Formal Analysis and Synthesis of Bilateral Switching Networks

Formal procedures for the analysis and synthesis of two-terminal combinational bilateral switching networks are presented. A bilateral switching network is one which contains only elements having the same switching transmission characteristic in both directions. Following the definitions for the terminology and notation, where some new terms are introduced, the definitions for a series-parallel network, a bridge element, and a bridge network are given. A condition, called the bridge condition, to test a given transmission function for possible bridge network realizations is presented. A stepwise decomposition procedure is developed which may be used for the analysis and synthesis of the series and parallel parts of the network. The steps are described both with linear graphs and connection matrices. The bridge condition partially formalizes bridge network synthesis. Redundant variables also are considered as an aid to network synthesis. Under certain conditions, the synthesis yields network realizations with the fewest possible number of elements.