On the local stability of uniform sampling phase-locked loops

Digital phase-locked loops (DPLLs) are phase-locked loops implemented with digital circuitry. The resulting reliability, immunity to drifts and flexibility are of interest in communication. The DPLL is a nonlinear feedback device which tracks the phase of incoming waveform. The error of following up is called the instantaneous phase error and is obtained from the phase detector of the loop. In this paper the local stability of the uniform sampling DPLL, is studied. New rigorous theoretical approach, the discrete-time Volterra equation is used. This nonstationary discrete-time functional equation is obtained from the original equation of the loop by linearization. The devised methods of solving it and their anticipations are compared and justified by numerical results from a computer program which simulates the loop