Bond Graphs III: Bond Graphs and Electrical Networks

Electrical networks are defined and a definition of when a bond graph and an electrical network are equivalent is given. Bond graphs and electrical networks are defined to be primitive if they contain no transformers or gyrators. A bond graph is defined to be realisable if it is equivalent to an electrical network and primitively realisable if it is equivalent to a primitive electrical network. It is shown how to construct a bond graph equivalent to a given electrical network and how to construct an electrical network equivalent to a given bond graph. Chordless odd loops are defined and a characterisation of primitively realisable bond graphs in terms of chordless odd loops and forbidden induced subgraphs is given. It is shown how to construct a primitive network equivalent to a given primitively realisable bond graph.