New Proofs of the Two-Port Networks Unconditional Stability Criteria Based on the Rollett K Parameter

The stability criteria based on the Rollett parameter (
$K$
) plus one auxiliary condition is yet the most popular method used by designers to evaluate the stability of a two-port network although other criteria are available. In this paper, novel analytical proofs of the criteria utilizing
$K$
and a new geometrical proof of the relationship between the stability of the ports of a circuit are proposed. They are obtained by making use of relationships between the reflection coefficients at the ports of the network and novel expressions that bind stability circles and unit mapping circles. The developed relations make the proposed proofs easier and more immediate than the traditional ones. Moreover, a new auxiliary condition having the same complexity and a greater geometrical insight with respect to the traditional ones is used.