On the Passivity Criterion for LTI N-Ports

S. Boyd and L. O. Chua

International Journal of Circuit Theory and Applications, 10(4):323-333, October 1982.

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 gave 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.