Multiresolution Time Domain Scheme For Electromagnetic Engineering

, by Chen, Yinchao; Cao, Qunsheng; Mittra, Raj

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ISBN: 9780471272304 | 0471272302
Cover: Hardcover
Copyright: 1/28/2005

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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.

Preface

Acknowledgments

1 Introduction

(6)

1.1 Prologue

(1)

1.2 Objectives

(1)

1.3 Overview

(2)

References

(2)

2 Introduction to the Multiresolution Analysis

(28)

2.1 Introduction

(1)

2.2 Vectors and Signal Space

(6)

Vector Spaces

(1)

Inner Product in Vector Spaces

(1)

Orthogonality

(1)

Inner Product Space Rn

(1)

Subspaces

(1)

Linear Independence, Bases, and Dimensions

(1)

Orthonormal Bases, Projections, and Riesz Bases

(1)

Orthonormal Expansion in L²(R)

(2)

2.3 Multiresolution Analysis

(3)

Definition of the Multiresolution Analysis

(2)

Formal Definition of the Multiresolution Analysis

(1)

2.4 Scaling Functions and Wavelets

(1)

2.5 MRA in the Frequency Domain

(6)

2.6 Examples

(5)

Box Function and Haar MRA

(4)

Hat Function and Linear Spline MRA

(1)

2.7 Biorthogonal MRA and Wavelets

(2)

2.8 Multidimensional Wavelets

(1)

2.9 Field Expansions in the MRTD Analysis

(2)

References

(1)

3 MRA Families in MRTD Analysis

(43)

3.1 Introduction

(1)

3.2 Basic Spline MRA Family

(5)

3.3 Battle-Lemarie Spline MRA Family

(2)

3.4 Cubic Spline Battle-Lemarié MRA-An Example

(5)

3.5 Daubechies' Procedure of MRA Construction

(3)

3.6 Daubechies' Original Family

(8)

3.7 Coiflet Family

(7)

3.8 Biorthogonal MRA

(2)

3.9 Biorthogonal Cohen-Daubechies-Feauveau Family

(8)

References

(2)

4 Kernel of Multiresolution Time Domain Scheme

(30)

4.1 Introduction

(1)

4.2 Relationships Among the FDTD, MoM, and MRTD

(12)

FDTD Approach

(1)

MoM Method

(2)

MRTD Scheme

(9)

4.3 The MRTD Scheme

(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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Multiresolution Time Domain Scheme For Electromagnetic Engineering

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