Temporal Properties of Self-Timed Rings
Various researchers have proposed using self-timed networks to generate
and distribute clocks and other timing signals.
We consider one of the simplest self-timed networks, a ring, and note that
for timing applications,
self-timed rings should maintain uniform spacing of events.
In practice, all previous designs of which we are aware cluster
events into bursts.
In this paper, we describe a dynamical systems approach to verify
the temporal properties of self-timed rings.
With these methods, we can verify that a new design has the
desired uniform spacing of events.
The key to our methods is developing an appropriate model of the
timing behaviour of our circuits.
Our models are more accurate than the simplistic interval bounds
of timed-automata techniques, while providing a higher level of
abstraction than non-linear differential equation models such as SPICE.
Evenly spaced and clustered event behaviours are
distinguished by simple geometric features of our model.