Abstract-This paper presents a study of phase noise in two inductorless CMOS oscillators. First-order analysis of a linear
oscillatory system leads to a noise shaping function and a new definition of Q. A linear model of CMOS ring oscillators is used
to calculate their phase noise, and three phase noise phenomena, namely, additive noise, high-frequency multiplicative noise, and
low-frequency multiplicative noise, are identified and formulated. Based on the same concepts, a CMOS relaxation oscillator is also
analyzed. Issues and techniques related to simulation of noise in the time domain are described, and two prototypes fabricated in a
0.5-pm CMOS technology are used to investigate the accuracy of the theoretical predictions. Compared with the measured results, the calculated phase noise values of a 2-GHz ring oscillator and a 900-MHz relaxation oscillator at 5 MHz offset have an error of approximately 4 dB.