Phase noise in multi-gigahertz CMOS ring oscillatorsPhase Noise in Multi-Gigahertz CMOS Ring Oscillators Ali Hajimiri, Sotirios Limotyrakis, Thomas H. Lee Center for Integrated Systems, Stanford, CA 94305-4070 Abstract An analysis of the phase noise in differential and singleended ring oscillators using a time-variant model is presented. An expression for the RMS value of the impulse sensitivity function (ISF) is derived. A closed-form equation for phase noise of ring oscillators is calculated and a lower limit on the phase noise of ring oscillators is shown. Phase noise measurements of oscillators running up to 5.5GHz are in good agreement with the theory. Introduction Due to their integrated nature, ring oscillators have recently become an important building block in many digital and communication systems [ 13. They can also be used for ……