Augmented nodal matrices and normal trees ?
Augmented nodal matrices play an important role in the analysis of different features of electrical circuit models. Their study can be addressed in an abstract setting involving two- and three-colour weighted digraphs. By means of a detailed characterization of the structure of proper and normal trees, we provide a unifying framework for the rank analysis of augmented matrices. This covers in particular Maxwells tree-based determinantal expansions of (non-augmented) nodal matrices, which can be considered as a one-colour version of our results. Via different colour assignments to circuit devices, we tackle the DC-solvability problem and the index characterization of certain differentialalgebraic models which arise in the nodal analysis of electrical circuits, extending several known results of passive circuits to the non-passive context.
normal tree electrical circuit weighted digraph index nodal analysis proper tree differentialalgebraic equation