Abstract
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 accumu- lation within ILOs, an equivalent linear frequency-domain feed- back 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.