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Noise simulation of oscillators modeled in an analog mixed signal environment is challenging since both conventional steady-state simulation methods, such as shooting and harmonic balance ones, cannot be used. This brief proposes an improved approach based on saltation matrices and an extended formulation that considers the registers of the digital part of the circuit as state variables to determine the steady-state solution and phase noise. The proposed approach allows the correct computation of the fundamental matrix evaluated on the steady-state solution and therefore of the left eigenfunctions that are a key aspect in determining phase noise by exploiting the variational model of the oscillator and Floquet theory. The proposed approach is applied to compute the phase noise of an archetype circuit that implements an energy-restore pulsed oscillator. In these oscillators, the energy lost by the tank is refilled at peculiar time instants determined by a digital controller to maximize efficiency and minimize effects due to flicker noise sources.