Frequency noise in current-starved CMOS LC tank oscillators

In this paper we present analytical expressions for the frequency noise of a current-starved CMOS LC tank oscillator originating from the white noise in the coil resistance and the cross-coupled transistor pair. We derive our results by using a Langevin approach to account for the device noise and subsequently solving the resulting stochastic differential equation with the help of a combination of the Stratonovich stochastic averaging method and linearization around the trajectories of the smoothly averaged system.