In this paper, a generalized theory for passivity verification of delayed rational function (DRF) macromodels representing electrically long networks that are characterized by multiport tabulated scattering parameters is presented. In the proposed approach, passivity verification of DRF macromodels is formulated as a quasi-periodic frequency-dependent generalized eigenvalue problem, using which, the necessary search region for passivity violations is reduced to just a single period along the imaginary axis. Necessary theoretical foundations and the related proofs are developed. Further, a computationally more efficient method based on half-Hamiltonian size frequency-dependent generalized eigenvalue problem is developed. Numerical validations for both the full-size and half-size formulations are also presented.

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Keywords Delayed differential equations, delayed rational functions, frequency-dependent generalized eigenvalue problem, Hamiltonian matrix, high-speed interconnects, macromodeling, passivity, scattering parameters, tabulated data networks, transient analysis
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Journal IEEE Transactions on Components, Packaging and Manufacturing Technology
Charest, A. (Andrew), Nakhla, M.S, Achar, R, & Saraswat, D. (Dharmendra). (2011). Passivity verification of delayed rational function based macromodels of tabulated networks characterized by scattering parameters. IEEE Transactions on Components, Packaging and Manufacturing Technology, 1(3), 386–398. doi:10.1109/TCPMT.2010.2099750