Passivity Verification in Delay-Based Macromodels of Multiconductor Electrical Interconnects

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 macro-model 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.