Using trees to build non-singular bond graphs from electric circuit graphs

Abstract

A commonly used method to build bond graphs for electric circuits can lead to causal bond graphs with unity gain causal loops. Deriving equations from such causal bond graphs is problematic. This paper shows that, for electric circuits, unity gain causal loops are not a property inherent in the system but rather are due to the nature of the causal bond graphs. A method is proposed for building an acausal bond graph to which a modified version of the sequential causality assignment procedure can be applied, in order to guarantee a non-singular causal bond graph. This approach can also be applied to the problem of joining sub-systems.