含有非线性电阻的动态电路唯一稳态的λ参数判定法

The Study of the Uniqueness of the Steady State of the Nonlinear Non-Autonomous Circuits With Nonlinear Resistors by λ-Coefficient Method

非线性电路的唯一稳态 ,是一个很重要问题。目前已有的绝大部分成果 ,只能处理电路中含有线性电阻的情况。虽然个别结果理论上可以扩展为非线性的情形 ,但由于其应用的复杂性 ,在实际应用中并无多大的价值。然而在大量的工程应用和理论研究中 ,非线性电阻是普遍存在的元件。因此研究和确立含有非线性电阻的电路网络的唯一稳态的条件 ,具有重要的意义。由于该课题的研究 ,已进行了近 30年 ,已有的成果也相当成熟。所以要进一步推广原有经典结果 ,就要采用与已有研究不同的方法。以元件成分关系斜率变化区间对应的常数矩阵为基础 ,通过引入一个参变量构造出多个新的矩阵。通过对这些包含参变量的矩阵分析 ,从而确定原电路的唯一稳态。结果可以很方便地处理含有非线性电阻的非线性网络的唯一稳态问题。

It is important to determine the unique steady state of nonlinear circuit networks. In almost all the present results, only the nonlinear circuit networks with linear resistors can be handled. Although a few of them can be expanded to the scope where nonlinear resistors exist theoretically, but their complexity in practice makes it very difficult even impossible for researchers to use them. So for conditions where nonlinear resistors exist as in many practical engineering fields, it is a very meaningful work to build up corresponding principles for the unique state of such nonlinear networks. To gain new conclusions for this problem, it is necessary to use methods different from the existing ones. In this paper, based upon the constant matrix composed of the constant interval of the slopes of the elements' constitutive relations, a coefficient λ was introduced to construct several new matrixes relative to this coefficient. And the uniqueness of the unique steady state of the nonlinear non-autonomous circuit with nonlinear resistors was decided by the analysis of those matrixes. The conclusion can be easily used in the circuits with nonlinear resistors. This is a great extension of the results already known, where only the dynamic circuits with linear resistors are dealt with.