HFSS15: Passivity

Passive devices can only dissipate or temporarily store energy, but never generate it. The mathematical definition of passivity is based upon the following condition:

Q = I - conjugate(transpose(S)) * S must be a positive semidefinite matrix.

where:

• S is the S-parameter matrix

• I is an identity matrix.

A positive semidefinite matrix has only non-negative eigenvalues. The passivity test computes the eigenvalues of the matrix Q above at each frequency in the sweep. If any of the eigenvalues is negative, and larger (in magnitude) than the specified passivity tolerance, then a violation of passivity is reported to the user. The default value for passivity tolerance is .0001 tolerance above 1.0 magnitude.