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Electrostatic Discharge Currents Representation using the Multi-Peaked Analytically Extended Function by Interpolation on a D-Optimal Design
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (Engineering mathematics)ORCID iD: 0000-0003-3204-617X
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.ORCID iD: 0000-0001-9635-0301
University of Nis, Faculty of Electronic Eng., Serbia..ORCID iD: 0000-0002-2356-8710
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.ORCID iD: 0000-0003-4554-6528
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Multi-peaked analytically extended function (AEF), previously applied by the authors to modelling of lightning discharge currents, is used in this paper for representation of the electrostatic discharge (ESD) currents. The fitting to data is achieved by interpolation of certain data points. In order to minimize unstable behaviour, the exponents of the AEF are chosen from a certain arithmetic sequence and the interpolated points are chosen according to a D-optimal design. ESD currents' modelling is illustrated through two examples: one corresponding to an approximation of the IEC Standard 61000-4-2 waveshape, and the other to representation of some measured ESD current.

National Category
Computational Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-34861OAI: oai:DiVA.org:mdh-34861DiVA: diva2:1073685
Available from: 2017-02-13 Created: 2017-02-13 Last updated: 2017-02-14Bibliographically approved
In thesis
1. Generalized Vandermonde matrices and determinants in electromagnetic compatibility
Open this publication in new window or tab >>Generalized Vandermonde matrices and determinants in electromagnetic compatibility
2017 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Matrices whose rows (or columns) consists of monomials of sequential powers are called Vandermonde matrices and can be used to describe several useful concepts and have properties that can be helpful for solving many kinds of problems. In this thesis we will discuss this matrix and some of its properties as well as a generalization of it and how it can be applied to curve fitting discharge current for the purpose of ensuring electromagnetic compatibility.

In the first chapter the basic theory for later chapters is introduced. This includes the Vandermonde matrix and some of its properties, history, applications and generalizations, interpolation and regression problems, optimal experiment design and modelling of electrostatic discharge currents with the purpose to ensure electromagnetic compatibility.

The second chapter focuses on finding the extreme points for the determinant for the Vandermonde matrix on various surfaces including spheres, ellipsoids, cylinders and tori. The extreme points are analysed in three dimensions or more.

The third chapter discusses fitting a particular model called the p-peaked Analytically Extended Function (AEF) to data taken either from a standard for electromagnetic compatibility or experimental measurements. More specifically the AEF will be fitted to discharge currents from the IEC 62305-1 and IEC 61000-4-2 standards for lightning protection and electrostatic discharge immunity as well as some experimentally measured data of similar phenomena.

Place, publisher, year, edition, pages
Västerås: Mälardalen University, 2017
Series
Mälardalen University Press Licentiate Theses, ISSN 1651-9256 ; 253
National Category
Mathematics Mathematical Analysis Computational Mathematics Probability Theory and Statistics Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-34864 (URN)978-91-7485-312-4 (ISBN)
Presentation
2017-03-23, Kappa, Västerås, 13:15 (English)
Opponent
Supervisors
Available from: 2017-02-14 Created: 2017-02-14 Last updated: 2017-09-28Bibliographically approved

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Other links

https://arxiv.org/abs/1701.03728

Authority records BETA

Lundengård, KarlRancic, MilicaSilvestrov, Sergei

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