Nonlinear dynamics of gear-shifting digital phase-locked loops

The nonlinear dynamics of a gear-shifting algorithm applied to a digital phase-looked loop (DPLL) are investigated. Adaptive techniques such as these are being increasingly introduced, in order to improve loop performance. Fixed point stability analysis and other techniques of nonlinear dynamics reveal a significant change in system behavior from previously analyzed DPLLs. The DPLL is a uniformly sampled first-order loop, whose dynamics have been extensively investigated in the absence of gear-shifting. The loop with gear-shifting added is found to have two fixed points, one of which is stable. A heightened sensitivity to initial conditions was also found.