Noise and Transmission Delays in Mutual Synchronization Systems
- 1 September 1975
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Aerospace and Electronic Systems
- Vol. AES-11 (5), 756-767
- https://doi.org/10.1109/taes.1975.307985
Abstract
This paper considers the effects of noise and transmission delays in a phase-averaging mutual synchronization system. The basic analytical ideas are developed with respect to a two-station system which contains first-or second-order analog phase-lock loops. From the equation describing the phase error dynamics of each system, a generalized Fokker-Planck equation is derived. It is used to obtain a good approximate analytic expression for the phase error probability density function (PDF), which is confirmed by simulation. An important quantity for such mutual synchronization systems, under random disturbances, is the variance of the frequency deviation. This may be obtained directly from a knowledge of the phase error PDF. The above development is then extended to a mutual synchronization system of arbitrary size.Keywords
This publication has 12 references indexed in Scilit:
- Analysis of a Dual Mode Digital Synchronization System Employing Digital Rate-Locked LoopsBell System Technical Journal, 1972
- Dynamic Behavior of a System of Mutually Synchronized OscillatorsIEEE Transactions on Communications, 1971
- Some Properties of a Nonlinear Model of a System for Synchronizing Digital Transmission Networks*Bell System Technical Journal, 1969
- On Conditions Under Which It Is Possible To Synchronize Digital Transmission SystemsBell System Technical Journal, 1969
- Synchronizing Digital NetworksBell System Technical Journal, 1969
- Organic Synchronization: Design of the Controls and Some Simulation ResultsBell System Technical Journal, 1968
- Dynamic Response of Systems of Mutually Synchronized OscillatorsBell System Technical Journal, 1967
- Generalizations and extensions of the Fokker- Planck-Kolmogorov equationsIEEE Transactions on Information Theory, 1967
- The Determination of Frequency in Systems of Mutually Synchronized OscillatorsBell System Technical Journal, 1966
- A Model for the Organic Synchronization of Communications SystemsBell System Technical Journal, 1966