Electromagnetics Modeling in COMSOL Multiphysics

1 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 AC/DC Module Application Examples Motors & Generators Electronics Inductors Capacitors Ion Optics and Charged Joule Heating and Induction Heating Particle Tracing 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 x Wavelength The device does not see the direction of an electromagnetic wave but just a uniform time l varying electric field x l Electrical size AC/DC Simulations Statics (DC) Quasi-statics (AC) Transient E.

2 0 E sin t E t . 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.

3 (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).

4 Non-linear power input-heat relationships Material Properties, Frequency Domain Materials can simultaneously be: complex valued directly type in values as * 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*( *( )) or 5e6*exp( *( )). 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.

5 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).

6 Finite Elements Element shapes, for any physics, Geometrically same mesh can be can be triangular, quadrilateral, shared for any types of physics . tetrahedral, prismatic, pyramidal, independent layers with physics and hexahedral and shape functions, : Element orders are 1st, 2nd, 3rd for 2nd order hexahedral element for thermal + 1st order hexahedral vector element for EM Waves with vector/edge waves elements 2nd order tetrahedral element for Element orders are 1st, 2nd, 3rd, thermal + 2nd order tetrahedral vector 4th, etc. for thermal, flow and element for waves 2nd order tetrahedral element for structural analysis 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 .

7 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 Electric field strength in a 3D model of a high Multiphysics couplings voltage breaker surrounded by a porcelain insulator.

8 Model by Dr. G ran 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 Cable heating for Power-over- Ethernet cable bundle Piezoresistivity 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.

9 Steel billet has stationary conditions continuous vertical velocity w= AC coil with axial magnetic flux frequency = 100Hz J0 = 10 106 A/m2. 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.

10 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.