Guaranteed passive direct lumped-element modeling of transmission lines

A novel approach to the reduced-order modeling of the frequency-dependent skin-effect (R-L) parameters of a transmission-line interconnect is proposed. A lumped-element circuit model for a short length of the lines is obtained directly from the finite-element method matrix equations. Only the most "important" eigenvalues and eigenvectors of the finite-element matrix are used, based on the contribution they make to the line parameters. The resulting reduced-order equivalent circuit is always passive and stable without the need for special modifications. The model can thus be immediately applied to problems where the transmission line is connected to nonlinear circuits. The model should find practical use in the design of flexible interconnect circuits as well as in other areas of high-speed digital electronics.