On the Relationships Between Input and Output Stability in Two-Ports

In this paper, relationships between conditional stability at the input and at the output of a linear non-unilateral 2-port are analyzed for the first time. For this purpose, the existence of a duality mapping between the two ports is shown and, by using the main properties of Möbius transforms, new mutual relationships between conditional stability configurations at input and output ports are demonstrated. Such new relationships add to the case of unconditional stability for which it is well known that unconditional stability at the input implies unconditional stability at the output (and vice versa). To this end, all the possible cases of reciprocal position between the stability area and the Smith circle have been analyzed showing that, for a given situation at the input, only one corresponding situation can be observed at the output (and vice versa). Limit cases are further considered.