Time-domain parametric sensitivity analysis of multiconductor transmission lines

Abstract

We present a new parametric macromodeling technique for lossy and dispersive multiconductor transmission lines (MTLs). This technique can handle design parameters, such as substrate or geometrical layout features, and provide time-domain sensitivity information for voltage and currents at the ports of the lines. It is based on a recently introduced spectral approach for the analysis of lossy and dispersive MTLs [1], [2] and it is suited to generate state-space models and synthesize equivalent circuits, which can be easily embedded into conventional SPICE-like solvers. Parametric macromodels which provide sensitivity information are well suited for design space exploration, design optimization and crosstalk analysis. A numerical example validates the proposed approach in both frequency and time domain. IntroductionThe recent advances in fabrication methods and the rapid increase in operating speeds, density, and complexity of modern integrated circuits has made signal integrity a challenging task for high-frequency circuit designers. Consequently, highspeed interconnect modeling has become of paramount importance to properly capture physical effects such as reflection, crosstalk and propagation delays. The increased circuit complexity requires that designers make the proper trade-offs between conflicting design requirements using optimization techniques, in order to obtain the best possible performance. To achieve this goal, efficient and accurate sensitivity information with respect to interconnect parameters can be used to boost the efficiency of powerful optimizers that employ gradient-based techniques.In [3] a parametric macromodeling technique for lossy and dispersive MTLs is presented: it provides time-domain information for voltage and current at the ports of the lines, starting from the knowledge of the MTL per-unit-length (p.u.l.) parameters. In the present paper the cited method is extended to perform the parametric sensitivity analysis of MTLs with respect to either geometric or physical parameters directly in the time-domain. the proposed technique it is based on the spectral decomposition proposed in [1], [2] and on the numerical interpolation of the p.u.l. parameters.