Criteria for the evaluation of linear two-port stability using two geometrically derived parameters

Two geometrically derived stability parameters, mu' (or mu) and nu' (or nu), are used to analyze the stability of a two-port network. The magnitudes of both mu' (or nu) and nu' (or nu) parameters determine geometrical relations between the stability circle and the unit Smith chart in the Gamma(S) (or Gamma(L)) plane, vertical bar mu'vertical bar (or vertical bar mu vertical bar) is defined as the minimum distance from the stability circle to the origin of the unit Smith chart in the Gamma(S) (or Gamma(L)) plane, while vertical bar nu'vertical bar (or vertical bar nu vertical bar) is defined as the maximum distance. Moreover, the signs of nu' (or nu) and mu' (or mu) parameters determine which region of the stability circle is stable (inside or outside) and whether the stable region includes the origin of the Smith chart, respectively. There are totally 12 situations between the stability circle and the unit Smith chart in the Gamma(S) (or Gamma(L)) plane by using mu' (or mu) and nu' (or nu) parameters. This paper classifies 12 situations in the Gamma(S) plane and also presents the corresponding practical two-port networks.