到現在為止，power electronics的converter的modeling領域，一共有哪些電流模式的小信號建模法呢？發展歷程與特點差異是什么？

下面我將進行一些總結。基本均是基于CPES的Doctoral Dissertations的成果來進行歸納的。如果疏漏敬請補充。

Ray Ridley, 1990，只適用于對peak current mode進行small-signal model建模, 建模方法包含了Sampled-Data Model，準確度可到fsw/2，對average current mode失效；

Wei Tang, 1994，方法為averaged three-terminal switch model，accurate up to half the switching frequency，把ray ridley的對于PCM的建模方法沿用并擴展到了對avg current mode的建模；

Yang Qiu, 2005，對peak current mode進行了建模，方法為multi-frequency small-signal modeling，考慮了sideband effect，建模準確度可達到fsw。“the model predicts the performance very well up to the switching frequency.”；

Jian Li, 2009，對ridley的方法進行了升級，paper講述了peak current mode的Describing Function Method建模，把解析解算出來了，而且還給出了近似模型。future work里說，這個new model也可以用在對avg current mode進行小信號建模，不過至今2019貌似還沒有人做了這個work，這里用的是time-domain Describing Function Method把the inductor, the switches, and the pulsewidth-modulated modulator看做是一個整體來建模的。“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為止貌似是最新最為準確的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之間的橋梁；文中，利用此方法對peak current mode, average current mode, Digital Predictive Current Mode Controls, V2 Control, I2 Control, 還給出了“Valley current mode control, Charge control, Constant on-time control, Constant off-time control”這些控制方式的利用本文建模方法的公式結論，總結于page46。文中說“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”這篇paper里提到，上面即他的博士畢業論文里說的用的describing function是linearized describing function，這個要比“Feng Yu, A Small Signal Model for Average Current Mode Control Based On Describing Function Approach, 2011”里用的time domain describing method的數學計算要簡單的多，用time domain的describing function來建模的計算比較復雜。

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

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

準確度可達到fsw，但計算較為復雜。

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

這篇paper里講了用Krylov–Bogoliubov– Mitropolsky algorithm（奇怪的是這篇paper里并沒有提到這個算法的字眼，在“Jian Sun, A New Approach to Averaged Modeling of PWM Converters with Current-Mode Control, 1997”里面倒是明確說是用的這個算法來建模的）來建模，paper里沒說準確度具體可達到多少，不過“Yingyi Yan, Analysis and Design of Average Current Mode Control Using a Describing-Function-Based Equivalent Circuit Model, 2013”里說他的準確度很好，provides a pretty accurate prediction，但計算較為復雜。

如果覺得寫的還不錯，幫忙點個贊。

有不懂的地方，或者想問的問題，均可在評論區留言。

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