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Mathematicians at Saint Petersburg State University (SPbU) have developed a novel algorithm that significantly improves the performance of communication and navigation devices. This innovation optimizes Phase-Locked Loop (PLL) systems, which are crucial for synchronizing signals between a device and external sources, such as routers or satellites. While essential for wireless communication and satellite navigation, these systems are susceptible to interference and unstable oscillations.

Current PLL systems face limitations related to their hold and capture ranges—the thresholds within which synchronization is maintained. Precisely calculating the capture range (the area of guaranteed synchronization) has historically been highly complex, often leading to errors and a loss of stability.

SPbU scientists have devised a method to simplify and refine the calculation of the capture range for a widely used PLL system by applying a variable substitution technique. As noted by Nikolay Kuznetsov, Head of the Applied Cybernetics Department at SPbU, this approach yielded a precise formula for the capture range, thereby preventing unexpected synchronization loss. This is particularly vital for systems utilized in navigation and energy sectors.

Computer simulations have confirmed that this new methodology offers enhanced stability and resilience against synchronization loss compared to conventional methods. Furthermore, it allows for more accurate prediction of PLL behavior, which is highly significant for practical applications. The researchers intend to further develop this approach and collaborate with engineers to create prototypes.

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