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

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.