Ladder Network Analysis by Signal-Flow Graph-Application to Analog Computer Programming

Abstract

S. Mason's signal flow graph technique is applied to the analysis of ladder networks. Briefly, the flow graph of a ladder is developed using Ohm's and the two Kirchhoff's equations. The graph is then reciprocated so that it contains only forward paths. The transfer function, in the case of a simple ladder, is the reciprocal of the sum of all distinct paths from the output to the input node. In the case of ladders containing internal generators, independent or dependent, the transfer function can be found in a similar way with slight modifications. Other relations, such as the input impedance, transfer admittance, etc., can also be found directly from the flow graph. In essence, instead of writing mesh equations or applying recursion formulas of continuants, we construct a flow graph by inspection and analyze the network from the graph. In the last part of the paper, the striking similarities between the flow graph of a network and its analog computer simulation are pointed out. Indeed, the flow graph is the computer set-up in a schematic form.