A Deep Investigation of the Synchronization Mechanisms in LC-CMOS Frequency Dividers

The behavior of LC-CMOS frequency dividers is investigated in depth obtaining a new and clearer insight into the synchronization phenomenon. We show that it occurs according to two mechanisms, which are referred to as “synchronization by mixing” and “synchronization by harmonics.” This latter, still not known, may be the dominant mechanism in some practical circuits, and justifies the presence of locked states when the well known mechanism by mixing fails to predict them. A new model of CMOS frequency dividers that includes both mechanisms is presented, and its utility is demonstrated by analyzing the locked states of a divider by 3 and of a divider by 4, which are predicted in closed form. The calculation results show a close correspondence between the theory and the circuit simulations and measurements.