This paper presents a generalized theory of passivity verification in delay-based macromodels for multiconductor transmission line networks generated using the method of characteristics (MoCs). We demonstrate that the passivity in an MoC macromodel is equivalent to the nonnegative definiteness in the admittance matrices of two submodels. We then provide the necessary and sufficient conditions for each submodel to have a nonnegative definite admittance matrix. The presented theory develops an algebraic test to verify the passivity in MoC macromodels. Numerical results demonstrate the validity of the proposed theory.

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Keywords Delay systems, High-speed interconnects, Method of characteristics, Passivity, Positive-realness
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Journal IEEE Transactions on Advanced Packaging
Chen, C. (Changzhong), Gad, E. (Emad), Nakhla, M.S, & Achar, R. (2007). Passivity verification in delay-based macromodels of multiconductor electrical interconnects. In IEEE Transactions on Advanced Packaging (Vol. 30, pp. 246–256). doi:10.1109/TADVP.2007.895610