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This paper presents a new methodology of analyzing phase noise in a ring oscillator by time-scaling the thermal noise. Close-form solutions that relate the probability distribution and power-spectral density of the phase noise to circuit parameters have been obtained. These close-form solutions characterize the behavior of phase noise even when the circuit is varying with time in a nonlinear fashion. Specifically, the theory predicts that for a given oscillation frequency, phase noise roughly decreases as the cube of the delay cell charging current value at threshold crossing; thus, it provides new design insights. Simulations were run and verified this dependency.