No abstract

Abstract-This paper deals with the stability of so-called "selfsampled" digital phase-locked-loops (PLLs). These systems are meant to be used as the nodes of autonomous clock distribution networks, where clock signals are locally generated in each node and each node is synchronized with its neighbours. Despite the absence of an absolute reference clock, it is possible to use the local irregular clock to trigger the operations of the digital loop filter. In this paper, we show that, in this mode of operation, PLLs can be modeled as autonomous piecewise-linear systems. We investigate what filter coefficients to choose in order to ensure stability and, hence synchronization. Two methods are explored, the first based on transient simulations, the second on linear matrix inequalities. It is shown that the second method yields much more conservative results than the first but that it cannot apply to all design options of self-sampled PLLs.

Clock distribution networks of synchronized oscillators are an alternative approach to classical tree-like clock distribution methods. Each node of the network may consist of a phase-locked loop (PLL) trying to match the phase of its neighbors. Then a network of independent oscillators takes the place of the centralized clock source, providing separate clock signals to the physically distant parts of the system. In the discrete case, the digital filter is necessarily operated asynchronously: each operation is triggered by a rising edge of the locally-generated clock, the frequency and phase of which vary as the whole system tries to synchronize. The locking behavior, the synchronous state and the stability conditions of such a system are analyzed. Similarly, the synchronization of an autonomous network of two self-sampled PLLs is studied. Surprisingly, its analysis is much simpler than that of the single PLL.I.

This paper addresses the problem of the stability and the performance analysis of N -nodes cartesian networks of self-sampled all digital phase-locked loops. It can be demonstrated that under certain conditions (such as proper filter coefficient values), a global and a local synchronization can be obtained. Our approach to find the optimal conditions consists of analyzing a corresponding linear average system of the cartesian network rather than constructing a piecewise-linear system which is extremely difficult to analyse. The constructed corresponding system takes into account the non-linearity of the network and especially the self-sampling property. It is then analyzed by linear performance criteria such as modulus margin to guarantee a robust stability of the cartesian network. The reliability of our approach is proved by transient simulations in networks of different sizes.