Modeling of the Control Behavior of Current-Mode Constant On-Time Boost Converters

近年來，由於固定導通時間控制具有同時在輕載及重載時，轉換效率高的優點，因此被廣泛應用在直流電源轉換器上。但是，目前大多數刊登及發表的期刊和論文，主要集中在探討降壓型電源轉換器，在本篇論文中，將探討一個使用電流模式定導通時間控制之昇壓型電源轉換器，且該電路主要應用在手持式行動裝置中。 此論文的研究重點在於建立電流模式定導通時間控制之昇壓型電源轉換器的小訊號控制模型，由於傳統的低頻狀態空間平均法之小訊號模型推導方式不適合用於固定導通時間控制的架構，因此本篇將闡述描述函數的模型，為了適應不同的應用情形，電阻性負載以及電流性負載皆有考慮在模型中。從模型裡可以得到控制迴路增益的方程式，並且用於研究轉換器控制的穩定度控制。另外，也建立了輸出阻抗的小訊號模型。由於實際推導出的模型相當複雜，因此，藉由數學的近似方法，得到簡化的版本，並且可以用來預估輸出的步階負載響應。接著，根據該模型建立起一個補償器的設計流程，來達到理想的穩定度邊限及步階負載的暫態響應，所提出的模型會用模擬及實測結果來驗證。The constant on-time (COT) controller for DC converters has received much attention recently for the reason of its unique feature of high conversion efficiency under both the heavy-load and light-load conditions. However, most of the published papers on this subject have been focused on the buck converters. In this thesis, a boost converter using the current-mode COT controller is considered. It finds applications in hand-held mobile devices. The focus of the efforts is to establish a small-signal control model for the current-mode constant on-time (CMCOT) controlled boost converter. Since the conventional low-frequency average model cannot be applied in a COT control scheme, a describing function model is developed. Both the resistive load and the current load are considered in the modeling to adapt to different applications. From the model, control loop gain functions are used for the investigation of the converter control stability. In addition, the output impedance model is also developed. From the complicated model, a simplified version is obtained by mathematical approximations from which the output step-load response can be estimated. Based on the model, a compensation design procedure is developed to achieve desired stability margin and step-load transient response. Simulations and experimental results are given to confirm the proposed model