Lyapunov Redesign of Analog Phase-Lock Loops

In general, the design of phase-lock loops has been done by a combination of linear analysis, phase plane plots, rule of thumb, and simulation. Very few analytical tools have been used to determine the stability of the nonlinear models used for these devices. A method from the control literature known as Lyapunov redesign[1] has recently been used to design a third order phase-lock loop whose nonlinear model is guaranteed to be stable [2]. In this paper, this technique is demonstrated to be an effective stability analysis and design technique for many analog phase-lock loops. The ability of loops designed using these techniques to track a phase step is also proven.