The Gardner problem and cycle slipping bifurcation for type 2 phase-locked loops

TL;DR

This paper analyzes a second-order type 2 phase-locked loop with a piecewise-linear phase detector, providing an exact solution to the Gardner problem on lock-in range through cycle slipping bifurcation analysis.

Contribution

It offers a precise analytical solution to the Gardner problem for this specific PLL model, enhancing existing engineering estimates.

Findings

Exact solution to the Gardner problem on lock-in range

Cycle slipping bifurcation analysis applied to PLLs

Improved accuracy over traditional estimates

Abstract

In the present work, a second-order type 2 PLL with a piecewise-linear phase detector characteristic is analysed. An exact solution to the Gardner problem on the lock-in range is obtained for the considered model. The solution is based on a study of cycle slipping bifurcation and improves well-known engineering estimates.