Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification

Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a set of orthonormal polynomials and a proper numerical quadrature rule. The former are used as the basis functions in a generalized polynomial chaos expansion. The latter is used to compute the integrals involved in stochastic spectral methods. Obtaining such information requires knowing the density function of the random input {\it a-priori}. However, individual system components are often described by surrogate models rather than density functions. In order to apply stochastic spectral methods in hierarchical uncertainty quantification, we first propose to construct physically consistent closed-form density functions by two monotone interpolation schemes. Then, by exploiting the special forms of the obtained density functions, we determine the generalized polynomial-chaos basis functions and the Gauss quadrature rules that are required by a stochastic spectral simulator. The effectiveness of our proposed algorithm is verified by both synthetic and practical circuit examples.Comment: Published by IEEE Trans CAD in May 201

Parametric Macromodels of Differential Drivers and Receivers

This paper addresses the modeling of differential drivers and receivers for the analog simulation of high-speed interconnection systems. The proposed models are based on mathematical expressions, whose parameters can be estimated from the transient responses of the modeled devices. The advantages of this macromodeling approach are: improved accuracy with respect to models based on simplified equivalent circuits of devices; improved numerical efficiency with respect to detailed transistor-level models of devices; hiding of the internal structure of devices; straightforward circuit interpretation; or implementations in analog mixed-signal simulators. The proposed methodology is demonstrated on example devices and is applied to the prediction of transient waveforms and eye diagrams of a typical low-voltage differential signaling (LVDS) data link

Chip level simulation of fault tolerant computers

Chip level modeling techniques, functional fault simulation, simulation software development, a more efficient, high level version of GSP, and a parallel architecture for functional simulation are discussed

A new nonlinear time-domain op-amp macromodel using threshold functions and digitally controlled network elements

A general-purpose nonlinear macromodel for the time-domain simulation of integrated circuit operational amplifiers (op amps), either bipolar or MOS, is presented. Three main differences exist between the macromodel and those previously reported in the literature for the time domain. First, all the op-amp nonlinearities are simulated using threshold elements and digital components, thus making them well suited for a mixed electrical/logical simulator. Secondly, the macromodel exhibits a superior performance in those cases where the op amp is driven by a large signal. Finally, the macromodel is advantageous in terms of CPU time. Several examples are included illustrating all of these advantages. The main application of this macromodel is for the accurate simulation of the analog part of a combined analog/digital integrated circui

ToPoliNano: Nanoarchitectures Design Made Real

Many facts about emerging nanotechnologies are yet to be assessed. There are still major concerns, for instance, about maximum achievable device density, or about which architecture is best fit for a specific application. Growing complexity requires taking into account many aspects of technology, application and architecture at the same time. Researchers face problems that are not new per se, but are now subject to very different constraints, that need to be captured by design tools. Among the emerging nanotechnologies, two-dimensional nanowire based arrays represent promising nanostructures, especially for massively parallel computing architectures. Few attempts have been done, aimed at giving the possibility to explore architectural solutions, deriving information from extensive and reliable nanoarray characterization. Moreover, in the nanotechnology arena there is still not a clear winner, so it is important to be able to target different technologies, not to miss the next big thing. We present a tool, ToPoliNano, that enables such a multi-technological characterization in terms of logic behavior, power and timing performance, area and layout constraints, on the basis of specific technological and topological descriptions. This tool can aid the design process, beside providing a comprehensive simulation framework for DC and timing simulations, and detailed power analysis. Design and simulation results will be shown for nanoarray-based circuits. ToPoliNano is the first real design tool that tackles the top down design of a circuit based on emerging technologie

Locally-Stable Macromodels of Integrated Digital Devices for Multimedia Applications

This paper addresses the development of accurate and efficient behavioral models of digital integrated circuits for the assessment of high-speed systems. Device models are based on suitable parametric expressions estimated from port transient responses and are effective at system level, where the quality of functional signals and the impact of supply noise need to be simulated. A potential limitation of some state-of-the-art modeling techniques resides in hidden instabilities manifesting themselves in the use of models, without being evident in the building phase of the same models. This contribution compares three recently-proposed model structures, and selects the local-linear state-space modeling technique as an optimal candidate for the signal integrity assessment of data links. In fact, this technique combines a simple verification of the local stability of models with a limited model size and an easy implementation in commercial simulation tools. An application of the proposed methodology to a real problem involving commercial devices and a data-link of a wireless device demonstrates the validity of this approac

Modeling of thermally induced skew variations in clock distribution network

Clock distribution network is sensitive to large thermal gradients on the die as the performance of both clock buffers and interconnects are affected by temperature. A robust clock network design relies on the accurate analysis of clock skew subject to temperature variations. In this work, we address the problem of thermally induced clock skew modeling in nanometer CMOS technologies. The complex thermal behavior of both buffers and interconnects are taken into account. In addition, our characterization of the temperature effect on buffers and interconnects provides valuable insight to designers about the potential impact of thermal variations on clock networks. The use of industrial standard data format in the interface allows our tool to be easily integrated into existing design flow

Validation by Measurements of a IC Modeling Approach for SiP Applications

The growing importance of signal integrity (SI) analysis in integrated circuits (ICs), revealed by modern systemin-package methods, is demanding for new models for the IC sub-systems which are both accurate, efficient and extractable by simple measurement procedures. This paper presents the contribution for the establishment of an integrated IC modeling approach whose performance is assessed by direct comparison with the signals measured in laboratory of two distinct memory IC devices. Based on the identification of the main blocks of a typical IC device, the modeling approach consists of a network of system-level sub-models, some of which with already demonstrated accuracy, which simulated the IC interfacing behavior. Emphasis is given to the procedures that were developed to validate by means of laboratory measurements (and not by comparison with circuit-level simulations) the model performance, which is a novel and important aspect that should be considered in the design of IC models that are useful for SI analysi