ANALYSIS OF THE TIME-FREQUENCY LOCKED LOOPS USING TABLES - PART 1 (REVUE ROUMAINE DES SCIENCES TECHNIQUES — SÉRIE ÉLECTROTECHNIQUE ET ÉNERGÉTIQUE, 2026)
Time-frequency locked loops (Time-FLL) are linear discrete systems based on the processing of the input signal periods. This article describes one tabular approach to analyzing Time-FLL. This tabular method of analysis enables the complete escaping of a very long mathematical procedure. The approach is presented in the tracking and prediction applications of Time-FLLs, but it can also be used in its other applications, for instance, in digital filtering of the input periods, noise suppression, and others. This approach can also be applied to any linear discrete system. The paper first presents a mathematical procedure for analyzing systems of the lowest order. Based on these results, the table approach was discovered and extended up to Time-FLLs of the tenth order. The table can be simply extended to the Time-FLL of any order. Mathematical analysis and time-domain simulation were performed, along with frequency-domain analysis. To prove the correctness of the tabular approach, the properties of the third-order Time-FLL3 and the seventh-order Time-FLL7 are demonstrated in the time and frequency domains.
Keywords: Frequency locked loop (FLL); Digital filter; Phase locked loop (PLL); Digital circuit; Discrete linear system