A unified model for injection-locked frequency dividers

Injection-locked frequency dividers (ILFDs) are versatile analog circuit blocks used, for example, within phase-locked loops (PLLs). An important attribute is substantially lower power consumption relative to their digital counterparts. The model described in this paper unifies the treatment of injection-locked and regenerative systems. It also provides useful design insights by clarifying the nature and role of the nonlinearity present in many mixer-based frequency conversion circuits. The utility of the model is demonstrated in the calculation of both the steady-state and dynamic properties of ILFD systems, and the subsequent computation of the corresponding phase noise spectrum. Illustrative circuit examples show close correspondence between theory and simulation. Finally, measurement results from a 5.4-GHz divide-by-2 ILFD fabricated in 0.24-μm CMOS show close correspondence between experiment and theory.