M. V. Kapranov, A. R. Safin

Phase synchronisation systems (PSS) are widely applied in various areas of a radio engineering. Among a considerable quantity various PSS a special place occupy discrete PSS (DPSS), working with samples of the entrance signal, allowing to receive on an exit of system oscillations with the fractionally rational relation of frequencies. For example, in the theory of frequencies synthesis such systems allow to receive high-precision oscillations, without using frequency dividers, irreplaceable in continuous PSS. However, at an inevitable mismatch of own frequencies of synchronizable oscillations there is a non-uniformity in sample reference (arriving on a system input) of a signal. This phenomenon generates essential "fouling" of a spectrum of a target signal with appreciable decrease in the basic conponents of a spectrum. In this paper, the nature of destruction of a spectrum of target signal in DPSS with non-uniform sample is investigated. In the first part known data about working of DPSS with non-uniform sample are presented. Comparison of work continuous PSS and DPSS with samples in problems of synthesis of oscillations with the frectionally rational relation of frequencies (synthesizers of frequencies) is made. Mathematical expressions describing work of investigated system are deduced, and the technique of studying of the transitive and established processes by use of diagrammes of Lamereja-Kenigsa (and their expansitons) is considered. Problem about heterogeneity influence in sample of an entrance signal on a spectrum of generated oscillations is put. In the second part the technique of delimitation of zones of synchronism of various frequency rates with beforehand set accuracy is investigated. Adjustment cases 1:1, 1:2 and 1:3 are in detail studied. The higher frequency rates 1:n which can be reached in DPSS, are considered to a similar case 1:3. Some results about multistability occurrence in system are presented. In the third part spectra of fluctuations in zones with frequency rates 1:1, 1:2 and 1:3 are investigated at the approach to borders of zones of corresponding frequency rates. There are numerical dependences of spectral components on frequency mismatch size. Parasitic effects in zones of the higher (more than 3) frequency rates are considered. Spectra of two types of target signals are investigated: sinusoidal and rectangular impulses.