Improving robustness to termination conditions in passivity enforcement of rational macromodels

Common design and verification flows of electronic systems under Signal and/or Power Integrity (SI/PI) constraints often rely on the availability of accurate macromodels of components and interconnects. Such macromodels enable fast transient analysis at the system level and consequently the possibility to efficiently verify the quality of the design. Several approaches are available to construct macromodels whose response accurately matches the raw data used for their identification, most often tabulated scattering responses. However, for the sake of SI/PI optimization, it is mandatory that such models reproduce accurately the underlying structure response when inserted as a component in a larger network, possibly subjected to different or uncertain port termination schemes. This capability is not inherently guaranteed by standard macromodeling approaches. Recently, the authors proposed a modified Vector Fitting (VF) iteration that overcomes this issue, by optimizing the macromodel accuracy with respect to sets of arbitrary terminations. This work completes this robust macromodeling framework by introducing a companion perturbation-based passivity enforcement scheme that preserves the macromodel accuracy with respect to the prescribed set of loads. The main innovation is the definition of a novel loss function to drive the perturbation routine, that allows to correct the non-passive model while preserving the required robust performance. Numerical evidence on a set of relevant Power Delivery Network (PDN) benchmarks confirms the effectiveness of the proposed approach.