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Passivity verification and enforcement of delayed rational function macromodels from networks characterized by tabulated data

Passivity has become a critical issue while modeling high-speed networks characterized by tabulated data. For modules containing long delays, macromodeling based on delayed rational functions has been gaining popularity in recent years. However, there are currently no passivity verification or enforcement methods available for such macromodels. To address this issue, this paper proposes passivity verification and enforcement algorithms for delayed rational function macromodels of high-speed modules, characterized by tabulated data. Necessary theoretical foundation and validating examples are presented.