Development of Software for Antenna Analysis and Design using FDTD Engenharia Electrotécnica ...

114 Pages·2007·2.96 MB·English

GUIA DE PREPARAÇÃO
DA DISSERTAÇÃO E RESUMO ALARGADO
PARA OS CURSOS DE MESTRADO NO IST

Development of Software for Antenna Analysis and
1. TRAMITAÇÃO DE DISSERTAÇÃO/PROJECTO..................................................................................2
Design using FDTD
2. INFORMAÇÃO A INTRODUZIR NO SISTEMA FÉNIX........................................................................4
3. CONFIDENCIALIDADE.............................................................................................................................4
4. ESTRUTURA E FORMATO DA DISSERTAÇÃO..................................................................................5
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4.2 Capa e Lombada...............................................................................................................................5
4.3 Equações e Expressões...................................................................................................................5
4.4 Referências e Bibliografia................................................................................................................5
4.5 Tabelas e Figuras..............................................................................................................................5
5. ESTRUTURAD DisOs ReErtSaU¸cM˜aOo ApLAaRraGAaDOob...t...e..n...¸c...˜a...o.....d...o.....G....r..a...u.....d...e....M......e..s...t..r..e....e...m.....................5
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7. MODELO DE CAPA E LOMBADA...........................................................................................................6
8. MODELO DE CAPA DE CD......................................................................................................................9
9. FICHA DE HOMOLOGAÇÃO de JÚRI..................................................................................................10
10. CONTEÚDO DE identificacao.pdf..........................................................................................................11
11. DECLARAÇÃO RESPEITANTE À DIVULGAÇÃO DA DISSERTAÇÃO..........................................13
Ju´ri
12. EXEMPLO DE DECLARAÇÃO DE CONFIDENCIALIDADE.............................................................13
Presidente: Prof. Doutor Ant´onio Rodrigues
Orientador: Prof. Doutor Ant´onio Alves Moreira
Co-Orientador: Prof. Doutor Vitor Mal´o Machado
Vogais: Prof. Doutor Carlos Fernandes
Setembro 2007
1
Acknowledgments
First, I must thank Professor Ant´onio Alves Moreira and Professor Vitor Mal´o Machado for the
excellent support and guidance they have given me during the execution of this work. I am very grateful for
their faith in me.
IwouldalsoliketothankInstitutodeTelecomunica¸c˜oesformakingavailablethecommercialsoftware
used for the validation of the obtained results, and the ACE network (Antenna Centre of Excellence) for
accepting the attendance, as a student, of the European Course on Time Domain Techniques for Antenna
Analysis, held in the university of Nice-Sophia Antipolis, 20-24 November 2006.
At last, my warmest thanks go to my parents, my brother and my girlfriend, not only for the
constantsupportandmotivation,butalsoforthepatienceandunderstandingdemonstratedduringthiswork’s
execution. I dedicate this thesis to them.
i
Agradecimentos
Primeiro que tudo, gostaria de agradecer aos Professores Ant´onio Alves Moreira e Vitor Mal´o
Machado pelo excelente apoio e orienta¸c˜ao que me dispensaram na realiza¸c˜ao deste trabalho. Estou muito
grato pela confianc¸a que em mim depositaram.
Agrade¸cotamb´emoapoiodoInstitutodeTelecomunica¸c˜oes, quefacultouosoftwarecomercialuti-
lizadonavalida¸c˜aodosresultadosobtidos,eaoprogramaACE(AntennaCentreofExcellence)pelaaceita¸c˜ao,
como estudante, na frequˆencia do “European Course on Time Domain Techniques for Antenna Analysis”,
realizado na universidade de Nice-Sophia Antipolis entre 20 e 24 de Novembro de 2006.
Finalmente, queria deixar um agradecimento especial aos meus pais, ao meu irm˜ao e `a minha
namorada, n˜ao s´o pelo apoio e incentivo constantes, mas tamb´em pela paciˆencia e compreens˜ao que demons-
traram durante a realizac¸˜ao deste trabalho. E´ a eles que dedico esta disserta¸c˜ao.
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Abstract
Thisworkpresentsthedevelopmentofacompletesoftwarepackageforantennaanalysisanddesign
using the Finite-Difference Time-Domain (FDTD) method. The formulation of the implemented FDTD algo-
rithm is described, as well as the analysis of its fundamental properties. A description of the complementary
techniques and algorithms that allow the effective implementation of a simulator for the analysis of problems
of engineering value is also presented. These include a Perfectly Matched Layer (PML) capable of terminat-
ing heterogeneous media, a thin-wire model, excitation source models and a near-to-far-field transformation.
The aforementioned techniques are implemented in a modular fashion and integrated into a graphical user
interface that, besides allowing the configuration and three-dimensional visualization of the structures being
analyzed,alsofeaturesanon-uniformmeshgenerationalgorithmthatautomaticallyperformsthediscretization
of the 3D objects. Different solutions for the visualization of simulation results have been developed, namely
three-dimensional radiation pattern plots and field animations.
The new software, named FDTD Antenna Simulator, has an open-source license and has been
entirely written in Java, which not only makes it compatible with the major operating systems, but also
facilitates its future expansion.
The effectiveness and flexibility of the developed software are illustrated by the analysis of different
types of antennas, namely dipoles, monopoles and printed and horn antennas. The obtained results are
compared with simulations and measurements published by other authors.
Keywords
FDTDmethods,softwarepackages,perfectlymatchedlayers,meshgeneration,antennafeedmodels,
graphical user interfaces.
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Resumo
Este trabalho descreve o desenvolvimento de uma ferramenta de software para projecto e an´alise
de antenas utilizando o m´etodo das diferen¸cas finitas no dom´ınio do tempo (FDTD). E´ apresentada a for-
mula¸c˜ao do algoritmo FDTD utilizado, bem como o estudo das suas principais caracter´ısticas. S˜ao descritas
as t´ecnicas e algoritmos que, complementando o algoritmo FDTD, possibilitam a implementa¸c˜ao de um si-
mulador para a an´alise de problemas de real interesse em engenharia. Destacam-se a implementa¸c˜ao de uma
camada perfeitamente adaptada (Perfectly Matched Layer - PML) compat´ıvel com meios heterog´eneos, um
modelodecondutoresfinos,modelosdefontesdeexcita¸c˜aoeumatransforma¸c˜aodecamposdezona-pr´oxima
para zona-distante. Estas t´ecnicas s˜ao implementadas de forma modular e integradas numa interface gr´afica
cuidada que, al´em de permitir a configura¸c˜ao e visualiza¸c˜ao tridimensional das estruturas que comp˜oem a
simula¸c˜ao, possui ainda um algoritmo de gera¸c˜ao de malha n˜ao-uniforme que, de forma autom´atica, efectua
a discretiza¸c˜ao dos objectos tridimensionais. O software possui diversas funcionalidades para a visualiza¸c˜ao
dos resultados de simula¸c˜ao, destacando-se a possibilidade de representar tridimensionalmente diagramas de
radia¸c˜ao e anima¸c˜oes dos campos.
O novo programa, denominado FDTD Antenna Simulator, possui uma licen¸ca open-source e foi
totalmente desenvolvido em Java, o que al´em de o tornar compat´ıvel com os principais sistemas operativos,
facilita a sua expans˜ao futura.
A efic´acia e flexibilidade do software desenvolvido s˜ao ilustradas pela an´alise de diferentes tipos
de antenas, nomeadamente dipolos, monopolos, antenas impressas e cornetas, sendo os resultados obtidos
comparados com simula¸c˜oes e medidas publicadas por outros autores.
Palavras chave
M´etodo FDTD, pacotes de software, PML - camadas perfeitamente adaptadas, gera¸c˜ao de malha,
modelos de excitac¸˜ao de antenas, interfaces gr´aficas.
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Contents
1 Introduction 1
1.1 Brief historical background of Computational Electromagnetics . . . . . . . . . . . . . . . . . 1
1.2 Currently available software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Objectives of this work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Why FDTD? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4.1 Techniques in Computational Electromagnetics . . . . . . . . . . . . . . . . . . . . . 3
1.4.2 FDTD advantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.5 List of implemented features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 The Finite-Difference Time-Domain Method 6
2.1 Maxwell’s Equations in Three Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 The Yee Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.1 The Yee cell and the leapfrogging scheme . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.2 Discretization of Maxwell’s Equations using the Yee algorithm . . . . . . . . . . . . . 9
2.2.3 Computer Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Numerical Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.1 Derivation of the numerical dispersion relation for three-dimensional wave propagation 15
2.3.2 Comparison with the ideal dispersion case and anisotropy of the numerical phase velocity 16
2.3.3 Choice of the spatial sampling density and other sources of numerical error . . . . . . 17
2.4 Numerical Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4.1 The Courant stability criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4.2 Other potential sources of instability . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5 Extension to non-uniform Cartesian meshes . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5.1 Benefits of non-uniform meshes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5.2 Required modifications to the algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5.3 Numerical accuracy and stability for non-uniform FDTD . . . . . . . . . . . . . . . . 21
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3 Absorbing Boundary Conditions 22
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2 B´erenger’s Split-Field PML . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3 Uniaxial PML . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3.1 UPML Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3.2 Theoretical and Practical Performance of the UPML . . . . . . . . . . . . . . . . . . 28
3.3.3 Application to a Three-Dimensional Problem Space . . . . . . . . . . . . . . . . . . . 29
3.3.4 Implementation in FDTD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3.5 Computer Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.6 UPML validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4 Sub-cellular methods 35
4.1 FDTD Formulation using the Integral Form of Maxwell’s Equations . . . . . . . . . . . . . . 36
4.2 Thin-wire model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.3 Effective material parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5 Antenna Feed Models 42
5.1 Excitation Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.2 Point Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.3 Resistive voltage source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.3.1 Model description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.3.2 Calculation of Impedance and S parameters . . . . . . . . . . . . . . . . . . . . . . . 46
5.4 Simple Waveguide Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.4.1 Model description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.4.2 Calculation of S parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
6 Near-to-Far-Field Transformation 51
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6.2 Frequency-Domain Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
6.2.1 Analytical expressions for the transformation . . . . . . . . . . . . . . . . . . . . . . . 52
6.2.2 Calculation of the equivalent M¯ and J¯ currents . . . . . . . . . . . . . . . . . . . . 55
S S
6.2.3 Averaging of the E~ and H~ fields on the virtual surface . . . . . . . . . . . . . . . . . 56
7 Mesh Generation Algorithm 57
7.1 Meshing Algorithm Structure and Architecture of the FDTD Simulator. . . . . . . . . . . . . 57
7.2 Spatial Discretization Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
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7.3 Material Mapping Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
8 Numerical Experiments and Results Validation 66
8.1 Dipole Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
8.2 Monopole Antenna on a Conducting Box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
8.3 Microstrip Patch Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
8.4 UWB Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
8.5 Pyramidal Horn Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
9 Conclusions 78
9.1 Suggestions for Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
A Finite-difference schemes and order of accuracy 81
A.1 Forward-differences approximation to the first derivative . . . . . . . . . . . . . . . . . . . . . 81
A.2 Backward-differences approximation to the first derivative . . . . . . . . . . . . . . . . . . . . 82
A.3 Central-differences approximation to the first derivative . . . . . . . . . . . . . . . . . . . . . 82
A.4 Central-differences approximation to the second derivative . . . . . . . . . . . . . . . . . . . 83
B Verification of Gauss’ laws for the Yee Algorithm 84
C Code Examples 87
C.1 Simple Three-Dimensional FDTD Update Algorithm. . . . . . . . . . . . . . . . . . . . . . . 87
C.2 Three-Dimensional FDTD Update Algorithm with the UPML . . . . . . . . . . . . . . . . . . 88
D UPML Update Equations and Coefficients 89
D.1 Update equations for the E-field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
D.2 Update equations for the H-field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
E Modeling of Thin Metalizations 92
F Other Experiments and Applications 94
F.1 Low-pass microstrip filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
F.2 SAR Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
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List of Figures
1.1 Categories within computational electromagnetics. . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 Position of the electric and magnetic field vector components about the cell(i,j,k) of the Yee
space lattice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Space-timechartthatillustratesYeealgorithm’suseofcentraldifferencesforthespacederiva-
tives and leapfrogging for the time derivatives for a simplified one-dimensional case. . . . . . . 10
2.3 Variation of the numerical phase velocity along the grid’s axes and diagonals as a function of
the sampling density N , for S =0.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
λ
2.4 (a) A circular metallic patch and (b) its meshed version where the staircased approximation of
the curved boundary can be observed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.5 Comparisonbetween(a)anuniformmeshand(b)anon-uniformmeshregardingthecapability
to adapt to the geometry of multiple objects. . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.6 Comparisonbetween(a)anuniformmeshand(b)anon-uniformmeshregardingthecapability
to use different levels of spatial resolution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.1 2D-cut of a three-dimensional FDTD grid employing the Berenger PML ABC. . . . . . . . . . 25
3.2 Reflection error versus frequency for different values of the UPML thickness.. . . . . . . . . . 32
3.3 GeometryofthemicrostriplineandcomputationaldomainusedtoassessUPML’scapacityfor
terminating heterogeneous media. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4 Return loss of the microstrip line terminated with a 10 cell UPML. . . . . . . . . . . . . . . . 34
4.1 IntegrationcontoursC andassociatedsurfacesS usedforthederivationoftheYeealgorithm
i i
using the integral form of Maxwell’s equations. . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.2 (a)ApplicationofFaraday’sLawforderivationofthethinwiremodel. (b)H-fieldcomponents
updated using the thin wire model and integration path for calculation of the current I. . . . 38
4.3 Interface between cells of different materials and integration path C for the application of
Maxwell-Ampere’s Law for effective parameters calculation. . . . . . . . . . . . . . . . . . . . 40
5.1 Excitation signals available in the developed software. . . . . . . . . . . . . . . . . . . . . . . 43
5.2 Representation of the unidimensional virtual transmission line used to implement the resistive
voltage source and coupling to the 3D FDTD grid. . . . . . . . . . . . . . . . . . . . . . . . 45
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5.3 Illustration of the application of a waveguide source to a rectangular waveguide connected to
an arbitrary structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.4 Calculation of the incident field distribution for a rectangular waveguide. (a) Initial electric
field distribution; (b) Numerically calculated electric field distribution of the TE mode. . . . 48
01
6.1 Virtual surface used for the near-to-far-field transformation and coordinate system used for its
calculation.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
6.2 Geometry used for the averaging of the E~ and H~ fields’ tangential components for the calcu-
lation of the equivalent currents M~ and J~ . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
S S
7.1 Flowchart illustrating the high-level architecture of the FDTD simulator. . . . . . . . . . . . . 58
7.2 Geometry of the structure used to illustrate the spatial discretization algorithm’s operation.. . 61
7.3 Two-dimensionalCartesiangridthatresultsfromthenon-uniformdiscretizationofthestructure
of Fig. 7.2 using the spatial discretization algorithm with parameters D = D = 10
x,min y,min
and D =D =30. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
x,max y,max
7.4 Illustration of the material mapping algorithm’s operation. (a) Two-dimensional view of the
component being meshed and the Cartesian grid that resulted from spatial discretization; (b)
Operation of the ray-crossing algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
7.5 Illustration of how the assignment of different meshing priorities to the elements of a three-
dimensional model can influence the characteristics of the resultant component. (a) Three-
dimensional view of the mesh for a coaxial cable; (b) Three-dimensional view of the mesh for
a cylindrical waveguide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
8.1 FDTD problem space for the analysis of coupling between two dipoles. . . . . . . . . . . . . . 66
8.2 Mesh used to discretize the computational domain. . . . . . . . . . . . . . . . . . . . . . . . 66
8.3 Self-admittanceforantenna1calculatedwiththedevelopedsoftwareandcomparedwithresults
obtained with other methods/applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
8.4 Mutualadmittancecalculatedwiththedevelopedsoftwareandcomparedwithresultsobtained
with other methods/applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
8.5 Comparison of the mutual admittances Y and Y calculated with the developed software,
12 21
for the purpose of port reciprocity analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
8.6 Geometry and dimensions of the monopole antenna on a conducting box. The monopole wire
radius is r=0.5 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
8.7 2D view of the mesh used to discretize the problem. . . . . . . . . . . . . . . . . . . . . . . . 69
8.8 Input impedance for monopole antenna on a conducting box computed using the developed
software and compared with measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
8.9 Calculated x-z plane radiation pattern at 1.5 GHz for the monopole antenna on a conducting
box and comparison with reference results obtained with MoM. . . . . . . . . . . . . . . . . . 70
8.10 Geometry of the line fed rectangular microstrip patch antenna. (a) Top view (b) Perspective
view, dimensions of the computational domain and placement of the excitation. . . . . . . . 71
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