First-Harmonic Injection-Locked Ring Oscillators

This paper presents an analysis of first-harmonic injection locking in CMOS ring oscillators. In this analysis, Adler´s equation is proved by using a new analytical approach based on the propagation delay of an inverter stage. Also the behavior of the injection-locked ring oscillators from phase noise point of view is discussed and a closed-form equation for the phase noise of such oscillators is derived. According to the measurement results on a DLL-based frequency multiplier implemented in 0.13-mum CMOS process, good agreement between theoretical prediction and measurements is observed