Solvability of bond graph junction structures with loops

The purpose of this paper is to present a simple computational rule for determining the solvability of the linear junction structure equations of multiport systems. This rule is derived from the bond graph for the system. Three types of junction structures are considered; namely, simple, weighted, and general. Weighted junction structures include transformers and general junction structures include gyrators. The concept of causal loop gain is defined, and its calculation is indicated. Necessary and sufficient conditions, based on the loop gain, are given regarding the solvability of linear junction structure equations. Examples are presented highlighting the results.