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Simulation of Higher-Order Electrical Circuits with Stochastic Parameters via SDEsBRANCIK, L.   , KOLAROVA, E. |
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Author keywords
circuit noise, circuit simulation, differential equations, stochastic processes, stochastic systems
References keywords
stochastic(14), equations(11), analysis(9), circuits(7), brancik(6), kolarova(5), applications(4)
Blue keywords are present in both the references section and the paper title.
About this article
Date of Publication: 2013-02-28
Volume 13, Issue 1, Year 2013, On page(s): 17 - 22
ISSN: 1582-7445, e-ISSN: 1844-7600
Digital Object Identifier: 10.4316/AECE.2013.01003
Web of Science Accession Number: 000315768300003
SCOPUS ID: 84875361883
Abstract
The paper deals with a technique for the simulation of higher-order electrical circuits with parameters varying randomly. The principle consists in the utilization of the theory of stochastic differential equations (SDE), namely the vector form of the ordinary SDEs. Random changes of both excitation voltage and some parameters of passive circuit elements are considered, and circuit responses are analyzed. The voltage and/or current responses are computed and represented in the form of the sample means accompanied by their confidence intervals to provide reliable estimates. The method is applied to analyze responses of the circuit models of optional orders, specially those consisting of a cascade connection of the RLGC networks. To develop the model equations the state-variable method is used, afterwards a corresponding vector SDE is formulated and a stochastic Euler numerical method applied. To verify the results the deterministic responses are also computed by the help of the PSpice simulator or the numerical inverse Laplace transforms (NILT) procedure in MATLAB, while removing random terms from the circuit model. |
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| [1] B. Oksendal, "Stochastic Differential Equations, An Introduction with Applications", Springer-Verlag, 2000.
[2] L. Arnold, "Stochastic Differential Equations: Theory and Applications", Krieger Publishing, 1992. [3] P. Kloeden, E. Platen, H. Schurz, "Numerical Solution of SDE Through Computer Experiments", Springer-Verlag, 1997. [4] S. Cyganowski, P. Kloeden, J. Ombach, "From Elementary Probability to Stochastic Differential Equations with Maple", Springer-Verlag, 2000. [5] D. Ham, A. Hajimiri, "Complete Noise Analysis for CMOS switching Mixers via Stochastic Differential Equations," in Proc. IEEE Custom Integrated Circuits Conference, Orlando, pp. 439-442, 2000. [CrossRef] [Web of Science Times Cited 34] [6] K. Wang, M. L. Crow, "Numerical Simulation of Stochastic Differential Algebraic Equations for Power System Transient Stability with Random Loads," in Proc. IEEE Power and Energy Society General Meeting, San Diego, pp. 1-8, 2011. [CrossRef] [Web of Science Times Cited 11] [SCOPUS Times Cited 64] [7] A. Zjajo, Q. Tang, M. Berkelaar, J. P. de Gyvez, A. Di Bucchianico, N. van der Meijs, "Stochastic Analysis of Deep-Submicrometer CMOS Process for Reliable Circuits Designs," IEEE Transactions on Circuits and Systems I: Reg. Papers, vol. 58, no. 1, pp. 164-175, 2011. [CrossRef] [Web of Science Times Cited 16] [SCOPUS Times Cited 22] [8] E. Kolarova, "Modelling RL Electrical Circuits by Stochastic Diferential Equations," in Proc. IEEE R8 International Conference on Computer as a Tool, Belgrade, pp. 1236-1238, 2005. [CrossRef] [Web of Science Times Cited 19] [9] E. Kolarova, "Statistical Estimates of Stochastic Solutions of RL Electrical Circuits," in Proc. IEEE International Conference on Industrial Technology ICIT2006, Mumbai, pp. 2546-2550, 2006. [CrossRef] [Web of Science Times Cited 13] [SCOPUS Times Cited 19] [10] N. S. Patil, B. G. Gawalwad, S. N. Sharma, "A Random Input-Driven Resistor-Capacitor Series Circuit," in Proc. 2011 International Conference on Recent Advancements in Electrical, Electronics and Control Engineering, Sivakasi, pp. 100-103, 2011. [CrossRef] [SCOPUS Times Cited 9] [11] F. Rahman, N. Parisa, "A Stochastic Perspective of RL Electrical Circuit Using Different Noise Terms," COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 30, no. 2, pp. 812-822, 2011. [CrossRef] [Web of Science Times Cited 23] [SCOPUS Times Cited 31] [12] E. Kolarova, L. Brancik, "Application of Stochastic Differential Equations in Second-Order Electrical Circuits Analysis," Przeglad Elektrotechniczny, vol. 88, no. 7a, pp. 103-107, 2012. [13] L. Brancik, E. Kolarova, "Analysis of Higher-Order Electrical Circuits with Noisy Sources via Stochastic Differential Equations Approach," in Proc. 22nd International Conference Radioelektronika 2012, Brno, pp. 81-84, 2012. [14] E. Kolarova, L. Brancik, "Vector Linear Stochastic Differential Equations and Their Applications to Electrical Networks," in Proc. 35th International Conference on Telecommunications and Signal Processing TSP2012, Prague, pp. 311-315, 2012. [15] C. K. Cheng, J. Lillis, S. Lin, N. Chang, "Interconnect Analysis and Synthesis", John Wiley & Sons, 2000. [16] M. P. Li, "Jitter, Noise, and Signal Integrity at High-Speed", Prentice Hall, 2007. [17] U. M. Ascher, L. R. Petzold, "Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations", SIAM: Society for Industrial and Applied Mathematics, 1998. [CrossRef] [18] A. Papoulis, S. U. Pillai, "Probability, Random Variables and Stochastic Processes", McGraw-Hill, 2002. [19] S. Lum, M. S. Nakhla, Q. J. Zhang, "Sensitivity Analysis of Lossy Coupled Transmission Lines," IEEE Transactions on Microwave Theory and Techniques, vol. 39, no. 12, pp. 2089-2099, 1991. [CrossRef] [Web of Science Times Cited 59] [SCOPUS Times Cited 75] [20] L. Brancik, "Time and Laplace-Domain Methods for MTL Transient and Sensitivity Analysis," COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 30, no. 4, pp. 1205-1223, 2011. [CrossRef] [Web of Science Times Cited 12] [SCOPUS Times Cited 15] [21] L. Brancik, "Modified Technique of FFT-Based Numerical Inversion of Laplace Transforms with Applications," Przeglad Elektrotechniczny, vol. 83, no. 11, pp. 53-56, 2007. [22] H. Qinshu, L. Xinen, X. Shifu, "A Fast Approximate Method for Parametric Probabilistic Sensitivity Estimation," in Proc. the 3rd International Conference on Advanced Computer Theory and Engineering ICACTE2010, Chengdu, pp. 349-351, 2010. [CrossRef] [SCOPUS Times Cited 1] [23] D. V. Ginste, D. De Zutter, D. Deschrijver, T. Dhaene, P. Manfredi, F. Canavero, "Stochastic Modeling-Based Variability Analysis of On-Chip Interconnects," IEEE Transactions on Components, Packaging, and Manufacturing Technology, vol. 2, no. 7, p. 1182-1192, 2012. [CrossRef] [Web of Science Times Cited 81] [SCOPUS Times Cited 93] [24] C. R. Paul, "Analysis of Multiconductor Transmission Lines," John Wiley & Sons, 2008. [25] L. Brancik, B. Sevcik, "Computer Simulation of Nonuniform MTLs via Implicit Wendroff and State-Variable Methods," Radioengineering, vol. 20, no. 1, pp. 221-227, 2011. 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Faculty of Electrical Engineering and Computer Science
Stefan cel Mare University of Suceava, Romania
All rights reserved: Advances in Electrical and Computer Engineering is a registered trademark of the Stefan cel Mare University of Suceava. No part of this publication may be reproduced, stored in a retrieval system, photocopied, recorded or archived, without the written permission from the Editor. When authors submit their papers for publication, they agree that the copyright for their article be transferred to the Faculty of Electrical Engineering and Computer Science, Stefan cel Mare University of Suceava, Romania, if and only if the articles are accepted for publication. The copyright covers the exclusive rights to reproduce and distribute the article, including reprints and translations.
Permission for other use: The copyright owner's consent does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific written permission must be obtained from the Editor for such copying. Direct linking to files hosted on this website is strictly prohibited.
Disclaimer: Whilst every effort is made by the publishers and editorial board to see that no inaccurate or misleading data, opinions or statements appear in this journal, they wish to make it clear that all information and opinions formulated in the articles, as well as linguistic accuracy, are the sole responsibility of the author.
