Topological Rules for Linear Networks and Their Application

Nathan's rules are stated and their applications are illustrated. The rules provide the expansion of admittance functions of linear networks which may include reciprocal and nonreciprocal branches, infinite-gain operational amplifiers, dependent current or voltage sources, vacuum tubes, transistors, and ideal transformers. Kirchhoff's rules for reciprocal networks as well as signal-flow-graph rules are included as special cases. The rules are purely topological and, in contradistinction to some prior work, do not include sign rules dependent upon an arbitrary assisgnment of labels to nodes, or directions to branches. The applications include transistor, vacuum tube, analog computation, and transformer networks.