Nonlinear dynamics of alias-locked loop

Abstract

This paper examines the nonlinear dynamics of an alias-locked loop (ALL) which uses an aliasing divider instead of a traditional frequency divider in the feedback loop of a phase-locked loop. A nonlinear model of the ALL is developed and used to study the global and local nonlinear dynamics of the system. In the global dynamics, we see disconnected regions of stability, which arise as a direct result of the aliasing operation. In the local dynamics, we see how the orbits observed have a particular dependence on the ratio of sample and reference frequencies.