| We propose new methodologies to improve the current state-of-the-art in macromodeling techniques pertinent to the rational function interpolation of broadband electromagnetic responses of linear, passive, multiport, high-speed interconnect networks.;First, we propose and demonstrate a new methodology that combines the efficiency of low-frequency and high-frequency resistance and inductance extraction for electrically-short interconnects using magneto-quasi-static field solvers with the accuracy of rational function interpolation using the Vector Fitting method to generate accurate SPICE-compatible dispersive macromodels for multiple, coupled wire bonds. Computational efficiency in the development of the macromodel is achieved by limiting the application of the field solver to only low frequencies, at which field penetration inside the wires is accurately resolved with a coarse discretization of the cross section of the wires, and to frequencies high enough that the skin effect is well developed and a surface impedance condition suffices to capture the frequency dependence of the wire resistance and inductance due to the skin effect.;Second, we investigate ways in which the computational cost of enforcing passivity of the generated multiport macromodel can be reduced. More specifically, two strategies were examined. The first one involved transfer function matrix element-by-element passivity assessment and enforcement. The second considered transfer function matrix bock-wise passivity enforcement. Our investigation of the two strategies and comparison to the full transfer matrix (common pole) passivity enforcement option, helped illustrate advantages and shortcomings of the various options. In summary, the advantage of working with a single set of poles often outweighs the computational savings associated with element-by-element and block-wise fitting for the case of networks with a large number of ports.;Third, we examine ways to improve the quality and physical consistency of the original data while at the same time both pruning them in a manner that preserves the accuracy of the rational fit and reducing the computational cost of the fitting process. Toward this we propose and demonstrate an adaptive sampling Vector Fitting algorithm, which adaptively reduces the number of the original sample data subject to the constraint that the causality of the data is ensured. In addition, in order to reduce the computational cost of the Vector Fitting process, we introduce the Vector Fitting via Repeated Random Sampling (VFRS) algorithm. VFRS achieves significant reduction in the computational cost of the Vector Fitting process by extracting the poles used for the rational fit of the complete set of samples through the rational function fitting of subsets of randomly selected samples.;Finally, a fast methodology is introduced for the assessment of the impact of the electromagnetic loading by adjacent wiring on a high-speed channel, in the presence of uncertainty in the geometry of the wiring layout. This is achieved by employing the mathematical framework of stochastic collocation and parametric macromodeling to provide for a computationally efficient development of a passive, broadband, stochastic electromagnetic macromodel of the channel over the random space defined by the random variables that define the uncertainty of the routing of the adjacent wiring. |
