Immittance and ${ S}$-Parameter-Based Criteria for the Unconditional Stability of Linear Two-Ports: Relations and Invariance Properties

Unconditional stability criteria for a linear two-port have been derived in the literature from the two-port immittance matrix (the Rollett approach), or from the
S
-parameters (as proposed by Kurokawa). In this paper, we stress some relations between the two strategies. First, we express the two- or single-condition stability criterion as a functions of immittances, and then we demonstrate that, besides being independent from the normalization immittances, they do not depend on the imaginary part of the input and output immittances. (The term
immitance
refers to an impedance or admittance. With input (output) immittances we refer to
Z

₁₁
or
Y

₁₁
(
Z

₂₂
or
Y

₂₂
), respectively.) Using these invariance properties, we define the
stability

equivalent

two-port

class
as a set of two-ports such as the unconditional stability of one element of the set implies the unconditional stability of all other elements. We finally show that a proper choice of an element of the set allows the single-condition criterion to be expressed in a particularly simple form, which suggests a purely mathematical way to generate alternative equivalent single condition stability criteria.