Constructive Signal Approximations for Fast Transient Simulation of Coupled Channels

Abstract

This paper addresses the problem of fast transient simulation of high-speed coupled channels driven by transceivers that include Transmitter Feed-Forward Equalization (TX-FFE). Practical circuit hardware implementations of such drivers may not be correctly represented by industry standard algorithmic modeling interfaces, which are usually based on ideal digital finite impulse response filters. In particular, slow transients may arise when aggressive FFE is activated and particular switching sequences significantly stress local voltage regulators integrated in the output buffers. In this paper, we model this effect using a constructive hierarchical approximation of the analog waveforms that form a linearized vector Thevenin or Norton representation of the driver. This representation enables the accurate simulation of coupled channels including both differential and common-mode signals. Analog waveforms at the receiver input are readily obtained by standard time-frequency transformations, while including channel characteristics and any additional linear equalization block, if present. This proposed framework is compatible with industry-standard Algorithmic Modeling Interfaces (AMI), extending their scope to coupled channels with non-ideal TX-FFE circuit blocks. Eye diagrams and transient waveforms corresponding to millions of bits are computed in few seconds using a non-optimized software implementation. Random jitter and crosstalk are seemlessly included as in standard AMI frameworks. The results of various numerical experiments on commercial transceivers are reported in this paper, confirming both the accuracy and the efficiency of the proposed framework.

Worst-Case Optimization of a Digital Link for Wearable Electronics in a Stochastic Framework

“…For the sake of simplicity linear models (similar to the ones implemented in IBIS-AMI simulations were used to model the buffers). If needed enhanced models of such devices can be adopted [11][12][13].…”

Stochastic Time-Domain Mapping for Comprehensive Uncertainty Assessment in Eye Diagrams

“…At this stage of the investigation, the driver and the receiver are modeled using compact, linear models, very similar to the ones implemented in IBIS-AMI simulations. Specifically, an equivalent Norton-based voltage controlled circuital representation of the differential drivers and receivers is used, according to the method developed in [31]. This representation enables the accurate simulation of coupled channels including both differential-and commonmode signals.…”

“…For a detailed presentation of the buffer models see (2) and Fig. 2 in [31] and the explanations therein.…”

“…However, the methodology described in this article can be used as is with nonlinear buffer models. For applications where such models are required for increased accuracy, they may readily be used [31], [32], [33]. It is important to note that the geometrical specifications of the interconnect, including the fabrication tolerances, are based on the experimental work published in [19].…”

A Data Compression Strategy for the Efficient Uncertainty Quantification of Time-Domain Circuit Responses

“…In this section, the feasibility and performance of the proposed methodology are assessed based on two application examples: a 16-bit channel with 54 uncertain parameters driven by Flash memory chips and a single-channel electronic link with 115 uncertain parameters [8] and driven by a DDR buffer. For the drivers, we use behavioral macromodels constructed using the method in [32], [33], but any other model, either behavioral or transistor-level, may be used.…”