Passivity Check of $S$-Parameter Descriptor Systems via $S$-Parameter Generalized Hamiltonian Methods

This paper extends the generalized Hamiltonian method (GHM) (Zhang , 2009; Zhang and Wong, 2010) and its half-size variant (HGHM) (Zhang and Wong, 2010) to their
S
-parameter counterparts (called S-GHM and S-HGHM, respectively), for testing the passivity of
S
-parameter descriptor-form models widely used in high-speed circuit and electromagnetic simulations. The proposed methods are capable of accurately detecting the possible nonpassive regions of descriptor-form models with either scattering or hybrid (impedance or admittance) transfer matrices. Their effectiveness and accuracy are verified with several practical examples. The S-GHM and S-HGHM methods presented here provide a foundation for the passivity enforcement of
S
-parameter descriptor systems.