FREQUENCY LOCKED LOOPS OF THE THIRD AND HIGHER ORDER
Keywords:
Frequency locked loops, Time non-recursive processing, Phase locked loop, Digital circuitsAbstract
This work describes a new model of Frequency Locked Loop (FLL) with three outputs, which is based on the time measurement and non-recursive processing of the input periods only. FLL is a linear discrete system of the third order. All mathematical analyzes were performed using the Z transform approach. The general form of difference equation, describing FLL of any order, is developed and compared with the corresponding difference equation of digital filters. Analysis of FLL was performed in the time and frequency domain. It was shown, that the Matlab tools, dedicated to FIR (Finite Impulse Response) digital filters, can be used for the analysis of FLL in the frequency domain. FLL is very fast. Depending on the choice of the system parameters, FLL can be used for the tracking and predicting applications, digital filtering of pulse periods, as well as in the applications of FLL which require short transient time. Computer simulation of FLL in the time domain is made to enable precise insight into the FLL properties.
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