Title :
Nonlinear dynamics and chaotic behavior of the sampling phase-locked loop
Author :
Kolumban, G. ; Vizvàri, Béla
Author_Institution :
RUTCOR, Rutgers Univ., New Brunswick, NJ, USA
fDate :
4/1/1994 12:00:00 AM
Abstract :
Nonlinear dynamics and chaotic behavior of the hybrid-type sampling phase-locked loop (SPLL) are studied. To perform the analysis correctly from a mathematical point of view, the nonlinear autonomous model of the SPLL has been formulated as a fixed point problem. If the loop-filter is omitted, bifurcations and chaotic behavior can be observed. If the SPLL has a loop-filter, more than one attractor has to be used to describe the acquisition properties of the circuit. One of them is the fixed-point to be achieved, but the others are periodic orbits, i.e., false locks. The regions of convergence for the different attractors are studied and plotted as a function of the loop parameters
Keywords :
bifurcation; chaos; nonlinear dynamical systems; nonlinear network analysis; phase-locked loops; sample and hold circuits; attractor; bifurcations; chaotic behavior; false locks; fixed point problem; loop parameters; nonlinear autonomous model; nonlinear dynamics; periodic orbits; sampling phase-locked loop; Chaos; Circuits; Convergence; Frequency conversion; Mathematical model; Orbits; Phase locked loops; Sampling methods; Switches; Voltage-controlled oscillators;
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
