On the passivity criterion for lti <i>N</i>‐ports

Abstract Existing proofs of the passivity criterion for linear, time‐invariant, distributed N ‐ports are either incorrect or too involved, requiring the use of advanced mathematics such as distribution theory . This paper presents a simple but completely rigorous proof using only basic real and complex analysis. For the sake of completeness we have included simple proofs of the Paley‐Wiener theorem and the Poisson formula for the half plane . We show that solvability , a non‐intuitive technical assumption made in rigorous theories of LTI passive networks, is virtually always satisfied. Finally, we give a passivity criterion applicable to N ‐ports described by general co‐ordinates, from which passivity criteria for any specific representation (e.g. impedance, admittance, hybrid, transmission, scattering, etc.) can be trivially derived.