  This paper proposes a hierarchical adaptive sampling scheme for passivity
characterization of large-scale linear lumped macromodels. Here, large-scale is
intended both in terms of dynamic order and especially number of input/output
ports. Standard passivity characterization approaches based on spectral
properties of associated Hamiltonian matrices are either inefficient or
non-applicable for large-scale models, due to an excessive computational cost.
This paper builds on existing adaptive sampling methods and proposes a hybrid
multi-stage algorithm that is able to detect the passivity violations with
limited computing resources. Results from extensive testing demonstrate a major
reduction in computational requirements with respect to competing approaches.
