Electromagnetics Modeling in COMSOL
Multiphysics The AC/DC and RF Modules
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
COMSOL Product Suite Version 4.2a
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
Quasi-statics (AC)
0
t
E tsinE tE
Statics (DC) Transient
AC/DC Simulations
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 Modules electromagnetic potential (A+V) formulation is full wave with no intrinsic approximations
RF Modules electric field (E) formulations are full wave as well
RF Modules 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
Helix and Sweep for Coil Creation
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
AC/DC Examples and Important Features
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. Gran 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 = 10106 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 COMSOLs 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
RF Examples and Important Features
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
Radiation plots and S11 vs. frequency
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
Vivaldi Antenna
PML
Lumped port
Perfect electric
conductor
f = 1.5 4.2 GHz
Vivaldi Antenna
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 Water: EM+CFD
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
Structural Loading on Radar or Microwave Dish
Antenna
Unloaded Loaded
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
Response Surfaces
S12 vs. frequency & post diameter
S12 vs. frequency & permittivity
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]
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