A Novel Modelling Approach of RLC Electrical Circuits for Symbolic Circuit Analysis by the Direct Topological Method

Symbolic circuit analysis is a renowned technique to represent the behaviour of electrical circuits in terms of symbolic parameters. The choice of the analysis method influences on the awaited performance; therefore, the Direct Topological Method (DTM) is adopted, which consists of applying direct topological rules based on the topology of the electrical circuit to get the result under its definitive compact form with fewer steps and more flexibility when compared to other methods. The milestone of this method is the analysis of RLC circuits because it permits analysing more complex types of electrical/electronic circuits. To ensure the harnessing of the DTM best features for the symbolic circuit analysis of RLC electrical circuits with independent sources, the thorough study of the topology of the graph is essential; for this reason, a novel modelling approach is proposed in this paper. This modelling is achieved by the abstraction of the electrical circuit to its unique, reversible equivalent topological graph from its most basic elements while developing the necessary customized data structures for the storage and further processing based on the STL C ++ data structure templates. Finally, an example is provided to describe how such modelling is accomplished.