A new method of circuit analysis and central trees of a graph

Abstract

As a method of analysis for the general linear lumped circuit including active elements, this paper proposes a new method called the primal dual analysis, in which the backward parts of the cut‐set and tieset analysis are applied in two steps. the problem to determine the minimum number of independent variables for the analysis is formulated from the graph‐theoretic viewpoint. the essential difference between the proposed method and the traditional methods is described from the viewpoint of minimizing the required set of variables. In the case of passive circuits, the problem of determining the minimum independent variables in the primal dual analysis is seen to be reduced to the problem of determining the central tree of the graph. This problem is known to be difficult to solve. In the latter part of this paper, some results for this problem, obtained by the authors up to present, are described.