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Electrostatic Discharge Currents Representation using the Multi-Peaked Analytically Extended Function by Interpolation on a D-Optimal Design
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. (Engineering mathematics)ORCID-id: 0000-0003-3204-617X
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.ORCID-id: 0000-0001-9635-0301
University of Nis, Faculty of Electronic Eng., Serbia..ORCID-id: 0000-0002-2356-8710
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.ORCID-id: 0000-0003-4554-6528
(Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
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.

Nationell ämneskategori
Beräkningsmatematik
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
URN: urn:nbn:se:mdh:diva-34861OAI: oai:DiVA.org:mdh-34861DiVA, id: diva2:1073685
Tillgänglig från: 2017-02-13 Skapad: 2017-02-13 Senast uppdaterad: 2017-02-14Bibliografiskt granskad
Ingår i avhandling
1. Generalized Vandermonde matrices and determinants in electromagnetic compatibility
Öppna denna publikation i ny flik eller fönster >>Generalized Vandermonde matrices and determinants in electromagnetic compatibility
2017 (Engelska)Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
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.

Ort, förlag, år, upplaga, sidor
Västerås: Mälardalen University, 2017
Serie
Mälardalen University Press Licentiate Theses, ISSN 1651-9256 ; 253
Nationell ämneskategori
Matematik Matematisk analys Beräkningsmatematik Sannolikhetsteori och statistik Algebra och logik
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
urn:nbn:se:mdh:diva-34864 (URN)978-91-7485-312-4 (ISBN)
Presentation
2017-03-23, Kappa, Västerås, 13:15 (Engelska)
Opponent
Handledare
Tillgänglig från: 2017-02-14 Skapad: 2017-02-14 Senast uppdaterad: 2017-09-28Bibliografiskt granskad

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Övriga länkar

https://arxiv.org/abs/1701.03728

Personposter BETA

Lundengård, KarlRancic, MilicaSilvestrov, Sergei

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Lundengård, KarlRancic, MilicaJavor, VesnaSilvestrov, Sergei
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Beräkningsmatematik

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