NONLINEAR DYNAMICS AND CHAOTIC BEHAVIOR OF THE SAMPLING PHASE-LOCKED LOOP

Nonlinear dynamics and chaotic behavior of the hybrid-type sampling ph ase-locked loop (SPLL) are studied. To perform the analysis correctly from a mathematical point of view, the nonlinear autonomous model of t he SPLL has been formulated as a fixed point problem. If the loop-filt er is omitted, bifurcations and chaotic behavior can be observed If th e SPLL has a loop-filter, more than one attractor has to be used to de scribe the acquisition properties of the circuit. One of them is the f ixed-point to be achieved, but the others are periodic orbits, i.e.. f alse locks. The regions of convergence for the different attractors ar e studied and plotted as a function of the loop parameters.