Version 4.3b

Introduction toAC/DC Module

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Part No. CM020104

I n t r o d u c t i o n t o t h e A C / D C M o d u l e 19982013 COMSOL

Protected by U.S. Patents 7,519,518; 7,596,474; and 7,623,991. Patents pending.

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Version: May 2013 COMSOL 4.3b

Contents

Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .i

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

The Use of the AC/DC Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

The AC/DC Module User Interfaces . . . . . . . . . . . . . . . . . . . . . . 6

The P

The Mo

Tutoria | i

hysics List by Space Dimension and Study Type . . . . . . . . . 11

del Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

l Example: Modeling a 3D Inductor. . . . . . . . . . . . . . . . . 14

ii |

Introduction

The AC/DC Module is used by engineers and scientists to understand, predict, and design electric and magnetic fields in static, low-frequency and transient applications. Simulations of this kind result in more powerful and efficient products and engineering methods. It allows its users to quickly and accurately predict electromagnetic field distributions, electromagnetic forces, and power dissipation in a proposed design. Compared to traditional prototyping, COMSOL helps to lowermeasurable in that would deThe AC/DC Min two-dimenscircuit-based mare based on Mwith material lare accessed viainterfaces, whiAC/DC user iand transient celectromagnetUnder the hooform of Maxwequations are selement discrepreconditioninare presented magnetic fieldthat you can decapacitance, insimulation.The work flowsteps: define thinterface, definselect a solver,COMSOL Deusing the defainterface.The AC/DC Mand benchmarIntroduction | 1

costs and can evaluate and predict entities that are not directly experiments. It also allows the exploration of operating conditions stroy a real prototype or be hazardous.

odule includes stationary and dynamic electric and magnetic fields ional and three-dimensional spaces along with traditional odeling of passive and active devices. All modeling formulations axwells equations or subsets and special cases of these together

aws like Ohms law for charge transport. The modeling capabilities a number of predefined user interfaces, referred to as AC/DC user ch allow you to set up and solve electromagnetic models. The nterfaces cover electrostatics, DC current flow, magnetostatics, AC urrent flow, AC and transient magnetodynamics, and AC ic (full Maxwell) formulations.d, the AC/DC user interfaces formulate and solve the differential

ells equations together with initial and boundary conditions. The olved using the finite element method with numerically stable edge tization in combination with state-of-the-art algorithms for g and solution of the resulting sparse equation systems. The results

in the graphics window through predefined plots of electric and s, currents and voltages or as expressions of the physical quantities fine freely, and derived tabulated quantities (for example resistance, ductance, electromagnetic force, and torque) obtained from a

in the module is straightforward and is described by the following e geometry, select materials, select a suitable AC/DC user e boundary and initial conditions, define the finite element mesh, and visualize the results. All these steps are accessed from the sktop. The solver selection step is usually carried out automatically ult settings, which are already tuned for each specific AC/DC user

odule Model Library describes the available features using tutorial k examples for the different formulations. The library contains

2 | Introduction

models for industrial equipment and devices, tutorial models, and benchmark models for verification and validation of the AC/DC user interfaces. See The Model Library on page 13 to start exploring now.This guide will give you a jump start to your modeling work. It has examples of the typical use of the module, a list of all the AC/DC user interfaces including a short description for each, and a tutorial example that introduces the modeling workflow.

The Use of tThe AC/DC Mstatics and lowmodeling of dThus, it can bedevices operatAC/DC simuthe next page micro-scale sqmicroelectromelectrically conthat in turn geThe distributiocurrent and vovalues for an eboth qualitativof a simplifiedAnother commmotors and ache AC/DC Moduleodule can model electric, magnetic, and electromagnetic fields in

-frequency applications. The latter means that it covers the evices that are up to about 0.1 electromagnetic wavelengths in size. used to model nanodevices up to optical frequencies or human size ed at frequencies up to 10 MHz.lations are frequently used to extract circuit parameters. Figure 1 on shows the electric potential and the magnetic flux lines for a uare inductor, used for LC bandpass filters in echanical systems (MEMS). A DC voltage is applied across the ducting square shaped spiral, resulting in an electric current flow nerates a magnetic field through and around the device. n and strength of electric and magnetic fields arising from applied ltage can be translated into resistance, capacitance, and inductance quivalent circuit model that is easy to understand and analyze from e and quantitative perspectives. This kind of understanding in terms model is usually the first step when creating or improving a design.on use of this module is to predict forces and motion in electric

tuators of a wide range of scales.

Figure 1: Electric p

In Figure 2, FThe brake conmagnet generaconductor mofrom the curreThe braking todistributions. Ispinning disc tIntroduction | 3

otential distribution and magnetic flux lines for a MEMS inductor.

igure 3, and Figure 4, the dynamics of a magnetic brake is shown. sists of a disc of conductive material and a permanent magnet. The tes a constant magnetic field, in which the disc is rotating. When a ves in a magnetic field it induces currents, and the Lorentz forces nts counteracts the spinning of the disc.rque is computed from the magnetic flux and eddy current t is then fed into a rigid body model for the dynamics of the hat is solved simultaneously with the electromagnetic model.

4 | Introduction

Figure 2: The eddy

Figure 3: The time current magnitude and direction in the spinning disc of a magnetic brake.

evolution of the braking torque.

Figure 4: The time

The AC/DC Mexample, the eresistance, cap(S-parameters)format.The combinatsimplified circuoptimization. modeling whilallowing for dIntroduction | 5

evolution of the angular velocity.

odule includes a range of tools to evaluate and export results, for valuation of force, torque, and lumped circuit parameters like acitance, inductance, impedance, and scattering matrices . Lumped parameters can also be exported in the Touchstone file

ion of fully distributed electromagnetic field modeling and it based modeling is an ideal basis for design, exploration, and

More complex system models can be exploited using circuit-based e maintaining links to full field models for key devices in the circuit esign innovation and optimization on both levels.

6 | The AC/DC

The AC/DC Module User Interfaces

The AC/DC physics user interfaces are based upon Maxwells equations or subsets and special cases of these together with material laws. Different subsets of Maxwells equations in combination with special material laws result in different electric, magnetic, or electromagnetic formulations. In the module, these laws of physics are translated by the AC/DC user interfaces to sets of partial differential equations with corresponding initial and boundary conditions.An AC/DC uterm or condidefined in a ge3D models), oFigure 5 on thDC Module Mwindow for thConservation equations for Furthermore, obtain physicadielectric. Thefunctions of thModule User Interfaces

ser interface defines a number of features. Each feature represents a tion in the underlying Maxwell-based formulation and may be ometric entity of the model, such as a domain, boundary, edge (for r point.e next page uses the Capacitor Tunable model (found in the AC/odel Library) to show the Model Builder window and the settings

e selected Charge Conservation 1 feature node. The Charge 1 node adds the terms representing Electrostatics to the model a selected geometrical domain in the model. the Charge Conservation 1 node may link to the Materials node to l properties, in this case the relative permittivity of a user-defined properties, defined by the Dielectric material node, may be e modeled physical quantities, such as temperature. The Zero

Charge 1 boundary condition feature adds the natural boundary conditions that limit the Electrostatics domain.

Figure 5: The Modselected feature nequations and theterms are underlinrepresented by theThe AC/DC Module User Interfaces | 7

el Builder window (to the left), and the Charge Conservation 1 settings window for the ode (to the right). The Equation section in the settings window shows the model terms added to the model equations by the Charge Conservation 1 node. The added ed with a dotted line. The text also explains the link between the material properties Dielectric node and the values for the Relative permittivity.

8 | The AC/DC

The AC/DC Module has several AC/DC user interfaces ( ) for different types of electric and magnetic modeling. Figure 6 shows the AC/DC user interfaces as well as those under the Heat Transfer branch, which contains the Joule Heating and Induction Heating user interfaces. Also see The Physics List by Space Dimension and Study Type on page 11. A brief overview of the AC/DC user interfaces follows.

Figure 6: The AC/D

ELECTRIC CUThe Electric Celectric currena current consare designing

ELECTRIC CUThe Electric Caxisymmetric, electric currencurrent-condua boundary cuground returnof simulationsModule User Interfaces

C Module physics as displayed in the Model Wizard.

RRENTS

urrents user interface ( ) is used to model DC, AC, and transient t flow in conductive and capacitive media. This user interface solves ervation equation for the electric potential. Some examples of its use busbars for DC current distribution and designing AC capacitors.

RRENTS, SHELLurrents, Shell user interface ( ) is available in 2D, 2D and 3D geometries. It is used to model DC, AC, and transient t flow confined to conductive and capacitive thin cting shells of fixed or varying thickness. This user interface solves rrent conservation equation for the electric potential. Modeling current flow in the hull of a ship or in the body of a car are examples that can be done with this user interface.

ELECTRICAL CIRCUITThe Electrical Circuit user interface ( ) has the equations to model electrical circuits with or without connections to a distributed fields model, solving for the voltages, currents, and charges associated with the circuit elements. Circuit models can contain passive elements like resistors, capacitors, and inductors as well as active elements such as diodes and transistors.

ELECTROSTATICSThe Electrostathe electric poprimarily to muser interface combined withtransport. SucEngineering Mand used especStructural Mecsimulated in thbushings for h

MAGNETIC FIThe Magneticmagnetic H-fiein conductingconductivity e

MAGNETIC FIThe Magneticvector potentimagnetodynaminduction baseapplications fomagnetic satur

MAGNETIC FIThe Magneticmagnetostaticmagnet-basedmagnetic scalamedia with maThe AC/DC Module User Interfaces | 9

tics user interface ( ) solves a charge conservation equation for tential given the spatial distribution of the electric charge. It is used odel charge conservation in dielectrics under static conditions. This applies also under transient conditions but then it is usually a separate transport model for single species or multispecies charge

h transport models can be found in the Chemical Reaction odule and in the Plasma Module. AC simulations are supported ially together with the piezoelectric user interface in the Acoustics, hanics and MEMS Modules. Some typical applications that are e Electrostatics user interface are capacitors, dielectric sensors, and igh voltage DC insulation.

ELD FORMULATION Field Formulation user interface ( ) solves Faradays law for the ld. It is used to model mainly AC, and transient magnetodynamics

domains. It is especially suitable for modeling involving nonlinear ffects, for example in superconductors.

ELDS

Fields user interface ( ) solves Ampres law for the magnetic al. It is used to model magnetostatics, AC, and transient

ics. Magnets, magnetic actuators, electric motors, transformers, d nondestructive testing, and eddy current generation are typical r this user interface. It supports both linear media and media with ation.

ELDS, NO CURRENTS Fields, No Currents user interface ( ) is used to efficiently model s in current free regions, for example, when designing permanent devices. It solves a magnetic flux conservation equation for the r potential. This user interface supports both linear media and gnetic saturation.

10 | The AC/D

MAGNETIC AND ELECTRIC FIELDSThe Magnetic and Electric Fields user interface ( ) is used to model magnetostatics and AC magnetodynamics. It solves Ampres law for the magnetic vector potential together with a current conservation equation for the electric potential. The application areas are mostly the same as for the Magnetic Fields user interface. The addition of the electric potential makes it more flexible as also electric boundary conditions are available.

ROTATING MACHINERY, MAGNETICThe Rotating fields (magnetpotential) formrotation or rotFields user inteassembly from

INDUCTION HThe Inductionfrom the MagnHeat Transferpredefined inta heat source. cycle time is sh

JOULE HEATINThe Joule HeaElectric Curreresistive heatinadds the electrC Module User Interfaces

Machinery, Magnetic user interface ( ) combines the magnetic ic vector potential) and magnetic fields, no currents (scalar magnetic ulations with a selection of predefined frames for prescribed

ation velocityit shares most of its features with the Magnetic rface. This user interface requires that the geometry is created as an individual parts for the rotor and stator.

EATING

Heating multiphysics user interface ( ) combines all features etic Fields user interface in the time-harmonic formulation with the

user interface to model induction and eddy current heating. The eraction adds the electromagnetic losses from the magnetic fields as This user interface is based on the assumption that the magnetic ort compared to the thermal time scale (adiabatic assumption).

G

ting multiphysics user interface ( ) combines all features from the nts user interface with the Heat Transfer user interface to model g and heating due to dielectric losses. The predefined interaction omagnetic losses from the electric currents as a heat source.

The Physics List by Space Dimension and Study TypeThe table list the physics user interfaces available specifically with this module in addition to the COMSOL Multiphysics basic license.

PHYSICS ICON TAG SPACE DIMENSION PRESET STUDY TYPE

AC/DC

Electric Currents* ec all dimensions stationary; frequency domain; time dependent;

Electric Current

Electrical Circuit

Electrostatics*

Magnetic Field F

Magnetic Fields*

Magnetic Fields,

Magnetic and El

Rotating MachinThe AC/DC Module User Interfaces | 11

small signal analysis, frequency domain

s - Shell ecs 3D, 2D, 2D axisymmetric

stationary; frequency domain; time dependent; small signal analysis, frequency domain

cir Not space dependent

stationary; frequency domain; time dependent

es all dimensions stationary; time dependent; frequency domain; small signal analysis, frequency domain

ormulation mf 3D, 2D, 2D axisymmetric

stationary; frequency domain; time dependent; small signal analysis, frequency domain

mf 3D, 2D, 2D axisymmetric

stationary; frequency domain; time dependent; small signal analysis, frequency domain; coil current calculation

No Currents mfnc

3D, 2D, 2D axisymmetric

stationary; time dependent

ectric Fields mef 3D, 2D, 2D axisymmetric

stationary; frequency domain; small signal analysis, frequency domain

ery, Magnetic rmm

3D, 2D stationary; time dependent; coil current calculation

12 | The AC/D

Electromagnetic Heating

Induction Heating ih 3D, 2D, 2D axisymmetric

stationary; frequency domain; time dependent; frequency stationary; frequency transient

Joule Heating* jh all dimensions stationary; frequency domain; time dependent;

* This is an enhhas added funct

PHYSICS ICON TAG SPACE DIMENSION PRESET STUDY TYPEC Module User Interfaces

frequency stationary; frequency transient

anced user interface, which is included with the base COMSOL package but ionality for this module.

The Model Library

To open an AC/DC Module Model Library model, select View > Model Library from the main menu in COMSOL Multiphysics. In the Model Library

window that opens, expand the AC/DC Module folder and browse or search the contents. Click Open Model and PDF to open the model in COMSOL Multiphysics and a PDF to read background theory about the model including the step-by-step instructions to build it. The MPH-files in the COMSOL model libraries can ha Full MPH-

these modea tip with ththe cursor a

Compact Mand solutiosolutions foand to meshversionswModel Libr

icon. If window, a Nfor downloFull Model ite

The next sectioModeling a 3DThe Model Library | 13

ve two formatsFull MPH-files or Compact MPH-files.files, including all meshes and solutions. In the Model Library ls appear with the icon. If the MPH-files size exceeds 25MB, e text Large file and the file size appears when you position t the models node in the Model Library tree.PH-files with all settings for the model but without built meshes

n data to save space on the DVD (a few MPH-files have no r other reasons). You can open these models to study the settings and re-solve the models. It is also possible to download the full ith meshes and solutionsof most of these models through ary Update. These models appear in the Model Library with the you position the cursor at a compact model in the Model Library o solutions stored message appears. If a full MPH-file is available

ad, the corresponding nodes context menu includes a Download m ( ).

n uses a model from the Model Library. Go to Tutorial Example: Inductor to get started.

14 | Tutorial Ex

Tutorial Example: Modeling a 3D Inductor

Inductors are used in many applications for low-pass filtering or for impedance matching of predominantly capacitive loads. They are used in a wide frequency range from near static up to several MHz. An inductor usually has a magnetic core to increase the inductance while keeping its size small. The magnetic core also reduces the electromagnetic interference with other devices as the magnetic flux tends to stay within it. Because there are only crude analytical or empirical formulas availameasurementsmodeling is mprinciples applthe geometry domain analys

Figure 7: The indu

96 mmample: Modeling a 3D Inductor

ble to calculate impedances, computer simulations or are necessary during the design stage. In general, inductor ore complex than modeling resistors and capacitors but similar y. Using an external CAD software to design and draw the model, is imported into the AC/DC Module for static and frequency is. The inductor geometry is shown in Figure 7.

ctor geometry.

Core

Feed gap

Cu winding

First a magnetostatic simulation is performed to get the DC inductance. At low frequencies capacitive effects are negligible. A relevant equivalent circuit model is an ideal inductor in a series with an ideal resistor. The inductance and the resistance are both computed in the magnetostatic simulation. At a high frequency, capacitive effects become significant. The equivalent circuit model involves connecting an ideal capacitor in parallel with the DC circuit. The circuit parameters are obtained by analyzing the frequency dependent impedance obtained from a frequency domain simulation. In this tutorial, the AC analysis is done up to the point when the frequency dependent impedance is computed.These step-by-inductor in 3Dcircuits, whichto perform a D

Model Wi

1 Double-clic2 In the Mod3 In the Add 4 Click Add S5 In the Stud6 Click Finish

Geometry

The main geomCAD geometradditional domfeed gap wherNote: The locainstallation. Fomight be similTutorial Example: Modeling a 3D Inductor | 15

step instructions guide you through the detailed modeling of an . The module also has a physics user interface to model electrical

is detailed in the magnetostatic part of this model. The first step is C simulation.

zard

k the COMSOL Multiphysics icon on the desktop.el Wizard, the space dimension defaults to 3D. Click Next .Physics tree under AC/DC, select Magnetic Fields (mf) .elected then click Next .ies tree, select Preset Studies>Stationary . .

1

etry is imported from a file. Air domains are typically not part of a y, so these are added to the model. For convenience, three ains are defined in the CAD file and then used to define a narrow

e an excitation is applied.tion of the files used in this exercise varies based on the r example, if the installation is on your hard drive, the file path ar to C:\Program Files\COMSOL43a\models\.

16 | Tutorial Ex

Import 11 Under Model 1, right-click Geometry 1

and select Import .2 In the settings window under Import,

click Browse. Then navigate to your COMSOL Multiphysics installation folder, locate the subfolder ACDC_Module\Inductive_Devices_and_Coils, select the file inductor_

3 Click Impor

Sphere 1 1 In the Mod

Geometry 12 Go to the Sp

Size and Sh0.2.

3 Click to expassociated ta0.05.

4 Click the Bu

Form Union1 In the Mod

click Form U2 In the Final

Build All ample: Modeling a 3D Inductor

3d.mphbin and click Open. t.

el Builder, right-click and choose Sphere .here settings window. Under

ape in the Radius field, enter

and the Layers section. In the ble, under Thickness enter

ild All button.

el Builder under Geometry 1, nion .

ize settings window, click .

3 On the Graphics window toolbar, click the Zoom Extents button and then the Wireframe Rendering button.The geometry should match this figure.

Definit ion

Use the Selectof materials anwinding and coto set up the E1 In the Mod

Selections>ETutorial Example: Modeling a 3D Inductor | 17

s - Selections

ion feature available under the Definitions node to make the set up d physics easier. Start by defining the domain group for the inductor ntinue by adding other useful selections. These steps illustrate how xplicit nodes and rename the geometric selections accordingly.

el Builder under Model 1, right-click Definitions and choose xplicit .

18 | Tutorial Ex

2 Repeat Step 1 and add a total of six (6) Explicit nodes . Or right-click the first Explicit node and select Duplicate .

The followin3 In the Mod4 In the settin

entity level ldomains as

There are mto add, suchenter the innode, enterabout selectMultiphysic

DEFAULT NODE N

Explicit 1

Explicit 2

Explicit 3

Explicit 4

Explicit 5

Explicit 6ample: Modeling a 3D Inductor

g steps are done one at a time for each node using the table below. el Builder click an Explicit node to open its settings window. gs window under Input Entities, select Domain from the Geometric ist. Use the table as a guide, and in the Graphics window, select the indicated. Then press F2 and rename the node.

any ways to select geometric entities. When you know the domain as in this exercise, you can click the Paste Selection button and formation in the Selection field. In this example for the Explicit 1 7,8,14 in the Paste Selection window. For more information ing geometric entities in the Graphics window, see the COMSOL s Reference Manual.

AME SELECT THESE DOMAINS NEW NAME FOR THE NODE

7, 8, and 14 Winding

9 Gap

6 Core

14 and 1013 Infinite Elements

16 and 913 Non-conducting

5,6, and 9 Non-conducting without IE

5 After renaming all the nodes under Definitions, the sequence of nodes should match this figure.

Definit ion

Use the Infinitan infinite opescaling is recoginterfaces are a1 In the Mod

Infinite Elem2 Go to the In

Infinite Elem3 Under GeomTutorial Example: Modeling a 3D Inductor | 19

s - Inf inite Elements

e Element feature available under the Definitions node to emulate n space surrounding the inductor. The infinite element coordinate nized by any physics user interface supporting it - other physics user utomatically disabled in the infinite element domains.el Builder under Model 1, right-click Definitions and choose

ent Domain . finite Elements settings window. Under Domain Selection select ents from the Selection list.etry from the Type list, select Spherical.

20 | Tutorial Ex

Materials

Now define the material settings for the different parts of the inductor. Use the Selections defined in the previous section.

Copper1 From the main menu, select

View>Material Browser .2 Go to the M

Materials trCopper andModel from

3 In the Mod4 Go to the M

Under GeomWinding fro

Air1 Go to the M

Materials trAir and chofrom the me

2 In the Mod3 Go to the M

Under GeomNon-conduample: Modeling a 3D Inductor

aterial Browser. In the ee under AC/DC, right-click choose Add Material to the menu.

el Builder, click Copper.aterial settings window. etric Entity Selection select

m the Selection list.

aterial Browser. In the ee under Built-In right-click ose Add Material to Model nu.

el Builder, click Air.aterial settings window. etric Entity Selection select

cting from the Selection list.

User-Defined Material 3

The core material is not included in the material library so it is entered as a user-defined material.1 In the Model Builder, right-click Materials

and choose Material . 2 Go to the Material settings window. Under

Geometric Entity Selection select Core from the Se

3 Under Mate- 0 for the - 1 for the - 1e3 for th

4 Right-click box and ent

5 Click OK. Tmatch the fi

To view differmat3) next to Tutorial Example: Modeling a 3D Inductor | 21

lection list.

rial Contents in the table, enter these settings in the Value column:Electrical conductivityRelative permittivitye Relative permeability

Material 3 and choose Rename . In the Rename Material dialog er Core in the New name field.he node sequence under Materials should gure to the right.

ent labels such as the Identifier (mat1, mat2, the material node name, select View>Model

22 | Tutorial Ex

Builder Node Label and select one of the options. This changes what combinations of labels are displayed in the Model Builder next to each node.ample: Modeling a 3D Inductor

Magnetic Fields (mf)

The model is solved everywhere except in the feed gap region. By keeping this void, its default boundary conditions support surface currents closing the current loop. In inductor modeling it is crucial to respect current conservation as this is a law of nature (Ampres law).1 In the Model Builder under Model 1, click Magnetic

Fields .2 In the Magn

domains 1Or first clickthe Paste Sethe Selectio

Single-Turn CA dedicated fefeature makes 1 Right-click

Coil .2 In the Singl

Winding fro3 Right-click S

.4 In the Boun

list, click the5 Click the Pa

Click OK.

Ground 11 In the Mode

condition G2 In the Grou

the Clear Se3 Click the Pa

Click OK.Tutorial Example: Modeling a 3D Inductor | 23

etic Fields settings window, select 8 and 1014 only (all domains except 9). the Clear Selection button , then click

lection button and enter 18, 1014 in n field.

oil 1 and Boundary Feed 1ature is added for the solid copper winding of the inductor. This it easier to excite the model in various ways.Magnetic Fields and choose the domain setting Single-Turn

e-Turn Coil settings window, under Domain Selection, choose m the Selection list.ingle-Turn Coil 1 and at the boundary level choose Boundary Feed

dary Feed settings window, to the right of the Boundary Selection Clear Selection button . ste Selection button and enter 58 in the Selection field.

l Builder, right-click Single-Turn Coil 1 and choose the boundary round .nd settings window, to the right of the Boundary Selection list, click lection button . ste Selection button and enter 79 in the Selection field.

24 | Tutorial Ex

The node sequence under Magnetic Fields should at this point match the figure to the right.

Mesh 1

The steep radial scaling of the infinite elements region requires a swept mesh to maintain a rea

Free Triangul1 In the Mod

Operations>2 Select Boun

button a

3 In the Modunder Elem

4 Click to expsize field, en

5 In the ModBuild Selectample: Modeling a 3D Inductor

sonably effective element quality.

ar 1 and Sizeel Builder under Model 1, right-click Mesh 1 and choose More Free Triangular .daries 912, 68, 69, 73, and 76 only. Or click the Paste Selection nd enter 912, 68, 69, 73, 76 in the Paste Selection field.

el Builder under Mesh 1, click Size . In the Size settings window ent Size, click the Predefined button. From the list select Coarser.and the Element Size Parameters section. In the Minimum element ter 0.005.

el Builder, right-click Free Triangular 1 and select ed .

Swept 1 and Distribution 11 Right-click Mesh 1 and choose Swept .2 Go to the Swept settings window. Under Domain Selection:

- From the Geometric entity level list, select Domain.- From the Selection list, select Infinite Elements.

3 Right-click Swept 1 and choose Distribution .

4 Go to the DUnder Distrelements fie

5 Click Build

Free Tetrahed1 Right-click

Tetrahedral2 In the Mod

Tetrahedral Selected .

The final node

Study 1

The magnetos1 In the ModTutorial Example: Modeling a 3D Inductor | 25

istribution settings window. ibution in the Number of ld, enter 4.Selected .

ral 1Mesh 1 and choose Free .el Builder, right-click Free 1 and choose Build

sequence under Mesh should match the figure.

tatic model is now ready to solve.el Builder, right-click Study 1 and choose Compute .

26 | Tutorial Ex

Results

Magnetic Flux Density The default plot group shows the magnetic flux density norm. At this point it is important to consider whether the results make sense and to try and detect any modeling errors.ample: Modeling a 3D Inductor

Data Sets and Selections

By adding Selections and adjusting the Data Sets under the Results node you can create more interesting plots.1 In the Model Builder, expand the Results>Data Sets node. Right-click Solution

1 and choose Duplicate . 2 Right-click Solution 2 and choose Add

Selection . 3 Go to the S

Under Geom- From the

select Do- From the

4 Right-click Duplicate

5 Right-click added to th

6 Go to the S- From the- From theTutorial Example: Modeling a 3D Inductor | 27

election settings window. etric entity selection:

Geometric entity level list, main. Selection list, select Winding.

Solution 1 and choose .

Solution 3 and choose Add Selection . A Selection node is e Model Builder.

election settings window. Under Geometric Entity Selection: Geometric entity level list, select Domain. Selection list, select Core.

28 | Tutorial Ex

3D Plot Group 21 In the Model Builder, right-click Results and choose 3D Plot Group .2 Right-click 3D Plot Group 2 and choose Volume .3 Go to the Volume settings window. Under Data from the Data set list, select

Solution 2.4 Click Replace Expression in the upper-right corner of the Expression

section. From the menu, choose Magnetic Fields>Coil parameters>Coil potential (mf.VCoil).

5 Under Colotable list, se

6 In the ModGroup 2 Volume 2 nBuilder.

7 Go to the VUnder DataSolution 3.ample: Modeling a 3D Inductor

ring and Style from the Color lect Thermal.

el Builder, right-click 3D Plot and choose Volume . A ode is added to the Model

olume settings window. from the Data set list, select

8 Click the Plot button.

On the Graphics window toolbar, click the Zoom In button twice.

Derived V

The coil inducdisplayed as fo1 In the Mod

Global EvalTutorial Example: Modeling a 3D Inductor | 29

alues

tance and resistance are available as predefined variables, which are llows.el Builder under Results, right-click Derived Values and choose uation .

30 | Tutorial Ex

2 In the Global Evaluation settings window, locate the Expression section.3 In the Expression edit field, enter mf.VCoil_1/mf.ICoil_1.4 Click the Evaluate button. The results are available in the Table window

located in the lower-right side of the COMSOL Desktop. Or select View>Table from the main menu to open the Table window.

5 In the Model Builder, right-click Derived Values and choose Global Evaluation .

6 In the Global Evaluation settings window, in 2*mf.intW

7 Click the Evcompare thewindow.

You can alsowindow to vrespectively.ample: Modeling a 3D Inductor

the Expression field, enter m/mf.ICoil_1^2.aluate button and results in the Table

click the down arrow next to the Evaluate button on the settings iew each table. You should get about 0.29 m and 0.11 mH, Below, both evaluations were made to the same table.

Magnetic Fields (mf)

As can be seen in the Magnetic Flux Density plot, this is effectively contained within the core. Thus, there should be little need to use infinite elements in this model. Solve the model without the infinite elements to test this hypothesis.1 In the Model Builder under Model 1,

click Magnetic Fields .2 In the Magnetic Fields settings

window, selonly.

Study 1

1 In the Mod

Derived V

1 In the ModGlobal Eval

2 In the GlobInductance

3 In the Mod4 In the Glob

Resistance vTutorial Example: Modeling a 3D Inductor | 31

ect domains 58 and 14

el Builder, right-click Study 1 and choose Compute .

alues

el Builder under Results>Derived Values, click uation 1 .

al Evaluation settings window, click the Evaluate button. The value displays in the Table window. el Builder, click Global Evaluation 2 .al Evaluation settings window, click the Evaluate button. The alue displays in the Table window. The results change very little.

32 | Tutorial Ex

Model Wizard

Next, add a simple circuit to the model.1 In the Model Builder, right-click Model 1 and choose Add Physics .2 In the Add physics tree under AC/DC, double-click Electrical Circuit (cir)

to add it to the Selected physics list. You do not need to add any studies. 3 Click Finish .

Magnetic

Change the fie1 In the Mod

Fields>SingFeed 1. .

2 In the BounSingle-Turnthe Coil exc

Electrical

Add a resistorapplying a volample: Modeling a 3D Inductor

Fields (MF)

ld excitation so that it can connect to the circuit part of the model.el Builder, under Magnetic le-Turn Coil 1 click Boundary

dary Feed settings window under Coil, choose Circuit (current) from itation list.

Circuit (cir)

in series with the inductor and drive. This is done for both by tage source.

Voltage Source 11 In the Model Builder under Model 1,

right-click Electrical Circuit and choose Voltage Source .

The default settings correspond to a DC source of 1 V between nodes 1and 0 in the circuit net. Keep these settings.

Resistor 11 In the Mode

Circuit a2 Go to the R

Under Nodethe Node nathe right.

3 Under Devienter 100[mTutorial Example: Modeling a 3D Inductor | 33

l Builder, right-click Electrical nd choose Resistor .esistor settings window. Connections enter 1 and 2 in mes table as in the figure to

ce Parameters in the R field, ohm].

34 | Tutorial Ex

External I Vs. U 1There is a special feature for connecting the circuit to the finite elements model.1 In the Model Builder, right-click Electrical Circuit and choose

External I Vs. U .2 In the External I Vs. U settings window

under Node Connections, enter Node names as in to the figure to the right.

3 Under External Device, from the Electric potential V (mf/stcd1/The sequenCircuit shou

Study 1

1 In the Modample: Modeling a 3D Inductor

list choose Coil voltage stcdp1).ce of nodes under Electrical ld match this figure.

el Builder, right-click Study 1 and choose Compute .

Results

The current is now limited to approximately 10 A by the external resistor which has a much larger resistance than that of the winding.

Model Wi

Now, set up th1 In the Mode

Add Study Tutorial Example: Modeling a 3D Inductor | 35

zard - Add a Second Study

e model for computing the frequency-dependent impedance.l Builder, right-click the top node Untitled.mph (root) and choose .

36 | Tutorial Ex

2 In the Select Study Type window that opens, under Studies>Preset Studies for Selected Physics click Frequency Domain .

3 Find the Selected physics subsection. 4 In the Selected physics table under Solve for, click to change the check mark

to an and remove the Electrical Circuit (cir) user interface.

5 Click Finish

A Study 2 nModel Buildample: Modeling a 3D Inductor

.

ode with a Frequency Domain study step is added to the er.

Definit ions

At high frequencies, the skin depth of the copper conductor in the winding becomes difficult to resolve. The solution is to exclude the interior of the copper domain from the simulation and instead represent the winding by a boundary condition, which introduces surface losses via an equivalent surface impedance. For this purpose add a boundary selection and an associated surface material.

Conductor Boundaries1 In the Mod

right-click DSelections>E

2 Select Dom3 Go to the E

Output Entlist, select A

4 Press F2.5 In the RenaConductor field. Click OTutorial Example: Modeling a 3D Inductor | 37

el Builder under Model 1, efinitions and choose xplicit .

ains 7, 8, and 14 only.xplicit settings window. Under ities from the Output entities djacent boundaries.

me Explicit window enter Boundaries in the New name K.

38 | Tutorial Ex

Materials

Copper (2)1 From the main menu, select

View>Material Browser . In the Materials tree under AC/DC, right-click Copper and choose Add to Current Geometry.

2 In the Mod

3 Go to the MUnder Geom- From the

select Bou- From the

Conducto

Magnetic

1 In the ModFields .

2 Go to the MDomain SelNon-conduample: Modeling a 3D Inductor

el Builder, click Copper (2).

aterial settings window. etric Entity Selection:

Geometric entity level list, ndary.

Selection list, select r Boundaries.

Fields (mf)

el Builder under Model 1, click Magnetic

agnetic Fields settings window. Under ection from the Selection list, select cting without IE.

Ampre's Law 2Apart from the surface loss in the copper conductor, there are also AC losses in the core. The loss in the core is introduced as an effective loss tangent. For this purpose an extra equation/constitutive relation is required.1 In the Model Builder, right-click Magnetic Fields and choose Ampre's Law

. A second Ampre's Law node is added to the Model Builder.2 Go to the Ampre's Law settings window. Under Domain Selection from the

Selection list, select Core.3 Under Elect

the field.

Impedance Bo1 In the Mode

choose Imp2 Go to the Im

Selection fro

Disable the SThe Single Tube disabled. In the Mod

and chooseTutorial Example: Modeling a 3D Inductor | 39

ric Field from the r list, select User defined and enter 1-5e-4*j in

undary Condition 1l Builder, right-click Magnetic Fields and at the boundary level,

edance Boundary Condition .pedance Boundary Condition settings window. Under Boundary

m the Selection list, select Conductor Boundaries.

ingle-Turn Coil 1rn Coil does not apply to an active domain anymore so it needs to

el Builder, under Magnetic Fields right-click Single-Turn Coil 1 Disable . The node is grayed out.

40 | Tutorial Ex

Lumped Port 1The electric potential is not available in this physics user interface, so to excite the model a different boundary feature, which is more appropriate for high frequency modeling, must be used.1 In the Model Builder, right-click Magnetic Fields and at the boundary level

choose Lumped Port . A Lumped Port node is added to the sequence in the Model Builder.

2 Go to the LSelect bounThe geometboundary se

3 Under Portport list, sel- In the hpo- In the wp

4 Specify the the right.

5 From the Te

The Model Magnetic Fiample: Modeling a 3D Inductor

umped Port settings window. daries 5962 only. rical parameters of the t need to be entered manually. Properties from the Type of ect User defined.

rt field, enter 0.024.

ort field, enter 0.046.ah vector as in the figure to

rminal type list, select Current.

Builder node sequence under elds should match this:

Study 2

Set up a frequency sweep from 1-10 MHz in steps of 1 MHz.1 In the Model Builder, expand the Study 2 node and click Step 1: Frequency

Domain .2 Under Study Settings, click the

Range button .3 In the Range window, enter these

settings:- In the Sta- In the Ste- In the Sto

4 Click Replac

Near the resonno loss, it wouinfinity. Thus fa direct solver a more robust

Solver 21 In the Mod

.2 In the Mod

Study 2 >nodes as in then click th

3 Go to the ItUnder GenePreconditio

4 In the ModStudy 2 aTutorial Example: Modeling a 3D Inductor | 41

rt field, enter 1e6. p field, enter 1e6.p field, enter 1e7.

e.

ance frequency, the problem becomes ill-conditioned. If there were ld even become singular as the field solution then would approach or a high Q factor, the iterative solver may fail to converge and then must be used. Here it is sufficient to tweak the iterative solver to use preconditioner.

el Builder, right-click Study 2 and choose Show Default Solver

el Builder, expand the Solver Configurations

the figure to the right and e Iterative 1 node. erative settings window. ral select Right from the

ning list.el Builder, right-click nd choose Compute .

42 | Tutorial Ex

Results

Magnetic Flux Density Again check the default plot for any modeling errors. Note that the magnetic flux density inside the copper winding is not computed as this domain was excluded.

Plot the surfacfrequency is b

Data Sets 1 In the Mod

right-click S2 Right-click

Add Selectio3 Go to the S

Geometric Elevel list, ch

4 From the SeBoundaries.ample: Modeling a 3D Inductor

e current distribution at the lowest frequency solved for. This elow resonance and the device is still of an inductive nature.

el Builder under Results>Data Sets, olution 4 and choose Duplicate .Solution 5 and choose n .

election settings window. Under ntity Selection from the Geometric entity

oose Boundary.lection list, choose Conductor

3D Plot Group 41 In the Model Builder, right-click Results

and choose 3D Plot Group . A 3D Plot Group 4 node is added to the sequence.

2 Go to the 3D Plot Group settings window. Under Data from the Data set list, choose Solution 5.

3 From the Pachoose 10e5

4 Right-click choose Surf

5 Go to the Supper-right section, clic

6 From the mMagnetic FiSurface curr(when you kthis exercisedirectly in th

7 Click the PlTutorial Example: Modeling a 3D Inductor | 43

rameter value (freq) list, .

3D Plot Group 4 and ace . urface settings window. In the corner of the Expression k Replace Expression . enu, choose elds>Currents and charge>ent density norm (mf.normJs) now the variable name, as in

, you can also enter mf.normJs e Expression field).

ot button.

44 | Tutorial Ex

The plot shows the surface current distribution and should match this figure.

Change to themodeling sess

1D Plot Grou1 In the Mod2 In the 1D P

Data set list3 Under Resu4 Go to the G

column, entport impeda

Note: In geneare available indirectly into thample: Modeling a 3D Inductor

highest frequency solved for and compare the results. Finish the ion by plotting the real and imaginary parts of the coil impedance.

p 5el Builder, right-click Results and choose 1D Plot Group .lot Group settings window under Data, select Solution 4 from the .lts right-click 1D Plot Group 5 and choose Global .lobal settings window. Under y-Axis Data in the Expression er real(mf.Zport_1). In the Description column, enter Lumped nce.

ral, you can click the Replace Expression to see what variables the predefined lists. In this case, you can enter the information e table.

5 Click the Plot button.

The resistive part

1D Plot Grou1 In the Mod2 Go to the 1

select Soluti3 Under Resu4 Go to the G

column, entport impedaTutorial Example: Modeling a 3D Inductor | 45

of the coil impedance peaks at the resonance frequency.

p 6el Builder, right-click Results and choose 1D Plot Group .D Plot Group settings window. Under Data from the Data set list, on 4.lts right-click 1D Plot Group 6 and choose Global .lobal settings window. Under y-Axis Data in the Expression er imag(mf.Zport_1). In the Description column, enter Lumped nce.

46 | Tutorial Ex

5 Click the Plot button.

The reactive part going from inducti

As a final step,1 In the Mod2 From the Fi

To view the thThumbnail secthe toolbar buThis concludeample: Modeling a 3D Inductor

of the coil impedance changes sign when passing through the resonance frequency, ve to capacitive.

pick one of the plots to use as a model thumbnail.el Builder under Results click 3D Plot Group 2 .le menu, choose Save Model Thumbnail.

umbnail image, click the Root node and look under the Model tion. Make adjustments to the image in the Graphics window using ttons until the image is one that is suitable to your purposes.s this introduction.

ContentsIntroductionThe Use of the AC/DC Module

The AC/DC Module User InterfacesThe Physics List by Space Dimension and Study Type

The Model LibraryTutorial Example: Modeling a 3D InductorModel WizardGeometry 1Definitions - SelectionsDefinitions - Infinite ElementsMaterialsUser-Defined Material 3Magnetic Fields (mf)Mesh 1Study 1ResultsData Sets and SelectionsDerived ValuesMagnetic Fields (mf)Study 1Derived ValuesModel WizardMagnetic Fields (MF)Electrical Circuit (cir)Study 1ResultsModel Wizard - Add a Second StudyDefinitionsMaterialsMagnetic Fields (mf)Study 2Results