A nonlinear analysis of differential LC injection-locked frequency dividers

We present a nonlinear analysis of differential LC injection-locked frequency dividers (ILFDs) operating at high-level injection regime. We derive the general second-order equation which describes their behaviour and its approximate solution in explicit form, by solving the shortened equations for the amplitude and phase of the synchronized oscillation. These equations are obtained by the classical method of slowly varying amplitudes and are solved by using the perturbation theory. The solution found improves the results stemming from the Adler approach, because it enables to predict both the phase and the amplitude of the synchronized oscillation, without the limitation of low-level injection. Numerical results are presented to validate the presented results.