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 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

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. 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

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