Optimizing the design of an injection-locked frequency divider by means of nonlinear analysis

Injection-locked frequency dividers (ILFDs) are versatile analog circuit blocks used, for example, within phase-locked loops (PLLs). With respect to their digital counterparts, they have the advantages of a low power consumption and division ratios greater than two. The price for these advantages is believed to be a limited locking range. Here we show that this is not the case; indeed, by combining nonlinear systems theory (bifurcation analysis) with optimization techniques, we have significantly increased the locking range of a classical (LC oscillator-based) injection-locked frequency divider, predicting a locking range that is about twenty times greater than what has been reported in the literature to date. The wider locking range predicted by the theory has been confirmed by SPICE simulations.