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: info@comsol.com