Determining stability circle using two geometrically derived parameters

Abstract

Two new stability parameters and /spl Gt/OPEN are defined for linear two port circuits using a geometrically approach. The magnitudes of both /spl mu/ and /spl nu/ parameters determine the geometrical relation between SC (stability circle) and USC (Unit Smith Chart) in /spl Gamma//sub L/ plane. If |/spl nu/|>|/spl mu/|>1, SC is outside the USC. If |/spl nu/|>1>|/spl mu/|>, SC intersects the USC. If 1>|/spl nu/|>|/spl mu/|>, SC is inside the USC. The signs of /spl nu/ parameter determine that the region inside SC (disk) is stable if /spl nu/>0 or the region outside the SC (disk complement) is stable if /spl nu/<0. The stable region includes the USC origin if /spl mu/ parameter is positive. Otherwise, the stable region excludes the USC origin when /spl mu/ parameter is negative. This paper illustrates the relationship between SC and USC for all the twelve situations.