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Sommerfeld’s integrals and Hallen’s integral equation in Data Analysis for Horizontal Dipole Antenna above Real Ground
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (Mathematics and Applied Mathematics)ORCID iD: 0000-0002-5604-493X
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (Mathematics and Applied Mathematics)ORCID iD: 0000-0001-9635-0301
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (Mathematics and Applied Mathematics)ORCID iD: 0000-0003-4554-6528
University of Nis, Faculty of Electronic Eng., Serbia.
2014 (English)In: SMTDA 2014 Proceedings / [ed] Christos H. Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2014, 507-518 p.Conference paper, Published paper (Refereed)
Abstract [en]

Increase of the radiation power in different frequency bands during the last decades, has called for a study of harmful effects on the living organisms and electronic equipment of the radio frequency energy. An accurate determination of the near field strength, electric as well as magnetic, in the vicinity of higher-power transmitting antennas is necessary for assessing any possible radiation hazard. In that sense, it is of great importance to account for the influence of the finite ground conductivity on the electromagnetic field structure in the surroundings of these emitters. The estimation of this influence has been intensively studied, and a number of approaches has been applied in that sense, ranging from the exact full-wave based ones to different forms of approximate, less time-consuming, ones. Although the approximate methods introduce a certain level of calculation error, their simplicity is of interest in the electomagnetic compatibility (EMC) studies. For that reason, finding an approximate, but satisfyingly accurate method, applicable to wide range of parameters is often a goal of researches done in this field.

In this paper, the authors perform an analysis of a thin horizontal dipole antenna (HDA) above real ground of known electrical parameters. The approach is based on the electric-field integral equation method, and formulation of the Hallén’s integral equation (HIE). This equation is then solved for the current, which is assumed in a polynomial form, using the point-matching method (PMM). This way obtained system of linear equations involves improper Sommerfeld’s integrals, which express the influence of the real ground and are here solved approximately using simple, so-called OIA and TIA, approximations (one- and two-image approximations). Both types of approximations are in an exponential form, and therefore are similar to those obtained applying the method of images. It should be kept in mind that the goal of this approach is to develop approximations that have a simple form, whose application yields satisfyingly accurate calculations of the Sommerfeld`s type of integrals, and are widely applicable, i.e. their employment is not restricted by the values of electrical parameters of the ground, or the geometry.

Thorough analysis is performed in order to observe the influence of different parameters of the geometry, and the ground, on current distribution and the input impedance/admittance of the HDA in a wide frequency range. Furthermore, the verification of the method is done by comparison to the exact model based on the full-wave theory, and experimental data. Obtained results indicate a possibility of applying the described methodology to inverse problem involving evaluation of electrical parameters of the ground (or detection of ground type change) based on measured input impedance/admittance of the antenna.

Place, publisher, year, edition, pages
ISAST: International Society for the Advancement of Science and Technology , 2014. 507-518 p.
Keyword [en]
Horizontal dipole antenna, Hallén’s integral equation, Point-matching method, Polynomial current approximation, Real ground, Sommerfeld’s integrals
National Category
Mathematics Computational Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-26057ISBN: 978-618-81257-6-6 (print)OAI: oai:DiVA.org:mdh-26057DiVA: diva2:752658
Conference
3rd Stochastic Modelling Techniques and Data Analysis International Conference (SMTDA 2014), 11-14 June 2014, Lisbon, Portugal
Projects
RALF3 project funded by the Swedish Foundation for Strategic Research (SSF)EUROWEB Project funded by the Erasmus Mundus Action II programme of the European Commission
Available from: 2014-10-06 Created: 2014-10-06 Last updated: 2016-02-02Bibliographically approved
In thesis
1. Mathematical Tools Applied in Computational Electromagnetics for a Biomedical Application and Antenna Analysis
Open this publication in new window or tab >>Mathematical Tools Applied in Computational Electromagnetics for a Biomedical Application and Antenna Analysis
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

To ensure a high level of safety and reliability of electronic/electric systems EMC (electromagnetic compatibility) tests together with computational techniques are used. In this thesis, mathematical modeling and computational electromagnetics are applied to mainly two case studies. In the first case study, electromagnetic modeling of electric networks and antenna structures above, and buried in, the ground are studied. The ground has been modelled either as a perfectly conducting or as a dielectric surface.  The second case study is focused on mathematical modeling and algorithms to solve the direct and inverse electromagnetic scattering problem for providing a model-based illustration technique. This electromagnetic scattering formulation is applied to describe a microwave imaging system called Breast Phantom. The final goal is to simulate and detect cancerous tissues in the human female breast by this microwave technique.  

The common issue in both case studies has been the long computational time required for solving large systems of equations numerically. This problem has been dealt with using approximation methods, numerical analysis, and also parallel processing of numerical data. For the first case study in this thesis, Maxwell’s equations are solved for antenna structures and electronic networks by approximation methods and parallelized algorithms implemented in a LAN (Local Area Network). In addition, PMM (Point-Matching Method) has been used for the cases where the ground is assumed to act like a dielectric surface. For the second case study, FDTD (Finite-Difference Time Domain) method is applied for solving the electromagnetic scattering problem in two dimensions. The parallelized numerical FDTD-algorithm is implemented in both Central Processing Units (CPUs) and Graphics Processing Units (GPUs).

Abstract [sv]

För att säkerställa människors säkerhet och tillförlitligheten hos elektriska/elektroniska system används EMC (elektromagnetisk kompatibilitet)-tester i kombination med matematisk modellering. För att undersöka biologiska vävnaders egenskaper används så kallade elektromagnetiska spridningsmetoder vid sidan om elektromagnetisk modellering. I denna avhandling har matematisk modellering och beräkningsmetoder använts för huvudsakligen två fallstudier. Den första fallstudien handlar om att analysera antennstrukturer och elektriska nät ovanför, och nergrävda i marken. Marken har modellerats antingen som en elektriskt ledande yta eller en dielektrisk yta. Den andra fallstudien fokuserar på matematisk modellering och algoritmer för att lösa ett elektromagnetiskt spridningsproblem för att beskriva en modellbaserad illustrationsteknik. Spridningsformuleringen tillämpas för att modellera ett avbildningssystem som använder mikrovågor, kallat Bröstfantomen. Det slutliga målet är att upptäcka cancervävnader i kvinnobröst genom denna mikrovågsteknik.

Flaskhalsen i de båda fallstudierna har visat sig vara de långa beräkningstider som krävs för att lösa stora numeriska system. För att lösa problemet har approximationsmetoder, numerisk analys och även parallella beräkningar genomförts i detta arbete. För den första fallstudien har Maxwells ekvationer lösts genom CEM (Complex Image Methods) och med parallellisering i ett LAN (Local Area Network). I de fall där marken betraktas som en dielektrisk yta, har PMM (Point-Matching Method) tillämpats. I samband med den andra fallstudien har FDTD (Finite-Difference Time Domain) metoder tillämpats för att lösa ett elektromagnetiskt spridningsproblem i två dimensioner. En parallelliserad FDTD-algoritm har implementerats i både CPU:s (Central Processing Units) och GPU:s (Graphics Processing Units).

Place, publisher, year, edition, pages
Västerås: Mälardalen University, 2015
Series
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 176
National Category
Mathematics Computational Mathematics Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-27764 (URN)978-91-7485-200-4 (ISBN)
Public defence
2015-05-12, Delta, Mälardalens högskola, Västerås, 13:15 (English)
Opponent
Supervisors
Projects
RALF3
Funder
Swedish Foundation for Strategic Research
Available from: 2015-04-02 Created: 2015-03-27 Last updated: 2015-06-29Bibliographically approved

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