锁相环动态频相跟踪特性分析

Analysis of the dynamic frequency-and phase-tracking characteristics of phase-locked loop

在分析锁相环工作原理的基础上,利用传递函数法建立了锁相环跟踪误差的二阶等效模型,并对锁相环的动态频相跟踪特性进行了理论分析.利用MATLAB构建了锁相环的仿真模型,针对输入信号中发生频率和相位突变、频率连续瞬变以及谐波畸变等多种情形,开展了仿真研究.理论分析与仿真结果表明,锁相环具有与二阶控制系统类似的特征,必然存在着响应时间、超调、偏差等现象,对输入信号的准确跟踪也需要一定具体条件.研究结果为锁相环的应用条件确定、外围电路参数设计以及性能改进等提供了参考依据.

Based on analysis of the operating mechanism of phase-locked loop （PLL）, a second-order equivalent model was established for PLL＇ s tracking error by use of transfer function methodology, and theoretical analysis was done regarding the dynamic frequency-and phase-tracking performance of PLL. A simulation medel of PLL was constructed on MATLAB for verification, with which simulations were carried out with regard to various circumstances of input signals, such as frequency and phase stepchange, continuous temporary change of frequency, harmonics distortion, etc. Both theoretical analysis and numerical simulation show that PLL renders typical behaviors similar to that of a second-order control system, which will inevitably result in response time, over-adjust and deviation, and thereby some concrete conditions are required to realize accurate tracking to input signals. The research results present valuable reference basis for application prerequisites determination, peripheral circuit parameters design and performance amelioration of PLLs.