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-μm CMOS process, good agreement between theoretical prediction and measurements is observed.
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