An invariant stability factor and its physical significance

Abstract

Relationships between the maximum power gain and the internal loop gain of a general linear two-port network are developed. A new stability factor is defined from the maximum-gain potentiality of the network without external feedback, and is physically identifiable as the modulus of the internal loop loss (the inverse of loop gain) at maximum available power gain where this is finite. Several theorems on this loop gain show the relationships between the new stability factor, Stern's stability factor and the author's `performance factor?. Though the earlier factors may be obtained by constraints on the internal loop gain, they are shown not to be exactly related to the internal loop gain of the two-port network at maximum power gain; also, they are not exact invariants in matrix environments save in exceptional cases. The new stability factor is an exact invariant for all its values in the possible matrix environments, demarcates the regions of potential instability and absolute stability, and is directly related to the maximum available power gain of the two-port network, when this gain is finite.