modeling, analysis, and experimental validation of frequency dividers with direct injection

An analytical model and a methodology are presented for the analysis of CMOS injection-locked frequency dividers with direct injection, which are used in modern wireless communication systems. The amplitude and phase of the oscillation in the synchronous operation mode, as well as the locking range, are found in explicit form. The width of the locking range is determined by the condition of the existence and stability of synchronous oscillations. The accuracy of the model and of the presented formulas is validated through a comparison with experimental results, which are in good agreement with the analytical ones.