The Finite-Difference Time-Domain Method for Electromagnetics with MATLAB Simulations

Transcription

1 The Finite-Difference Time-Domain Method for Electromagnetics with MATLAB Simulations Atef Z. Elsherbeni and Veysel Demir SciTech Publishing, Inc Raleigh, NC scitechpublishing.com

2 Contents Preface Author Acknowledgements Acknowledgement of Reviewers xxi xxv xxvii Chapter 1 Introduction to FDTD The Finite-Difference Time-Domain Method Basic Equations Approximation of Derivatives by Finite Differences FDTD Updating Equations for Three-Dimensional Problems FDTD Updating Equations for Two-Dimensional Problems FDTD Updating Equations for One-Dimensional Problems Exercises 32 Chapter 2 Numerical Stability and Dispersion Numerical Stability J Stability in Time Domain Algorithm CFL Condition for the FDTD Method Numerical Dispersion Exercises 41 Chapter 3 Building Objects in the Yee Grid Definition of Objects Defining the Problem Space Parameters Defining the Objects in the Problem Space Material Approximations Subcell Averaging Schemes for Tangential and Normal Components Defining Objects Snapped to the Yee Grid Creation of the Material Grid Improved Eight-Subcell Averaging Exercises 67 Chapter 4 Active and Passive Lumped Elements FDTD Updating Equations for Lumped Elements Voltage Source Hard Voltage Source Current Source Resistor Capacitor Inductor Lumped Elements Distributed over a Surface or within a Volume Diode Summary 85 VII

3 VIII Contents 4.2 Definition, Initialization, and Simulation of Lumped Elements Definition of Lumped Elements Initialization of FDTD Parameters and Arrays Initialization of Lumped Element Components Initialization of Updating Coefficients Sampling Electric and Magnetic Fields, Voltages and Currents Definition and Initialization of Output Parameters Running an FDTD Simulation: The Time-Marching Loop Displaying FDTD Simulation Results Simulation Examples A Resistor Excited by a Sinusoidal Voltage Source A Diode Excited by a Sinusoidal Voltage Source A Capacitor Excited by a Unit-Step Voltage Source Exercises 139 Chapter 5 Source Waveforms and Transformation from Time Domain to Frequency Domain Common Source Waveforms for FDTD Simulations Sinusoidal Waveform Gaussian Waveform Normalized Derivative of a Gaussian Waveform Cosine-Modulated Gaussian Waveform Definition and Initialization of Source Waveforms for FDTD Simulations Transformation from Time Domain to Frequency Domain Simulation Examples Recovering a Time Waveform from Its Fourier Transform An RLC Circuit Excited by a Cosine-Modulated Gaussian Waveform Exercises 166 Chapter 6 Scattering Parameters S-Parameters and Return Loss Definitions S-Parameter Calculations Simulation Examples Quarter-Wave Transformer Exercises 184 Chapter 7 Perfectly Matched Layer Absorbing Boundary Theory of PML Theory of PML at the Vacuum-PML Interface Theory of PML at the PML-PML Interface PML Equations for Three-Dimensional Problem Space PML Loss Functions 195

4 Contents IX 7.4 FDTD Updating Equations for PML and MATLAB Implementation PML Updating Equations Two-Dimensional TE Z Case PML Updating Equations Two-Dimensional TM Z Case MATLAB Implementation of the Two-Dimensional FDTD Method with PML Simulation Examples Validation of PML Performance Electric Field Distribution Electric Field Distribution Using DFT Exercises 229 Chapter 8 The Convolutional Perfectly Matched Layer Formulation of CPML PML in Stretched Coordinates Complex Stretching Variables in CFS-PML The Matching Conditions at the PML-PML Interface Equations in the Time Domain Discrete Convolution The Recursive Convolution Method The CPML Algorithm 236 * Updating Equations for CPML Addition of Auxiliary CPML Terms at Respective Regions CPML Parameter Distribution MATLAB Implementation of CPML in the Three-Dimensional FDTD Method Definition of CPML Initialization of CPML Application of CPML in the FDTD Time-Marching Loop Simulation Examples Microstrip Low-Pass Filter Microstrip Branch Line Coupler Characteristic Impedance of a Microstrip Line Exercises 267 Chapter 9 Near-Field to Far-Field Transformation Implementation of the Surface Equivalence Theorem Surface Equivalence Theorem Equivalent Surface Currents in FDTD Simulation Antenna on Infinite Ground Plane Frequency Domain Near-Field to Far-Field Transformation Time-Domain to Frequency-Domain Transformation Vector Potential Approach 277

5 X Contents Polarization of Radiation Field Radiation Efficiency MATLAB Implementation of Near-Field to Far-Field Transformation Definition of NF-FF Parameters Initialization of NF-FF Parameters NF-FF DFT during Time-Marching Loop Postprocessing for Far-Field Calculation Simulation Examples Inverted-F Antenna Strip-Fed Rectangular Dielectric Resonator Antenna Exercises 310 Chapter 10 Thin-Wire Modeling Thin-Wire Formulation MATLAB Implementation of the Thin-Wire Formulation Simulation Examples Thin-Wire Dipole Antenna Exercises 327 Chapter 11 Scattered Field Formulation Scattered Field Basic Equations The Scattered Field Updating Equations Expressions for the Incident Plane Waves MATLAB Implementation of the Scattered Field Formulation Definition of the Incident Plane Wave Initialization of the Incident Fields Initialization of the Updating Coefficients Calculation of the Scattered Fields Postprocessing and Simulation Results Simulation Examples Scattering from a Dielectric Sphere Scattering from a Dielectric Cube Reflection and Transmission Coefficients of a Dielectric Slab Exercises 366 Chapter 12 Graphics Processing Unit Acceleration of Finite-Difference Time-Domain Graphics Processors and General Math Introduction to Brook Sample Two-Dimensional FDTD Implementation Using Brook Extension to Three-Dimensional Three-Dimensional Parameter Exploration 379 Appendix A One-Dimensional FDTD Code 399

6 Contents Appendix В Convolutional Perfectly Matched Layer Regions and Associated Field Updates for a Three-Dimensional Domain 403 B.l Updating E x at Convolutional Perfectly Matched Layer (CPML) Regions 403 B.2 Updating E Y at CPML Regions 405 B.3 Updating E z at CPML Regions 406 B.4 Updating H x at CPML Regions 408 B.5 Updating H y at CPML Regions 409 B.6 Updating H z at CPML Regions 411 XI AppendixC MATLAB Code for Plotting 413 Bibliography 417 About the Authors 421 Index 423