New simple proofs of the two-port stability criterium in terms of the single stability parameter μ1 (μ2)

The classical scattering-parameter stability criterium for a linear two-port makes use of two conditions involving the Rollet parameter K plus one additional parameter. A new stability criterium was developed by Edwards and Sinksky [1992] on the basis of a condition on a single parameter, i.e., μ1 or μ2. This paper presents a new, simpler, and more straightforward set of proofs of the single-parameter stability criterium for a linear two-port. The first proof is algebraic and shows the equivalence of the conditions K>1, b 1>1 with the condition μi>1 (i=1, 2). The second proof, which is geometrical, relies only on the classical stability circle concepts in an improved way with respect to the treatment by Edwards and Sinksky.