In a recent paper, this author presented a new substitutiontheorem specific of a class of linear lumped time-invanant RCLEJnetworks. The theorem dealt with the conditions a network N of thiskind must meet in order its associated resistive counterpart N~ar(C,) to be uniquely solvable. In this connection, remember thatN~ar(C,) is obtained from N by substituting independent capacitors ofthe maximal set C and dependent inductors with independent voltagesources, and independent inductors of the maximal set and dependentcapacitors with independent current sources (see Figure l, wherevector circuit symbols are used). The fundamental motivation for thisstudy lies in the fact that the unique solvability of N~ar(C,) isneeded to succeed in formulating the state equations of N, both inthe tree~2 and in the source~3 method. In the previous paper, it hasbeen shown that, for whatever choice of (C,),N~ar(C) is uniquelysolvable, provided that (i) N is made of two-terminal capacitors,two-terminal inductors, any number of multi-terminal resistors, andvoltage and/or current independent sources, and (ii) N is uniquelysolvable and strictly topologically degenerate only. N is said to bestrictly topologically degenerate, if it is degenerate only becauseof loops made of capacitors and independent voltage sources, and/orcut-sets made of inductors and independent current sources. In thispaper, the above theorem has been extended to cover the importantcase in which N also contains multi-terminal (i.e. coupled)inductors. It must be expressly observed that the other assumptions of the theorem remained unchanged, while the proof has beenconsiderably modified.
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