Compact Macromodeling of High-Speed Circuits via Delayed Rational Functions

Charest, Andrew; Saraswat, D.; Nakhla, M.; Achar, R.; Soveiko, N.

doi:10.1109/lmwc.2007.910468

Cited by 35 publications

(38 citation statements)

References 6 publications

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“…Thanks to the factor e −2sτ in the denominator d(s), the proposed macromodel can directly and efficiently represent all infinite multiple reflections that take place in a mismatched line. We will show that this feature significantly improves the model efficiency with respect to previously published techniques that account only for a finite number of reflections [3,4,5,6]. In particular, we will compare the performance of proposed macromodels with both VF (no delays) and DVF [6].…”

Section: Model Formulationmentioning

confidence: 87%

Black-box identification of delay-based macromodels from measured terminal responses

Triverio

Grivet-Talocia

Chinea

2009

2009 IEEE Workshop on Signal Propagation on Interconnects

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This paper proposes a new formulation of black-box macromodels for electrically-long scalar interconnects, together with an efficient numerical identification scheme and an optimized SPICE synthesis. The proposed methodology explicitly preserves in the macromodel structure the infinite reflections due to termination mismatch, thus allowing for compact and lowcomplexity equivalent circuits. Numerical examples show the excellent performance of the proposed technique. IntroductionSignal Integrity and Electromagnetic Compatibility issues can seriously compromise the reliability of electronic systems unless properly taken into account since early design stages. A realistic assessment of these complex phenomena requires the availability of accurate, broadband, and efficient models for all interconnect structures, as well as their integration in the Computer Aided Design (CAD) suite adopted by the designer.This work focuses on the derivation of accurate and very efficient models for interconnect paths. When these structures are short compared to the minimum signal wavelength, rational identification algorithms such as Vector Fitting (VF) [2] provide a good solution to obtain a lumped macromodel, compatible with circuit simulators. For electrically long interconnects, however, this approach leads to very inefficient macromodels, with a huge number of poles, and the transition to distributed macromodels becomes essential. The latter should correctly reproduce the signal propagation effects via explicit extraction of delay elements.Several good solutions are available in the literature for straight interconnects of uniform cross section. The approaches based on the Method of Characteristics [8] and on Matrix Rational Approximations with delays [9] are the most efficient. Unfortunately, many real interconnects do not have a uniform cross section: examples are twisted pairs or high-speed PCB channels where connectors, junctions and vias are present. This paper presents a new method for the formulation and identification of efficient macromodels for long scalar interconnects, based only on their measured terminal frequency responses. The proposed macromodel formulation can be cast into a SPICE compatible subcircuit and has the remarkable feature of explicitly reproducing all infinite multiple reflections that take place in a transmission line. This feature guarantees a superior simulation efficiency with respect to previous solutions [6], as demonstrated by two application examples.

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Section: Model Formulationmentioning

confidence: 87%

Black-box identification of delay-based macromodels from measured terminal responses

Triverio

Grivet-Talocia

Chinea

2009

2009 IEEE Workshop on Signal Propagation on Interconnects

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“…Representation (21) belongs to the so-called two-piece model class and represents a modified version of the classic relation expressed in terms of port voltage and current [6]. Specifically, a H and a L and w H and w L are described as follows.…”

Section: A Single-ended Driversmentioning

confidence: 99%

“…Since our intention is to plug the model into proposed WR solver, which operates in the discrete time, the macromodel equation (21) is formulated and its parameters identified directly in discrete time with a time step t k = k δt, such that the output reflected wave at a given time step t k can be computed directly from (21) knowing its past samples as well as present and past samples of the incident wave. This description is compliant with (10) and with our proposed WR solver.…”

Section: A Single-ended Driversmentioning

confidence: 99%

Macromodel-Based Iterative Solvers for Simulation of High-Speed Links With Nonlinear Terminations

Olivadese

Grivet-Talocia

Siviero

et al. 2014

IEEE Trans. Compon., Packag. Manufact. Technol.

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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.

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“…When dealing with the electrical large system, this technique requires a large order of approximation and may lead to serious accuracy degradation in system-level simulation. Recently, the delay-based macromodeling techniques [24][25][26][27][28] are developed for more general electrical large networks. Their models include the propagation delay terms mixed with suitable rational coefficients.…”

Section: Introductionmentioning

confidence: 99%

An Extended Delay-Rational Macromodel for Electromagnetic Interference Analysis of Mixed Signal Circuits

Luo¹

2012

PIER

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Abstract-This paper presents an extended delay-rational macromodel for electromagnetic interference analysis of mixed signal circuits. Firstly, an S-parameter matrix based delay-rational macromodel of the associated microwave network or system is established. Then, we extend the macromodel to include the external electromagnetic interference effects. The forced waves induced by the excitation fields are computed using full-wave method and treated as additional equivalent sources. Next, the macromodel is modified to embed the additional sources at each corresponding port. Finally, the resulting macromodel is converted into equivalent circuit for circuit analysis with the corresponding linear and non-linear port terminations. Several examples are computed by using the proposed method and the numerical results are compared with those obtained by 3-D FDTD method only. They are all in a good agreement that validate this method.

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Compact Macromodeling of High-Speed Circuits via Delayed Rational Functions

Cited by 35 publications

References 6 publications

Black-box identification of delay-based macromodels from measured terminal responses

Black-box identification of delay-based macromodels from measured terminal responses

Macromodel-Based Iterative Solvers for Simulation of High-Speed Links With Nonlinear Terminations

An Extended Delay-Rational Macromodel for Electromagnetic Interference Analysis of Mixed Signal Circuits

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