Charge pump phase-locked loop with phase-frequency detector: closed form mathematical model

TL;DR

This paper presents a rigorous non-linear second-order mathematical model of a charge pump phase-locked loop with a phase-frequency detector, improving upon previous models and estimating its pull-in time for better analysis.

Contribution

The paper introduces a new, rigorous non-linear second-order model of CP-PLL that addresses limitations of earlier models and provides a method to estimate pull-in time.

Findings

The model accurately captures CP-PLL dynamics.

It overcomes shortcomings of previous models.

Pull-in time can be estimated using the new model.

Abstract

Charge pump phase-locked loop with phase-frequency detector (CP-PLL) is an electrical circuit, widely used in digital systems for frequency synthesis and synchronization of the clock signals. In this paper a non-linear second-order model of CP-PLL is rigorously derived. The obtained model obviates the shortcomings of previously known second-order models of CP-PLL. Pull-in time is estimated for the obtained second-order CP-PLL.