Exact analyses for locking range in injection-locked frequency dividers

In this paper, new equations are introduced for the locking rang of the injected locked LC frequency divider by the tail current. The injection current at the source is analyzed and replaced by two equivalent injection currents at drains. Then, two new simple closed-form equations are derived for the locking range. Geometrical interpretations lead to more clear and accurate results, rather than what considered in previously published works. To evaluate the accuracy of the proposed equations, different simulations and experiments have been performed. Results show a good conformance among simulation, experimental and analytical results.