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9780471272304

Multiresolution Time Domain Scheme For Electromagnetic Engineering

by ; ;
  • ISBN13:

    9780471272304

  • ISBN10:

    0471272302

  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2005-01-28
  • Publisher: Wiley-Interscience
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Summary

Multiresolution Time Domain Scheme for Electromagnetic Engineering examines the multiresolution time domain (MRTD) scheme and shows how it can be used to satisfy a variety of technical needs. This comprehensive resource presents a combination of theoretically advanced mathematical topics and their application in time domain Maxwell solution techniques. These topics include concepts of signal space, the multiresolution analysis (MRA), and scaling and wavelet functions; construction of MRA families; interconnection among the MRTD, finite difference time domain (FDTD), and MoM; MRTD boundary truncations; MRTD plane wave incidence, near-to-far-field transform, and scattering analysis; MRTD applications on microwave and millimeter wave integrated circuits; and generalized differential matrix operators (GDMOs). This text offers an invaluable, stand-alone reference for scientists, engineers, and students in a wide range of fields.

Author Biography

YINCHAO CHEN, PHD, is Associate Professor in the Department of Electrical Engineering at the University of South Carolina. Dr. Chen has published over 140 international articles in refereed journals (and conference proceedings), and is also the coauthor, coeditor, and contributing author of several books.

QUNSHENG CAO, PHD, earned his doctorate degree at the Hong Kong Polytechnic Institute in 2001. He is currently a postdoctoral research associate in the Army High Performance Computing Research Center at the University of Minnesota in Minneapolis.

RAJ MITTRA, PHD, is Professor in the Electrical Engineering Department of The Pennsylvania State University and the Director of the Electromagnetic Communication Laboratory. Dr. Mittra is a Life Fellow of the IEEE, a past president of APS, and has served as the editor of the IEEE Transactions of Antennas and Propagation.

Table of Contents

Preface xi
Acknowledgments xv
1 Introduction
1(6)
1.1 Prologue
1(1)
1.2 Objectives
2(1)
1.3 Overview
3(2)
References
5(2)
2 Introduction to the Multiresolution Analysis
7(28)
2.1 Introduction
7(1)
2.2 Vectors and Signal Space
8(6)
Vector Spaces
8(1)
Inner Product in Vector Spaces
9(1)
Orthogonality
9(1)
Inner Product Space Rn
9(1)
Subspaces
10(1)
Linear Independence, Bases, and Dimensions
10(1)
Orthonormal Bases, Projections, and Riesz Bases
11(1)
Orthonormal Expansion in L²(R)
12(2)
2.3 Multiresolution Analysis
14(3)
Definition of the Multiresolution Analysis
14(2)
Formal Definition of the Multiresolution Analysis
16(1)
2.4 Scaling Functions and Wavelets
17(1)
2.5 MRA in the Frequency Domain
18(6)
2.6 Examples
24(5)
Box Function and Haar MRA
24(4)
Hat Function and Linear Spline MRA
28(1)
2.7 Biorthogonal MRA and Wavelets
29(2)
2.8 Multidimensional Wavelets
31(1)
2.9 Field Expansions in the MRTD Analysis
32(2)
References
34(1)
3 MRA Families in MRTD Analysis
35(43)
3.1 Introduction
35(1)
3.2 Basic Spline MRA Family
36(5)
3.3 Battle-Lemarie Spline MRA Family
41(2)
3.4 Cubic Spline Battle-Lemarié MRA-An Example
43(5)
3.5 Daubechies' Procedure of MRA Construction
48(3)
3.6 Daubechies' Original Family
51(8)
3.7 Coiflet Family
59(7)
3.8 Biorthogonal MRA
66(2)
3.9 Biorthogonal Cohen-Daubechies-Feauveau Family
68(8)
References
76(2)
4 Kernel of Multiresolution Time Domain Scheme
78(30)
4.1 Introduction
78(1)
4.2 Relationships Among the FDTD, MoM, and MRTD
79(12)
FDTD Approach
79(1)
MoM Method
80(2)
MRTD Scheme
82(9)
4.3 The MRTD Scheme
91(11)
4.4 Stability Criteria
102(2)
4.5 Computation of Total Fields
104(1)
4.6 Orthogonal and Integral Relations
105(1)
Orthogonal Relations
105(1)
Integral Relations
105(1)
References
106(2)
5 PEC Boundary Truncations
108(16)
5.1 Introduction
108(1)
5.2 Method of Analysis
109(12)
MRTD Update Equations
109(2)
MRTD-MIT Constitutive Relationship
111(6)
AIG Technique
117(1)
MIT in Update Equations
118(3)
5.3 Numerical Results
121(2)
5.4 Conclusions
123(1)
References
123(1)
6 Open Boundary Truncation
124(21)
6.1 Introduction
124(1)
6.2 MRTD Update Equations in APML Regions
125(8)
Governing Equations in APML Regions
125(1)
MRTD Scheme in Face-APML Regions
126(3)
MRTD Scheme in Edge-APML Regions
129(1)
MRTD Scheme in Corner-APML Regions
130(2)
Excitation and APML Parameters
132(1)
6.3 Numerical Results
133(10)
Empty and Partially Dielectric-Loaded Rectangular Waveguides
133(1)
Open Microstrip Lines with Low and High Dielectric Substrates
134(9)
6.4 Conclusion
143(1)
References
143(2)
7 One-Dimensional MRTD Analysis
145(32)
7.1 Introduction
145(1)
7.2 MRTD Formulations
145(22)
Maxwell Governing Equations
145(1)
SW-MRTD Field Expansions
146(1)
SW-MRTD Update Equations for TEMx Model
147(20)
S-MRTD Update Equations for TEMx Model
167(1)
7.3 Application Results
167(8)
7.4 Conclusion
175(1)
References
175(2)
8 Two-Dimensional MRTD Analysis
177(31)
8.1 Introduction
177(1)
8.2 MRTD Analysis for Printed Transmission Lines
177(15)
Field Construction
177(2)
MRTD Algorithm for Printed Transmission Lines
179(4)
APML Algorithm for Open Structures
183(4)
Computation of the Propagation Characteristics
187(3)
Window Modulation and Truncation
190(2)
8.3 Application Results for Printed Transmission Lines
192(4)
8.4 MRTD Analysis for Parallel Waveguide Structures
196(6)
Governing Equations for TEz, and TMz, Waves
197(1)
MRTD Algorithm for TEz, Wave
198(3)
MRTD Algorithm for TMz, Wave
201(1)
8.5 Application Results for Parallel-Waveguide Structures
202(3)
8.6 Conclusions
205(1)
References
206(2)
9 Three-Dimensional MRTD Analysis
208(15)
9.1 Introduction
208(1)
9.2 Method of Analysis
208(8)
Maxwell Governing Equations
208(1)
MRTD Scheme in a Dielectric-Conductor Hybrid Region
209(7)
9.3 Application Results
216(5)
Double-Layer Dielectric-Filled Cavity
216(1)
Microstrip Lines
216(5)
9.4 Conclusions
221(1)
References
221(2)
10 MRTD Analysis for MMICs 223(15)
10.1 Introduction
223(1)
10.2 Microwave Networks
224(4)
Voltages and Currents for a TEM Mode Structure
224(1)
Impedance and Admittance Matrices
225(2)
Scattering Matrix
227(1)
10.3 Extraction of MMIC Characteristics
228(3)
Time Domain Voltage and Current
228(2)
Propagation Characteristics for a Transmission Line
230(1)
Scattering Parameters for a Multiport Millimeter-Wave Circuit
231(1)
10.4 Application Results
231(4)
A Rectangular Microstrip Patch Antenna
231(1)
A Microstrip Low-Pass Filter
232(2)
A Microstrip Band-Pass Filter
234(1)
10.5 Conclusions
235(1)
References
236(2)
11 MRTD Scattering Analysis: 2D Cases 238(33)
11.1 Introduction
238(1)
11.2 Scattering Fundamentals
239(2)
Incident, Scattered, and Total Fields
239(1)
Radar Cross Section (RCS)
239(1)
Monostatic and Bistatic Scattering
240(1)
Pure Scattered Electromagnetic Field Formulation
240(1)
11.3 Governing Equations of MRTD
241(3)
11.4 MRTD Scattering Algorithm for TMz, Wave
244(13)
MRTD Update Equations Inside the Target
244(6)
MRTD Update Equations Outside the Target
250(2)
Plane Wave Excitation
252(2)
MRTD Near-to-Far-Zone Transform for TMz, Wave
254(3)
11.5 MRTD Scattering Algorithm for TEz, Wave
257(4)
MRTD Update Equations Inside the Target
257(2)
MRTD Update Equations Outside the "Target
259(1)
MRTD Near-to-Far-Zone Transform for TEz, Wave
260(1)
11.6 Application Results
261(8)
11.7 Conclusions
269(1)
References
269(2)
12 MRTD Scattering Analysis: 3D Cases 271(26)
12.1 Introduction
271(1)
12.2 Governing Equations of MRTD
271(2)
12.3 MRTD Implementations
273(13)
MRTD Update Equations Inside the Target
273(8)
Lossless Target
274(3)
PEC Target
277(2)
Lossy Target
279(2)
MRTD Update Equations Outside the Target
281(1)
Incident Plane-Wave and Linear Interpolation
282(2)
MRTD Near-to-Far-Zone Transformation
284(2)
12.4 Application Results
286(9)
Co-, Cross-, and θ-Polarizations
286(1)
Validation of Near Fields for a PEC Cube
286(1)
Scattering Analysis for a PEC Plate
287(5)
Scattering Analysis for a Lossless Dielectric Flat Plate
292(1)
Scattering from a Lossy Dielectric Flat Plate
292(3)
12.5 Conclusions
295(1)
References
295(2)
APPENDIX A Generalized Differential Matrix Operators 297(10)
A.1 Generalized Differential Matrix Operators
297(2)
A.2 GDMO Representation of Maxwell and Wave Equations
299(3)
A.3 GDMOs for Differential and Integral Formulations
302(4)
Differential Formulations
302(1)
Integral Formulations
303(3)
References
306(1)
APPENDIX B MRTD Orthogonal and Integral Relations 307(21)
B.1 Orthogonal and Integral Relations
307(1)
B.2 Orthogonal Relations
307(2)
B.3 Integral Relations of the Pulse Function
309(1)
B.4 Integral Relations for the Scaling Functions
310(3)
B.5 Integral Relations for Mixed Functions
313(7)
Proof of (B.13)
313(2)
Proof of (B.14)
315(1)
Proof of (B.15)
316(2)
Proof of (B.17)
318(2)
B.6 Integral Relations for Wavelet Functions
320(3)
B.7 Integral Coefficients
323(4)
Proof of (B.26)
324(1)
Proof of (B.27)
324(1)
Proof of (B.28)
325(1)
Proof of (B.29)
326(1)
References
327(1)
APPENDIX C Update Equations in APML Regions 328(22)
C.1 Maxwell Equations in APML Regions
328(1)
C.2 Field Expansions
329(1)
C.3 Update Equations for Face-APML Regions
330(8)
Face-APMLx, Regions
330(4)
Face-APMLy Regions
334(2)
Face-APMLz, Regions
336(2)
C.4 Update Equations for Edge-APML Regions
338(7)
Edge-APMLxy Regions
339(2)
Edge-APMLxz, Regions
341(2)
Edge-APMLyz, Regions
343(2)
C.5 Update Equations for Corner-APML Regions
345(3)
References
348(2)
APPENDIX D Expressions and Properties of the Cubic Battle-Lemarié Functions 350(7)
D.1 Expression for the B-Spline Function in the Frequency Domain
350(2)
D.2 Orthogonality Condition in the Frequency Domain
352(1)
D.3 Expression of B-Spline Functions in the Frequency and Space Domains
353(2)
D.4 Cubic Spline Battle-Lemarié Wavelet Function in the Frequency Domain
355(1)
References
356(1)
Index 357

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