Phase and Frequency Transfer Analysis of N Mutually Synchronized Oscillators

A mathematical model and a theory for the phase and frequency transfer between N mutually synchronized oscillators is presented. Mathematical equations are given for evaluating the phase and frequency transfer accuracy achievable. The Fokker-Planck technique is applied and an approximation solution is obtained for the phase difference process between a pair of network oscillators. The case of the three-nodal network is analyzed and it is shown that path delays and network coupling give mean bias error variations and signal-to-noise ratio (SNR) fluctuations in the phase difference process. The analysis is then extended to an N-nodal network to show that the SNR fluctuations tend to stabilize while the mean bias error variations are averaged between nodes as N becomes larger.