Nonlinear analysis of cycle slips in injection-locked oscillators

A method is presented for the analysis of cycle slips in injection-locked oscillators. This nonlinear phenomenon gives rise to a temporal desynchronization between the injected oscillator and the input source due to noise perturbations. It involves very different time scales, so even envelope-transient based Monte Carlo analyses may suffer from high computational cost. The method presented is based on the extraction of a semi-analytical nonlinear model of the injected oscillator. This reduced order model enables an efficient stochastic analysis of this oscillator, based on the use of the associated Fokker-Planck equation in the phase probability density. The analysis allows predicting the parameter-space regions that are best protected against cycle slips. The method has been applied to an injection-locked oscillator at 5 GHz, with good agreement with commercial software simulations and measurements.