Abstract
Synchronization is an essential feature for the use of digital systems in telecommunication networks, integrated circuits, and manufacturing automation. Formerly, master‐slave (MS) architectures, with precise master clock generators sending signals to phase‐locked loops (PLLs) working as slave oscillators, were considered the best solution. Nowadays, the development of wireless networks with dynamical connectivity and the increase of the size and the operation frequency of integrated circuits suggest that the distribution of clock signals could be more efficient if distributed solutions with fully connected oscillators are used. Here, fully connected networks with second‐order PLLs as nodes are considered. In previous work, how the synchronous state frequency for this type of network depends on the node parameters and delays was studied and an expression for the long‐term frequency was derived (Piqueira, 2006). Here, by taking the first term of the Taylor series expansion for the dynamical system description, it is shown that for a generic network with N nodes, the synchronous state is locally asymptotically stable.
Highlights
Digital engineering technologies for communications, control, and computation require reliable clock distribution systems to guarantee the correct temporal order in the information processing by the several parts of a spatially distributed system 1–4
Synchronization network is the general denomination of the part of the whole system responsible for this temporal order and the several possible solutions for its design are presented in 5
Master-slave architectures were used to distribute a precise clock signal generated by a master node to the other points of the systems where PLLs regenerate the phase and frequency information 1, 5
Summary
Digital engineering technologies for communications, control, and computation require reliable clock distribution systems to guarantee the correct temporal order in the information processing by the several parts of a spatially distributed system 1–4. The evolution of the telecommunication services to wireless and dynamical networks hasshown the inadequacy of centralized clock distribution structures in these cases, motivating the study of fully connected architectures to generate reference signals with the phase-locked loops operating as nodes of the synchronization networks 1, 5–7. The main fields for the application of fully connected systems are time signal distribution in digital electronic circuits 2, 7–9 and wireless sensor networks 10. Another very important application of networks is the implementation of oscillatory neural-computing devices, where the vector of phase-differences amongst a group of synchronized oscillators is associated with some memory information 11, 12. Considering the first term of the Taylor series development around the synchronous state , it is shown that the synchronous state is locally asymptotically stable for any number N of nodes
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