Delay-free phase-locked loop ring: Equilibrium and phase perturbation

Clock signal distribution networks have been studied since the 1960s in the search of topologies and parameters that can optimize performance. The problem can be viewed as the mutual synchronization of coupled oscillators, a field being extensively investigated. However, the majority of these investigations consider a linear coupling factor, unlike in the case of time signal distribution systems, wherein nonlinear coupling terms appear. The latter complicates the analysis, mainly because the nodes are phase-locked loops. In the literature pertaining to telecommunications, this problem is studied using linear analysis and is supported by corrections provided by the experimental work. In this paper, a different approach to this problem is presented: here, it is considered that the basic unit of a fully connected time distribution network is a triangular ring of phase-locked loops. The stability of equilibrium states is derived, starting with a delay-free analytical model for the spatial phase and frequency errors. Perturbations of the equilibrium, step, ramp, and accidental phase modulation are included in the model, producing results reflecting the performance of the entire loop.