Transient Noise Simulation: Modeling and Simulation of 1/f -Noise

Abstract

In this paper we present a new approach for the transient noise simulation of electronic circuits with stochastic differential algebraic equations (SDAEs). The first part treats the modeling of noise in the time domain which is accomplished with generalized stochastic processes. This allows not only to model white noise like thermal and shot noise, but also 1/f-noise or flicker noise. It is shown that fractional Brownian motion reflects the properties of 1/f -noise, namely a spectrum proportional to 1/f with f denoting the frequency. Some consequences of this approach on the solvability of the circuit equations are presented. In the second part we give remarks on the implementation of numerical schemes for SDAEs. Besides the integration scheme itself the generation of appropriate random numbers is a major issue. Finally we present some numerical experiments.Key words and phrasesnoisecircuit simulationflicker noise1/f -noisemodelingfractional Brownian motionstochastic differential-algebraic equations