Pull-In Behavior of Third-Order Generalized Phase-Locked Loops

This paper analyzes third-order phase-locked loops with an arbitrary phase-detector characteristic and imperfect integration by the quasi-stationary approach with a suitable linearization of the non-linear differential equation deseribing the loop behavior; ideal integration is also considered. The main feature of this technique is the use of an easy mathematical approach which allows a direct physical insight into acquisition behavior and the development of simple expressions for the time and pull-in range.