V.F. Kravchenko, O.V. Kravchenko, A.R. Safin

Phase locked loop (PLL) systems used in the tasks of generating high precision oscillation (frequency synthesis) the coherent filtering of analog and digital signals, the optimal reception of digital signals, the organization of parallel computations in multiprocessor systems, the generation and processing of ultra wideband (chaotic) signals, etc. Special place in the theory of the PLLs occupy systems with samples. Such systems can achieve synchronization of oscillations with fractional multiplicities of frequency without using blocks of frequency division indispensable in classical systems. This is achieved using a special type of pulse-phase discriminator (PPD) performed on a «sample and memorization». When mismatch frequency synchronized oscillations relative to the center of zones of synchronous regimes of different multiplicity is a noticeable weakening of the main spectral component of the output signal with an increase in weight of side components. When approaching the limits of the zone matching the spectrum of output fluctuations completely destroyed. Applications of the theory of atomic functions (AF) for tasks of generating of complex signals in phase-locked loop (PLL) systems with samples are considered. Principles of working and methods of analysis of this system using the theory of discrete mappings are researched. Various methods of generating of the signals made from AF for improvement of spectral responses of PLL with samples oscillations are presented. It is shown that using of signals composed of atomic functions expands the possibilities of using the PLL with samples as a synthesizer of frequencies by increasing the boundaries of synchronous mode fractional multiplicities.