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Application of the mixed potential for formulating normal form equations for nonlinear rlc‐networks with ideal transformers
Author(s) -
Horneber E.H.
Publication year - 1978
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.4490060405
Subject(s) - rlc circuit , nonlinear system , uniqueness , transformer , mathematics , control theory (sociology) , network analysis , ideal (ethics) , topology (electrical circuits) , mathematical optimization , computer science , mathematical analysis , engineering , voltage , control (management) , physics , law , quantum mechanics , artificial intelligence , combinatorics , political science , electrical engineering , capacitor
For the class of complete nonlinear RLC‐networks the normal form equations can be established by a method given in Brayton and Moser 1 using the mixed potential. Before applying this approach it is a crucial point to investigate whether a network is complete. To this end in the present paper an algorithm is given which additionally leads to a partitioning of the network under consideration. Two theorems are given enabling the direct construction of the mixed potential starting from the obtained subnetworks. It is shown that complete nonlinear RLC‐networks with ideal two‐port transformers (RLCT‐networks) can be remodelled into complete RLC‐networks using a new approach to model non‐hybrid transformers. Noncomplete RLCT‐networks often can be remodelled into complete RLCT‐networks by inserting additional branches containing controlled sources which do not affect the mixed potential. Further simplifications are possible using the rules given to derive the so‐called ‘potential‐equivalent’ networks which contain less controlled sources but lead to the same normal form equations. Finally some theorems are given concerning the existence and uniqueness of solutions of a complete network where the conditions can be examined directly at the network before establishing the network equations.