This paper describes one recursive model of the Phase Locked Loop (PLL) of the second order based on the measurement and processing of the time difference between the input and output periods. The stability and the other conditions, under which the described system can have the properties of a PLL, are investigated using the Z transform analyses. 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 the wide range of applications. For the corresponding system parameters, PLL possesses the power noise rejection ability. For some other system parameters this PLL possesses the power tracking ability. It can also be used for the measurement of the period of the input signal in the noise environment. The oscilloscope picture of the input and output signals recorded on the realized PLL is presented.
This paper describes a digital frequency multiplier for a pulse rate. The multiplier is based on the recursive processing of the input and output periods and their time differences. Special emphasis is devoted to the techniques which provide the development of multipliers based on this principle. The circuit is defined by two system parameters. One is the ratio of two clock frequencies and the other is a division factor of a binary counter. The realization of the circuit is described. The region of the system parameters for the stable circuit is presented. The different aspects of applications and limitations in realization of the circuit are considered. All mathematical analyses are made using a Z transform approach. It is shown that the circuit can be also used in tracking and prediction applications. Computer simulations are performed to prove the correctness of the math and the whole approach.
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