Lumped, inductorless oscillators: how far can they go? [phase noise reduction limit]

The fundamental question of how much we can ultimately reduce the phase noise of a lumped, inductorless oscillator through careful design is addressed and it is shown that the fluctuation dissipation theorem of thermodynamics imposes a lower limit on the phase noise. An analytical formulation of this limit is presented and it is shown that the phase noise of ring oscillators with long-channel MOS devices is closer to this limit compared to that of the relaxation oscillators or ring oscillators with short channel MOS devices.