小编推荐：开关电源电流模式小信号建模方法Review

到现在为止，power electronics的converter的modeling领域，一共有哪些电流模式的小信号建模法呢？发展历程与特点差异是什么？

下面我将进行一些总结。基本均是基于CPES的Doctoral Dissertations的成果来进行归纳的。如果疏漏敬请补充。

Ray Ridley, 1990，只适用于对peak current mode进行small-signal model建模, 建模方法包含了Sampled-Data Model，准确度可到fsw/2，对average current mode失效；

Wei Tang, 1994，方法为averaged three-terminal switch model，accurate up to half the switching frequency，把ray ridley的对于PCM的建模方法沿用并扩展到了对avg current mode的建模；

Yang Qiu, 2005，对peak current mode进行了建模，方法为multi-frequency small-signal modeling，考虑了sideband effect，建模准确度可达到fsw。“the model predicts the performance very well up to the switching frequency.”；

Jian Li, 2009，对ridley的方法进行了升级，paper讲述了peak current mode的Describing Function Method建模，把解析解算出来了，而且还给出了近似模型。future work里说，这个new model也可以用在对avg current mode进行小信号建模，不过至今2019貌似还没有人做了这个work，这里用的是time-domain Describing Function Method把the inductor, the switches, and the pulsewidth-modulated modulator看做是一个整体来建模的。“A new modeling approach for current-mode control is proposed based on the time-domain analysis. The inductor, the switches and the PWM modulator are treated as a single entity to model instead of breaking them into parts to do it. Describing function method is used. Proposed approach can be applied not only to constant-frequency modulation but also to variable-frequency modulation. The fundamental difference between different current-mode controls is elaborated based on the models obtained from the new modeling approach. ”；

Yingyi Yan, 2013，至2019为止貌似是最新最为准确的avg current mode的建模方法了，用的three-terminal switch model的方法，“The proposed small signal model is accurate up to half switching frequency, predicting the sub-harmonic instability. ”，打通了ACM PCM VM之间的桥梁；文中，利用此方法对peak current mode, average current mode, Digital Predictive Current Mode Controls, V2 Control, I2 Control, 还给出了“Valley current mode control, Charge control, Constant on-time control, Constant off-time control”这些控制方式的利用本文建模方法的公式结论，总结于page46。文中说“primary objective is to develop a unified three-terminal switch model for current-mode controls using the results of describing function derivation. Its application is extended to average current mode control, V2 control and other proposed novel current mode control schemes.”“A three-terminal equivalent circuit is developed to represent the small signal behavior of this common sub-circuit. The proposed model is applicable in both constant frequency and variable frequency modulation.”在Yingyi Yan的“Yingyi Yan, Analysis and Design of Average Current Mode Control Using a Describing-Function-Based Equivalent Circuit Model”这篇paper里提到，上面即他的博士毕业论文里说的用的describing function是linearized describing function，这个要比“Feng Yu, A Small Signal Model for Average Current Mode Control Based On Describing Function Approach, 2011”里用的time domain describing method的数学计算要简单的多，用time domain的describing function来建模的计算比较复杂。

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以上均源于PhD Dissertation, 以下为journals的一些：

Feng Yu, A Small Signal Model for Average Current Mode Control Based On Describing Function Approach, 2011

准确度可达到fsw，但计算较为复杂。

The proposed model is based on the describing function method and so that all the frequency components in the current feedback loop is considered. The small signal model can be accurate up to switching frequency, so the potential sub-harmonic oscillation can be accurately predicted. Time domain describing method has been proved to be very effective in modeling current mode control. Many different types of current mode control have been modeled except average current mode control [10]. It is quite complicated to describe the time domain waveform in average current mode control. This paper proposes the small signal model for average current mode control by analogy to V2 model [9], avoiding the complicated mathematical derivation.

Chunxiao Sun, Discussions on Control Loop Design in Average Current Mode Control, 2000

这篇paper里讲了用Krylov–Bogoliubov– Mitropolsky algorithm（奇怪的是这篇paper里并没有提到这个算法的字眼，在“Jian Sun, A New Approach to Averaged Modeling of PWM Converters with Current-Mode Control, 1997”里面倒是明确说是用的这个算法来建模的）来建模，paper里没说准确度具体可达到多少，不过“Yingyi Yan, Analysis and Design of Average Current Mode Control Using a Describing-Function-Based Equivalent Circuit Model, 2013”里说他的准确度很好，provides a pretty accurate prediction，但计算较为复杂。

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