求解线性集总参数电路的变分方法  

Variational Method for Solving a Linear Lumped Electrical Circuit

作　　者：邹军[1] 蒋陶宁[1] 顿月芹[2] 

机构地区：[1]清华大学电机工程与应用电子技术系,北京100084 [2]山东轻工业学院电子信息与控制工程学院,山东济南250353

出　　处：《电气电子教学学报》2010年第2期20-22,28,共4页Journal of Electrical and Electronic Education

摘　　要：变分原理在电磁场有限元计算中已获广泛应用,本文讨论如何将该原理应用于线性集总参数电路的求解中。笔者从特勒根定理出发,导出了基于节点电压和回路电流的功率泛函,给出了通过变分获得电路解答的方法和步骤,借助功率泛函的概念,指出了电路解答与电路系统的功率最小点或者功率驻定点相对应。数值算例验证了这一结论。本文目的是提供一个清晰的视角理解线性集总参数电路求解的物理本质。同时,集总参数电路的泛函是求解电磁场-电路耦合问题的桥梁之一。Variational energy method has been widely utilized in finite element method in computational electromagetics. In this paper, the variational solution for a linear lumped electrical circuit is deliberately discussed. In accordance with Tellegen＇s theorem, the power functional, which is based on nodal voltages and branch currents respectively, is derived, and the pertinent approach to obtain a solution is summarized. In light of the concept of the power functional, it is pointed that the solution of a linear lumped electrical circuit actually corresponds a minimum power point or a stationary saddle point. Several numerical examples demonstrate the idea of the paper. Instead of presenting an alternative way to solve the circuit, the purpose of this paper is to provide a more distinct viewpoint to understand the nature of solution of a linear circuit. Apparently, the power functional can also serve as a bridge to connect circuit and electro- magnetic field problem.

关 键 词：变分 功率泛函 线性电路 

分 类 号：TM131[电气工程—电工理论与新技术]