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### Recursive PLL of the First Order

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This paper describes a new type of Recursive Phase Locked Loop (PLL) of the first order. The PLL is a linear discrete system described by two recursive equations. The hardware implementation of PLL is described. Different analyses of PLL parameters are made. Computer simulation of PLL is introduced in order to give better insight into the PLL characteristics and to confirm the mathematical analyses, too. Made analysis shows that PLL is suitable for different applications. Precise digital phase shifting of pulse rate is one of the applications which is described. The picture of the input and output pulse rates, recorded on the simulated PLL by professional software package “Multisim", is presented. Streszczenie. Opisano nowy typ rekurencyjnej pętli synchronizacji fazowej (PLL). Przedstawiono różne metody analizy układu oraz symulację komputerową. Opisano możliwość precyzyjnego cyfrowego przesunięcia fazowego impulsów. (Rekursyjna pętla synchronizacji fazowej PLL pierwszego rzędu). Keywords: Phase Locked Loop, Discrete linear system, Recursive algorithm. Słowa kluczowe: układ PLL, rekursyjna pętla fazowa PLL. Introduction Different kinds of PLL are described in theory and practice and different kind of division of PLL can be made. Some earlier systematizations of PLL identified analog, hybrid, discrete and digital kinds of PLL. Although convenient in usage, this division was not precise enough because these groups were made according to different criterions. For instance, analog and hybrid PLL were defined according to the applied technology. Analog PLL are based on analog circuits, but hybrid ones use both analog and digital circuits. Discrete PLL represent discrete systems. They were separated in the independent group due to their principle of work. Namely, they make one correction of the output signal at each discrete time, i.e. once per period of the input signal. All the others PLL belonged to the digital ones, although th[...]

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