非正弦稳态网络和正弦稳态网络统一的场论说

【作者】 李强；

【导师】 陈燊年； 王建成；

【作者基本信息】 华侨大学 ， 电工理论与新技术， 2000， 硕士

【摘要】 本论文在场论说已有成果的基础上，把场论说的体系从正弦稳态扩展到非正弦稳态，并初步建立两者统一的关系；提出非正弦稳态下非线性网络中的积分形式的两组独立方程组是网络理论中场论学说的基本方程组，即它普遍适用于任何满足似稳条件的线性或非线性的集中参数网络。 本论文分四章。在前二章中，从实时形式的麦克斯韦方程组（其中E、H、j等物理量是时间的任意函数，从而不受正弦稳态条件的限制）和三种物质的线性和非线性的电磁性质方程出发，分别推导出适用于非正弦稳态线性网络和非正弦稳态非线性网络的电荷守恒定律和电磁场能量转换与守恒定律，然后通过两守恒定律分别在线性网络和非线性网络联立求得在此两网络中积分形式的两组独立方程组。从它们又推论得到非正弦稳态线性网络和非正弦稳态非线性网络的基尔霍夫电压定律和电流定律的新表式、包含互感的支路特性方程和四种基本网络元件理论等，组成场论说的基本内容。在此二章中，引入电容容抗率和电感感抗率的新概念，并由它们对元件线度的积分，直接引入了倒电容和电感系数的元件参数，同时由于j是时间的任意函数，在演绎过程中保留了和的形式，使得出的结论具有普遍性。对矢量C的微分方程求解的技术性上，并没有沿用现有场论说中的方法，而是创新地用一种更为严密和简洁的矩阵方程坐标变换的解法。在求非线性磁矢势A的表达式时，同样没有沿用场论说中现有的二种方法，而是独立地用第三种方法求A：由C求H，由H求B，再由B求A，所得结果与场论二种方法的结果完全一致。 第三章研究了非正弦稳态网络与正弦稳态网络的统一，这里网络指线性网络和非线性网络。由于积分形式的两组独立方程组包含了元件的信息——四种元件的阻抗率。因此，本章首先讨论了四种元件的阻抗率由非线性过渡到线性，则电网络的基本规律性——积分形式的两组独立方程组也从非正弦稳态下的非线性网络过渡到线性网络，达到两者的统一。其次，正弦稳态是非正弦稳态的特例，从而可能把积分形式的两组独立方程组从实时形式过渡到复数形式，达到二者的统一。最后，讨论了元件特性公式从非线性过渡到线性的统一。 第四章广义毕奥—萨伐尔定律的应用，是场论说开辟的对各向异性电磁场研究的继续，举了三个例子，有很实际的应用和较大的难度，是独立创造性地完成的。更多还原

【Abstract】 Based on the field theory of sinusoidal-steady state, this paper extended field theory to non-sinusoidal-steady state, and constructed a universal field theory for these two different situations. Furthermore, it is proposed that the two systems of integral equations in non-sinusoidal-steady state of nonlinear network are fundamental equations for the field theory, in other words, those are applicable to all linear or nonlinear lumped-parameter networks under the quasi-static condition. This paper contains four chapters. Chapter 1 and 2 are focused on linear and nonlinear networks of non-sinusoidal-steady state, respectively. Each of these two chapters derived two systems of integral equations of linear or nonlinear network in the non-sinusoidal-steady state, by starting from the real-time form Maxwell equations and electromagnetic property equations. Subsequently, basic theoretical contents of field theory were deduced, which include the new forms of Kirchhoffs voltage law and current law in the non-sinusoidal-steady state of linear and nonlinear networks, the equations of branch characteristic including mutual-conductance, and the general characteristic equations of four fundamental electronic elements. Chapter 3 is devoted to integrating the field theory of linear and nonlinear networks for sinusoidal-steady state into that for non-sinusoidal-steady state. In this chapter, three important components of field theory of network were discussed: fundamental equations of field theory, transforming Kirchhoffs law from real-time form to complex form, and unifying general characteristic equations of four fundamental electronic elements in non-sinusoidal-steady state with those in sinusoidal-steady state. Chapter 4 treats the applications of generalized Biot-Savart law. In this chapter, there are three examples, which can be employed in the practical engineering to evaluate the influence of medium anisotropy on the magnetic field distribution.更多还原