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首页> 外文期刊>IEEE Transactions on Circuits and Systems. 1 >On limit cycles and the describing function method in periodically switched circuits
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On limit cycles and the describing function method in periodically switched circuits

机译：周期性开关电路中的极限循环及其描述功能方法

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Examines existence, uniqueness, and stability of limit cycles in periodically switched circuits. The motivation comes from the field of power electronics where switched circuit models composed of passive elements, independent sources, and ideal switches are studied. The paper then studies the describing function method for computation of limit cycles in these switched circuits. Typical power circuit models have nonlinear elements with characteristics that do not satisfy a Lipschitz continuity condition. As a result of these nonsmooth characteristics, previously developed justifications for the describing function method are not applicable. The present paper develops a justification for the describing function method that relies on the incrementally passive characteristics of the network elements comprising typical power electronic circuit models. This justification holds for nonsmooth circuit nonlinearities, and takes the form of a set of asymptotically convergent bounds on the errors incurred with the describing function method. In particular, the developed bounds become arbitrarily tight as the number of harmonics included in the analysis increases.
机译：检查周期性开关电路中极限循环的存在，唯一性和稳定性。其动机来自电力电子领域，在该领域中，研究了由无源元件，独立电源和理想开关组成的开关电路模型。然后，本文研究了描述函数方法，用于计算这些开关电路中的极限环。典型的电源电路模型具有非线性元件，其特性不满足Lipschitz连续性条件。由于这些不平滑的特性，以前开发的描述函数方法的理由不适用。本文提出了描述功能方法的依据，该功能方法依赖于包含典型功率电子电路模型的网络元件的增量无源特性。这种证明适用于非平滑电路非线性，并采用描述函数方法所产生的误差的一组渐近收敛边界的形式。尤其是，随着分析中包含的谐波数量的增加，所形成的边界会变得任意紧缩。

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