Synchronous state in a fully connected phase-locked loop network

Fully connected phase-locked networks are built with all nodes exchanging phase and frequency signals. The nodes are phase-locked loops (PLLs) with slightly different free-running frequencies. The synchronous state emerges from a dynamic process with the phase interactions generating a common frequency steady state. In this work, an estimation is analytically obtained for the synchronous state in a generic N-node network. Numerical experiments complete the analysis of the fully connected network relating free-running frequencies, node gains, and propagation delays.