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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] Coloured Noise Analysis of a Phase-Locked Loop System: Beyond Itô and Stratonovich Stochastic Calculi, Gawalwad, Balaji G., Sharma, Shambhu N., Differential Equations and Dynamical Systems, ISSN 0971-3514, Issue 2, Volume 24, 2016.
Digital Object Identifier: 10.1007/s12591-014-0212-z [CrossRef]
[2] Confidence intervals for RLCG cell influenced by coloured noise, Kolarova, Edita, Brancik, Lubomir, COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, ISSN 0332-1649, Issue 4, Volume 36, 2017.
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Digital Object Identifier: 10.4316/AECE.2015.04010 [CrossRef] [Full text]
[5] Numerical simulation of fractional-order dynamical systems in noisy environments, Mostaghim, Zeinab Salamat, Moghaddam, Behrouz Parsa, Haghgozar, Hossein Samimi, Computational and Applied Mathematics, ISSN 0101-8205, Issue 5, Volume 37, 2018.
Digital Object Identifier: 10.1007/s40314-018-0698-z [CrossRef]
[6] Stochastic Differential Equations Describing Systems with Coloured Noise, Kolářová, Edita, Brančík, Lubomír, Tatra Mountains Mathematical Publications, ISSN 1210-3195, Issue 1, Volume 71, 2018.
Digital Object Identifier: 10.2478/tmmp-2018-0009 [CrossRef]
[7] Simulation of multiconductor transmission lines with random parameters via stochastic differential equations approach, Brančík, Lubomír, Kolářová, Edita, SIMULATION, ISSN 0037-5497, Issue 6, Volume 92, 2016.
Digital Object Identifier: 10.1177/0037549716645198 [CrossRef]
[8] Confidence intervals at multiconductor transmission lines with stochastic excitations: Stochastic differential equations approach, Brancik, Lubomir, Kolarova, Edita, 2015 European Conference on Circuit Theory and Design (ECCTD), ISBN 978-1-4799-9877-7, 2015.
Digital Object Identifier: 10.1109/ECCTD.2015.7300057 [CrossRef]
[9] Characterization of MTL Hybrid Circuits with Stochastic Parameters through SDAE Approach, Brancik, Lubomir, Kolarova, Edita, Sigmund, Milan, 2018 25th International Conference "Mixed Design of Integrated Circuits and System" (MIXDES), ISBN 978-83-63578-14-5, 2018.
Digital Object Identifier: 10.23919/MIXDES.2018.8436915 [CrossRef]
[10] Time-domain simulation of transmission line models with multiple stochastic excitations, Brancik, Lubomir, Kolarova, Edita, 2014 24th International Conference Radioelektronika, ISBN 978-1-4799-3715-8, 2014.
Digital Object Identifier: 10.1109/Radioelek.2014.6828407 [CrossRef]
[11] SDE-based variance simulation in transmission line models with random excitations, Brancik, Lubomir, Kolarova, Edita, Al-Zubaidi R-Smith, Nawfal, 2015 25th International Conference Radioelektronika (RADIOELEKTRONIKA), ISBN 978-1-4799-8117-5, 2015.
Digital Object Identifier: 10.1109/RADIOELEK.2015.7129053 [CrossRef]
[12] The Milstein numerical scheme in solving stochastic second order networks, Kolarova, Edita, Brancik, Lubomir, 2015 38th International Conference on Telecommunications and Signal Processing (TSP), ISBN 978-1-4799-8498-5, 2015.
Digital Object Identifier: 10.1109/TSP.2015.7296267 [CrossRef]
[13] Simulation of stochastic responses at multiconductor transmission lines with fluctuating parameters, Brancik, L., Kolarova, E., 2013 23rd International Conference Radioelektronika (RADIOELEKTRONIKA), ISBN 978-1-4673-5519-3, 2013.
Digital Object Identifier: 10.1109/RadioElek.2013.6530890 [CrossRef]
[14] Simulation of hybrid MTL systems with random parameters based on stochastic DAEs, Brancik, Lubomir, 2013 European Conference on Circuit Theory and Design (ECCTD), ISBN 978-3-00-043785-4, 2013.
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[15] Third-order continuous-discrete filtering for a Stochastic Duffing System, Patel, Hiren G., 2015 International Conference on Industrial Instrumentation and Control (ICIC), ISBN 978-1-4799-7165-7, 2015.
Digital Object Identifier: 10.1109/IIC.2015.7150734 [CrossRef]
[16] The effect of the colored noise to RLC(G) electrical circuits, Kolarova, Edita, Brancik, Lubomir, 2016 26th International Conference Radioelektronika (RADIOELEKTRONIKA), ISBN 978-1-5090-1674-7, 2016.
Digital Object Identifier: 10.1109/RADIOELEK.2016.7477355 [CrossRef]
[17] Multiconductor Transmission Line System with Stochastically Affected Boundary Conditions, Brancik, Lubomir, Kolarova, Edita, 2019 MIXDES - 26th International Conference "Mixed Design of Integrated Circuits and Systems", ISBN 978-83-63578-16-9, 2019.
Digital Object Identifier: 10.23919/MIXDES.2019.8787203 [CrossRef]
[18] Variance assessment at transmission lines with randomly varying parameters via SDE theory, Brancik, Lubomir, Kolarova, Edita, IEEE EUROCON 2015 - International Conference on Computer as a Tool (EUROCON), ISBN 978-1-4799-8569-2, 2015.
Digital Object Identifier: 10.1109/EUROCON.2015.7313785 [CrossRef]
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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.
