模拟锁相环的李雅普诺夫新设计法

Lyapunov Redesign of Analog Phase—Lock Loops

锁相环一般采用线性分析,相平面图,近似计算法以及计算机模拟来设计。设计中对锁相环非线性模型的稳定性缺乏分析手段。控制理论中称为李雅普诺夫的新方法近来已用于三阶环的设计中,证明其非线性模型是稳定的。本文所述的方法对于大多数模拟锁相环是稳定性分析和设计的一种有效方法。业已证明用此法设计的锁相环确能跟踪相位跃变。

In general, the design of phase-lock loops has been done by a combina-tion of linear analysis, phase plane plots, rule of thumb, and simulation. Very fewanalytical tools have been used to determine the stability of the nonlinear modelsused for these devices. A method from the control literature known as Lyapunovredesign [1]has recently been used to design a third--order phase--lock loopwhose nonlinear model is guaranteed to be stable[2]. In this paper, this technique isdemonstrated to be an effective stability analysis and design technique for manyanalog phase--look loops. The ability of loops designed using these techniques totrack a phase step is also proven.