The Use of Parenthesis-Free Notation for the Automatic Design of Switching Circuits

A parenthesis-free notation is introduced for the representation of series-parallel switching networks. The notation facilitates the calculation of circuit parameters and permits an unambiguous characterization of the circuit topology. Given certain criteria for feasibility of a switching network related to the circuit parameter values, it is shown how an infeasible series-parallel network can be transformed into an equivalent feasible network by ``cascading´´ operations applied to the two-terminal sub-networks of the original network. A systematic method is developed, resulting in an optimum choice of cascading operations such that the number of switching elements required to implement the transformed circuit is minimized relative to cascading.