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This paper presents a general strategy for the electrical performance and Signal Integrity assessment of electrically long multi-chip links. A black-box time-domain macromodel is first derived from tabulated frequency responses in scattering form. This model is structured as a combination of ideal delay terms with frequency-dependent rational coefficients. A new identification scheme is presented, based on an initial blind delay estimation process, followed by a refinement loop based on an iterative Delayed Vector Fitting (DVF) process. Two alternative passivity enforcement schemes based on local perturbations are then presented. The result is an accurate and guaranteed passive delay-based macromodel, which is synthesized as a SPICEcompatible netlist for channel analysis. The proposed procedure enables safe and reliable circuit-based transient simulations of complex multi-chip links, including nonlinear drivers and receivers. The performance of the proposed flow is demonstrated on a large number of channel benchmarks.

This work presents a fast transient solver for Signal Integrity analysis of high-speed channels. We consider general chip-to-chip coupled interconnect structures, including arbitrary discontinuities at chip, package and board level. An external characterization of the interconnect in terms of tabulated scattering frequency samples is first converted to a closed-form macromodel, whose transient effects on input signals can be computed very efficiently through recursive convolutions. When combined with suitable models for drivers and receivers, a large-scale but very sparse system of equations is obtained. The latter is solved by an iterative scheme based on the Generalized Minimal RESidual (GMRES) method, further enhanced by a preconditioner based on Waveform-Relaxation. Contrary to previous formulations, the proposed scheme is guaranteed to converge in few iterations. Numerical examples show that the proposed solver outperforms standard SPICE in terms of runtime, with no loss of accuracy.

This paper presents an optimized Waveform Relaxation solver for electrically-long high-speed channels terminated by nonlinear networks. The time-domain scattering operators of channel and terminations are cast as recursive convolutions and nonlinear discrete-time filters, respectively. A transverse and longitudinal decoupling is then applied to the channel operator, with the introduction of suitable relaxation sources, and solved iteratively until convergence. A frequency-dependent over-relaxation parameter is introduced in order to optimize the convergence rate. Numerical results show significantly reduced runtime and iteration count for critical benchmarks with respect to previous Waveform Relaxation formulations.

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