Parameterized models for crosstalk analysis in high-speed interconnects

Abstract

Abstract-We present a new parametric macromodeling technique for lossy and dispersive multiconductor transmission lines (MTLs), that is suitable to interconnect modeling. It is based on a recently introduced spectral approach for the analysis of lossy and dispersive MTLs extended by utilizing the Multivariate Orthonormal Vector Fitting (MOVF) technique to build parametric macromodels in a rational form. They can handle design parameters, such as substrate or geometrical layout features, in addition to frequency. The presented technique is suited to generate state-space models and synthesize equivalent circuits, which can be easily embedded into conventional SPICE-like solvers. Parametric macromodels allow to carry out design space exploration, design optimization and crosstalk analysis efficiently. A numerical example validates the proposed approach in both frequency and time domain and is focused on the crosstalk analysis.

Time-Domain Green's Function-Based Parametric Sensitivity Analysis of Multiconductor Transmission Lines

“…parameters with the Green's function, which is used to expand the solution of the Sturm-Liouville problem, allows us to compute the poles and residues of the impedance matrix independently for each mode, reducing the complexity of the system identification significantly. In fact, the technique described in [3] and [4] first builds parametric macromodels for the p.u.l. parameters or for the modal impedance, using the multivariate orthonormal vector fitting technique [17], and then it combines the initial macromodels according to (4) to obtain the desired macromodel for the impedance matrix Z(s, g) in the entire design space.…”

“…In fact, the technique described in [3] and [4] first builds parametric macromodels for the p.u.l. parameters or for the modal impedance, using the multivariate orthonormal vector fitting technique [17], and then it combines the initial macromodels according to (4) to obtain the desired macromodel for the impedance matrix Z(s, g) in the entire design space. Our goal, however, it is to build a parametric macromodel also for the Z(s, g) matrix, to be able to perform a parametric sensitivity analysis.…”

“…For example, once the fabrication technology is decided, an optimization step is required at the early design stages to select the geometrical and material features of the structure, such as length and width of conductors, dielectric permittivity, and metal conductivity, yielding the optimum electrical performance, often under stringent signal integrity and electromagnetic compatibility constraints. To perform these design activities using full electromagnetic simulations on the entire parameter space is often computationally expensive, and therefore parametric macromodeling techniques that take into account design parameters in addition to frequency (or time) are needed [3], [4].…”

“…The major advantage of such an approach over other existing techniques [7], [8] is the rational nature of the dyadic Green's function which is appropriate for time-domain macromodeling, and is therefore suitable to generate a finite statespace representation and an equivalent SPICE circuit by using standard realization [9] and circuit synthesis techniques [10]. In [3] and [4], a parametric macromodeling technique for lossy and dispersive MTLs is proposed, which is based on the spectral approach [5]. 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.)…”

Spectral models for 1D blood flow simulations

“…The order of the spectral model is set to n modes = 60. The algorithm to choose the number of modes is described in [23]. Fig.…”