Frequency-Domain Modeling and Analysis of Injection-Locked Oscillators

This article presents a complete frequency-domain model for injection-locked oscillators (ILOs), which is applicable to all ILO topologies. Based on the essence of the phase accumulation within ILOs, an equivalent linear frequency-domain feedback loop is constructed. By introducing an injection factor that depicts the proportion of the phase shift perturbation with respect to the injection phase disturbance, the phase transfer function (PTF)/noise transfer function (NTF) and tracking bandwidth equation of ILOs are formulated. In addition, a general single transient simulation-based injection factor-extraction procedure is proposed. Theoretical analysis for the injection factor based on both traditional vector diagram and the impulse sensitivity function is also demonstrated. Based on a ring oscillator-based pulse ILO fabricated in a 65-nm CMOS process, the deduced PTF/NTF, tracking bandwidth equation, and their properties are verified using the simulated results and measured phase noise, respectively.