Future Directions in Computational Electromagnetics for Digital Applications

Transcription

1 Prof. Dr.-Ing. Future Directions in Computational Electromagnetics for Digital Applications Technische Universität Darmstadt Fachbereich Elektrotechnik und Informationstechnik Schloßgartenstr. 8, D64289 Darmstadt, Germany - URL: Gesellschaft für Computer-Simulationstechnik m.b.h Bad Nauheimerstr. 19, D4289 Darmstadt, Germany URL:

2 Contents 2 Introduction State of the art - Three steps in solving an EM Problem - Finite Integration Technique as universal method - Wide choice of solution methods Future trends - Geometrically complex problems - EMC, Signal and Power integrity - Network Extraction, Passivity - Coupled problems - Integrated flows Conclusions

3 Motivation: Why 3D EM simulation? 3 Growing frequencies / clock rates High density of components Increasing parasitics relevance Sophisticated packaging technologies 3D packaging No simple models available Increase in crosstalk problems EMI / EMC concerns Signal / power integrity issues 2 ½D solvers cannot cope with all 3D effects

4 Contents 4 Introduction State of the art - Three steps in solving an EM Problem - Finite Integration Technique as universal method - Wide choice of solution methods Future trends - Geometrically complex problems - EMC, Signal and Power integrity - Network Extraction, Passivity - Coupled problems - Integrated flows Conclusions

5 EM Solution = 3 Steps 5 1 Spatial Discretization of geometry Staircase grid Tetrahedral grid Surface mesh Boundary fitted meshes. 2 Local approximation of Maxwell s Equations Finite Difference Finite Integration Technique Finite Element Finite Volume. 3 Solving the algebraic system Direct solver Iterative solver Eigenvalue solver Time stepping solver.

6 EM Solution = 3 Steps 6 1 Spatial Discretization of geometry Staircase grid Tetrahedral grid Surface mesh Boundary fitted meshes. 2 Local approximation of Maxwell s Equations Finite Difference Finite Integration Technique Finite Element Finite Volume. 3 Solving the algebraic system Direct solver Iterative solver Eigenvalue solver Time stepping solver.

7 EM Solution = 3 Steps 7 1 Spatial Discretization of geometry Staircase grid Tetrahedral grid Surface mesh Boundary fitted meshes. 2 Local approximation of Maxwell s Equations Finite Difference Finite Integration Technique Finite Element Finite Volume. 3 Solving the algebraic system Direct solver Iterative solver Eigenvalue solver Time stepping solver.

8 EM Solution = 3 Steps 8 1 Spatial Discretization of geometry Staircase grid Tetrahedral grid Surface mesh Boundary fitted meshes. 2 Local approximation of Maxwell s Equations Finite Difference Finite Integration Technique Finite Element Finite Volume. 3 Solving the algebraic system Direct solver Iterative solver Eigenvalue solver Time stepping solver.

9 9 With D as linear dimension Method of Moments Surface Meshing Each patch talks to each patch

10 10

11 11 CST GmbH 2006 High Voltage - Bushing CST STUDIO SUITE 2006B

12 12 CST GmbH 2006 Hexahedral - Subgrids CST STUDIO SUITE 2006B

13 13 CST STUDIO SUITE 2006B Wide choice of mesh type Hexahedral Tetrahedral Surface

14 EM Solution = 3 Steps 14 1 Spatial Discretization of geometry Staircase grid Tetrahedral grid Surface mesh Boundary fitted meshes. 2 Local approximation of Maxwell s Equations Finite Difference Finite Integration Technique Finite Element Finite Volume. 3 Solving the algebraic system Direct solver Iterative solver Eigenvalue solver Time stepping solver.

15 Contents 15 Introduction State of the art - Three steps in solving an EM Problem - Finite Integration Technique as universal method - Wide choice of solution methods Future trends - Geometrically complex problems - EMC, Signal and Power integrity - Network Extraction, Passivity - Coupled problems - Integrated flows Conclusions

16 Measurable=Integral Quantities F = QE E = F/ Q Fds i = E ids = Q( Eids) = QU ( Q ) F = Qv B Δp= Fdt Q ( = v B) dt = Qn Bvdt = Qn Bds = Q Ψ ( ) n ( ) n Q ds Q = vdt ds 16 Tonti 75, Weiland 77

17 17 Grid G FIT - Voltage and Flux v 4 ϕ v 3 v v 2 1

18 18 FIT - Voltage and Flux d Cv = - ϕ dt d Ce = - b dt

19 Magnetic voltage 19 Grid and : FIT Degrees of Freedom b = Bi da A e = Ei ds L Surface charge

20 Maxwell s Grid Equations Almost Complete Discrete Form of Maxwell s Equations continuous Developed since 1975 discrete? EXACT!! 20

21 21 A d e E i ds + Material Equations Material relations Equivalent of branch constitutive equations Similarly:

22 22 Maxwell s Grid Equations Developed since 1975 EXACT!! Choice of FD/FE/FI/FV.

23 Allocation of integral components van Rienen 1983 FIT on Triangular Grids e 23 w (1) 1 ( r) L 1 d Discrete Material Relation based on Whitney elements R. Schuhmann nd order Convergence

24 Circuits vs. FIT Circuit mesh analysis t = 0 Field analysis 24 Circuit equations Field equations Cv = 0 Ce = 0 T C im = i C h T = j v= Ri+ v e = Mρ j + es T CRC im S = Cv S C CM C : incidence matrix of edges to the independent meshes of the network ρ T h = Ce S

25 Contents 25 Introduction State of the art - Three steps in solving an EM Problem - Finite Integration Technique as universal method - Wide choice of solution methods Future trends - Geometrically complex problems - EMC, Signal and Power integrity - Network Extraction, Passivity - Coupled problems - Integrated flows Conclusions

26 26 Input port Simple Via Structure Output port

27 27 HEX Transient Solution HEX Frequency Domain TET Frequency Domain Model Order Reduction

28 HEX Transient Solution CM Ce + M e M e = - j ν κ ε 2 d d d + 2 dt dt dt s HEX Frequency Domain TET Frequency Domain Model Order Reduction FFT(Output) / FFT(Input) 28

29 HEX Transient Solution HEX Frequency Domain 2 (CMνC + iωm κ -ω M ε)e =-iω j s TET Frequency Domain Model Order Reduction Ae=r 29

30 HEX Transient Solution HEX Frequency Domain TET Frequency Domain Model Order Reduction 2 (CMνC + iωm κ -ω M ε)e =-iω j s Ae=r 30

31 HEX Transient Solution HEX Frequency Domain TET Frequency Domain Model Order Reduction 2 (CMνC + iωm κ -ω M ε)e =-iω j s ANXNe=r A MOR e=r nxn 31

32 EM Solution = 3 Steps 32 1 Spatial Discretization of geometry Staircase grid Tetrahedral grid Surface mesh Boundary fitted meshes. 2 Local approximation of Maxwell s Equations Finite Difference Finite Integration Technique Finite Element Finite Volume. Which combination is the best? 3 Solving the algebraic system Direct solver Iterative solver Eigenvalue solver Time stepping solver.

33 33 Selection of the best Algorithm Required accuracy Reliability Robustness Absolute Calc. Time. $ CPU Memory Manpower.

34 34 Type of solver Type of mesh Example of User Choice

35 Contents 35 Introduction State of the art - Three steps in solving an EM Problem - Finite Integration Technique as universal method - Wide choice of solution methods Future trends - Geometrically complex problems - EMC, Signal and Power integrity - Network Extraction, Passivity - Coupled problems - Integrated flows Conclusions

36 36 Stuctures get more complex

37 Can handle differential signals up to 10 GBit/s ERNI ERmet zeroxt High Speed SMT Connector simulated measured 37 ERNI: the connector could be manufactured without a major re-design in one pass...

38 38 IBM Example 32 mm Very Large Problems 3.5 mm 0.9 mm

39 39 E-Small Very Large Problems 0.8 mm

40 Three Solutions Use commerical software as is Limited by memory size of my computer (5GB) Size of domain only 25% of entire structure - Time domain hexahedral mesh (30 million cells) - Frequency domain tetrahedral mesh (5.3 million tet s) Could be easily extended by a bigger computer New parallel software - Time domain hexahedral mesh (650 million cells) Not yet with all features 40

41 Three Solutions Use commerical software as is Limited by memory size of my computer (5GB) Size of domain only 25% of entire structure - Time domain hexahedral mesh (30 million cells) - Frequency domain tetrahedral mesh (5.3 million tet s) Could be easily extended by a bigger computer New parallel software - Time domain hexahedral mesh (650 million cells) Not yet with all features 41

42 42

43 43 Model of a section used in commercial software Input Output

44 44 Input Output Cross talk

45 45 FFT(Output) / FFT(Input) S-Parameter for 0 to 20 GHZ in One Go!

46 46 All S-parameter in one Plot FFT(Output) / FFT(Input) S-Parameter for 0 to 20 GHZ in One Go! 1600 curves!

47 Three Solutions Use commerical software as is Limited by memory size of my computer (5GB) Size of domain only 25% of entire structure - Time domain hexahedral mesh (30 million cells) - Frequency domain tetrahedral mesh (5.3 million tet s) Could be easily extended by a bigger computer New parallel software - Time domain hexahedral mesh (650 million cells) Not yet with all features 47

48 48

49 49

50 50 S-Parameter Frequency Domain 5.3 million tet s, broad band frequency domain

51 Three Solutions Use commerical software as is Limited by memory size of my computer (5GB) Size of domain only 25% of entire structure - Time domain hexahedral mesh (30 million cells) - Frequency domian tetrahedral mesh (5.3 million tets) Could be easily extended by a bigger computer New parallel software - Time domain hexahedral mesh (650 million cells) Not yet with all features 51

52 New dedicated parallelized code FIT method Hexahedral discretization time domain Parallelized Domain partitioning algorithm The complete model was simulated (not only a small part of it!) The complete model was simulated without any geometrical simplification 3,900,000,000 DoFs 24-CPU Cluster - Meshing: 3 hours 52

53 25 Parallelization Speedup for a simple test model (no ports) Speedup e6 Cells 10e6 Cells 50e6 Cells 100e6 Cells 200e6 Cells Ideal Number of Processors

54 Input 1,2 1 Results inp_01_inp_01 inp_01_out_01 54 Output Good agreement with the measured results provided by IBM: Voltage / [V] 0,8 0,6 0,4 0,2 0-0, Time / [ps] Dedicated talk/paper on Wednesday EPEP - Session XIII

55 Large geometrically complex structures can be automatically imported automatically healed automatically stripped simulated in time domain and frequency domain without any geometrical simplification = solved problem 55

56 Hardware acceleration Mcells / 1 sec for a realistic application (ideal up to 400 Mcells/sec) ~ Factor 10 with respect to 32 bit processor ~ Factor 5 with respect to 64 bit processor ~ Factor 2 with respect to Woodcrest

57 57 The Real Challenge of Very Large Structures

58 The Real Challenge of Very Large Structures Allegro: smallest / largest edge 1:1,500,000, CST MICROWAVE STUDIO : Fully automatic clean-up and healing No simplification of the model, Just healing and stripping unnecessary edges

59 Contents 59 Introduction State of the art - Three steps in solving an EM Problem - Finite Integration Technique as universal method - Wide choice of solution methods Future trends - Geometrically complex problems - EMC, Signal and Power integrity - Network Extraction, Passivity - Coupled problems - Integrated flows Conclusions

60 60 Wire Bonding and Package Simulation Model

61 61 10 GHZ 10 GHZ

62 Multilayer structure mesh cells - cpu time/port: 560 s - PIV M, 1.7 GHz Multilayer structure: 7 layers Size: 11.2mm x 9.2mm x 0.9mm Frequency range: 0-5 GHz 62

63 63 Port 2 Port 1 2-Port Study Layer 6 Layer 5 Layer 4 Layer 3 Layer 2: Excitation Layer 1 Ground

64 GHz S 11, S 21 f/ghz

65 GHz S 11, S 21 f/ghz

66 GHz S 11, S 21 f/ghz

67 67 Allegro import of backplane pair

68 68 S21 Thru via vs. back drilled via Surface Current Distribution on signal/ground vias

69 69 Backplane pair Eye Pattern Through vs. Back Drill Via Through Hole Via Back Drill Via

70 Stripline and via hole on PCB board 70 SMC details measured simulated Model and simulation: UAq EMC Lab (L Aquila, Italy) Test board: UMR EMC Lab (Rolla, MO, USA) Courtesy Prof. A. Orlandi

71 Cross SSN Analysis Different Board Stack-ups 71 Swapping PWR1 and PWR2 drastically reduces the coupling between the power planes Test board: Siemens C.N.X.- UAq EMC Lab Model and simulation: UAq EMC Lab (L Aquila, Italy) Courtesy Prof. A. Orlandi

72 72 IC Package Digital signal simulation 152 port structure

73 Contents 73 Introduction State of the art - Three steps in solving an EM Problem - Finite Integration Technique as universal method - Wide choice of solution methods Future trends - Geometrically complex problems - EMC, Signal and Power integrity - Network Extraction, Passivity - Coupled problems - Integrated flows Conclusions

74 SPICE Model Extraction Static extraction Dynamic extraction Based on quasistatic fields Computes SPICE network from L,C Does not contain dynamic effects Based on dynamic EM fields Computes SPICE network from S-parameters Allows cascaded networks Full EM-SPICE 74

75 SPICE Model 1 3D structure Fixed described topology, R,L,C,G by equivalent elements SPICE model: Pin i Ground Pin j: Ground Ri/2 Kij Rj/2 Li/2 Ci Lj/2 Cij Cj Li/2 Gi Lj/2 Gj Ri/2 Kij Rj/2 Cascaded SPICE models needed to fit for larger frequency bands! 75

76 SPICE Model 2: Extraction 3D structure Flexible described topology, by R,L,C,G equivalent elements SPICE + model: controlled sources Fits naturally large frequency bands Model should be stable and passive! 76

77 Automatically Generated Netlist Section of BGA integrated circuit package Full-wave 5 Port structure (discrete) Port impedance: 50 Ohm Extracted network model 77

78 78 Full Wave Model Order Reduction SPICE Model Accuracy S21 of MWS simulation and extracted model

79 79 Challenges Cross Talk on Micro Chips

80 Challenges R-L-C Network parameter extraction for a 152x152 S-parameter matrix is network with same transfer functions still 80 a challenge for many extractors! SPICE Model 3D Field solution f/ghz

81 Contents 81 Introduction State of the art - Classification of EM Problems and Algorithms - Finite Integration Technique as universal method - Wide choice of solution methods Future trends - Geometrically complex problems - EMC, Signal and Power integrity - Network Extraction, Passivity - Coupled problems - Integrated flows Conclusions

82 82 HF- Thermal Solver Coupling Thermal Analysis of electric losses 1. Currents: CST MWS 2. Temperature Analysis: CST EMS

83 Contents 83 Introduction State of the art - Three steps in solving an EM Problem - Finite Integration Technique as universal method - Wide choice of solution methods Future trends - Geometrically complex problems - EMC, Signal and Power integrity - Network Extraction, Passivity - Coupled problems - Integrated flows Conclusions

84 Circuit / EM Integrated simulation Full integration from one hand is already available How about 3D integration into standard flows? 84

85 Design Flow Integration Present 85 Layout Tool (e.g. ADS, Allegro, APD, Virtuoso,...) EM parts Design Kit Future Back-Annotation Schematic Tool (e.g. ADS, Cadence Composer, CST DS) EM Simulator Back-Annotation Circuit simulator (e.g. ADS, Spectre, Spice, MWO CST DS) Other Sources (e.g. CAD, CST MWS,...)

86 Conclusions EM field computation tools - Flexibility in Mesh Generation - Flexibility in local approximation (FI,FE,FV,..) - Wide choice of tools for one problem - for comparison + validation - Choose the best tool for your current problem Future trends - Larger problems: Parallel computing, hardware acceleration - Power and signal integrity, EMC issues - EM Simulation will need to be fully integrated in automated design flows 86