computational electromagnetics technical training course sampler
DESCRIPTION
This 3-day course teaches the basics of CEM withapplication examples. Fundamental concepts in the solution ofEM radiation and scattering problems are presented. Emphasisis on applying computational methods to practical applications.You will develop a working knowledge of popular methods suchas the FEM, MOM, FDTD, FIT, and TLM including asymptoticand hybrid methods. Students will then be able to identify themost relevant CEM method for various applications, avoidcommon user pitfalls, understand model validation and correctlyinterpret results. Students are encouraged to bring their laptop towork examples using the provided FEKO Lite code. You willlearn the importance of model development and meshing, post-processing for scientific visualization and presentation of results.Participants will receive a complete set of notes, a copy of FEKOand textbookTRANSCRIPT
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Coarse Outline• Day 1
– Review EM Theory– Review Antennas– Review Antenna Arrays– Review Scattering– Introduction to FEKO Lite
• Day 2– CEM Introduction– FEM Introduction– MoM Introduction– FDTD Introduction– FVTD, TLM and FIT– Examples
• Day 3– FEM Tutorial– MoM and FDTD Tutorial– Summary and Advanced Topics
• High-frequency Methods• Hybrid Methods
– Discussion and Examples
Electromagnetics (EM)
Actual solution for realistic problems is complex and requires simplifying assumptions and/or numerical approximations
Solutions to Maxwell’s equations using numerical approximations is known as the study of Computational Electromagnetics (CEM)
D
DJHt
0 B
BEt
Faraday’s Law: Ampère’s Circuital Law:
Gauss’ Laws:
HB ED
Constitutive Equations:
Maxwell’s Equations
Why Computer-Aided Methods Are Used?
Importance• Key to analysis, design & optimization of RF to
optical systems.• Basis for field-theory based and process-oriented
CAD (virtual prototyping).• Key to economical success of a product through
shortening of development time.• Only means for dealing with complex (non-canonical)
electromagnetic structures.• Theoretical models must be validated by
experiments.• Theoretical and experimental work are of equal
importance.
Classic Electromagnetic Solution
Examples:• Closed-form expressions for microstrip/transmission lines;• Spectral domain program for coplanar waveguides;• Eigenvalue solvers for guided waves and cavities;
Postprocessing
Maxwell’sEquations
AnalyticalModel
BoundaryConditions
MaterialProperties
User Data
Computation
ComputerProgram
Results
MathematicalFormulation
AnalyticalPreprocessing
Discretization
User Interface
Problem-Dependent
Modern Electromagnetic Solution
Examples:• Finite Element or MoM Frequency Domain Solver• FVTD or FDTD Time Domain Numerical Simulation
Postprocessing
Maxwell’sEquations
NumericalModel
Huygens’Principle
VariationalPrinciple
Boundary ConditionsMaterial Properties
Computation
ComputerProgram
Results
NumericalFormulation
AndDiscretization
User Interface
Problem-Independent
Conventional Microwave Design
Initial Design
Circuit/AntennaSpecifications
DesignData
Modifications
Measurements
LaboratoryModel
Loop
Expensive,Time-ConsumingNot Automated
Conventional Microwave Design
Compare
FinalFabrication
Pass
Fail
RapidPrototyping
Computer-Aided Design (CAD)
VirtualPrototyping
Initial Design
Circuit/AntennaSpecifications
Design DataSynthesis Methods
Modifications
Measurements
Analysis
OptimizationLoop
Compare
PrototypeFabrication
Pass
Fail
SensitivityAnalysis
Models
• Physical Modeling Error• Discretization Error• Numerical Modeling Error• Measurement Error
Inexpensive,Fast,Automated
Electromagnetic Simulators• An Electromagnetic Simulator is a modeling tool that:
– solves electromagnetic field problems by numerical analysis;– extracts engineering parameters from the field solution and
visualize fields and parameters;– allows design by means of analysis combined with
optimization (PSO, GA, parameterized models, etc.).• The field solver engine employs one or several numerical
methods obtained through the practice of CEM:– is the theory and practice of solving electromagnetic field
problems on digital computers;– provides the only viable approach to solving “real world” field
problems;– enables Computer-Aided Engineering (CAE) and Computer-
Aided Design (CAD) of EM components and systems.
Solving EM Field Problems• Find electromagnetic field and/or source functions
such that they– obey Maxwell’s equations,– satisfy all boundary conditions,– satisfy all interface and material conditions,– satisfy all excitation conditions.
(In both time and space, or at one frequency in space)• Field solutions are then unique when tangential
fields on conductors and initial conditions are known• But numerical solution depends on
• Physical Modeling Error• Discretization Error• Numerical Modeling Error• Measurement Error
Field-Solving MethodsMethods for solving Maxwell’s Equations:• Analytical Methods
– Exact explicit solutions (only a few ideal cases)• Semi-Analytical Methods
– Explicit solutions requiring final numerical evaluation– Numerical solutions with analytical “preprocessing”
• Approximate analytical models– Approximate analytical solutions for simplified structures
(provides physical insight)– Only practical way to handle very large electrical structures
• Numerical Methods– Differential or integral equations are transformed into matrix
equations by numerical approximations (sampling) and solved iteratively or by matrix inversion
Overview of CEM• Central to all CEM techniques is the idea of discretizing some
unknown EM property, for example:– In MoM the surface current is typically used– In FE, the Electric Field– In FDTD, the Electric and Magnetic Field
• Meshing is used to subdivide a large geometry into a number of nonoverlapping subregions or elements, for example:– In two dimensional regions triangles maybe used– In three dimensional geometries a tetrahedral shape may be used
• Within each element, a simple functional dependence (basis functions) is assumed for the spatial variation of the unknown
• CEM is a modeling process and therefore a study in acceptable approximation and numerical solution
In other words, CEM replaces a real field problem with an approximate one which causes physical (geometric) and numerical limitations that one must keep in mind
Overview of CEM• During the creation of the approximate “model”, assumptions and
simplifications are generally introduced so limitations on the solution accuracy, for example:– Assuming an infinite ground plane or substrate in an antenna
structure– Simplifying a thin wire by a current filament (dipole impedance)
• When analyzing solutions generated from a CEM techniques keep inmind limitations of the solution introduced by manufacturing tolerances:– Small changes in dimensions may affect the performance– Frequency dependent (or unknown) material properties
• Limitations are also introduced by the finite discretization– The mesh must be fine enough so that the basis functions can
adequately represent the electromagnetic fields– Fine mesh required for critical variations such as source region
• Numerical approximations and finite precision will limit the analysis– Limited computational resources (i.e., mesh size)– Double precision accuracy will not help if the problem is ill conditioned– Finer mesh is often the only choice (multi-scale codes)
Fundamentals of Simulations
Fundamentals of Simulations
Fundamentals of Simulations
Accuracy ChecklistTo use verified CEM tools successfully requires:• Knowledge and understanding of electromagnetics and RF engineering• Validation of simulation results (analytical models, code-to-code, experiments, prototyping)
Computational Hierarchy
computationalelectromagnetics
High frequencynumerical methods
IE DE
MoMFDTDTLM
field based current based
GO/GTD PO/PTD
TD FD TD FD
TWTD FDFD
Classification of Methods• Maxwell’s Equations-based methods
• Optics-based methods
19
Method Frequency Domain
Time Domain
Boundary Element
Method of Moments (MoM)
Finite Element FEMFinite Difference FDTD
Finite Volume FVTD
MethodPhysical Optics
GTD/UTD
Classification of Methods
• This distinction is based more on human experience than on physical or mathematical considerations.
• The time dimension can be treated as a fourth dimension in Minkowski space in the form jct, where c is the speed of light.
• The user requires knowledge of different methods to be able to choose the most suitable design tool and setup the calculation correctly.
• In the most general sense, solution methods can thus beclassified according to the number of dimensions uponwhich the field and source functions depend.
Frequency Domain Methods(Time-Harmonic)
Time Domain Methods(Transient)
FourierTransform
1D Methods: Fields and voltage/current vary in one spacedimension (Transmission Line Problems)
(…Touchstone, Supercompact, SPICE…)2D Methods: Fields and currents vary in two space
dimensions (Cross-section problems,TEn0 waveguide problems)
(…FEM-2D, MEFiSTo-2D…)2 1/2 D Methods: Fields vary in three space dimensions,
currents vary in two space dimensions(Planar multilayer circuits)
(…Sonnet, Momentum, Ensemble...) frequency domain3D Methods: Fields and currents vary in three space
dimensions (General propagation, scatteringand radiation problems)
(…HFSS, FEKO, CST, XFDTD, GEMS, GEMACS…)
Classification of Methods
What Have All Methods In Common?
1. In all methods, the unknown solution is expressed as a sum of known functions (expansion functions or basis functions).
2. The weight (coefficient) of each expansion function is determined for best fit.
What distinguishes them?
• the electromagnetic quantity approximated,• the expansion functions used,• the strategy employed for determining the coefficients of the
expansion functions, and• the numerical solution method.
Other ClassificationsQuasi-TEM or full-wave?Quasi-TEM use notions of effective dielectric constant, singlemode impedance, axial current, dispersionless propagation.
Circuit or antenna?Circuit or antenna?Static and quasi-static techniques are applicable to analysis of circuits, except for spurious effects: radiation & surface waves.Open or closed problem space?Circuits are at some point usually enclosed within a metal box, similarly, antennas are designed to operate in free space. One would expect that techniques for boxed in structures would be used to analyse circuits and those techniques for open structures for antennas.This is not what happens in practice!Common assumptions are: infinite dielectrics and ground planes, zero thickness of strips, etc.
Frequency and Time Domain Concepts
• Time dependence• Delay• Real permittivity and conductivity• Reflection/Transmissiontime response• Impulse response• Decay time• Time domain convolution
• Complex Frequency• Phase angle• Complex Dielectric Constant• Complex Reflection/Transmission Coeff.• Complex Impedance• Q-Factor• Complex multiplication
Why Model In The Frequency Domain?
• Most microwave engineers are more familiar with FD concepts than with TD concepts
• Frequency domain simulations are steady-state• Complex notation is elegant and efficient• Specifications are traditionally formulated in theFD (S-Parameters, loss tangent, dispersion)• Time domain information can be obtained byinverse Fourier Transform (Causality issues!)• Dispersive materials and boundaries are easilydescribed by frequency-dependent parameters
Finite Element Method (FEM)
Finite Element Method (FEM)
Method of Moments (MoM)
Method of Moments (MoM)
Why Model In The Time Domain?• Time domain simulations are “life-like” and allow
visualization of signal propagation• Virtual experiments are set up as in the lab
(Source, reference planes, output probes)• Cause and effect can be distinguished• One simulation can cover a wide bandwidth• Transient phenomena can be simulated• Nonlinear behavior is modeled naturally• Dispersive materials and boundaries are modeled
in a more physical manner• Frequency domain information can be obtained via
Fourier transform
Finite Difference Time Domain (FDTD)
Finite Difference Time Domain (FDTD)
Comparison
Comparison
Summary and Conclusions• Numerical Methods allow us to solve real life EM problems
(within certain limits). They form the engine(s) of electromagnetic simulators.
• Electromagnetic simulators are not merely Maxwell equation solvers, but powerful simulation and design tools with visualization capabilities.
• Understanding EM phenomena and knowledge of radio engineering are necessary for successful use of codes.
• Understanding the underlying numerical methods is essential in assessing the accuracy, performance and limitations of a particular simulation tool.
• Electromagnetic simulators are the heart of modern CAD tools for analog microwave, digital high-speed and mixed signal design, EMC and signal integrity engineering and other applications of electromagnetic fields and waves.