Relation Between Delay Line Phase Noise and Ring Oscillator Phase Noise

The phase noise of a ring oscillator can be obtained by multiplying its open-loop phase noise by a simple shaping function. The shaping function is computed using first principles and is applicable to both flicker-noise-induced and white-noise-induced phase noise, leading to compact equations for ring oscillators. It is also shown that flicker noise upconversion in ring oscillators is primarily a function of the total gate capacitance and inevitable regardless of the risetime and falltime symmetry. Two oscillator prototypes fabricated in 65-nm CMOS technology verify the validity of the results.