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Transient noise simulation: Modeling and simulation of $$1/f$$-noise. (English) Zbl 1043.65009
Antreich, K. (ed.) et al., Modeling, simulation, and optimization of integrated circuits. Proceedings of a conference, Oberwolfach, Germany, November 25–December 1, 2001. Basel: Birkhäuser (ISBN 3-7643-2192-X/hbk). ISNM, Int. Ser. Numer. Math. 146, 251-267 (2003).
Summary: 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.
For the entire collection see [Zbl 1029.00036].

MSC:
 65C30 Numerical solutions to stochastic differential and integral equations 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 34F05 Ordinary differential equations and systems with randomness 34A09 Implicit ordinary differential equations, differential-algebraic equations 60H35 Computational methods for stochastic equations (aspects of stochastic analysis) 60G18 Self-similar stochastic processes 60G20 Generalized stochastic processes 60J65 Brownian motion