AC/DC Module
Electromagnetics in COMSOL Multiphysics is extended by add-on Modules 1) Start Here 2) Add Modules based upon your needs 3) Additional Modules extend the physics you can address 4) Interface with your CAD data and MATLAB
Types of Electromagnetics Modeling Static Low Frequency Transient High Frequency AC/DC Module RF Module Wave Optics Module E t 0 Esin t Et Esint Electric and magnetic fields do not vary in time. Fields vary sinusoidally in time, but there is negligible radiation. Fields vary arbitrarily in time, radiation may or may not be significant. Objects can be moving. Fields vary sinusoidally in time, energy transfer is via radiation.
Static Field Modeling DC Electric Currents solves for current flow in conductors Electrostatics solves for electric fields in perfect insulators Magnetostatics solves for the magnetic fields around magnets, and the fields around current carrying objects Parallel Plate Capacitor, Electrostatics Inductor, DC current flow and Magnetostatics Permanent Magnet, Magnetostatics
Low Frequency Modeling AC Electric Currents considers both conduction and displacement currents in conductive and insulating media The Magnetic Fields can be solved for in the frequency domain to find the conduction, displacement, and induction currents The Magnetic and Electric fields can be solved for, if skin effects in coils require a high accuracy model Inductive Heating, Magnetic Fields Mutual Inductance, Magnetic Fields Analysis Inductor, Magnetic and Electric Fields
Transient Modeling Transient Electric Currents solves for displacement and conduction currents in insulators and conductors Transient Magnetic Fields is suitable for modeling current pulses and nonlinear material response to field strength Rotating Machinery considers rotary velocity and acceleration Generator, Rotating Machinery E-Core Transformer, Transient Magnetic Fields
Whenever there are Electromagnetic Losses, there is a Rise in Temperature Joule Heating Induction Heating Specialized user interfaces and solvers address the two-way coupled frequency-domain electromagnetic and time-domain thermal problems
Electric Circuits The Electric Circuits formulation can model a lumped system of circuit elements and couple this to the finite element model
Formulations per Module COMSOL Multiphysics 1 RF Module Wave Optics Module AC/DC Module Static Electric Currents Static Joule Heating Electrostatics Magnetic Fields 2 Electromagnetic Waves - Frequency Domain - Time Explicit - Transient Microwave Heating Transmission Line Equations Electrical Circuits Electromagnetic Waves - Frequency Domain - Time Explicit - Transient - Beam Envelopes Laser Heating Electric Currents in Solids Electric Currents in Shells Joule Heating Electrostatics Magnetic Fields Induction Heating Magnetic and Electric Fields Magnetic Field Formulation Rotating Machinery Electric Circuits 1) Core package contains a reduced set of boundary conditions for these formulations 2) 2D and 2D-axisymmetric geometries and static and low frequency formulations only
Material Models All material properties can be: Constant or nonlinearly dependent upon the fields Isotropic, Diagonal, or Fully Anisotropic Defined via Rule-of-Mixtures models Bi-directionally coupled to any other physics, e.g. Temperature, Strain Fully User-Definable AC/DC Module supports magnetic nonlinearities, B-H curves and electric nonlinearities (superconductors), E-J curves r r r D E D P E D E D 0 0 0 r r r B H B M H B H B 0 0 0 0 J E
Data Extraction Resistance, Capacitance, Inductance, & Mutual Inductance Impedance, Admittance, and S-parameters (optional Touchstone file export) Force calculation due to electric and magnetic fields Z Z 11 21 Z Z 12 22 Lumped Parameters Magnetic Forces
Additional Modules for Electromagnetics Plasma Module 1 MEMS Module 2 Particle Tracing Module 3 Solves DC Discharge, Capacitively Coupled Plasmas, Inductively Coupled Plasmas, and Microwave Plasmas. Couples structural mechanics and electrostatics for the modeling of electroactuation, as well as piezoelectric devices. Computes paths of charged particles through electric and magnetic fields as well as fluid fields. Microwave Plasma Tunable Cavity Filter Multipactor 1) Depending upon the type of plasma being modeled, the AC/DC or the RF Module may also be needed 2) Contains the same 3D electrostatic, electric currents in solids, and electric circuits capabilities as the AC/DC Module 3) Does not require any other Modules
Additional Modules for Electromagnetics (cont d) Semiconductor Module 1 Wave Optics Module 1 Solves for the electric potential and electron and hole concentrations in semiconductor materials. Computes electric and magnetic fields for optical systems where the wavelength is comparable to or much smaller than the studied device or system. MOSFET Mach-Zehnder Modulator 1) Does not require any other Modules
The Optimization Module Gradient-Free optimization allows for optimization of geometric parameters, and allows for remeshing of the geometry. - Nelder-Mead, Coordinate Search, and Monte Carlo algorithms. - Optimize one or more geometric dimensions for a CAD model created directly in COMSOL Multiphysics or via the LiveLink products Gradient-Based optimization requires more user interaction to set up a differentiable objective function and a moving mesh, but can handle many more design variables, and can solve much faster. - Adjoint method is used to compute exact sensitivities Bowtie Antenna Optimization
Example Models, AC/DC Module Resistors Magnets Capacitors Motors and Actuators Inductors and Coils Electromagnetic Heating
Resistor and Capacitor Modeling DC Resistive device analysis assumes that all materials are conductors, and solves the equation: V 0 Electrostatic analysis assumes all materials are insulators, thus: r V 0 0 AC resistive and AC capacitive devices are both solved in the frequency domain using the same governing equation: j V 0 r 0 Transient analysis also uses the same governing equation: V t V 0 r 0
Electrostatic, Transient, and Frequency Domain modeling of a Parallel Plate Capacitor A parallel plate capacitor is modeled under electrostatic, frequency domain, and transient conditions Fringing fields and domain size effects on capacitance are studied Frequency domain modeling resolves the losses in dielectric materials Transient modeling of the charging behavior agrees with analytic solution http://www.comsol.com/showroom/gallery/12695/
Advanced boundary conditions Electric Currents examples: Contact Impedance Distributed Impedance Electric Shielding Floating Potential Periodic Condition etc. Corresponding conditions exist in Electrostatics: Distributed Capacitance Thin Low Permittivity Gap Dielectric Shielding Floating Potential Periodic Condition
Contact Impedance Thin high impedance layer between domains Only interior boundaries No current tangential to the surface Handles resistive and capacitive effects Domain 1 Contact impedance Thin high impedance layer d Domain 2
Distributed impedance Thin high impedance layer on surface Only exterior boundaries No current tangential to the surface Handles resistive and capacitive effects Resistor Distributed impedance Thin high impedance layer d s V ref
Electric shielding Thin conducting layer Current path along the surface Domain 1 Electric shielding Thin conductive layer d s Domain 2
Floating potential Thin metallic sheet voltage sensing Unknown isopotential surface COMSOL solves an extra equation to find this unknown voltage, such that
Inductor and Coil Modeling Static Magnetic Fields are computed by solving: H J BA 1 H B Where A is the Magnetic Vector Potential, and J is the current density, which can be solved simultaneously, or in a separate analysis AC Magnetic Fields are computed by solving: BA 1 H B 2 j AH J The additional terms represent the induced and the displacement currents Transient Magnetic Fields are computed by solving: A H J t BA 1 H B The displacement currents are not included in the governing equations
Inductance of a Power Inductor At the operating frequency (1kHz) of this power inductor, the skin depth in the coil is comparable to the thickness of the current-carrying wires The Magnetic and Electric fields interface is used to capture the skin effect in the wires The admittance and inductance is computed http://www.comsol.com/showroom/gallery/1250/
E-core Single Phase Transformer Full non-linear time domain analysis at 50 Hz is solved for the induced voltages Non-linear magnetic material (with saturation effect) is used for the magnetic core Windings are treated as coil bundles, without modeling each turn of wire Primary winding Secondary winding E core http://www.comsol.com/showroom/gallery/5700/
Inductor in Amplifier Circuit A nonlinear 2D axisymmetric finite element model is combined with a lumped circuit model A 1000 turn coil is wrapped around a core with nonlinear magnetic response, the multi-turn coil domain is used A DC bias is applied, and the AC response at this bias is computed The voltage and current in the device is predicted over time http://www.comsol.com/showroom/gallery/990/ http://www.comsol.com/showroom/gallery/2128/
Magnets, Motors & Actuators If there is no current flow in the model, solve: H 0 HV m When modeling rotating objects, solve for the transient magnetic fields and induced currents in the conductive and current carrying domains, but only the magnetic fields only in the surrounding air A H vbj t BA 1 H B H 0 HV m Where V m is the Magnetic Scalar Potential
Magnetic Prospecting of Iron Ore Deposits Underground iron ore deposits result in magnetic anomalies Here, disturbances in the background magnetic field of the Earth, due to the presence of a ore deposit are computed The Reduced Field formulation solves for small perturbations to a background field Assumed ore deposit http://www.comsol.com/showroom/gallery/3807/
Simulating the Moving Parts of a Generator The Rotating Machinery, Magnetic interface solves for rotating 2D and 3D domains composed of magnetic materials The finite element mesh is allowed to slide at the interface Nonlinear magnetic materials are included in the model Induced voltages as a function of rotational speed are computed http://www.comsol.com/showroom/gallery/2122/
Electromagnetic Heating e - Conduction Current Losses Electrons moving through a conductor lose energy E(t) + Displacement Current Losses Dipolar molecules rotate in time varying electric field H(t) J(t) Induction Current Losses Time varying magnetic fields induce currents in a conductor C T t kt p Q Electromagnetic Losses All of the above losses can be included in the generalized heat transfer equation
Example: Inductive Heating of a Billet Inductive heating is common in the steel industry. This model concerns the re-heating of a billet traveling through a coil. Frequency Domain (AC) modeling of the magnetic fields is combined with stationary heat transfer. Billet heat loss through convection and radiation AC coil velocity of billet = 0.1m/s
Results for 50 Hz Central cross-section of heat source
Results for 500 Hz Using Symmetry Central cross-section of heat source