Preventing Global Convergence Failure in Mixed-Signal Systems via Indeterminate State (‘X’) Elimination

摘要

Global convergence failures (GCFs), accounting for many of the start-up failures in analog/mixed-signal (AMS) systems, occur when a nonlinear circuit starts from a poorly initialized state. That is, a circuit may or may not converge to the correct mode of operation depending on how it is started upon power-on. This paper proposes a practical procedure to eliminate the uncertainty of initial states and hence prevent GCFs in AMS systems by introducing the notion of an indeterminate value that is analogous to the ‘don't know’ value (‘X’) used in digital logic simulators. Basically, the procedure finds all the nodes in a circuit whose voltages do not settle at some deterministic value within a prescribed amount of time and suggests locations where proper reset circuits must be added. Examples with a digitally controlled oscillator (DCO) and a phase-locked loop (PLL) demonstrate that the proposed design flow is effective in preventing GCFs as it eliminates uncertainty in the circuit's initial states.