VPW: Homotopy Methods for Analysis and Simulation of Electronic Circuits

VPW：电子电路分析和仿真的同伦方法

• 批准号: 9550153
• 负责人: Ljiljana Trajkovic
• 金额: $ 18.47万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-09-01 至 1997-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9550153&HistoricalAwards=false
• 关键词: VPW; Homotopy; Methods; Analysis; Simulation

Finding dc operating points, steady state, and transient responses of electronic circuits are essenntial tasks in electrical circuit simulation and involve nonlinear differential/algebraic equations. Traditional methods for solving such systems of equations often fail, are difficult to converge, and, often cannot find all the solutions. Dr. Trajkovic will investigate the application of homotopy methods to solving nonlinear equations describing power electronic and switching circuits and power systems flow equations, that traditionally pose simulation difficulties. Experiments with homotopies may lead to the development of better circuit simulation tools and to better understanding of relationships between homotopy methods and the behavior of nonlinear circuits. Dr. Trajkovic will spend three months with the Electrical Engineering Department at the University of Wuppertal, Germany where she will collaborate with Professor Wolfgang Mathis and his students. Their "Theory and Computer Aided Design of Electronic Circuits " group actively pursues research in circuit theory and simulation. This will be a continuation of her research activities at Berkeley, with emphasis on theoretical work based on experiments with various homotopies. Interactive activities include: teaching a graduate course in "Advanced Circuit Theory" that will introduce students to analytical results that provide insights and understanding of complex behavior of electronic circuits; holding a workshop/seminar series on "Application of Homotopy Methods in Solving Engineering Problems," with special emphasis on circuit simulation and solving equations describing nonlinear circuits; and organizing informal workshops where female students make presentations and get advice about their research and career goals.

求出电子电路的直流工作点、稳态响应和暂态响应是电路仿真中的基本任务，涉及到非线性的微分/代数方程。求解这类方程组的传统方法往往失败，难以收敛，而且往往找不到所有的解。Trajkovic博士将研究同伦方法在求解描述电力电子和开关电路的非线性方程以及电力系统流动方程方面的应用，这些方程传统上会造成模拟困难。同伦实验可能会导致更好的电路仿真工具的开发，并更好地理解同伦方法与非线性电路行为之间的关系。特拉伊科维奇博士将在德国伍珀塔尔大学电气工程系工作三个月，在那里她将与沃尔夫冈·马西斯教授及其学生合作。他们的“电子线路理论与计算机辅助设计”课题组积极开展电路理论与仿真研究。这将是她在伯克利研究活动的继续，重点是基于各种同伦实验的理论工作。互动活动包括：教授“高级电路理论”的研究生课程，向学生介绍分析结果，这些分析结果提供对电子电路复杂行为的见解和理解；举办关于“同伦方法在解决工程问题中的应用”的工作坊/研讨会系列，重点是电路模拟和求解描述非线性电路的方程；以及组织非正式研讨会，让女学生做报告，并获得关于他们的研究和职业目标的建议。