Modeling Oscillator Injection Locking Using the Phase Domain Response

This paper presents a simulation-based model for the behavior of injection-locked oscillators (ILOs) that can be applied to any oscillator topology under any strength of injected signal. By using the phase domain response (PDR) of an oscillator, the proposed model is shown to accurately predict the behavior of ILOs with asymmetric lock ranges or those using injection into multiple locations. It can also model subharmonic injection locking behavior. The model is validated through comparison with SPICE simulations as well as measured results of a multiplying ILO fabricated in 65-nm CMOS.