This paper presents an approach for the extraction of passive macromodels of large-scale interconnects from their frequency-domain scattering responses. Here, large-scale is intended both in terms of number of electrical interface ports and required dynamic model order. For such structures, standard approaches based on rational approximation via Vector Fitting and passivity enforcement via model perturbation may fail due to excessive computational requirements, both in terms of memory occupation and runtime. Our approach addresses this complexity by first reducing the redundancy in the raw scattering responses through a projection and approximation process based on a truncated Singular Value Decomposition. Then, we formulate a compressed rational fitting and passivity enforcement framework, that is able to obtain speedup factors up to 2-3 orders of magnitude with respect to standard approaches, with full control over the approximation errors. Numerical results on a large set of benchmark cases demonstrate the effectiveness of the proposed technique.

Rational macromodeling via Vector Fitting algorithms is a standard practice in Signal and Power Integrity analysis and design flows. However, despite the robustness and reliability of the Vector Fitting scheme, some challenges remain for those applications requiring models with a very large port count. Fully coupled signal and/or power distribution networks may require concurrent modeling of hundreds of simultaneously coupled ports over extended frequency bands. Direct rational fitting is impractical for such structures due to a large computational cost. In this work, we present a compression strategy aimed at representing the dynamic behavior of the structure through few carefully selected "basis functions". We show that model accuracy can be traded for complexity, with full control over approximation errors. Application of standard Vector Fitting to the obtained low-dimensional compressed system leads to the construction of a global state-space macromodel with significantly reduced runtime and memory consumption. Several benchmarks demonstrate the effectiveness of the approach.

This paper proposes a compact synthesis approach for reduced-order behavioral macromodels of linear circuit blocks for RF and Mixed-Signal design. The proposed approach revitalizes the classical synthesis of lumped linear and timeinvariant multiport networks by reactance extraction, which is here exploited to obtain reduced-order equivalent SPICE netlists that can be used in any type of system-level simulations, including transient and noise analysis. The effectiveness of proposed approach is demonstrated on a real design application.

Data transmission on high-speed channels may be affected by several undesired effects, including coupling from nearby interconnects, dispersion, losses, signal reflections from terminations and from internal discontinuities, and nonlinear/dynamic effects of drivers and receivers. The latter are often neglected, leading to very fast solvers, whose results may, however, be questionable when driver/receiver nonlinearities are important. This paper presents a framework for the transient analysis of complex high-speed channels with arbitrary nonlinear termination circuits. The approach is based on decoupling channel and terminations through a scattering-based waveform relaxation (WR) formulation. The channels are here cast as delay-rational macromodels, which are solved in discrete time domain through fast delayed recursive convolutions. The terminations can be either arbitrary circuits, solved by SPICE, or nonlinear behavioral macromodels, which are here formulated in discrete-time scattering representations. To overcome the known convergence issues of standard WR methods, we apply here more general iterative solution schemes, such as generalized minimal residual and biconjugate gradient stabilized, integrated into inexact Newton iterations, obtaining a set of numerical schemes with guaranteed convergence. The excellent performance of the proposed approach is illustrated on a large set of benchmarks.

This paper presents a new approach for the generation of reduced-order compact macromodels of analog circuit blocks in highly integrated Radio Frequency (RF) and Analog-Mixed-Signal (AMS) design. The circuits under investigation are designed and assumed to operate at certain bias points, where they should perform as linear as possible. So, they can be well approximated to first order by linearized transfer function models, assuming small-signal excitation around these operating points. This work concentrates on a number of key aspects. First, a fully-parameterized macromodeling flow is described, for the closed-form inclusion of external geometrical or design parameters in the macromodel responses. This aspect is important for fast optimization, design centering, and whatif analyses. Second, a parameterized DC correction strategy is presented, in order to guarantee that the DC response of the linearized macromodel matches to machine precision the true DC responses of the original circuit block. This aspect is fundamental when the macromodel is used in a system-level simulation deck that combines linearized and fully nonlinear models of other components. The main result of proposed approach is a SPICEcompatible reduced-order macromodel that can replace complex transistor-level circuit blocks plus passive interconnect networks, thus enabling dramatic speedup in transient system-level analyses and Signal Integrity verifications.