This paper presents a new approach to the transient noise analysis of integrated circuits. This approach consists of two parts, the modelling of noise sources in the time domain and the development of numerical schemes for stochastic differential-algebraic equations. The noise sources include thermal noise, shot noise, and flicker noise and their modelling is based on generalized stochastic processes. Brownian motion is the starting point for the modelling of white-noise sources (thermal and shot noise), while fractional Brownian motion is used for flicker noise sources. The numerical schemes employed for the computation of solution paths adapt well-known methods for stochastic differential equations to the specific situation within circuit simulation. Under the assumption of small noise the convergence properties of the driftimplicit Euler scheme and the drift-implicit Milstein scheme are proved. Finally numerical experiments with real-world circuits are presented.
Transient noise analysis means time domain simulation of noisy electronic circuits. We consider mathematical models where the noise is taken into account by means of sources of Gaussian white noise that are added to the deterministic network equations, leading to systems of stochastic differential algebraic equations (SDAEs). A crucial property of the arising SDAEs is the large number of small noise sources that are included. As efficient means of their integration we discuss adaptive linear multi-step methods, in particular stochastic analogues of the trapezoidal rule and the two-step backward differentiation formula, together with a new step-size control strategy. Test results including real-life problems illustrate the performance of the presented methods.
Transient noise analysis in circuit simulationThe increasing scale of integration, high clock frequencies and low supply voltages cause smaller signal-to-noise ratios. Reduced signal-to-noise ratio means that the difference between the wanted signal and noise is getting smaller. A consequence of this is that the circuit simulation has to take noise into account. In several applications the noise influences the system behaviour in an essentially nonlinear way such that linear noise analysis is no longer satisfactory and transient noise analysis, i.e., the simulation of noisy systems in the time domain, becomes necessary (see [4,16]). For an implementation of an efficient transient noise analysis in an analog simulator, both an appropriate modelling and integration scheme is necessary (see [3]).Here we deal with the thermal noise of resistors as well as the shot noise of semiconductors that are modelled by additional sources of additive or multiplicative Gaussian white noise currents that are shunt in parallel to the noise-free elements. Thermal noise i th of resistors is caused by the thermal motion of electrons and is described by Nyquist's theorem. Shot noise i shot of
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