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Stefan cel Mare
University of Suceava
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ROMANIA

Print ISSN: 1582-7445
Online ISSN: 1844-7600
WorldCat: 643243560
doi: 10.4316/AECE


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  1/2013 - 3

Simulation of Higher-Order Electrical Circuits with Stochastic Parameters via SDEs

BRANCIK, L. See more information about BRANCIK, L. on SCOPUS See more information about BRANCIK, L. on IEEExplore See more information about BRANCIK, L. on Web of Science, KOLAROVA, E. See more information about KOLAROVA, E. on SCOPUS See more information about KOLAROVA, E. on SCOPUS See more information about KOLAROVA, E. on Web of Science
 
Click to see author's profile on See more information about the author on SCOPUS SCOPUS, See more information about the author on IEEE Xplore IEEE Xplore, See more information about the author on Web of Science Web of Science

Download PDF pdficon (854 KB) | Citation | Downloads: 535 | Views: 3,253

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
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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.


References | Cited By  «-- Click to see who has cited this paper

[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 19]


[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] [SCOPUS Times Cited 25]


[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 11] [SCOPUS Times Cited 13]


[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 8]


[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 12] [SCOPUS Times Cited 16]


[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 8]


[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 12] [SCOPUS Times Cited 17]


[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 50] [SCOPUS Times Cited 61]


[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 10] [SCOPUS Times Cited 11]


[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 Record]


[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 46] [SCOPUS Times Cited 59]


[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. [Online] Available: Temporary on-line reference link removed - see the PDF document



References Weight

Web of Science® Citations for all references: 168 TCR
SCOPUS® Citations for all references: 210 TCR

Web of Science® Average Citations per reference: 6 ACR
SCOPUS® Average Citations per reference: 8 ACR

TCR = Total Citations for References / ACR = Average Citations per Reference

We introduced in 2010 - for the first time in scientific publishing, the term "References Weight", as a quantitative indication of the quality ... Read more

Citations for references updated on 2017-12-09 11:49 in 79 seconds.




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