SHF: Small: Variational and Bound Performance Analysis of Nanometer Mixed-Signal/Analog Circuits

模拟和混合信号电路对工艺变化非常敏感，因为它们需要大量的匹配和布局规律。由于工艺引起的变异性增加，随着技术继续扩展到40纳米以下，这种情况变得更糟。由于工艺变化导致的晶体管电平失配是在sub-90nm技术中达到高良率的模拟设计的主要障碍。模拟电路设计人员通常采用蒙特卡罗（MC）分析来分析统计失配，并预测其设计在变化下的变分响应。MC分析需要大量的重复电路仿真，计算成本昂贵。混合信号/模拟电路的高效变分性能分析，如最坏情况、边界情况和统计分析，将成为纳米模拟/混合信号设计的必要条件。本研究旨在开发新颖有效的非蒙特卡罗技术，用于模拟/混合信号电路的最坏情况和统计分析。pi提出了基于基于图的符号分析技术，仿射区间算法和控制理论方法的模拟/混合信号电路的新的最坏情况分析方法。该方法首先利用基于行列式决策图（DDD）的符号分析和仿射区间算法，从线性化的模拟电路中构建变分传递函数。然后在变分传递函数的基础上，利用控制理论计算性能界。我们还将研究更保守的仿射区间算法来降低守恒性。在给定频域边界的情况下，我们还将研究时域的性能边界。pi计划开发快速的非蒙特卡罗随机分析方法来计算统计响应，例如由于工艺变化而导致的不匹配。该问题将被建模为求解非线性随机微分代数方程。非线性随机方法（Galerkin或配点法）和新的非线性宏观建模方法将被研究以解决由此产生的问题。本研究的结果将显著增加模拟/混合信号电路的变分和统计分析技术的核心知识，这将使模拟/混合信号系统的统计优化和设计更有效。通过与行业合作伙伴的合作，PI希望开发的技术将对设计界产生直接影响，以提高纳米集成模拟/混合信号系统的设计效率。拟议的研究和相关培训的跨学科性质将使学生在竞争激烈的高科技就业市场中获得关键技能。这笔拨款将使PI能够雇用更多的女性和代表性不足的少数民族学生，进一步为美国科技劳动力的多样性做出贡献。

Analog and mixed-signal circuits are very sensitive to the process variations as many matching and regularities of the layout are required. This situation becomes worse as technology continues to scale to sub-40nm owning to the increasing process-induced variability. Transistor level mismatch due to process variation is the primary barrier to reach a high-yield rate for analog designs in sub-90nm technologies. Analog circuit designers usually perform a Monte-Carlo (MC) analysis to analyze the statistical mismatch and predict the variational responses of their designs under variations. As MC analysis requires a large number of repeated circuit simulations, its computational cost is expensive. Efficient variational performance analysis of mixed-signal/analog circuits such as worst-case, bounding case and statistical analysis will become imperative for nanometer analog/mixed-signal designs. This research seeks to develop novel and efficient non-Monte-Carlo techniques for worst-case and statistical analysis of analog/mixed-signal circuits. The PIs propose to develop novel worst-case analysis methods for analog/mixed-signal circuits based on graph-based symbolic analysis technique, affine-like interval arithmetic and a control-theoretic method. The new method will first build variational transfer functions from linearized analog circuit by determinant decision diagram (DDD) based symbolic analysis and affine-like interval arithmetic. Then the performance bounds will be computed by control-theoretic theory based on the variational transfer functions. More conservative affine-like interval arithmetic to reduce conservation will also be investigated. The performance bounds in the time domains given frequency domain bounds will be investigated as well. The PIs plan to develop fast non-Monte-Carlo stochastic analysis methods to calculate statistical responses such as mismatch due to process variations. The problem is to be modeled as solving nonlinear stochastic differential-algebra-equations. Nonlinear stochastic methods (Galerkin or collocation methods) and new nonlinear macromodeling method will be investigated to solve the resulting problems.The outcome of this research will add significantly to the core knowledge of variational and statistical analysis techniques for analog/mixed-signal circuits, which will enable more efficient statistical optimization and design of analog/mixed-signal systems. By working with the industry partner, the PI expects that the developed techniques will bring immediate impacts on the design community to improve the design productivity for nanometer integrated analog/mixed-signal systems. The interdisciplinary nature of proposed research and relevant training will allow students to gain critical skills in the highly competitive high-tech job market. This grant will enable the PI to hire more female and underrepresented minority students to further contribute to the diversity in America's science and technology workforce.