Inevitability of Phase-locking in a Charge Pump Phase Lock Loop using Deductive Verification

Phase-locking in a charge pump (CP) phase lock loop (PLL) is said to be inevitable if all possible states of the CP PLL eventually converge to the equilibrium, where the input and output phases are in lock and the node voltages vanish. We verify this property for a CP PLL using deductive verification. We split this complex property into two sub-properties defined in two disjoint subsets of the state space. We deductively verify the first...