电路的并行拓扑分析

【作者】 张源；

【导师】 李锋；

【作者基本信息】 复旦大学 ， 电路与系统， 2008， 硕士

【摘要】 近年来对线性模拟电路的符号分析逐渐成为了电路分析中的热门研究课题。推动符号分析成为关注热点的因素主要是符号分析相比于数值分析的独特优势。符号分析允许电路元件参数以符号形式参与分析,它全面揭示了电路与系统的性能与元件参数之间的关系,从而可以加快模拟电路的设计过程。然而符号分析常被限制用来分析较小规模的电路。这是因为它往往需要寻找电路拓扑图中的全部树,而树的数量又是随着电路的节点和回路元件数量的增加呈指数增长的。因此如何对较大规模的模拟电路进行符号分析成为了本文的主要研究课题。本文采用了无向图拓扑法和有向图拓扑法分别对无源电路和有源电路进行符号分析。针对拓扑分析方法不适用于分析大规模电路这一问题,本文将数值分析中常用的撕裂法与拓扑分析方法结合起来,提出了电路的并行拓扑分析方法。在实现上述算法与应用过程中,本文完成了以下工作:首先分析了拓扑分析方法的优势和劣势,在此基础上提出了将一个大规模电路分解成几个较小规模的子电路后再用拓扑分析法并行求解的方案,并采用了数值分析中常用于分解电路的撕裂法,实现了对大规模电路的并行拓扑分析。提出了针对无源电路的无向图并行拓扑分析方法,给出了该方法的具体实现步骤,并通过一个例子进行了说明。提出了针对有源电路的有向图并行拓扑分析方法,给出了该方法的具体实现步骤,以及撕裂时选取撕裂节点的基本原则,并通过一个例子进行了说明。最后本文对该算法进行了总结,并指出了该算法的不足之处。本文将节点撕裂法引入拓扑分析,完成对电路的并行处理,实现计算机对较大规模电路的并行符号分析,拓宽了符号分析法的应用“瓶颈”,提高了符号分析的速度与效率。更多还原

【Abstract】 In recent years, symbolic analysis of linearized analog circuit has been a major topic of research. The driving force behind this research is that symbolic analysis can obtain symbolic network functions with all circuit elements represented by symbols. It can improve the insight into the analog circuits, and therefore it can accelerate the design process of these circuits. But it is always limited to small-size circuits because of the exponential growth of the number of the terms(trees or loops) with the circuits size. So the symbolic analysis becomes the major topic of this article.In this paper, non-directed graph topological method and directed graph topological method has been applied to complete the symbolic analysis of the analog circuits. And the parallel topological analysis for circuits is proposed. The method combines node tearing with topological analysis to realize symbolically parallel analysis for larger scale circuits.The following works have been done in the implementation of the algorithm and its application.First, analyzed the advantage and disadvantage of the topological analysis method, and proposed a new method, the parallel topological analysis method.Secondly, proposed the parallel non-directed graph topological method which is applied to inactive network ; described the implementation of this method in detail; gave a example on applying the parallel non-directed graph topological method to an inactive network.Thirdly, proposed the parallel directed graph topological method which is applied to the active network; described the implementation of this method in detail; listed the rules of choosing the tearing node; gave a example on applying the parallel directed graph topological method to an active network.The parallel topological analysis method combines node tearing with topological analysis to realize symbolically parallel analysis for larger scale circuits. The method not only successfully enhances the applicability of symbolic analysis, but also improves operational speed and efficiency.更多还原