Mode Theory of Multiterminal Transducer Chains

The mode concept is applied to the analysis of linear multiterminal transducers, operating at a discrete frequency. The transfer matrix of the most general transducer is considered, restrictions of reciprocity, symmetry and losslessness being introduced as special cases. A classification of proper modes of signal transmission into reactive, pseudo-active and power-handling modes is attempted. Single and multiple mode operation is investigated and a mode-sorter termination is described for the latter. Investigation of special multiterminal transducers shows that qualitative restrictions like losslessness and reciprocity impose orthogonality relations among the modes, whereas configurative restrictions like symmetry and reciprocity reduce the complexity of the problem by constraining the modes into pairs having reciprocal properties. An example is provided to indicate the possibility of pseudo-active, growing modes in lossless nonreciprocal transducers. Mode sorters are shown to be realizable as transformer banks in symmetrical chains.