A time-domain technique for computation of noise-spectral density in linear and nonlinear time-varying circuits

This paper presents a new time-domain technique for computing the noise-spectral density. The power-spectral density (PSD) is interpreted as the asymptotic value of the expected energy-spectral density per unit time. The methodology of stochastic differential equations is used to derive a set of ordinary differential equations for the expected energy-spectral density. This set of equations can then be integrated in time until the steady-state value of the PSD is obtained. The method can be used to find the noise spectrum in any circuit in which noise can be treated as a perturbation. The general nature of this algorithm has been illustrated in this paper by using it to get the noise-spectral density in switched-capacitor circuits, externally linear circuits and oscillators. The results match well with published experimental/analytical data.