A numerical noise analysis method for oscillators is proposed. Noise sources are usually small and can be considered as perturbations to a large amplitude oscillation. Transfer functions from each noise source to the oscillator output can be calculated by modeling the oscillator as a linear periodic time-varying circuit. The proposed method is a time domain method and can be applied to strongly nonlinear circuits. Thermal noise, shot noise and flicker noise are considered as noise sources. Error in the time domain method is also discussed.

One of the excitations, 'carrier', is a large signal and an arbitrary T-periodic function of time. The other excitation, 'signal', is considered as a small perturbation to the periodic steady-state response driven by the carrier. To find a small signal frequency response for the 'signal', the method uses variational equations around the periodic steady-state response. These linearized time-varying differential equations are solved in the frequency domain using a time discretization method. The method can be used to compute the small signal frequency responses of nonideal switched capacitor filters, mixers, and other nonlinear circuits, if the circuit has a stable periodic response. The formulation of the problem, computational complexity of the method, error analysis, sensitivity analysis, implementation of the method, and some applications are covered.>