A Rigorous Analysis of a Phase-Locked Oscillator Under Injection

Abstract—This study presents injection-pulling effects on a local oscillator (LO) for wireless applications. A discrete-time analysis is provided to predict output spectra of the LO pulled by a sinusoidal and angle-modulated injection signal. A phase-locked loop synthe-sizer with an injection signal is analyzed in frequency domain to account for the inherent bandpass filtering on the injection signal. In addition, a phase noise model is developed by using the proposed frequency-domain approach to characterize the overall phase noise of a phase-locked oscillator under injection. Comparison between theoretical predictions and experimental results shows excellent agreement. Index Terms—Injection locking, injection pulling, local oscil-lator (LO) pulling, phase-locked loop (PLL). I