Brief Overview of EM Computational Modeling Techniques for Real-World Engineering Problems

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1 Brief Overview of EM Computational Modeling Techniques for Real-World Engineering Problems Bruce Archambeault, Ph.D. IEEE Fellow, IBM Distinguished Engineer Emeritus Archambeault EMI/EMC Enterprises

2 Why Use Modeling? Being safe costs money Reducing costs usually increase risk Need to Reduce cost Reduce time to market Manage risk Increase credibility Eliminate Voodoo and Magic Often no other way to get the job done! Bruce Archambeault, PhD 2

3 Bruce Archambeault, PhD 3

4 Bruce Archambeault, PhD 4

5 EMI/EMC Modeling State-of of-the-art Modeling is here NOW! Many papers at Symposia Can t t do everything Too much information in CAD files Need to break the overall problem into individual mini-problems GIGO applies! Bruce Archambeault, PhD 5

6 What can Modeling Do? Eliminate use of Out-of of-contet equations and graphs Update Rules-of of-thumb Relative analysis of particular design features What if? analysis Analysis of individual problems to be eventually combined to find overall result Bruce Archambeault, PhD 6

7 Tool Bo Approach There is NO ONE modeling technique that will do everything Vendor claims must be carefully eamined For Real-World applications EMC engineers need Tools at various modeling levels A variety of modeling techniques Bruce Archambeault, PhD 7

8 Range of Modeling Tools Quasi-Static Tools L,C,R Etraction Quick calculators Loop current emissions from PCB traces into near field locations Full Wave techniques Magic Bruce Archambeault, PhD 8

9 Quasi-Static Models Electrically small elements Typically 1/20 th of wavelength Lumped circuit approimation Commonly used for parameter etraction (RLC) in signal integrity tools Solve less comple equations for the problem geometry Assumes no propagation delay! Bruce Archambeault, PhD 9

10 Quasi-Static Advantages Simplified equations result in more efficient computer codes. Solutions are specific to the task at hand and do not generate etra unnecessary data. Often written to complement a circuit modeling tool such as SPICE. Bruce Archambeault, PhD 10

11 Quasi-Static Disadvantages It is important to ensure that the problem meets the criteria for the quasi-static static solution to be valid. All dimensions must be electrically small. No Propagation delay!!! This is becoming very difficult with the ever increasing frequencies of concern Eample: 3cm backplane high speed connector QS accurate to about < 5 GHz! Bruce Archambeault, PhD 11

12 Quasi Static Eamples Bruce Archambeault, PhD 12

13 Full Wave Modeling Techniques Finite-Difference Time-Domain (FDTD) Method of Moments (MoM) Partial Element Equivalent Circuit (PEEC) Transmission Line Method (TLM) Finite Element Method Others Bruce Archambeault, PhD 13

14 Popular Modeling Techniques Don t t need Ph.D. to use them Codes are available in many forms Free from Universities User beware Purchase from vendors User beware User should understand basic techniques and their limitations Bruce Archambeault, PhD 14

15 Popular Modeling Techniques Each technique has areas where it ecels and areas where limitations apply Different modeling tasks require different techniques Bruce Archambeault, PhD 15

16 Mathematical Foundation Electromagnetic Simulation Analytic formulas Integral equation methods (Integral calculus) MoM PEEC Differential equation methods (differential calculus) FEM FDTD TLM... Bruce Archambeault, PhD 16

17 Read CAD File Directly? Too much information! Models too large for practical solution Need human to decide what is important Models take days to run Models may require BlueGene computer! Human can usually decide what is most important and simplify problem to a reasonable size BEWARE of models with too much detail! Bruce Archambeault, PhD 17

18 Number of Unknowns Huge! Bruce Archambeault, PhD 18

19 Finite-Difference Time-Domain Technique (FDTD)

20 Introduction to FDTD All of space must be divided into electrically small grids Fields are assumed to be constant over cell Each grid location assigned as Air, Metal, Dielectric, etc. Usually cube or rectangular grids Time Domain Technique Wide band of frequencies analyzed at once FFT to get frequency domain information Bruce Archambeault, PhD 20

21 Mawell s s Equations Differential Form A difference in Magnetic Field across a small piece of space A difference in Electric Field across a small piece of space H E = J = + B t D t A change in Electric Flu Density with respect to time A change in Magnetic Flu Density with respect to time Bruce Archambeault, PhD 21

22 Changing to Difference Equations E = B t E n i E n i 1 µ = ( ) H n i + 1 H n i t Bruce Archambeault, PhD 22

23 Bruce Archambeault, PhD Bruce Archambeault, PhD One One-Dimensional FDTD Dimensional FDTD Equations Equations [ ] [ ] n i n i n i n i n i n i n i n i H H t E t E E E t H H ) 1 ( = = ε ε σ µ

24 FDTD Fields at Each Time Step Electric field found from: Old electric field at that point Difference in magnetic field around that point Magnetic field found from: Old magnetic field at that point Difference in electric field around that point Bruce Archambeault, PhD 24

25 One-Dimensional FDTD Grid E H E H E H E H E H E H E Bruce Archambeault, PhD 25

26 FDTD Time Marching Initial Time E H E H E H E H E H E H E Initial Time + 1 E H E H E H E H E H E H E Initial Time + 2 E H E H E H E H E H E H E Bruce Archambeault, PhD 26

27 Two-Dimensional FDTD Grid E-Field H-Field Bruce Archambeault, PhD 27

28 Two-Dimensional FDTD Can use TE or TM Case Only three fields available 2 Electric Fields and 1 Magnetic Field 1 Electric Field and 2 Magnetic Fields Assume all structures are infinite in 3rd dimension Bruce Archambeault, PhD 28

29 Three Dimensional FDTD Grid Ez Hy H Ey E Hz Bruce Archambeault, PhD 29

30 FDTD Cells Hy Ez Ey Cell 1,1,2 Cell 1,2,2 Hy Ez H H Ey E Hz E Hz Hy Cell 1,1,1 Ez H Ey Hy Ez Ey Cell 1,2,1 H E Hz E Hz Bruce Archambeault, PhD 30

31 FDTD 3-D3 Cell 1,1,2 Cell 1,2,2 Hy Hz E Hz Cell 1,1,1 Hy Cell 1,2,1 Bruce Archambeault, PhD 31

32 FDTD 3-D3 Cell 1,1,2 Cell 1,2,2 Ey E Hz E Cell 1,1,1 Cell 1,2,1 Bruce Archambeault, PhD 32

33 FDTD Materials Each Cell is Assigned as PEC, Metal, Dielectric, etc. Must Know --- σ µ ε Bruce Archambeault, PhD 33

34 FDTD Model Outputs Monitor Points Only fields directly Perfect receive antennas Both E and H fields X,Y,Z Components individually Animations Slice Through space Provide confidence and understanding Bruce Archambeault, PhD 34

35 FDTD Mesh Truncation FDTD Computational Domain Boundary Acts as if free-space continues to infinity E-Field H-Field Bruce Archambeault, PhD 35

36 FDTD Mesh Truncation Types Must match the impedance of the fields at the boundary point. Most require far field conditions, so impedance is well known Based upon the Wave Equation Liao Higdon Bruce Archambeault, PhD 36

37 Perfectly Matched Layer Loss is added to both E and H field Equations Acts similar to absorbing material in anechoic rooms Far fields required for lowest error (Reflection) Bruce Archambeault, PhD 37

38 Other Considerations Time Step Size Time step must be small enough so that fields do NOT propagate faster than the Speed of Light.. Courant s s stability condition t v y z 2 v = c µ ε r r Bruce Archambeault, PhD 38

39 Summary -- FDTD FDTD is a volume based technique Entire domain must be gridded Wide range of frequencies with one simulation Finds E and H Fields everywhere in domain Simple to learn and use Brute force approach Bruce Archambeault, PhD 39

40 FDTD Strengths and Weaknesses Strengths Very well suited to shielding problems, or problems with dielectrics, lossy materials, etc. Allows infinite planes to remove resonances Weaknesses Not well suited to problems with long wires Sensitive to resonances Bruce Archambeault, PhD 40

41 The Method of Moments

42 Method of Moments (MoM) Boundary Element Method (BEM) Break all surfaces into electrically small patches Break all wires into electrically small segments Assume RF current does not vary across a patch or segment Frequency domain technique Model must be run for each harmonic frequency of interest Bruce Archambeault, PhD 42

43 Method of Moments (MoM) RF Current on every patch and segment found Due to source and currents on all other patches and segments Electric/Magnetic fields found at any point by summing the contribution of all currents May include assumptions about far field locations Bruce Archambeault, PhD 43

44 MoM: Modeling Eamples Current on Eternal Wires IDENTIFY SEGMENTS, PATCHES & SOURCE LOCATION Bruce Archambeault, PhD 44

45 MoM: Modeling Eamples Current on Eternal Wires RF CURRENTS ARE FOUND ON EACH SEGMENT/PATCH DUE TO SOURCE & CURRENT ON EVERY OTHER SEGMENT/PATCH Bruce Archambeault, PhD 45

46 MoM: Modeling Eamples Current on Eternal Wires RF CURRENTS ARE FOUND ON EACH SEGMENT/PATCH DUE TO SOURCE & CURRENT ON EVERY OTHER SEGMENT/PATCH Bruce Archambeault, PhD 46

47 MoM: Basis Functions Sub-domain basis functions Pulse functions (piecewise constant) Linear Piecewise sinusoidal Bruce Archambeault, PhD 47

48 Impulse and Pulse Basis Functions level impulse pulse Position Note: Discontinuous current Bruce Archambeault, PhD 48

49 Triangle Basis Functions triangle1 triangle2 triangle3 triangle4 triangle sum 0.4 level position Note: Continuous current but discontinuous di/dt Bruce Archambeault, PhD 49

50 Sine Squared Basis Function sine1 sine2 sine3 sine4 sine sum 0.4 level position Note: Continuous current and continuous di/dt Bruce Archambeault, PhD 50

51 Basis Functions Simplest basis function requires one calculation per grid Requires more grids per wavelength to correctly estimate current/field/etc More comple basis function requires many calculations per grid Requires less grids per wavelength More comple calculations (longer calculation time) Bruce Archambeault, PhD 51

52 MoM: Summary MoM is a Surface based technique Frequency domain technique simulation must be repeated for each harmonic frequency Currents are found everywhere Fields found from currents Good for wire and surface structures Simple to learn and use Bruce Archambeault, PhD 52

53 MoM Strengths and Weaknesses Strengths Very well suited to problems with long wires Well suited to problems with large distances Weaknesses Not well suited to shielding problems Not well suited to problems with dielectrics or lossy materials Bruce Archambeault, PhD 53

54 The Finite Elements Method Bruce Archambeault, PhD 54

55 Finite Element Method (FEM) All space must be divided into electrically small elements Each grid location assigned as air, metal, dielectric, etc. Usually triangular or tetrahedral elements Fields found in each element using variational techniques Frequency domain technique Model must be run for each harmonic frequency of interest Bruce Archambeault, PhD 55

56 Why FEM? Ideal for problems with irregular geometry Can handle different material easily Results in sparse matrices which can be solved very efficiently with efficient storage Bruce Archambeault, PhD 56

57 FEM in English Entire volume is broken into small elements Energy in each element is due to the electric (or magnetic) field in that element Take 1 st derivative of sum of energy in all elements to find minimum energy overall Electric (or magnetic) fields are found from this final energy in each element Bruce Archambeault, PhD 57

58 FEM: Elements Construction Construction of Finite Elements triangular elements Bruce Archambeault, PhD 58

59 Bruce Archambeault, PhD Bruce Archambeault, PhD FEM: System Matri FEM: System Matri Sparse and banded

60 FEM: Any Advantage? Significant advantage over Method of Moments for equal number of unknowns (non-homogeneous,, non-metallic objects) Mesh generation is becoming easier and more powerful Mesh geometry can sometimes be shared with other non-em solvers (thermal/mechanical CAD tools) Bruce Archambeault, PhD 60

61 FEM: Summary FEM is a Volume Based Technique (Entire domain must be meshed) Frequency-domain FEM (classical FEM) A single simulation for one frequency Time-domain FEM (not widely available) One simulation for wide band frequency response. Calculates E or H everywhere in domain Bruce Archambeault, PhD 61

62 FEM Strengths and Weaknesses Strengths Well suited to bound problems Waveguides, Resonant Cavity, etc. Well suited to problems with large size differences within model Weaknesses Not well suited for problems with long wires or problems with open boundaries Absorbing Boundary Conditions may cause spurious response Bruce Archambeault, PhD 62

63 Model Validation GIGO Works!!!!

64 Validation Summary Three different levels of validation Most important to practicing engineer is specific model validation Intermediate results and different simulation technique are the best source of validation Use other approaches as desired BEWARE of measurement comparison NEVER TRUST a single model result! Bruce Archambeault, PhD 64

65 Validation Summary (2) It is not sufficient to simply believe the results are correct Previous model validation on different problems does not guarantee results from new models GIGO applies!!! Need to understand the physics of the problem Need to understand the limitations of the modeling technique and software tools Bruce Archambeault, PhD 65

66 Where to go for More Information Web sites Books EMI/EMC Computational Modeling Handbook Conferences Seminars Validation IEEE Std 1597 Bruce Archambeault, PhD 66

67 Computational Electromagnetics Web Sites Bruce Archambeault, PhD 67

68 Modeling Information Unofficial NEC Page Mesh Generation users.informatik.rwth-aachen aachen.de/~roberts/meshgeneration.html FDTD Information Html FEM Books Modeling techniques Books on Modeling Bruce Archambeault, PhD 68

69 Where To Go For More IBM offers EMC Tools, training, and consulting University of Missouri-Rolla Most complete graduate program on EMC Bruce Archambeault, PhD 69

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71 Bruce Archambeault, PhD 71

The analysis of microstrip antennas using the FDTD method

Computational Methods and Experimental Measurements XII 611 The analysis of microstrip antennas using the FDTD method M. Wnuk, G. Różański & M. Bugaj Faculty of Electronics, Military University of Technology,