Electronics Letters · 1991 · 10 citations · 0 references
Natural SciencesElectrical EngineeringPhysicsComplex SystemsDynamical SystemsSystem DynamicsBifurcation TheoryChaos TheoryControl Of Dynamical SystemsControl TheoryLyapunov ExponentsNonlinear DynamicsChaos ControlChaotic DynamicsChaotic OscillatorsNonlinear OscillationsPhase-locked LoopsPhase-locked Oscillators
The chaotic behaviour of phase-locked loops (PLL) in tracking a received signal whose frequency is varying linearly with time is studied. This system is described by a third-order nonlinear autonomous equation. The Lyapunov exponents and dimension of the system are calculated to confirm the chaotic phenomenon. Numerical results indicate that the parameter ranges where the chaos could occur are realistic in the typical designs.