Model for a synchronous p.c.m. transmission complex

One of the proposed synchronisation systems for a large-scale p.c.m. transmission and switching complex uses independent oscillators at each station, which are phase-locked to the average phase of all the incoming lines. This paper derives a simple analogue to the system which allows a sufficient stability condition to be stated by inspection. The effect of parameter changes upon the equilibrium frequency is discussed, and a detailed discussion of the initial conditions shows that, for a 2-oscillator system, there are two stable-equilibrium frequencies that the system may reach. The Appendix contains rigorous proofs of the more intuitive statements in the paper.