Humboldt-Universitšt zu Berlin

Thorsten Sickenberger [Homepage]

Efficient Transient Noise Analysis in Circuit Simulation


Dissertation (≈ PhD thesis), Humboldt-Universität zu Berlin, under supervision of Prof. Dr. Werner Römisch,
submitted Januar 08, 2008; defended April 25, 2008; published 2008 by Logos Verlag Berlin, Germany.
ISBN 978-3-8325-1954-4, 160 pages.
Abstract The current technological progress in microelectronics is driven by the desire to decrease feature sizes, increase frequencies and the need for low supply voltages. Amongst other effects the signal-to-noise ratio decreases and the transient noise analysis becomes necessary in the simulation of electronic circuits. Taking the inner electronic noise into account by means of Gaussian white noise currents, mathematical modelling leads to stochastic differential algebraic equations (SDAEs) with a large number of small noise sources. The simulation of such systems requires an efficient numerical time integration by mean-square convergent numerical methods.
In this thesis, adaptive linear multi-step Maruyama schemes to solve stochastic differential equations (SDEs) and SDAEs are developed. A reliable local error estimate for systems with small noise is provided and a strategy for controlling the step-size and the number of solution paths simultaneously in one approximation is presented.
Numerical experiments on industrial relevant real-life applications illustrate the theoretical findings.
Keywords /
Stichworte
• transient noise analysis / transiente Rauschanalyse
• stochastic differential-algebraic equations, stochastische Algebro-Differentialgleichungen (SDAE, SDAEs)
• adaptive stochastic linear multi-step methods with variable step-sizes / adaptive stochastische lineare Mehrschritt-Verfahren mit variablen Schrittweiten
• step-size control / Schrittweitensteuerung
• circuit simulation / Schaltungs-Simulation
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Slides / Vortragsfolienpdf file [1.3 MB]
Contact /
Kontakt
Dr. Thorsten Sickenberger [Homepage]
e-mail: sickenberger@math.hu-berlin.de