Criteria for the evaluation of unconditional stability of microwave lineartwo-ports: A critical review and new proof

The problem of unconditional stability for active two-port networks has bee n widely discussed in literature. A geometrical condition involving the sta bility circles and the Smith circle is generally found. Then, depending on the authors, several criteria, involving the two-port S-parameters, and equ ivalent to the geometrical one, are derived. The equivalence among the diff erent stability criteria has been clearly shown and some complete proof exi sts in the literature. In this paper, after a critical outlook on the mater ial existing in the literature, a new proof of the unconditional stability criterion is presented. This proof has the advantage of being directly rela ted to the concept of stability circles and to some geometrical conditions on the Smith chart, Moreover, a straightforward proof is given in which the unconditional stability at the input port implies that at the output port and vice versa.