應用於被動漣波定導通控制電源轉換器之精準小訊號建模方法

Abstract

被動漣波恆定導通時間(Passive Ripple Constant On-Time, PRCOT)控制的轉換器被廣泛地使用在行動裝置上，以提高輕載效率和瞬態響應。為了能夠設計PRCOT控制的迴路穩定度以及頻寬，需要一精準的小訊號模型用於控制器設計。在先前的研究，描述函數(Describing Function, DF)法被廣泛的使用來推導恆定導通控制的小訊號模型。然而先前的小訊號模型，皆假設被動漣波斜率為一固定斜率，這造成模型在小RC時間常數的情況下不能精準地預測頻率響應，因為被動漣波斜率在小RC時間常數下呈現指數型斜率。此篇論文提出一種改進的描述函數方法，此新方法可以用來處理指數型斜率。提出的方法利用微分方程去描述被動漣波，以此在小訊號建模上達到較高的精準度。此篇論文以被動漣波恆定導通控制的升壓轉換器當作小訊號模型推導的範例。驗證用的電路參數分別是輸入電壓3.3V，輸出電壓5V，切換頻率100kHz到300kHz以及輸出電流1A。不管是在固定斜率或者指數型斜率的條件下，模擬與實驗結果皆驗證提出的模型精準度超過切換頻率。

Passive ripple constant on-time (PRCOT) controlled converters have been widely used for mobile applications to improve light-load efficiency and transient response. An accurate small-signal model is inevitable for PRCOT control to estimate stability and design high loop gain bandwidth. The describing function (DF) method has been used to model the constant on-time control. However, previous research assumes a constant passive ripple slope, which is different at small RC time-constant conditions and causes inaccurate modeling results. In this dissertation, an improved describing function modeling approach is proposed to handle exponentially varying slope. The proposed method employs differential equations to characterize passive ripple, which achieves high accuracy in small signal modeling. This paper takes a PRCOT controlled boost converter as an example to demonstrate the modeling approach. The specifications for verification are input voltage 3.3V, output voltage 5V, switching frequency 100kHz to 300kHz and output current 1A. Simulation and experiment results verified the accuracy of the proposed model even beyond the switching frequency for both constant slope or exponentially varying slope passive ramp cases.