Translation. Region: Russian Federal
Source: Saint Petersburg State University –
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The proposed calculation method avoids the inaccuracies that were allowed by previously used approaches and offers engineers simple formulas that are convenient for use in real projects.
Phase-locked loop systems are widely used in satellite navigation and wireless communication devices. They provide precise synchronization of the frequency and phase of the signal coming to the device and the signal generated by the device itself. For example, in the case of a Wi-Fi connection between a router and a phone, the signals from the devices may differ slightly due to interference or instability of the transmitter (router). The phase-locked loop system compares the characteristics of the incoming signal and adjusts them to those characteristic of the device. This reduces the number of errors in the transmission of information, even if the original signal is “noisy”.
Research results, supported with a grant from the Russian Science Foundation (RSF), published in a scientific journal IEEE Access.
However, phase-locked loop systems operate stably only if a number of conditions are met. For example, there are limitations on the so-called hold range, the frequency difference at which synchronization can still be maintained. Another important parameter is the capture range, i.e. the frequency spectrum within which synchronization is guaranteed under any initial conditions. At the same time, it is difficult to accurately determine the capture range, since its calculation requires solving systems of nonlinear equations with a large number of variables. Previously, engineers used approximate methods that could lead to errors, and therefore did not always ensure stable operation of the system.
Researchers from St. Petersburg University analyzed operation of one of the most common phase-locked loop systems and found a simpler way to accurately calculate its capture range. To do this, scientists from St. Petersburg State University used a mathematical method of replacing variables, which allows equations used in other approaches to be reduced to a simpler form. In addition, the researchers used graphs to display how the state of the phase-locked loop system changes over time when transmitting and receiving signals with different parameters (frequencies and phases).
We have proposed a comprehensive approach that combines qualitative analysis of the system and the theory of hidden oscillations, the creation and development of which was this year. was noted State Prize of the Russian Federation in the field of science and technology.
Head of the Department of Applied Cybernetics at St. Petersburg State University, Head of the Laboratory of Information and Control Systems at the Institute of Mechanical Engineering of the Russian Academy of Sciences, Corresponding Member of the Russian Academy of Sciences, Professor Nikolay Kuznetsov
"This approach allowed us to obtain an accurate formula for the capture range and avoid a situation where the device unexpectedly loses synchronization, which can be critical in the case of systems used in navigation and energy. In the future, we plan to develop methods of the theory of hidden oscillations for the analysis of more complex phase-locked loop systems and collaborate with engineers to create prototypes of such systems based on the proposed methods of analysis and synthesis. The relevance of this work is associated with the import substitution program in Russian electronics and a wide range of engineering applications," explained Nikolai Kuznetsov, Head of the Department of Applied Cybernetics at St. Petersburg State University, Head of the Laboratory of Information and Control Systems at the Institute of Mechanics of the Russian Academy of Sciences, Corresponding Member of the Russian Academy of Sciences, Professor.
St Petersburg University mathematician receives State Prize in Science and Technology
The derived formulas made it possible to correct inaccuracies previously proposed approaches, in particular ignoring hidden oscillations that can lead to loss of synchronization. Computer modeling confirmed that the calculations accurately describe the real behavior of the automatic frequency control system, which makes them suitable for practical use.
Saint Petersburg State University is the oldest university in Russia. It was founded on January 28 (February 8), 1724, when Peter the Great issued a decree establishing the University and the Russian Academy of Sciences. Today, SPbU is one of the largest scientific and educational centers. More than 20 thousand students study here, more than 15 large laboratories and 23 resource centers have been created, which are part of the country's leading Science Park. Graduates of the University have repeatedly become Nobel and Fields Medal laureates.
Recently, the Northern capital has officially celebrated a new holiday: Saint Petersburg State University Day. contributed in the Law of St. Petersburg “On Holidays and Memorable Dates in St. Petersburg”.
In February 2025, a ceremony was held during which Roscosmos cosmonauts handed over To the University flag "300 years of St. Petersburg State University", which made its way to the International Space Station and back.
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