Simulation of Electromagnetic Fields: The Finite-Difference Time-Domain (FDTD) Method and Its Applications

Transcription

1 Simulation of Electromagnetic Fields: The Finite-Difference Time-Domain (FDTD) Method and Its Applications Veysel Demir, Ph.D. Department of Electrical Engineering, Northern Illinois University, DeKalb, IL /34

2 Veysel Demir Bachelor of Science, Electrical and Electronics Engineering, Middle East Technical University, Ankara, Turkey, System Analyst and Programmer, Pamukbank, Software Development Department, Istanbul, Turkey, July 1997 August Master of Science, Electrical Engineering, Syracuse University, Syracuse, NY, Doctor of Philosophy, Electrical Engineering, Syracuse University, Syracuse, NY, Research Assistant, Sonnet Software, Inc. Liverpool, NY, August 2000 July Visiting research scholar, University of Mississippi, Electrical Engineering Department, University, MS, July 2004 Present. Assistant Professor, Department of Electrical Engineering, Northern Illinois University, DeKalb,IL, August 2007 present 2/34

3 Computational Electromagnetics Maxwell s equations can be given in differential or integral form Finite-difference time-domain (FDTD) Transmission line matrix (TLM) Finite element method (FEM) Finite-difference frequency-domain (FDFD) Differential equation methods Method of Moments (MoM) Fast multipole method (FMM) Integral equation methods 3/34

4 Computational Electromagnetics Maxwell s equations can be given in time domain or frequency domain Time-domain methods Finite-difference time-domain (FDTD) Transmission line matrix (TLM) Finite element method (FEM) Method of Moments (MoM) Finite-difference frequency-domain (FDFD) Fast multipole method (FMM) Frequency domain methods 4/34

5 Commercial software packages Commercial software packages Finite element method (FEM) Method of Moments (MoM) ADS Momentum HFSS Transmission line matrix (TLM) Finite-difference time-domain (FDTD) CST Microstripes 5/34

6 The Finite-Difference Time-Domain Method 6/34

7 FDTD Books 7/34

8 Yearly FDTD Publications The most popular method in computational electromagnetics Source: Allen Taflove, A Perspective on the 40-Year History of FDTD Computational Electrodynamics, Applied Computational Electromagnetics Society (ACES) Conference, Miami, Florida, March 15, Can be found at 8/34

9 Maxwell s Equations The basic set of equations describing the electromagnetic world Shows that light is an electromagnetic wave. Gauss s law Gauss s law for magnetism Faraday s law Ampere s law Constitutive relations D= ρv B= 0 B E= t D H= J+ t D = ε E,and B = µ H 9/34

10 FDTD Overview Finite Differences Represent the derivatives in Maxwell s curl equations by finite differences We use the second-order accurate central difference formula df ( x) f ( x + x) f ( x x) = f ( x) dx 2 x 10/34

11 FDTD Overview Cells A three-dimensional problem space is composed of cells 11/34

12 FDTD Overview The Yee Cell The FDTD (Finite Difference Time Domain) algorithm was first established by Yee as a three dimensional solution of Maxwell's curl equations. K. Yee, IEEE Transactions on Antennas and Propagation, May /34

13 FDTD Overview Material grid A three-dimensional problem space is composed of cells 13/34

14 FDTD Overview Updating Equations Three scalar equations can be obtained from one vector curl equation. E ε = H t H x Ey µx = t z H y Ez µy = t x H z Ex µz = t y Ez y Ex z Ey Ex H z εx = t y Ey H x εy = t z Ez H y εz = t x µ Hy z Hz x Hx y H = E t x 14/34

15 FDTD Overview Updating Equations Represent derivatives by finite-differences Ex H z H y εx = t y z Exn + 1 (i, j, k ) Exn (i, j, k ) ε x (i, j, k ) = t n n H zn (i, j, k ) H zn (i, j 1, k ) H y (i, j, k ) H y (i, j, k 1) y z 15/34

16 FDTD Overview Updating Equations Represent derivatives by finite-differences H x E y Ez µx = t z y H xn (i, j, k ) H xn 0.5 (i, j, k ) µ x (i, j, k ) = t E yn (i, j, k + 1) E yn (i, j, k ) Ezn (i, j + 1, k ) Ezn (i, j, k ) z y 16/34

17 FDTD Overview Updating Equations Express the future components in terms of the past components H zn (i, j, k ) H zn (i, j 1, k ) y t Exn + 1 (i, j, k ) = Exn (i, j, k ) ε x (i, j, k ) H yn (i, j, k ) H yn (i, j, k 1) z E yn (i, j, k + 1) E yn (i, j, k ) t z H xn (i, j, k ) = H xn 0.5 (i, j, k ) + n n µ x (i, j, k ) Ez (i, j + 1, k ) Ez (i, j, k ) y 17/34

18 FDTD Overview Leap-frog Algorithm Exercise 1D 18/34

19 Absorbing Boundary Conditions The three-dimensional problem space is truncated by absorbing boundaries Most popular absorbing boundary is Perfectly Matched layers (PML) Exercise 2D PML 19/34

20 Active and Passive Lumped Elements Active and passive lumped elements can be modeled in FDTD E H= ε + σ E+ J t Voltage source Current source 20/34

21 Active and Passive Lumped Elements Resistor Capacitor Inductor Diode 21/34

22 Active and Passive Lumped Elements A diode circuit 22/34

23 Transformation from Time-Domain to Frequency-Domain Results can be obtained for frequency domain using Fourier Transform A low-pass filter S11 S22 Exercise 2D object 23/34

24 Near-Field to Far-field Transformations An inverted-f antenna 24 24/34

25 Modeling fine geometries It is possible to model fine structures using appropriate formulations A wire loop antenna 25/34

26 Incident plane wave 26/34

27 Scattering Problems ( H inc + H scat ) = ε ( Einc + Escat ) t H inc = ε 0 Einc t A dielectric sphere Exercise 3D PML 27/34

28 Scattering from a Dielectric Sphere 28/34

29 Earth / Ionosphere Models in Geophysics Snapshots of FDTD-Computed Global Propagation of ELF Electromagnetic Pulse Generated by Vertical Lightning Strike off South America Coast Source: Allen Taflove, A Perspective on the 40-Year History of FDTD Computational Electrodynamics, Applied Computational Electromagnetics Society (ACES) Conference, Miami, Florida, March 15, Can be found at 29/34

30 Wireless Personal Communications Devices Source: Allen Taflove, A Perspective on the 40-Year History of FDTD Computational Electrodynamics, Applied Computational Electromagnetics Society (ACES) Conference, Miami, Florida, March 15, Can be found at 30/34

31 Phantom Head Validation at 1.8 GHz Source: Allen Taflove, A Perspective on the 40-Year History of FDTD Computational Electrodynamics, Applied Computational Electromagnetics Society (ACES) Conference, Miami, Florida, March 15, Can be found at 31/34

32 Ultrawideband Microwave Detection of Early-Stage Breast Cancer Source: Allen Taflove, A Perspective on the 40-Year History of FDTD Computational Electrodynamics, Applied Computational Electromagnetics Society (ACES) Conference, Miami, Florida, March 15, Can be found at 32/34

33 Focusing Plasmonic Lens Source: Allen Taflove, A Perspective on the 40-Year History of FDTD Computational Electrodynamics, Applied Computational Electromagnetics Society (ACES) Conference, Miami, Florida, March 15, Can be found at 33/34

34 Thank You Exercise 2D PEC 34/34