Synchronous state in a fully connected phase-locked loop network

Piqueira, J. R. C.; Oliveira, M. Q.; Monteiro, L. H. A.

doi:https://doi.org/10.1155/MPE/2006/52356

Mathematical Problems in Engineering

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Volume 2006 | Article ID 052356 | https://doi.org/10.1155/MPE/2006/52356

Synchronous state in a fully connected phase-locked loop network

J. R. C. Piqueira,¹M. Q. Oliveira,¹and L. H. A. Monteiro^1,2

Received19 Apr 2006

Revised17 Aug 2006

Accepted13 Sept 2006

Published08 Nov 2006

Abstract

Fully connected phase-locked networks are built with all nodes exchanging phase and frequency signals. The nodes are phase-locked loops (PLLs) with slightly different free-running frequencies. The synchronous state emerges from a dynamic process with the phase interactions generating a common frequency steady state. In this work, an estimation is analytically obtained for the synchronous state in a generic N-node network. Numerical experiments complete the analysis of the fully connected network relating free-running frequencies, node gains, and propagation delays.

References

D. Abramovitch, “Phase-locked loops: a control centric tutorial,” in Proceedings of the American Control Conference, vol. 1, pp. 1–15, Alaska, May 2002.
View at: Publisher Site | Google Scholar
J. Bellamy, Digital Telephony, John Wiley & Sons, New York, 2nd edition, 1990.
S. Bregni, “A historical perspective on telecommunications network synchronization,” IEEE Communications Magazine, vol. 36, no. 6, pp. 158–166, 1998.
View at: Publisher Site | Google Scholar
S. Bregni and L. Barbieri, “Experimental evaluation of the impact of network frequency synchronization on GSM quality of service during handover,” in Proceedings of IEEE Global Telecommunications Conference (GLOBECOM '03), vol. 6, pp. 3457–3461, California, 2003.
View at: Publisher Site | Google Scholar
H. J. Choi and W. C. Lindsey, “Phase and frequency transfer analysis on N mutually synchronized oscillators,” IEEE Transactions on Aerospace and Electronic Systems, vol. 20, no. 6, pp. 748–753, 1984.
View at: Google Scholar
M. Curtin and P. O'Brien, “Phase-locked loops for high-frequency receivers and transmitters—part 1,” Analog Dialogue, vol. 33, no. 3, 1999.
View at: Google Scholar
K. Dessouky and W. C. Lindsey, “Phase and frequency transfer between mutually synchronized oscillators,” IEEE Transactions on Communications, vol. 32, no. 2, pp. 110–117, 1984.
View at: Publisher Site | Google Scholar
F. M. G. Gardner, Phaselock Techniques, John Wiley & Sons, New York, 1966.
A. Gersho and B. Karafin, “Mutual synchronization of geographically separated oscillators,” The Bell System Technical Journal, vol. 45, pp. 1689–1704, 1966.
View at: Google Scholar
F. C. Hoppensteadt and E. Izhikevich, “Pattern recognition via synchronization in phase-locked loop neural networks,” IEEE Transactions on Neural Networks, vol. 11, no. 3, pp. 734–738, 2000.
View at: Publisher Site | Google Scholar
P. Kartaschoff, “Synchronization in digital communications networks,” Proceedings of the IEEE, vol. 79, no. 7, pp. 1019–1028, 1991.
View at: Publisher Site | Google Scholar
W. C. Lindsey, F. Ghazvinian, W. C. Hagmann, and K. Dessouky, “Network synchronization,” Proceedings of the IEEE, vol. 73, no. 10, pp. 1445–1467, 1985.
View at: Google Scholar
J. Lü and G. Chen, “A time-varying complex dynamical network model and its controlled synchronization criteria,” IEEE Transactions on Automatic Control, vol. 50, no. 6, pp. 841–846, 2005.
View at: Google Scholar | MathSciNet
H. Meyr and G. Ascheid, Synchronization in Digital Communications, vol. 1, John Wiley & Sons, New York, 1990.
D. L. Mills, “Improved algorithms for synchronizing computer network clocks,” in Proceedings of the Conference on Communications Architectures, Protocols and Applications, pp. 317–327, London, August-September 1994.
View at: Google Scholar
D. Mitra, “Network synchronization: analysis of a hybrid of master-slave and mutual synchronization,” IEEE Transactions on Communications, vol. 28, no. 8, part 2, pp. 1245–1259, 1980.
View at: Publisher Site | Google Scholar | MathSciNet
W. A. Moore, “Phase-locked loops for motor-speed control,” IEEE Spectrum, vol. 10, pp. 61–67, 1973.
View at: Google Scholar
J. R. C. Piqueira, F. M. Orsatti, and L. H. A. Monteiro, “Computing with phase locked loops: choosing gains and delays,” IEEE Transactions on Neural Networks, vol. 14, no. 1, pp. 243–247, 2003.
View at: Publisher Site | Google Scholar
T. Saito, “Application of phase-locked oscillator for PCM network synchronization,” IEEE Transactions on Communications, vol. 30, no. 10, pp. 2344–2354, 1982.
View at: Publisher Site | Google Scholar
M. Sexton and A. Reid, Transmission Networking: SONET and Synchronous Digital Hierarchy, Artech House, Boston, 1992.
H. A. Stover, “Network timing/synchronization for defense communications,” IEEE Transactions on Communications, vol. 28, no. 8, pp. 1234–1244, 1980.
View at: Publisher Site | Google Scholar
M. W. Williard, “Analysis of a system of mutually synchronized oscillators,” IEEE Transactions on Communications, vol. 18, no. 5, pp. 467–483, 1970.
View at: Publisher Site | Google Scholar
M. Żółtowski, “Some advances and refinements in digital phase-locked loops (DPLLs),” Signal Processing, vol. 81, no. 4, pp. 735–789, 2001.
View at: Publisher Site | Google Scholar

Copyright

Copyright © 2006 J. R. C. Piqueira et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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