The operation of the phase-lock loop

We examine the operation of the phase-lock loop (PLL). The PLL is one of th e fundamental tools of the electrical engineer. It is nonlinear, and its op eration is usually examined only after a number of simplifying assumptions are made. We derive an equation that governs this tool's operation and dete rmine the properties of the solutions of the equation. We show that the lin ear time invariant approximation that is generally used to model the PLL is a good approximation to the original nonlinear time-varying equation. (C) 2000 Elsevier Science Ltd. All rights reserved.