his paper presents a study of phase noise in twoinductorless CMOS oscillators. First-order analysis of a linearoscillatory system leads to a noise shaping function and a newdefinition of Q. A linear model of CMOS ring oscillators is usedto calculate their phase noise, and three phase noise phenomena,namely, additive noise, high-frequency multiplicative noise, andlow-frequency multiplicative noise, are identified and formulated.Based on the same concepts, a CMOS relaxation oscillator is alsoanalyzed. Issues and techniques related to simulation of noise inthe time domain are described, and two prototypes fabricated in a 0.5-μm CMOS technology are used to investigate the accuracy ofthe theoretical predictions. Compared with the measured results,the calculated phase noise values of a 2-GHz ring oscillator anda 900-MHz relaxation oscillator at 5 MHz offset have an errorof approximately 4 dB.