The New Algorithm for Symbolic Network Analysis.

A new and highly efficient tree identification algorithm is derived here for obtaining the determinant and the cofactors of a circuit's node admittance matrix, and hence, for obtaining various symbolic network functions for one-port and two-port reciprocal and nonreciprocal networks, with the network's topological description as its input. The algorithm is so devised that it is practically memory-storage free, and it is simple enough that even a microcomputer can obtain symbolic network functions for a fairly large circuit in a reasonably short time. It is worth noting that the algorithm can handle topological branches with infinite admittance values. Making use of this special feature, we have derived a simple topological model for the ideal operational amplifier, hence providing the ability to obtain various topological formulas of operational amplifier circuits in a reasonable time. By choosing appropriate symbolic network functions, along with some measured transfer function data, the circuit's nominal element values, and a nonlinear-equation solving subroutine, we have constructed a computer program to perform analog circuit fault diagnosis. This program can identify which of a circuit's elements are faulty or out of design tolerances. In the course of this research we have also identified an application to a biological problem, one in which the resistor values of an electrical model of the guinea-pig cochlea can easily be deduced even when some nodes are inaccessible for measurements. All these features have been implemented on a very modest microcomputer, the Apple II. Obviously, a larger computer will not only accomplish the same result faster but also it will be capable of analyzing much larger circuits.