Electromagnetics Modeling in COMSOL Multiphysics The AC/DC and RF Modules

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 Capacitors Ion Optics and Charged Particle Tracing Joule Heating and Induction Heating

RF Module Application Examples Antennas Radiation Patterns Scattering Waveguides and Filters 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 0.1 x l Electrical size

AC/DC Simulations Statics (DC) Quasi-statics (AC) Transient E t 0 Esin t E t

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, hyperelastic (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 1 st, 2 nd, 3 rd for EM Waves with vector/edge elements Element orders are 1 st, 2 nd, 3 rd, 4 th, 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.: 2 nd order hexahedral element for thermal + 1 st order hexahedral vector element for waves 2 nd order tetrahedral element for thermal + 2 nd order tetrahedral vector element for waves 2 nd order tetrahedral element for thermal + 2 nd order tetrahedral element for stress + 2 nd 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 highvoltage 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-vstemperature 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

Inductive Heating of a Billet & The Skin Effect Temperature field T, stationary conditions AC coil with axial magnetic flux frequency = 100Hz J 0 = 10 10 6 A/m 2 Steel billet has continuous vertical velocity w=0.1m/s

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 smallsignal 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

Mechanical deformation + RF simulation of PCB Microwave Low-Pass Filter ECAD: ODB++ Import S-parameters, before and after mechanical deformation

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 S 11 vs. frequency

Vivaldi Antenna Exponential tapered slot Feeder strip 100mm Matching circle Short 145mm Substrate: e r = 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 Perfect electric conductor Lumped port 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 50x Deformation Stress

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

Biomedical Microwave Heating Effects Microwave heating of tissue Tissue has strongly varying dielectric properties with respect to temperature SAR computation Nonlinear simulation Damage integral computations and phase change

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

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