Short Term Frequency Instability Effects in Networks of Coupled Oscillators

A set of
N
identical oscillators (clocks) are connected to form a mutually synchronous network. General matrix expressions are derived for the phase error spectrum at each oscillator when the network operates in the linear regime. For certain topologies of practical interest the phase error variance and the correlation between the errors at different oscillators is computed and compared in their behavior for large
N
. The results presented assume no thermal noise and no delay between the oscillators. However, the theory can be easily extended to include these two effects.