S-Parameters are passive, if the matrix [I]-[S]†[S] is semi-positive definite. Here, [I] is the unity matrix, [S] is the scattering matrix, and † denotes the conjugation and transposition of a matrix. The calculated passivity measure is the minimum eigenvalue of [I]-[S]†[S] . S-Parameters are non-passive, if the passivity measure is negative. They are are lossless, if the passivity measure is zero.
See also