實現於積體電路之定導通時間控制降壓型轉換器之穩定度預測

Stability Prediction of Integrated-Circuit Based Constant On-time Controlled Buck Converters

王珽弘(Ting-Hung Wang)

指導教授 ： 陳德玉 ； 陳景然

國立臺灣大學/電機資訊學院/電機工程學研究所/博士(2022年)

https://doi.org/10.6342/NTU202200787

摘要

定導通時間控制為近年來的中央處理器之直流-直流轉換器設計趨勢。描述函數之數學模型方法於近年來被證明可有效分析定導通時間控制之穩定度，而描述函數模型中最主要的函數為「控制電壓至輸出電壓之轉移函數」，以下簡稱為GVC轉移函數。然而，使用描述函數所推導出之理想數學模型並未考慮實際電路應用時之非理想參數變化，因此通常與實際電路之特性相差甚遠。因此，在設計實際電路時，仍應將GVC轉移函數以量測的方式得出。然而量測實際電路之GVC轉移函數時，仍有若干問題導致量測無法進行。首先，傳統之「迴路增益」量測方法並不適用於定導通時間控制之直流-直流轉換器。其次，量測GVC轉移函數所需之電路節點皆已整合於積體電路封裝內而無法直接量測。因此，本論文提出一個有效的量測方式解決上述之量測問題，可應用於任何形式之定導通時間控制轉換器並有效預測實際電路之穩定度裕度。
本論文所提出之方法包含兩個階段。第一階段為量測定導通時間控制轉換器之電壓迴路小訊號響應(於此論文中命名為TMEAS函數)，第二階段將此TMEAS函數經由數學運算之方式推導出此電路之GVC轉移函數。在第一階段，定導通時間控制轉換器之電壓迴路並未整合於積體電路中，因此本論文提出之量測方法可應用於使用積體電路之轉換器。在第二階段，經由本論文提出之數學運算方式可準確地將TMEAS函數經由運算後轉換為GVC轉移函數，進而得知極點及零點之位置以及穩定度裕度。量測出GVC轉移函數後，本論文進一步提出設計優化之步驟，可經由本論文提出之穩定度界限方程式以及斜坡補償設計方程式，有效優化此轉換器之穩定度裕度以及暫態響應效能。
針對本論文所提出之方法，已建立一個商用筆記型電腦等級之實驗性平台實際驗證其有效性，此平台內含一個漣波基底定導通時間控制之降壓型轉換器，其參數為輸入電壓12V，輸出電壓1V，輸出功率20W，切換頻率450KHz。經由比較實驗結果及理想數學模型之結果，可證明本論文所提出之方法可有效增加30%之穩定度裕度以及22%之輸出電壓暫態響應漣波。
除了應用於漣波基底定導通時間控制之降壓型轉換器，本論文提出之方法亦可延伸應用至其他類型之定導通時間控制之降壓型轉換器，並已經由電路模擬之方式驗證其有效性。本論文提出之方法亦可延伸應用至其他類型之定導通時間控制轉換器，如升壓轉換器(boost)，升降壓轉換器(buck-boost)，以及返馳式轉換器(flyback)，且已經由模擬驗證其有效性。

關鍵字

定導通時間控制 ； 直流轉換器 ； 降壓變換器 ； 控制到輸出轉換函數

並列摘要

In recent years, constant on-time (COT) control schemes have been widely adopted for the DC-to-DC converters for central-processing-unit (CPU) applications. Describing function method was reported to analyze a COT converter’s stability by describing the control signal-to-output voltage transfer function, named GVC. For an ideal case, however, these ideal models often deviate from a real circuit significantly due to the non-ideal circuit parameters. Therefore, a measured GVC is desirable and important for a real-circuit stability prediction. However, there are two key issues related to GVC measurement. First, the conventional “loop gain” measurement method is meaningless for the converters with COT control schemes. Second, the GVC direct measurement method is not feasible, because the measuring points are usually not accessible due to integrated circuit (IC) implementation. In this dissertation, a method is firstly proposed and verified to measure the GVC for a practical COT circuit, followed by a rigorous analysis of the measured GVC to predict circuit stability and transient behavior. A design example will be used to illustrate the proposed method to design a practical buck converter with COT control scheme.
The proposed GVC measurement method contains two steps: 1) measure the small signal response of the COT converter’s voltage loop, named TMEAS, and 2) mathematically derive GVC small signal response from the measured TMEAS. In step 1), the COT converter’s voltage loop is not integrated into IC, so the proposed measurement method can be applied to COT IC implementations. In step 2), GVC Bode plot can be derived from the proposed “TMEAS to GVC“ equations, so the pole-zero locations and stability conditions can be analyzed. After GVC is measured, design optimization procedures are also proposed in this dissertation. The COT converter’s stability margin and transient performance can be optimized by the proposed stability boundary equations and ramp design target equations.
The proposed methods are verified in a real platform based on the latest generation commercial notebook computer’s design specifications. The platform contains a ripple-based COT buck converter with the following conditions: 12V to 1V, 20W, 450KHz. The results are compared between an ideal-model design and the proposed-method design, and the comparisons are executed both in simulations and experimental measurements. It was observed that the stability boundary accuracy was improved by 30%, and the step-load transient ring-back was improved by 22% by using the proposed-method. This is a significant improvement for a practical commercial product’s COT converter design.
Besides the ripple-based COT buck converter experimental verification, the method was extended to other COT buck control schemes and verified using simulations. The same method was also verified using simulations in boost, buck-boost, and flyback converters with RBCOT control.

並列關鍵字

constant on-time control ； DC converter ； buck converter ； control to output transfer function

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