer) networks. A topological approach based on the determinant polynomial of the matrix of hybrid equations, formed as a set of 1st‐order differential and algebraic equations, reveals the structure of the formulation tree and the subnetworks accountable for degeneracies. Topological and algebraic degeneracies are defined. Necessary and sufficient conditions for complete solvability are derived, and two algorithms are given to determine the order of complexity topologically, i.e. without having an explicit state‐space representation.