Rapid Locking Range Analysis of a Sub-Harmonic ILO considering Injection Waveforms of Different Multiplied Ratios

This paper aims to intuitively explain and numerically verify the locking range of a sub-harmonic injection-locked oscillator (ILO) when applying different injection multiplying ratios (M). By considering an impulse sensitivity function (ISF), which is the phase response of an oscillator against current impulse perturbation obtained from a periodic small-signal analysis using a PXF engine together with an injection waveform, the relative phase of the locked oscillator and consequently its locking range can be accurately predicted without requiring any time-consuming transient simulations. Through this approach, the study of which waveform patterns would be suitable for a locking range enhancement of an ILO can easily be carried out. Based on the proposed method, we have illustrated and numerically verified that, when injecting a sinusoidal signal to drain of the main NMOS cross-coupled pair, the ILO can achieve a much wider locking range when M is odd (i.e. 3) compared to when M is even (i.e. 2).