電荷幫浦式鎖相迴路之模型及分析

Abstract

非線性時變系統的電荷幫浦式鎖相迴路在諸多應用中相當重要，因而希望 建立能精確地描述此系統的模型。本論文針對採用電阻電容串聯而成的迴路濾波器，以及具有線性特性的電壓受控震盪器架構下電荷幫浦式鎖相迴路，提出完整描述此系統的模型。此模型考慮到鎖住模式、失鎖模式以及電壓受控震盪器過載等不同狀況，而推導出關於這些狀況的差分方程式，並以流程圖來表示此系統正確響應的計算過程及計算方式。藉由模擬結果可顯示本論文所提出的模型可以更正確地描述此系統。 此外，對於在電荷幫浦式鎖相迴路中，所謂週期二的限制循環之現象，本論文亦推導出使得週期二的限制循環具有局部穩定性的充分必要條件， 並求得在此狀況下平衡的時間誤差和電壓值。

The charge-pump PLL is a nonlinear time-varying system which is important in many applications. It is desired to have a model which can describe the system as accurately as possible. A complete model for the charge-pump PLL with RC loop filter and linear VCO characteristic is proposed in the thesis. The model derives all difference equations associated with the conditions of lock-in mode, out-of-lock mode, and VCO overload, and combines them to establish a flow chart for the calculations of the exact responses of the system. Simulations are performed to show that the proposed model can more completely describe the system. Further, one phenomenon arises in the charge-pump PLL is the limit cycle of period two. In the thesis we also present the necessary and sufficient condition for the charge-pump PLL to have locally stable limit cycle of period two, and the equilibrium values of timing error and voltage are obtained. Chapter 2: Modeling of the Charge-Pump PLL in Lock-in Mode Chapter 3: Modeling of the Charge-Pump PLL in Out-of-Lock Mode Chapter 4: Analysis of Limit Cycle of Period Two Chapter 5: Conclusions