Frequency noise of CMOS LC tank oscillators operating in weak inversion

In this paper, we present an analytical model for a CMOS LC tank oscillator with its active devices operating in weak inversion. Our model combines nonlinear, stochastic circuit analysis in the form of the so-called stochastic averaging method proposed by Stratonovich with advanced MOS device modeling in the form of the EKV-model. The presented approach not only provides - for the first time - simple, yet accurate closed-form expressions for the oscillation frequency and amplitude of a CMOS LC tank oscillator operating in weak inversion but also allows us to derive closed-form expressions for the phase and frequency noise of the oscillator originating from both the parasitic resistance of the tank coil and the white noise generated in the cross-coupled MOS transistor pair. Thanks to their relatively compact and closed form, the presented results can not only be used for circuit optimization during the initial design phase but also convey important insights into the dependency of phase noise on design parameters such as the transconductance of the active devices.