Delay Extraction Based Equivalent Elmore Model For RLC On-Chip Interconnects

As feature sizes for VLSI technology is shrinking, associated with higher operating frequency, signal integrity analysis of on-chip interconnects has become a real challenge for circuit designers. For this purpose, computer-aided-design (CAD) tools are necessary to simulate signal propagation of on-chip interconnects which has been an active area for research. Although SPICE models exist which can accurately predict signal degradation of interconnects, they are computationally expensive. As a result, more effective and analytic models for interconnects are required to capture the response at the output of high speed VLSI circuits. This thesis contributes to the development of efficient and closed form solution models for signal integrity analysis of on-chip interconnects. The proposed model uses a delay extraction algorithm to improve the accuracy of two-pole Elmore based models used in the analysis of on-chip distributed RLC interconnects. In the proposed scheme, the time of fight signal delay is extracted without increasing the number of poles or affecting the stability of the transfer function. This algorithm is used for both unit step and ramp inputs. From the delay rational approximation of the transfer function, analytic fitted expressions are obtained for the 50% delay and rise time for unit step input. The proposed algorithm is tested on point to point interconnections and tree structure networks. Numerical examples illustrate improved 50% delay and rise time estimates when compared to traditional Elmore based two-pole models

Enforcing passivity of parameterized LTI macromodels via Hamiltonian-driven multivariate adaptive sampling

We present an algorithm for passivity verification and enforcement of multivariate macromodels whose state-space matrices depend in closed form on a set of external or design parameters. Uniform passivity throughout the parameter space is a fundamental requirement of parameterized macromodels of physically passive structures, that must be guaranteed during model generation. Otherwise, numerical instabilities may occur, due to the ability of non-passive models to generate energy. In this work, we propose the first available algorithm that, starting from a generic parameter-depedent state-space model, identifies the regions in the frequency-parameter space where the model behaves locally as a non-passive system. The approach we pursue is based on an adaptive sampling scheme in the parameter space, which iteratively constructs and perturbs the eigenvalue spectrum of suitable Skew-Hamiltonian/Hamiltonian (SHH) pencils, with the objective of identifying the regions where some of these eigenvalues become purely imaginary, thus pinpointing local passivity violations. The proposed scheme is able to detect all relevant violations. An outer iterative perturbation method is then applied to the model coefficients in order to remove such violations and achieve uniform passivity. Although a formal proof of global convergence is not available, the effectiveness of the proposed implementation of the passivity verification and enforcement schemes is demonstrated on several examples

Delay Extraction based Macromodeling with Parallel Processing for Efficient Simulation of High Speed Distributed Networks

This thesis attempts to address the computational demands of accurate modeling of high speed distributed networks such as interconnect networks and power distribution networks. In order to do so, two different approaches towards modeling of high speed distributed networks are considered. One approach deals with cases where the physical characteristics of the network are not known and the network is characterized by its frequency domain tabulated data. Such examples include long interconnect networks described by their Y parameter data. For this class of problems, a novel delay extraction based IFFT algorithm has been developed for accurate transient response simulation. The other modeling approach is based on a detailed knowledge of the physical and electrical characteristics of the network and assuming a quasi transverse mode of propagation of the electromagnetic wave through the network. Such problems may include two dimensional (2D) and three dimensional (3D) power distribution networks with known geometry and materials. For this class of problem, a delay extraction based macromodeling approaches is proposed which has been found to be able to capture the distributed effects of the network resulting in more compact and accurate simulation compared to the state-of-the-art quasi-static lumped models. Furthermore, waveform relaxation based algorithms for parallel simulations of large interconnect networks and 2D power distribution networks is also presented. A key contribution of this body of work is the identification of naturally parallelizable and convergent iterative techniques that can divide the computational costs of solving such large macromodels over a multi-core hardware

Analyse et caractérisation des couplages substrat et de la connectique dans les circuits 3D : Vers des modèles compacts

The 3D integration is the most promising technological solution to track the level of integration dictated by Moore's Law (see more than Moore, Moore versus more). It leads to important research for a dozen years. It can superimpose different circuits and components in one box. Its main advantage is to allow a combination of heterogeneous and highly specialized technologies for the establishment of a complete system, while maintaining a high level of performance with very short connections between the different circuits. The objective of this work is to provide consistent modeling via crossing, and / or contacts in the substrate, with various degrees of finesse / precision to allow the high-level designer to manage and especially to optimize the partitioning between the different strata. This modelization involves the development of multiple views at different levels of abstraction: the physical model to "high level" model. This would allow to address various issues faced in the design process: - The physical model using an electromagnetic simulation based on 2D or 3D ( finite element solver ) is used to optimize the via (materials, dimensions etc..) It determines the electrical performance of the via, including high frequency. Electromagnetic simulations also quantify the coupling between adjacent via. - The analytical compact of via their coupling model, based on a description of transmission line or Green cores is used for the simulations at the block level and Spice type simulations. Analytical models are often validated against measurements and / or physical models.L’intégration 3D est la solution technologique la plus prometteuse pour suivre le niveau d’intégration dictée par la loi de Moore (cf. more than Moore, versus more Moore). Elle entraine des travaux de recherche importants depuis une douzaine d’années. Elle permet de superposer différents circuits et composants dans un seul boitier. Son principal avantage est de permettre une association de technologies hétérogènes et très spécialisées pour la constitution d’un système complet, tout en préservant un très haut niveau de performance grâce à des connexions très courtes entre ces différents circuits. L’objectif de ce travail est de fournir des modélisations cohérentes de via traversant, ou/et de contacts dans le substrat, avec plusieurs degrés de finesse/précision, pour permettre au concepteur de haut niveau de gérer et surtout d’optimiser le partitionnement entre les différentes strates. Cette modélisation passe par le développement de plusieurs vues à différents niveaux d’abstraction: du modèle physique au modèle « haut niveau ». Elle devait permettre de répondre à différentes questions rencontrées dans le processus de conception :- le modèle physique de via basé sur une simulation électromagnétique 2D ou 3D (solveur « éléments finis ») est utilisé pour optimiser l’architecture du via (matériaux, dimensions etc.) Il permet de déterminer les performances électriques des via, notamment en haute fréquence. Les simulations électromagnétiques permettent également de quantifier le couplage entre via adjacents. - le modèle compact analytique de via et de leur couplage, basé sur une description de type ligne de transmission ou noyaux de Green, est utilisé pour les simulations au niveau bloc, ainsi que des simulations de type Spice. Les modèles analytiques sont souvent validés par rapport à des mesures et/ou des modèles physiques

Small business innovation research. Abstracts of completed 1987 phase 1 projects

Non-proprietary summaries of Phase 1 Small Business Innovation Research (SBIR) projects supported by NASA in the 1987 program year are given. Work in the areas of aeronautical propulsion, aerodynamics, acoustics, aircraft systems, materials and structures, teleoperators and robotics, computer sciences, information systems, spacecraft systems, spacecraft power supplies, spacecraft propulsion, bioastronautics, satellite communication, and space processing are covered

An Adaptive Sampling Process for Automated Multivariate Macromodeling Based on Hamiltonian-Based Passivity Metrics

This paper introduces a fully automated greedy algorithm for the construction of parameterized behavioral models of electromagnetic structures, targeting at the same time uniform model stability and passivity. The proposed algorithm is able to determine a small set of parameter configurations for which an external solver provides on the fly the sampled scattering parameters of the structure over a predetermined frequency band. These samples are subjected to a multivariate rational/polynomial fitting process, which iteratively leads to a parameterized descriptor realization of the model. The main novel contribution in this work is the adoption of a model-based approach for the adaptive augmentation of an initially small set of frequency responses, each corresponding to a randomly-selected parameter configuration. In particular, the locations of the in-band passivity violations of intermediate macromodels constructed at each iteration are used as a proxy for the model-data error in those regions where input data are not available. This physics-based consistency check, which is enabled by recent developments in multivariate passivity characterization based on Skew-Hamiltonian-Hamiltonian (SHH) spectra, is combined with standard space exploration metrics to obtain a small-size and automatically-determined distribution of points in the parameter space, leading to the construction of an accurate macromodel with a very limited number of external field solver runs. The embedded passivity check and enforcement process guarantees that either the final model is passive throughout the parameter space, or the residual violations, if present, are negligible for practical purposes. Several examples validate the proposed approach for up to three concurrent parameters

NASA SBIR abstracts of 1991 phase 1 projects

The objectives of 301 projects placed under contract by the Small Business Innovation Research (SBIR) program of the National Aeronautics and Space Administration (NASA) are described. These projects were selected competitively from among proposals submitted to NASA in response to the 1991 SBIR Program Solicitation. The basic document consists of edited, non-proprietary abstracts of the winning proposals submitted by small businesses. The abstracts are presented under the 15 technical topics within which Phase 1 proposals were solicited. Each project was assigned a sequential identifying number from 001 to 301, in order of its appearance in the body of the report. Appendixes to provide additional information about the SBIR program and permit cross-reference of the 1991 Phase 1 projects by company name, location by state, principal investigator, NASA Field Center responsible for management of each project, and NASA contract number are included

Parameterized macromodeling of passive and active dynamical systems

L'abstract è presente nell'allegato / the abstract is in the attachmen

Time-Domain Macromodeling of High Speed Distributed Networks

With the rapid growth in density, operating speeds and complexity of modern very-large-scale integration (VLSI) circuits, there is a growing demand on efficient and accurate modeling and simulation of high speed interconnects and packages in order to ensure the signal integrity, reliability and performance of electronic systems. Such models can be derived from the knowledge of the physical characteristics of the structure or based on the measured port-to-port response.In the first part of this thesis, a passive macromodeling technique based on Method of Characteristics (referred as Passive Method of Characteristics or PMoC) is described which is applicable for modeling of electrically long high-speed interconnect networks. This algorithm is based on extracting the propagation delay of the interconnect followed by a low order rational approximation to capture the attenuation effects. The key advantage of the algorithm is that the curve fitting to realize the macromodel depends only on per-unit-length (p.u.l.) parameters and not on the length of the transmission line. In this work, the PMoC is developed to model multiconductor transmission lines.Next, an efficient approach for time domain sensitivity analysis of lossy high speed interconnects in the presence of nonlinear terminations is presented based on PMoC. An important feature of the proposed method is that the sensitivities are obtained from the solution of the original network, leading to significant computational advantages. The sensitivity analysis is also used to optimize the physical parameters of the network to satisfy the required design constraints. A time-domain macromodel for lossy multiconductor transmission lines exposed to electromag¬netic interference is also described in this thesis based on PMoC. The algorithm provides an efficient mechanism to ensure the passivity of the macromodel for different line lengths. Numerical examples illustrate that when compared to other passive incident field coupling algorithms, the proposed method is efficient in modeling electrically long interconnects since delay extraction without segmentation is used to capture the frequency response.In addition, this thesis discusses macromodeling techniques for complex packaging structures based on the frequency-domain behavior of the system obtained from measurements or electromagnetic simulators. Such techniques approximate the transfer function of the interconnect network as a rational function which can be embedded with modern circuit simulators with integrated circuit emphasis (SPICE). One of the most popular tools for rational approximations of measured or simulated data is based on vector fitting (VF) algorithms. Nonetheless, the vector fitting algorithms usually suffer convergence issues and lack of accuracy when dealing with noisy measured data. As a part of this thesis, a methodology is presented to improve the convergence and accuracy issues of vector fitting algorithm based on instrumental variable technique. This methodology is based on obtaining the “instruments” in an iterative manner and do not increase the complexity of vector fitting to capture the frequency response and minimize the biasing