A Model for Stability, Noise, and Angle Modulation Analysis of Injection-Locked Oscillators

A model is presented for an injection-locked oscillator. It is derived from a perturbation of the free-running oscillator steady state, which is accurately determined from a harmonic balance (HB) simulation. As a first application, the proposed model is used to trace the existing solutions of the injection-locked system and their stability. It is then extended to include the effect of noise on the stability. Finally, the injection-locked system performance is studied under phase modulation. Sinusoidal phase modulation is considered and the stability of the modulated solutions is examined by Floquet theory. The validity of the model is verified for a 4.422-GHz oscillator, by HB and envelope transient simulations, as well as measurements.