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The AC/DC Module User's Guide - Numerical Modelling Laboratory

1. 119 Dielectric Shielding 120 Terminal sco aptior A sol aii ops GAD ee em rd v M24 Floating Potential 122 Electric Displacement Field 123 Distributed Capacitance 124 Periodic 125 Zero Charger amp 2 Gt estem odes deque cou M25 Thin Low Permittivity Gap 126 Line Charge we SN Reo crues Line Charge on 177 Line Charge Out of Plane 128 129 Point Charge on Axis 129 Change 130 Change Thickness Out of Plane 13 Infinite Elements 2 2 lll lll slc sc 132 Electrostatic Point Dipole 132 The Electric Currents Interface 133 Domain Boundary Edge Point and Pair Features for the Electric Currents Interface oe IR 8 Be Oe eso N85 Current 137 Floating Potential 139 Archie s Law 140 Porous Media 1m 6 die entem ws External Current Density 142 CurrentSourCe 2 voe he eee at ee von go 43 Initial Values 148 Boundary Current 144 N
2. NEM i an open unconnected circuit port is just a continuity condition CHAPTER 3 MODELING WITH THE AC DC MODULE Parameters and Ports In this section S Parameters in Terms of Electric Field S Parameter Calculations in COMSOL Multiphysics Lumped Ports S Parameter Variables S Parameters in Terms of Electric Field Scattering parameters or S parameters are complex valued frequency dependent matrices describing the transmission and reflection of electromagnetic waves at different ports of devices like filters antennas waveguide transitions and transmission lines S parameters originate from transmission line theory and are defined in terms of transmitted and reflected voltage waves All ports are assumed to be connected to matched loads that is there is no reflection directly at a port For a device with n ports the S parameters are S3 Sip ys Sin So Soo S Sit s Snn where S141 is the voltage reflection coefficient at port 1 S91 is the voltage transmission coefficient from port 1 to port 2 and so on The time average power reflection transmission coefficients are obtained as ISl Now for high frequency problems voltage is not a well defined entity and it is necessary to define the scattering parameters in terms of the electric field For details on how COMSOL Multiphysics calculates the S parameters see S Parameter Calculations S PARAMETERS AND PORTS 93 94
3. The Electric Currents Interface which simulates the current in a conductive and capacitive material under the influence of an electric field All three study types stationary frequency domain and time dependent are available The Electric Currents Shell Interface which simulates the current in a conductive and capacitive shell under the influence of an electric field All three study types stationary frequency domain and time dependent are available MAGNETIC FIELDS The Magnetic Field Interfaces chapter describes these interfaces and includes the underlying theory for each interface at the end of the chapter The Magnetic Fields Interface which handles problems for magnetic fields with prescribed currents All three study types stationary frequency domain and time dependent are available The Magnetic Fields No Currents Interface which handles magnetic fields without currents When no currents are present the problem is easier to solve using the magnetic scalar potential The stationary and time dependent study types are available The Rotating Machinery Magnetic Interface is available with 2D models only It combines an out of plane magnetic fields magnetic vector potential formulation with a selection of predefined frames for prescribed rotation or rotation velocity it shares most of its features with the Magnetic Fields interface This interface requires that the geometry is created as an assembl
4. Using Coils in 3D Models Computing Coil Currents Solver Features in the COMSOL Multiphysics Reference Guide CHAPTER 5 Output Right click the Automatic Current Calculation node to add an Output subnode and specify the boundaries where the wires exit the domain The wire direction is forced to be orthogonal to the boundary Used in combination with the Input node it also defines the direction of the current flow from Input to Output THE MAGNETIC FIELD INTERFACES BOUNDARY SELECTION From the Selection list choose the boundaries to define the output for the automatic current calculation Using Coils in 3D Models Computing Coil Currents see Also Solver Features in the COMSOL Multiphysics Reference Guide Coil Group Domain 1 2D Axi The Coil Group Domain feature is available for 2D and 2D axisymmetric models The Coil Group Domain node adds an externally generated current density to the right hand side of the equation that the Magnetic Fields interface defines This current density is calculated in three different ways depending on whether a fixed current in each coil turn a total voltage drop across the coil or a fixed power into the coil is specified Right click to add Reversed Current Direction and Harmonic Perturbation nodes DOMAIN SELECTION From the Selection list choose the domains to define the coil group domain COIL GROUP DOMAIN Enter a Coil n
5. Multiphysics User s Guide and Convert in the COMSOL Multiphysics See Also Reference Guide CHAPTER 3 The imported geometry often consists of objects with very high aspect ratios which are hard to mesh with a free tetrahedron mesh generator As a result it is often necessary to use interactive meshing of the imported geometry in a by layer fashion The following section describes this procedure in general terms This procedure assumes that the top and bottom layers are metal layers All metal layers can often be meshed using swept meshing but dielectric layers usually cannot be meshed that way Begin by meshing from the bottom or top layer starting with a MODELING WITH THE AC DC MODULE boundary mesh Then mesh layer by layer where each metal layer gets a swept mesh and each dielectric layer with vias gets a free mesh The dielectric layers cannot use a swept mesh because the source and target boundaries usually do not look the same If there is a surrounding air domain it is usually not possible to use swept meshes for the metal layers either Use tetrahedrons or convert the swept mesh to tetrahedrons before meshing the surrounding domain Troubleshooting ECAD Import TUNING IMPORT SETTINGS Delete Interior Edges A complex layout produces a large number offaces that can be hard to render A simple way to reduce the number of faces is to clear the Keep interior boundaries check box in the ECAD import options
6. ibd Rds O Rg Figure 7 2 circuit for the MOS transistor The following equations are used to compute the relations between currents and voltages in the circuit 274 CHAPTER 7 THE ELECTRICAL CIRCUIT INTERFACE wkp L2 1 Avgs as 20 4 Uds Yas Uu las L 1 AVe Uh Uds Uth 0 Vas Ug lt O Ug Vgs Vrg t T fb v 4 ba NV _ Ubs rfe yom q lbs Vr There are also several capacitances between the terminals Coa CgaoW gsoW 1 59 Vox FoPg Cap 1 M 2 FoP 1 Foy I 1 Foa My My jo cm B The model parameters are as follows TABLE 7 2 MOS TRANSISTOR MODEL PARAMETERS PARAMETER DEFAULT DESCRIPTION 0 F m Bulk drain zero bias capacitance Capo 0 F m Gate drain overlap capacitance Caso 0 F m Gate source overlap capacitance Fo 0 5 Capacitance factor Ig le I3 Bulk junction saturation current Kp 2e 5 AIV Transconductance parameter L 50e 6 m Gate length 0 5 Bulk junction grading coefficient N Bulk junction ideality factor THEORY FOR THE ELECTRICAL CIRCUIT INTERFACE 275 276 TABLE 7 2 MOS TRANSISTOR MODEL PARAMETERS PARAMETER DEFAULT DESCRIPTION Pp 0 75 V Bulk junction potential 00 Bulk resistance Rp 00 Drain resistance Rps Inf Q Drain source resistance Rg 00
7. Coil Group Domain Features See Also Solver Features in the COMSOL Multiphysics Reference Guide 84 CHAPTER 3 MODELING WITH THE AC DC MODULE Lumped Parameters Lumped parameters are matrices describing electromagnetic properties such as resistance capacitance and inductance In the time harmonic case the lumped parameter matrix is either an impedance matrix or an admittance matrix depending on how the model is excited current or voltage In a static calculation only the resistive capacitive or inductive part of the lumped parameter matrix is obtained In this section e Calculating Lumped Parameters with Ohm s Law e Calculating Lumped Parameters Using the Energy Method Studying Lumped Parameters Lumped Parameter Conversion Calculating Lumped Parameters with Ohm s Law To calculate the lumped parameters there must be at least two electrodes in the system one of which must be grounded Either a voltage or a current can be forced on the electrodes After the simulation extract the other property or the energy and use it when calculating the lumped parameter There are several available techniques to extract the lumped parameters Which one to use depends on the physics interface the parameter of interest and how the model is solved The overview of the techniques in this section use a 4 by 4 matrix example for the lumped parameter matrix This represents a system of at least five electrodes where four a
8. Edges The path of the bond wire is represented only as a geometrical edge This option has the least complexity and does not produce a large number of mesh elements There might be some limitations when using these edges in modeling Blocks The bond wire is modeled as a solid with a square cross section Cylinders Same as above but with a circular cross section MODELING WITH THE AC DC MODULE Select the Manual control of elevations check box to manually position the layers in the z direction This check box is enabled when Grouping of geometries is set to By layer or No grouping When Manual control of elevations is not enabled the z positions of the layers are calculated automatically from the layer Thickness values The layer information from the file appears in the Layers to import table In addition to the layer Name the table includes the following columns The Type column This column declares the type of layer The import treats layers of different types differently For example a layer of type Metal converts to faces if the option Type of import is set to Metal shell The Outline type uses a union of the Objects in the selected layer as a PCB outline For ODB files the Drill type means that the objects in the layer define drilled via holes through the PCB For NETEX G files the vias are defined within each metal and dielectric layer The numbers in the Thickness column can be changed The Thickness colum
9. 1 Wirebonds are currently not supported with the grouping option set to All Using this option ignores all wirebonds Important ECAD Import Options ECAD IMPORT Most PCB layout files mainly contain definitions of 2D objects The Netex file also contains information about wirebonds The ECAD import engine first creates the 2D objects for each layer possibly grouped as one object Then it extrudes all the objects in each layer according to the information in the file GDS files contain no information about thickness so a default value of 100 um is used for all layers The ECAD Import allows the layer thickness to be changed prior to import Another alternative is to first import the objects into 2D and then manually extrude them to 3D IMPORTING ECAD FILES 103 104 CHAPTER 3 Right click the Geometry node to add an Import node Under Geometry import in the Import section decide the type of CAD file to import ECAD file GDS NETEX G or ECAD file ODB Enter the path to the file or click Browse to locate the file to import Before clicking the Import button consider the import options described below THE ECAD IMPORT OPTIONS There are a number of settings that control how to treat the information in the layout file The content of this section depends on the file type to be imported For GDS NETEX G files enter a net name in the Net to import blank means top net field if you want to import a single elect
10. 42 0 V oy fon tfo or as stated in the structural mechanics physics interfaces V ou f where f cf Forces on an Elastic Solid Surrounded by Vacuum or Air Consider a solid Material 1 surrounded by vacuum Material 2 It is natural to associate the surface force on the boundary between the materials with the solid In many applications air can be approximated by vacuum In practice the equation for the force balance also needs to include an external boundary force ge It is nonzero on those parts of the boundary where it is necessary to compensate for the contributions to the stress tensor that you are not interested in or do not have enough information on These contributions come from the influence of the adjacent domains By approximating the surroundings by vacuum or air the influence of these boundaries and their adjacent domains that are not part of our model on the electromagnetic fields are neglected On the boundary the following equations apply n T2 T 0 nT nT Sext The external boundary force Sext can represent the reaction force from another body that the solid is attached to The equations for the balance of forces on the solid now become V T f 0 nj T T Sy 0 For calculating the total force F on the solid these equations need to be integrated over the entire solid and the solid vacuum boundary V T f dV n4 T5 T g dS 0 Q 00 According to Gauss
11. CONSTRAINT SETTINGS To display this section click the Show button gt and select Advanced Physics Options Select a Constraint type Bidirectional symmetric or Unidirectional If required select the Use weak constraints check box CHAPTER 4 THE ELECTRIC FIELD INTERFACES Surface Charge Density The Surface Charge Density node provides the following surface charge boundary condition for exterior boundaries left and interior boundaries right n D p n D D Specify the surface charge density p at an outer boundary or at an interior boundary between two nonconducting media BOUNDARY SELECTION From the Selection list choose the boundaries to apply a surface charge density PAIR SELECTION If Surface Charge Density is selected from the Pairs menu choose the pair to define An identity pair has to be created first Ctrl click to deselect SURFACE CHARGE DENSITY Enter the value or expression for the Surface charge density o SI unit C m External Surface Charge Accumulation The External Surface Charge Accumulation node implements the boundary condition n D p where p is the solution of the following distributed ODE on the boundary ai n J n J where n J is the normal component of the total ion current density on the wall and n J is the normal component of the total electron current density on the wall which are feature inputs BOUNDARY SELECTION From the Selection list
12. Change Thickness Out of Plane SWEEP SETTINGS Select the Activate terminal sweep check box to switch on the sweep and invoke a parametric sweep over the terminals Enter a Sweep parameter name to assign a specific name to the variable that controls the terminal number solved for during the sweep The Sweep parameter name must also be declared as a model parameter The default is PortName In the Model Builder right click Global Definitions and choose Parameters and enter the chosen name and assign to it a temporary Expression of unity into the Parameters table Only a temporary expression needs to be entered at this stage During the analysis process the solver assigns a proper value to this parameter The 0 generated lumped parameters are in the form of capacitance matrix Important elements The terminal settings must consistently be of either fixed voltage or fixed charge type DISCRETIZATION To display this section select click the Show button and select Discretization Select an element order for the Electric potential Linear Quadratic the default Cubic Quartic or in 2D only Quintic Specify the Value type when using splitting of complex variables Real or Complex the default THE ELECTROSTATICS INTERFACE DEPENDENT VARIABLES The dependent variable field variable is for the Electric potential V The name can be changed but the names of fields and dependent variables must be uniqu
13. LE 3D The Electrostatic Point Dipole represents the limiting case of zero separation distance between two equally strong point sources of opposing signs while maintaining the product between separation distance and source strength at a fixed value p The dipole moment is a vector entity with positive direction from the negative charge to the positive one POINT SELECTION From the Selection list choose the points also on axis to add an electrostatic point dipole ELECTROSTATIC POINT DIPOLE Select a Dipole specification Magnitude and direction the default or Electric dipole moment f Magnitude and direction is selected enter coordinates for the Electric dipole moment direction n and the Electric dipole moment magnitude p SI unit C m fDipole moment is selected enter coordinates for the Electric dipole moment p SI unit C m CHAPTER 4 THE ELECTRIC FIELD INTERFACES The Electric Currents Interface The Electric Currents interface found under the AC DC branch X in the Model Wizard has the equations boundary conditions and current sources for modeling electric currents in conductive media solving for the electric potential Current Conservation is the main feature which adds the equation for the electric potential and provides a settings window for defining the electrical conductivity as well as the constitutive relation for the electric displacement field and its associated material
14. NODE CONNECTIONS Set two Node names for the connection nodes for the voltage source The first node in pair represents the positive reference terminal If the ground node is involved the convention is to use zero for this DEVICE PARAMETERS Enter the voltage Gain and the Device any two pin device name The resulting voltage is this number multiplied by the control current through the named Device any two pin device Thus it formally has the unit of resistance Current Controlled Current Source The Current Controlled Current Source node lt gt connects a current controlled current source between two nodes in the electrical circuit The input control current is the one flowing through a named device that must be a two pin device NODE CONNECTIONS Specify two Node names for the connection nodes for the current source The first node in a pair represents the positive reference terminal from which the current flows through the source to the second node If the ground node is involved the convention is to use zero for this DEVICE PARAMETERS Enter the current Gain and the Device any two pin device name The resulting current is this number multiplied by the control current through the named Device any two pin device Subcircuit Definition The Subcircuit Definition node 227 is used to define subcircuits Right click a subcircuit definition node to add all circuit features available except for the s
15. Relative permeability Nonlinear BH curves Refractive index The AC DC database is included with this module and contains electromagnetic and other material properties for these materials PREDEFINED MATERIALS Copper Soft Iron without losses Soft Iron with losses Quartz Graphite Graphite felt Silicon Carbide Some properties depend on the magnetic flux density location or temperature The database contains depending on the material and in addition to the more common material properties the following properties PREDEFINED PROPERTIES Remnant flux density Reference temperature Temperature coefficient Nonlinear BH curves Resistivity at reference temperature USING THE AC DC MATERIAL DATABAsE 299 300 CHAPTER 9 MATERIALS 0 Glossary This Glossary of Terms contains finite element modeling terms in an electromagnetics context For mathematical terms as well as geometry and CAD terms specific to the COMSOL Multiphysics software and documentation please see the glossary in the COMSOL Multiphysics User s Guide For references to more information about a term see the index 301 302 Glossary of Terms anisotropy Variation of material properties with direction constitutive relation The relation between the D and E fields and between the B and H fields These relations depend on the material properties eddy currents Induced currents normal to a time varying magnetic
16. Type of port section for the Lumped Port node 1 For 2D and 2D axisymmetric models and when In plane vector potential 2D or Three component vector potential is selected a Gauge Fixing for A field i subnode can be added to the Amp re s Law node 2D Axi THE MAGNETIC FIELDS INTERFACE 181 182 THICKNESS Enter a value or expression for the global Out of plane thickness d SI unit m The default value of 1 m is typically not representative for a thin domain Instead it describes a unit thickness that makes the 2D equation identical to the equation used for 3D models 2D Use the Change Thickness Out of Plane node described for the Electrostatics interface to define specific geometric entities for example domains instead of a global setting for the thickness SWEEP SETTINGS Enter a Reference impedance Zef SI unit The default is 50 Select the Activate port sweep check box to switch on the sweep and invoke a parametric sweep over the ports Enter a Sweep parameter name to assign a specific name to the variable that controls the port number solved for during the sweep The generated lumped parameters are in the form of capacitance matrix elements The port settings must consistently be of either fixed voltage or fixed charge type The default is PortName The lumped parameters are subject to Touchstone file export Enter a file path or Browse for a file Select an Output format for the Touchst
17. U c a9 9 i uU 4 5 8 re E gt gt 5 wn Electrostatics es x y 2 Electric ec V x x v VN Currents y y 2 2 Electric ecs V x x vN N N Currents y y Shell 2 2 Magnetic mf A x x x x V v v v Fields z 2 2 2 Magneticand mef VA x x x x v NN Electric Fields y y z 2 2 2 ABOUT THE AC DC MODULE 17 TABLE 1 1 AC DC MODULE DEPENDENT VARIABLES FIELD COMPONENTS AND PRESET STUDY AVAILABILITY 3 PHYSICS TAG DEPENDENT FIELD PRESET STUDIES INTERFACE VARIABLES COMPONENTS gt o 2 E E o a z 4 z gt zr lt 2 2 a 5 gt 4 gt lt a a m v mj 49 d 2 qo 4 amp ui gt a a a 2 gt z gt gt gt lt o E 2 2 52 2 2 a 2 o u 2 2 2 a 5 42 2 2 o U U c o a 9 o lt 3 4 15 E g Fd 7 H Magnetic mfnc Vm x Fields No y Currents 2 Rotating rmm x z jz W iW Machinery y Magnetic Electrical cir not NN Circuit applicable Induction ih x x x x Ww N V Heating y Z 2 2 2 These are the nonzero field components For Cartesian coordinates these are indexed by x y and 2 for cylindrical coordinates 7 and z are used Custom studies are also available based on the interface for example Eigenfrequency and Eigenvalue The Model Build
18. Zero Charge The Zero Charge node adds the condition that there is zero charge on the boundary so that n D 0 This boundary condition is also applicable at symmetry boundaries where the potential is known to be symmetric with respect to the boundary This is the default boundary condition at exterior boundaries At interior boundaries it means THE ELECTROSTATICS INTERFACE 125 126 that no displacement field can penetrate the boundary and that the electric potential is discontinuous across the boundary BOUNDARY SELECTION From the Selection list choose the boundaries to apply a zero charge condition PAIR SELECTION If Zero Charge is selected from the Pairs menu choose the pair to define An identity pair has to be created first Ctrl click to deselect Thin Low Permittivity Gap Use the Thin Low Permittivity Gap node 808 n D q Vi Vo S Ee n D q Ve VD S to model a thin gap of a material with a small permittivity compared to the adjacent domains The layer has the thickness d and the relative permittivity The indices 1 and 2 refer to the two sides of the boundary BOUNDARY SELECTION From the Selection list choose the boundaries to apply a thin low permittivity gap condition MATERIAL TYPE Select a Material type Solid Non solid or From material PAIR SELECTION When Thin Low Permittivity Gap is selected from the Pairs menu choose the pair to define An identity pair has to
19. displacement currents can be neglected Also assume that the objects modeled are not moving v 0 so that there is no contributions from Lorentz forces These are treated later on THE ELECTROMAGNETIC STRESS TENSOR To apply the stress tensor in air to calculate the total force and torque on a magnetizable rod close to a permanent magnet see Permanent Magnet Model Model Library path ACDC Module Magnetostatics permanent magnet The expressions for the stress tensor in a general electromagnetic context stems from a fusion of material theory thermodynamics continuum mechanics and electromagnetic field theory With the introduction of thermodynamic potentials for mechanical thermal and electromagnetic effects explicit expressions for the stress tensor can be derived in a convenient way by forming the formal derivatives with respect to the different physical fields Ref 1 and Ref 3 Alternative derivations can be made for a vacuum Ref 4 but these cannot easily be generalized to polarized and magnetized materials Air and Vacuum For air the stress tensor is E T p1 2E E z B B I 4EE BB 2 2 Ho where p is the air pressure J is the identity 3 by 3 tensor or matrix and E and B are 3 by 1 vectors In this expression of the stress tensor air is considered to be nonpolarizable and nonmagnetizable When air is approximated by vacuum p 0 CHAPTER 2 REVIEW OF ELECTROMAGNETICS This expre
20. where J is an externally generated current density Maxwell Amp re s law for quasi static systems is consequently extended to VxH c E vx whereas Faraday s law remains unchanged Material Properties Until now there has only been a formal introduction of the constitutive relations These seemingly simple relations can be quite complicated at times There are four main groups of materials where they require some consideration A given material can belong to one or more of these groups The groups are Inhomogeneous materials Anisotropic materials Nonlinear materials Dispersive materials A material can belong to one or more of these groups CHAPTER 2 REVIEW OF ELECTROMAGNETICS INHOMOGENEOUS MATERIALS Inhomogeneous materials are the least complicated An inhomogeneous medium is one in which the constitutive parameters vary with the space coordinates so that different field properties prevail at different parts of the material structure ANISOTROPIC MATERIALS For anisotropic materials the field relationships at any point differ for different directions of propagation This means that a 3 by 3 tensor is necessary to properly define the constitutive relationships If this tensor is symmetric the material is often referred to as reciprocal In such cases rotate the coordinate system such that a diagonal matrix results If two of the diagonal entries are equal the material is uniaxially anisotropic
21. MODEL INPUTS This section contains field variables that appear as model inputs if the current settings include such model inputs By default this section is empty If a linear temperature relation is added for the conductivity then define the source for the temperature From the Temperature list select an existing temperature variable from another physics interface if available or select User defined to define a value or expression for the temperature SI unit K in the field that appears underneath the list CONDUCTION CURRENT EI See the settings for Conduction Current under Amp re s Law for the Magnetic Fields interface Note ELECTRIC FIELD EI See the settings for Electric Field under Charge Conservation described for the Electrostatics interface Note MAGNETIC FIELD See the settings for Magnetic Field under Amp re s Law for the Magnetic Fields interface with one difference Ei Note HB curve Do not select this option for time harmonic modeling as it is not relevant when using the Induction Heating interface THE INDUCTION HEATING INTERFACE 287 288 8 HEAT CONDUCTION The default Thermal conductivity k SI unit W m K uses values From material If User defined is selected choose Isotropic Diagonal Symmetric or Anisotropic based on the characteristics of the thermal conductivity and enter other values or expressions in the field or matrix Th
22. Note 122 CHAPTER 4 THE ELECTRIC FIELD INTERFACES The Circuit type should not be used for lumped parameter calculations 1 For the terminal also enter the value of the electric potential or current charge used if required If zero is entered the terminal acts as a floating Important electrode The Floating Potential node is used when modeling a metallic electrode at floating potential The electrode may have a charge Qo deposited on it For circuit connections use the Terminal feature instead BOUNDARY SELECTION From the Selection list choose the boundaries to define the floating electrode PAIR SELECTION If Floating Potential is selected from the Pairs menu choose the pair to define An identity pair has to be created first Ctrl click to deselect FLOATING POTENTIAL Specify an optionally non zero Charge Q SI unit C CONSTRAINT SETTINGS To display this section click the Show button z and select Advanced Physics Options Select a Constraint type Bidirectional symmetric or Unidirectional If required select the Use weak constraints check box Electric Displacement Field The Electric Displacement Field node adds the following electric displacement boundary condition n D n Dy It specifies the normal component of the electric displacement field at a boundary BOUNDARY SELECTION From the Selection list choose the boundaries to use the normal component of the displacement field
23. The Quasi Static Approximation and the Lorentz Term consequence of Maxwell s equations is that changes in time of currents and charges are not synchronized with changes of the electromagnetic fields The changes of the fields are always delayed relative to the changes of the sources reflecting the finite speed of propagation of electromagnetic waves Under the assumption that this effect can be ignored it is possible to obtain the electromagnetic fields by considering stationary currents at every instant This is called the quasi static approximation The approximation is valid provided that the variations in time are small and that the studied geometries are considerably smaller than the wavelength Ref 5 FUNDAMENTALS OF ELECTROMAGNETICS 35 36 The quasi static approximation implies that the equation of continuity can be written as V J 0 and that the time derivative of the electric displacement 00 0 can be disregarded in Maxwell Amp re s law There are also effects of the motion of the geometries Consider a geometry moving with velocity v relative to the reference system The force per unit charge F q is then given by the Lorentz force equation E vxB This means that to an observer traveling with the geometry the force on a charged particle can be interpreted as caused by an electric field E E v x B Ina conductive medium the observer accordingly sees the current density J o E vx B J
24. Typographical Conventions What Can the AC DC Module Do The AC DC Module provides a unique environment for simulation of AC DC electromagnetics in 2D and 3D The module is a powerful tool for detailed analysis of coils capacitors and electrical machinery With this module you can run static quasi static transient and time harmonic simulations in an easy to use graphical user interface The available physics interfaces cover the following types of electromagnetics field simulations Electrostatics Electric currents in conductive media Magnetostatics Low frequency electromagnetics Material properties include inhomogeneous and fully anisotropic materials media with gains or losses and complex valued material properties Infinite elements makes it possible to model unbounded domains In addition to the standard results and visualization functionality the module supports direct computation of lumped parameters such as capacitances and inductances as well as electromagnetic forces Like all COMSOL modules there is a library of ready to run models that make it quicker and easier to analyze discipline specific problems In addition any model you develop is described in terms of the underlying partial differential equations offering a unique way to see the underlying physical laws of a simulation INTRODUCTION The interfaces are fully multiphysics enabled couple them to any other interface in COMSOL Multiphys
25. statics is not to be interpreted literally it is the observation time or time scale at which the applied excitation changes is short compared to the charge relaxation time and that the electromagnetic wavelength and skin depth are very large compared to the size of the domain of interest Ifyou do not know whether to use the Electric Currents or the Electrostatics interface which both solve for the scalar electric potential V consider using an explicit charge transport model See Charge Relaxation Theory Electrostatics Equations Under static conditions the electric potential V is defined by the relationship VV Combining this equation with the constitutive relationship D P between the electric displacement D and the electric field E it is possible to represent Gauss law as the following equation V egVV P p In this equation the physical constant o SI unit F m is the permittivity of vacuum P SI unit C m is the electric polarization vector and p SI unit C m is a space charge density This equation describes the electrostatic field in dielectric materials For in plane 2D modeling the Electrostatics interface assumes a symmetry where the electric potential varies only in the x and y directions and is constant in the z direction This implies that the electric field E is tangential to the xy plane With this symmetry the same equation is solved as in the 3D case The interface s
26. theorem CHAPTER 2 REVIEW OF ELECTROMAGNETICS n T dS 0 004 this means that the external force f feed ZextdS 20 is needed to balance the term for the boundary integral of the stress tensor in the surrounding vacuum n T 4S 00 to keep the solid stationary That is F4 0 If the external forces are suddenly removed the solid is no longer stationary but F causes the solid to begin to move with an initial acceleration according to 2 d r ma 201 2 di where is the total mass and a is the acceleration of the solid To summarize the total force F is computed as a boundary integral of the stress tensor in vacuum on the outside of the solid To obtain this result the contribution from the air pressure gradient has been neglected This is equivalent of assuming that 0 A more detailed treatment shows that the pressure gradient contributes with a lifting buoyancy force on the solid Torque The torque in the case of Forces on an Elastic Solid Surrounded by Vacuum or Airis given by Mo r rg x ni T3 dS 00 where rq is a point on the axis of rotation This follows from a derivation similar to the one made for forces ELECTROMAGNETIC FORCES 43 44 Forces in Stationary Fields The electromagnetic fields are stationary if Bo ot aD _ a that is if the fields vary so slowly that the contributions from induced currents and
27. where in o E B the dependence of E and B has not been separated out Thus o is not a purely mechanical stress tensor in this general case Different material models give different appearances of o E B The electromagnetic contributions to o E B typically represent pyroelectric pyromagnetic piezoelectric piezomagnetic dielectric and magnetization effects The expression for the stress tensor in vacuum air and pure conductors can be derived from this general expression by setting M P 0 T must be symmetric The terms EP and MB7 are symmetric in the case ofa linear dielectric and magnetic material because Here the magnetic susceptibility differs slightly from the classical y The other explicit terms are all symmetric as is o E B In the general case this imposes constraints on the properties of o E B For a nonlinear material o E B might need to include terms such as or MB to compensate for asymmetric EP or MBT To instantiate the stress tensor for the general elastic case an explicit material model including the magnetization and polarization effects is needed Such material models can easily be found for piezoelectric materials Ref 3 Forces in a Moving Body Calculating forces in moving objects is important especially for electric motors and other moving electromagnetic devices When performing the computations in a coordinate system that moves with the object the electromagnetic f
28. If none of the elements has the same value the material is biaxially anisotropic Ref 2 Anisotropic parameters are needed for example to examine permittivity in crystals Ref 2 and when working with conductivity in solenoids NONLINEAR MATERIALS Nonlinearity is the effect of variations in permittivity or permeability with the intensity of the electromagnetic field Nonlinearity also includes hysteresis effects where not only the current field intensities influence the physical properties of the material but also the history of the field distribution DISPERSIVE MATERIALS Dispersion describes changes in a wave s velocity with wavelength In the frequency domain dispersion is expressed with a frequency dependence of the constitutive laws About the Boundary and Interface Conditions To get a full description of an electromagnetics problem boundary conditions must be specified at material interfaces and physical boundaries At interfaces between two media the boundary conditions can be expressed mathematically as n x E E 0 ns D D3 p J 5 0 Ny x H B Bj FUNDAMENTALS OF ELECTROMAGNETICS 37 38 where p and J denote surface charge density and surface current density respectively and ng is the outward normal from medium 2 Of these four conditions only two are independent This is an overdetermined system of equations so it needs to be reduced First select either
29. Liquids and Gases available with specific modules MEMS Xj Piezoelectric 5s Piezoresistivity User defined material database library 1 User Defined Library 7 MATERIALS All COMSOL modules have predefined material data available to build models The most extensive material data is contained in the separately purchased Material Library but all modules contain commonly used or module specific materials For example the Built In database is available to all users but the MEMS database is included with the MEMS Module and Structural Mechanics Module Also create custom materials and material libraries by researching and entering material properties All the material databases including the Material Library are accessed from the Material Browser These databases are briefly described below RECENT MATERIALS From the Recent Materials folder select from a list of recently used materials with the most recent at the top This folder is available after the first time a material is added to a model MATERIAL LIBRARY An optional add on database the Material Library contains data for over 2500 materials and 20 000 property functions BUILT IN Included with COMSOL Multiphysics the Built In database 3 contains common solid materials with electrical structural and thermal properties Predefined Built In Materials for all COMSOL Modules in the COMSOL See Also Multiphy
30. POROUS MEDIA This section is always available and is used to define the mixture model for the domain Select the Number of materials up to 5 to be included in the mixture model For each material Material Material 2 and so on select either Domain material to use the material specified for the domain or one of the other materials specified in the Materials node For each material enter a Volume fraction 04 02 and so on The Volume fractions specified for the materials should add to 1 in normal cases Each subsequent volume fraction is automatically set to 1 04 The availability of the Effective Electrical Conductivity Effective Relative Permittivity and Effective Relative Permeability sections depend on the g material properties used in the interface Moreover these sections are Note only active if the corresponding material property in the parent feature is set to Porous media EFFECTIVE ELECTRICAL CONDUCTIVITY EFFECTIVE RELATIVE PERMITTIVITY OR EFFECTIVE RELATIVE PERMEABILITY Select the averaging method to use in the mixture model between the volume average of the material property the volume average ofits inverse or the power law For each material specify either From material to take the value from the corresponding material specified in the Porous Media section or User defined to manually input a value Q Effective Relative Permeability in Porous Media and Mixtures See Also Effective
31. See Also Guide Computing Coil Currents In 3D models it is possible to solve an eigenvalue problem for the current flow in a Multi Turn Coil Domain that gives the current density likely produced by a bundle of conductive wires The best results are obtained when the coil has a constant cross section without sharp bends and bottlenecks The eigenvalue problem is loosely based on the equation for the incompressible fluid flow with some modifications and is solved by the specialized Coil Current Calculation study step If e is the vector field representing the direction of the wires the equation solved is V sVe Xe where s is a square 3 by 3 matrix with 1 on the diagonal and a scaling value default 0 1 in the other elements This off diagonal scaling value can be changed in the Automatic Current Calculation feature but the default value should give good results in most cases The eigenvalue solver solves for the eigenfunction with eigenvalue closest to zero The current profile for this eigenfunction depends on the shape of the domain and the boundary conditions applied These boundary conditions are of two kinds Electric Insulation that forces the normal component ofthe current flow to the boundary to be zero n e 0 and Input or Output that set the tangential component to zero n x e 0 The Input and Output features have the same effect on the equation system but the Input feature also is used to determine the boundary
32. but the Conduction Current section is not available The material properties specified in these sections should be the homogenized electric and magnetic properties of the materials insulator and wires present in the coil domain Right click the node to add a Reference Edge subnode as required In 2D and 2D axisymmetric models the wires are assumed to be in the 2D out of plane direction 2D Axi a See Coil Domains in the modeling section to learn more about using this node See Also MAGNETIC FIELDS INTERFACE ADVANCED FEATURES 199 200 DOMAIN SELECTION From the Selection list choose the domains to define the multi turn coil domain MODEL INPUTS This section contains field variables that appear as model inputs if the current settings include such model inputs By default this section is empty COORDINATE SYSTEM SELECTION The Global coordinate system is sclected by default The Coordinate system list contains any additional coordinate systems that the model includes MATERIAL TYPE Select a Material type Non solid the default Solid or From material COIL TYPE This section is available for 3D models and is used to specify the coil geometry the direction of the wires X Select a Coil Type Linear Circular Numeric or User defined and then go to 3b the sections that follow Also see Using Coils in 3D Models for more information about the options 0 In three out of four
33. choose the boundaries to apply a surface charge accumulation PAIR SELECTION If External Surface Charge Accumulation is selected from the Pairs menu choose the pair to define An identity pair has to be created first Ctrl click to deselect THE ELECTROSTATICS INTERFACE 119 120 EXTERNAL SURFACE CHARGE ACCUMULATION Enter values or expressions for the Normal ion current density n J SI unit A m and the Normal electron current density n J SI unit A m Dielectric Shielding The Dielectric Shielding node adds dielectric shielding as a boundary condition It describes a thin layer with thickness d and a bulk relative permittivity that shields the electric field n D V 9 d ViV rss Use this boundary condition when approximating a thin domain with t boundary to reduce the number of mesh elements ip BOUNDARY OR EDGE SELECTION From the Selection list choose the geometric entity boundaries or edges to apply a dielectric shielding as the condition PAIR SELECTION If Dielectric Shielding is selected from the Pairs menu choose the pair to define An identity pair has to be created first Ctrl click to deselect MATERIAL TYPE Select a Material type Solid Non solid or From material ELECTRIC SHIELDING The default is to take the Relative permittivity unitless values From material It takes it from the adjacent domains if not explicitly defined If User defined is selec
34. on which to integrate to compute the total current For this reason only one Input boundary is allowed for each Automatic Current Calculation node For a correct setup one Input and at least one Output feature are required for the coil if applied on external boundaries or as an alternative a single Input feature can be applied to an internal boundary to create a closed loop coil In any case an Electric Insulation feature must be applied on all the external boundaries of the coil domain Once the vector field e is obtained from the eigenvalue problem the coil current density vector field is computed by normalizing e and if needed changing its sign so that the current flow is inward at the Input feature It is advised to always plot the coil direction variable after solving the eigenvalue problem to verify that the current flow has the intended profile COIL DOMAINS 83 The Coil Current Calculation study step must precede the main study step for example a Stationary study step in which the Multi Turn Coil Note Domain is used The Coil Current Calculation study step solves for the current flow in the coil feature whose Coil Name is the same as the name specified in the study step If more Numeric coils are present in the interface an Important equivalent number of study steps must be solved and each of them must precede the main study step About the Single Turn Coil Domain Multi Turn Coil Domain and
35. order Also see Table 6 1 for a list of interior and exterior boundary conditions Most features are described for the Magnetic Fields and Electrostatics interfaces e Amp re s Law e Amp re s Law and Current Conservation Coil Group Domain Edge Current Electric Insulation Electric Point Dipole Electric Point Dipole on Axis Electric Potential External Current Density Floating Potential Force Calculation Gauge Fixing for A field Ground Impedance Boundary Condition Initial Values Lumped Port Magnetic Field Magnetic Insulation the default boundary condition 250 CHAPTER 6 THE MAGNETIC AND ELECTRIC FIELDS INTERFACE Magnetic Point Dipole Magnetic Potential Multi Turn Coil Domain Normal Current Density Perfect Magnetic Conductor Periodic Condition Single Turn Coil Domain Surface Current Terminal Thin Low Permeability Gap Transition Boundary Condition Velocity Lorentz Term Sector Symmetry In the COMSOL Multiphysics User s Guide About Infinite Element Domains and Perfectly Matched Layers Continuity on Interior Boundaries See Identity and Contact Pairs Specifying Boundary Conditions for Identity Pairs Destination Selection The links to the features described in the COMSOL Multiphysics User s Guide do not work in the PDF only from within the online help Important To locate an
36. 3 MODELING WITH THE AC DC MODULE Infinite Elements In this section Modeling Unbounded Domains Known Issues When Modeling Using Infinite Elements For more information about this feature see About Infinite Element Domains and Perfectly Matched Layers in the COMSOL Multiphysics Note User s Guide Modeling Unbounded Domains Many environments modeled with finite elements are unbounded or open meaning that the fields extend toward infinity The easiest approach to modeling an unbounded domain is to extend the simulation domain far enough that the influence of the terminating boundary conditions at the far end becomes negligible This approach can create unnecessary mesh elements and make the geometry difficult to mesh due to large differences between the largest and smallest object Another approach is to use infinite elements There are many implementations of infinite elements available and the elements used in this module are often referred to as mapped infinite elements see Ref 6 This implementation maps the model coordinates from the local finite sized domain to a stretched domain The inner boundary of this stretched domain coincides with the local domain but at the exterior boundary the coordinates are scaled toward infinity The principle can be explained in a one coordinate system where this coordinate represents Cartesian cylindrical or spherical coordinates Mapping multiple coordinate
37. Ako Transistor Diode The Diode device model 44 is a large signal model for a diode It is an advanced device model and no thorough description and motivation of the many input parameters is attempted here The interested reader is referred to Ref 2 for more details on semiconductor modeling within circuits Many device manufacturers provide model parameters for this diode model For any particular make of diode the device manufacturer should be the primary source of information NODE CONNECTIONS Specify two Node names for the positive and negative nodes for the Diode device If the ground node is involved the convention is to use zero for this MODEL PARAMETERS Specify the Model Parameters Reasonable defaults are provided but for any particular diode the device manufacturer should be the primary source of information For an explanation of the Model Parameters see Diode See Also THE ELECTRICAL CIRCUIT INTERFACE 265 266 External I vs U The External I vs U node u connects an arbitrary voltage measurement for example a circuit terminal or circuit port boundary or a coil domain from another physics interface as a source between two nodes in the electrical circuit The resulting circuit current from the first node to the second node is typically coupled back as a prescribed current source in the context of the voltage measurement NODE CONNECTIONS Specify the two Node names for the connecting no
38. B v x ug Vx A M ov x Vx A The term involving the velocity only applies in the 2D and 2D axisymmetric formulations 2D Axi 242 CHAPTER 5 THE MAGNETIC FIELD INTERFACES Theory for the Magnetic Fields No Currents Interface In magnetostatic problems where no electric currents are present it is possible to formulate and solve the problem using a scalar magnetic potential In a current free region you have V x 0 This implies that the magnetic scalar potential V4 can be defined from the relation V Vm which is analogous to the definition of the electric potential for static electric fields Using the constitutive relation the equation V B 0 becomes V ugVVa 0 5 5 The Magnetic Fields No Currents Interface uses this equation for modeling of magnetostatics in the absence of electric currents In planar 2D the dynamic formulations also involves the thickness d in the z direction V d ugVVa 0 THEORY FOR THE MAGNETIC FIELDS NO CURRENTS INTERFACE 243 244 CHAPTER 5 THE MAGNETIC FIELD INTERFACES The Magnetic and Electric Fields Interface In this chapter the Magnetic and Electric fields interface found under the AC DC branch Xx in the Model Wizard is described The Magnetic and Electric Fields Interface Theory for the Magnetic and Electric Fields Interface 245 The Magnetic and Electric Fields Interface Th
39. By default the Electrical conductivity oj SI unit S m for the fluid is defined From material This uses the value of the conductivity of the material domain If User defined is selected enter a value or expression If another type of temperature dependence is used other than a linear temperature relation enter any expression for the conductivity as a function of temperature Enter these unitless parameters as required e Cementation exponent m Saturation exponent 7 Fluid saturation ST Enter Porosity to set up the volume fraction of the fluid Porous Media This subfeature is available only when Porous media is selected as the material parameter in the parent feature node on any AC DC interface for example the Charge Conservation or Current Conservation nodes Note Then right click the Charge Conservation or Current Conservation nodes to add this subnode Use the Porous Media subfeature to specify the material properties of a domain consisting of a porous medium using a mixture model The Porous Media subfeature is available for all the AC DC physics interfaces and depending on the specific interface can be used to provide a mixture model for the electric conductivity o the relative dielectric permittivity amp or the relative magnetic permeability DOMAIN SELECTION From the Selection list choose the domains to define the porous media THE ELECTRIC CURRENTS INTERFACE 141 142
40. CONTENTS Electromagnetic Energy and Virtual Work Electromagnetic Quantities References for the AC DC Interfaces Chapter 3 Modeling with the AC DC Module Preparing for Modeling What Problems Can You Solve Selecting the Space Dimension for the Model Geometry Simplifying the Geometry Using Boundary Conditions Applying Electromagnetic Sources Selecting a Study Type 2D Field Variables Meshing and Solving Infinite Elements Modeling Unbounded Domains Known Issues When Modeling Using Infinite Elements Force and Torque Computations Calculating Electromagnetic Forces and Torques Model Examples Electromagnetic Forces Coil Domains 50 52 54 56 57 58 60 6l 62 63 63 65 65 68 70 70 7l 72 About the Single Turn Coil Domain Multi Turn Coil Domain and Coil Group Domain Features About the Coil Name Coil Excitation Lumped Parameter Calculations Using Coils in 3D Models Computing Coil Currents Lumped Parameters Calculating Lumped Parameters with Ohm s Law 72 74 74 78 80 83 85 85 Calculating Lumped Parameters Using the Energy Method 87 Studying Lumped Parameters 88 Lumped Parameter Conversion 89 Lumped Ports with Voltage Input 90 About Lumped Ports a a a a s l l s 90 LumpedPortParameters 9l S Parameters and P
41. Conductivity in Porous Media and Mixtures External Current Density The External Current Density node adds an externally generated current density Je which appears in Ohm s law J oE Jd and in the equation that the interface defines CHAPTER 4 THE ELECTRIC FIELD INTERFACES DOMAIN SELECTION From the Selection list choose the domains to define an external current density El For the Electric Currents Shell interface select boundaries instead of domains Note COORDINATE SYSTEM SELECTION The Global coordinate system is selected by default The Coordinate system list contains any additional coordinate systems that the model includes EXTERNAL CURRENT DENSITY Based on space dimension enter the coordinates x y and z for 3D models for example of the External current density J SI unit A m Current Source The Current Source node adds a distributed current source Qj in the equation that the interface defines Use this feature with caution as it may violate the current conservation law that is inherent in Maxwell Ampe re s law DOMAIN SELECTION From the Selection list choose the domains to define a current source CURRENT SOURCE Enter a value or expression for the Current source 6 SI unit A m Initial Values The Initial Values node adds an initial value for the electric potential that can serve as an initial condition for a transient simulation or as an initial guess for a n
42. Contents Chapter Introduction About the AC DC Module 14 What Can the AC DC Module Do 14 AC DC Module Physics 15 AC DC Module Study Availability 17 The Model Builder Show and Hide Physics Options 18 Where Do Access the Documentation and Model Library 20 Typographical 22 Overview of the User s Guide 25 Chapter 2 Review of Electromagnetics Fundamentals of Electromagnetics 30 Maxwel s Equations a ew ee 30 Constitutive 3 Potentials ise mone ae Ee ae Nora 33 Reduced Potential PDE 33 Electromagnetic 34 The Quasi Static Approximation and the Lorentz Term 35 Material _ 36 About the Boundary and Interface Conditions 37 Phasorsic s lt 2 2o uu em Vei UR une ot iuh ae 38 References for Electromagnetic Theory 39 Electromagnetic Forces 40 Overview of Forces in Continuum Mechanics 40 Forces on an Elastic Solid Surrounded by Vacuum or Air 42 26 tn eos ar Bee ytd ves s on A AS Forces in Stationary Fields 44 Forces in a 47 CONTENTS 3 4
43. Default to reset to display only the Equation and Override and Contribution sections For most physics nodes both the Equation and Override and Contribution sections are always available Click the Show button z and then select Equation View to display the Equation View node under all physics nodes in the Model Builder Availability of each feature and whether it is described for a particular physics node is based on the individual physics selected For example the Discretization Advanced Settings Consistent Stabilization and Inconsistent Stabilization sections are often described individually throughout the documentation as there are unique settings SECTION CROSS REFERENCE LOCATION IN COMSOL MULTIPHYSICS USER GUIDE OR REFERENCE GUIDE Show More Options and Showing and Expanding Advanced User s Guide Expand Sections Physics Sections The Model Builder Window Discretization Show Discretization User s Guide Element Types and Discretization Finite Elements Reference Guide Discretization of the Equations ABOUT THE AC DC MODULE 19 20 SECTION CROSS REFERENCE LOCATION IN COMSOL MULTIPHYSICS USER GUIDE OR REFERENCE GUIDE Discretization Splitting Compile Equations Reference Guide of complex variables Pair Selection Identity and Contact Pairs User s Guide Specifying Boundary Conditions for Identity Pairs Consistent and Show Stabilization User s Guide Inconsisten
44. Geometry Troubleshooting ECAD Import Overview of the ECAD Import This section explains how to import ECAD files into COMSOL Multiphysics An ECAD file can for example be a 2D layout of a printed circuit board PCB that is imported and converted to a 3D geometry EXTRUDING LAYERS A PCB layout file holds information about all traces in several 2D drawings or layers During import each 2D layer is extruded to a 3D object so that all traces get a valid thickness A standard extrude operation requires that the source plane is identical to the destination plane This makes it impossible to extrude an entire PCB with several layers where the source and destination planes in almost all cases do not match It is possible to do several extrude operations one for each layer For complex PCBs it is not easy to put these layers together and it might take a very long time to go from the Geometry node to the Material node or a physics interface node in the Model Builder In some situations this operation might fail As a result of these performance issues the ECAD Import has its own extrude operation that automatically connects non matching planes In one operation this functionality extrudes and connects all layers so there is only one geometry object after the import With only one object it is easy to switch to the physics modes Use this special extrude operation when using the grouping option All MODELING WITH THE AC DC MODULE T
45. In the most simple case that is for magnetostatics Amp re s law for the magnetic vector potential reads V x ug V x A M Jd THEORY OF MAGNETIC AND ELECTRIC FIELDS 237 238 CHAPTER 5 The equation for y is used to impose the Coulomb gauge V 0 However to get a closed set of equations y must be able to affect the first equation and this is obtained by modifying the first equation to V x u V xA M J Vy The additional term on the right hand side can be seen as a Lagrange multiplier that not only imposes the Coulomb gauge but also eliminates any divergence in the externally generated current density J and makes it comply with the current continuity inherent in Amp re s law The gauge fixing feature similarly imposes the Coulomb gauge also for the dynamic frequency domain study type in the Magnetic and Electric Fields interface For the dynamic frequency domain and time dependent study types for the Magnetic Fields interface the gauge is already determined so the gauge fixing feature is not allowed to impose the Coulomb gauge but reduces to help imposing current conservation The first one is for the frequency domain study and the second one is for the time dependent study type V J 0 0 The main benefit of using this kind of divergence constraint is improved numerical stability especially when approaching the static limit when the inherent gauge deteriorates Ungauged Form
46. Reactance X al z imag Zooil Admittance _ 1 Y adl COIL DOMAINS 79 80 FREQUENCY DOMAIN PERTURBATION STUDIES In frequency domain perturbation studies small signal analysis the parameters defined are the same as in the frequency domain study but the impedance is computed using the harmonic voltage and current around the linearization point that is lindev V 1 coil lindev 1 The Lindev Operator in the COMSOL Multiphysics User s Guide Q Multi Turn Coil Domain See Also Single Turn Coil Domain Coil Group Domain CHAPTER 3 Using Coils in 3D Models The coil features require additional settings in 3D models to determine the geometry and the direction of the current flow SINGLE TURN COIL DOMAIN 3D Single Turn Coil Domain represents a solid conducting domain typically a wire or a coil with a non negligible cross section To enforce the current conservation in the domain an additional dependent variable with the dimension of an electric potential SI unit V is added to the problem and the continuity equation for the current is introduced in the system of equations This variable is referred to as the potential but it is only loosely related to the electrostatic potential and it should be considered a help variable rather than representing a tangible physical quantity In the Single Turn Coil Domain node it is possible to specify the material properties that are us
47. Select User defined to manually specify the direction of the wires as a vector field and the length ofthe coil Then enter values or expressions in the matrix for the Coil current flow unitless for x y and z Enter Coil length Zoi SI unit m MULTI TURN COIL DOMAIN Coil Excitation Using Coils in 3D Models See Also Coil Name Enter a Coil name This name is appended to the global variables current voltage defined by this coil and it is used to identify the coil in a Coil Current Calculation study step Coil Conductivity Enter a Coil conductivity SI unit S m The default value is approximately the conductivity for copper 6 107 s m This parameter represents the conductivity of the metal wires forming the coil This is not the domain s bulk conductivity that is instead set to Zero according to the lumped model of a bundle of wires MAGNETIC FIELDS INTERFACE ADVANCED FEATURES 201 Number of Turns Enter the Number of turns N the default is 10 This is the number of tiny wires constituting the coil With the same current applied more turns create a higher current density but the total coil resistance increases as well Coil Wire Cross Section Area Enter a Coil wire cross section area agoi SI unit m The default value is 1079 This is the cross section area of the individual wire in the bundle It is used to compute the lumped resistance of the coil Coil Excitation Select
48. These domain boundary edge point and pair features are described for the Heat Transfer and Joule Heating interfaces in the COMSOL Multiphysics User s Guide listed in alphabetical order Important The links to features described the COMSOL Multiphysics User s Guide do not work in the PDF only from within the online help To locate and search all the documentation in COMSOL select g Help gt Documentation from the main menu and either enter a search term Tip or look under a specific module in the documentation tree CHAPTER 8 Auxiliary Dependent Variable Boundary Electromagnetic Heat Source Boundary Heat Source and Pair Boundary Heat Source Continuity on Interior Boundaries Heat Flux Heat Source Heat Transfer in Fluids Heat Transfer in Solids Line Heat Source Outflow Point Heat Source The Pointwise Constraint Node Surface to Ambient Radiation Symmetry Temperature Thermal Insulation Thin Thermally Resistive Layer and Pair Thin Thermally Resistive Layer Translational Motion The Weak Constraint Node The Weak Contribution Node THE HEAT TRANSFER BRANCH The Weak Contributions on Mesh Boundaries Node Induction Heating Model The Induction Heating Model feature has settings to define the Conduction Current Electric Field Magnetic Field Heat Conduction and Thermodynamics DOMAIN SELECTION The default feature settings cannot be edited and include all domains in the model
49. a Background magnetic vector potential A SI unit Wb m The total field used in the physics and equations are given by the sum of the reduced and background fields COMPONENTS The Components section is only available in 2D and 2D axially symmetric models Select Components Out of plane vector the default In plane vector or 2D Three component vector for the magnetic vector potential From the i practical viewpoint this choice is equivalent to deciding in what directions 2D Axi the electric current is allowed to flow out of plane currents in plane currents or currents flowing in all three coordinate directions THE INDUCTION HEATING INTERFACE 283 284 THICKNESS Enter a value or expression for the Out of plane thickness d SI unit m The default value of 1 m is typically not representative for a thin domain Instead it describes a unit thickness that makes the 2D equation identical to the equation used for 3D models SWEEP SETTINGS Select the Activate terminal sweep check box and enter a Sweep parameter name in the field The default is PortName DEPENDENT VARIABLES The dependent variables field variables are for the Temperature T and the Magnetic Vector potential A The name can be changed but the names of fields and dependent variables must be unique within a model DISCRETIZATION To display this section click the Show button z and select Discretization Select Quadratic Linear
50. and 270 quasi static approximation 235 theory 30 mesh resolution 63 method of virtual work 50 Model Builder settings 19 Model Library 21 Model Library examples ac dc materials 292 boundary conditions 61 cartesian coordinates 59 contact impedance 149 electric currents interface 133 electric shielding 147 electrical circuits 95 electromagnetic forces 71 electrostatics interface 110 impedance boundary condition 216 induction heating interface 282 magnetic and electric fields interface 247 magnetic fields interface 180 magnetic fields no currents interface 221 multi turn coil domain 73 rotating machinery magnetic interface 230 single turn coil domain 73 stress tensors 44 symmetries 60 total forces 46 model M file 15 MPH files 21 multi turn coil domain node 199 n Channel MOS transistor node 264 n Channel MOS transistor theory 273 n Channel MOSFET node 264 NETEX G file format 101 netlists SPICE 268 270 nonlinear materials 36 normal current density node electric currents interface 144 electric currents shell interface 164 NPN bipolar junction transistor 264 270 NPN BJT node 264 numerical coil 82 ODB X files 99 Ohm s law and charge relaxation theory 166 output node coil domains 208 override and contribution settings 19 P pair conditions electric currents interface 135 electric currents shell interface 159 electrostatics interface 112 magnetic fields interface 183 magnetic fiel
51. be created first Ctrl click to deselect THIN LOW PERMITTIVITY GAP The default is to take the Relative permittivity 5 values From material Select User defined to enter a different value or expression Enter a Surface thickness d SI unit m CHAPTER 4 THE ELECTRIC FIELD INTERFACES Line Charge T For 3D models use the Line Charge node to specify line charges along the edges of a geometry 35 g g y EDGE SELECTION From the Selection list choose the edges to add a line charge a Beware that constraining the potential on edges usually yields a current outflow that is mesh dependent Caution LINE CHARGE Enter a value or expression to apply a Line charge Qr SI unit C m This source represents electric charge per unit length Line Charge Axis See Also Line Charge Out of Plane Line Charge on Axis For 2D axisymmetric models use the Line Charge on Axis node to specify i line charges along the symmetry axis 2D Axi 5 2 E 7 BOUNDARY SELECTION From the Selection list choose the boundaries on axis to add a line charge THE ELECTROSTATICS INTERFACE 127 128 LINE CHARGE AXIS Enter a value or expression to apply a Line charge Qz SI unit C m This source represents electric charge per unit length Line Charge Line Charge Out of Plane a See Also Line Charge Out of Plane For 2D and 2D axisymmetric models poi
52. box Perfect Magnetic Conductor The Perfect Magnetic Conductor boundary condition n x 0 is a special case of the surface current boundary condition that sets the tangential component of the magnetic field and thus also the surface current density to zero On external boundaries this can be interpreted as a high surface impedance boundary condition or used as a symmetry type boundary condition It imposes symmetry for electric fields and electric currents Electric currents volume surface or edge currents are not allowed to flow into a perfect magnetic conductor boundary as that would violate current conservation On interior boundaries the perfect magnetic conductor boundary condition literally sets the tangential magnetic field to zero which in addition to setting the surface current density to zero also makes the tangential magnetic vector potential and in dynamics the tangential electric field discontinuous e The perfect magnetic conductor boundary condition is used on exterior boundaries representing the surface of a high impedance region or a symmetry cut The shaded high impedance region is not part of the model but nevertheless carries effective mirror images 194 CHAPTER 5 THE MAGNETIC FIELD INTERFACES of the sources Note also that amy electric current flowing into the boundary is forbidden as it cannot be balanced by induced electric surface currents The tangential magnetic field vanishes at th
53. coil is equal to the out of plane thickness in 2D and 2ar 2D Axi for 2D axisymmetric models 72 CHAPTER 3 MODELING WITH THE AC DC MODULE For 3D model geometries the current flow is not easily determined The coil domains have settings and subfeatures to solve this problem LY 3D SINGLE TURN COIL DOMAIN The Single Turn Coil Domain feature models a single solid domain of a conducting material for example metal in which the current flows The lumped voltage and current of the coil correspond respectively to the integral of the electric field along the coil length and to the integral of the current density on a cross section Use this feature to model a single wire with a non negligible cross section g Selecting unconnected domains with a Single Turn Coil Domain connects them in parallel ip i Induction Currents from Circular Coils Model Library path ACDC Module Inductive Devices and Coils coil above plate Model MULTI TURN COIL DOMAIN The Multi Turn Coil Domain feature implements a homogenized model of a coil consisting of numerous tightly wound conducting wires separated by an electrical insulator The computation of the voltage and current of the coil is performed in a similar way as for the Single Turn Coil Domain but it also takes into account parameters such as the number of wires and the cross section area Use this feature to model a coil containing a large number of wires without
54. condition and is hence also fulfilled unless surface currents are explicitly introduced Available Features These features are available for this interface and listed in alphabetical order Also see Table 5 1 for a list of interior and exterior boundary conditions e Amp re s Law Boundary Feed Change Thickness Out of Plane described for the Electrostatics interface Coil Group Domain Edge Current Electric Point Dipole described for the Electric Currents interface THE MAGNETIC FIELDS INTERFACE 183 Electric Point Dipole on Axis described for the Electric Currents interface External Current Density External Magnetic Vector Potential Force Calculation described for the Electrostatics interface Gap Feed Impedance Boundary Condition Initial Values Line Current Out of Plane Lumped Port Magnetic Field Magnetic Insulation the default boundary condition Magnetic Point Dipole Magnetic Point Dipole on Axis Magnetic Potential Magnetic Shielding Multi Turn Coil Domain Perfect Magnetic Conductor Reference Edge e Reversed Current Direction Sector Symmetry Single Turn Coil Domain Surface Current Thin Low Permeability Gap Transition Boundary Condition Velocity Lorentz Term To locate and search all the documentation in COMSOL select Help gt Documentation from the main menu and either enter a search term Tip or look under a speci
55. contact resistance PAIR SELECTION If Contact Impedance is selected from the Pairs menu choose the pair to define An identity pair has to be created first Ctrl click to deselect MATERIAL TYPE Select a Material type Solid the default Non solid or From material 150 CHAPTER 4 THE ELECTRIC FIELD INTERFACES SURFACE IMPEDANCE Select a potentially complex valued Layer specification Thin layer the default or Surface impedance fThin layer is selected enter values or expressions for the Surface thickness d SI unit m The default is 5 10 m 5 mm Electrical conductivity SI unit S m and Relative permittivity The defaults take values From material Select User defined to enter different values or expressions IfSurface impedance is selected enter values or expressions for the Surface resistance p SI unit Qm and for the Surface capacitance C SI unit E m2 Sector Symmetry Select Sector Symmetry at interfaces between rotating objects where sector symmetry is used It is only available for pairs This feature assumes rotation around the origin Note BOUNDARY SELECTION From the Selection list choose the boundaries from an existing identity pair This pair first has to be created PAIR SELECTION When Sector Symmetry is sclected from the Pairs menu choose the pair to define An identity pair has to be created first Ctrl click to deselect SECTOR SETTING
56. created first Ctrl click to deselect MODEL INPUTS This section has field variables that appear as model inputs if the current settings include such model inputs By default this section is empty MATERIAL TYPE Select a Material type Solid Non solid or From material THIN LOW PERMEABILITY GAP The default Relative permeability unitless uses values From material Select User defined to enter a different value or expression Enter a value or expression for the Surface thickness d SI unit m THE MAGNETIC FIELDS NO CURRENTS INTERFACE 229 230 The Rotating Machinery Magnetic Interface The Rotating Machinery Magnetic interface found under the AC DC branch Xx of the Model Wizard combines an out of plane magnetic fields magnetic vector potential formulation with a selection of predefined frames for prescribed rotation or rotation velocity It is used for 2D models only The interface only works correctly if the geometry is created as an assembly pair from individual composite objects for the rotor and stator parts respectively An identity pair must also be defined for the Important rotor stator interface boundaries under the Model Definitions node in the Model Builder Only features unique to the Rotating Machinery Magnetic interface are described in this section Most features are described for The Magnetic Note Fields Interface and Magnetic Fields Interface Advanced F
57. current per unit length Line Current Source Axis See Also Line Current Source om Axis The Line Current Source on Axis node adds a line source to boundaries in i 2D axisymmetric models The line source represents electric current per 2D Axi unit length BOUNDARY SELECTION From the Selection list choose the boundaries to add a line current source on axis LINE CURRENT SOURCE ON AXIS Enter a value or expression to apply a Line current source Q SI unit A m to boundaries This source represents electric current per unit length Line Current Source See Also Point Current Source The Point Current Source node adds a point source and represents an LY electric current flowing out of the point Add point sources to 3D models 3D from the Points menu THE ELECTRIC CURRENTS INTERFACE 153 154 POINT SELECTION From the Selection list choose the points to add a current source i Beware that constraining the potential on points usually yields a current outflow that is mesh dependent Caution POINT CURRENT SOURCE Enter a value or expression to apply a Point current source SI unit A to points This source represents an electric current flowing out of the point Line Current Source to apply it to points for 2D models Point Current Source on Axis to apply to points for 2D axisymmetric See Also models Point Current Source
58. default temperature is 293 15 K 20 C THE INDUCTION HEATING INTERFACE 289 290 CHAPTER 8 THE HEAT TRANSFER BRANCH Materials This chapter describes the materials databases included with the AC DC Module Material Library and Databases Using the AC DC Material Database 291 292 Material Library and Databases See Also For detailed information about all the other materials databases and the separately purchased Material Library see Materials in the COMSOL Multiphysics User s Guide Model For an example of the AC DC materials database see Small Signal Analysis of an Inductor Model Library path ACDC_Module Inductive_Devices_and_Coils small_signal_analysis_of_inductor CHAPTER 9 In this section About the Material Databases About Using Materials in COMSOL Opening the Material Browser Using Material Properties About the Material Databases Material Browser select predefined materials in all applications Recent Materials Select from recent materials added to the model Material Browser 23 Material Library Purchased Materials separately Select from over 2500 Search predefined materials 28 Recent Materials ry Built In database Available to all Material Library F Built In users and contains common materials X AC DC Batteries and Fuel Cells Application specific material databases
59. directions for Cartesian and cylindrical systems only is just the sum of the individual coordinate mappings INFINITE ELEMENTS 65 p ro t A scaled region P w unscaled region unscaled region Figure 3 2 The coordinate transform used for the mapped infinite element technique The meaning of the different variables are explained in the text Figure 3 2 shows a simple view of an arbitrary coordinate system The coordinate r is the unscaled coordinate that COMSOL Multiphysics draw the geometry in reference system The position r is the new origin from where the coordinates are scaled is the coordinate from this new origin to the beginning of the scaled region also called the pole distance and A is the unscaled length of the scaled region The scaled coordinate t approaches infinity when approaches A To avoid solver issues with near infinite values it is possible to change the infinite physical width of the scaled region to a finite large value Ap The true coordinate that the PDEs are formulated in is given by rT rg where comes from the formula fs toz yt t t pede pw tp The pole distance 5 and the physical width of the infinite element region A are pw input parameters for the region The software automatically computes the transform for infinite element regions that are Cartesian cylindrical or spherical There is no check that the geometry of the
60. electrical conductivity and the surface thickness d The condition is represented by the following equation for interior boundaries and setting 0 exterior boundaries assuming DC currents CHAPTER 4 THE ELECTRIC FIELD INTERFACES n J J5 V d o VV For the frequency domain and time dependent study types also displacement currents are accounted for via the bulk relative permittivity of the sheet and the conservation laws change to n J1 J2 V d o Jo 9 ViV n Ji J 2 V d o VV soe V Use this boundary condition when approximating a thin domain with a boundary to reduce the number of mesh elements i Electric Shielding Model Library path ACDC Module Resistive Devices electric shielding Model BOUNDARY SELECTION From the Selection list choose the boundaries to apply an electric shielding as the boundary condition MODEL INPUTS Any model inputs such as temperature for a temperature dependent electrical conductivity appear here COORDINATE SYSTEM SELECTION The Global coordinate system is selected by default The Coordinate system list contains any additional coordinate systems that the model includes THICKNESS Enter a value or expression for the Surface thickness d SI unit m PAIR SELECTION If Electric Shielding is selected from the Pairs menu choose the pair to define An identity pair has to be created first Ctrl click to deselect THE ELECTR
61. equation one or equation four Then select either equation two or equation three Together these selections form a set of two independent conditions From these relationships the interface condition is derived for the current density n5 J1 J5 E INTERFACE BETWEEN A DIELECTRIC AND A PERFECT CONDUCTOR perfect conductor has infinite electrical conductivity and thus no internal electric field Otherwise it would produce an infinite current density according to the third fundamental constitutive relation At an interface between a dielectric and a perfect conductor the boundary conditions for the E and D fields are simplified Assume that subscript 1 corresponds to a perfect conductor then D 0 and E 0 in the relationships just given If in addition it is a time varying case then B 0 and H 0 as well as a consequence of Maxwell s equations The result is the following set of boundary conditions for the fields in the dielectric medium for the time varying case No x 0 No x H J 05 05 p ns B 0 Phasors Whenever a problem is time harmonic the fields can be written in the form E r t E r cos ot 6 Instead of using a cosine function for the time dependence it is more convenient to use an exponential function by writing the field as E r t E r cos ot 0 R E I R E CHAPTER 2 REVIEW OF ELECTROMAGNETICS The field E r is a phasor which contains amplitude and phase in
62. flux in a ferromagnetic material edge element See vector element electric dipole Two equal and opposite charges q and q separated a short distance The electric dipole moment is given by p qd where d is a vector going from q to 0 gauge transformation variable transformation ofthe electric and magnetic potentials that leaves Maxwell s equations invariant magnetic dipole small circular loop carrying a current The magnetic dipole moment is m where I is the current carried by the loop A its area and e a unit vector along the central axis of the loop Nedelec s edge element See vector element phasor complex function of space representing a sinusoidally varying quantity quasi static approximation The electromagnetic fields are assumed to vary slowly so that the retardation effects can be neglected This approximation is valid when the geometry under study is considerably smaller than the wavelength vector element A finite element often used for electromagnetic vector fields The tangential component of the vector field at the mesh edges is used as a degree of freedom Also called Nedelec s edge element or just edge element CHAPTER 10 GLOSSARY Index 2D axisymmetric models coil domains 209 guidelines for solving 58 2D models coil domains 209 guidelines for solving 58 3D models guidelines for solving 60 importing GDS II files 100 infinite elements and 69 A AC DC Module 14 AC DC p
63. gap voltage breaks down unless the gap is much smaller than the local wavelength A lumped port specified as an input port calculates the impedance and 511 S parameter for that port The parameters are directly given by the relations Z V bort 1 port V ont Sis E in in where is the extracted voltage for the port given by the electric field line integral between the terminals averaged over the entire port The current Iport is the averaged total current over all cross sections parallel to the terminals Ports not specified as input ports only return the extracted voltage and current e Lumped Port Parameters See Also CHAPTER 3 MODELING WITH THE AC DC MODULE Lumped Port Parameters In transmission line theory voltages and currents are dealt with rather than electric and magnetic fields so the lumped port provides an interface between them The requirement on a lumped port is that the feed point must be similar to a transmission line feed so its gap must be much less than the wavelength It is then possible to define the electric field from the voltage as Ve 4 GE adi h h where A is a line between the terminals at the beginning of the transmission line and the integration is going from positive phase V to ground The current is positive going into the terminal at positive V v V J ET NEL Rm Lumped port boundary The transmission line cur
64. in thin current conducting shells solving for the electric potential Current Conservation is the main feature which adds the equation for the electric potential and provides a settings window for defining the electrical conductivity as well as the constitutive relation for the electric displacement field and its associated material properties such as the relative permittivity When this interface is added these default nodes are also added to the Model Builder Current Conservation Electric Insulation the default edge or point condition and Initial Values Right click the Electric Currents Shell node to add other features that implement for example edge or point conditions and current sources Except where described below the majority of the settings windows are the same as for the Electrostatics and Electric Currents interfaces as referenced The only real difference are El For 3D models boundaries are selected instead of domains and edges Note instead of boundaries For 2D and 2D axisymmetric models boundaries are selected instead of domains and points instead of edges and boundaries For more extensive introduction to the physics and equations e implemented by this interface see the Theory for the Electric Currents See Also Shell Interface INTERFACE IDENTIFIER The interface identifier is a text string that can be used to reference the respective physics interface if appropriate Such situatio
65. interface using variables coupling operators and so forth In the settings window for the Electrical Circuit interface feature selecting the User defined option and entering the name of the variable or expression using coupling operators defined in the previous step DETERMINING A CURRENT OR VOLTAGE VARIABLE NAME To determine a current or voltage variable name it may be necessary to look at the Dependent Variables node under the Study node To do this In the Model Builder right click the Study node and select Show Default Solver 2 Expand the Solver gt Dependent Variables node and click the state node in this example modlOdel The variable name is shown on the State settings window 4 Study 2 5 Stati 100 Step 1 Frequency Domain sue 4 Solver Configurations Computeto Selected Compute All a 4 Solver 2 oed ET Compile Equations Frequency Domain 4 uw Dependent Variables 1 State 09 modL A modl cir R1l i modi Odel 175 Stationary Solver 1 Typically voltage variables are named cir Xn v and current variables g cir Xn i where is the External device number that is 1 2 and Tip so on CONNECTING TO ELECTRICAL CIRCUITS 97 98 3 Importing ECAD Files In this section Overview of the ECAD Import Importing ODB X Files Importing GDS II Files Importing NETEX G Files ECAD Import Options Meshing an Imported
66. is set to a unique number but can be changed as long as it is unique between all the coil features in a model Multi Turn Coil Domain Single Turn Coil Domain See Also Coil Group Domain CHAPTER 3 Coil Excitation The current density flowing in the coil domain is computed from a lumped quantity that constitutes the coil excitation The choice of this quantity can be done by setting the coil excitation parameter while the value is specified in the associated text box the coil features can be excited either with a current or a voltage The supplied value or expression is translated to a current density or electric field applied to the domain according to the coil model used Coil features can also retrieve the value ofthe current MODELING WITH THE AC DC MODULE or the voltage from a circuit connection if the parameter coil excitation is set to Circuit current or Circuit voltage respectively Circuit current excitation works similarly to the Current excitation but in this case the inputs are provided by a circuit connection Tib Circuit voltage excitation works similarly to the Voltage excitation but in this case the inputs are provided by a circuit connection CURRENT EXCITATION Single Turn Coil Domains When specifying a total current the out of plane component of the current density is defined as oV 2 3 2 where L is equal to the physics interface thickn
67. makes the 1D equation identical to the equation used for 3D models For 2D models see Change Thickness Out of Plane See Also Change Thickness Out of Plane This feature is available for 2D models This setting overrides the global Thickness setting made in any interface that uses this feature Use the Change Thickness Out of Plane feature to set the out of plane thickness for specific geometric entities DOMAIN OR BOUNDARY SELECTION From the Selection list choose the geometric entity domains or boundaries to define the change thickness PAIR SELECTION When Change Thickness Out of Plane is selected from the Pairs menu choose the pair to define An identity pair has to be created first Ctrl click to deselect CHANGE THICKNESS OUT OF PLANE Enter a value or expression for the Out of plane thickness d SI unit m The default value of 1 unit length is typically not representative for a thin domain Instead it describes a unit thickness that makes the 2D equation identical to the equation used for 3D models For 1D models see Change Cross Section See Also THE ELECTROSTATICS INTERFACE 131 132 Infinite Elements For information about this feature see About Infinite Element Domains and Perfectly Matched Layers in the COMSOL Multiphysics User s Note Guide Electrostatic Point Dipole 2D Add an Electrostatic Point Dipole node to 2D and 3D models
68. models an additional subfeature is needed to completely define the geometry Important P y 8 y CHAPTER 5 Linear Coil Types In a Linear coil the wires are all parallel and straight lines and a Reference Edge subfeature is required Right click the Multi Turn Coil Domain node to add a Reference Edge subfeature and select an edge or a group of co linear edges The direction of the wires and the coil length is taken to be the direction and the length of the edge s To avoid unphysical currents a Linear coil should be terminated on external boundaries Circular Coil Types In a Circular coil the wires are wound in circles around the same axis and a Reference Edge subfeature is required Right click the Multi Turn Coil Domain node to add a THE MAGNETIC FIELD INTERFACES Reference Edge subfeature and select a group of edges forming a circle around the coil s axis From the selected edge the coil axis is computed and the direction of the wires is taken to be the azimuthal direction around the axis The coil length used is simply the length of the edges the best approximation is obtained when the radius of the edges is close to the average radius of the coil Numeric Coil Types In a Numeric coil the current flow is computed automatically in a Coil Current Calculation study step An Automatic Current Calculation subfeature is needed to set up the problem Computing Coil Currents See Also User Defined Coil Types
69. module in the documentation tree Initial Values The Initial Values feature adds an initial value for the magnetic vector potential DOMAIN SELECTION From the Selection list choose the domains to define an initial value INITIAL VALUES Enter a value or expression for the initial value of the Magnetic vector potential A SI unit Wb m THE ROTATING MACHINERY MAGNETIC INTERFACE 233 234 Electric Field Transformation The Electric Field Transformation feature imposes suitable transformations to the electric field definitions in all domains depending on rotational velocity DOMAIN SELECTION EI For the default node no user selection is required All domains is automatically selected Note CHAPTER 5 When additional nodes are added from the Selection list choose the domains to define the electric field transformation Prescribed Rotation The Prescribed Rotation feature imposes a coordinate transformation to the selected domain that effectively rotates it a prescribed angle It is used to model a rotating part DOMAIN SELECTION From the Selection list choose the domains to use prescribed rotation PRESCRIBED ROTATION Enter the Rotation angle c ot SI unit radians and the x and y coordinates for the Rotation axis base point r SI unit m Prescribed Rotational Velocity The Prescribed Rotational Velocity feature imposes a coordinate transformation to the selected doma
70. moment direction and the Magnetic dipole moment magnitude m SI unit Am If Dipole moment is selected under Dipole Specification enter coordinates for the Magnetic dipole moment m SI unit Am MAGNETIC FIELDS INTERFACE ADVANCED FEATURES 219 220 Magnetic Point Dipole on Axis This feature is available for 2D axisymmetric models See Magnetic Point i Dipole for settings for 2D and 3D models 2D Axi CHAPTER 5 Use the Magnetic Point Dipole on Axis to apply a point dipole to points on a 2D axisymmetric model POINT SELECTION From the Selection list choose the points to add an magnetic point dipole MAGNETIC POINT DIPOLE ON AXIS Enter a Magnetic dipole moment in z direction m SI unit Am THE MAGNETIC FIELD INTERFACES The Magnetic Fields No Currents Interface The Magnetic Fields No Currents interface ffh found under the AC DC branch X of the Model Wizard has the equations boundary conditions and point features for modeling magnetostatics solving for the magnetic scalar potential The main feature is the Magnetic Flux Conservation feature which adds the equation for the magnetic potential and provides an interface for defining the material properties and the constitutive relation for the magnetic flux density It is used when there are no currents When this interface is added these default nodes are also added to the Model Builder Magnetic Fields No Current
71. naming conventions and scoping mechanisms To access a material property throughout the model across several materials and not just in a specific material use the special material container root material For example root material rho is the density p as defined by the materials in each domain in the geometry For plotting you can type the expression material rho to create a plot that shows the density of all materials If you use a temperature dependent material each material contribution asks for a special model input For example rho T in a material mat1 E asks for root mat1 def T and you need to define this variable T Note manually if the temperature is not available as a dependent variable to make the density variable work CHAPTER 9 To access a material property from a specific material you need to know the tags for the material and the property group Typically for the first material Material 1 the tag is mat1 and most properties reside in the default Basic property group with the tag def The variable names appear in the Variable column in the table under Output properties in the settings window for the property group for example Cp for the MATERIALS heat capacity at constant pressure The syntax for referencing the heat capacity at constant pressure in Material 1 is then mat1 def Cp Some properties are anisotropic tensors and each of the components can be accessed such as mat1 def k11 ma
72. or for toolbar buttons in the corresponding tip For example the Model Builder window 7 is often referred to and this is the window that contains the model tree As another example the instructions might say to click the Zoom Extents button and this means that when you hover over the button with your mouse the same label displays on the COMSOL Desktop The forward arrow symbol gt is instructing you to select a series of menu items in a specific order For example Options Preferences is equivalent to From the Options menu choose Preferences A Code monospace font indicates you are to make a keyboard entry in the user interface You might see an instruction such as Enter or type 1 25 in the Current density field The monospace font also is an indication of programming code or a variable name 22 CHAPTER 1 INTRODUCTION CONVENTION EXAMPLE Italic Code monospace italic Code monospace font indicates user inputs and font Arrow brackets lt gt following the Code monospace or Code italic fonts parts of names that can vary or be defined by the user The arrow brackets included in round brackets after either a monospace Code or an italic Code font means that the content in the string can be freely chosen or entered by the user such as feature tags For example model geom lt tag gt where lt tag gt is the geometry s tag an identifier of your choice When the st
73. region is correct so it is important to draw a proper geometry and select the corresponding region Important type 66 CHAPTER 3 MODELING WITH THE AC DC MODULE The following figures show typical examples of infinite element regions that work nicely for each of the infinite element types These types are Stretching in Cartesian coordinate directions labeled Cartesian Stretching in cylindrical directions labeled Cylindrical Stretching in spherical direction labeled Spherical User defined coordinate transform for general infinite elements labeled General Figure 3 3 A cube surrounded by typical infinite element regions of Cartesian type Figure 3 4 A cylinder surrounded by typical cylindrical infinite element regions Figure 3 5 A sphere surrounded by a typical spherical infinite element region INFINITE ELEMENTS 67 68 CHAPTER 3 Ifother shapes are used for the infinite element regions not similar to the shapes shown in the previous figures it might be necessary to define the infinite element parameters manually The poor element quality causes poor or slow convergence for iterative solvers and make the problem ill conditioned in general Especially vector element formulations like the ones using two or more components of the magnetic vector potential are sensitive to low element quality For this reason it is strongly recommended to use swept meshing in the infinite element domai
74. sections the Shell Thickness and Out of Plane Thickness available as well as two feature nodes Change Shell Thickness and Change Thickness Out of Plane TERMINAL SWEEP SETTINGS Enter a Reference impedance Zef SI unit The default is 50 Select the Activate terminal sweep check box to switch on the sweep and invoke a parametric sweep over the terminals Enter a Sweep parameter name to assign a specific name to the variable that controls the terminal number solved for during the sweep The default is PortName The generated lumped parameters are in the form of capacitance matrix elements The terminal settings must consistently be of either fixed voltage or fixed charge type CHAPTER 4 THE ELECTRIC FIELD INTERFACES The lumped parameters are subject to Touchstone file export Enter a file path or Browse for a file Select an Output format for the Touchstone export Magnitude angle Magnitude dB angle or Real imaginary Select a Parameter to export Z the default Y or S Lumped Parameters See Also DEPENDENT VARIABLES The dependent variable field variable is for the Electric potential V The name can be changed but the names of fields and dependent variables must be unique within a model DISCRETIZATION To display this section click the Show button 2 and select Discretization Select an element order for the Electric Potential Linear Quadratic the default Cubic Quartic or in 2D only
75. the dependent variable and the equations needed for the computation and takes care of the coupling with the parent Multi Turn Coil Domain feature To define boundary conditions for the current computation right click the Automatic Current Calculation node and add the Electric Insulation Input and Output subfeatures The Electric Insulation feature should be applied on the boundaries delimiting the coil domain and it constrains the coil wires to be parallel to the boundary The Input and Output features work similarly constraining the wires to be orthogonal to the boundary and together define the direction of the current flow from Input to Output A single Input feature can also applied to an internal boundary if the coil domain is a closed loop that is if Input and Output should be on the same boundary For the problem to be correctly set up exactly one Input feature must be present To complete the set up add a Coil Current Calculation study step to the study before the main study step Ensure that the Coil Name in the Coil Current Calculation study step is 1 the same as the name of the numerical coil During the solution process the current flow direction is computed in the Coil Current Calculation Important step and subsequently used in the following study steps CHAPTER 3 MODELING WITH THE AC DC MODULE Computing Coil Currents e Coil Current Calculation Study in the COMSOL Multiphysics User s
76. the need to model each wire individually Eddy Currents in a Cylinder Model Library path ACDC Module Inductive Devices and Coils coil eddy currents Inductor in an Amplifier Circuit Model Library path ACDC Module Inductive Devices and Coils inductor in circuit COIL DOMAINS 73 74 COIL GROUP DOMAIN The Coil Group Domain feature can be used in 2D and 2D axisymmetry to easily model one or more Single Turn Coil Domain features connected in a series Each domain in the coil domain selection is considered a separate turn of the coil 3 When a Coil Group Domain selection only consists of a single domain then it is effectively the same as a Single Turn Coil Domain Note The Coil Group Domain automatically sets up the relations between the variables associated to each domain Current and voltage variables for each domain or turn are computed the same as for the Single Turn Coil Domain while the total variables for the coil are computed using the rules for series connection the total voltage is the sum of the voltages while the total current is equal to the current flowing in each domain Use this feature in 2D and 2D axisymmetric models for coils with non negligible cross sections that cross the modeling plane more than once About the Coil Name For all types of coil features a Coil Name is entered to allow the identification of the feature and the variables it creates By default this
77. the potentials THEORY OF MAGNETIC AND ELECTRIC FIELDS 235 B VxA 9 vv 7 and the constitutive relation B M Amp re s law can be rewritten as okt Vx ug Vx A M ov x Vx A amp oVV J 5 3 The equation of continuity which is obtained by taking the divergence of the above equation adds the following equation A oVV J 0 5 4 Equation 5 3 and Equation 5 4 form a system of equations for the two potentials A and V Gauge Transformations The electric and magnetic potentials are not uniquely defined from the electric and magnetic fields through E 2 VV ot B VxA Introducing two new potentials A V oF V2V gives the same electric and magnetic fields OA ov KA VV 0 9 OA t i t Tes m B VxA Vx A VY The variable transformation of the potentials is called a gauge transformation To obtain a unique solution choose the gauge that is put constraints on that make the solution unique Another way of expressing this additional condition is to put a 236 CHAPTER 5 THE MAGNETIC FIELD INTERFACES constraint on A vector field is uniquely defined up to a constant if both V A and V x A are given This is called Helmholtz s theorem One particular gauge is the Coulomb gauge given by the constraint V A 0 Selecting a Particular Gauge Important observations are that in the dyn
78. the system of equations becomes V goo o g A o josg VV J joP 0 joo o A Vx ug V x A M ovx V x A o jme VV J joP The constitutive relation D e9E P has been used for the electric field To obtain a particular gauge that reduces the system of equation choose jV in the gauge transformation This gives A A Lyy V 0 When V vanishes from the equations only the second one is needed oc o A V x ug V x A M ov x V x A J joP Working with A is often the best option when it is possible to specify all source currents as external currents J or as surface currents on boundaries THEORY OF MAGNETIC AND ELECTRIC FIELDS 239 240 Theory for the Magnetic Fields Interface Simulation of magnetic fields is of interest when studying magnets motors transformers and conductors carrying static or alternating currents The Magnetic Fields Interfaceis used for 3D 2D in plane and 2D axisymmetric models Unless you have a license for the AC DC Module only 2D modeling involving out of plane currents and axisymmetric modeling involving azimuthal currents are supported In this section Magnetostatics Equation Frequency Domain Equation Transient Equation For deeper theoretical background to the magnetic vector potential a used below see the section starting with Maxwell s Equations ee Also CHAPTER 5 Magnetostatics
79. those formats are used when sending the layout to manufacturing The output file is an ASCII file with a GDS like structure containing information about the layout of each layer the layer thickness vias and dielectric layers The geometry objects are defined and instantiated in the same way as GDS file see Importing GDS II Files for a more detailed description File Extension The file extension of the NETEX G format is not set but the ECAD import requires it to be asc otherwise it cannot identify the file as a NETEX G file If the file has a different extension change the name before importing it Throughout the rest of this section files of this type are referred to as a Netex file USING NETEX G This is a brief description of the main steps to produce a Netex file for import into COMSOL Multiphysics For specific details see the NETEX G user guide IMPORTING ECAD FILES 101 102 CHAPTER 3 GERBER Layer Files The first type of input files to NETEX G is a collection of Gerber files one for each layer The ECAD software generates these files when the PCB layout is sent to manufacturing but they can also be used for interfacing to other programs like COMSOL Multiphysics The layer files do not contain any information about layer thickness layer materials dielectrics and electrical connectivity nets Furthermore a standard layout usually consists of large number of conductors vias and symbols p
80. to gds before importing the file SUPPORTED FEATURES There are several record types in a GDS file that are of no interest in a geometry import and these are ignored There are also a few record types that actually could be imported as a geometry object but are also ignored One such example is the Text record which produce a lot of mesh elements and is usually of no interest in a simulation Below is a list of the supported record types Boundary a closed polyline object Box a box object Path a path with a thickness e Sref an instance of a cell that can be translated rotated scaled and mirrored e Aref an n by m array of Sref objects Element specification of a cell 3D IMPORT OF 605 11 FILES The GDS II format does not contain any information about layer thickness and layer position so any such information has to be supplied by the user When importing a GDS II file with the ECAD import it creates a table for all layers included in the file In that table it is possible to specify a thickness for each layer and thereby get a 3D structure This procedure has a few limitations regarding how the GDS layers are organized One layer represents one position in height so if the file contains two GDS layers that define two objects on the same height the ECAD import still positions the layers with one layer on top of the other Several GDS layers on the same height is common for semiconductor layouts where the fabric
81. where described below the majority of the settings windows are the same as for the Magnetic Fields Electrostatics and Electric Currents Note interfaces 246 CHAPTER 6 THE MAGNETIC AND ELECTRIC FIELDS INTERFACE e Magnetic Brake Model Library path Module n Motors and Actuators magnetic brake Inductance of a Power Inductor Model Library path ACDC Module Inductive Devices and Coils power inductor Model Use the Coil Domain features where possible See Multi Turn Coil El Domain Single Turn Coil Domain and Coil Group Domain for node Note information and Coil Domains for modeling information INTERFACE IDENTIFIER The interface identifier is a text string that can be used to reference the respective physics interface if appropriate Such situations could occur when coupling this interface to another physics interface or when trying to identify and use variables defined by this physics interface which is used to reach the fields and variables in expressions for example It can be changed to any unique string in the Identifier field The default identifier for the first interface in the model is mef DOMAIN SELECTION The default setting is to include All domains in the model to define the electric potential the magnetic vector potential and the equations that describe the magnetic and electric fields To choose specific domains select Manual from the Selection list BACKGROUND FIELD T
82. where the electromagnetic field penetrates only a short distance outside the nxH4E n E n n E n E 9 J0 0 The boundary condition approximates this penetration to avoid the need to include boundary another domain in the model The material properties that appear in the equation are those for the domain outside the boundary The skin depth that is the distance where the electromagnetic field has decreased by a factor el is for a good conductor MAGNETIC FIELDS INTERFACE ADVANCED FEATURES 215 The impedance boundary condition is a valid approximation if the skin depth is small compared to the size of the conductor The source electric field can be used to specify a source surface current on the boundary N The impedance boundary condition is used on exterior boundaries representing the lossy region is not part of the model The surface of a lossy domain The shaded effective induced image currents are of reduced magnitude due to losses Any current flowing into the boundary is perfectly balanced by induced surface currents as for the perfect electric conductor boundary condition The tangential electric field is generally small but non zero at the boundary i Cold Crucible Model Library path Module Electromagnetic Heating Model cold crucible BOUNDARY SELECTION From the Selection list choose the boundaries to specify the impedance boundary condition MODEL I
83. which can be tuned to minimize its influence on the results CHAPTER 3 Connecting Electrical Circuits Using Predefined Couplings In addition to these circuit features physics interfaces in the AC DC Module RF Module MEMS Module and Plasma Module the modules that include the Electrical Circuit interface also contain features that provide couplings to the Electrical Circuit interface by accepting a voltage or a current from one of the specific circuit features External I vs U External U vs I and External I Terminal This coupling is typically activated when Achoice is made in the settings window for the non circuit physics interface feature which then announces that is includes the coupling to the Electrical Circuit interface Its voltage or current is then included to make it visible to the connecting circuit feature Avoltage or current that has been announced that is included is selected in a feature node s settings window These circuit connections are supported in Terminal Coils and Lumped Ports Connecting Electrical Circuits by User Defined Couplings more general way to connect a physics interface to the Electrical Circuit interface is to Apply the voltage or current from the connecting External circuit feature as an excitation in the non circuit physics interface MODELING WITH THE AC DC MODULE Define your own voltage or current measurement in the non circuit physics
84. 176 saturation exponent 141 scattering parameters see S parameters sector symmetry node 151 selecting solvers 64 space dimensions 58 study types 62 semiconductor device models 270 show button 19 single turn coil domain node 202 skin effects 63 solver settings 64 space charge density node 116 space dimensions selecting 58 S parameter calculations electric field and 93 SPICE netlists 268 270 stabilization settings 20 stationary fields forces 44 stress tensors 44 46 48 49 study types electric currents interface 176 electromagnetic theory 33 induction heating interface 282 physics interface availability 17 selecting 62 subcircuit definition node 263 subcircuit instance node 264 surface charge density node 119 surface current node 192 sweeps and lumped parameters 88 technical support COMSOL 21 terminal node 121 theory constitutive relations 31 32 electric currents 172 electric currents shell interface 178 electric fields 166 electrical circuit 269 electromagnetics 30 electrostatics interface 170 lumped ports 91 magnetic and electric fields 235 magnetic and electric fields interface 255 magnetic fields interface 240 magnetic fields no currents interface 243 thin low permeability gap node magnetic fields interface 218 magnetic fields no currents interface 228 thin low permittivity gap node 126 thin shells conductive media 178 time dependent study 62 168 176 tolerance relative re
85. 233 234 234 234 235 235 235 236 237 237 237 238 239 240 240 241 242 CONTENTS 9 10 CONTENTS Theory for the Magnetic Fields No Currents Interface Chapter 6 The Magnetic and Electric Fields Interface The Magnetic and Electric Fields Interface 243 246 Domain Boundary Edge Point and Pair Features for the Magnetic and Electric Fields Interface Amp re s Law and Current Conservation Initial Values Theory for the Magnetic and Electric Fields Interface Magnetostatics Equations Frequency Domain Equations Chapter 7 The Electrical Circuit Interface The Electrical Circuit Interface Ground Node Resistor Capacitor Inductor Voltage Source Current Source ger e Voltage Controlled Voltage Source Voltage Controlled Current Source Current Controlled Voltage Source Current Controlled Current Source Subcircuit Definition Subcircuit Instance NPN BJT n Channel MOSFET Diode External vs U 249 253 254 255 255 256 258 259 260 260 260 260 261 262 262 262 263 263 264 264 264 265 266 External U vs I External l Terminal SPICE Circuit Import Theory for the Electrical Circuit Interface Electric Circuit Modeling and the Semiconductor Device Models NPN Bipolar Transistor n Channel MOS Transistor Diode References for the Electrical Circuit Interface Chapter 8 The Heat Transfer Branch The Induction Heating Inte
86. 67 168 type That typically involves either prescribing the charge dynamics or coupling separate formulation for this g Such separate charge transport formulations can be found in the Plasma Tp Module and the Chemical Reaction Engineering Module 1 SECOND CASE lt lt T Ifthe external time scale is long compared to the charge relaxation time the stationary solution to the equation of continuity has been reached In a stationary coordinate system a slightly more general form than above of Ohm s law states that J where J is an externally generated current density The static form of the equation of continuity then reads V J V oVV J 0 To handle current sources the equation can be generalized to V cVV J5 Q This equation is used in the static study type for the Electric Currents interface GENERAL CASE CHARGE DYNAMICS If the charge relaxation time is comparable to the external time scale the time dependent or frequency domain study types for the Electric Currents interface must be used Combining the time harmonic equation of continuity V J V cE J jop with the equation D p yields the following equation for the frequency domain study type V josg VV J joP 0 For the time dependent study type use the transient equation of continuity CHAPTER 4 THE ELECTRIC FIELD INTERFACES V J V 0E J 2 and the resulting equation becomes y
87. AC DC Module Users Guide VERSION 4 3 Hl COMSOL AC DC Module User s Guide 1998 2012 COMSOL Protected by U S Patents 7 519 518 7 596 474 and 7 623 991 Patents pending This Documentation and the Programs described herein are furnished under the COMSOL Software License Agreement www comsol com sla and may be used or copied only under the terms of the license agree ment COMSOL COMSOL Desktop COMSOL Multiphysics and LiveLink are registered trademarks or trade marks of COMSOL AB Other product or brand names are trademarks or registered trademarks of their respective holders Version May 2012 COMSOL 4 3 Contact Information Visit www comsol com contact for a searchable list of all COMSOL offices and local representatives From this web page search the contacts and find a local sales representative go to other COMSOL websites request information and pricing submit technical support queries subscribe to the monthly eNews email newsletter and much more If you need to contact Technical Support an online request form is located at www comsol com support contact Other useful links include Technical Support www comsol com support Software updates www comsol com support updates Online community www comsol com community Events conferences and training www comsol com events Tutorials www comsol com products tutorials Knowledge Base www comsol com support knowledgebase Part No CM020101
88. AGNETIC FIELDS INTERFACE ADVANCED FEATURES 203 204 Coil Name Enter a Coil name This name is appended to the global variables current voltage defined by this coil and it is used to identify the coil in a Coil Current Calculation study step Coil Excitation Select a Coil excitation Current Voltage Circuit voltage Circuit current or Power If Current is selected also enter a Coil current SI unit A The default value is IfVoltage is selected enter a Coil potential SI unit V The default value is 1 V fCircuit current is sclected it works similarly to the Current excitation but in this case the inputs are provided by a circuit connection e fCircuit voltage is selected it works similarly to the Voltage excitation but in this case the inputs are provided by a circuit connection If Power is selected enter a Coil power SI unit W The default value is 1 W EI Selecting Power makes the problem nonlinear For more information see Power Excitation Note SINGLE TURN COIL DOMAIN 3D MODELS For 3D models the parameters Coil conductivity and Coil relative permittivity define the material model to be used with the current M continuity equation Normally these parameters are the same used in the 3D Amp re s Law feature active in the domain CHAPTER 5 Coil Conductivity Select a Coil conductivity SI unit S m From material or Use
89. C FORCES 45 46 Elastic Pure Conductor For an example of how to compute the total force on two parallel wires either by integrating the volume force or by integrating the stress tensor on the surrounding surface see Electromagnetic Forces on Parallel Model Current Carrying Wires Model Library path ACDC Module Verification Models parallel wires A material that is nonpolarizable and nonmagnetizable P 0 and M 0 is called a pure conductor This is not necessarily equivalent to a perfect conductor for which E 0 but merely a restriction on the dielectric and magnetic properties of the material The stress tensor becomes identical to the one for air except for pI being replaced by the purely mechanical stress tensor oy 1 1 T T T oy 3E D 3H BJ ED HB where D and B The situation is slightly different from the case of air because there can be currents and volume charges in the conductor The current density is lvxpB Ho J VxH and the volume charge density p V D 80 E The equation for the balance of forces now becomes 0 V oy pE J3xB f and this means that fem General Elastic Material For an elastic solid in the general case ofa material that is both dielectric and magnetic nonzero P and M the stress tensor is given by the expression CHAPTER 2 REVIEW OF ELECTROMAGNETICS T o E B 2 1 1 o B SE E 5 B B M B I E EP MB 0
90. Cubic or Quartic for the Temperature Surface radiosity and Magnetic vector potential Specify the Value type when using splitting of complex variables Real or Complex the default The Model Builder Show and Hide Physics Options Domain Boundary Edge Point and Pair Features for the Induction Heating Interface See Also Theory of Magnetic and Electric Fields Theory for the Heat Transfer Interfaces in the COMSOL Multiphysics User s Guide CHAPTER 8 Domain Boundary Edge Point and Pair Features for the Induction Heating Interface The Induction Heating Interface shares most of its settings windows with the Magnetic Fields Heat Transfer and Joule Heating interfaces THE HEAT TRANSFER BRANCH These domain boundary edge point and pair features are described in this guide for the Magnetic Fields interface listed in alphabetical order Amp re s Law Edge Current Electric Point Dipole Electric Point Dipole on Axis Electromagnetic Heat Source External Current Density Force Calculation Gauge Fixing for A field Induction Heating Model Infinite Elements Initial Values Impedance Boundary Condition Lumped Port Magnetic Field Magnetic Insulation Magnetic Point Dipole Magnetic Potential Periodic Condition Perfect Magnetic Conductor Sector Symmetry Surface Current Thin Low Permeability Gap Transition Boundary Condition THE INDUCTION HEATING INTERFACE 285 286
91. D The default Relative permittivity unitless for the media is used From material and defined on the shell domain If User defined is selected choose Isotropic Diagonal Symmetric or Anisotropic based on the characteristics of the permittivity and then enter values or expressions in the field or matrix MAGNETIC FIELD Specify the Constitutive relation that describe the macroscopic properties of the medium relating the magnetic flux density B and the magnetic field H and the applicable material properties such as the relative permeability THE MAGNETIC FIELDS INTERFACE 187 Select a Constitutive relation Relative permeability the default HB curve Magnetic losses Remanent flux density or Magnetization The equation for the selected constitutive relation displays under the list For all options the default uses values From material or select User defined Note to enter a different value or expression e Select Relative permeability L1 unitless to use the constitutive relation B pou H If User defined is selected choose Isotropic Diagonal Symmetric or Anisotropic and enter values or expressions in the field or matrix Select HB curve H SI unit A m to use a curve that relates magnetic flux density B and the magnetic field as H ABJ Do not select this option if using the Induction Heating interface This option is not relevant for time harmonic modeling Important e Sele
92. E 155 156 DIPOLE PARAMETERS e fMagnitude and direction is selected under Dipole Specification enter coordinates for the Electric current dipole moment direction n and the Electric current dipole moment magnitude p SI unit A m fDipole moment is selected under Dipole Specification enter the components of the Electric current dipole moment SI unit Electric Point Dipole on Axis See Also Electric Point Dipole om Axis 1 The Electric Point Dipole on Axis node is available for 2D axisymmetric models 2D Axi The Electric Point Dipole on Axis represents the limiting case of zero separation distance between two equally strong point current sources and current sinks of opposing signs while maintaining the product between separation distance and source strength at a fixed value P The positive direction is from the current sink to the current source POINT SELECTION From the Selection list choose the points to add an electrostatic point dipole ELECTRIC POINT DIPOLE ON AXIS Enter the Electric current dipole moment in z direction p SI unit m A Electric Point Dipole See Also CHAPTER 4 THE ELECTRIC FIELD INTERFACES The Electric Currents Shell Interface The Electric Currents Shell interface D found under the AC DC branch X in the Model Wizard adds the equations boundary conditions and current sources for modeling steady electric currents
93. ECTION The default setting is to include All domains in the model to define the magnetic vector potential and the equations that describe the potential field for magnetic fields To choose specific domains select Manual from the Selection list THE MAGNETIC FIELD INTERFACES BACKGROUND FIELD Select an option from the Solve for list Full field the default or Reduced field If Reduced field is selected specify a Background magnetic vector potential A SI unit Wb m The total field used in the physics and equations are given by the sum of the reduced and background fields COMPONENTS 2D This section is only available in 2D and 2D axially symmetric models 2D Axi The current vector has the same direction as the magnetic vector EI potential so this setting also controls the direction in which applied and induced currents can flow in the model The default option is to solve for Not the out of plane component for 2D and 2D axisymmetric models Select Components Out of plane vector potential the default In plane vector potential or Three component vector potential for the magnetic vector potential From the practical viewpoint this choice is equivalent to deciding in what directions the electric current is allowed to flow out of plane currents in plane currents or currents flowing in all three coordinate directions and affects other settings in the model for example the Port Properties
94. EL PARAMETERS Vox 1 Fo 1 M My Jx V EAS x Up lt P oV jy vp 2 FOV V table below PARAMETER DEFAULT DESCRIPTION Br 100 Ideal forward current gain Br Ideal reverse current gain 0 F m Base collector zero bias depletion capacitance CJE 0 F m Base emitter zero bias depletion capacitance Fo 0 5 Breakdown current Ir Inf Alm Corner for forward high current roll off Ikr Inf Alm Corner for reverse high current roll off CHAPTER 7 THE ELECTRICAL CIRCUIT INTERFACE TABLE 7 1 BIPOLAR TRANSISTOR MODEL PARAMETERS PARAMETER DEFAULT DESCRIPTION Ig 15 A m Saturation current Isc 0 A m Base collector leakage saturation current Isg 0 A m Base emitter leakage saturation current Myc 1 3 Base collector grading coefficient Myr 1 3 Base emitter grading coefficient 2 Base collector ideality factor Ng 1 4 Base emitter ideality factor Np Forward ideality factor Ng Reverse ideality factor Rp 0 om Base resistance Minimum base resistance Rc 0 Om Collector resistance Rg 0 Om Emitter resistance TNOM 298 15 Device temperature VAF Inf V Forward Early voltage VAR Inf V Reverse Early voltage Vic 0 71 V Base collector built in potential VJE 0 71 V Base emitter built in potential n Channel MOS Transistor Figure 7 2 illustrates an equivalent circuit for the MOS transistor THEORY FOR THE ELECTRICAL CIRCUIT INTERFACE 273 Rp
95. EW OF ELECTROMAGNETICS The method of virtual work can be employed by using the features for deformed mesh and sensitivity analysis in COMSOL Multiphysics See The Deformed Geometry and Moving Mesh Interfaces and Sensitivity Analysis in the COMSOL Multiphysics User s Guide Note ELECTROMAGNETIC FORCES 51 52 Electromagnetic Quantities The table below shows the symbol and SI unit for most of the physical quantities that appear in the AC DC Module TABLE 2 1 ELECTROMAGNETIC QUANTITIES QUANTITY SYMBOL __ SI UNIT ABBREVIATION Angular frequency 0 radian second rad s Attenuation constant a meter m Capacitance C farad F Charge q coulomb Charge density surface Ps coulomb meter C m Charge density volume p coulomb meter C m Current I ampere A Current density surface J ampere meter Alm Current density volume J ampere meter Alm Electric displacement D coulomb meter C m Electric field E volt meter V m Electric potential V volt V Electric susceptibility Xe dimensionless Electrical conductivity o siemens meter S m Energy density W joule meter Jim Force F newton N Frequency hertz Hz Impedance 2 1 ohm Q Inductance L henry H Magnetic field H ampere meter A m Magnetic flux weber Wb Magnetic flux density B tesla T Magnetic potential scalar Vin ampere A Magnetic potential vector A weber meter Wb m Magnetic susceptibility Xo dimensionless Magnetization M ampere meter A m CHA
96. Equation To derive the magnetostatic equation start with Amp re s law for static cases V x H J The current is J ovxB J where J is an externally generated current density and v is the velocity of the conductor Using the definitions of magnetic potential B V x A and the constitutive relationship B M rewrite Amp re s law as V ug V x A M ovx VxA J THE MAGNETIC FIELD INTERFACES which is the equation used in magnetostatics 1 2D Axi The term involving the velocity only applies in the 2D and 2D axisymmetric formulations Frequency Domain Equation To derive the time harmonic equation this physics interface solves start with Amp re s law including displacement currents then called Maxwell Amp re s law as these do not involve any extra computational cost in the frequency domain oD VxH J o0E ovxB J P at at Now assume time harmonic fields and use the definitions of the fields B VxA E joA and combine them with the constitutive relationships B M and D egE to rewrite Amp re s law as oc o eg A V x ug V x A M ov x V x A J The term involving the velocity only applies in the 2D and 2D axisymmetric formulations 2D Axi THEORY FOR THE MAGNETIC FIELDS INTERFACE 241 Transient Equation The transient equation this physics interface solves is Amp re s law here illustrated with the constitutive relation
97. Gate resistance Rg 00 Source resistance TNOM 298 15 K Device temperature 0v Zero bias threshold voltage W 50e 6 m Gate width T GAMMA o vo5 Bulk threshold parameter PHI 0 5 V Surface potential A LAMBDA Channel length modulation Diode Figure 7 3 illustrates equivalent circuit for the diode CHAPTER 7 THE ELECTRICAL CIRCUIT INTERFACE o idhl Rs Y Y idrec idb f Vq Figure 7 3 circuit for the diode The following equations are used to compute the relations between currents and voltages in the circuit THEORY FOR THE ELECTRICAL CIRCUIT INTERFACE 277 278 lq ldhl drec lab Ua NV 1 DD id 4j 1 i uit Ikr NV ldrec Ie Ua t By ONayVr lap Igye 1 eT Fov as U Vy d C J U 1 Foy M 1 Fo 1 M v2 FeV J EN kpT vom q where the following model parameters are required TABLE 7 3 DIODE TRANSISTOR MODEL PARAMETERS PARAMETER DEFAULT DESCRIPTION By Inf V Reverse breakdown voltage Zero bias junction capacitance Fo 0 5 Forward bias capacitance coefficient Ipy le 09 A Current at breakdown voltage Ip Inf A Corner for high current roll off Ig le I3 Saturation current M 0 5 Grading coefficient N Ideality factor Ngy Breakdown ideality factor Ng 2 Recombination ideality factor Rg 00 Series resistance TNOM 298 15 Device temp
98. IC CURRENTS INTERFACE 147 ELECTRIC FIELD EI See Electric Field as described for the Charge Conservation node for the Electrostatics interface Note CONDUCTION CURRENT j See Conduction Current as described for Current Conservation Note Electric Insulation Electric Insulation is the default boundary condition and this feature adds electric insulation as the boundary condition This boundary condition means that no electric current flows into the boundary At interior boundaries it means that no current can flow through the boundary and that the electric potential is discontinuous across the boundary It is also applicable at symmetric boundaries where the potential is known to be symmetric with respect to the boundary To add electric insulation to an interior boundary add an Electric Insulation node in addition to the one that represents the default g boundary condition Electric insulation as the default boundary condition T is not applicable to interior boundaries BOUNDARY SELECTION From the Selection list choose the boundaries to apply electric insulation For some interfaces All boundaries are selected by default and cannot be changed For the Electric Currents Shell interface select edges 3D or Note points 2D instead of boundaries 148 CHAPTER 4 THE ELECTRIC FIELD INTERFACES PAIR SELECTION If Electric Insulation is selected from the Pairs menu choose the pair to def
99. Interfaces This chapter summarizes the functionality of the Electric Field interfaces which are found under the AC DC branch Xx in the Model Wizard The AC DC Module enhances the Electrostatics and Electric Currents interfaces included with the basic COMSOL Multiphysics license In this chapter The Electrostatics Interface The Electric Currents Interface The Electric Currents Shell Interface Theory of Electric Fields Theory for the Electrostatics Interface Theory for the Electric Currents Interface Theory for the Electric Currents Shell Interface 109 HO The Electrostatics Interface The Electrostatics interface found under the AC DC branch X in the Model Wizard has the equations boundary conditions and space charges for modeling electrostatic fields solving for the electric potential Charge Conservation is the main feature which adds the equation for the electric potential and has a settings window for defining the constitutive relation for the electric displacement field and its associated properties such as the relative permittivity When this interface is added these default nodes are also added to the Model Builder Charge Conservation Zero Charge default boundary condition and Initial Values Right click the Electrostatics node to add other features that implement for example boundary conditions and space charges Electric Sensor Model Library path COMSOL Multip
100. LECTRICAL CIRCUIT INTERFACE External U vs I The External U vs I node ui connects an arbitrary current measurement for example from another physics interface as a source between two nodes in the electrical circuit The resulting circuit voltage between the first node and the second node is typically coupled back as a prescribed voltage source in the context of the current measurement NODE CONNECTIONS Specify the two Node names for the connecting nodes for the current source The current flows from the first node to the second node If the ground node is involved the convention is to use zero for this EXTERNAL DEVICE Enter the source of the Current Voltage excited terminals or lumped ports defined on boundaries in other physics interfaces are natural candidates but do not appear as options in the Voltage list because those do not have an accurate built in current measurement variable A User defined option must be selected and a current variable entered for example using a suitable coupling operator The voltage variable must be manually coupled back in the electrical circuit to the context of the current measurement This applies also when coupling to a voltage excited terminal or lumped port The name of this o voltage variable follows the convention cirn UvsIm v where cirnisthe Important tag of the Electrical Circuit interface node and UvsIm is the tag of the External U vs node The mentioned tags are typicall
101. MODELING WITH THE AC DC MODULE There are usually two approaches that lead to 2D cross section view of a problem When it is known that there is no variation of the solution in one particular dimension When there is a problem where the influence of the finite extension in the third dimension can be neglected Electromagnetic Forces on Parallel Current Carrying Wires Model Model Library path ACDC Module Verification Models parallel wires ode The geometry has a finite width but the model neglects the end effects from the faces parallel to the cross section because the strongest forces are between the perpendicular faces those seen as lines in the cross section Figure 3 1 The cross sections and their real geometry for Cartesian coordinates and cylindrical coordinates axial symmetry Axial Symmetry Cylindrical Coordinates m Ifthe 3D geometry can be constructed by revolving a cross section about ID Axi an axis and no variations in any variable occur when going around the axis i of revolution an axisymmetric physics interface can be used 2D Axi The spatial coordinates are called r and z where r is the radius The flow at the boundaries is given per unit length along the third dimension Because this dimension is a revolution you have to multiply all flows with ar where a is the revolution angle for example 27 for a full turn PREPARING FOR MODELING 59 60 3D PROBLEMS This
102. NPUTS This section contains field variables that appear as model inputs if the current settings include such model inputs By default this section is empty If a linear temperature relation is added for the conductivity then define the source for the temperature T From the Temperature list select an existing temperature variable from another physics interface if available or select User defined to define a value or expression for the temperature SI unit K in the field that appears underneath the list MATERIAL TYPE Select a Material type Solid Non solid or From material 216 CHAPTER 5 THE MAGNETIC FIELD INTERFACES IMPEDANCE BOUNDARY CONDITION The following material properties can be defined for the domain outside the boundary which this boundary condition approximates The default uses the values From material Or sclect User defined to enter different values or expressions e Relative permittivity unitless e Relative permeability unitless Electrical conductivity o SI unit S m Based on space dimension enter coordinate values or expressions for the Source electric field E SI unit V m Transition Boundary Condition E This feature is available with the Frequency Domain study type Note The Transition Boundary Condition is used on interior boundaries to model a sheet of a medium that should be geometrically thin but does not have to be electrically thin It represents a discontinuit
103. OMAGNETICS In the stationary case there is no acceleration and the equation representing the force balance is 0 V T f The stress tensor must be continuous across a stationary boundary between two materials This corresponds to the equation ni T5 T 0 where Ty and represent the stress tensor in Materials 1 and 2 respectively and n4 is the normal pointing out from the domain containing Material 1 This relation gives rise to a surface force acting on the boundary between Material 1 and 2 Material 2 CB ny In certain cases the stress tensor T can be divided into one part that depends on the electromagnetic field quantities and one part that is the mechanical stress tensor For the special case of an elastic body the mechanical stress tensor is proportional to the strain and the temperature gradient The exact nature of this split of the stress tensor into an electromagnetic and a mechanical part depends on the material model if it can be made at all For more information on the mechanical stress tensor for elastic materials see the documentation for the interfaces For example The Structural See Also Mechanics Branch in the COMSOL Multiphysics User s Guide Itis sometimes convenient to use a volume force instead of the stress tensor This force is obtained from the relation fu This changes the force balance equation to ELECTROMAGNETIC FORCES 4l
104. PTER 2 REVIEW OF ELECTROMAGNETICS TABLE 2 1 ELECTROMAGNETIC QUANTITIES QUANTITY SYMBOL SI UNIT ABBREVIATION Permeability u henry meter H m Permittivity farad meter F m Polarization P coulomb meter C m Poynting vector S watt meter W m Propagation constant radian meter rad m Reactance X ohm Q Relative permeability Ly dimensionless Relative permittivity Er dimensionless Resistance R ohm W Resistive loss Q watt meter Wim Torque T newton meter N m Velocity meter second m s Wavelength meter m Wave number k radian meter rad m ELECTROMAGNETIC QUANTITIES 53 References for the AC DC Interfaces 1 A Kovetz The Principles of Electromagnetic Theory Cambridge University Press 1990 2 Jianming Jin The Finite Element Method in Electromagnetics 2nd ed Wiley IEEE Press May 2002 3 Wilson Introduction to Theory and Design of Sonar Transducers Peninsula Publishing 1988 4 R K Wangsness Electromagnetic Fields 2nd ed John Wiley amp Sons 1986 5 Cheng Field and Wave Electromagnetics 2nd ed Addison Wesley 1991 6 O C Zienkiewicz C Emson and Bettess A Novel Boundary Infinite Element International Journal for Numerical Methods in Engineering vol 19 no 3 pp 393 404 1983 54 CHAPTER 2 REVIEW OF ELECTROMAGNETICS Modeling with the AC DC Module The goal of this chapter is to familiarize you with the modeling procedure in the AC DC Module Beca
105. Pairs menu choose the pair to define An identity pair has to be created first Ctrl click to deselect THE ELECTROSTATICS INTERFACE 118 CONSTRAINT SETTINGS To display this section click the Show button 2 and select Advanced Physics Options Select a Constraint type Bidirectional symmetric or Unidirectional If required select the Use weak constraints check box Electric Potential The Electric Potential node provides an electric potential Vo as the boundary condition V Vo Because the electric potential is being solved for in the interface the value of the potential is typically defined at some part of the geometry For some interfaces also select additional Electric Potential features from the Edges 3D models or Points 2D and 3D models submenus For 2D axisymmetric models it can be applied on the Symmetry axis BOUNDARY EDGE OR POINT SELECTION From the Selection list choose the geometric entity boundaries edges or points to apply an electric potential as the boundary condition Beware that constraining the potential on edges or points 3D or on m points in 2D usually yields a current outflow that is mesh dependent aution PAIR SELECTION If Electric Potential is selected from the Pairs menu choose the pair to define An identity pair has to be created first Ctrl click to deselect ELECTRIC POTENTIAL Enter the value or expression for the Electric potential Vo SI unit V
106. Porous Media subnode THE ELECTROSTATICS INTERFACE 115 116 Space Charge Density The Space Charge Density node adds a space charge density p which appears on the right hand side of the equation that the interface defines DOMAIN SELECTION From the Selection list choose the domains to define a space charge density SPACE CHARGE DENSITY Enter a value or expression for the Space charge density p SI unit C m Force Calculation Use the Force Calculation node to define globally available force and torque variables for the selected domains DOMAIN SELECTION From the Selection list choose the domains to define a force calculation FORCE CALCULATION Enter a Force name which is then appended to global variables The method used to compute forces and torques is integration of the Maxwell s stress tensor over the exterior surfaces of the set of domains This feature also gives access to the normal component of the Maxwell stress tensor on the external surfaces EI For the Magnetic and Electric Fields and Magnetic Fields interfaces the force calculation includes both electric and magnetic forces Note Enter a direction vector for the Torque axis r4 and coordinates for the Torque rotation point rp A torque calculation about a given point Torque rotation point is made and defined as a global vector variable es T force name component The resulting torque component parallel to the given
107. Quintic Specify the Value type when using splitting of complex variables Real or Complex the default The Model Builder Show and Hide Physics Options Boundary Edge Point and Pair Conditions for the Electric Currents See Also Shell Interface Boundary Edge Point and Pair Conditions for the Electric Currents Shell Interface The Electric Currents Shell Interface has the following boundary edge point and pair conditions available as indicated About the Edge and Point Conditions The conditions in Table 4 1 are available at interfaces between different media and interior edges in 3D models and point conditions in 2D and 2D axisymmetric models in continuity that is n5 Ji J 0 THE ELECTRIC CURRENTS SHELL INTERFACE 159 160 which is the natural edge point condition Available Features These features are described in this section Change Shell Thickness Current Conservation Current Source Electric Shielding Initial Values Normal Current Density These features are available for this interface and described for the Electric Currents and Electrostatics interfaces listed in alphabetical order Boundary Current Source Change Thickness Out of Plane Current Source Distributed Impedance Electric Insulation Electric Point Dipole Electric Potential External Current Density Ground Initial Values ine Current Source Point Current So
108. S Enter the Number of sectors lt 50 The default is 2 Select a Type of periodicity Continuity or Antiperiodicity Based on space dimension enter values or expressions in the table for the Axis of rotation THE ELECTRIC CURRENTS INTERFACE 151 CONSTRAINT SETTINGS To display this section click the Show button gt and select Advanced Physics Options Select a Constraint type Bidirectional symmetric or Unidirectional If required select the Use weak constraints check box In the COMSOL Multiphysics User s Guide Identity and Contact Pairs See Al E T E SOLEM Specifying Boundary Conditions for Identity Pairs Line Current Source 2D The Line Current Source node adds a line source to edges in 3D models i and to points in 2D and 2D axisymmetric models The line source 2D Axi represents electric current per unit length 3D EDGE OR POINT SELECTION From the Selection list choose the edges or points to add a current source EI For the Electric Currents Shell interface this feature is only available for 3D models and on edges Note i Beware that constraining the potential on edges or points usually yields a current outflow that is mesh dependent Caution 152 CHAPTER 4 THE ELECTRIC FIELD INTERFACES LINE CURRENT SOURCE Enter a value or expression to apply a Line current source Q SI unit A m This source represents electric
109. S INTERFACE The Electrical Circuit Interface The Electrical Circuit interface found under the AC DC branch Xx in the Model Wizard has the equations for modeling electrical circuits with or without connections to a distributed fields model solving for the voltages currents and charges associated with the circuit elements In this chapter The Hlectrical Circuit Interface Theory for the Electrical Circuit Interface 257 258 The Electrical Circuit Interface The Electrical Circuit interface 21 found under the AC DC branch X in the Model Wizard has the equations for modeling electrical circuits with or without connections to a distributed fields model solving for the voltages currents and charges associated with the circuit elements When this interface is added it adds a default Ground Node feature and associates that with node zero in the electrical circuit Circuit nodes are nodes in the electrical circuit and should not be 1 confused with nodes in the model tree of COMSOL Multiphysics Circuit node names are not restricted to numerical values but can be arbitrary Important character strings i Inductor in an Amplifier Circuit Model Library path ACDC_Module Inductive Devices and Coils inductor in circuit Model INTERFACE IDENTIFIER The interface identifier is a text string that can be used to reference the respective physics interface if appropriate Such situations could occur when
110. S Parameter Calculations in COMSOL Multiphysics Lumped Ports The AC DC interfaces have a built in support for S parameter calculations To set up an S parameter study use a Lumped Port boundary feature for each port in the model The lumped ports should only be used when the port width is much smaller than the wavelength For more details about lumped ports see Lumped Ports with Voltage Input See Also See Lumped Port for instructions to set up a model CHAPTER 3 S Parameter Variables The AC DC Module automatically generates variables for the S parameters The port names use numbers for sweeps to work correctly determine the variable names If for example there are two lumped ports with the numbers 1 and 2 and Lumped Port 1 is the inport the software generates the variables 11 and 21 11 is the S parameter for the reflected wave and 21 is the S parameter for the transmitted wave For convenience two variables for the S parameters on a dB scale 11dB and S21dB are also defined using the following relation 5 11 20log10 S The model and physics interface names also appear in front of the variable names so they may vary The S parameter variables are added to the predefined quantities in appropriate plot lists MODELING WITH THE AC DC MODULE Connecting to Electrical Circuits In this section About Connecting Electrical Circuits to Physics Interfaces Connecting Electrical Circuits
111. Selecting the Space Dimension for the Model Geometry Most ofthe problems solved with COMSOL Multiphysics are three dimensional 3D in the real world In many cases it is sufficient to solve a two dimensional 2D problem that is close or equivalent to the real problem g It is good practice to start a modeling project by building one or several Tp 2D models before going to a 3D model 1 This is because 2D models are easier to modify and solve much faster Thus modeling mistakes are much easier to find when working in 2D Once the 2D model is verified you are in a much better position to build a 3D model 2D PROBLEMS The following is a guide through some of the common approximations made for 2D problems Remember that modeling in 2D usually represents some 3D geometry under the assumption that nothing changes in the third dimension CHAPTER 3 Cartesian Coordinates In this case you view a cross section in the xy plane of the actual 3D geometry The geometry is mathematically extended to infinity in both directions along the z axis assuming no variation along that axis All the total flows in and out of boundaries are per unit length along the z axis A simplified way of looking at this is to assume that the geometry is extruded one unit length from the cross section along the z axis The total flow out of each boundary is then from the face created by the extruded boundary a boundary in 2D is a line
112. T condition CHAPTER 5 THE MAGNETIC FIELD INTERFACES About the Boundary Conditions In magnetostatics the relevant interface condition between two domains 1 and 2 is 0 This condition provides continuity of the normal component of the magnetic flux density and is automatically satisfied by the natural boundary condition for interior boundaries which is n ug VV M HoV Vm M n B B5 0 Available Features These features are available for this interface and listed in alphabetical order Also see Table 5 2 for a list of interior and exterior boundary conditions External Magnetic Flux Density Initial Values Force Calculation described for the Electrostatics interface Magnetic Flux Conservation Magnetic Flux Density Magnetic Insulation the default boundary condition Magnetic Potential Magnetic Shielding Periodic Condition Sector Symmetry described for the Electric Currents interface Thin Low Permeability Gap Zero Magnetic Scalar Potential In the COMSOL Multiphysics User s Guide About Infinite Element Domains and Perfectly Matched Layers Continuity on Interior Boundaries See M Identity and Contact Pairs Specifying Boundary Conditions for Identity Pairs THE MAGNETIC FIELDS NO CURRENTS INTERFACE 223 224 The links to the features described in the COMSOL Multiphysics User s Guide do not work in the PDF only
113. TER 3 ii 2 2 0 j i La w do Eee iQ I L L i w da l 3L n n h ksi LI NI XT Jo J J I k 0 This is the technique used when Fixed current is selected Studying Lumped Parameters To study lumped parameters use the terminal boundary condition for each electrode This boundary condition is available in the following interfaces and the methods described in the previous section are used to calculate the lumped parameters Electrostatics Uses a stationary study and the energy method Electric Currents Uses a stationary or frequency domain study type using the method based on Ohm s law Magnetic and Electric Fields when the electric potential is one of the dependent variables For the stationary study the energy method is used For the frequency domain study type the method based on Ohm s law is used The lumped parameters are defined as global variables Evaluate these from the Derived Values node under Results in the Model Builder or define 1D plot groups SWEEP SETTINGS AND TOUCHSTONE EXPORT In the main node of the interface activate a sweep to loop the excitation over the terminals in the model and calculate a lumped parameter matrix For frequency domain models there is also an inner loop with a frequency sweep for each terminal and the lumped parameters are exported to a Touchstone file The generated lumped parameters are in the form of an impedance or admittance matrix depending on the t
114. This removes all faces internal to the nets within a layer Removing Features Remove all features that are not important for the simulation This is usually best to do before the import in NETEX G or in the ECAD software When importing with Grouping of geometries set to None it is possible to manually delete certain objects after import but it is recommended to do this only for relatively simple geometries PROBLEMS WHEN EXTRUDING LAYERS Most ECAD or EDA programs support design rule checks DRC which test the entire layout and check that all features vias conductors and components are separated according to certain rules With such checks the layout is free from overlapping vias and conductors touching other conductors or vias This also ensures that the special extrude functionality of the ECAD import works properly If the file contains such design rule violations the extrude might fail and throw an error message stating that it could not handle the topology of the layout The best approach to handle such problems is to perform a DRC with your ECAD software and produce new layout files If this is not possible import the layout in 2D and try to identify the problematic features They can either be in a single layer or at the interface between two adjacent layers When identified it is possible to remove them manually using a text editor ifa NETEX G file or an ODB file is being imported It can be hard to find a certain feature bu
115. Torque axis is given as a global variable typically es Tax force name CHAPTER 4 THE ELECTRIC FIELD INTERFACES Initial Values The Initial Values node adds an initial value for the electric potential V that can serve as an initial condition for a transient simulation or as an initial guess for a nonlinear solver DOMAIN SELECTION From the Selection list choose the domains to define an initial value INITIAL VALUES Enter a value or expression for the initial value of the Electric potential V The default value is 0 V Ground The Ground node is the default boundary condition and implements ground as the boundary condition V 0 Ground means that there is a zero potential on the boundary This boundary condition is also applicable at symmetry boundaries where the potential is known to be antisymmetric with respect to the boundary For some interfaces also select additional Ground features from the Edges 3D models or Points 2D and 3D models submenus For 2D axisymmetric models it can be applied on the Symmetry axis BOUNDARY EDGE OR POINT SELECTION From the Selection list choose the geometric entity boundaries edges or points to apply a ground zero potential boundary condition i Beware that constraining the potential on edges or points in 3D or on points in 2D usually yields a current outflow that is mesh dependent aution PAIR SELECTION If Ground is selected from the
116. Using Predefined Couplings Connecting Electrical Circuits by User Defined Couplings Inductor in an Amplifier Circuit Model Library path ACDC Module n Inductive Devices and Coils inductor in circuit Model Tutorial Example Modeling a 3D Inductor Model Library path ACDC Module Inductive Devices and Coils inductor 3d About Connecting Electrical Circuits to Physics Interfaces This section describes the various ways electrical circuits can be connected to other physics interfaces in COMSOL Multiphysics If you are not familiar with circuit modeling it is recommended that you review the Theory for the Electrical Circuit Interface In general electrical circuits connect to other physics interfaces via one or more of three special circuit features External I vs U External U vs I External I Terminal CONNECTING TO ELECTRICAL CIRCUITS 95 96 These features either accept a voltage measurement from the connecting non circuit physics interface and return a current from the circuit interface or the other way around The External features are considered ideal current or voltage sources by the Electrical Circuit interface Hence you cannot connect them directly in parallel voltage sources or in series current sources with other ideal sources This results in the error message The DAE is Note structurally inconsistent A workaround is to provide a suitable parallel or series resistor
117. a Coil excitation Current Voltage Circuit voltage or Circuit current f Current is selected enter a Coil current SI unit A The default is 1 A If Voltage is selected enter a Coil voltage SI unit V The default is 1 V fCircuit current is selected it works similarly to the Current excitation but in this case the inputs are provided by a circuit connection e fCircuit voltage is selected it works similarly to the Voltage excitation but in this case the inputs are provided by a circuit connection 1 For 2D and 2D axisymmetric models Power is also available as Coil 2D excitation option If Power is selected enter a Coil power SI unit W i The default value is 1 W 2D Axi Selecting Power makes the problem nonlinear For more information see Power Excitation Note Single Iurn Coil Domain The Single Turn Coil Domain node models a conductive for example metallic domain subject to a lumped excitation such as voltage or current The excitation specified is translated into a conduction current flowing in the domain The Single Turn Coil Domain feature is a contributing feature that is it is applied on top of an Amp re s Law feature that provides the material model for the domain 202 CHAPTER 5 THE MAGNETIC FIELD INTERFACES In 2D and 2D axisymmetric models the direction of the applied electric field is assumed to be out of plane The settings specify h
118. alar BOUNDARY SELECTION From the Selection list choose the boundaries to define a magnetic flux density THE MAGNETIC FIELD INTERFACES COORDINATE SYSTEM SELECTION The Global coordinate system is selected by default The Coordinate system list contains any additional coordinate systems the model includes MAGNETIC FLUX DENSITY Select a Type of the boundary condition to use Inward flux density the default or Magnetic Flux density If Inward flux density is selected it defines the boundary condition according to Equation 5 2 Enter a scalar value or expression for the normal component of the Inward flux density B SI unit T A positive value represents an inward flux If Magnetic flux density is selected it defines the boundary condition according to Equation 5 1 Enter a value or expression for each component of the Magnetic flux density Bo SI unit T in the corresponding fields Zero Magnetic Scalar Potential The Zero Magnetic Scalar Potential feature provides a boundary condition that specifies a zero magnetic potential on the boundary V 0 BOUNDARY OR POINT SELECTION From the Selection list choose the geometric entity boundaries or points to define a zero magnetic potential CONSTRAINT SETTINGS To display this section click the Show button and select Advanced Physics Options Select a Constraint type Bidirectional symmetric or Unidirectional If required select the Use wea
119. ame This name is appended to the global variables current voltage defined by this coil and it is used to identify the coil in a Coil Current Calculation study step Select a Coil excitation Current Voltage Power Circuit voltage or Circuit current If Current is selected also enter a Coil current SI unit A The default is 1 A If Voltage is selected also enter a Coil potential Voj SI unit V The default is 1 V MAGNETIC FIELDS INTERFACE ADVANCED FEATURES 209 210 fCircuit current is selected it works similarly to the Current excitation but in this case the inputs are provided by a circuit connection e fCircuit voltage is selected it works similarly to the Voltage excitation but in this case the inputs are provided by a circuit connection If Power is selected enter a Coil power SI unit W The default value is 1 W EI Selecting Power makes the problem nonlinear For more information see Power Excitation Note Coil Domains See Also Coil Excitation Reversed Current Direction Right click the Coil Group Domain node to add the Reversed Current Direction node DOMAIN SELECTION From the Selection list choose the domains to define the reversed current direction Coil Domains See Also CHAPTER 5 Harmonic Perturbation Right click the Coil Group Domain node to add the Harmonic Perturbation feature Use a Harmonic Perturbatio
120. amic case and V are coupled via the selected gauge For a dynamic formulation it is also possible to select a such that the scalar electric potential vanishes and only the magnetic vector potential has to be considered The dynamic formulations frequency domain and time dependent study types of the Magnetic Fields interface are operated in this gauge as it involves only A The Magnetic and Electric fields interface in the AC DC Module involves both and V and is inherently ungauged for all study types In the static limit A and V are not coupled via the gauge selection and thus any gauge can be chosen for when performing magnetostatic modeling The Gauge and the Equation of Continuity for Dynamic Fields After eliminating the electric potential by choosing the appropriate gauge and disregarding the velocity term The equation of continuity obtained by taking the divergence of Amp re s law reads V 525 4 0 It is clear that unless the electrical conductivity is uniform the particular gauge used to eliminate V cannot be the Coulomb gauge as that would violate the equation of continuity and would thereby also violate Amp re s law Explicit Gauge Fixing Divergence Constraint The AC DC Module has a gauge fixing feature that is imposed by adding an extra scalar field variable y not to be confused with V used in the gauge transformation in the preceding section The y field is used to impose a divergence constraint
121. arameter output is turned off SETTINGS This section is available if Cable or Current is selected as the Terminal type E If Cable is selected enter the Characteristic impedance SI unit Note If Current is selected enter a Terminal current SI unit A Edge Current Use the Edge Current feature to specify a line current along one or more edges EDGE SELECTION From the Selection list choose the edges to apply an edge current EDGE CURRENT Specify the Edge current T SI unit A 214 CHAPTER 5 THE MAGNETIC FIELD INTERFACES External Magnetic Vector Potential This feature is only available when solving a problem with a background magnetic vector potential Reduced field is selected from the Solve for list Note under Background Field on the interface settings window The External Magnetic Vector Potential boundary condition forces the reduced magnetic vector potential to be zero on the boundary or equivalently forces the total field to be equal to the background field Apply this boundary condition on external boundaries that are at a distance far enough from the system so that its effect on the background field is negligible BOUNDARY SELECTION From the Selection list choose the boundaries to specify the external magnetic vector potential Impedance Boundary Condition The Impedance Boundary Condition provides a boundary condition that is useful at boundaries
122. as the boundary condition THE ELECTROSTATICS INTERFACE 123 124 PAIR SELECTION If Displacement Field is selected from the Pairs menu choose the pair to define An identity pair has to be created first Ctrl click to deselect COORDINATE SYSTEM SELECTION The Global coordinate system is selected by default The Coordinate system list contains any additional coordinate systems that the model includes ELECTRIC DISPLACEMENT FIELD Enter the coordinates of the Boundary electric displacement field Do SI unit C m Distributed Capacitance The Distributed Capacitance node adds a distributed capacitance boundary condition according to the following equations for exterior boundaries left and interior boundaries right Vref y ref n D S98 q n D Dj S Use this boundary condition to model a thin sheet or film of a dielectric p material The sheet has the relative permittivity and the surface Tip thickness dg and it is connected to the reference potential V BOUNDARY SELECTION From the Selection list choose the boundaries to apply a distributed capacitance PAIR SELECTION If Distributed Capacitance is selected from the Pairs menu choose the pair to define An identity pair has to be created first Ctrl click to deselect MATERIAL TYPE Select a Material type Solid Non solid or From material DISTRIBUTED CAPACITANCE Enter the values or expressions for Relat
123. ated current density and v is the velocity of the conductor Add the constitutive relationship B M and rewrite Amp re s law as V x up V x A M ov x Vx A oVV J THEORY FOR THE MAGNETIC AND ELECTRIC FIELDS INTERFACE 255 The equation of continuity is obtained by taking the divergence of Amp re s law It is the equation solved for the electric potential Thus the following equations for V and A apply V ovx VxA oVV J5 0 V x ug V xA M ov x Vx A oVV 4 Frequency Domain Equations To derive the time harmonic equation this physics interface solves start with Maxwell Amp re s law including displacement current then called Maxwell Amp re s law Including this does not involve any extra computational cost in the frequency domain Assume time harmonic fields VxH J o E vxB joD J and use the definitions of the fields B VxA E VV joA and combine them with the constitutive relationships B M and D to rewrite Amp re s law as goo uy V x A M ovx V x A o joae VV joP J The equation of continuity is again obtained by taking the divergence of Amp re s law It is the equation solved for the electric potential Thus the following equations for V and A apply V joo ov x V x A o josg VV J joP 0 Joo o sA Vx ug V xA M ovx VxA o jos9 VV joP J 256 CHAPTER 6 THE MAGNETIC AND ELECTRIC FIELD
124. aterial Browser The materials databases shipped with COMSOL Multiphysics are Oo read only This includes the Material Library and any materials shipped Important with the optional modules Creating Your Own User Defined Libraries in COMSOL See Also Multiphysics User s Guide CHAPTER 9 MATERIALS About Using Materials in COMSOL USING THE MATERIALS IN THE PHYSICS SETTINGS The physics set up in a model is determined by a combination of settings in the Materials and physics interface nodes When the first material is added to a model COMSOL automatically assigns that material to the entire geometry Different geometric entities can have different materials The following example uses the heat sink mph model file contained in the Heat Transfer Module and CFD Module Model Libraries Materials Air 4 amp Aluminum 3003 H18 10 40 Figure 9 1 Assigning materials to a heat sink model Air is assigned as the material to the box surrounding the heat sink and aluminum to the heat sink itself Ifa geometry consists of a heat sink in a container Air can be assigned as the material in the container surrounding the heat sink and Aluminum as the heat sink material itself see Figure 9 1 The Conjugate Heat Transfer interface selected during model set up has a Fluid flow model defined in the box surrounding the heat sink and a Heat Transfer model defined in both the aluminum heat sink and
125. ation process includes MODELING WITH THE AC DC MODULE deposition followed by etching and then redepositing of a different layer Such advanced process schemes cannot be automatically handled correctly by the ECAD import With the grouping option All objects on adjacent layers must not cross each other because the original edge of the objects must be kept unchanged when two adjacent layers are merged to form the interface between them You can get around this by selecting a different grouping option see ECAD Import Use the 3D GDS II import with the ECAD import The standard CAD import of COMSOL Multiphysics does not support pre reading of the file so it is not possible to specify any properties the layers like thickness for example The ECAD import always reads the file before displaying the import options The best way to solve any of these issues is to do the import with the grouping option By layer and manually rearrange the layers by simple move operations so the elevation of the layers are correct You can do etching by removing a layer from other objects using the Difference button on the main toolbar or the Difference feature from the Boolean Operations submenu on the Geometry node s context menu Importing NETEX G Files The NETEX G file format is a special format produced by the application NETEX G by Artwork www artwork com NETEX G can read Gerber and drill files that almost any ECAD software can export to because
126. atures available See Also In the COMSOL Multiphysics User s Guide Continuity on Interior Boundaries Identity and Contact Pairs Specifying Boundary Conditions for Identity Pairs p Tip To locate and search all the documentation in COMSOL select Help gt Documentation from the main menu and either enter a search term or look under a specific module in the documentation tree Charge Conservation The Charge Conservation node adds the equations for charge conservation according to Gauss law for the electric displacement field It provides an interface for defining the constitutive relation and its associated properties such as the relative permittivity DOMAIN SELECTION From the Selection list choose the domains to define the electric potential and the equation based on Gauss law that describes the potential field CHAPTER 4 THE ELECTRIC FIELD INTERFACES MODEL INPUTS This section contains field variables that appear as model inputs if the current settings include such model inputs By default this section is empty MATERIAL TYPE Select a Material type Solid Non solid or From material COORDINATE SYSTEM SELECTION The Global coordinate system is selected by default The Coordinate system list contains any additional coordinate systems that the model includes ELECTRIC FIELD Select a Constitutive relation to describe the macroscopic properties of the medium relat
127. branch Xx in the Model Wizard has the equations boundary conditions and currents for modeling magnetic fields solving for the magnetic vector potential The main feature is the Amp re s Law feature which adds the equation for the magnetic vector potential and provides an interface for defining the constitutive relations and its associated properties such as the relative permeability When this interface is added these default nodes are also added to the Model Builder Magnetic Fields Amp re s Law Magnetic Insulation the default boundary condition and Initial Values Right click the Magnetic Fields node to add other features that implement for example boundary conditions and external currents Quadrupole Lens Model Library path COMSOL Multiphysics Electromagnetics quadrupole Eddy Currents Model Library path ACDC Module Inductive Devices and Coils eddy currents Model CHAPTER 5 INTERFACE IDENTIFIER The interface identifier is a text string that can be used to reference the respective physics interface if appropriate Such situations could occur when coupling this interface to another physics interface or when trying to identify and use variables defined by this physics interface which is used to reach the fields and variables in expressions for example It can be changed to any unique string in the Identifier field The default identifier for the first interface in the model is mf DOMAIN SEL
128. ced Features For the AC DC Module several advanced features and subfeatures are available with this interface In addition to the nodes described in The Magnetic Fields Interface this section details these nodes and subnodes listed in alphabetical order Automatic Current Calculation Boundary Feed Coil Group Domain Edge Current Electric Insulation External Magnetic Vector Potential Gap Feed Gauge Fixing for A field Impedance Boundary Condition Input Lumped Port Magnetic Point Dipole Magnetic Point Dipole on Axis Multi Turn Coil Domain Output Reference Edge Reversed Current Direction Single Turn Coil Domain MAGNETIC FIELDS INTERFACE ADVANCED FEATURES 197 Thin Low Permeability Transition Boundary Condition See Also Electric Point Dipole and Electric Point Dipole on Axis as defined for the Electric Currents interface Force Calculation as defined for the Electrostatics interface About Infinite Element Domains and Perfectly Matched Layers in the COMSOL Multiphysics Users Guide To locate and search all the documentation COMSOL select Help gt Documentation from the main menu and either enter a search term or look under a specific module in the documentation tree Gauge Fixing for A field 2D Axi For 2D and 2D axisymmetric models Gauge fixing is available when vector curl shape functions are used that is when having in plane de
129. cify a surface current PAIR SELECTION If Surface Current is selected from the Pairs menu choose the pair to define An identity pair has to be created first Ctrl click to deselect SURFACE CURRENT Enter values or expressions for the Surface current density J SI unit A m coordinates a Magnetic Fields Interface Advanced Features for more boundary conditions See Also Magnetic Potential The Magnetic Potential feature adds a boundary condition for the magnetic vector potential nxA BOUNDARY SELECTION From the Selection list choose the boundaries to specify the magnetic potential COORDINATE SYSTEM SELECTION The Global coordinate system is selected by default The Coordinate system list contains any additional coordinate systems that the model includes PAIR SELECTION If Magnetic Potential is selected from the Pairs menu choose the pair to define An identity pair has to be created first Ctrl click to deselect THE MAGNETIC FIELDS INTERFACE 193 MAGNETIC POTENTIAL Enter a value or expression for the Magnetic vector potential Ag SI unit Wb m coordinates Magnetic Fields Interface Advanced Features for more boundary conditions See Also CONSTRAINT SETTINGS To display this section click the Show button gt and select Advanced Physics Options Select a Constraint type Bidirectional symmetric or Unidirectional If required select the Use weak constraints check
130. coupling this interface to another physics interface or when trying to identify and use variables defined by this physics interface which is used to reach the fields and variables in expressions for example It can be changed to any unique string in the Identifier field The default identifier for the first interface in the model is cir CHAPTER 7 THE ELECTRICAL CIRCUIT INTERFACE See Also Theory for the Electrical Circuit Interface Connecting to Electrical Circuits Ground Node Resistor Capacitor Inductor Voltage Source Current Source Voltage Controlled Voltage Source Voltage Controlled Current Source Current Controlled Voltage Source Current Controlled Current Source Subcircuit Definition Subcircuit Instance NPN BJT n Channel MOSFET Diode External I vs U External U vs I External I Terminal SPICE Circuit Import Ground Node The Ground Node node L adds a ground node with the default node number zero to the electrical circuit This is the default feature in the Electrical Circuit interface GROUND CONNECTION Set the Node name for the ground node in the circuit The convention is to use zero for the ground node THE ELECTRICAL CIRCUIT INTERFACE 259 260 Resistor The Resistor node connects a resistor between two nodes in the electrical circuit NODE CONNECTIONS Set the two Node names for the connecting nodes for the resistor If the ground node is involve
131. ct Magnetic losses and unitless to describe the relative permeability as complex valued quantity iu where and are the real and imaginary parts respectively j This option is not available for the Magnetic Fields No Currents interface Note Select Remanent flux density B SI unit T to use the constitutive relation B uou H B where B is the remanent flux density the flux density when no magnetic field is present The default relative permeability 44 unitless uses values From material If User defined is selected choose Isotropic Diagonal Symmetric or Anisotropic based on the characteristics of the relative permeability and enter another value or expression in the field or matrix Enter x and y components for the for the remanent flux density B For 3D models enter x y and z components 188 CHAPTER 5 THE MAGNETIC FIELD INTERFACES Select Magnetization M SI unit A m to use the constitutive relation B uoM Enter x and y components For 3D models enter x y and z components External Current Density The External Current Density feature adds an externally generated current density Je which appears on the right hand side of the equation that the Magnetic Fields interface defines DOMAIN SELECTION From the Selection list choose the domains to define an external current density COORDINATE SYSTEM SELECTION The Global coordinate sys
132. ct information contact COMSOL at info comsol com To receive technical support from COMSOL for the COMSOL products please contact your local COMSOL representative or send your questions to support comsol com An automatic notification and case number is sent to you by email ABOUT THE AC DC MODULE COMSOL WEB SITES Main Corporate web site www comsol com Worldwide contact information www comsol com contact Technical Support main page www comsol com support Support Knowledge Base Product updates www comsol com support knowledgebase www comsol com support updates COMSOL User Community www comsol com community Typographical Conventions All COMSOL user s guides use a set of consistent typographical conventions that make it easier to follow the discussion understand what you can expect to see on the graphical user interface GUI and know which data must be entered into various data entry fields In particular these conventions are used throughout the documentation CONVENTION EXAMPLE text highlighted in blue boldface font Forward arrow symbol gt Code monospace font Click text highlighted in blue to go to other information in the PDF When you are using the online help desk in COMSOL Multiphysics these links also work to other modules model examples and documentation sets A boldface font indicates that the given word s appear exactly that way on the COMSOL Desktop
133. current flows inward in the domain CHAPTER 4 THE ELECTRIC FIELD INTERFACES BOUNDARY SELECTION From the Selection list choose the boundaries to apply a current flow as the boundary condition using the normal current density COORDINATE SYSTEM SELECTION The Global coordinate system is selected by default The Coordinate system list contains any additional coordinate systems that the model includes NORMAL CURRENT DENSITY Select an option from the Type list Inward current density or Current density finward current density is selected enter a value or expression for the Normal current density J SI unit A m Use a positive value for an inward current flow or a negative value for an outward current flow f Current density is selected enter values or expressions for the components of the Current density SI unit A m in the J fields Distributed Impedance The Distributed Impedance node adds a distributed impedance boundary condition to a model Use this boundary condition to model a thin sheet of resistive material connected to a reference potential Vref 1 The layer impedance can be specified either with the bulk material conductivity the relative permittivity and the layer thickness d or directly with the surface resistance ps and capacitance C Assuming DC currents the equation is Os n Ji J qe Vief S n Ji J5 P Viet S For the frequency domai
134. d the convention is to use zero for this DEVICE PARAMETERS Enter the Resistance of the resistor Capacitor The Capacitor node 4 connects a capacitor between two nodes in the electrical circuit NODE CONNECTIONS Set the two Node names for the connecting nodes for the capacitor If the ground node is involved the convention is to use zero for this DEVICE PARAMETERS Enter the Capacitance of the capacitor Inductor The Inductor node connects an inductor between two nodes in the electrical circuit NODE CONNECTIONS Set the two Node names for the connecting nodes for the inductor If the ground node is involved the convention is to use zero for this DEVICE PARAMETERS Enter the Inductance of the inductor Voltage Source The Voltage Source node connects a voltage source between two nodes in the electrical circuit CHAPTER 7 THE ELECTRICAL CIRCUIT INTERFACE NODE CONNECTIONS Set the two Node names for the connecting nodes for the voltage source The first node represents the positive reference terminal If the ground node is involved the convention is to use zero for this DEVICE PARAMETERS Enter the Source type that should be adapted to the selected study type It can be DC source AC source or a time dependent Sine source Depending on the choice of source also specify the Voltage the offset Voltage Voff the Frequency and the Source phase All values are peak val
135. d emitter nodes respectively If the ground node is involved the convention is to use zero for this MODEL PARAMETERS Specify the Model Parameters Reasonable defaults are provided but for any particular BJT the device manufacturer should be the primary source of information For an explanation of the Model Parameters see NPN Bipolar Transistor See Also n Channel MOSFET The n Channel MOSFET device model 48 is a large signal model for an n Channel MOS transistor MOSFET It is an advanced device model and no thorough description and motivation of the many input parameters is attempted here The interested reader is referred to Ref 2 for more details on semiconductor modeling CHAPTER 7 THE ELECTRICAL CIRCUIT INTERFACE within circuits Many device manufacturers provide model parameters for this MOSFET model For any particular make of MOSFET the device manufacturer should be the primary source of information NODE CONNECTIONS Specify four Node names for the connection nodes for the n Channel MOSFET device These represent the drain gate source and bulk nodes respectively If the ground node is involved the convention is to use zero for this MODEL PARAMETERS Specify the Model Parameters Reasonable defaults are provided but for any particular MOSFET the device manufacturer should be the primary source of information 6 For an explanation of the Model Parameters see n Channel MOS one See
136. d search all the documentation in COMSOL select g Help Documentation from the main menu and either enter a search term Tip or look under a specific module in the documentation tree THE MAGNETIC AND ELECTRIC FIELDS INTERFACE 251 Table 6 1 lists the interior and exterior boundaries available with this interface TABLE 6 1 INTERIOR AND EXTERIOR ELECTRIC AND MAGNETIC BOUNDARY CONDITIONS FOR THE MAGNETIC AND ELECTRIC FIELDS INTERFACE FEATURE INTERIOR EXTERIOR MAGNETIC BOUNDARIES Impedance Boundary Condition x Lumped Port x x Magnetic Field x Magnetic Insulation x x Magnetic Potential x x Perfect Magnetic Conductor x x Surface Current x x Thin Low Permeability Gap x Transition Boundary Condition x ELECTRIC BOUNDARIES Electric Insulation x x Electric Potential x x Floating Potential x x Ground x x Normal Current Density x Periodic Condition x Terminal x x For axisymmetric models COMSOL Multiphysics takes the axial E ID Axi symmetry boundaries at 0 into account and automatically adds an Axial Symmetry feature to the model that is valid on the axial symmetry 4 boundaries only 2D Axi 252 CHAPTER 6 THE MAGNETIC AND ELECTRIC FIELDS INTERFACE Ampere s Law and Current Conservation The Amp re s Law and Current Conservation node adds Amp re s law and the equation of continuity for the electric current It provides an interface for defining the constitutive relations and their a
137. del Magnetostatics one sided magnet Use boundary conditions for known solutions A body with a high conductivity at high frequency has the current density confined to a thin region beneath the surface of the wire You can often replace the current in the body by either a surface current boundary condition or an impedance boundary condition i Cold Crucible Model Library path ACDC Module Electromagnetic Heating Model cold_crucible Applying Electromagnetic Sources Electromagnetic sources can be applied in many different ways The typical options are volume sources boundary sources line sources and point sources where point sources in 2D formulations are equivalent to line sources in 3D formulations The way sources are imposed can have an impact on what quantities can be computed from the model For example a point source in an electrostatics model represents a singularity and the electric potential does not have a finite value at the position of the source PREPARING FOR MODELING l 62 CHAPTER 3 In a COMSOL Multiphysics model a point source has a finite but mesh dependent potential value Thus it does not make sense to compute a point to point capacitance because this is defined as the ratio of charge to voltage and for a point charge the potential is not well defined In general using volume or boundary sources is more flexible than using line or point sources but the meshing of the source domains b
138. deling situation requires a basic understanding of the charge dynamics in conductors This section is a brief introduction to Charge Relaxation Theory Physics interfaces for the modeling of dynamic quasi static that is without including wave propagation effects electric fields and currents Tip are available with the AC DC Module and MEMS Module Charge Relaxation Theory The different physics interfaces involving only the scalar electric potential can be interpreted in terms of the charge relaxation process The fundamental equations involved are Ohm s law J the equation of continuity Z ar J 0 and Gauss law V sE p By combining these one can deduce the following differential equation for the space charge density in a homogeneous medium Op p 0 This equation has the solution t p t poe where o CHAPTER 4 THE ELECTRIC FIELD INTERFACES is called the charge relaxation time For a good conductor like copper is of the order of 1071 s whereas for a good insulator like silica glass it is of the order of 10 s For a pure insulator it becomes infinite When modeling real world devices there is not only the intrinsic time scale of charge relaxation time but also an external time scale t at which a device is energized or the Observation time It is the relation between the external time scale and the charge relaxation time that determines what physics i
139. density J unitless Electric Shielding A This feature is available for 3D models only 3D The Electric Shielding feature can be used to models a geometrically thin section of shell made ofa highly conductive medium The Layer Thickness parameter d 1 specifies the thickness in the direction tangential to the shell while the thickness in the direction normal to the shell is taken from the physics interface or if present from a Change Shell Thickness node The layer has an electrical conductivity of o and a relative permittivity of EDGE SELECTION From the Selection list choose the edges to apply an electric shielding as the boundary condition CHAPTER 4 THE ELECTRIC FIELD INTERFACES PAIR SELECTION If Electric Shielding is selected from the Pairs menu choose the pair to define An identity pair has to be created first Ctrl click to deselect ELECTRIC SHIELDING The default Relative permittivity unitless and Electrical conductivity SI unit S m take values From material Select User defined to enter different values or expressions Enter a value or expression for the Layer thickness d SI unit m The default is 1 cm THE ELECTRIC CURRENTS SHELL INTERFACE 165 166 Theory of Electric Fields COMSOL Multiphysics includes physics interfaces for the modeling of static electric fields and currents Deciding what specific physics interface and study type to select for a particular mo
140. des for the voltage source The first node represents the positive reference terminal If the ground node is involved the convention is to use zero for this EXTERNAL DEVICE Enter the source of the Voltage If circuit or current excited terminals or circuit ports are defined on boundaries or a multiturn coil domains is defined in other physics interfaces these display as options in the Voltage list Also select the User defined option and enter your own voltage variable for example using a suitable coupling operator For inductive or electromagnetic wave propagation models the voltage measurement must be performed as an integral of the electric field as the electric potential only does not capture induced EMF Also the integration must be performed over a distance that is short compared to the local wavelength Except for when coupling to a circuit terminal or circuit port the current flow variable must be manually coupled back in the electrical circuit to the context of the voltage measurement This applies also when coupling to a o current excited terminal The name of this current variable follows the convention cirn IvsUm i where is the tag of the Electrical Circuit interface node and IvsUm is the tag of the External I vs U node The mentioned tags are typically displayed within curly braces in the model tree Model Couplings in the COMSOL Multiphysics User s Guide See Also CHAPTER 7 THE E
141. disabled when Manual control of elevations is enabled With the Keep interior boundaries check box cleared the import removes all interior boundaries of the imported nets This keeps the geometry complexity to a minimum and can also make the import more robust in some situations Clearing the Ignore text objects check box tells the importer to skip all objects in an ODB file that have the TEXT tag set It is common that PCB layouts have text written in copper Such objects increase the problem size and are usually of no interest in a physical simulation For NETEX G GDS import other options that can significantly reduce the complexity of imported layouts are the recognition of arcs and straight lines With the Recognize arcs set to Automatic all polygon chains that represent arcs are identified and replaced with more efficient curve objects With the fields appearing when setting this to Manual the arc recognition can be fine tuned The Find straight lines check box also controls whether to convert several polygon segments that lie on a single straight line into a single straight segment This option uses the number in the Minimum angle between segments field to determine if a group of segments lies on the same straight line Geometry repair is controlled via the Repair imported data check box and the Relative repair tolerance ficld Meshing an Imported Geometry Creating Meshes and Generating a 3D Swept Mesh in the COMSOL
142. ditional coordinate systems that the model includes ELECTRIC FIELD Ej See Electric Field as described for the Charge Conservation node for the Electrostatics interface Note CONDUCTION CURRENT By default the Electrical conductivity SI unit S m for the media is defined From material Or select User defined Linearized resistivity Porous media or Archie s law THE ELECTRIC CURRENTS SHELL INTERFACE 161 162 User Defined If User defined is selected select Isotropic Diagonal Symmetric or Anisotropic depending on the characteristics of the electrical conductivity and then enter values or expressions in the field or matrix If another type of temperature dependence is used other than a linear temperature relation enter any expression for the conductivity as a Note function of temperature Linearized Resistivity Select Linearized resistivity for a temperature dependent conductivity this occurs in for example Joule heating and is also called resistive heating The equation describing the conductivity _ 1 where is the resistivity at the reference temperature and a is the temperature coefficient of resistance which describes how the resistivity varies with temperature The default Reference temperature SI unit Resistivity temperature coefficient a SI unit 1 K and Reference resistivity SI unit are taken From material which means tha
143. ds no currents interface 222 pair selection 20 pair thin low permeability gap node 229 parameters infinite elements 68 PDE formulations 33 perfect conductors and dielectrics 38 perfect magnetic conductor node 194 periodic condition node 125 permeability volume average 174 phasors 38 physics settings windows 19 plotting material properties 296 PMC see perfect magnetic conductor point charge node 129 point charge on axis node 129 point conditions electric currents interface 135 electric currents shell interface 159 electrostatics interface 12 magnetic and electric fields interface 249 magnetic fields interface 183 magnetic fields no currents interface 222 point current source node 153 point current source on axis node 154 point dipoles magnetic 219 porous media node 141 port boundary conditions 94 ports lumped 90 91 potentials scalar and magnetic 33 INDEX 307 308 INDEX power law porous media 174 175 Poynting s theorem 35 predefined couplings electrical circuits 96 prescribed rotation node 234 prescribed rotational velocity node 234 principle of virtual displacement 50 pure conductor stress tensor 46 48 quasi static approximation 35 235 reciprocal permeability volume average 175 reference edge node 206 relative repair tolerance 106 resistor node 260 reversed current direction node 210 rotating machinery magnetic interface 230 saturation coefficient
144. e Magnetic and Electric Fields interface found under the AC DC branch of the Model Wizard has the equations boundary conditions and external currents for modeling electric and magnetic fields solving for the electric potential and magnetic vector potential Ifthe conduction current in the modeled system is confined only in some regions for example a metallic coil and most of the domains are g non conductive it may be better to use the Magnetic Fields interface and Tip apply the Coil Group Domain feature on the conductive regions instead of using this interface Use the Magnetic and Electric Fields interface when the current continuity equation is needed everywhere in the simulation domain The main feature is the Amp re s Law and Current Conservation feature which adds the equation for the electric potential and magnetic vector potential and provides an interface for defining the constitutive relations and their associated properties such as the relative permeability relative permittivity and electrical conductivity When this interface is added these default nodes are also added to the Model Builder Amp re s Law and Current Conservation Magnetic Insulation the default boundary condition for the magnetic vector potential and Initial Values Right click the Magnetic and Electric Fields node to add other features that implement for example boundary conditions and external currents Except
145. e boundary On interior boundaries the perfect magnetic conductor boundary condition literally sets the tangential magnetic field to zero which in addition to setting the surface current density to zero also makes the tangential magnetic vector potential and in dynamics the tangential electric field discontinuous BOUNDARY SELECTION From the Selection list choose the boundaries to model as perfect magnetic conductors PAIR SELECTION If Perfect Magnetic Conductor is selected from the Pairs menu choose the pair to define An identity pair has to be created first Ctrl click to deselect Magnetic Fields Interface Advanced Features for more boundary conditions See Also Line Current Out of Plane 2D This feature is available for 2D and 2D axially symmetric models 1 2D Axi Use the Line Current Out of Plane feature selected from the Points menu to specify a line current out of the modeling plane In axially symmetric geometries this is the rotational direction in 2D geometries this is the z direction POINT SELECTION From the Selection list choose the points to add a line current THE MAGNETIC FIELDS INTERFACE 195 LINE CURRENT OUT OF PLANE Enter a value or expression for the Out of plane current T SI unit A Magnetic Fields Interface Advanced Features for more point conditions See Also 196 CHAPTER 5 THE MAGNETIC FIELD INTERFACES Magnetic Fields Interface Advan
146. e harmonic distortion of a sinusoidal signal It might also be more efficient to use a time dependent study if there is a periodic input with many harmonics like a square shaped signal There are some special predefined study types for the Induction Heating multiphysics interface This interface is based on the assumption that the magnetic cycle time is short compared to the thermal time scale adiabatic assumption Thus it is associated with two predefined study types MODELING WITH THE AC DC MODULE Frequency Stationary Time harmonic magnetic fields Stationary heat transfer Frequency Transient Time harmonic magnetic fields Transient heat transfer AC DC Module Study Availability See Also 2D Field Variables When solving for a vector field in 2D the physics interface has three options to solve for the out of plane vector the in plane vector or the three component vector Depending on the choice the available source specification options on the domain boundary edge and point levels change accordingly Meshing and Solving MESH RESOLUTION The finite element method approximates the solution within each element using some elementary shape function that can be constant linear or of higher order Depending on the element order in the model a finer or coarser mesh is required to resolve the solution In general there are three problem dependent factors that determine the necessary mesh
147. e thermal conductivity k describes the relationship between the heat flux vector q and the temperature gradient VT as q AVT which is Fourier s law of heat conduction Enter this quantity as power per length and temperature THERMODYNAMICS The default uses values From material for the Heat capacity at constant pressure C SI unit J kg K and Density p SI unit kg m Select User defined to enter other values or expressions for one or both variables Electromagnetic Heat Source The Electromagnetic Heat Source feature represents the electromagnetic losses Qe SI unit W m as a heat source in the heat transfer part of the model It is given by Qe E Qu Qui where the resistive losses are 1 Qn gRe J E and the magnetic losses are ZRe ioB H DOMAIN SELECTION From the Selection list choose the domains to apply the model The default feature settings cannot be edited and include all domains in the model Initial Values The Initial Values feature adds initial values for the temperature surface radiosity and magnetic vector potential THE HEAT TRANSFER BRANCH DOMAIN SELECTION From the Selection list choose the domains to apply the initial values The default setting is to include all domains in the model INITIAL VALUES Enter values or expressions for the Temperature T SI unit Surface radiosity J SI unit W m and Magnetic vector potential A SI unit Wb m The
148. e within a model The Model Builder Show and Hide Physics Options Domain Boundary Edge Point and Pair Conditions for the Electrostatics Interface See Also Theory for the Electrostatics Interface Domain Boundary Edge Point und Pair Conditions for the Electrostatics Interface The Electrostatics Interface has these domain boundary edge point and pair features available About the Boundary Conditions The relevant interface condition at interfaces between different media is ns D1 D3 In the absence of surface charges this condition is fulfilled by the natural boundary condition n 9VV P s VV P n D D3 0 Available Features These features are available for this interface and listed in alphabetical order Also see Table 4 1 for a list of interior and exterior boundary conditions including edge point and pair availability Change Cross Section Change Thickness Out of Plane Charge Conservation Dielectric Shielding Distributed Capacitance Electric Displacement Field Electric Potential 112 CHAPTER 4 THE ELECTRIC FIELD INTERFACES Electrostatic Point Dipole External Surface Charge Accumulation Floating Potential Force Calculation Ground Initial Values Line Charge Line Charge on Axis Line Charge Out of Plane Periodic Condition Point Charge Point Charge on Axis Space Charge Density Surface Charge Density Termina
149. eatures i Generator in 2D Model Library path ACDC Module Model Motors_and_Actuators generator_2d CHAPTER 5 INTERFACE IDENTIFIER The interface identifier is a text string that can be used to reference the respective physics interface if appropriate Such situations could occur when coupling this interface to another physics interface or when trying to identify and use variables defined by this physics interface which is used to reach the fields and variables in expressions for example It can be changed to any unique string in the Identifier field The default identifier for the first interface in the model is rmm DOMAIN SELECTION The default setting is to include All domains in the model To choose specific domains select Manual from the Selection list THE MAGNETIC FIELD INTERFACES BACKGROUND FIELD Select an option from the Solve for list Full field the default or Reduced field If Reduced field is selected specify a Background magnetic vector potential A SI unit Wb m The total field used in the physics and equations are given by the sum of the reduced and background fields COMPONENTS Select the Components Out of plane vector potential the default In plane vector potential or Three component vector potential THICKNESS Enter a value or expression for the global Out of plane thickness d SI unit m The default value of 1 m is typically not representative for a thin domain Instead it desc
150. ecause only some combinations of electric and magnetic boundary conditions are physically relevant whereas others may lead to nonphysical models and thus violate current conservation The basic steps for this are to right click the Magnetic and Electric Fields node to add the magnetic boundary conditions Then right click these y magnetic boundary condition nodes to add the electric boundary conditions as subnodes STEP I MAGNETIC BOUNDARY CONDITIONS With no surface currents present the interface conditions 0 0 x A Ay ns x H H3 need to be fulfilled Because the physics interface solves for A the tangential component of the magnetic potential is always continuous and thus the first condition is automatically fulfilled The second condition is equivalent to the natural boundary condition and is hence also fulfilled unless surface currents are explicitly introduced THE MAGNETIC AND ELECTRIC FIELDS INTERFACE 249 STEP 2 ELECTRIC BOUNDARY CONDITIONS The relevant interface condition at interfaces between different media and interior boundaries is continuity that is n9 Ji J 0 which is the natural boundary condition For the Magnetic and Electric Fields interface a default Electric Insulation feature is also added to Magnetic Insulation Also right click to add other Note nodes Available Features Because the These features are available for this interface and listed in alphabetical
151. ecomes more expensive Selecting a Study Type When variations in time are present there are two main approaches to how to represent the time dependence The most straightforward is to solve the problem in the time domain by calculating the changes in the solution for each time step This approach can be time consuming if small time steps are necessary for the desired accuracy It is necessary to use this approach when the inputs are transients like turn on and turn off sequences An efficient simplification is to assume that all variations in time occur as sinusoidal signals Then the problem is time harmonic and it can formulated as a stationary problem in the frequency domain with complex valued solutions The complex value represents both the amplitude and the phase of the field while the frequency is specified as a predefined scalar input or for frequency sweeps provided as a solver parameter This approach is useful because combined with Fourier analysis it applies to all periodic signals with the exception of nonlinear problems Examples of typical frequency domain simulations are quasi static problems where the input variables are sinusoidal signals For nonlinear problems use a frequency domain study after a linearization of the problem which assumes that the distortion of the sinusoidal signal is small Specify a time dependent study when you think that the nonlinear influence is very strong or if you are interested in th
152. ect User defined Porous media Archie s law or Linearized resistivity from the list If User defined is selected choose Isotropic Diagonal Symmetric or Anisotropic based on the characteristics of the electrical conductivity and then enter values or expressions in the field or matrix Linearized Resistivity If Linearized resistivity is selected it defines the electric resistivity and conductivity as a linear function of temperature and this equation describes the conductivity 1 po 1 a T TQ where is the resistivity at the reference temperature Tp a is the temperature coefficient of resistance which describes how the resistivity varies with temperature The default Reference temperature Tef SI unit Resistivity temperature coefficient SI unit 1 K and Reference resistivity p SI unit are taken From material which means that the values are taken from the boundary material To specify other values for any of these properties select User defined from the list and then enter a value or expression T is the current temperature which can be a value specified as a model input or the temperature from a heat transfer interface The definition of the temperature field is in the Model Inputs section Porous Media When Porous media is selected right click to add a Porous Media subnode Archie s Law When Archie s law is selected right click to add an Archie s Law subnode ELECTRIC FIEL
153. ectromagnetic material properties that you can store in the material databases such as electrical conductivity and resistivity relative permittivity relative permeability nonlinear BH curves and refractive index OVERVIEW OF THE USER S GUIDE 27 28 CHAPTER 1 INTRODUCTION Review of Electromagnetics This chapter contains an overview of the theory behind the AC DC Module It is intended for readers that wish to understand what goes on in the background when using the physics interfaces In this chapter Fundamentals of Electromagnetics Electromagnetic Forces Electromagnetic Quantities References for the AC DC Interfaces 29 30 Fundamentals of Electromagnetics In this section Maxwell s Equations Constitutive Relations Potentials Reduced Potential PDE Formulations Electromagnetic Energy The Quasi Static Approximation and the Lorentz Term Material Properties About the Boundary and Interface Conditions Phasors References for Electromagnetic Theory Maxwell s Equations The problem of electromagnetic analysis on a macroscopic level is that of solving Maxwells equations subject to certain boundary conditions Maxwell s equations are a set of equations written in differential or integral form stating the relationships between the fundamental electromagnetic quantities These quantities are Electric field intensity E Electric displacement or electric flux density D Magnetic f
154. ed from the relation g 8 854 107 E m s 10 E m The electromagnetic constants 9 and are available in COMSOL Multiphysics as predefined physical constants The electric polarization vector describes how the material is polarized when an electric field E is present It can be interpreted as the volume density of electric dipole FUNDAMENTALS OF ELECTROMAGNETICS 3l 32 moments P is generally a function of E Some materials can have a nonzero P also when there is no electric field present The magnetization vector M similarly describes how the material is magnetized when a magnetic field H is present It can be interpreted as the volume density of magnetic dipole moments M is generally a function of H Permanent magnets for instance have a nonzero M also when there is no magnetic field present For linear materials the polarization is directly proportional to the electric field 29 y E where y is the electric susceptibility Similarly in linear materials the magnetization is directly proportional to the magnetic field M where y is the magnetic susceptibility For such materials the constitutive relations are D 1 47 E yg E E B 1 7 ugu H pH The parameter e is the relative permittivity and p is the relative permeability of the material Usually these are scalar properties but can in the general case be 3 by 3 tensors when the material is a
155. ed in the continuity equation MODELING WITH THE AC DC MODULE The excitation is applied by means of specialized subfeatures a Boundary Feed subfeature applies constraints on the coil potential to an external boundary while a Ground subfeature enforces the coil potential to be zero on the selected boundaries 1 To ensure that the current continuity equation has a physical solution terminate a coil domain on external boundaries only Important Gap Feed subfeature models a thin gap in the conductive domain across which a difference of potential or a current is applied This feature should be applied on internal boundaries to the conductive domain and is useful for modeling closed loops For the Single Turn Coil Domain feature only one active feed feature can Oo be used at a time That is either a Boundary Feed or Gap Feed feature can Important be used not both The Gap Feed should be used with care in high frequency modeling as there will be a mesh dependent displacement current density flowing in the elements just outside the bounding edges of the Gap Feed boundary Important If these elements have non zero conductivity this problem may appear even at lower frequencies MULTI TURN COIL DOMAIN A Multi Turn Coil Domain used in 3D models requires additional settings compared to 2D models A Coil Type parameter is used to specify the geometry of the coil that is the direction of the wires and the len
156. ed port PAIR SELECTION If Lumped Port is selected from the Pairs menu choose the pair to define An identity pair has to be created first Ctrl click to deselect PORT PROPERTIES Enter a unique Port Name It is recommended to use a numeric name as it is used to define the elements of the S parameter matrix and numeric port names are also required for port sweeps and Touchstone file export 212 CHAPTER 5 THE MAGNETIC FIELD INTERFACES Type of Port The geometry of the port is specified by the Type of Port A Uniform lumped port applies a constant electric field between the metallic electrodes A Coaxial lumped port applies a radial electric field between two concentric circular metallic boundaries For these two cases the dimension of the port is computed automatically by analyzing the geometry i Select a Type of Port Uniform Coaxial or User defined 3D The Type of Port options available depend on the Components selected on the physics interface Out of plane vector potential the default In plane vector potential or Three component vector potential 1 fOut of plane vector potential is selected the Type of Port is User 2D defined IfIn plane vector potential or Three component vector potential is selected choose a Type of Port Uniform or User defined The Type of Port options available depend on the Components selected on the physics interface Out of plane vector potential the defau
157. ements do not work properly Element Quality The coordinate scaling resulting from infinite elements also yields an equivalent stretching or scaling of the mesh that effectively results in a poor element quality The MODELING WITH THE AC DC MODULE element quality displayed by the mesh statistics feature does not account for this effect The poor element quality causes poor or slow convergence for iterative solvers and make the problem ill conditioned in general Especially vector element formulations like the ones using two or more components of the magnetic vector potential are sensitive to low element quality For this reason it is strongly recommended to use swept meshing in the infinite element domains The sweep direction should be selected the same as the direction of scaling For Cartesian infinite elements in regions with more than one direction of scaling it is recommended to first sweep the mesh in the domains with only one direction of scaling then sweep the domains with scaling in two directions and finish by sweeping the mesh in the domains with infinite element scaling in all three direction Complicated Expressions The expressions resulting from the stretching get quite complicated for spherical infinite elements in 3D This increases the time for the assembly stage in the solution process After the assembly the computation time and memory consumption is comparable to a problem without infinite elements The number of
158. ents magnetic fields and magnetic and electric fields interfaces In electrostatics and electric currents the force is calculated by integrating 1 T nT oni E D n E D 3 1 on the surface of the object that the force acts on In the magnetic fields interface the expression 1 T n T 9ni H B n H B is integrated on the surface to obtain the force In the magnetic and electric fields interface both expressions are included E is the electric field D the electric displacement the magnetic field B the magnetic flux density and n4 the outward normal from the object For a theoretical discussion about the stress tensor see Electromagnetic Forces LORENTZ FORCES The Lorentz force is defined as F J x B The Lorentz force is very accurate for electromagnetic force calculations in electrically conducting domains The Lorentz MODELING WITH THE AC DC MODULE force variables are available both in domains and on boundaries in the case of surface currents Model Examples Electromagnetic Forces There are a number of examples in the AC DC Module Model Library showing how to calculate electromagnetic forces in different situations The Electromagnetic Forces on Parallel Current Carrying Wires model uses both Maxwell s stress tensor and the Lorentz force method to compute magnetic forces It shows how to compute the total force on a device by integrating the volume force J x B the most important method fo
159. eov P V oVV J 0 These dynamic formulations are valid as long as induced electric fields can be ignored and hence the electric field is essentially curl free This condition is fulfilled provided that skin effect and wave propagation effects can be ignored The skin depth must be much larger than the geometrical dimensions of the modeled device and so must the wavelength Note also that these formulations can be used to model dielectric regions of capacitive resistive devices even though the interior of electrodes may not meet the large skin depth condition In that case the electrodes must only be represented as boundary conditions fixed or floating potential The interior metallic domains are not included in the analysis Obviously this is only a valid approach for devices where metallic electrodes do not entirely bypass short circuit the capacitive resistive layers If metallic electrodes short circuit the capacitive resistive layers the time evolution of the current is determined by inductive and resistive effects with very little influence from the capacitive layers Then the Magnetic Fields interface is the appropriate modeling tool THEORY OF ELECTRIC FIELDS 169 170 Theory for the Electrostatics Interface The Electrostatics Interface is available for 3D 2D in plane and 2D axisymmetric models Applications with Electrostatics Equations include high voltage apparatus electronic devices and capacitors The term
160. er Show and Hide Physics Options There are several features available on many physics interfaces or individual nodes This section is a short overview of the options and includes links to the COMSOL Multiphysics User s Guide or COMSOL Multiphysics Reference Guide where additional information is available The links to the features described in the COMSOL Multiphysics User s Guide and COMSOL Multiphysics Reference Guide do not work in the Important PDF only from within the online help 18 CHAPTER INTRODUCTION To locate and search all the documentation for this information in g COMSOL select Help Documentation from the main menu and either T enter a search term or look under a specific module in the documentation ip tree SHOW MORE PHYSICS OPTIONS To display additional features for the physics interfaces and feature nodes click the Show button z on the Model Builder and then select the applicable option After clicking the Show button z some sections display on the settings window when a node is clicked and other features are available from the context menu when a node is right clicked For each the additional sections that can be displayed include Equation Advanced Settings Discretization Consistent Stabilization and Inconsistent Stabilization You can also click the Expand Sections button in the Model Builder to always show some sections or click the Show button 2 and select Reset to
161. erature Vy 1 0 V Junction potential CHAPTER 7 THE ELECTRICAL CIRCUIT INTERFACE References for the Electrical Circuit Interface 1 http bwrc eecs berkeley edu Classes IcBook SPICE 2 P Antognetti and G Massobrio Semiconductor Device Modeling with Spice 2nd ed McGraw Hill Inc 1993 THEORY FOR THE ELECTRICAL CIRCUIT INTERFACE 279 280 CHAPTER 7 THE ELECTRICAL CIRCUIT INTERFACE The Heat Transfer Branch The AC DC Module license includes an interface found under the Heat Transfer gt Electromagnetic Heating branch in the Model Wizard This interface combines magnetic fields with heat transfer for modeling of electromagnetic heating such as induction heating In this chapter The Induction Heating Interface 281 282 The Induction Heating Interface The Induction Heating interface found under the Heat Transfer gt Electromagnetic Heating branch in the Model Wizard combines all features from the Magnetic Fields interface in the time harmonic formulation with the Heat Transfer interface for modeling of induction heating and eddy current heating The interface has the equations boundary conditions and sources for modeling such electromagnetic heating The predefined interaction adds the electromagnetic losses from the magnetic field as a heat source This interface is based on the assumption that the magnetic cycle time is short compared to the thermal time scale adiabatic assumpt
162. erminal connected to an external circuit The Circuit type should not be used for lumped parameter calculations For the terminal also enter the value of the electric potential or current charge used if required If zero is entered the terminal acts as a Important floating electrode Terminated to connect the terminal to an impedance that may represent a load or a transmission line When Terminated is selected the scattering parameters S parameters are computed Enter a Terminal power Po SI unit W to specify the input power at this terminal from the transmission line This excitation can be toggled using a port sweep Select an option from the Characteristic impedance from list to define the value of the impedance Physics interface or User defined If Physics interface is sclected the Reference impedance Z defined on the physics interface settings window under Sweep Settings is used If User defined is selected enter a specific impedance SI unit for this terminal The default is 50 CONSTRAINT SETTINGS To display this section click the Show button gt and select Advanced Physics Options Select a Constraint type Bidirectional symmetric or Unidirectional If required select the Use weak constraints check box Floating Potential Lumped Parameters See Also EI For the Electric Currents Shell interface select edges 3D or points 2D instead of boundaries
163. erminal settings They must consistently be of either fixed voltage for an admittance matrix or fixed current type for an impedance matrix ACCURACY Use reaction terms to be accurate when calculating the total current over the boundary This is necessary for the forced voltage input property The reaction terms representing current or charge density come from default information stored in the solution which gives an exact calculation of the total fluxes on boundaries with MODELING WITH THE AC DC MODULE constraints They do not change the system of equations in any way no special solver settings are required The reaction terms are also stored by default It is recommended to use forced voltage input property with reaction terms in the extraction of the lumped parameters Lumped parameter variables based on voltage excitation are only available when reaction fluxes are included in the output The optional current excitation performs a coupling that guarantees that the total current is equal to the specified value although one cannot verify this without using reaction terms Lumped Parameter Conversion When the impedance matrix Z or the admittance matrix Y is available it is possible to calculate all other types of lumped parameter matrices from the relations below 1 ref Z Yt L C mA S Gep E Ze Y Zet YTG ref R Re Z G Re Y where L is the inductance is the capacitance R i
164. ersion also specify the source and destination layers for the drill file NETEX G Export Settings To reduce the complexity of the output file it is recommended that vias are exported as circles and not as polygon chains Although the arc recognition utility can detect these polygons the former option is a bit more robust MODELING WITH THE AC DC MODULE IMPORTING WIREBONDS The Netex file can contain information about wirebonds or bond wires Including wirebonds in the geometry often increases the problem size significantly To get more control over the problem size control the complexity of the imported wires Types of Wirebonds The ECAD import can model the wirebond at three different complexity levels As geometrical edges This is the simplest form which works well when the current in the wires is known Assolids with a square shaped cross section This cross section often produces fewer mesh elements than when using a circular cross section and is also easier for the geometry engine to analyze As solids with a circular cross section Wirebonds Models The Netex file format supports wirebonds models according to the JEDEC standard It is possible to define the wirebond as a JEDEC3 or a JEDEC4 model These models define the bond wire as 3 or 4 segment paths with user supplied coordinates and elevations In a Netex file the bond wire goes from a layer to a special die layer representing the semiconductor die
165. es how the resistivity varies with temperature The default Reference temperature T ef SI unit Resistivity temperature coefficient SI unit 1 K and Reference resistivity po SI unit Om are taken From material which means that the values are taken from the domain material E Only certain material models see Materials support the Linearized resistivity Note To specify other values for any of these properties select User defined from the list and then enter a value or expression T is the current temperature which can be a value that is specified as a model input or the temperature from a heat transfer interface The definition of the temperature field appears in the Model Inputs section Porous Media When Porous media is selected right click to add a Porous Media subnode Archie s Law When Archie s law is selected right click to add an Archie s Law subnode ELECTRIC FIELD E See Electric Field as described for the Charge Conservation node for the Electrostatics interface Note Floating Potential The Floating Potential node is useful when modeling a metallic electrode at floating potential The electrode may have a charge Qo deposited on it For circuit connections use the Terminal feature instead BOUNDARY SELECTION From the Selection list choose the boundaries to define the floating electrode THE ELECTRIC CURRENTS INTERFACE 139 PAIR SELECTION If Floating Potential i
166. es to all the external boundaries Note THE MAGNETIC FIELDS INTERFACE 191 Magnetic Fields Interface Advanced Features for more domain features Ses An and boundary conditions When additional nodes are added from the Selection list choose the boundaries to define the magnetic insulation CONSTRAINT SETTINGS To display this section click the Show button 2 and select Advanced Physics Interface Options Select a Constraint type Bidirectional symmetric or Unidirectional If required select the Use weak constraints check box Magnetic Field The Magnetic Field feature adds a boundary condition for specifying the tangential component of the magnetic field at the boundary nxH BOUNDARY SELECTION From the Selection list choose the boundaries to specify the magnetic field PAIR SELECTION If Magnetic Field is selected from the Pairs menu choose the pair to define An identity pair has to be created first Ctrl click to deselect MAGNETIC FIELD Enter the value or expression for the Magnetic Field Hg SI unit A m coordinates Magnetic Fields Interface Advanced Features for more boundary conditions See Also Surface Current The Surface Current feature adds a boundary condition for a surface current density Jg 192 CHAPTER 5 THE MAGNETIC FIELD INTERFACES nxH J n x H H3 J BOUNDARY SELECTION From the Selection list choose the boundaries to spe
167. ess d for 2D models and 2ar for 2D axially symmetric models and V is an unknown applied potential The potential V is solved for using an additional algebraic equation which constrains the total integrated current to be equal to the current value eoi specified Multi Turn Coil Domains When specifying total current the component of the current density is defined in the direction of the wires as in Equation 3 3 where N is the number of turns which are specified and is the total cross section area of the coil domain coil 3 8 Coil Group Domains When specifying a total coil current the out of plane component of the current density is defined as where L is equal to the physics interface thickness d for 2D models and equal to 2nr for 2D axially symmetric models and V is an unknown applied potential on the i turn of the coil The potential V is solved for using an additional algebraic equation COIL DOMAINS 75 76 CHAPTER 3 which constrains the total integrated current to be equal to the current value that is specified vas 1 VOLTAGE EXCITATION Single Turn Coil Domains When specifying a total voltage the out of plane component of the current density is defined as oY coil J 3 4 where Vooi is the applied voltage specified and L is equal to the physics interface s thickness d for 2D models and equal to 2nr for 2D axially symmetric models Multi T
168. f the Physics Interfaces and Building a COMSOL Model in COMSOL See Also Multiphysics Users Guide GENERAL TIPS These general tips about modeling help you to decide what to include in a simulation and what can be done to minimize the size ofa problem Before starting to model try to answer the following questions first What is the purpose of the model What information do you want to extract from the model Models never capture all the details of reality Important 56 CHAPTER 3 MODELING WITH THE AC DC MODULE Increasing the complexity of a model to make it more accurate usually makes it more expensive to simulate A complex model is also more difficult to manage and interpret than a simple one It can be more accurate and efficient to use several simple models instead 3 of a single complex one Tip What Problems Can You Solve The AC DC Module interfaces handle static time dependent and time harmonic problems The time dependent and time harmonic formulations use a quasi static approximation See Table 1 1 in Overview of the User s Guide for a list of the preset study types available by interface One major difference between quasi static and high frequency modeling is that the formulations depend on the electrical size of the structure This dimensionless measure is the ratio between the largest distance between two points in the structure divided by the wavelength of the electromag
169. feature adds an initial value for the magnetic vector potential and electric potential that can serve as an initial value for a transient simulation or as an initial guess for a nonlinear solver BOUNDARY SELECTION From the Selection list choose the boundaries to define an initial value INITIAL VALUES Enter a value or expression for the initial value of the Magnetic vector potential A SI unit Wb m and initial value of the Electric potential V SI unit V The default values are 0 254 CHAPTER 6 THE MAGNETIC AND ELECTRIC FIELDS INTERFACE Theory for the Magnetic and Electric Fields Interface The Magnetic and Electric Fields Interface can be used for modeling full coupling between electric and magnetic fields Use this physics interface for 3D 2D in plane and 2D axisymmetric models For a deeper theoretical background to the magnetic vector potential and electric scalar potential used below see the Theory of Magnetic and Electric Fields The Magnetic and Electric Currents interface only supports the stationary and frequency domain study types that is there is no transient Note formulation available In this section Magnetostatics Equations Frequency Domain Equations Magnetostatics Equations To derive the magnetostatics equations start with Amp re s law for static cases V x H J Define the potentials B VxA VV and the current J ovxB cVV4 J where J is an externally gener
170. fic module in the documentation tree 184 CHAPTER 5 THE MAGNETIC FIELD INTERFACES Table 5 1 lists the interior and exterior boundaries available with this interface TABLE 5 1 INTERIOR AND EXTERIOR BOUNDARY CONDITIONS FOR THE MAGNETIC FIELDS INTERFACE FEATURE INTERIOR EXTERIOR Change Thickness Out of Plane x x External Magnetic Vector Potential x x Impedance Boundary Condition x Lumped Port x x Magnetic Field x x Magnetic Insulation x x Magnetic Potential x x Magnetic Shielding x x Perfect Magnetic Conductor x x Periodic Condition x Surface Current x x Thin Low Permeability Gap x Transition Boundary Condition x For 2D axisymmetric models COMSOL Multiphysics takes the axial symmetry boundaries at r 2 0 into account and automatically adds an A Axial Symmetry node to the model that is valid on the axial symmetry 2D Axi boundaries only About Infinite Element Domains and Perfectly Matched Layers in the COMSOL Multiphysics User s Guide p ETI di See Also THE MAGNETIC FIELDS INTERFACE 185 186 Amp re s Law The Amp re s Law feature adds Amp re s law for the magnetic field and provides an interface for defining the constitutive relation and its associated properties such as the relative permeability as well as electric properties For 3D models right click the Amp re s Law node to add a Gauge Fixing LE A for A field feature 3D For 2D and 2D axisymmetr
171. finite Elements node imposes a coordinate transformation to the selected domain that effectively moves one or more sides ofthe domain to infinity Infinite elements are THE MAGNETIC FIELDS NO CURRENTS INTERFACE 225 226 used for the modeling of open boundary problems default Magnetic Flux Conservation node is also added Magnetic Insulation The Magnetic Insulation feature for the Magnetic Fields No Currents interface provides magnetic insulation using the following boundary condition which sets the normal component of the magnetic flux density to zero B 0 Magnetic insulation is the default boundary condition g This condition is useful at boundaries confining a surrounding region of air or to model symmetry cuts ip CHAPTER 5 BOUNDARY SELECTION From the Selection list choose the boundaries to define magnetic insulation Magnetic Flux Density The Magnetic Flux Density feature adds a boundary condition for the magnetic flux density The following equation defines the normal component of the magnetic flux density using a magnetic flux vector B0 n B n B 5 1 Using this boundary condition specify the normal component of the magnetic flux density at the boundary Alternatively specify an inward or outward flux density using the following equation B 5 2 Using this formulation it is possible to specify the normal component of the magnetic flux density as a sc
172. for a thin domain Instead it describes a unit thickness that makes the 1D equation identical to the ID equation used for 3D models See also Change Cross Section described for the Electrostatics interface Enter a default value for the Out of plane thickness d SI unit m see Equation 4 1 The default value of 1 is typically not representative for a thin dielectric medium for example Instead it describes a unit thickness that makes the 2D equation identical to the equation used for 3D models See also Change Thickness Out of Plane described for the Electrostatics interface TERMINAL SWEEP SETTINGS Enter a Reference impedance Zef SI unit The default is 50 Select the Activate terminal sweep check box to switch on the sweep and invoke a parametric sweep over the terminals Enter a Sweep parameter name to assign a specific name to the variable that controls the terminal number solved for during the sweep The default is PortName The generated lumped parameters are in the form of capacitance matrix elements The terminal settings must consistently be of either fixed voltage or fixed charge type The lumped parameters are subject to Touchstone file export Enter a file path or Browse for a file Select an Output format for the Touchstone export Magnitude angle the default Magnitude dB angle or Real imaginary Select a Parameter to export Z the default Y or S Lumped Parameters See Al
173. formation of the field but is independent of One thing that makes the use of phasors suitable is that a time derivative corresponds to a multiplication by ja 9E _ Rej E r e ot This means that an equation for the phasor can be derived from a time dependent equation by replacing the time derivatives by a factor jo All time harmonic equations in the AC DC Module are expressed as equations for the phasors The tilde is dropped from the variable denoting the phasor When analyzing the solution ofa time harmonic equation it is important to remember that the field that has been calculated is a phasor and not a physical field Important For example all plot functions visualize Re E r by default which is E at time 0 To obtain the solution at a given time specify a phase factor in all results pages and in the corresponding functions References for Electromagnetic Theory 1 D K Cheng Field and Wave Electromagnetics Addison Wesley Reading Massachusetts 1989 2 J Jin The Finite Element Method in Electromagnetics John Wiley amp Sons New York 1993 3 B D Popovic Introductory Engineering Electromagnetics Addison Wesley Reading Massachusetts 1971 FUNDAMENTALS OF ELECTROMAGNETICS 39 40 Electromagnetic Forces There are several ways to compute electromagnetic forces in COMSOL Multiphysics In the most general case the calculation of electromagnetic forces involves the computation
174. from within the online help Important To locate and search all the documentation in COMSOL select Help gt Documentation from the main menu and either enter a search term Tip or look under a specific module in the documentation tree CHAPTER 5 Table 5 1 lists the interior and exterior boundaries available with this interface TABLE 5 2 INTERIOR AND EXTERIOR BOUNDARY CONDITIONS FOR THE MAGNETIC FIELDS NO CURRENTS INTERFACE FEATURE INTERIOR EXTERIOR Magnetic Flux Density x Magnetic Insulation x x Magnetic Potential x Magnetic Shielding x x Periodic Condition x Thin Low Permeability Gap x Zero Magnetic Scalar Potential x Magnetic Flux Conservation The Magnetic Flux Conservation feature adds Equation 5 5 above or a similar equation depending on the selected constitutive relation for the magnetic potential and provides an interface for defining the constitutive relation and the relevant material properties for example the relative permeability DOMAIN SELECTION From the Selection list choose the domains to define the magnetic potential and the equation that describes the magnetic potential field MODEL INPUTS This section has field variables that appear as model inputs if the current settings include such model inputs By default this section is empty If a linear temperature relation is added for the conductivity then the source can be defined for the temperature T From the Temperature l
175. gth of the coil Select a Linear Circular Numeric or User defined coil Linear Coil Types Ina linear coil the wires are straight and parallel To specify the direction ofthe wires right click the Multi Turn Coil Domain node add a Reference Edge subfeature and select a straight edge or a group of collinear straight edges along the entire length of the coil The coil direction is taken to be the tangential vector to the edges while the coil length is the total length of the edges COIL DOMAINS 81 82 Circular Coil Types Ina circular coil the wires are wound in circles around a common axis To specify the direction of the wires right click the Multi Turn Coil Domain node add a Reference Edge subfeature and select a group of edges forming a circle with the same axis as the coil The wires are assumed to be wound around the circle s axis while the length of the coil is taken from the length of the edges To obtain the best approximation possible ensure that the circle radius is close to the average radius of the circular coil Numerical Coil Types In a numerical coil the current path is computed numerically in an additional study step during the solution This allows the modeling of coils having complex shapes To set up the numerical computation of the current flow in a coil additional steps are required Right click the Multi Turn Coil Domain node and add an Automatic Current Calculation subfeature This subfeature defines
176. he stationary equation of continuity In a stationary coordinate system the point form of Ohm s law states that J cE J where is the electrical conductivity SI unit S m and J is an externally generated current density SI unit m The static form of the equation of continuity then states V J V cVV J 0 To handle current sources you can generalize the equation to V 6VV J Q CHAPTER 4 THE ELECTRIC FIELD INTERFACES In planar 2D the Electric Currents interface assumes that the model has a symmetry where the electric potential varies only in the x and y directions and is constant in the Z direction This implies that the electric field E is tangential to the xy plane The Electric Currents interface then solves the following equation where d is the thickness in the z direction V d oVV J dQ 4 1 In 2D axisymmetry the Electric Currents interface considers the situation where the fields and geometry are axially symmetric In this case the electric potential is constant in the direction which implies that the electric field is tangential to the rz plane Effective Conductivity in Porous Media and Mixtures When handling electric currents in porous media or mixtures of solids with different electric properties you must consider different ways for obtaining the Effective conductivity of the mixture There are several possible approaches to do this starting from the values defined by t
177. he Selection list choose the domains to define the automatic current calculation AUTOMATIC CURRENT CALCULATION The parameter Off diagonal scaling is the scaling used to stabilize the eigenvalue problem The default value is 0 1 and should be valid for most cases Using Coils in 3D Models C Computing Coil Currents aces Solver Features in the COMSOL Multiphysics Reference Guide MAGNETIC FIELDS INTERFACE ADVANCED FEATURES 207 208 Electric Insulation Right click the Automatic Current Calculation node to add a Electric Insulation subnode This is the default boundary condition Apply it to the boundaries delimiting the coil domain which then constrains the coil wires to be parallel to the boundary BOUNDARY SELECTION From the Selection list choose the boundaries to define the electric insulation for the automatic current calculation Using Coils in 3D Models Computing Coil Currents Serin Solver Features in the COMSOL Multiphysics Reference Guide Input Right click the Automatic Current Calculation node to add an Input subnode and specify the boundaries where the wires enter the domain The wire direction is forced to be orthogonal to the boundary Used in combination with the Output node it also defines the direction of the current flow from Input to Output BOUNDARY SELECTION From the Selection list choose the boundaries to define the input for the automatic current calculation
178. he only option available from the Solve for list is Full field COMPONENTS Select Components Out of plane vector potential the default In plane i vector potential or Three component vector potential From the practical 2D viewpoint this choice is equivalent to deciding in what directions the i electric current is allowed to flow out of plane currents in plane currents 2D Axi or currents flowing in all three coordinate directions THE MAGNETIC AND ELECTRIC FIELDS INTERFACE 247 THICKNESS Enter a value or expression for the Out of plane thickness d The default value of 1 unit length is typically not representative for a thin domain t Instead it describes a unit thickness that makes the 2D equation identical to the equation used for 3D models SWEEP SETTINGS Enter a Reference impedance SI unit The default is 50 Select the Activate terminal sweep check box to switch on the sweep and invoke a parametric sweep over the terminals Select an option from the Sweep on list Terminals or Ports Enter a Sweep parameter name to assign a specific name to the variable that controls the terminal number solved for during the sweep The default is PortName The generated lumped parameters are in the form of capacitance matrix elements The terminal settings must consistently be of either fixed voltage or fixed charge type The lumped parameters are subject to Touchstone file export Enter a file path
179. he special extrude operation is bound to certain rules that the 2D layout must fulfill If the 2D layout does not comply with these rules the operation might fail Then switch to one of the other grouping options to import the geometry Importing ODB X Files If your ECAD software supports the ODB X format it is recommended it is used as it usually gives the most efficient geometry Tip model of the layout The ODB file format is a sophisticated format that handles most of the information needed to manufacture a PCB Some ofthe information is not needed when importing the file and the program ignores such information during import ODB exists in two different format versions Asingle XML file containing all information organized in a hierarchy of XML tags This file format is usually referred to as ODB X and it is the only format that can be imported into COMSOL Multiphysics directory structure with several files each containing parts of information about the PCB An entire PCB layout is often distributed as zipped or unzipped tar archives This version is currently not possible to import The ODB import reads the layer list and the first step in the file Multiple step files are not yet supported From the first step it reads all the layer features and the board outline but currently skips all the package information EXTRACTING LAYER STACKUP The import can read stackup information from the ODB fi
180. he user composed by a volume fraction of material 1 and a volume fraction 05 1 0 of material 2 The effective conductivity o is then given as input for the electric current conservation specified in Equation 4 1 in the same way of modeling an effective single phase material VOLUME AVERAGE CONDUCTIVITY If the electric conductivities of the two materials are not so different from each other a simple form of averaging can be used such as a volume average 010 0565 here is the conductivity of the material 1 and o is that of material 2 This is equivalent to a parallel system of resistivities E If the conductivities are defined by second order tensors such as for anisotropic materials the volume average is applied element by element Note THEORY FOR THE ELECTRIC CURRENTS INTERFACE 173 174 VOLUME AVERAGE RESISTIVITY A similar expression for the effective conductivity can be used which mimics a series 3 connection of resistivities Equivalently the effective conductivity is obtained from 0 1_ 91 08 G 95 EI If the conductivities are defined by second order tensors the inverse of the tensors are used Note POWER LAW A power law gives the following expression for the equivalent conductivity _ 8 61 O9 The effective conductivity calculated by Volume Average Conductivity is the upper bound the effective conductivity calculated b
181. hysics Electromagnetics electric sensor Model E INTERFACE IDENTIFIER The interface identifier is a text string that can be used to reference the respective physics interface if appropriate Such situations could occur when coupling this interface to another physics interface or when trying to identify and use variables defined by this physics interface which is used to reach the fields and variables in expressions for example It can be changed to any unique string in the Identifier field The default identifier for the first interface in the model is es DOMAIN SELECTION The default setting is to include All domains in the model to define the electric potential and the equations that describe the potential field for dielectrics To choose specific domains select Manual from the Selection list CHAPTER 4 THE ELECTRIC FIELD INTERFACES THICKNESS Enter a default value for the Cross section area A SI unit m The default value of 1 is typically not representative for a thin domain Instead it describes a unit thickness that makes the 1D equation identical to the x equation used for 3D models See also Change Cross Section Enter a default value for the Out of plane thickness d SI unit m The default value of 1 is typically not representative for a thin dielectric 1 medium for example Instead it describes a unit thickness that makes the 2D 2D equation identical to the equation used for 3D models See also
182. hysics interfaces 15 adiabatic assumption 62 advanced settings 19 air stress tensors 44 48 Amp re s law node 186 Amp re s law and current conservation node 253 anisotropic materials 36 37 applying electromagnetic sources 61 Archie s law node 140 automatic current calculation node 207 axial symmetry cylindrical coordinates 59 B bond wires 103 104 boundary conditions electric currents interface 135 electric currents shell interface 159 electromagnetics theory 37 electrostatics interface 112 forced voltage port 86 magnetic and electric fields interface 249 magnetic fields interface 183 magnetic fields no currents interface 222 minimizing problem size 60 boundary current source node 144 boundary feed node 205 built in materials database 293 calculating electromagnetic forces 40 71 forces in moving objects 47 S parameters 94 capacitance matrix 86 87 capacitor node 260 Cartesian coordinates 18 58 67 cementation exponent 141 176 change cross section node 130 change shell thickness node 163 change thickness out of plane node 131 charge conservation node 114 charge relaxation theory 166 168 Chemical Reaction Engineering Module 168 circuit import SPICE 268 circular coil 82 coil domain multi turn 199 coil domain single turn 202 coil group domain node 209 conductive media 158 178 consistent stabilization settings 20 constitutive relations theory 31 32 constraint settings 20 c
183. ic currents interface 139 electrostatics interface 123 fluid saturation 141 force calculation node 116 forced voltage port 86 forces calculating 70 continuum mechanics and 40 elastic solids and 42 electromagnetic calculating 40 in moving objects 47 stationary fields 44 torque 43 formation factor 176 Fourier s law of heat conduction 288 frequency domain study 176 theory electric currents interface 168 Galilei invariants and transformations 47 gap feed node 205 gauge fixing for A field node 198 gauge transformation and fixing 236 237 Gauss law and charge relaxation theory 166 Gauss law equation 170 GDS II file format 99 general elastic materials 46 49 geometry 20 58 Gerber layer files 102 ground node electrostatics interface 117 single turn coil domain feature 206 ground node node 259 harmonic perturbation node 210 Helmholtz s theorem 237 hide button 19 impedance boundary condition node 215 importing ECAD files 98 GDS II files 99 NETEX G files 101 OBD X files 99 SPICE netlists 268 wirebonds 103 inconsistent stabilization settings 20 induction heating interface 282 induction heating model node 287 inductor node 260 infinite elements node 225 inhomogeneous materials 36 initial values node INDEX 305 306 INDEX electric currents interface 143 electric currents shell interface 163 electrostatics interface 117 induction heating interface 288 magnetic and elec
184. ic models and when In plane vector potential 1 or Three component vector potential is sclected from the Components 2D section on The Magnetic Fields Interface settings window right click the 1 Amp re s Law node to add a Gauge Fixing for A field feature 1 2D Axi For some interfaces this feature is added by default CHAPTER 5 DOMAIN SELECTION From the Selection list choose the domains to define the magnetic vector potential and the equation based on Amp re s law that defines the potential MODEL INPUTS This section contains field variables that appear as model inputs if the current settings include such model inputs By default this section is empty If a linear temperature relation is added for the conductivity then define the source for the temperature From the Temperature list select an existing temperature variable from another physics interface if available or select User defined to define a value or expression for the temperature SI unit K in the field that appears underneath the list MATERIAL TYPE Select a Material type Non solid the default Solid or From material COORDINATE SYSTEM SELECTION The Global coordinate system is sclected by default The Coordinate system list contains any additional coordinate systems that the model includes THE MAGNETIC FIELD INTERFACES CONDUCTION CURRENT By default the Electrical conductivity c SI unit S m for the media is defined From material Also sel
185. ic pure conductor 46 48 electric currents interface 133 theory 172 electric currents shell interface 157 theory 178 electric displacement field node 123 electric field transformation node 234 electric fields theory 166 electric forces and torques 50 electric insulation node 148 electric insulation node coil domains 208 electric point dipole node 155 electric point dipole on axis node 156 electric potential node 118 electric shielding node 146 164 electrical circuit interface 258 theory 269 electrical circuits modeling techniques 95 electrical conductivity porous media 175 electrical size 57 electromagnetic energy theory 34 electromagnetic forces and torques 70 electromagnetic forces calculating 40 electromagnetic heat source node 288 electromagnetic quantities 52 electromagnetic sources applying 61 electromagnetic stress tensors 44 electrostatic point dipole node 132 electrostatics interface 110 theory 170 emailing COMSOL 21 equation view 19 error message electrical circuits 96 expanding sections 19 external vs U node 266 external l terminal node 267 external magnetic flux density node 227 external magnetic vector potential node 215 external surface charge accumulation node 119 external U vs node 267 extruding layers 98 field variables in 2D 63 file formats 05 11 99 NETEX G 101 file Touchstone 88 fixed current ports 86 floating potential node electr
186. ics or the other modules For example to find the heat distribution in a motor first find the current in the coils using one of the quasi static interfaces in this module and then couple it to a heat equation in the main COMSOL Multiphysics package or the Heat Transfer Module This forms a powerful multiphysics model that solves all the equations simultaneously COMSOL Multiphysics also has an interface to the MATLAB technical computing environment If you have a MATLAB license save it as a Model M file a script file that runs in MATLAB This module also provides interfaces for modeling electrical circuits and importing ECAD drawings Building COMSOL Model in the COMSOL Multiphysics User s Guide a AC DC Module Physics Guide See Alo e AC DC Module Study Availability Where Do I Access the Documentation and Model Library Typographical Conventions AC DC Module Physics Guide The physics interfaces in the AC DC Module form a complete set of simulation tools for electromagnetic field simulations To select the right physics interface for describing the real life physics the geometric properties and the time variations of the fields need to be considered The interfaces solve for these physical quantities the electric scalar potential V the magnetic vector potential A and the magnetic scalar potential Vm Each interface has a Tag which is of special importance when performing multiphysics simulations This tag help
187. ield intensity H Magnetic flux density B Current density J Electric charge density p The equations can be formulated in differential form or integral form The differential form is presented here because it leads to differential equations that the finite element method can handle For general time varying fields Maxwell s equations can be written as CHAPTER 2 REVIEW OF ELECTROMAGNETICS VxH J at eB at V B 0 The first two equations are also referred to as Maxwell Amp re s law and Faraday s law respectively Equation three and four are two forms of Gauss law the electric and magnetic form respectively Another fundamental equation is the equation of continuity _9 Vod Out of the five equations mentioned only three are independent The first two combined with either the electric form of Gauss law or the equation of continuity form such an independent system Constitutive Relations To obtain a closed system the equations include constitutive relations that describe the macroscopic properties of the medium They are given as D amp E P H M 2 1 J cE where amp 0 is the permittivity of vacuum Ug is the permeability of vacuum and o the electrical conductivity In the SI system the permeability of vacuum is chosen to be 47 10 H m The velocity of an electromagnetic wave in vacuum is given as and the permittivity of vacuum is deriv
188. ields are transformed The most well known relation for moving objects is the one for the electric field The transformed quantity of the electric field is called the electromotive intensity FIELD TRANSFORMATIONS AND GALILEI INVARIANTS Assume that the object modeled is moving with a constant velocity v Vo The equations now take on a slightly different form that includes the Galilei invariant ELECTROMAGNETIC FORCES 47 48 versions ofthe electromagnetic fields The term Galilei invariant is used due to the fact that they remain unchanged after a coordinate transformation of the type r r Vot In continuum mechanics this transformation is commonly referred to as a Galilei transformation The Galilei invariant fields of interest are E E vxB Electromotive intensity J J pv Free conduction current density P T Polarization flux derivative M vxP Lorentz magnetization moz B T Lr ejvx E M Magnetomotive intensity Ho The electromotive intensity is the most important of these invariants The Lorentz magnetization is significant only in materials for which neither the magnetization M nor the polarization P is negligible Such materials are rare in practical applications The same holds for the magnetization term of the magnetomotive intensity Notice that the term gv x E is very small compared to B u except for cases when v and E are both very large Thus in many
189. ies to model a thin low permeability gap MODEL INPUTS This section contains field variables that appear as model inputs if the current settings include such model inputs By default this section is empty THIN LOW PERMEABILITY GAP The default Relative permeability unitless is taken From material If User defined is selected choose Isotropic Diagonal Symmetric or Anisotropic based on the THE MAGNETIC FIELD INTERFACES characteristics of the relative permeability and then enter a value or expression in the field or matrix Enter a Surface thickness d SI unit m for the gap Magnetic Point Dipole 2 LE 3D Magnetic point dipoles are available with 2D and 3D models See Magnetic Point Dipole on Axis for the 2D axisymmetric settings Apply a Magnetic Point Dipole SI unit Am to points This represents the limiting case of when the cross section area a of a circular current loop carrying uniform current I approaches zero at while maintaining the product between J and a The dipole moment is a vector entity with the positive direction set by the curl of the current POINT SELECTION From the Selection list choose the points to add a magnetic point dipole DIPOLE SPECIFICATION Select a Dipole specification Magnitude and direction or Dipole moment DIPOLE PARAMETERS If Magnitude and direction is selected under Dipole Specification enter coordinates for the Magnetic dipole
190. il group POWER EXCITATION In 2D and 2D axisymmetric models Power is an option available for the coil excitation parameter When Power is selected the feature sets up the equation as specified in the Current Excitation section plus the constraint ale SP 2 coil coil coil between the coil current and voltage Select this option to specify the input power for the coils The problem becomes nonlinear with these settings EI The Power option is not available for 3D models due to the increased x complexity of the problem compared to 2D models ote COIL DOMAINS 77 This nonlinear system of equations requires special solver settings in order to converge COMSOL automatically adds these solver settings when Power is selected Be aware that in general the values of the voltage and the current may p not uniquely be determined by this constraint Particularly in the Important frequency domain the absolute phase of the quantities can be arbitrary This indeterminacy can have an impact on the solution process See Compile Equations in the COMSOL Multiphysics Reference Guide for a possible solution to this problem e Multi Turn Coil Domain Single Turn Coil Domain Coil Group Domain e Solver Features in the COMSOL Multiphysics Reference Guide See Also In the COMSOL Multiphysics User s Guide e Solvers and Study Types The Realdot Operator Lumped Parameter Calculations All the types of coil d
191. ilable with this interface It also includes edge point and pair availability TABLE 4 2 INTERIOR AND EXTERIOR BOUNDARY CONDITIONS INCLUDING EDGE POINT AND PAIR AVAILABILITY FOR THE ELECTRIC CURRENTS INTERFACE FEATURE INTERIOR EXTERIOR ALSO AVAILABLE FOR Boundary Current Source x pairs Contact Impedance x pairs Distributed Impedance x x not applicable Electric Insulation x x pairs Electric Potential x x edges points and pairs Electric Shielding x x pairs Floating Potential x x pairs Ground x x edges points and pairs Normal Current Density x not applicable Periodic Condition x not applicable Terminal x x pairs Current Conservation The Current Conservation node adds the continuity equation for the electrical potential and provides an interface for defining the electric conductivity as well as the constitutive relation and the relative permittivity for the displacement current THE ELECTRIC CURRENTS INTERFACE 137 138 DOMAIN SELECTION From the Selection list choose the domains to define the electric potential and the continuity equation that describes the potential field MODEL INPUTS This section contains field variables that appear as model inputs if the current settings include such model inputs By default this section is empty If a linear temperature relation is added for the conductivity then the source for the temperature T can be defined From the Temperature list select an exi
192. in that effectively rotates it a prescribed angle that grows linearly with time It is used to model a rotating part DOMAIN SELECTION From the Selection list choose the domains to use prescribed rotational velocity PRESCRIBED ROTATIONAL VELOCITY Enter the Revolutions per second rps SI unit Hz and the X and Y coordinates for the Rotation axis base point r SI unit m THE MAGNETIC FIELD INTERFACES Theory of Magnetic and Electric Fields Quasi static analysis of magnetic and electric fields is valid under the assumption that OD 6t 0 In this section Maxwell s Equations Magnetic and Electric Potentials Gauge Transformations Selecting a Particular Gauge The Gauge and the Equation of Continuity for Dynamic Fields Explicit Gauge Fixing Divergence Constraint Ungauged Formulations and Current Conservation Time Harmonic Magnetic Fields Maxwells Equations This implies that it is possible to rewrite Maxwell s equations in the following manner VxH J o E vxB J oB VxE 5 V B 0 V D 2p V J 0 Here J is an externally generated current density and v is the velocity of the conductor The crucial criterion for the quasi static approximation to be valid is that the currents and the electromagnetic fields vary slowly This means that the dimensions of the structure in the problem need to be small compared to the wavelength Magnetic and Electric Potentials Using the definitions of
193. in the air box The Heat Transfer in Solids settings use the material properties associated to the Aluminum 3003 H18 materials node and the Fluid I settings define the flow using the Air material properties The other nodes under Conjugate Heat Transfer define the initial and boundary conditions MATERIAL LIBRARY AND DATABASES 295 296 physics interface properties automatically use the correct Materials properties when the default From material setting is used This means that one node can be used to define the physics across several domains with different materials COMSOL then uses the material properties from the different materials to define the physics in the domains If material properties are missing the Material Contents section on the Materials page displays a stop icon to warn about the missing properties and a warning icon A if the property exists but its value is undefined The Material Page in the COMSOL Multiphysics User s Guide See Also There are also some physics interface properties that by default define a material as the Domain material that is the materials defined on the same domains as the physics interface For such material properties select any other material that is present in the model regardless of its selection EVALUATING AND PLOTTING MATERIAL PROPERTIES You can access the material properties for evaluation and plotting like other variables in a model using the variable
194. industry There are two fundamental ways that an electrical circuit model relates to a physical field model Either the field model is used to get a better more accurate description of a single device in the electrical circuit model or the electrical circuit is used to drive or terminate the device in the field model in such a way that it makes more sense to simulate both as a tightly coupled system The Electrical Circuit interface makes it is possible to add nodes representing circuit elements directly to the model tree in a COMSOL Multiphysics model The circuit variables can then be connected to a physical device model to perform co simulations of circuits and multiphysics The model acts as a device connected to the circuit so that its behavior is analyzed in larger systems THEORY FOR THE ELECTRICAL CIRCUIT INTERFACE 269 The fundamental equations solved by the electrical circuit interface are Kirchhoff s circuit laws which in turn can be deduced from Maxwell s equations The supported study types are Stationary Frequency Domain and Time Dependent The circuit definition in COMSOL Multiphysics adheres to the SPICE format developed at University of California Berkeley Ref 1 and SPICE netlists can also be imported generating the corresponding Note features in the COMSOL Multiphysics model Most circuit simulators can export to this format or some dialect of it There are three more advanced large signa
195. ine An identity pair has to be created first Ctrl click to deselect Contact Impedance Use the Contact Impedance node on interior boundaries to model a thin layer of resistive material It can also be added as a pair n J a 5 Vi V o n J qUa Y 8 1 Vi V3 Ps 1 n J Ps The layer impedance can be specified either with the bulk material conductivity o the relative permittivity and the layer thickness d or directly with the surface resistance and capacitance C The indices 1 and 2 refer to the two sides of the boundary These parameters work the same as with Distributed Impedance Note Thin Film Resistance Model Library path COMSOL Multiphysics Electromagnetics thin film resistance Model Ee For the frequency domain and time dependent study types this boundary condition is slightly more sophisticated and accounts also for capacitive coupling The corresponding equations are given below For the Frequency Domain study type THE ELECTRIC CURRENTS INTERFACE 149 Jo 98 n J d Vi 8 JMEgE n J Vo Vj 8 NES n J ix joC V Vj S I n J 5 joC J V Vj S For the Time Dependent study type n J doi V eos A Vg n J V9 ege 8 re 55 V 4 V uds BOUNDARY SELECTION From the Selection list choose the boundaries to apply a
196. ing the electric displacement D with the electric field E and the applicable material properties such as the relative permittivity Select a Constitutive relation from the list Select Relative permittivity to use the constitutive relation D ege E the default Select Polarization to use the constitutive relation D z9E P Select Remanent electric displacement to use constitutive relation D sgg E D where D is the remanent displacement the displacement when no electric field is present e fRelative permittivity is selected the default is to take the Relative permittivity values From material If User defined is selected select Isotropic Diagonal Symmetric or Anisotropic and enter values or expressions in the field or matrix Select Porous media to then be able to right click the Charge Conservation node to add a Porous Media subnode If Polarization is selected enter the components based on space dimension for the Polarization vector P SI unit C m IfRemanent electric displacement is selected the default is to take the Relative permittivity values From material If User defined is selected select Isotropic Diagonal Symmetric or Anisotropic and enter values or expressions in the field or matrix Then enter the components based on space dimension for the Remanent electric displacement D SI unit C m Select Porous media to then be able to right click the Charge Conservation node to add a
197. ion Thus it is associated with two predefined study types Frequency Stationary time harmonic magnetic fields and stationary heat transfer Frequency Transient time harmonic magnetic fields and transient heat transfer When this interface is added the following default nodes are also added to the Model Builder Induction Heating Model Electromagnetic Heat Source Boundary Electromagnetic Heat Source Thermal Insulation Magnetic Insulation and Initial Values Right click the Induction Heating node to add other features that implement for example boundary conditions and sources Inductive Heating of a Copper Cylinder Model Library path Model ACDC_Module Electromagnetic_Heating inductive_heating ode CHAPTER 8 INTERFACE IDENTIFIER The interface identifier is a text string that can be used to reference the respective physics interface if appropriate Such situations could occur when coupling this interface to another physics interface or when trying to identify and use variables defined by this physics interface which is used to reach the fields and variables in expressions for example It can be changed to any unique string in the Identifier field The default identifier for the first interface in the model is ih DOMAIN SELECTION The default setting is to include All domains in the model To choose specific domains select Manual from the Selection list THE HEAT TRANSFER BRANCH PHYSICAL MODEL Se
198. ires Permanent Magnet Model Library path ACDC Module Magnetostatics permanent magnet FORCE AND TORQUE COMPUTATIONS 71 Coil Domains In this section About the Single Turn Coil Domain Multi Turn Coil Domain and Coil Group Domain Features About the Coil Name Coil Excitation Lumped Parameter Calculations Using Coils in 3D Models Computing Coil Currents The Magnetic Fields Interface See Also Magnetic Fields Interface Advanced Features About the Single Turn Coil Domain Multi Turn Coil Domain and Coil Group Domain Features The coil domains are features that are used to simplify the set up of magnetostatics and low frequency electromagnetic models In many such applications the magnetic field is generated by electric currents flowing in conductive domains for example cables wires coils or solenoids The coil domains can be used to easily model these structures and to translate lumped quantities currents and voltages into distributed quantities current densities and electric fields There are three types of coil domain features which differ by the physical system represented the modeling details and the applicability to a model In 2D and 2D axisymmetric the direction of the current flow in the coil is assumed to be in the out of plane direction The coil domains model 2D straight coils in 2D and circular coils in 2D axisymmetry i The length of the
199. is outside of the current PDF document the text indicates this for example See The Laminar Flow Interface in the COMSOL Multiphysics User s Guide Note that if you are in COMSOL Multiphysics online help the link will work ABOUT THE AC DC MODULE 24 CHAPTER 1 ICON NAME DESCRIPTION in Model Space Dimension The Model icon is used in the documentation as well as in COMSOL Multiphysics from the View gt Model Library menu If you are working online click the link to go to the PDF version of the step by step instructions In some cases a model is only available if you have a license for a specific module These examples occur in the COMSOL Multiphysics User s Guide The Model Library path describes how to find the actual model in COMSOL Multiphysics for example If you have the RF Module see Radar Cross Section Model Library path RF Module Tutorial Models radar cross section Another set of icons are also used in the Model Builder the model space dimension is indicated by OD ID ID axial symmetry 4 2D f 2D axial symmetry i and 3D X icons These icons are also used in the documentation to clearly list the differences to an interface feature node or theory section which are based on space dimension INTRODUCTION Overview of the User s Guide The AC DC Module User s Guide gets you started with modeling using COMSOL Multiphysics The information in this guide is specific to this m
200. ist select an existing temperature variable from THE MAGNETIC FIELD INTERFACES another physics interface if available or select User defined to define a value expression for the temperature SI unit K MATERIAL TYPE Select a Material type Solid Non solid or From material COORDINATE SYSTEM SELECTION The Global coordinate system is selected by default The Coordinate system list contains any additional coordinate systems the model includes MAGNETIC FIELD See the settings for Magnetic Field under Amp re s Law for the Magnetic Fields interface except for these differences Magnetic losses is not an option for this interface E e Select BH curve instead of HB curve to use a curve that relates magnetic flux density B and the magnetic field H as f H define B select From material the default to use the value from the Note material or select User defined to specify a value or expression for the magnitude of the magnetic flux density in the field that appears Initial Values The Initial Values feature adds an initial value for the magnetic scalar potential that can serve as an initial guess for a nonlinear solver DOMAIN SELECTION From the Selection list choose the domains to define an initial value INITIAL VALUES Enter a value or expression for the initial value of the Magnetic scalar potential V The default value is 0 A Infinite Elements The In
201. iterations for iterative solvers might increase if the infinite element regions have a coarse mesh Erroneous Results Infinite element regions deviating significantly from the typical configurations shown in the beginning of this section can cause the automatic calculation of the infinite element parameter to give erroneous result Enter the parameter values manually if this is the case See General Stretching Use the Same Material Parameters or Boundary Conditions The infinite element region is designed to model uniform regions extended toward infinity Avoid using objects with different material parameters or boundary conditions that influence the solution inside an infinite element region INFINITE ELEMENTS 69 70 Force and Torque Computations CHAPTER 3 In this section e Calculating Electromagnetic Forces and Torques Model Examples Electromagnetic Forces Calculating Electromagnetic Forces and Torques Two methods are available to calculate electromagnetic forces and torques The most general method is to use the Maxwell stress tensor Another method that works for the special case of computation of magnetic forces on nonmagnetic current carrying domains uses a predefined physics interface variable for the Lorentz force distribution in a magnetic flux density B MAXWELL STRESS TENSOR Force and torque calculations using Maxwell s stress tensor are available in the electrostatics electric curr
202. ive permittivity Surface thickness d SI unit m and Reference potential SI unit V The default value for the surface thickness is 107 m 1 mm CHAPTER 4 THE ELECTRIC FIELD INTERFACES Periodic Condition The Periodic Condition node defines periodicity or antiperiodicity between two boundaries If required activate periodic conditions on more than two boundaries in which case the Periodic Condition tries to identify two separate surfaces that can each consist of several connected boundaries For more complex geometries it might be necessary to use the Destination Selection subnode With this subnode the boundaries which constitute the g source and destination surfaces can be manually specified To add the Tip subnode right click the Periodic Condition node and select Destination Selection BOUNDARY SELECTION From the Selection list choose the boundaries to apply a periodic condition PERIODIC CONDITION Select a Type of periodicity Continuity or Antiperiodicity CONSTRAINT SETTINGS To display this section click the Show button gt and select Advanced Physics Options Select a Constraint type Bidirectional symmetric or Unidirectional If required select the Use weak constraints check box In the COMSOL Multiphysics User s Guide Periodic Condition 7 Rcx Destination Selection See Also Using Periodic Boundary Conditions Periodic Boundary Condition Example
203. k constraints check box External Magnetic Flux Density This feature is only available when solving a problem with a background magnetic flux density Reduced field is selected from the Solve for list under Note Background Field on the interface settings window The External Magnetic Flux Density boundary condition forces the reduced magnetic flux density to be zero on the boundary or equivalently forces the total field to be equal to the background field Apply this boundary condition on external boundaries THE MAGNETIC FIELDS NO CURRENTS INTERFACE 227 228 5 that are at a distance far enough from the system so that its effect on the background field is negligible BOUNDARY SELECTION From the Selection list choose the boundaries to define an external magnetic flux density Magnetic Shielding The Magnetic Shielding feature adds a boundary condition for magnetic shielding It describes a thin layer of a permeable medium that shields the magnetic field The boundary condition uses the following equation n B B5 In this equation V represents a tangential derivative gradient and d is the surface thickness BOUNDARY SELECTION From the Selection list choose the boundaries to define magnetic shielding PAIR SELECTION If Magnetic Shielding is selected from the Pairs menu choose the pair to define An identity pair has to be created firs
204. l Thin Low Permittivity Gap Zero Charge the default boundary condition Table 4 1 lists the interior and exterior boundaries available with this interface It also includes edge point and pair availability TABLE 4 1 INTERIOR AND EXTERIOR BOUNDARY CONDITIONS INCLUDING EDGE POINT AND PAIR AVAILABILITY FOR THE ELECTROSTATICS INTERFACE FEATURE INTERIOR EXTERIOR ALSO AVAILABLE FOR Change Cross Section x x pairs Change Thickness Out of Plane x x pairs Dielectric Shielding x x pairs Distributed Capacitance x x pairs Electric Displacement Field x x pairs Electric Potential x x edges points and pairs External Surface Charge x pairs Accumulation Floating Potential x x pairs Ground x x edges points and pairs Periodic Condition x not applicable THE ELECTROSTATICS INTERFACE 113 114 TABLE 4 1 INTERIOR AND EXTERIOR BOUNDARY CONDITIONS INCLUDING EDGE POINT AND PAIR AVAILABILITY FOR THE ELECTROSTATICS INTERFACE FEATURE INTERIOR EXTERIOR ALSO AVAILABLE FOR Surface Charge Density x x pairs Terminal x x not applicable Thin Low Permittivity Gap x not applicable Zero Charge the default x pairs For axisymmetric models COMSOL Multiphysics takes the axial symmetry boundaries at r 2 0 into account and automatically adds an Axial Symmetry feature to the model that is valid on the axial symmetry boundaries only There are also Line Charge on Axis and Point Charge on Axis fe
205. l semiconductor device features available in the Electrical Circuit interface The equivalent circuits and the equations defining their non ideal circuit elements are described in this section For a more detailed account on semiconductor device modeling see Ref 2 NPN Bipolar Transistor Figure 7 1 illustrates the equivalent circuit for the bipolar transistor 270 CHAPTER 7 THE ELECTRICAL CIRCUIT INTERFACE b e Rc lejc bct e e o Cjbc ann Vbc Dg Dc ip d b e e ice f VbeVbe v Vbe Dr DE ipeticje B o icje RE Figure 7 1 circuit for the bipolar transistor The following equations are used to compute the relations between currents and voltages in the circuit THEORY FOR THE ELECTRICAL CIRCUIT INTERFACE 271 272 1 R Up lp q _ Ube _ Ube 1 1 e 1 fi 1 1 41 ba Ube Ube IggA IggA 211 Var VA I IE MI lee Deva e uU foq There are also two capacitances that use the same formula as the junction capacitance of the diode model In the parameter names below replace x with C for the base collector capacitance and for the base emitter capacitance Ca x jb J 1 Ma 1 Fg The model parameters are listed in the TABLE 7 1 BIPOLAR TRANSISTOR MOD
206. lculate the Z matrix in a more direct way Similar to the Y calculation the Z calculation can be done by forcing the current through one terminal at the time to a nonzero value while the others are set to zero Then the columns of the impedance matrix are proportional to the voltage values on all terminals MODELING WITH THE AC DC MODULE Vi Zi 219 213 214 1 V 23 2 293 Zog Ij V3 231 239 2 234 13 V4 Zu 245 243 214 I In magnetostatics this option means that the energy method is used see Calculating Lumped Parameters Using the Energy Method below FIXED CHARGE The Electrostatics interface can use total charge instead of total current This gives the inverted capacitance matrix in a similar manner as the Z and Y matrices x Vi C12 Cig Q V C5 Cog Css Q2 V3 C5 Cao Css C34 Q V4 C45 Q Calculating Lumped Parameters Using the Energy Method When using this method the potential or the current is nonzero on one or two terminals at a time and the energy density is extracted and integrated over the whole geometry The following formulas show how to calculate the capacitance matrix from the integral of the electric energy density 2 0 JH Ci wado v Jai 2 J V x 0 kzij l 1021 hes Si C Fv wao 7 V r i j J Calculate the inductance matrix in the same way from the magnetic energy density LUMPED PARAMETERS 87 88 CHAP
207. le such as thickness for metal layers and dielectric layers It is quite common that the layer thickness is not included in the export from the ECAD program so the layers only get a default thickness The thickness can always be changed prior to import on the Layers to import table in the settings window for the ECAD import so it is recommended that these values are checked before importing Importing GDS II Files The GDS II file format is commonly used for mask layout production used in the manufacturing process of semiconductor devices and MEMS devices The file is a IMPORTING ECAD FILES 99 100 CHAPTER 3 binary file containing information about drawing units geometry objects and object drawing hierarchy The drawing hierarchy is made up of a library of cell definitions where each cell can be instantiated drawn several times with scaling translation mirroring and rotation It is also possible to repeat a cell as an array of drawn objects This is very useful for mask layouts of integrated circuits which often consist of millions of transistors There are usually only a few transistor configurations present on the layout and each transistor configuration only has to be defined once File Extension The file extension of the GDS II format is usually gds and the ECAD import requires it to be so otherwise it cannot identify the file as GDS II file If the file has a different extension it must be changed
208. lect the Out of plane heat transfer check box 2D models only to include heat transfer out of the plane If your license includes the Heat Transfer Module you can select the Surface to surface radiation check box to include surface to surface radiation as part of the heat transfer This adds a Radiation Settings section See the Physical Model section in The Heat Transfer Interface for details If your license includes the Heat Transfer Module you can select the Radiation in participating media check box to include radiation in participating media as part of the heat transfer This adds a Participating media Settings section See the Physical Model section in The Heat Transfer Interface for details If your license includes the Heat Transfer Module you can select the Heat Transfer in biological tissue check box to enable the Biological Tissue feature See the Physical Model section in The Bioheat Transfer Interface for details CONSISTENT AND INCONSISTENT STABILIZATION To display this section click the Show button and select Stabilization There are two consistent stabilization methods available Streamline diffusion and Crosswind diffusion Streamline diffusion is active by default There is one inconsistent stabilization method Isotropic diffusion which is not activated by default BACKGROUND FIELD Select an option from the Solve for list Reduced field or Full field the default If Reduced field is selected specify
209. lectric and magnetic energies are defined as aD av f T S W f 20 The time derivatives of these expressions are the electric magnetic power P JE a g 5B av These quantities are related to the resistive and radiative energy or energy loss through Poynting s theorem Ref 1 oD oB 2 2 J EdV f nas where V is the computation domain and S is the closed boundary of V The first term on the right hand side represents the resistive losses P J EdV CHAPTER 2 REVIEW OF ELECTROMAGNETICS which result in heat dissipation in the material The current density J in this expression is the one appearing in Maxwell Amp re s law The second term on the right hand side of Poynting s theorem represents the radiative losses f xH ndS The quantity S E x H is called the Poynting vector Under the assumption the material is linear and isotropic it holds that OD p cE _ 901 EP g T 2 5 OB _1 0B 0 1 H Ot uy 2 By interchanging the order of differentiation and integration justified by the fact that the volume is constant and the assumption that the fields are continuous in time the result is dips eske ajav a save menus The integrand of the left hand side is the total electromagnetic energy density 1l gj B W W tWy E
210. lt In plane vector potential or Three component vector potential i If Out of plane vector potential is selected the Type of Port is User 2D Axi defined IfIn plane vector potential or Three component vector potential is selected choose a Type of Port Coaxial or User defined Select User defined for non uniform ports for example a curved port and enter values or expressions in the fields for these additional settings Height of lumped port 7 SI unit m port e Width of lumped port Wport SI unit m The coordinates based on space dimension for the Direction between lumped port terminals aj MAGNETIC FIELDS INTERFACE ADVANCED FEATURES 213 Terminal Type For all Types of ports select a Terminal type a Cable port for a voltage driven transmission line a Current driven port or a Circuit port Wave Excitation at this Port This section is available if Cable is selected as the Terminal type Select On or Off from the Wave excitation at this port list to set whether it is an inport or a listener port If On is selected enter a Voltage Vo SI unit V and Port phase 0 SI unit rad Note It is only possible to excite one port at a time if the purpose is to compute S parameters In other cases for example when studying microwave g heating more than one inport might be wanted but the S parameter Tip variables cannot be correctly computed so if several ports are excited the S p
211. me dependent small signal analysis frequency domain Magnetic Fields n mf 3D 2D 2D stationary frequency domain axisymmetric time dependent small signal analysis frequency domain coil current calculation Magnetic and Electric E mef 3D 2D 2D stationary frequency domain Fields axisymmetric small signal analysis frequency domain Magnetic Fields No A mfnc all dimensions stationary time dependent Currents Rotating Machinery A rmm 2D stationary time dependent E Magnetic Electrical Circuit cir Not space stationary frequency domain dependent time dependent CHAPTER 1 INTRODUCTION PHYSICS ICON TAG SPACE PRESET STUDIES DIMENSION x Electromagnetic Heating Induction Heating jt ih 3D 2D 2D stationary frequency domain axisymmetric time dependent frequency stationary frequency transient This is an enhanced interface which is included with the base COMSOL package but has added functionality for this module AC DC Module Study Availability TABLE 1 1 AC DC MODULE DEPENDENT VARIABLES FIELD COMPONENTS AND PRESET STUDY AVAILABILITY PHYSICS TAG DEPENDENT FIELD PRESET STUDIES INTERFACE VARIABLES COMPONENTS gt 2 E 4 E z E z 5z 2 Zz 4 2 2 E E z lt 5 d 2 Za E E gt a 4 1 0 E a z gt 25 gt gt 4 a o 2 2 52 2 2 ul 2 u 2 7 9 a 2 42 2 2
212. n and time dependent study types this boundary condition is slightly more sophisticated and accounts also for capacitive coupling The equations are THE ELECTRIC CURRENTS INTERFACE 145 146 Jo 98 d S i n J J5 1 jo6 V V9 n J J V V ief 1 n J J z ov Veg soe 1 Jy Ja iv Vief cv V BOUNDARY SELECTION From the Selection list choose the boundaries to apply a distributed impedance EI For the Electric Currents Shell interface select edges 3D or points 2D instead of boundaries Note DISTRIBUTED IMPEDANCE Enter the Reference potential SI unit V Select a potentially complex valued Layer specification Thin layer the default or Surface impedance If Thin layer is selected enter values or expressions for the Surface thickness d SI unit m The default is 5 107 m 5 mm Electrical conductivity c SI unit S m and Relative permittivity amp The defaults take values From material Select User defined to enter different values or expressions If Surface impedance is selected enter values or expressions for the Surface resistance o SI unit Qm and for the Surface capacitance C SI unit E m2 Electric Shielding The Electric Shielding node provides an electric shielding boundary condition Use this feature to model a thin layer of a highly conductive medium that shields the electric field The sheet has the
213. n is especially important when importing GDS files o because that format does not contain any thickness information so all Important layers get a default thickness that you probably want to change The number in the Elevation column can be changed The Elevation column controls the lower Z position of a layer The Elevation column is only displayed when Manual control of elevations is enabled The Import column Clear the check box for layers that do not need to be imported If the Metal shells import type is used isolated boundaries cannot be EI imported if the import also includes another solid layer Then two imports must be performed The only exception to this rule is when the Note import results in only face objects In most electromagnetic simulations the material between the metal layers is important for the simulation result For NETEX G GDS import the Import dielectric regions check box controls if the import engine also includes the dielectric layers which in most cases are the actual PCB materials An ODB file usually has the outline of the PCB board defined in the file Ifa NETEX G file or a GDS file is imported it is possible to define the PCB outline using left right top and bottom margins for the dielectric material They define the distance between the exterior of the PCB and the IMPORTING ECAD FILES 105 106 bounding box of all metal layers The Import dielectric regions check box is
214. n node to add harmonic perturbation to the right hand side contributions of the parent node The perturbation of the contribution is entered in THE MAGNETIC FIELD INTERFACES the settings window which is used when solving for a Frequency Domain Perturbation study type Q Harmonic Perturbation Prestressed Analysis and Small Signal Analysis in the COMSOL Multiphysics User s Guide See Also DOMAIN SELECTION From the Selection list choose the domains to impose the harmonic perturbation HARMONIC PERTURBATION Enter a Coil current SI unit A The default is 0 Lumped Port Use the Lumped Port condition to apply a uniform electric field between two metallic boundaries The excitation at the port can be expressed as a voltage or as a current or via the connection to a circuit interface The use of this feature is justified when the distance between the metallic boundaries is much smaller than the wavelength of the electromagnetic radiation or for stationary studies EI See S Parameters and Ports and Lumped Ports with Voltage Input for more information Note The geometry of the port is specified by the Type of Port A Uniform lumped port applies a constant electric field between the metallic electrodes A Coaxial lumped port applies a radial electric field between two concentric circular metallic boundaries For these two cases the dimension of the port is computed automatically by analyzing the ge
215. nal Magnetic Vector Potential 215 Impedance Boundary Condition 215 Transition Boundary Condition 217 Thin Low Permeability Gap 218 8 CONTENTS Magnetic Point Dipole Magnetic Point Dipole on Axis The Magnetic Fields No Currents Interface 219 220 221 Domain Boundary Point and Pair Features for the Magnetic Fields No Currents Interface Magnetic Flux Conservation Initial Values Infinite Elements Magnetic Insulation Magnetic Flux Density Zero Magnetic Scalar Potential External Magnetic Flux Density Magnetic Shielding Thin Low Permeability Gap The Rotating Machinery Magnetic Interface 222 224 225 225 226 226 227 227 228 228 230 Domain and Shared Features for the Rotating Machinery Magnetic Interface 232 Initial Values Electric Field Transformation Prescribed Rotation Prescribed Rotational Velocity Theory of Magnetic and Electric Fields Maxwell s Equations Magnetic and Electric Potentials Gauge Transformations Selecting a Particular Gauge The Gauge and the Equation of Continuity for Dynamic Fields Explicit Gauge Fixing Divergence Constraint Ungauged Formulations and Current Conservation Time Harmonic Magnetic Fields Theory for the Magnetic Fields Interface Magnetostatics Equation Frequency Domain Equation Transient Equation
216. nd pair availability e Archie s Law Boundary Current Source THE ELECTRIC CURRENTS INTERFACE 135 Contact Impedance Current Conservation Current Source Distributed Impedance Electric Insulation Electric Point Dipole Electric Point Dipole on Axis Electric Shielding External Current Density Floating Potential Initial Values Line Current Source Line Current Source on Axis Normal Current Density Point Current Source Porous Media Sector Symmetry These features are described for the Electrostatics interface Change Cross Section Change Thickness Out of Plane Electric Potential Force Calculation Ground Periodic Condition Terminal In the COMSOL Multiphysics User s Guide Continuity on Interior Boundaries See Also Identity and Contact Pairs Specifying Boundary Conditions for Identity Pairs 136 CHAPTER 4 THE ELECTRIC FIELD INTERFACES For axisymmetric models COMSOL Multiphysics takes the axial Asi symmetry boundaries at r 2 0 into account and automatically adds an Axial Symmetry node to the model that is valid on the axial symmetry i boundaries only 2D Axi To locate and search all the documentation in COMSOL select g Help Documentation from the main menu and either enter a search term Tip or look under a specific module in the documentation tree Table 4 1 lists the interior and exterior boundaries ava
217. netic fields The quasi static physics interfaces in this module are suitable for simulations of structures with an electrical size in the range up to 1 10 The physical assumption of these situations is that the currents and charges generating the electromagnetic fields vary so slowly in time that the electromagnetic fields are practically the same at every instant as if they had been generated by stationary sources When the variations in time ofthe sources of the electromagnetic fields are more rapid it is necessary to solve the full Maxwell equations for high frequency electromagnetic waves They are appropriate for structures of electrical size 1 100 and larger Thus an overlapping range exists where both the quasi static and the full Maxwell formulations can be used g Interfaces for high frequency electromagnetic waves are available in the RF Module Tip Independent of the structure size the AC DC Module accommodates any case of nonlinear inhomogeneous or anisotropic media It also handles materials with PREPARING FOR MODELING 57 58 properties that vary as a function of time as well as frequency dispersive materials Examples of applications that successfully simulate with this module include electric motors generators permanent magnets induction heating devices and dielectric heating For a more detailed description of some of these applications refer to the Model Library included with the module
218. nisotropic The properties and without subscripts are the permittivity and permeability of the material GENERALIZED CONSTITUTIVE RELATIONS The Charge Conservation feature describes the macroscopic properties of the medium relating the electric displacement D with the electric field E See Also and the applicable material properties For nonlinear materials a generalized form of the constitutive relationships is useful The relationship used for electric fields is D z E D where D is the remanent displacement which is the displacement when no electric field is present Similarly a generalized form of the constitutive relation for the magnetic field is B uou H where B is the remanent magnetic flux density which is the magnetic flux density when no magnetic field is present For some materials there is a nonlinear relationship between B and H such that B fH CHAPTER 2 REVIEW OF ELECTROMAGNETICS The relation defining the current density is generalized by introducing an externally generated current Je The resulting constitutive relation is J Je Potentials Under certain circumstances it can be helpful to formulate the problems in terms of the electric scalar potential V and the magnetic vector potential A They are given by the equalities B VxA ot The defining equation for the magnetic vector potential is a direct consequence of the magnetic Ga
219. ns a flow of homogeneous conducting fluid past a magnet liquid metal pumps Hall generators thrusters g If in doubt contact COMSOL Technical Support E www comsol com support ip DOMAIN SELECTION From the Selection list choose the domains to define the velocity COORDINATE SYSTEM SELECTION The Global coordinate system is selected by default The Coordinate system list contains any additional coordinate systems that the model includes VELOCITY LORENTZ TERM Select User defined to enter the components for the Velocity vector v SI unit m s or if present select any velocity field Velocity field spf pfl for example defined in the model g For example using the velocity field is useful when coupling to the velocity field of a fluid for magnetohydrodynamic model 1 CHAPTER 5 Initial Values The Initial Values feature adds an initial value for the magnetic vector potential A that can serve as an initial value for a transient simulation or as an initial guess for a nonlinear solver BOUNDARY SELECTION From the Selection list choose the boundaries to define an initial value INITIAL VALUES Enter values or expressions for the initial value of the Magnetic vector potential A SI unit Wb m The default is 0 THE MAGNETIC FIELD INTERFACES Magnetic Insulation The Magnetic Insulation node is the default boundary condition for the Magnetic Fields interface and adds a bounda
220. ns The sweep direction should be selected the same as the direction of scaling For Cartesian infinite elements in regions with more than one direction of scaling it is recommended to first sweep the mesh in the domains with only one direction of scaling then sweep the domains with scaling in two directions and finish by sweeping the mesh in the domains with infinite element scaling in all three direction GENERAL STRETCHING With manual control of the stretching the geometrical parameters that defines the stretching are added as Manual Scaling subnodes These subnodes have no effect unless the type of the Infinite Elements node is set to General Each Manual Scaling subnode has three parameters Scaling direction which sets the direction from the interface to the outer boundary Geometric width which sets the width of the region Coordinate at interface which sets an arbitrary coordinate at the interface When going from any of the other types to the General type subnodes that represent stretching of the previous type are added automatically Known Issues When Modeling Using Infinite Elements Be aware of the following when modeling with infinite elements Use of One Single Infinite Elements Node Use a separate Infinite Elements node for each isolated infinite element domain That is to use one and the same Infinite Elements node all infinite element domains must be in contact with each other Otherwise the infinite el
221. ns could occur when coupling this interface to another physics interface or when trying to identify and use variables defined by this physics interface which is used to reach the fields and variables in expressions for example It can be changed to any unique string in the Identifier field The default identifier for the first interface in the model is ecs THE ELECTRIC CURRENTS SHELL INTERFACE 157 158 BOUNDARY SELECTION Select the boundaries shells where you want to define the electric potential and the equations that describe the potential field for conductive media The default setting is to include all boundaries in the model OUT OF PLANE THICKNESS Enter a value or expression for the Thickness d The default value is 1 unit length Use the Change Thickness Out of Plane node to define specific boundaries or points instead of a global setting for the thickness SHELL THICKNESS Enter a value or expression for the Shell thickness d SI unit m The default value is l When modeling with shells the Shell Thickness section defines a parameter that enters the equations everywhere It is available in all dimensions This is unrelated to the Change Thickness Out of Plane node which is only available in 2D and represents the out of plane length of the shell El which is being modeled as a cross section Note When modeling in 2D this means that on the interface settings window there are two
222. nterface and study type to use The results are summarized in Table 4 3 below TABLE 4 3 SUITABLE PHYSICS INTERFACE AND STUDY TYPE FOR DIFFERENT TIME SCALE REGIMES CASE PHYSICS INTERFACE STUDY TYPE gt gt Electrostatics Stationary lt lt Electric Currents Stationary Electric Currents Time Dependent or Frequency Domain in AC DC Module or MEMS Module FIRST CASE gt gt T If the external time scale is short compared to the charge relaxation time the charges do not have time to redistribute to any significant degree Thus the charge distribution can be considered as given model input and the best approach is to solve the Electrostatics formulation using the electric potential V By combining the definition of the potential with Gauss law you can derive the classical Poisson s equation Under static conditions the electric potential V is defined by the equivalence E Using this together with the constitutive relation D P between D and E you can rewrite Gauss law as a variant of Poisson s equation V sjVV P p This equation is used in the Electrostatics interface It is worth noting that Gauss law does not require the charge distribution to be static Thus provided dynamics are slow enough that induced electric fields can be neglected and hence a scalar electric potential is justified the formulation can be used also in the Time Dependent study THEORY OF ELECTRIC FIELDS 1
223. nts are selected and this is the same as a line out of plane 20 Use the Line Charge Out of Plane node to specify line charges along the points of a geometry for 2D and 2D axisymmetric models POINT SELECTION From the Selection list choose the points to add a line charge i Beware that constraining the potential on points usually yields a current outflow that is mesh dependent Caution LINE CHARGE OUT OF PLANE Enter a value or expression to apply a Line charge Qr SI unit C m This source represents electric charge per unit length Line Charge a See Also Line Charge on Axis CHAPTER 4 THE ELECTRIC FIELD INTERFACES Point Charge The Point Charge node adds a point source to 3D models The point charge represents an electric displacement field flowing out of the point 3D POINT SELECTION From the Selection list choose the points to add a point charge i Beware that constraining the potential on points usually yields a current outflow that is mesh dependent Caution POINT CHARGE Enter a value or expression to apply a Point charge Qp SI unit C to points This source represents an electric displacement field flowing out of the point Point Charge on Axis See Also Line Charge Out of Plane Point Charge on Axis The Point Charge on Axis node adds a point source to 2D axisymmetric i models The point charge
224. odule Instructions how to use COMSOL in general are included with the COMSOL Multiphysics User s Guide As detailed in the section Where Do I Access the Documentation and Model Library this information is also searchable from the COMSOL Tip Multiphysics software Help menu TABLE OF CONTENTS GLOSSARY AND INDEX To help you navigate through this guide see the Contents Glossary and Index THEORY OF ELECTROMAGNETICS In the Review of Electromagnetics chapter contains an overview of the theory behind the AC DC Module It is intended for readers that wish to understand what goes on in the background when using the physics interfaces and discusses the Fundamentals of Electromagnetics Electromagnetic Forces and Electromagnetic Quantities MODELING WITH THE AC DC MODULE In the Modeling with the AC DC Module chapter the goal is to familiarize you with the modeling procedure using this particular module Topics include Preparing for Modeling Infinite Elements Force and Torque Computations Lumped Parameters and Importing ECAD Files ELECTRIC FIELDS The Electric Field Interfaces chapter describes these interfaces and includes the underlying theory for each interface at the end of the chapter The Electrostatics Interface which simulates electric fields in dielectric materials with a fixed charge present Preset stationary and time dependent study types are available OVERVIEW OF THE USER S GUIDE 25 26 CHAPTER 1
225. of volume forces acting on a body and of surface forces originating from jumps in the electromagnetic fields on the boundaries The volume and surface forces are derived from a general stress tensor that includes electromagnetic terms The derivation of the expressions for the electromagnetic stress tensor utilizes thermodynamic potential energy principles Ref 1 and Ref 3 The distribution of electromagnetic forces in a system depends on the material Accordingly the techniques and expressions used when calculating electromagnetic forces are different for different types of materials Another technique for calculating forces using the method of virtual work is described in the section Electromagnetic Energy and Virtual Work In this section Overview of Forces in Continuum Mechanics Forces on an Elastic Solid Surrounded by Vacuum or Air Torque Forces in Stationary Fields Forces in a Moving Body Electromagnetic Energy and Virtual Work Overview of Forces in Continuum Mechanics Cauchy s equation of continuum mechanics reads 2 dr dt where p is the density r denotes the coordinates of a material point T is the stress tensor and feyt is an external volume force such as gravity fox pg This is the equation solved in the structural mechanics physics interfaces for the special case ofa linear elastic material neglecting the electromagnetic contributions CHAPTER 2 REVIEW OF ELECTR
226. olves the following equation where d is the thickness in the z direction V d egVV P p CHAPTER 4 THE ELECTRIC FIELD INTERFACES The axisymmetric version of the interface considers the situation where the fields and geometry are axially symmetric In this case the electric potential is constant in the direction which implies that the electric field is tangential to the rz plane THEORY FOR THE ELECTROSTATICS INTERFACE 171 172 Theory for the Electric Currents Interface The Electric Currents Interface solves a current conservation problem for the scalar electric potential V and is available for 3D 2D in plane and 2D axisymmetric models Electrolysis and the computation of resistances of grounding plates are examples that involve conductive media with electrical conductivities and electric currents If you are uncertain whether to use the Electric Currents interface or the Electrostatics interface which both solve for the scalar electric potential V refer to the section on Charge Relaxation Theory In this section Electric Currents Equations in Steady State Effective Conductivity in Porous Media and Mixtures Effective Relative Permeability in Porous Media and Mixtures e Archie s Law Theory Dynamic Electric Currents Equations Reference for the Electric Currents Interface Electric Currents Equations in Steady State When handling stationary electric currents in conductive media you must consider t
227. omains define lumped variables during the solution These variables are defined in the global scope and have the template variable CcO0il name where variable is the basic variable name V for voltage Z for impedance and so forth and name is the string specified in the Coil name field These variables can be evaluated during the analysis phase or used in expressions in this case the physics interface identifier for example mf for the Magnetic Fields interface must be added to the beginning of the variable name A brief description of each of the variables follows 78 CHAPTER 3 MODELING WITH THE AC DC MODULE THE VOLTAGE CURRENT AND POWER VARIABLES The coil features define the variables and Peoi The variable corresponding to the quantity used for the coil excitation contains the input value while the others have values computed from the solution according to the coil model EI For the Coil Group Domain feature is the total voltage across the coil that is the sum of the voltages across each domain Note STATIONARY AND TIME DEPENDENT STUDIES In stationary and time dependent studies the coil feature defines the coil resistance variable Roi with the formula R V coil 7 ran FREQUENCY DOMAIN STUDIES In frequency domain studies the following lumped variables are defined Impedance Z m um coil 7 Loil Resistance Ro real Zooi Inductance _ imag Zoi coil 7 m
228. ometry Generally select User defined to manually specify the direction between the MAGNETIC FIELDS INTERFACE ADVANCED FEATURES 211 lumped port terminals a_h and the dimensions of the port h_port Height of lumped port and w port Width of lumped port For 2D models a Uniform port applies an in plane electric field Therefore the Uniform value is available for the Port Type parameter only if the in plane vector potential is solved for according to the settings in 2D the Physics interface node If the Components selected are Out of plane vector potential the Uniform lumped port is not available For 2D axisymmetric models the radial direction is in plane with respect to the geometry Therefore the Uniform value is available for the Port Type parameter only if the in plane vector potential is solved for 1 B B 4 according to the settings in the Physics interface node If the Components 2D Axi 1 A selected are Out of plane vector potential the Coaxial lumped port is not available For 2D and 2D axisymmetric models if the Components selected in the 1 Physics interface is Out of plane vector potential the dimension of the 2D port cannot be obtained by analyzing the geometry and must be specified manually by the user Therefore User defined is the only option available 2D Axi for the Port Type parameter BOUNDARY SELECTION From the Selection list choose the boundaries to specify the lump
229. on e Prescribed Rotational Velocity These boundary edge pair and point conditions are described for other interfaces including the Magnetic Fields Magnetic Fields No Currents and Electrostatics interfaces listed in alphabetical order e Amp re s Law Change Thickness Out of Plane Coil Group Domain Electric Point Dipole Electric Point Dipole on Axis External Current Density e External Magnetic Vector Potential Force Calculation Impedance Boundary Condition Infinite Elements Line Current Out of Plane Lumped Port Magnetic Field Magnetic Insulation Magnetic Point Dipole Magnetic Potential Magnetic Shielding Multi Turn Coil Domain 232 CHAPTER 5 THE MAGNETIC FIELD INTERFACES Perfect Magnetic Conductor Periodic Condition Sector Symmetry Single Turn Coil Domain Surface Current Thin Low Permeability Gap Transition Boundary Condition Velocity Lorentz Term In the COMSOL Multiphysics User s Guide Continuity on Interior Boundaries See Also Identity and Contact Pairs Specifying Boundary Conditions for Identity Pairs o The links to the features described in the COMSOL Multiphysics User s Guide do not work in the PDF only from within the online help To locate and search all the documentation in COMSOL select g Help Documentation from the main menu and either enter a search term Tip or look under a specific
230. on Axis The Point Current Source on Axis node adds a point source and represents 1 i an electric current flowing out of the point in 2D axisymmetric models 2D Axi POINT SELECTION From the Selection list choose the points to add a current source i Beware that constraining the potential on points usually yields a current outflow that is mesh dependent Caution CHAPTER 4 THE ELECTRIC FIELD INTERFACES POINT CURRENT SOURCE Enter a value or expression to apply a Point current source Q SI unit to points This source represents an electric current flowing out of the point Point Current Source to apply this feature to points on 3D models G See Also Line Current Source to apply it to points for 2D models Electric Point Dipole 2 The Electric Point Dipole node is available for 2D and 3D models LE 3D The Electric Point Dipole represents the limiting case of zero separation distance between two equally strong point current sources and current sinks of opposing signs while maintaining the product between separation distance and source strength at a fixed value P The positive direction is from the current sink to the current source POINT SELECTION From the Selection list choose the points to add an electrostatic point dipole DIPOLE SPECIFICATION Select a Dipole specification Magnitude and direction or Dipole moment THE ELECTRIC CURRENTS INTERFAC
231. one export Magnitude angle Magnitude dB angle or Real imaginary Lumped Parameters See Also CHAPTER 5 DEPENDENT VARIABLES The dependent variables field variables are for the Magnetic vector potential and its components The name can be changed but the names of fields and dependent variables must be unique within a model THE MAGNETIC FIELD INTERFACES DISCRETIZATION To display this section click the Show button z and select Discretization Select a Magnetic vector potential Quadratic the default Linear Cubic or Quartic Specify the Value type when using splitting of complex variables Real or Complex the default The Model Builder Show and Hide Physics Options Domain Boundary Point and Pair Conditions for the Magnetic Fields See Also Interface Theory for the Magnetic Fields Interface Domain Boundary Point and Pair Conditions for the Magnetic Fields Interface The Magnetic Fields Interface has these domain boundary point and pair features available Features are listed in alphabetical order About the Boundary Conditions With no surface currents present the interface conditions n x A A5 ns x H H3 0 0 need to be fulfilled Because A is being solved for the tangential component of the magnetic potential is always continuous and thus the first condition is automatically fulfilled The second condition is equivalent to the natural boundary
232. onlinear solver If more than one set of initial values is required right click to add additional Initial Values features DOMAIN SELECTION From the Selection list choose the domains to define an initial value THE ELECTRIC CURRENTS INTERFACE 143 144 INITIAL VALUES Enter a value or expression for the initial value of the Electric potential V SI unit V The default value is Boundary Current Source The Boundary Current Source node adds a current source Q on the boundary It is applicable to interior boundaries that represent either a source or a sink of current BOUNDARY SELECTION From the Selection list choose the boundaries to apply a current source EI For the Electric Currents Shell interface select edges 3D or points 2D instead of boundaries Note PAIR SELECTION If Boundary Current Source is selected from the Pairs menu choose the pair to define An identity pair has to be created first Ctrl click to deselect BOUNDARY CURRENT SOURCE Enter a value or expression for the Boundary current source Q SI unit A m Normal Current Density The Normal Current Density node is applicable to exterior boundaries that represent either a source or a sink of current It provides a condition for specifying the normal current density as an inward or outward current flow n J J Or alternatively as a current density Jg n J n dy The normal current density is positive when the
233. ontact impedance node 149 continuum mechanics forces 40 coordinate systems infinite elements and 66 Coulomb gauge 237 coupling to electrical circuits 96 INDEX 303 304 INDEX current conservation node 137 161 current conservation ungauged formula tions 238 current source node electric current interface 143 electric currents shell interface 163 electrical circuit interface 261 current sources line 152 theory 168 current controlled current source node 263 current controlled voltage source node 262 cylindrical coordinates 18 59 device models electrical circuits 270 dielectric shielding node 120 dielectrics and perfect conductors 38 diode node 265 diode transistor model 276 discretization settings 19 dispersive materials 36 distributed capacitance node 124 distributed impedance node 145 documentation finding 20 domain features electric currents interface 135 electrostatics interface 112 magnetic and electric fields interface 249 magnetic fields interface 183 magnetic fields no currents interface 222 domain material 296 drill files 102 ECAD import 98 options 104 troubleshooting 107 edge conditions electric currents interface 135 electric currents shell interface 159 electrostatics interface 112 magnetic and electric fields interface 249 edge current node 214 effective conductivity porous media 173 effective relative permeability 174 elastic material stress tensor 46 49 elast
234. or Browse for a file Select an Output format for the Touchstone export Magnitude angle Magnitude dB angle or Real imaginary When Terminals is selected under Sweep on also select a Parameter to export Z the default Y or S Lumped Parameters See Also DEPENDENT VARIABLES The dependent variables field variables are for the Electric potential V and Magnetic vector potential A The name can be changed but the names of fields and dependent variables must be unique within a model DISCRETIZATION To display this section click the Show button 2 and select Discretization Select Quadratic the default Linear Cubic or Quartic for the Electric potential and Magnetic 248 CHAPTER 6 THE MAGNETIC AND ELECTRIC FIELDS INTERFACE vector potential Specify the Value type when using splitting of complex variables Real or Complex the default The Model Builder Show and Hide Physics Options Domain Boundary Edge Point and Pair Features for the Magnetic and Electric Fields Interface See Also Theory for the Magnetic and Electric Fields Interface Domain Boundary Edge Point and Pair Features for the Magnetic and Electric Fields Interface The Magnetic and Electric Fields Interface has these domain boundary edge point and pair features About the Boundary Conditions The Magnetic and Electric Fields interface boundary conditions are applied in a two step procedure This is b
235. ormal Current 144 Distributed Impedance 145 Electric 146 Electric Insulation 148 Contact Impedance 2 a eee ewe 149 6 CONTENTS Sector Symmetry Line Current Source Line Current Source on Axis Point Current Source Point Current Source on Axis Electric Point Dipole Electric Point Dipole on Axis The Electric Currents Shell Interface Boundary Edge Point and Pair Conditions for the Electric Currents Shell Interface Current Conservation Initial Values Current Source Change Shell Thickness Normal Current Density Electric Shielding Theory of Electric Fields Charge Relaxation Theory Theory for the Electrostatics Interface Electrostatics Equations Theory for the Electric Currents Interface Electric Currents Equations in Steady State Effective Conductivity in Porous Media and Mixtures Effective Relative Permeability in Porous Media and Mixtures Archie s Law Theory Dynamic Electric Currents Equations Reference for the Electric Currents Interface Theory for the Electric Currents Shell Interface Electric Currents Shell Equations in Steady State Dynamic Electric Currents Equations 151 152 153 153 154 155 156 157 159 161 163 163 163 164 164 166 166 170 170 172 172 173 174 175 176 177 178 178 178 CONTENTS 7 Chapte
236. orts 93 S Parameters in Terms of Electric Field 93 S Parameter Calculations in COMSOL Multiphysics Lumped Ports 94 S Parameter Variables 5 94 Connecting to Electrical Circuits 95 About Connecting Electrical Circuits to Physics Interfaces 95 Connecting Electrical Circuits Using Predefined Couplings 96 Connecting Electrical Circuits by User Defined Couplings 96 Importing ECAD Files 98 Overview ofthe ECAD Import 98 Importing 99 Importing GDS Il Files a cllc ccs 99 Importing NETEX GFiles 101 ECAD Import Options 103 Meshing an Imported 106 Troubleshooting ECAD Import 107 Chapter 4 The Electric Field Interfaces The Electrostatics Interface 110 Domain Boundary Edge Point and Pair Conditions for the Electrostatics Interfaces Ge Se ne eee GR eoe oe he ord LE Charge Conservation 2 2 2 ee ee ee ee we I4 Space Charge Density 2 2 ee eee ee ew I6 Force Calculation we eee ee MS Initial Values a se cene Ce ae a es at ke ok cl CONTENTS 5 Grounds a caos d See Be ek ey ee Electric Potential TB Surface Charge Density 119 External Surface Charge Accumulation
237. ow to compute the electric field and the relative current density The approach for 3D models is different than for 2D and 2D axisymmetric models An additional dependent variable with the dimension of an electric potential is defined in the domain and the current continuity equation is added to the system of equations The problem solved in the domain becomes effectively an formulation of Maxwell s equation and current conservation similar to the one used in the Magnetic and Electric Fields interface For 3D models right click the Single Turn Coil Domain node to add Gap Feed Boundary Feed and Ground subnodes to define the geometry of the coil typical setup for a 3D model is to add a Gap Feed if the coil is closed in a loop or a Boundary Feed and a Ground if the coil is open In order to y avoid unphysical current distribution in the Boundary Feed and Ground case the boundary conditions should be applied on external boundaries See Coil Domains in the modeling section to learn more about using this See Also node DOMAIN SELECTION From the Selection list choose the domains to define the single turn coil domain SINGLE TURN COIL DOMAIN 2D AND 2D AXISYMMETRIC MODELS In 2D and 2 axisymmetric models the direction of the applied electric 2D field is assumed to be out of plane These settings specify how to compute i the electric field and the relative current density 2D Axi M
238. pair 106 torque forces 43 torques calculating 70 Touchstone and port sweeps 88 transformations Galilei 47 transient study 62 transition boundary condition node 217 typographical conventions 22 unbounded domains modeling 65 user community COMSOL 22 vacuum stress tensors 44 48 variables coil domains 78 for material properties 296 physical quantities 52 S parameters 94 velocity Lorentz term node 189 voltage input ports 90 voltage source node 260 voltage controlled current source node 262 voltage controlled voltage source node 262 volume averages porous media 173 wavelength 64 weak constraint settings 20 web sites COMSOL 22 wirebonds importing 103 104 zero charge node 125 zero magnetic scalar potential node 227 INDEX 309 310 INDEX
239. pendent variables The node is made available when In plane vector potential or Three component vector potential is selected from the Components section on The Magnetic Fields Interface settings window 1 3D For 3D models and when applicable right click the Amp re s Law node to add a Gauge Fixing for A field feature No additional settings are required to add the feature The Gauge Fixing for A Field feature provides gauge fixing by adding an additional potential variable y and its associated conservation equation to the system This is 198 CHAPTER 5 THE MAGNETIC FIELD INTERFACES often necessary to get a unique and numerically stable solution to the equation solving for the magnetic vector potential A Explicit Gauge Fixing Divergence Constraint See Also DOMAIN SELECTION From the Selection list choose the domains to define the gauge fixing potential y GAUGE FIXING FOR A FIELD Enter a Divergence condition variable scaling y SI unit A m The default value is 1 which means no scaling Multi Iurn Coil Domain The Multi Turn Coil Domain feature is a lumped model for a bundle of tiny wires tightly wound together separated by an electrical insulator In this scenario the current in the domain flows only in the direction of the wires and is negligible in other directions As a consequence the settings for the Electric Field and Magnetic Field sections are the same as in Amp re s Law node
240. plies also when coupling to a current excited terminal The name ofthis current variable follows the convention M cirn termIm i where cirn is the tag of the Electrical Circuit interface node and termIm is the tag of the External I Terminal node The mentioned tags are typically displayed within curly braces in the model tree e Model Couplings in the COMSOL Multiphysics User s Guide See Also SPICE Circuit Import Right click the Electrical Circuit node 1 to import an existing SPICE netlist select Import Spice Netlist A window opens enter a file location or browse your directories to find one The default file extension for a SPICE netlist is cir The SPICE circuit import translates the imported netlist into Electrical Circuit interface nodes so these define the subset of SPICE features that can be imported CHAPTER 7 THE ELECTRICAL CIRCUIT INTERFACE Theory for the Electrical Circuit Interface The Electrical Circuit Interface theory is discussed in this section Electric Circuit Modeling and the Semiconductor Device Models NPN Bipolar Transistor n Channel MOS Transistor Diode References for the Electrical Circuit Interface Electric Circuit Modeling and the Semiconductor Device Models Electrical circuit modeling capabilities are useful when simulating all sorts of electrical and electromechanical devices ranging from heaters and motors to advanced plasma reactors in the semiconductor
241. practical cases this term can be neglected Air and Vacuum The stress tensor in the surrounding air or vacuum on the outside of a moving object is 1 1 T pI Ie 1n B r kD HB D Bv There is an additional term in this expression compared to the stationary case Elastic Pure Conductor The stress tensor in a moving elastic pure conductor is T oy 3E D 2H B r ED HB Dx Bv where D jE and B CHAPTER 2 REVIEW OF ELECTROMAGNETICS To get the equation for the balance of forces the divergence of this expression needs to be computed This requires an introduction of an extra term in Cauchy s equation corresponding to an additional electromagnetic contribution to the linear momentum Cauchy s equation with this extra term is 2 port DxB Y Tafa The extra term is canceled out by the additional term in the stress tensor and the final result is 2 pex V oy pE JxB f dt For the case of no acceleration with the explicit appearance of the transformed quantities 0 V o y p E v xB J pv xB f The terms containing v x B cancel out which yields the following equation 0 V oyt pE J3xB f which is the same expression as for the stationary case General Elastic Material The stress tensor for a moving general elastic material is p PA 1 gt o E B gt E E gt B B M BJI 2 2 0 cgEET EP MB E x B v 0 The magnetization M and the pola
242. properties such as the relative permittivity When this interface is added these default nodes are also added to the Model Builder Current Conservation Electric Insulation the default boundary condition and Initial Values Right click the Electric Currents node to add other features that implement for example boundary conditions and current sources Pacemaker Electrode Model Library path COMSOL Multiphysics Electromagnetics pacemaker electrode Model g P INTERFACE IDENTIFIER The interface identifier is a text string that can be used to reference the respective physics interface if appropriate Such situations could occur when coupling this interface to another physics interface or when trying to identify and use variables defined by this physics interface which is used to reach the fields and variables in expressions for example It can be changed to any unique string in the Identifier field The default identifier for the first interface in the model is ec DOMAIN SELECTION The default setting is to include All domains in the model to define the electric potential and the equations that describe the potential field for conductive media To choose specific domains select Manual from the Selection list THE ELECTRIC CURRENTS INTERFACE 133 THICKNESS ID OUT OF PLANE THICKNESS 2D Enter a default value for the Cross section area A SI unit m The default value of 1 is typically not representative
243. r 5 The Magnetic Field Interfaces The Magnetic Fields Interface 180 Domain Boundary Point and Pair Conditions for the Magnetic Fields Interface 183 Amp re s Law ll 186 External Current Density 189 Velocity Lorentz 189 Initial Values 190 Magnetic Insulation lll sc I9l Magnetic Field ue uk eo ee oom usps 192 Surface Current 5 192 Magnetic Potential 193 Perfect Magnetic Conductor 194 Line Current Out of Plane 195 Magnetic Fields Interface Advanced Features 197 Gauge Fixing for A field 198 Multi Turn Coil 199 Single Turn Coil 202 Feed 205 Boundary Feed 2 gt ee Ioue ARV 205 Ground 2 x cu ads d ueri 1 200 ReferenceEdge ll 206 Automatic Current Calculation 207 Electric Insulation 208 put t aptent cu iet ie enr tor Sect derit 208 Output Sayra met un der oem Rm gown uu 208 Coil Group Domain 2 209 Reversed Current Direction 210 Harmonic Perturbation 210 L umped Port a rv te bat 2 Edge Current s ll 214 Exter
244. r calculating forces in current carrying devices For materials that can be described as pure conductors see later on in this section this method gives the exact distribution of forces inside a device The quantity J x B is the Lorentz force and is available as a predefined variable on domains and boundaries The model also illustrates how to compute the force by integrating the Maxwell stress tensor on boundaries The Permanent Magnet model demonstrates how to compute the total force on a magnetizable rod close to a permanent magnet by integrating the Maxwell stress tensor in the air on the outside of the rod This is the most important method for accurately calculating the total force on magnetic devices for which the exact distribution of volume forces is not known To retrieve the exact distribution of volume forces requires a material that describes the interactions of the magnetizations and strains Such materials are not always available Therefore you are often limited to compute the total force by integrating the stress tensor or using the method of virtual work None of these methods can be used to compute and visualize the force EI distribution inside a domain only to compute the total force and torque in situations where the device is surrounded by air or when this is a good Note A A approximation Electromagnetic Forces on Parallel Current Carrying Wires Model i Library path ACDC Module Verification Models parallel w
245. r defined If User defined is selected choose Isotropic Diagonal Symmetric or Anisotropic based on the characteristics of the coil conductivity and then enter values or expressions in the field or matrix Coil Relative Permittivity Select a Coil relative permittivity coj unitless From material or User defined If User defined is selected choose Isotropic Diagonal Symmetric or Anisotropic based on the THE MAGNETIC FIELD INTERFACES characteristics of the coil relative permittivity and then enter values or expressions in the field or matrix Gap Feed Right click the Single Turn Coil Domain node to add the Gap Feed subnode Gap Feed is used to apply a discontinuity in the coil potential across a boundary This feature must be applied to an internal boundary in the coil domain and is typically used to excite a closed loop BOUNDARY SELECTION From the Selection list choose the boundaries to define the gap feed The default selects All boundaries MODEL INPUTS This section contains field variables that appear as model inputs if the current settings include such model inputs By default this section is empty SINGLE TURN COIL DOMAIN See Single Turn Coil Domain for all settings See Using Coils in 3D Models the modeling section to learn more about this node Boundary Feed Right click the Single Turn Coil Domain node to add the Boundary Feed subnode The Boundary Feed feat
246. rch term or look under a specific module in the documentation tree THE MODEL LIBRARY Each model comes with documentation that includes a theoretical background and step by step instructions to create the model The models are available in COMSOL as MPH files that you can open for further investigation You can use the step by step instructions and the actual models as a template for your own modeling and applications SI units are used to describe the relevant properties parameters and dimensions in most examples but other unit systems are available To open the Model Library select View Model Library III from the main menu and then search by model name or browse under a module folder name Click to highlight any model of interest and select Open Model and PDF to open both the model and the documentation explaining how to build the model Alternatively click the Dynamic Help button E or select Help gt Documentation in COMSOL to search by name or browse by module The model libraries are updated on a regular basis by COMSOL in order to add new models and to improve existing models Choose View gt Model Library Update to update your model library to include the latest versions of the model examples P y y P Ifyou have any feedback or suggestions for additional models for the library including those developed by you feel free to contact us at info comsol com CONTACTING COMSOL BY EMAIL For general produ
247. re used as terminals and the rest are grounded as illustrated in Figure 3 6 Vi J Ground B V2 V4 Figure 3 6 A five electrode system with 4 terminals and one ground electrode LUMPED PARAMETERS 85 86 CHAPTER 3 If a system specifies that all electrodes are terminals the results are redundant matrix elements This is better understood by considering a two electrode system If both electrodes are declared as terminals a 2 by 2 matrix is obtained for the system This is clearly too many elements because there is only one unique lumped parameter between the terminals If in addition one or more ground electrodes are declared the system has three unique electrodes and the lumped parameter matrix becomes a 2 by 2 matrix FORCED VOLTAGE Ifvoltages are applied to the terminals the extracted currents represent elements in the admittance matrix Y This matrix determines the relation between the applied voltages and the corresponding currents with the formula I Yu Yi Vi I Yor Yo Ys You V I Ya Yao Ys V3 1 4 Ys Y V4 so when V is nonzero and all other voltages are zero the vector I is proportional to the first column of Y In electrostatics the current is replaced with charge and the admittance matrix is replaced with the capacitance matrix Qi Cy Cis C vi Q2 C5 Css V Q C31 Css C34 V3 Q C5 V4 FIXED CURRENT It might be necessary to ca
248. rent can be represented with a surface current at the lumped port boundary directed opposite to the electric field The impedance of a transmission line is defined as 2 1 and an analogy to this is to define an equivalent surface impedance at the lumped port boundary 73 To calculate the surface current density from the current integrate along the width w of the transmission line I mxJ dl I ap di LUMPED PORTS WITH VOLTAGE INPUT 91 92 where the integration is taken in the direction of aj x n This gives the following relation between the transmission line impedance and the surface impedance a dl a dl h h V h Ep J a dl 27 where the last approximation assumed that the electric field is constant over the integrations A similar relationship can be derived for coaxial cables The transfer equations above are used in an impedance type boundary condition relating surface current density to tangential electric field via the surface impedance 1 1 nx Hy us where E is the total field and Ej the incident field corresponding to the total voltage V and incident voltage Vo at the port When using the lumped port as a circuit port the port voltage is fed as EI input to the circuit and the current computed by the circuit is applied as a uniform current density that is as a surface current condition Thus Note
249. represents an electric displacement field flowing 2D Axi out of the point THE ELECTROSTATICS INTERFACE 129 130 POINT SELECTION From the Selection list choose the points to add a point charge i Beware that constraining the potential on points usually yields a current outflow that is mesh dependent Caution POINT CHARGE ON AXIS Enter a value or expression to apply a Point charge p SI unit C to points on axis This source represents an electric displacement field flowing out of the point e Point Charge See Also Line Charge Out of Plane Change Cross Section This feature is available with 1D models This setting overrides the global Thickness setting made in any interface that uses this feature ID Use the Change Cross Section feature to set the cross section area for specific geometric entities DOMAIN OR BOUNDARY SELECTION From the Selection list choose the geometric entity domains or boundaries to define the change cross section PAIR SELECTION When Change Cross Section is selected from the Pairs menu choose the pair to define An identity pair has to be created first Ctrl click to deselect CHANGE CROSS SECTION Enter a value or expression for the Cross section area A SI unit m The default value of 1 unit length is typically not representative for a thin domain Instead it describes a CHAPTER 4 THE ELECTRIC FIELD INTERFACES unit thickness that
250. resolution Is the variation in the solution due to geometrical factors The mesh generator automatically generates a finer mesh where there is a lot offine geometrical details Try to remove such details if they do not influence the solution because they produce a lot of unnecessary mesh elements Is the skin effect or the field variation due to losses It is easy to estimate the skin depth from the conductivity permeability and frequency You need at least two linear elements per skin depth to capture the variation of the fields If you do not study the PREPARING FOR MODELING 63 64 skin depth you can replace regions with a small skin depth with a boundary condition thereby saving elements What is the wavelength To resolve a wave properly it is necessary to use about 10 linear or 5 2nd order elements per wavelength Keep in mind that the wavelength might be shorter in a dielectric medium SELECTING A SOLVER In most cases the solver that COMSOL Multiphysics suggests can be used The choice of solver is optimized for the typical case for each physics interface and study type in the AC DC Module However in special cases the solver settings might need fine tuning This is especially important for 3D problems because they use a large amount of memory For large 3D problems a 64 bit platform may be required In the COMSOL Multiphysics User s Guide Meshing e Solvers and Study Types CHAPTER
251. rface 267 267 268 269 269 270 273 276 279 282 Domain Boundary Edge Point and Pair Features for the Induction Heating Interface a 55 Induction Heating Model Electromagnetic Heat Source Initial Values Chapter 9 Materials Material Library and Databases About the Material Databases About Using Materials in COMSOL Opening the Material Browser Using Material Properties Using the AC DC Material Database Chapter 10 Glossary Glossary of Terms 284 287 288 288 292 292 295 297 298 299 302 CONTENTS 11 12 CONTENTS Introduction This guide describes the AC DC Module an optional add on package for COMSOL Multiphysics designed to assist you to solve and model low frequency electromagnetics This chapter introduces you to the capabilities of the module including an introduction to the modeling stages and some realistic and illustrative models A summary of the physics interfaces and where you can find documentation and model examples is also included The last section is a brief overview with links to each chapter in this guide In this chapter About the AC DC Module Overview of the User s Guide 14 About the AC DC Module CHAPTER 1 In this section What Can the AC DC Module Do AC DC Module Physics Guide AC DC Module Study Availability The Model Builder Show and Hide Physics Options Where Do I Access the Documentation and Model Library
252. ribes a unit thickness that makes the 2D equation identical to the equation used for 3D models Use the Change Thickness Out of Plane node to define specific domains instead of a global setting for the thickness SWEEP SETTINGS Select the Activate terminal sweep check box and enter a Sweep parameter name in the field The default is PortName DEPENDENT VARIABLES The dependent variable field variable is for the Magnetic vector potential A The name can be changed but the names of fields and dependent variables must be unique within a model DISCRETIZATION To display this section click the Show button 5 and select Discretization Select Magnetic vector potential Linear Quadratic the default or Cubic Specify the Value type when using splitting of complex variables Real or Complex the default The Model Builder Show and Hide Physics Options Domain and Shared Features for the Rotating Machinery Magnetic See Also Interface THE ROTATING MACHINERY MAGNETIC INTERFACE 23l Domain and Shared Features for the Rotating Machinery Magnetic Interface Because The Rotating Machinery Magnetic Interface is a multiphysics interface many features are shared with and described for other interfaces Below are links to the boundary edge pair and point features as indicated These domain features are described in this section Initial Values Electric Field Transformation Prescribed Rotati
253. rical net beneath the top net in the hierarchy Leave this field empty to import the top net top cell In GDS files the standard terminology is ce instead of net but structurally they mean the same thing The Grouping of geometries list specifies how the imported geometry objects are grouped in the final geometry The choices for 3D import are All Groups all objects into one single object This selection makes use of a more efficient extrude algorithm that extrudes and combines all layers directly Because the import results in only one geometry object COMSOL Multiphysics does not need to do a complicated analysis of several geometry objects layer Groups all objects in one layer into one geometry object The final geometry contains one object for each layer No grouping No grouping of objects is performed This can be useful for debugging purposes when the other choices fail for some reason This selection returns all the primitive objects found in the file so objects with negative polarity are not drawn correctly The Type of import list specifies how to treat metal layers The Full 3D option imports all metal layers with a thickness Select the Metal shell options if you want to import all metal layers as an embedded boundary between dielectric regions For NETEX G files bond wires or wirebonds can be imported using three different complexity levels Choose the level from the Type of bond wires list
254. ring is predefined by COMSOL no bracket is used and this indicates that this is a finite set such as a feature name KEY TO THE GRAPHICS Throughout the documentation additional icons are used to help navigate the information These categories are used to draw your attention to the information based on the level of importance although it is always recommended that you read these text boxes ICON NAME DESCRIPTION A Caution Important Note 9 Tip Q See Also A Caution icon is used to indicate that the user should proceed carefully and consider the next steps It might mean that an action is required or if the instructions are not followed that there will be problems with the model solution An Important icon is used to indicate that the information provided is key to the model building design or solution The information is of higher importance than a note or tip and the user should endeavor to follow the instructions A Note icon is used to indicate that the information may be of use to the user It is recommended that the user read the text A Tip icon is used to provide information reminders short cuts suggestions of how to improve model design and other information that may or may not be useful to the user The See Also icon indicates that other useful information is located in the named section If you are working on line click the hyperlink to go to the information directly When the link
255. rinted in metal that are not important for a finite element simulation With NETEX G the size of the exported layout can be reduced in the following ways Defining a region to include in the export This region is drawn directly on a top view of the layout Exclude entire layers from the layout Selecting electrical nets to include in the export in addition to the selected region tis also possible to let NETEX G include nets in the proximity of the selected nets Because the Gerber layer files do not contain any physical information about the layer and dielectrics this information must be specified in NETEX G Some of these steps can also be done during import to COMSOL Multiphysics for example excluding layers from the import and changing thickness of the layers Drill Files The connectivity between the layers is defined through drilled holes known as vias A via can go through the entire circuit board or just between certain layers Most ECAD programs use the Excellon drill file format to specify the vias which contains information about via diameter and position Before generating the final output file from NETEX G it is necessary to convert all drill files to Gerber format and include them to the export project in NETEX G For each drill file it is also necessary to specify between which layers the hole goes Within NETEX G a tool can be called that directly converts the Excellon drill format into Gerber After the conv
256. rization P occur explicitly in this expression To instantiate the stress tensor for the general elastic case a material model explicitly including the magnetization and polarization effects is needed ELECTROMAGNETIC FORCES 49 50 Electromagnetic Energy and Virtual Work Another technique to calculate forces is to derive the electromagnetic energy of the system and calculate the force by studying the effect of a small displacement This is known as the method of virtual work or the principle of virtual displacement The method of virtual work is used for the electric energy and magnetic energy separately for calculating the total electric or magnetic force as follows MAGNETIC FORCE AND TORQUE The method of virtual work utilizes the fact that under constant magnetic flux conditions Ref 5 the total magnetic force on a system is computed as F VW m If the system is constrained to rotate about an axis the torque is computed as where is the rotational angle about the axis Under the condition of constant currents the total force and torque are computed in the same way but with opposite signs F VW aW n Ty z ELECTRIC FORCE AND TORQUE Under the condition of constant charges the total electric force and torque on a system are computed as Fo VW oW 35 Under the condition of constant potentials the total electric force and torque on a system are computed as CHAPTER 2 REVI
257. rm to find a specific material by name UNS number Material Library materials only or DIN number Material Library materials only If the MATERIAL LIBRARY AND DATABASES 297 298 search is successful a list of filtered databases containing that material displays under Material Selection g To clear the search field and browse delete the search term and click Tp Search to reload all the databases 1 Click to open each database and browse for a specific material by class for example in the Material Library or physics module for example MEMS Materials Always review the material properties to confirm they are applicable for the model For example Air provides temperature dependent properties Important that are valid at pressures around 1 atm 4 When the material is located right click to Add Material to Model node with the material name is added to the Model Builder and the Material page opens Using Material Properties CHAPTER 9 m For detailed instructions see Adding Predefined Materials and Material Di 8 Properties Reference in the COMSOL Multiphysics User s Guide MATERIALS Using the AC DC Material Database physics interfaces in the AC DC Module support the use of the COMSOL Multiphysics material databases The electromagnetic material properties that can be stored in the material databases are Electrical conductivity and resistivity Relative permittivity
258. ry condition that sets the tangential components of the magnetic potential to zero at the boundary n x A 0 Magnetic insulation is a special case of the magnetic potential boundary g condition that sets the tangential component of the magnetic potential to Tip Zero It is used for the modeling of a lossless metallic surface for example a ground plane or as a symmetry type boundary condition It imposes symmetry for magnetic fields and magnetic currents In the transient and time harmonic formulations it also imposes antisymmetry for electric fields and electric currents It supports induced electric surface currents and thus any prescribed or induced electric currents volume surface or edge currents flowing into a perfect electric conductor boundary is automatically balanced by induced surface currents ww The magnetic insulation boundary condition is used on exterior and interior boundaries representing the surface of a lossless metallic conductor or on exterior boundaries representing a symmetry cut The shaded metallic region is not part of the model but still carries effective mirror images of the sources Note also that any current flowing into the boundary is perfectly balanced by induced surface currents The tangential vector potential and electric field vanishes at the boundary BOUNDARY SELECTION For the default node no user selection is required All boundaries is automatically selected it appli
259. s Magnetic Flux Conservation Magnetic Insulation the default boundary condition and Initial Values Right click the Magnetic Fields No Currents node to add other features that implement additional boundary conditions and point conditions E Except where described below the settings windows are described for the Magnetic Fields and Electrostatics interfaces Note Magnetic Prospecting of Iron Ore Deposits Model Library path ACDC Module Magnetostatics magnetic prospecting e Magnetic Signature of a Submarine Model Library path Module Magnetostatics submarine INTERFACE IDENTIFIER The interface identifier is a text string that can be used to reference the respective physics interface if appropriate Such situations could occur when coupling this interface to another physics interface or when trying to identify and use variables defined by this physics interface which is used to reach the fields and variables in expressions for example It can be changed to any unique string in the Identifier field The default identifier for the first interface in the model is mfnc THE MAGNETIC FIELDS NO CURRENTS INTERFACE 221 222 DOMAIN SELECTION The default setting is to include All domains in the model to define the magnetic scalar potential and the equations that describe the potential field for magnetostatics without currents To choose specific domains select Manual from the Selection lis
260. s distinguish between physics interfaces and the variables defined by the interface have an underscore plus the physics interface tag appended to their names The Model Wizard is an easy way to select the physics interface and study type when creating a model for the first time and physics interfaces can be added to an existing model at any time Full instructions for selecting interfaces and setting up a model are in the COMSOL Multiphysics User s Guide ABOUT THE AC DC MODULE 15 In 2D in plane and out of plane variants are available for problems with a planar symmetry as well as axisymmetric interfaces for problems with a cylindrical symmetry See When using an axisymmetric interface it is important that the horizontal 1 axis represents the r direction and the vertical axis the z direction and Important be created that the geometry in the right half plane that is for positive r only must What Problems Can You Solve and Table 1 1 for information about the available study types and variables See also Overview of the User s Guide for links to the chapters in this guide PHYSICS ICON SPACE PRESET STUDIES DIMENSION x ACIDC Electrostatics es all dimensions stationary time dependent Electric Currents x ec all dimensions stationary frequency domain time dependent small signal analysis frequency domain Electric Currents xa ecs 3D 2D 2D stationary frequency domain Shell axisymmetric ti
261. s selected from the Pairs menu choose the pair to define An identity pair has to be created first Ctrl click to deselect FLOATING POTENTIAL Specify an optionally non zero Charge Qy SI unit C For the Electric Currents and Magnetic and Electric Fields interfaces enter a Terminal current SI unit A Specify zero current for a disconnected Note electrode CONSTRAINT SETTINGS To display this section click the Show button gt and select Advanced Physics Options Select a Constraint type Bidirectional symmetric or Unidirectional If required select the Use weak constraints check box Archie s Law This subfeature is available only when Archie s law is selected as the EI Electric conductivity material parameter in the parent feature for example the Current Conservation node Then right click the Current Note E Conservation node to add this subnode Use the Archie s Law subnode to provide an electrical conductivity computed using Archie s Law This subnode can be used to model nonconductive porous media saturated or variably saturated by conductive liquids using the relation n m SLED or T em ul Archie s Law Theory See Also 140 CHAPTER 4 THE ELECTRIC FIELD INTERFACES DOMAIN SELECTION From the Selection list choose the domains to define Archie s law MATERIAL TYPE Select a Material type Solid Non solid or From material CONDUCTION CURRENT
262. s the resistance G is the conductance S is the S parameter The relations also include the following matrices 1000 g 0100 0010 0001 EZ 1 2 2 ref 7 where 20 is the characteristic impedance You can compute conversions between the impedance matrix Z the admittance matrix Y and the S parameter matrix S in a results table using the settings in the Global Matrix Evaluation node which you can add under Results gt Derived Values Sec Global Matrix Evaluation in the COMSOL Multiphysics User s Guide for more information LUMPED PARAMETERS 89 90 Lumped Ports with Voltage Input In this section About Lumped Ports Lumped Port Parameters About Lumped Ports The ports described in the S Parameters and Ports section require a detailed specification of the mode including the propagation constant and field profile In situations when the mode is difficult to calculate or when there is an applied voltage to the port a umped port might be a better choice This is also the appropriate choice when connecting a model to an electrical circuit For example attach a lumped port as an internal port directly to a printed circuit board or to the transmission line feed of a device The lumped port must be applied between two metallic objects separated by a distance much smaller than the wavelength that is a local quasi static approximation must be justified This is because the concept of port or
263. section discusses issues that should be addressed before starting to LE implement a 3D model 3D Although COMSOL Multiphysics fully supports arbitrary 3D geometries it is important to simplify the problem This is because 3D problems easily get large and require more computer power memory and time to solve The extra time spent on simplifying a problem is probably well spent when solving it Is it possible to solve the problem in 2D Given that the necessary approximations are small the solution is more accurate in 2D because a much denser mesh can be used See 2D Problems if this is applicable Are there symmetries in the geometry and model Many problems have planes where the solution on either side of the plane looks the same A good way to check this is to flip the geometry around the plane for example by turning it upside down around the horizontal plane You can then remove the geometry below the plane ifyou do not see any differences between the two cases regarding geometry materials and sources Boundaries created by the cross section between the geometry and this plane need a symmetry boundary condition which is available in all 3D physics interfaces Eddy Currents Model Library path ACDC Module Inductive Devices and Coils eddy currents Model CHAPTER 3 Do you know the dependence in one direction so it can be replaced by an analytical function You can use this approach either to convert 3D to 2D or
264. sics User s Guide AC DC Included in the AC DC Module the AC DC database has electric properties for some magnetic and conductive materials BATTERIES AND FUEL CELLS Included in the Batteries amp Fuel Cells Module the Batteries and Fuel Cells database 4 includes properties for electrolytes and electrode reactions for certain battery chemistries MATERIAL LIBRARY AND DATABASES 293 294 LIQUIDS AND GASES Included in the Acoustics Module CFD Module Chemical Reaction Engineering Module Heat Transfer Module MEMS Module Pipe Flow Module and Subsurface Flow Module the Liquids and Gases database includes transport properties and surface tension data for liquid gas and liquid liquid interfaces MEMS Included in the MEMS Module and Structural Mechanics Module the MEMS database u has properties for MEMS materials metals semiconductors insulators and polymers PIEZOELECTRIC Included in the Acoustics Module MEMS Module and Structural Mechanics Module the Piezoelectric database has properties for piezoelectric materials PIEZORESISTIVITY Included in the MEMS Module the Piezoresistivity database 2 has properties for piezoresistive materials including p Silicon and n Silicon materials USER DEFINED LIBRARY The User Defined Library folder n is where user defined materials databases libraries are created When any new database is created this also displays in the M
265. so 134 CHAPTER 4 THE ELECTRIC FIELD INTERFACES DEPENDENT VARIABLES The dependent variable field variable is for the Electric potential V The name can be changed but the names of fields and dependent variables must be unique within a model DISCRETIZATION To display this section click the Show button 5 and select Discretization Select an Electric potential Linear Quadratic the default Cubic Quartic or in 2D only Quintic Specify the Value type when using splitting of complex variables Real or Complex the default The Model Builder Show and Hide Physics Options Domain Boundary Edge Point and Pair Features for the Electric Currents Interface See Also Theory for the Electric Currents Interface Domain Boundary Edge Point and Pair Features for the Electric Currents Interface The Electric Currents Interface has these domain boundary edge point and pair conditions available About the Boundary Conditions The exterior and interior boundary conditions listed in Table 4 1 are available The relevant interface condition at interfaces between different media and interior boundaries is continuity that is n5 Ji J 0 which is the natural boundary condition Available Features These features and subfeatures are available for this interface and listed in alphabetical order Also see Table 4 1 for a list of interior and exterior boundary conditions including edge point a
266. ss SI unit m of the shell V d oV V J dQ o is the electrical conductivity SI unit S m J is an externally generated current density SI unit m and Qj is an external current source SI unit A m The operator V represents the tangential derivative along the shell Dynamic Electric Currents Equations In the frequency domain and time dependent study types dynamic formulations accounting for both conduction currents and displacement currents are used V d o josg V V J joP dQ For the transient case the resulting equation becomes V dE GN P Vo d ov V 3 dQ 178 CHAPTER 4 THE ELECTRIC FIELD INTERFACES The Magnetic Field Interfaces This chapter summarizes the functionality of the magnetic field interfaces found under the AC DC branch Xx in the Model Wizard In this chapter The Magnetic Fields Interface Magnetic Fields Interface Advanced Features The Magnetic Fields No Currents Interface The Rotating Machinery Magnetic Interface Theory of Magnetic and Electric Fields Theory for the Magnetic Fields Interface Theory for the Magnetic Fields No Currents Interface 179 180 The Magnetic Fields Interface The AC DC Module enhances the Magnetic Fields interface included with the basic COMSOL Multiphysics license These features are Note described in Magnetic Fields Interface Advanced Features The Magnetic Fields interface found under the AC DC
267. ssion with 0 of the stress tensor is also known as the Maxwell stress tensor Using the fact that for air D E and B the expression for the stress tensor can be written as 1 T pI IE D 1H B I ED HB The equation for the balance of forces becomes 0 v p1 2E D 2H B ED HB f pl 2 2 ext Maxwell s equations in free space give that the contribution of the electromagnetic part of the stress tensor is zero and the resulting expression is 0 Vp f Thus using the same terminology as earlier 44 0 for air with ow pl In the derivation of the total force on an elastic solid surrounded by vacuum or air the approximation Vp 0 has been used When operating with the divergence operator on the stress tensor the relation T V EE 9E EI E V E Ex VxE is useful and similarly for B From the right hand side it is clear using Maxwell s equations that this is zero for stationary fields in free space Consider again the case of a solid surrounded by air To compute the total force the projection of the stress tensor on the outside of the solid surface is needed n T pn E D 3H B n n4 E D n H B where n4 is the surface normal a 1 by 3 vector pointing out from the solid This expression can be used directly in the boundary integral of the stress tensor for calculating the total force F on the solid ELECTROMAGNETI
268. ssociated properties DOMAIN SELECTION From the Selection list choose the domains to define the magnetic vector potential and the equation based on Amp re s law that defines the potential MODEL INPUTS This section contains field variables that appear as model inputs if the current settings include such model inputs By default this section is empty If a linear temperature relation is added for the conductivity then define the source for the temperature From the Temperature list select an existing temperature variable from another physics interface if available or select User defined to define a value or expression for the temperature SI unit K in the field that appears underneath the list MATERIAL TYPE Select a Material type Solid Non solid or From material COORDINATE SYSTEM SELECTION The Global coordinate system is selected by default The Coordinate system list contains any additional coordinate systems that the model includes CONDUCTION CURRENT E See the settings for Conduction Current under Amp re s Law for the Magnetic Fields interface Note ELECTRIC FIELD See the settings for Electric Field under Charge Conservation for the Electrostatics interface Note THE MAGNETIC AND ELECTRIC FIELDS INTERFACE 253 MAGNETIC FIELD EI See the settings for Magnetic Field under Amp re s Law for the Magnetic Fields interface Note Initial Values The Initial Values
269. sting temperature variable from another physics interface if available or select User defined to define a value or expression for the temperature SI unit K in the field that appears underneath the list MATERIAL TYPE Select a Material type Solid the default Non solid or From material COORDINATE SYSTEM SELECTION The Global coordinate system is sclected by default The Coordinate system list contains any additional coordinate systems that the model includes CONDUCTION CURRENT By default the Electrical conductivity o SI unit S m for the media is defined From material Or select User defined Linearized resistivity Archie s law or Porous media f User defined is selected select Isotropic Diagonal Symmetric or Anisotropic depending on the characteristics of the electrical conductivity and then enter values or expressions in the field or matrix If another type of temperature dependence is used other than a linear temperature relation enter any expression for the conductivity as a Note function of temperature Select Linearized resistivity for a temperature dependent conductivity this occurs in for example Joule heating and is also called resistive heating The equation describing the conductivity _ 1 S T5 CHAPTER 4 THE ELECTRIC FIELD INTERFACES where is the resistivity at the reference temperature and a is the temperature coefficient of resistance which describ
270. t BACKGROUND MAGNETIC FIELD Select an option from the Solve for list Reduced field or Full field the default If Reduced field is selected specify a Background magnetic field SI unit A m The total field used in the physics and equations are given by the sum of the reduced and background fields DEPENDENT VARIABLES The dependent variable field variable is for the Magnetic scalar potential Vm The name can be changed but the names of fields and dependent variables must be unique within a model DISCRETIZATION To display this section click the Show button z and select Discretization Select Quadratic the default Linear Cubic or Quartic for the Magnetic scalar potential Specify the Value type when using splitting of complex variables Real or Complex the default The Model Builder Show and Hide Physics Options Domain Boundary Point and Pair Features for the Magnetic Fields No Currents Interface See Also Theory for the Magnetic Fields No Currents Interface Domain Boundary Point and Pair Features for the Magnetic Fields No Currents Interface The Magnetic Fields No Currents Interface has these domain boundary point and pair conditions available To obtain a unique solution the value of the magnetic potential must be provided at least at one point If the magnetic insulation boundary condition is used everywhere the potential has to be fixed using a point Note
271. t Ctrl click to deselect MATERIAL TYPE Select a Material type Solid Non solid or From material MAGNETIC SHIELDING The default Relative permeability unitless uses values From material If User defined is selected choose Isotropic Diagonal Symmetric or Anisotropic and enter other values or expressions For anisotropic material the relative permeability is a tensor Enter a value or expression for the Surface thickness d SI unit m Thin Low Permeability Gap The Thin Low Permeability Gap feature adds a boundary condition on an internal boundary which allows for a discontinuity in the magnetic scalar potential Enter a THE MAGNETIC FIELD INTERFACES relative magnetic permeability u for the thin layer material as well as a thickness ds The magnetic flux through this boundary is given by e sacs S where V is the magnetic scalar potential on the upside of the boundary selection and Vm is the magnetic scalar potential on the downside Use the thin low permeability gap boundary condition n B Vm2 PT ug Va to model a thin gap ofa low permeable material such as air The layer has the thickness d and the relative permeability BOUNDARY SELECTION From the Selection list choose the boundaries to define a thin low permeability gap PAIR SELECTION If Pair Thin Low Permeability Gap is selected from the Pairs menu choose the pair to define An identity pair has to be
272. t Stabilization Stabilization Techniques Reference Guide Numerical Stabilization Geometry Working with Geometry User s Guide Constraint Settings Using Weak Constraints User s Guide Where Do I Access the Documentation and Model Library number of Internet resources provide more information about COMSOL Multiphysics including licensing and technical information The electronic documentation Dynamic Help and the Model Library are all accessed through the COMSOL Desktop If you are reading the documentation as a PDF file on your computer the blue links do not work to open a model or content referenced in a different user s guide However if you are using the online help in Important COMSOL Multiphysics these links work to other modules model examples and documentation sets CHAPTER 1 THE DOCUMENTATION The COMSOL Multiphysics User s Guide and COMSOL Multiphysics Reference Guide describe all interfaces and functionality included with the basic COMSOL Multiphysics license These guides also have instructions about how to use COMSOL Multiphysics and how to access the documentation electronically through the COMSOL Multiphysics help desk INTRODUCTION To locate and search all the documentation in COMSOL Multiphysics Press Fl for Dynamic Help Click the buttons on the toolbar or Select Help gt Documentation 7 or Help gt Dynamic Help 1 from the main menu and then either enter a sea
273. t the values are taken from the domain material EI Only certain material models see Materials support the Linearized resistivity Note To specify other values for any of these properties select User defined from the list and then enter a value or expression 15 the current temperature which can be a value that is specified as a model input or the temperature from a heat transfer interface The definition of the temperature field appears in the Model Inputs section Porous Media When Porous media is selected right click to add a Porous Media subnode Archie s Law When Archie s law is selected right click to add an Archie s Law subnode CHAPTER 4 THE ELECTRIC FIELD INTERFACES Initial Values Initial Values adds an initial value for the electric potential that can serve as an initial condition for a transient simulation or as an initial guess for a nonlinear solver Right click to add additional Initial Values features BOUNDARY SELECTION Select the boundaries where you want to define an initial value INITIAL VALUES Enter a value or expression for the initial value of the Electric potential V SI unit V The default is 0 Current Source The Current Source node adds a distributed current source Q in the equation that the interface defines Use this feature with caution as it may violate the current conservation law that is inherent in Maxwell Amp re s law BOUNDARY SELECTION From the Selec
274. t use either the coordinate or the net information to find it The GDS format is a binary file format so it is very difficult to edit the file manually IMPORTING ECAD FILES 107 108 CHAPTER 3 PROBLEMS WITH SEVERAL GEOMETRY OBJECTS If the special extrude functionality is not used you get several geometry objects for example one for each layer if By layer is selected from the Grouping of geometries list After a CAD import COMSOL Multiphysics is in the Geometry branch of the model tree When you continue to the Materials branch if the model tree or to a physics interface node or the Mesh branch the program tries to combine all the objects into one geometry and this operation might fail if the objects are very complex and have high aspect rations Resolve this either by trying the option All in the Grouping of geometries list This creates one combined geometry object by using the special extrude functionality and with only one object this Another possibility is to use assemblies because then COMSOL Multiphysics does not have to combine the objects parts This is controlled by the Finalize node in the Geometry branch of the model tree When using an assembly use identity pairs to connect the interfaces between the layers As a final option do not import the dielectric layers The import then leaves isolated metal layers that have to connect with coupling variables MODELING WITH THE AC DC MODULE The Electric Field
275. t1 def k12 and so on for the thermal conductivity For material properties that are functions call these with input arguments such as mati def rho pA T where pA and T are numerical values or variables representing the absolute pressure and the temperature respectively The functions can be plotted directly from the function nodes settings window by first specifying suitable ranges for the input arguments Many physics interfaces also define variables for the material properties that they use For example solid rho is the density in the Solid Mechanics interface and is equal to the density in a material when it is used in the domains where the Solid Mechanics interface is active If you define the density in the Solid Mechanics interface using another value solid rho represents that value and not the density of the material If you use the density from the material everywhere in the model solid rho and material rho are identical Opening the Material Browser When using the Material Browser the words window and page are interchangeable For simplicity the instructions refer only to the Material Note Browser 1 Open or create a model file 2 From the View menu choose Material Browser or right click the Materials node and choose Open Material Browser The Material Browser opens by default in the same position as the settings window 3 Under Material Selection search or browse for materials Enter a Search te
276. tage source and the second pair defining the input control voltage The first node in a pair represents the positive reference terminal If the ground node is involved the convention is to use zero for this DEVICE PARAMETERS Enter the voltage Gain The resulting voltage is this number multiplied by the control voltage Voltage Controlled Current Source The Voltage Controlled Current Source node lt gt connects a voltage controlled current source between two nodes in the electrical circuit second pair of nodes define the input control voltage NODE CONNECTIONS Specify four Node names the first pair for the connection nodes for the current source and the second pair defining the input control voltage The first node in a pair represents the positive voltage reference terminal or the one from which the current flows through the source to the second node If the ground node is involved the convention is to use zero for this DEVICE PARAMETERS Enter the voltage Gain The resulting current is this number multiplied by the control voltage Thus it formally has the unit of conductance Current Controlled Voltage Source The Current Controlled Voltage Source node lt gt connects a current controlled voltage source between two nodes in the electrical circuit The input control current is the one flowing through a named device that must be a two pin device CHAPTER 7 THE ELECTRICAL CIRCUIT INTERFACE
277. ted select Isotropic Diagonal Symmetric or Anisotropic and enter values or expressions in the field or matrix Enter a Surface thickness d SI unit m of the shielding CHAPTER 4 THE ELECTRIC FIELD INTERFACES Terminal The Terminal node provides a boundary condition for connection to external circuits to transmission lines or with a specified voltage or current By specifying zero current a floating potential condition is obtained Lumped Parameters See Also BOUNDARY SELECTION From the Selection list choose the boundaries to model as terminals connected to external circuits or an external current or voltage EI For the Electric Currents Shell interface select edges 3D or points 2D instead of boundaries Note PAIR SELECTION If Terminal is selected from the Pairs menu choose the pair to define An identity pair has to be created first Ctrl click to deselect TERMINAL Specify the terminal s properties To indicate which boundaries that belong to the same terminal enter the same name in the Terminal name field The Terminal name should be numeric for sweeps to work properly Select a Terminal type Voltage Current Circuit or Terminated Select Voltage to enter an electric potential Vg SI unit V The default is 1 Charge to enter current SI unit C The default is zero current for an open circuit THE ELECTROSTATICS INTERFACE 121 Circuit to specify a t
278. tem is selected by default The Coordinate system list contains any additional coordinate systems that the model includes EXTERNAL CURRENT DENSITY Enter a value or expression for each component of the External current density J SI unit A m Velocity Lorentz Term The Velocity Lorentz term feature adds velocity v The external current is equal to ov x B This feature is only valid as follows When solving for both the electric potential and the magnetic vector potential using the Magnetic and Electric Fields interface In 2D and 2D axisymmetry when solving for only the out of plane component of the magnetic vector potential To use the velocity feature correctly requires deep physical insight In o situations when the moving domain is of bounded extent in the direction of the motion or material properties vary in this direction or it contains Important magnetic sources that also move the Lorentz term must not be used An operational definition of when it can be used is that the moving domain should only contain an induced magnetic source magnetization eddy currents that has to be stationary with respect to the motion Thus it cannot be used for modeling projectiles THE MAGNETIC FIELDS INTERFACE 189 190 of finite length or projectiles containing magnets It can be used to model conductive homogeneous spinning disks magnetic brakes magnets over a moving infinite homogenous plane maglev trai
279. th of the edge s To avoid unphysical currents a Linear coil should be terminated on external boundaries The Reference Edge subfeature is used with a Circular coil where the wires are wound in circles around the same axis Select a group of edges forming a circle around the coil s axis From the selected edge the coil axis is computed and the direction of the wires is taken to be the azimuthal direction around the axis The coil length used is simply the length of the edges the best approximation is obtained when the radius of the edges is close to the average radius of the coil THE MAGNETIC FIELD INTERFACES EDGE SELECTION From the Selection list choose the edges to define the reference edge The default selects All edges See Using Coils in 3D Models in the modeling section to learn more Esc about this node Automatic Current Calculation c This subnode is available for 3D models and when the Coil Type selected A is Circular 3D Right click the Multi Turn Coil Domain to add an Automatic Current Calculation subnode This subfeature is needed to set up the automatic computation ofthe current flow in the coil domain The boundary conditions for the current calculation study are specified using the Electric Insulation Input and Output subnodes To complete the setup for the computation of the coil direction a Coil Current Calculation study step must be added to the study DOMAIN SELECTION From t
280. that electric current are mainly caused by ion fluxes trough the pore network Originally Archie s law is an empirical law for the effective conductivity of a fully saturated rock or soil but it can be extended to variably saturated porous media Archie s law relates the effective conductivity to the fluid conductivity oz fluid saturation sz and porosity j _ n m Sp p or here m is the cementation exponent a parameters that describes the connectivity of the pores The cementation exponent normally varies between 1 3 and 2 5 for most sedimentary rocks and it is close to 2 for sandstones The lower limit m 1 represents a volume average of the conductivities of a fully saturated insulating zero conductivity porous matrix and a conducting fluid The saturation coefficient n is normally close to 2 g The ratio F or o is called the formation factor Tip Archie s Law does not take care of the relative permittivity of either fluids or solids so the effective relative permittivity of the porous medium is normally consider as e 1 Dynamic Electric Currents Equations In the frequency domain and time dependent study types dynamic formulations accounting for both conduction currents and displacement currents are used Combining the time harmonic equation of continuity V J V cE J jop with the equation CHAPTER 4 THE ELECTRIC FIELD INTERFACES and generalized to handle current so
281. ties Equivalently the effective reciprocal permeability is obtained from 0 0 421 2 Ur H H2 i If the permeability is defined by second order tensors the inverse of the tensors are used Note POWER LAW A power law gives the following expression for the equivalent permeability The effective permeability calculated by Volume Average Permeability is the upper bound the effective permeability calculated by Volume El Average Reciprocal Permeability is the lower bound and the Power Law Note average gives value somewhere in between these two Archie s Law Theory The electrical conductivity of the materials composing saturated rocks and soils can vary over many orders of magnitude For instance in the petroleum reservoirs normal sea water or brine has a typical conductivity of around 3 S m whereas hydrocarbons are typically much more resistive and have conductivities in the range 0 1 0 01 S m THEORY FOR THE ELECTRIC CURRENTS INTERFACE 175 176 The porous rocks and sediments may have even lower conductivities In variably saturated soils the conductivity of air is roughly ten orders of magnitude lower that the ground water A simple volume average of either conductivity or resistivity in rocks or soils might give different results compared to experimental data Since most crustal rocks sedimentary rocks and soils are formed by non conducting materials Archie Ref 1 assumed
282. tion list choose the boundaries to define a current source ELECTRODE CURRENT SOURCE Enter a value or expression for the Current source Q SI unit A m Change Shell Thickness Add a Change Shell Thickness node to specify a different shell thickness for a subset of the boundaries or edges where the Electric Currents Shell interface is defined BOUNDARY OR EDGE SELECTION Select the boundaries or edges where you want to specify a shell thickness that differs from that for the parent Electric Currents Shell interface CHANGE SHELL THICKNESS Enter a Shell thickness SI unit m The default is 1 cm THE ELECTRIC CURRENTS SHELL INTERFACE 163 164 Normal Current Density The Normal Current Density feature represents a current density flowing normally from the domain into the shell boundary This condition is different from the Current Source feature since it represents a net current density flowing from the adjacent domain into the shell and can be used to model for example a boundary acting as an electrode BOUNDARY SELECTION From the Selection list choose the boundaries to apply a current flow as the boundary condition using the normal current density COORDINATE SYSTEM SELECTION The Global coordinate system is sclected by default The Coordinate system list contains any additional coordinate systems that the model includes NORMAL CURRENT DENSITY Enter a value or expression for the Normal current
283. to convert a layer to a boundary condition see Simplifying the Geometry Using Boundary Conditions Simplifying the Geometry Using Boundary Conditions An important technique to minimize the problem of size is to use efficient boundary conditions Truncating the geometry without introducing large errors is one of the great challenges in modeling Following are some ideas of how to do this in both 2D and 3D problems MODELING WITH THE AC DC MODULE Does the solution only undergo small changes When a model extends to infinity it might have regions where the solution only undergoes small changes This problem is addressed in two related steps First truncate the geometry in a suitable position Second apply a suitable boundary condition there For static and quasi static models it is often possible to assume zero fields at the open boundary provided that this is at a sufficient distance away from the sources Can you replace the thin layers with boundary conditions There are several types of boundary conditions in COMSOL Multiphysics suitable for such replacements You can for example replace materials with high conductivity with the shielding boundary condition which assumes a constant potential through the thickness ofthe layer If you have a magnetic material with a high relative permeability you can also model it using the shielding boundary condition One Sided Magnet and Plate Model Library path ACDC Module Mo
284. tric fields interface 254 magnetic fields interface 190 magnetic fields no currents interface 225 rotating machinery magnetic interface 233 input node coil domains 208 Internet resources 20 Kirchhoffs circuit laws 270 knowledge base COMSOL 22 layers extruding 98 line charge node 127 line charge on axis node 127 line charge out of plane node 128 line current out of plane node 195 line current source node 152 line current source on axis node 153 linear coil 81 Lorentz forces calculating 70 Lorentz term 35 lumped parameters calculating 85 88 converting 89 lumped port node 211 lumped ports 90 91 magnetic and electric fields interface 246 theory 255 magnetic field node 192 magnetic fields interface 180 theory 240 magnetic fields no currents interface 221 theory 243 magnetic flux conservation node 224 magnetic flux density node 226 magnetic forces and torques 50 magnetic insulation node magnetic fields interface 191 magnetic fields no currents interface 226 magnetic point dipole node 219 magnetic point dipole on axis node 220 magnetic potential node 193 magnetic shielding node 228 mapped infinite elements 65 Material Browser opening 297 Material Library 293 materials databases 293 domain default 296 grouping of 36 properties evaluating and plotting 296 using 299 Maxwell stress tensor calculating 70 Maxwell s equations dielectrics 38 electrical circuits
285. ubcircuit definition feature itself Also right click to Rename the node SUBCIRCUIT PINS Define the Pin names at which the subcircuit connects to the main circuit or to other subcircuits when referenced by a Subcircuit Instance feature The Pin names refer to circuit nodes in the subcircuit The order in which the Pin names are defined is the order in which they are referenced by a Subcircuit Instance feature THE ELECTRICAL CIRCUIT INTERFACE 263 264 Subcircuit Instance The Subcircuit Instance node ic is used to refer to defined subcircuits NODE CONNECTIONS Select the Name of subcircuit link from the list of defined subcircuits in the circuit model and the circuit Node names at which the subcircuit instance connects to the main circuit or to another subcircuit if used therein NPN BJT The NPN BJT device model e is a large signal model for an NPN bipolar junction transistor BJT It is an advanced device model and no thorough description and motivation of the many input parameters is attempted here The interested reader is referred to Ref 2 for more details on semiconductor modeling within circuits Many device manufacturers provide model input parameters for this BJT model For any particular make of BJT the device manufacturer should be the primary source of information NODE CONNECTIONS Specify three Node names for the connection nodes for the NPN BJT device These represent the collector base an
286. ues rather than RMS EI For the AC source the frequency is a global input set by the solver so do not use the Sine source unless the model is time dependent Note Current Source The Current Source node connects a current source between two nodes the electrical circuit NODE CONNECTIONS Set the two Node names for the connecting nodes for the current source The first node represents the positive reference terminal from which the current flows through the source to the second node If the ground node is involved the convention is to use zero for this DEVICE PARAMETERS Enter the Source type which should be adapted to the selected study type It can be DC source AC source or a time dependent Sine source Depending on the choice of source also specify the Current Isro the offset Current loff the Frequency and the Source phase values are peak values rather than RMS EI For the AC source the frequency is a global input set by the solver so do not use the Sine source unless the model is time dependent Note THE ELECTRICAL CIRCUIT INTERFACE 261 262 Voltage Controlled Voltage Source The Voltage Controlled Voltage Source node lt gt connects a voltage controlled voltage source between two nodes in the electrical circuit A second pair of nodes define the input control voltage NODE CONNECTIONS Specify four Node names the first pair for the connection nodes for the vol
287. ulations and Current Conservation Current conservation is inherent in Amp re s law and it is known that if current is conserved explicit gauge fixing is not necessary as iterative solvers converge towards a valid solution However it is generally not sufficient for the source currents to be divergence free in an analytical sense as when interpolated on the finite element functional basis this property is not conserved When using the Magnetic and Electric Fields interface the electric potential is used to state current conservation so unless nonphysical current sources are specified inside the computational domain current conservation is fulfilled When using the Magnetic Fields interface current conservation is usually imposed either by the solver for magnetostatics or in the transient or time harmonic case by THE MAGNETIC FIELD INTERFACES the induced current density The explicit gauge or divergence constraint can also help imposing current conservation as described in the preceding section Time Harmonic Magnetic Fields In the time harmonic case there is no computational cost for including the displacement current in Amp re s law then called Maxwell Amp re s law VxH J c E vxB joD J In the transient case the inclusion of this term would lead to a second order equation in time but in the harmonic case there are no such complications Using the definition of the electric and magnetic potentials
288. urce Terminal To locate and search all the documentation in COMSOL select Help gt Documentation from the main menu and either enter a search term Tip or look under a specific module in the documentation tree CHAPTER 4 THE ELECTRIC FIELD INTERFACES Current Conservation The Current Conservation node adds the continuity equation for the electrical potential and provides an interface for defining the electric conductivity as well as the constitutive relation and the relative permittivity for the displacement current BOUNDARY SELECTION From the Selection list choose the boundaries to define the electric potential and the continuity equation that describes the potential field MODEL INPUTS This section contains field variables that appear as model inputs if the current settings include such model inputs By default this section is empty If a linear temperature relation is added for the conductivity then the source for the temperature T can be defined From the Temperature list select an existing temperature variable from another physics interface if available or select User defined to define a value or expression for the temperature SI unit K in the field that appears underneath the list MATERIAL TYPE Select a Material type Solid the default Non solid or From material COORDINATE SYSTEM SELECTION The Global coordinate system is selected by default The Coordinate system list contains any ad
289. urces yields the following equation V josg VV J joP Q For the transient case using the transient equation of continuity pest Bye _0 Vad eV and generalized to handle current sources the resulting equation becomes V Dev V P V oVV J Q 4 2 In planar 2D the dynamic formulations also involves the thickness d in the z direction V d c jog VV J amp joP dQ des dE eg V P V d ovV J dQ Reference for the Electric Currents Interface 1 Archie The Electric Resistivity as an Aid in Determining Some Reservoir Characteristics Trans Am Inst Metal Eng 146 54 62 1942 THEORY FOR THE ELECTRIC CURRENTS INTERFACE 177 Theory for the Electric Currents Shell Interface The Electric Currents Shell Interface in 3D to model thin shells of conductive media This physics interface is similar to the 2D Electric Currents interface solving for the electric potential on 2D surfaces in a 3D geometry The difference is that the shell does not have to be flat as they obviously are when using the 2D Electric Currents interface The Electric Currents Shell interface is also available on boundaries in 2D geometries In this section Electric Currents Shell Equations in Steady State Dynamic Electric Currents Equations Electric Currents Shell Equations in Steady State In the static study type the interface solves the following equation where d is the thickne
290. ure acts on the coil potential and must be applied to an external boundary of the coil domain BOUNDARY SELECTION From the Selection list choose the boundaries to define the gap feed The default selects All boundaries MODEL INPUTS This section contains field variables that appear as model inputs if the current settings include such model inputs By default this section is empty MAGNETIC FIELDS INTERFACE ADVANCED FEATURES 205 206 SINGLE TURN COIL DOMAIN See Single Turn Coil Domain for all settings See Using Coils in 3D Models in the modeling section to learn more p about this node Ground Right click the Single Turn Coil Domain node to add the Ground subnode The Ground subfeature enforces the condition 0 on a boundary BOUNDARY SELECTION From the Selection list choose the boundaries to define the ground The default selects All boundaries See Using Coils in 3D Models in the modeling section to learn more pm about this node CHAPTER 5 Reference Edge After selecting Linear or Circular as the Coil type for the Multi Turn Coil Domain feature right click the Multi Turn Coil Domain node to add the Reference Edge subnode The Reference Edge subfeature is used with Linear coils where the wires are all parallel and straight lines Select an edge or a group of co linear edges The direction of the wires and the coil length is taken to be the direction and the leng
291. urn Coil Domains When specifying a total voltage the component of the current density in the direction of the wires is defined as in Equation 3 5 and Equation 3 6 5 NW ooit 3 5 AR coil where is the applied voltage which is specified A is the total cross sectional area of the coil domain N is the number of turns specified Roi is the total resistance of the coil calculated as T 3 6 A 9 coil coi where L is equal to the physics interface s thickness d for 2D models and equal to 2 for 2D axially symmetric models The expression is the product of the wire bulk conductivity and wire cross section area Vinq is the induced voltage calculated by integrating the electric field along the coil Coil Group Domains When specifying total voltage the out of plane component of the current density is defined as MODELING WITH THE AC DC MODULE where V is an unknown applied potential on the i turn of the coil and L is equal to the physics interface thickness d for 2D models and equal to 2 for 2D axially symmetric models The applied potentials are computed through the integral constraint 4 48 1 Unlike the fixed current option the coil current is unknown The coil current is computed using the constraint N Voi Vi i l where Voi is the user defined voltage drop across the coil V is the individual applied potentials and is the number of turns in the co
292. use this module is fully integrated with COMSOL Multiphysics the modeling process is similar In this chapter Preparing for Modeling Infinite Elements Force and Torque Computations Coil Domains Lumped Parameters Lumped Ports with Voltage Input S Parameters and Ports Connecting to Electrical Circuits Importing ECAD Files 55 Preparing for Modeling This section is intended a guide through the selection process among the physics interfaces in the AC DC Module and does not contain detailed interface descriptions Several topics in the art of modeling are covered here that may not be in ordinary textbooks on electromagnetic theory This section discusses these topics e What Problems Can You Solve Can I use the quasi static physics interfaces or do I need wave propagation e Selecting the Space Dimension for the Model Geometry Is a 2D 3D or axisymmetric geometry best for my model Simplifying the Geometry Using Boundary Conditions When do I need to resolve the thickness of thin shells Applying Electromagnetic Sources What sources can I use to excite the fields Selecting a Study Type Is my problem suited for time dependent or time harmonic frequency domain formulations 2D Field Variables What do you need to do to solve for a vector field in 2D Meshing and Solving What issues might arise with respect to meshing and solving For general guidelines for effective modeling see Overview o
293. uss law The electric potential results from Faraday s law In the magnetostatic case where there are no currents present Maxwell Amp re s law reduces to V x H 0 When this holds it is also possible to define a magnetic scalar potential by the relation Reduced Potential PDE Formulations The reduced potential option introduces the substitution A eg A into Maxwell Amp re s law 7 0 DOMAIN EQUATIONS Time Harmonic For time harmonic quasi static systems solving for an A formulation the reduced potential formulation results in the following PDE 2 oc o Apeg Vx u Ared J red Here it is possible to interpret the term V x Ag as an additional remanent magnetic flux density and the term joo o A cst as an additional external current source Transient Similarly to the time harmonic formulation in the transient formulation the above substitution results in the reduced equation FUNDAMENTALS OF ELECTROMAGNETICS 33 34 1 o Vx u VX Aest i Acca J Static In static formulations the induced current is zero Maxwell Amp re s law reduces to Vx u Area J In this case it is also possible to express the external field through a known external magnetic flux density Bext The domain equation in reduced form then reads 1 Vx u Bext Se Electromagnetic Energy The e
294. y Volume EI Average Resistivity is the lower bound and the Power Law average is Note somewhere in between these two Effective Relative Permeability in Porous Media and Mixtures When handling electric currents in porous media or mixtures of solids with different electric properties you must consider different ways for obtaining the effective relative permeability of the mixture There are several possible approaches to do this starting from the values defined by the user composed by a volume fraction 0 of material 1 and a volume fraction 1 0 of material 2 The effective relative permeability is then given as input for the electric current conservation specified in Equation 4 2 in the same way of modeling an effective single phase material VOLUME AVERAGE PERMEABILITY If the relative permeability of the two materials are not so different from each other the effective relative permeability u is calculated by simple volume average CHAPTER 4 THE ELECTRIC FIELD INTERFACES B 0 04 Bobs here is the relative permeability of the material 1 and is that of material 2 If the permeability is defined by second order tensors such as for anisotropic materials the volume average is applied element by element Note VOLUME AVERAGE RECIPROCAL PERMEABILITY similar expression for the effective permeability can be used which mimics a series connection of resistivi
295. y displayed within curly braces in the model tree Model Couplings in the COMSOL Multiphysics User s Guide See Also External I Terminal The External I Terminal node 45 connects an arbitrary voltage to ground measurement for example a circuit terminal boundary from another physics interface as a voltage to ground assignment to a node in the electrical circuit The resulting THE ELECTRICAL CIRCUIT INTERFACE 267 268 circuit current from the node is typically coupled back as a prescribed current source in the context of the voltage measurement This feature does not apply when coupling to inductive or electromagnetic wave propagation models as then voltage must be defined as a line integral between two points rather than a single point measurement of electric potential For such couplings use the External I vs U feature instead NODE CONNECTIONS Set the Node name for the connecting node for the voltage assignment EXTERNAL TERMINAL Enter the source of the Voltage If circuit or current excited terminals are defined on boundaries in other physics interfaces these display as options in the Voltage list Also select the User defined option and enter a voltage variable for example using a suitable coupling operator Except for when coupling to a circuit terminal the current flow variable must be manually coupled back in the electrical circuit to the context of the voltage measurement This ap
296. y from individual parts for the rotor and stator MAGNETIC AND ELECTRIC FIELDS The Magnetic and Electric Fields Interface chapter describes the interface which handles problems for magnetic and electric fields It is based on the magnetic vector potential and the electric scalar potential The stationary and frequency domain study types are available The underlying theory for the interface is included at the end of the chapter ELECTRICAL CIRCUIT The Electrical Circuit Interface chapter describes the interface which has the equations for modeling electrical circuits with or without connections to a distributed fields model solving for the voltages currents and charges associated with the circuit elements The underlying theory for the interface is included at the end of the chapter INTRODUCTION HEAT TRANSFER The Heat Transfer Branch chapter describes the interface which combines all features from the Magnetic Fields interface in the time harmonic formulation with the Heat Transfer interface for modeling of induction and eddy current heating Heat transfer through conduction and convection in solids and free media fluids is supported by physics interfaces shipped with the basic COMSOL Multiphysics license The Heat Transfer Interface The Joule Heating Interface and Theory for the Heat Transfer Interfaces in the COMSOL Multiphysics User s See Also Guide MATERIALS The Materials chapter has details about the el
297. y in the tangential electric field Mathematically it is described by a relation between the electric field discontinuity and the induced surface current density _ ZgE ZrE45 sl 2 2 25 2 dion ZgE ZrE 4 827 2 2 25 2 z 1 8 tan kd z 2 Jon 1 T k sin kd k o4 amp o U0 u Where indices 1 and 2 refer to the different sides of the layer MAGNETIC FIELDS INTERFACE ADVANCED FEATURES 217 218 5 BOUNDARY SELECTION From the Selection list choose the boundaries to specify the transition boundary condition MATERIAL TYPE Select a Material type Solid Non solid or From material TRANSITION BOUNDARY CONDITION The Transition Boundary Condition section has the following material properties for the thin layer which this boundary condition approximates The defaults use the values From material Or select User defined to enter different values or expressions e Relative permittivity unitless e Relative permeability unitless e Electrical conductivity c SI unit S m Surface thickness d Si unit m Thin Low Permeability Gap Use the Thin Low Permeability Gap boundary condition n x H H Vx VQx A r to model gaps filled with a material with zero conductivity such as air This boundary condition is only applicable on interior boundaries and pair boundaries BOUNDARY SELECTION From the Selection list choose the boundar

The AC/DC Module User's Guide - Numerical Modelling Laboratory

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