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State‐space equations of regular and strictly topologically degenerate linear lumped time‐invariant networks: the multiport method
Author(s) -
Sommariva Antonino M.
Publication year - 2001
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.162
Subject(s) - degenerate energy levels , mathematics , state space , invariant (physics) , topology (electrical circuits) , simple (philosophy) , nonlinear system , state (computer science) , discrete mathematics , combinatorics , physics , algorithm , mathematical physics , quantum mechanics , philosophy , statistics , epistemology
Abstract A new complete approach to the multiport formulation of the state‐space equations of uniquely solvable regular or strictly topologically degenerate linear lumped time‐invariant networks is presented. It is based on a Gedankenexperiment during which the topological structure of the original network is manipulated in various ways. The final method requires one to calculate the describing matrices of three homogeneous multiports (i.e. a capacitive, an inductive and a resistive one), which are obtained from the network of interest in a very simple manner. As a by‐product, the equivalent partitioned network is also derived. As an example of application, the state‐space equations of a fourth‐order strictly topologically degenerate network are provided. Copyright © 2001 John Wiley & Sons. Ltd.