A new method, using the graph theoretical approach, for obtaining symbolic state equations of linear electronic circuits

The state-space modelling of linear time-invariant electronic circuits without degeneracies is considered in this paper. The principal idea is to represent an electronic circuit as the interconnection of several integrators. A special type of directed graph (digraph) is used to describe the electronic circuit from the topological equations (voltages and currents) and the equations of component parts. An algorithm based on the analysis of this digraph is proposed which directly obtains the symbolic matrices of the state-space model of the circuit. From this digraph, various symbolic transfer function equations can be generated that express the desired relationships between variables of interest. The algorithm to find symbolic transfer function produces the results of the well-known Mason's reduction formula. A topological interpretation of sensitivity has been made to obtain symbolic sensitivity functions easily.