468 research outputs found
Stochastic Testing Simulator for Integrated Circuits and MEMS: Hierarchical and Sparse Techniques
Process variations are a major concern in today's chip design since they can
significantly degrade chip performance. To predict such degradation, existing
circuit and MEMS simulators rely on Monte Carlo algorithms, which are typically
too slow. Therefore, novel fast stochastic simulators are highly desired. This
paper first reviews our recently developed stochastic testing simulator that
can achieve speedup factors of hundreds to thousands over Monte Carlo. Then, we
develop a fast hierarchical stochastic spectral simulator to simulate a complex
circuit or system consisting of several blocks. We further present a fast
simulation approach based on anchored ANOVA (analysis of variance) for some
design problems with many process variations. This approach can reduce the
simulation cost and can identify which variation sources have strong impacts on
the circuit's performance. The simulation results of some circuit and MEMS
examples are reported to show the effectiveness of our simulatorComment: Accepted to IEEE Custom Integrated Circuits Conference in June 2014.
arXiv admin note: text overlap with arXiv:1407.302
Uncertainty quantification for integrated circuits: Stochastic spectral methods
Due to significant manufacturing process variations, the performance of integrated circuits (ICs) has become increasingly uncertain. Such uncertainties must be carefully quantified with efficient stochastic circuit simulators. This paper discusses the recent advances of stochastic spectral circuit simulators based on generalized polynomial chaos (gPC). Such techniques can handle both Gaussian and non-Gaussian random parameters, showing remarkable speedup over Monte Carlo for circuits with a small or medium number of parameters. We focus on the recently
developed stochastic testing and the application of conventional
stochastic Galerkin and stochastic collocation schemes to nonlinear
circuit problems. The uncertainty quantification algorithms for static, transient and periodic steady-state simulations are presented along with some practical simulation results. Some open problems in this field are discussed.MIT Masdar Program (196F/002/707/102f/70/9374
Stochastic Testing Method for Transistor-Level Uncertainty Quantification Based on Generalized Polynomial Chaos
Uncertainties have become a major concern in integrated circuit design. In order to avoid the huge number of repeated simulations in conventional Monte Carlo flows, this paper presents an intrusive spectral simulator for statistical circuit analysis. Our simulator employs the recently developed generalized polynomial chaos expansion to perform uncertainty quantification of nonlinear transistor circuits with both Gaussian and non-Gaussian random parameters. We modify the nonintrusive stochastic collocation (SC) method and develop an intrusive variant called stochastic testing (ST) method. Compared with the popular intrusive stochastic Galerkin (SG) method, the coupled deterministic equations resulting from our proposed ST method can be solved in a decoupled manner at each time point. At the same time, ST requires fewer samples and allows more flexible time step size controls than directly using a nonintrusive SC solver. These two properties make ST more efficient than SG and than existing SC methods, and more suitable for time-domain circuit simulation. Simulation results of several digital, analog and RF circuits are reported. Since our algorithm is based on generic mathematical models, the proposed ST algorithm can be applied to many other engineering problems
Tensor Computation: A New Framework for High-Dimensional Problems in EDA
Many critical EDA problems suffer from the curse of dimensionality, i.e. the
very fast-scaling computational burden produced by large number of parameters
and/or unknown variables. This phenomenon may be caused by multiple spatial or
temporal factors (e.g. 3-D field solvers discretizations and multi-rate circuit
simulation), nonlinearity of devices and circuits, large number of design or
optimization parameters (e.g. full-chip routing/placement and circuit sizing),
or extensive process variations (e.g. variability/reliability analysis and
design for manufacturability). The computational challenges generated by such
high dimensional problems are generally hard to handle efficiently with
traditional EDA core algorithms that are based on matrix and vector
computation. This paper presents "tensor computation" as an alternative general
framework for the development of efficient EDA algorithms and tools. A tensor
is a high-dimensional generalization of a matrix and a vector, and is a natural
choice for both storing and solving efficiently high-dimensional EDA problems.
This paper gives a basic tutorial on tensors, demonstrates some recent examples
of EDA applications (e.g., nonlinear circuit modeling and high-dimensional
uncertainty quantification), and suggests further open EDA problems where the
use of tensor computation could be of advantage.Comment: 14 figures. Accepted by IEEE Trans. CAD of Integrated Circuits and
System
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
Robust simulation methodology for surface-roughness loss in interconnect and package modelings
In multigigahertz integrated-circuit design, the extra energy loss caused by conductor surface roughness in metallic interconnects and packagings is more evident than ever before and demands explicit consideration for accurate prediction of signal integrity and energy consumption. Existing techniques based on analytical approximation, despite simple formulations, suffer from restrictive valid ranges, namely, either small or large roughness/frequencies. In this paper, we propose a robust and efficient numerical-simulation methodology applicable to evaluating general surface roughness, described by parameterized stochastic processes, across a wide frequency band. Traditional computation-intensive electromagnetic simulation is avoided via a tailored scalar-wave modeling to capture the power loss due to surface roughness. The spectral stochastic collocation method is applied to construct the complete statistical model. Comparisons with full wave simulation as well as existing methods in their respective valid ranges then verify the effectiveness of the proposed approach. © 2009 IEEE.published_or_final_versio
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