A symbolic method for the solution of some switching and relay-circuit problems

A symbolic method, using ordinary algebra throughout, is developed for the solution of some switching and relay-circuit problems. It is applied initially to 2-terminal networks consisting of switch contacts only. Each element is identified by a letter and expressions representing the networks are derived. The values 0 and 1 indicate an open circuit and a closed circuit, respectively, as applied to both a network as a whole and to individual elements; for the latter these same values also indicate whether the associated relay is unoperated or operated. A simple notation is used to distinguish between make contacts and break contacts. The method is extended to include symbols representing relay coils, and expressions are derived which represent a complete 2-terminal circuit, consisting of contacts and coils, connected to the supply battery. Problems of circuit analysis, simplification and synthesis are treated both for reflex and non-reflex types of circuit. Time effects are ignored.