A Bound on the Scattering Parameters of Unconditionally Stable N-Ports

Unconditionally stable 2-ports exhibit the peculiar property of mapping regions in the passive termination plane into smaller regions in the input plane. Such a ‘contractive’ behavior is observed also when the number of ports, $N$ , is larger than two, provided the notion of output region is appropriately adjusted. Based on this premise, it is shown that the magnitudes of the scattering parameters of an unconditionally stable $N$ -port are bounded by a simple inequality. This necessary condition generalizes similar conditions which are already known to be valid for passive, reciprocal $N$ -ports, on the one hand, and for generic unconditionally stable 2-ports, on the other.