Efficient transient noise analysis in circuit simulation

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.

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