A Comprehensive and Modular Stochastic Modeling Framework for the Variability-Aware Assessment of Signal Integrity in High-Speed Links

Abstract

Abstract-This paper presents a comprehensive and modular modeling framework for stochastic signal integrity analysis of complex high-speed links. Such systems are typically composed of passive linear networks and nonlinear, usually active, devices. The key idea of the proposed contribution is to express the signals at the ports of each of such system elements or subnetworks as a polynomial chaos expansion. This allows one to compute, for each block, equivalent deterministic models describing the stochastic variations of the network voltages and currents. Such models are synthesized into SPICE-compatible circuit equivalents, which are readily connected together and simulated in standard circuit simulators. Only a single circuit simulation of such an equivalent network is required to compute the pertinent statistical information of the entire system, without the need of running a large number of time-consuming electromagnetic-circuit cosimulations. The accuracy and efficiency of the proposed approach, which is applicable to a large class of complex circuits, are verified by performing signal integrity investigations of two interconnect examples.

Machine-Learning-Based Hybrid Random-Fuzzy Uncertainty Quantification for EMC and SI Assessment

“…Nonetheless, the slow convergence of the MC sampling, to account for the aleatory variability of the RVs, renders the hybrid algorithm still slow. Therefore, in this paper, PC expansions [28] are adopted, given their accuracy and efficiency in characterizing stochastic variations [2], [3], [4], [29], [30], [31], [32]. Using the PC expansion, a suitable model is computed for both the minimum and maximum depending on the RVs and the α-cut, in the form:…”

“…Even in relatively simple test setups several parameters are inherently unknown and/or hard to control. For these reasons, advanced statistical techniques have recently been applied to EMC and SI problems [1], [2], [3], [4], [5], [6], [7] with the objective to outperform the standard brute-force approach, based on Monte Carlo (MC) repeated simulations, in terms of computational efficiency, while retaining comparable accuracy in predicting the variability of the output variables.…”

Stochastic process design kits for photonic circuits based on polynomial chaos augmented macro-modelling

“…The polynomial chaos formalism described in the previous section is exploited here to create an augmented-macro model of a building block embedding its stochastic behaviour. The formalism presented in this section is based on the concept of augmented macro-modelling which has recently been introduced in electronics and microwave for the stochastic analysis of printed circuit board [20], transmission line [19,21], micro-strip interconnects [22][23][24] and high-speed links [25]. The description provided is based on scattering matrix formalism and is only valid for linear and passive photonic devices.…”

Evaluation of Generative Modeling Techniques for Frequency Responses

“…Typically, performing uncertainty quantification requires to obtain a large number of statistical samples (or instances), which is time-consuming and costly. Hence, several stochastic modeling techniques have been presented in recent years to overcome these limitations, for example based on the Polynomial Chaos (PC) expansion [1] or on Stochastic Reduced Order Models (SROM) [2].…”