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Electromagnetics Modeling in COMSOL
• RF Module – High-frequency modeling
– Microwave Heating
• AC/DC Module – Statics and low-frequency modeling
– Induction Heating
• Plasma Module – Model non-equilibrium discharges
• MEMS Module (statics subset of AC/DC
Module) – Advanced statics
– Electromechanics
• Particle Tracing Module – Interaction of charged particles with
electromagnetic fields
AC/DC Module Application Examples
Motors & Generators Electronics Inductors
Joule Heating and Induction Heating Capacitors Ion Optics and Charged
Particle Tracing
RF Module Application Examples
Antennas
Waveguides and Filters
Radiation Patterns Scattering
Microwave Heating Plasmonics and Metamaterials
Low Frequency Modeling When AC/DC Module is applicable instead of RF Module
• What is low frequency?
– Low frequency when the
electrical device size is less than
0.1 x Wavelength
– The device does not “see” the
direction of an electromagnetic
wave but just a uniform time
varying electric field l
Electrical size
0.1 x l
AC/DC Physics Interfaces - Statics
• Conductive media DC – 3D
– Axisymmetric
– 2D In-plane
• Electrostatics – 3D
– Axisymmetric
– 2D In-plane
• Magnetostatics – 3D
– 3D no currents
– Axisymmetric (two cases dependent on current direction)
– 2D In-plane (two cases dependent on current direction)
AC/DC Physics Interfaces – Low Frequency
Electric (E), Magnetic (M) or Electromagnetic (EM)
• 3D Time Harmonic E, M, and EM
• 3D Transient E and M
• Axisymmetric E, M and EM
– Time Harmonic and Transient (E and M)
• 2D In-plane E, M and EM
– Time Harmonic and Transient (E and M)
RF Simulations
• Driven
– Local field excitation
– External field excitation
• Eigenvalue
– Cavity resonances
– Progagating modes
RF Physics Interfaces
• 3D Waves – Source driven or mode analysis
• 2D Waves – Source driven, eigenfrequency or mode analysis
• In-plane
• Axisymmetric
• Cross-sectional (guided waves mode analysis only)
– Solve for 1,2, or 3 field components, allows for TE, TM, TEM, and hybrid mode analysis in 2D (hybrid mode = neither TE, TM, or TEM polarization)
Differences: AC/DC vs. RF Module
• AC/DC Module’s electromagnetic potential (A+V) formulation is “full wave” with no intrinsic approximations
• RF Module’s electric field (E) formulations are “full wave” as well
• RF Module’s E formulations give boundary conditions more suitable for higher frequencies = port boundary conditions
• RF Module has absorbing/open boundary conditions and PMLs for waves
– Absorbs solutions of type sin(kr)
• AC/DC Module has infinite elements as absorbing/open boundary conditions
– Absorbs solutions of type exp(-ar)
General EM Modeling Features
• Frequency-Domain electric field propagation (sinusoidal input)
• Frequency-Domain electromagnetic potential (sinusoidal input)
• Time-domain electric field propagation (pulses and spikes)
• Time-domain electromagnetic potential for sub-wavelength
component design (pulses and spikes)
Electrical Circuit Components
• Electrical Circuit
Components can
be combined with
RF, AC/DC,
MEMS, Plasma,
and Piezo
simulations
Nonlinear Multiphysics, Strongly Coupled
• Bi-directional coupling with heat transfer
• Bi-directional coupling with structural analysis
• Tri-directional coupling for nonlinear thermal stress
• Quad-directional coupling for: – nonlinear thermal stress and large deformations with deformable mesh for computation of
thermally induced eigenfrequency shifts
• Arbitrary nonlinear couplings, generalizations of the above or other types
of physics including fluid flow (MHD/EHD)
• Non-linear power input-heat relationships
Material Properties, Frequency Domain
Materials can simultaneously be:
• complex valued • directly type in values as 2.5-j*0.1 or exp(-j*pi/2*(z+x)) etc. for permittivity, refractive index,
conductivity, or permeability
• frequency dependent
• anisotropic
• spatially varying
• discontinuous
• nonlinear in for instance temperature T: • Ex: for conductivity, directly type in values as
• 5e6*(1-0.01*(T-273.15)) or
• 5e6*exp(-0.01*(T-273.15))
Material Properties, Time Domain
Materials can simultaneously be:
• time-dependent
• time-dependent and nonlinear
• anisotropic
• spatially varying
• discontinuous
Boundary Conditions, Frequency Domain
Arbitrary excitation shapes, including:
• truncated gaussian
• rectangular
• mathematical expressions
• measured – look-up table based
• complex valued
• computed mode shapes for arbitrary cross-sections
• frequency dependent
• spatially varying
• discontinuous
Boundary Conditions, Time Domain
• Arbitrary excitation shapes, including:
• truncated gaussian
• rectangular
• measured – look-up table based, over space and time
• computed mode shapes for arbitrary cross-sections
• switched/pulsed
• nonlinear
• time-varying
• spatially varying
• discontinuous
Thermal Features
• Permittivity, conductivity, and permeability can be nonlinear in any
variables including temperature
• Boundary conditions cover convective cooling and heat
radiation/re-radiation with view-factor computations
• Continuous waves can be switched (on/off) while simultaneously
solving for transient nonlinear heat transfer
Stress Features
• Permittivity, conductivity, and
permeability can be nonlinear in any
variables including stress components
• Structural analysis includes solids and
shells, anisotropic, plastic, hyper-
elastic (rubber)
• Structural deflections are allowed to
change the shape of the microwave
cavities for frequency shift
computations
• Radiation pressure terms can be
included as loads on boundaries or
volumes (structural damage from very
high power spikes)
Finite Elements
• Element shapes, for any physics, can be triangular, quadrilateral, tetrahedral, prismatic, pyramidal, and hexahedral
• Element orders are 1st, 2nd, 3rd for EM Waves with vector/edge elements
• Element orders are 1st, 2nd, 3rd, 4th, etc. for thermal, flow and structural analysis
• Geometrically same mesh can be shared for any types of physics – independent layers with physics and shape functions, e.g.:
2nd order hexahedral element for thermal + 1st order hexahedral vector element for waves
– 2nd order tetrahedral element for thermal + 2nd order tetrahedral vector element for waves
– 2nd order tetrahedral element for thermal + 2nd order tetrahedral element for stress + 2nd order tetrahedral vector element for waves +…
Piezoelectric Devices and RF MEMS*
• *Available in the MEMS Module, Structural
Mechanics Module, and Acoustics Module
• Mix dielectric, conductive, structural, and
piezolayers
• Couple with electrical circuits and with any
other field simulation in COMSOL
Multiphysics
• Elastic shear and pressure waves
• Perfectly matched layers (PMLs) for elastic
and piezo waves
• Thermoelastic effects
• 2D or 3D modeling
• Retrieve Impedance, Admittance, Current,
Electric Field, Voltage, Stress-strain, Electric
Energy Density, Strain Energy Density
• Transient, frequency-response, fully coupled
eigenmode
CAD Interoperability
• CAD Import Module for all
major CAD formats
• LiveLink Products for
bidirectional and fully
associative modeling:
– LiveLink for AutoCAD®
– LiveLink for Inventor®
– LiveLink for Pro/ENGINEER®
– LiveLink for Creo™ Parametric
– LiveLink for SolidWorks®
– LiveLink for SpaceClaim®
MEMS Capacitor
• Electrostatically tunable parallel plate
capacitor
• Distance between plates is tuned via a
spring
• For a given voltage difference between
the plates, the distance of the two
plates can be computed, if the
characteristics of the spring are known
• The AC/DC Module features
automated computation of capacitance
for single+ground conductor structures
and full capacitance matric output for
multiconductor devices
High-Voltage Breaker
• Electrostatic analysis of a high-
voltage component
• Examine field distribution and
maximum field strength for
electric breakdown prevention
• Inhomogeneous materials with
complex properties and
multiphysics couplings Electric field strength in a 3D model of a high
voltage breaker surrounded by a porcelain
insulator. Model by Dr. Göran Eriksson, ABB Corporate Research,
Sweden
Electrostatic Comb Drive
• Electrostatic MEMS Device
• Moving Mesh to account for
electrostatic volume and
shape change
• Capacitive pressure sensors
is a similar application that
also benefits from the Moving
Mesh feature
Linear and Nonlinear DC Computations
• Electric conductivity can be temperature
dependent or function of any field
• Material Library provides conductivity-vs-
temperature curves for many common
materials
• Conductivity can be anisotropic due to
material anisotropy or multiphysics
couplings such as Hall effect or
Piezoresistivity
Cable heating for Power-over-
Ethernet cable bundle Model by Sandrine Francois, Nexans
Research Center & Patrick Namy Simtec,
France.
Joule Heating in a Surface Mounted Package
• Classic known-heat-source
thermal analysis – Power, current or voltage input can
be based on look-up table
– Sources can be time-varying and
moving
• DC simulation -> computed heat
source -> thermal simulation
• AC simulation -> computed heat
source -> thermal simulation
Hot-Wall Furnace Heating
• Furnace reactors are used in the
semiconductor industry for layer growth
and annealing
• The electromagnetic part solves for the
magnetic vector potential, A, at a fixed
frequency
• The thermal part solves for temperature, T,
and heat radiation
• The radiation fully controls the thermal flux
between the susceptor and the quartz tube
• The susceptor is heated by a RF coil to
high temperatures
• This model investigates the temperature in
a hot-wall furnace reactor used for silicon
carbide growth
Steel billet has
continuous vertical
velocity
w=0.1m/s AC coil with axial
magnetic flux
frequency = 100Hz
J0 = 10×106 A/m2
Temperature field T,
stationary conditions
Inductive Heating of a Billet & The Skin Effect
Power Inductor
• 60 Hz
• Full electromagnetic potential
{Ax,Ay,Az,V} formulation
• Accurate self-inductance
computation where conduction
effects inside of all conductors are
included
Cold Crucible
• 10 kHz
• Magnetic vector potential
{Ax,Ay,Az} formulation
• Skin effect modeled with
impedance boundary condition
to avoid large mesh and
increase simulation accuracy
Induction Heating
• Steel cylinder within copper coil
• AC 50 Hz
• Electromagnetic potential
{Ax,Ay,Az,V} formulation
• Bidirectional coupling to heat transfer
• Temperature dependent conductivity
• Picture shows T and B fields (T only in
Steel)
• Note: Transient Heat + Frequency
Response AC simultaneously
Magnetic Signature of a Submarine
• Magnetostatics simulation
• Reduced field formulation for
including external magnetic field –
here the geomagnetic field
• Magnetic shielding boundary
condition for very efficient accurate
modeling of thin sheets of high
permeability materials
• Similar shielding type of boundary
conditions are available for DC,
Electrostatics, and AC
Electromagnetic Shielding
• Boundary conditions for electromagnetic
shielding and current conduction in shells
are important for electromagnetic
interference and electromagnetic
compatibility calculations (EMI/EMC).
• These are used to represent thin surfaces
with much higher conductivity, permittivity or
permeability than the surroundings.
• Boundary conditions are also available for
the opposite case where the conductivity,
permittivity or permeability is much lower
than the surroundings.
AC/DC Currents in Porous Media
• The porous media interface for
electric currents allow for volume
averaging of electric conductivity
and relative permittivity.
• Similar volume averaging tools are
available for heat transfer problems
and the two can be combined.
Generator
• The generator analyzed in this model
consists of a rotor with permanent magnets
and a nonlinear magnetic material inside a
stator of the same magnetic material.
• The model calculates the static magnetic
fields inside and around the generator.
• The nonlinearity of the magnetic material is
modeled using an interpolating function.
Magnetic Prospecting of Iron Ore Deposits
• Magnetic prospecting is a method
for geological exploration of iron
ore deposits.
• Passive magnetic prospecting
relies on accurate mapping of local
geomagnetic anomalies.
• This model estimates the magnetic
anomaly for both surface and aerial
prospecting by solving for the
induced magnetization in the iron
ore due to the earth's magnetic
field.
• Geometry based on imported
Digital Elevation Map (DEM)
topographic data.
Small-Signal Analysis
• The AC/DC Module features small-
signal analysis with automated
differential inductance computations.
• Small-signal analysis is also available
for other lumped parameters such as
capacitance and impedance.
• Based on COMSOL’s automated
machinery for linearizing biased
components
• Modal analysis or frequency sweeps
PCB Planar Transformer:
Self and Mutual Inductance Calculation
• ECAD Import: ODB++ file import and preprocessing
• The ODB++ file contains the different layers of the PCB.
• It also contains footprint layers for the ferrite core of the transformer.
• With three separate import steps it is possible to create the full geometry of the PCB board with traces, the holes for the ferrite core, and the actual ferrite core.
• File: planar_transformer_layout.xml
• See also:
– www.valor.com and
– www.valor.com/en/Products/ODBpp.aspx
S-parameters, before and
after mechanical deformation ECAD: ODB++ Import
Mechanical deformation + RF simulation of PCB
Microwave Low-Pass Filter
Microstrip Patch Antenna
• Microstrip modeling
• Perfecly Matcher Layers (PMLs)
to absorb outgoing radiation
• Radiation pattern computations
• Different mesh types with prism
and tet elements in different
areas to optimize performance
Vivaldi Antenna
Matching circle Short
Exponential tapered slot
Feeder strip
100mm
145mm
Substrate: er = 3.38
J. Shin et al., “A Parameter Study of Stripline-fed Vivaldi Notch-antenna
Arrays,” IEEE Trans. Antennas Propag., Vol. 47, No. 5, May 1999
RF Coils
• Mode analysis to find the fundamental
resonance frequency of an RF coil
• Frequency sweep
• Extract the coil's Q-factor
• RF Coils are modeled using impedance
boundary conditions
• Skin-depth makes explicit modeling of
volumetric currents prohibitive
• Excitation is often done by lumped ports
• Calculate impedance-vs-frequency
Deformations Greatly Affect Coil Performance
• Consider a tuned RF filter with a matched array of inductors
(Used in high-power transmitters or amplifiers)
• If coil deflects – no longer matched
High Frequency – Small Skin Depth
• 1 GHz Signal
• Current confined to thin inside spiral
• Preferentially heats inside of coil – coil deforms
Thermal Mass of Board Cools Ends
• Thermal expansion in coil changes dimensions and inductance
Temperature
Stress
50x Deformation
Cavity Resonator Heating
• Mode computation, large cavity
• Use scaled mode shape scaled for
power input
• Thermal computation
• Very thin skin-depth
• Joule heating only on boundary
• Thermal diffusion in cavity walls
Microwave Sintering
• Zink oxide powder sintering
• Imaginary part of permittivity defined
via look-up table from measurement
• Strongly coupled simulation – Temperature and microwave problem needs
to be assembled and solved simultaneously
to converge (sequential solving not possible)
Microwave Oven
• Microwave heating
• Simultaneous modeling of
microwaves and heat in the same
integrated model
Thermal Drift in Microwave Filter
• Tridirectional strongly coupled microwave,
thermal, and structural
• Structural deflection changes the filter
geometry
• Different material options are investigated
to reduce thermal drift
• Simulation requires deformable meshes via
so called ALE technique
• Structural shell with thermal expansion
required
• Microwave heating of tissue
• Tissue has strongly varying
dielectric properties with
respect to temperature
• SAR computation
• Nonlinear simulation
• Damage integral computations
and phase change
Biomedical Microwave Heating Effects
Three-Port Ferrite Circulator
• Anisotropic material - gyrotropic
• Non-symmetric permeability matrix –
special solver needed
• Non-reciprocal
• S-Parameters
• CAD parameterization available
through native COMSOL or one of
the LiveLink Products for SolidWorks,
AutoCAD, Inventor, Pro/ENGINEER,
Creo Parametric, or SpaceClaim
• LiveLink for MATLAB can also be
used for parameterization
S-Parameter Sweeps
• Full matrix-output S-parameter
sweep
• Sweeps not only for frequency
but any modeling parameter
• Touchstone export
Radar Cross-Section Analysis
• The polar plot feature allows for efficient radiation pattern
visualizations
Plasmonic Wire Grating
• A plane wave is incident on a wire
grating on a dielectric substrate.
• Coefficients for refraction, specular
reflection, and first order diffraction
are all computed as functions of
the angle of incidence.
Simulation of an Electromagnetic Sounding
Method for Oil Prospecting
• The marine controlled source
electromagnetics method uses a
mobile horizontal electric dipole
transmitter and an array of seafloor
electric receivers.
• The seafloor receivers measure the
low-frequency electrical field generated
by the source.
• Some of the transmitted energy is
reflected by the resistive reservoir and
results in a higher received signal.
Step-Index Fiber
• The distribution of the magnetic and
electric fields for confined modes is
studied for a step index fiber made
of silica glass.
• Compared with analytical solution.
Photonic Crystals and Band-gap Materials
• A photonic waveguide is created by
removing some pillars in a photonic crystal
structure. Depending on the distance
between the pillars a photonic band gap is
obtained.
• Within the photonic bandgap, only waves
within a specific frequency range will
propagate through the outlined guide
geometry.
• COMSOL is used for design and
optimization of photonic crystal waveguides
and optical crystal fibers.
Metamaterials
• The RF Module has applications for
metamaterial and absorptive material
design for RF, Microwave, and Optical
frequencies.
• General solvers allow for microstructure
simulations and also macroscopic
simulations where negative values for
refractive index, permittivity, and
permeability is allowed.
• Anisotropic materials are supported. Cloaking model by Steven A.
Cummer and David Schurig -
Duke University, Durham, NC
Contact and Web Info
• Contact your local sales representative for more information
• See also: www.comsol.com
• Generic email: [email protected]