Designing complex systems of clocks as synchronization networks is not an obvious task, especially if aiming at guaranteeing the quality of service demanded by modern applications. Several years ago, specifying the quality requirements of clocks for telecommunications was often limited to not more than specifying their fractional deviation from the nominal frequency. More recently, since the introduction of SDH and of advanced digital services, clocks have been requested to comply with much more stringent and complex requirements for accuracy and stability, as specified by international standard bodies. A knowledge effusion occurred from the world of oscillator specialists to the world of telecommunication engineers, that imported methods and models conceived for time and frequency metrology and for the characterization of state-of-the-art oscillators.
Therefore, in order to describe the behaviour of clocks in synchronization networks and to accurately specify their characteristics, first it is necessary to identify a proper mathematical model of the clock and of the timing signals generated and distributed. This chapter supplies this basic knowledge: models of autonomous and slave clocks are defined and the mathematical tools for time and frequency stability characterization are provided. Finally, chains of slave clocks are considered, in order to assess the performance of timing transfer along synchronization trails.