Symbolic Analysis of Nullor-Based Circuits with the Two-Graph Technique

Symbolic analysis is a powerful tool which accelerates the electronic design process by providing insight about the behavior of a circuit. Recently, the analysis and synthesis of electronic circuits with nullors have received considerable attention. This is due to the fact that nullors are very flexible and versatile active elements. Very efficient analysis methods, such as nodal analysis, Coates flow graphs, and two-graphs are proposed in the literature and are widely used. It has arguably been reported (because it does not generate vanishing terms in the symbolic network functions) that the last cited analysis method may be considered as the most promising. Actually, using the two-graph method, symbolic transfer functions can be calculated via either signal flow graphs and Mason's formula, without any restriction on the type of the sources (dependent and independent), or the spanning tree enumeration method for RLC circuits with nullor equivalent circuits of independent voltage sources and all types of controlled sources. In this paper we propose a new method for symbolic analysis of circuits with nullors using the two-graph method in both versions, i.e. signal flow graphs and enumeration of spanning trees. This new method helps us to see distinctly the relationships between various circuit components (for the method using the signal flow graph) and enables us to calculate the symbolic network functions without the excess terms (for the method using the enumeration of spanning trees).