INTRODUCTION TO

AC/DC Module

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Part number: 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 19982015 COMSOL

Protected by U.S. Patents listed on www.comsol.com/patents, and U.S. Patents 7,519,518; 7,596,474; 7,623,991; 8,457,932; and 8,954,302. Patents pending.

This Documentation and the Programs described herein are furnished under the COMSOL Software License Agreement (www.comsol.com/comsol-license-agreement) and may be used or copied only under the terms of the license agreement.

COMSOL, COMSOL Multiphysics, Capture the Concept, COMSOL Desktop, LiveLink, and COMSOL Server are either registered trademarks or trademarks of COMSOL AB. All other trademarks are the property of their respective owners, and COMSOL AB and its subsidiaries and products are not affiliated with, endorsed by, sponsored by, or supported by those trademark owners. For a list of such trademark owners, see www.comsol.com/trademarks.

Version: COMSOL 5.1

Contents

Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

The Use of the AC/DC Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

The AC/DC Module Physics Interfaces. . . . . . . . . . . . . . . . . . . . 10

Physi

Tutoria | 3

cs Interface Guide by Space Dimension and Study Type . . . 14

l Example: Modeling a 3D Inductor. . . . . . . . . . . . . . . . . 17

4 |

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 viphysics interfaThe AC/DC iand transient celectromagnetUnder the hooof Maxwells eequations are selement discrepreconditioninare presented magnetic fieldthat you can decapacitance, insimulation.The work flowsteps: define thdefine boundasolver, and visDesktop. The default settingThe AC/DC Mtutorial and becontains mode | 5

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 a number of predefined physics interfaces, referred to as AC/DC ces, which allow you to set up and solve electromagnetic models. nterfaces cover electrostatics, DC current flow, magnetostatics, AC urrent flow, AC and transient magnetodynamics, and AC ic (full Maxwell) formulations.d, the AC/DC interfaces formulate and solve the differential form quations 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 interface,

ry and initial conditions, define the finite element mesh, select a ualize the results. All these steps are accessed from the COMSOL solver selection step is usually carried out automatically using the s, which are already tuned for each specific AC/DC interface.

odule application library describes the available features using nchmark examples for the different formulations. The library ls for industrial equipment and devices, tutorial models, and

6 |

benchmark models for verification and validation of the AC/DC interfaces. See Tutorial Example: Modeling a 3D Inductor 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 interfaces including a short description for each, and a tutorial example that introduces the modeling workflow.

The Use of the AC/DC ModuleThe 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 acodule 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 t | 7

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.

8 |

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 d | 9

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.

10 |

The AC/DC Module Physics Interfaces

The AC/DC 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 interfaces to sets of partial differential equations with corresponding initial and boundary conditions.An AC/DC inor condition ina geometric encomponents),Figure 5 on thAC/DC ModSettings windoCharge Consemodel equatioFurthermore, obtain physicadielectric. Thefunctions of thterface defines a number of features. Each feature represents a term the underlying Maxwell-based formulation and may be defined in tity of the model, such as a domain, boundary, edge (for 3D

or point.e next page uses the Capacitor Tunable model (found in the ule application library) to show the Model Builder window and the w for the selected Charge Conservation 1 feature node. The rvation 1 node adds the terms representing Electrostatics to the ns for 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 Modthe selected featuequations and theterms are underlinrepresented by the

The AC/DC Melectric and mthose under th | 11

el Builder window (to the left), and the Settings window for Charge Conservation 1 for re node (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.

odule has several AC/DC interfaces ( ) for different types of agnetic modeling. Figure 6 shows the AC/DC interfaces as well as e Heat Transfer branch, which contains the Joule Heating and

12 |

Induction Heating interfaces. Also see Physics Interface Guide by Space Dimension and Study Type. A brief overview of the AC/DC interfaces follows.

Figure 6: The AC/D

ELECTRIC CUThe Electric Celectric currensolves a currenits use are desicapacitors.

ELECTRIC CUThe Electric Cand 3D geomflow confined or varying thicequation for thull of a ship owith this phys

ELECTRICAL CThe Electricalwith or withoucurrents, and ccontain passivelements suchC Module physics interfaces as displayed in the Model Wizard.

RRENTS

urrents interface ( ) is used to model DC, AC, and transient t flow in conductive and capacitive media. This physics interface t conservation equation for the electric potential. Some examples of gning busbars for DC current distribution and designing AC

RRENTS, SHELLurrents, Shell interface ( ) is available in 2D, 2D axisymmetric,

etries. It is used to model DC, AC, and transient electric current to conductive and capacitive thin current-conducting shells of fixed kness. This physics interface solves a boundary current conservation he electric potential. Modeling ground return current flow in the r in the body of a car are examples of simulations that can be done

ics interface.

IRCUIT

Circuit interface ( ) has the equations to model electrical circuits t connections to a distributed fields model, solving for the voltages, harges associated with the circuit elements. Circuit models can

e elements like resistors, capacitors, and inductors as well as active as diodes and transistors.

ELECTROSTATICSThe Electrostatics interface ( ) solves a charge conservation equation for the electric potential given the spatial distribution of the electric charge. It is used primarily to model charge conservation in dielectrics under static conditions. This physics interface applies also under transient conditions but then it is usually combined with a separate transport model for single species or multispecies charge transport. Such transport models can be found in the Chemical Reaction Engineering Module and in the Plasma Module. AC simulations are supported and used especially together with the Piezoelectric Devices interface in the Acoustics, Struthat are simulaand bushings f

MAGNETIC FIThe Magneticmagnetic H-fiein conductingconductivity e

MAGNETIC FIThe Magneticpotential and, potential. It ismagnetodynaminduction baseapplications fowith magnetic

MAGNETIC FIThe Magneticmagnetostaticmagnet-basedmagnetic scalamedia with ma

MAGNETIC ANThe Magneticand AC magnpotential togeThe applicatio | 13

ctural Mechanics and MEMS Modules. Some typical applications ted in the Electrostatics interface are capacitors, dielectric sensors, or high voltage DC insulation.

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

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

ELDS

Fields interface ( ) solves Ampres law for the magnetic vector for coils, also a current conservation equation for the scalar electric 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 physics interface. It supports both linear media and media saturation.

ELDS, NO CURRENTS Fields, No Currents 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 physics interface supports both linear media and gnetic saturation.

D ELECTRIC FIELDS and Electric Fields interface ( ) is used to model magnetostatics etodynamics. It solves Ampres law for the magnetic vector ther with a current conservation equation for the electric potential. n areas are mostly the same as for the Magnetic Fields interface.

14 |

Note: In most cases, using the Magnetic Fields interface with its dedicated coil modeling features, introducing the electric potential only where it is needed, is the preferred choice over using the Magnetic and Electric Fields interface.

ROTATING MACHINERY, MAGNETICThe Rotating Machinery, Magnetic interface ( ) combines the magnetic fields (magnetic vector potential) and magnetic fields, no currents (scalar magnetic potential) formulations with a selection of predefined frames for prescribed rotation or rotFields interfacassembly from

INDUCTION HThe InductionFields interfaceto model inducouplings addelectromagnetinterface is bascompared to t

JOULE HEATINThe Joule Heainterface with due to dielectrelectromagnetmaterial prope

Physics InterThe table list taddition to thation velocityit shares most of its features with the Magnetic e. This physics interface requires that the geometry is created as an individual parts for the rotor and stator.

EATING

Heating interface ( ) combines all features from the Magnetic in the time-harmonic formulation with the Heat Transfer interface ction and eddy current heating. The predefined multiphysics the electromagnetic power dissipation as a heat source, and the ic material properties can depend on the temperature. This physics ed on the assumption that the magnetic cycle time is short he thermal time scale (adiabatic assumption).

G

ting interface ( ) combines all features from the Electric Currents the Heat Transfer interface to model resistive heating and heating ic losses. The predefined multiphysics couplings add the ic power dissipation as a heat source, and the electromagnetic rties can depend on the temperature.

face Guide by Space Dimension and Study Typehe physics interfaces available specifically with this module in e COMSOL Multiphysics basic license.

PHYSICS INTERFACE ICON TAG SPACE DIMENSION

AVAILABLE PRESET STUDY TYPE

AC/DC

Electric Currents1 ec all dimensions stationary; frequency domain; time dependent; small signal analysis,

Electric Current

Electrical Circui

Electrostatics1

Magnetic Fields1

Magnetic Field Formulation

Magnetic Fields,Currents

Magnetic and EleFields

Rotating MachinMagnetic | 15

frequency domain

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

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

t cir Not space dependent

stationary; frequency domain; time dependent

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

mf 3D, 2D, 2D axisymmetric

stationary; frequency domain; time dependent; small signal analysis, frequency domain; coil current calculation (3D only)

mfh 3D, 2D, 2D axisymmetric

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

No mfnc 3D, 2D, 2D axisymmetric

stationary; time dependent

ctric mef 3D, 2D, 2D axisymmetric

stationary; frequency domain

ery, rmm 3D, 2D stationary; time dependent, coil current calculation (3D only)

16 |

Heat Transfer

Electromagnetic Heating

Induction Heating2 3D, 2D, 2D axisymmetric

stationary; time dependent; frequency-stationary; frequency-transient;

Joule Heatin

1 This physics infunctionality for

2 This physics inphysics interface

PHYSICS INTERFACE ICON TAG SPACE DIMENSION

AVAILABLE PRESET STUDY TYPEsmall-signal analysis, frequency domain

g1,2 all dimensions stationary; time dependent; frequency-transient; small-signal analysis, frequency domain; frequency-stationary

terface is included with the core COMSOL package but has added this module.

terface is a predefined multiphysics coupling that automatically adds all the s and coupling features required.

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

First a magnetfrequencies caan ideal inducresistance are b

96 mm | 17

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.

ostatic simulation is performed to get the DC inductance. At low pacitive effects are negligible. A relevant equivalent circuit model is tor in a series with an ideal resistor. The inductance and the oth computed in the magnetostatic simulation. At a high

Core

Feed gap

Cu winding

18 |

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-step instructions guide you through the detailed modeling of an inductor in 3D. The module also has a physics interface to model electrical circuits, which is detailed in the magnetostatic part of this model. The first step is to perform a DC simulation.

Model Wi

Note: These inminor differen

1 To start thethe softwareCOMSOL mthe Model WIf COMSONew fro

The Model next window

2 In the Space3 In the Selec4 Click Add t5 In the Selec

Studies>Sta6 Click Done

Geometry

The main geoCAD geometradditional domfeed gap wherzard

structions are for the user interface on Windows but apply, with ces, also to Linux and Mac.

software, double-click the COMSOL icon on the desktop. When opens, you can choose to use the Model Wizard to create a new odel or Blank Model to create one manually. For this tutorial, click izard button.

L is already open, you can start the Model Wizard by selecting m the File menu and then click Model Wizard .

Wizard guides you through the first steps of setting up a model. The lets you select the dimension of the modeling space.

Dimension window click 3D .t Physics tree under AC/DC, select Magnetic Fields (mf) .hen click Study .t Study window under Preset Studies, click Preset tionary . .

1

metry 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.

Note: The location of the files used in this exercise varies based on the installation. For example, if the installation is on your hard drive, the file path might be similar to: C:\Program Files\COMSOL\COMSOL51\Multiphysics\applications\.

Import 11 On the Home toolbar, click Import . Note: On Linux and Mac, the Home toolbar refers to the specific set of controls near the top of the Desktop.

2 In the SettinCOMSOL MACDC_Moinductor_3

3 Click Impor | 19

gs window under Import, click Browse. Then navigate to your ultiphysics installation folder, locate the subfolder

dule\Inductive_Devices_and_Coils, select the file d.mphbin and click Open. t.

20 |

Sphere 1 1 On the Geometry toolbar, click Sphere .2 Go to the Settings window for Sphere.

Under Size in the Radius text field, enter 0.2.

3 Click to expassociated ta0.05.

4 Click the Bu

Form Union1 In the Mod

click Form U2 In the Settin

Union/Asseand the Layers section. In the ble, under Thickness enter

ild All Objects button.

el Builder under Geometry 1, nion .

gs window for Form mbly, click Build All .

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 anthe inductor willustrate how accordingly. 1 On the Defi | 21

s - Selections

ion feature available under the Definitions node to make the set up d physics interfaces easier. Start by defining the domain group for inding and continue by adding other useful selections. These steps to set up the Explicit nodes and rename the geometric selections

nitions toolbar, click Explicit .

22 |

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

Geometric eselect the do

There are mto add, suchenter the inf1 node, entabout selectMultiphysic

DEFAULT NODLABEL

Explicit 1

Explicit 2

Explicit 3

Explicit 4

Explicit 5

Explicit 6g steps are done one at a time for each node using the table below. el Builder click an Explicit node to open the Settings window.gs window under Input Entities, select Domain from the ntity level list. Use the table as a guide, and in the Graphics window, mains as indicated. Then press F2 and relabel 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 ormation in the Selection text field. In this example for the Explicit er 7,8,14 in the Paste Selection window. For more information ing geometric entities in the Graphics window, see the COMSOL s Reference Manual.

E SELECT THESE DOMAINS NEW LABEL 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 relabeling all the nodes under Definitions, the sequence of nodes should match this figure.

Definit ion

Use the Infinitan infinite opescaling is recoginterfaces are a1 On the Defi2 Go to the S

select Infini3 Under Geom

Materials

Now define thSelections defi

Copper1 On the Hom | 23

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 interface supporting it - other physics utomatically disabled in the infinite element domains.nitions toolbar click Infinite Element Domain . ettings window for Infinite Elements. Under Domain Selection te Elements from the Selection list.

etry from the Type list, select Spherical.

e material settings for the different parts of the inductor. Use the ned in the previous section.

e toolbar click Add Material .

24 |

2 Go to the Add Material window. In the Materials tree under AC/DC, right-click Copper and choose Add to Component 1 from the menu.

3 In the Mod4 Go to the S

select Wind

Air1 Go to the A

Materials trright-click Ato Compon

2 Close the A3 In the Mod4 Go to the Se

Under Geomselect Non-Selection lis

User-Defi

The core mateuser-defined mel Builder, click Copper .ettings window for Material. Under Geometric Entity Selection ing from the Selection list.

dd Material window. In the ee under Built-In, ir and choose Add

ent 1 from the menu.dd Material window.el Builder click Air .ttings window for Material. etric Entity Selection

conducting from the t.

ned Material 3

rial is not included in the material library so it is entered as a aterial.

1 On the Materials toolbar click Blank Material .2 In the Settings window for Material, in the Label text field, type Core.3 Under Geometric Entity Selection select Core from the Selection list.

4 Under Mate

- 0 for the - 1 for the - 1e3 for th

The node sequ

Magnetic

The model is svoid, its defaulloop. In induclaw of nature ( | 25

rial Contents in the table, enter these settings in the Value column:

Electrical conductivityRelative permittivitye Relative permeability

ence under Materials should match the figure.

Fields (mf)

olved everywhere except in the feed gap region. By keeping this t boundary conditions support surface currents closing the current tor modeling it is crucial to respect current conservation as this is a Ampres law).

26 |

1 In the Model Builder click Magnetic Fields .2 In the Settings window for Magnetic Fields, select

domains 18 and 1014 only (all domains except 9). Or first click the Clear Selection button , then click the Paste Selection button and enter 18, 1014 in the Selection text field.

Single-Turn Coil 1 and Boundary Feed 1A dedicated feature, Single-Turn Coil, is added for the solid copper winding of the inductor. Thisas a total curre1 On the Phy2 In the Settin

Winding fro3 Right-click

Feed .4 In the Settin

and enter 585 Click OK.

The Boundary

Ground 11 Right-click 2 Click the Pa3 Click OK.

The node sequ

Mesh 1

The infinite elelement qualitperform the fo feature makes it easier to excite the model with a lumped load, such nt or voltage.

sics toolbar click Domains and choose Single-Turn Coil .gs window for Single-Turn Coil, under Domain Selection, choose m the Selection list.

Single-Turn Coil 1 and at the boundary level choose Boundary

gs window for Boundary Feed, click the Paste Selection button in the Selection text field.

Feed with default settings will apply a current of 1 A to the coil.

Single-Turn Coil 1 and choose the boundary condition Ground .ste Selection button and enter 79 in the Selection text field.

ence under Magnetic Fields should at this point match this figure.

ements region requires a swept mesh to maintain a good effective y despite the steep radial scaling. To enable this meshing method, llowing steps.

1 In the Model Builder click Magnetic Fields .2 In the Settings window for Magnetic Fields, locate the Physics-Controlled

Mesh section.

3 Select the Enable check box.On the Mesh toolbar click Build Mesh .

Study 1

The magnetos1 On the Stud | 27

tatic model is now ready to solve.y toolbar click Compute .

28 |

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.

Data Sets

By adding Selecreate more in1 In the Mod

Study 1/So2 Right-click and Selections

ctions and adjusting the Data Sets under the Results node you can teresting plots.el Builder, expand the Results>Data Sets node. Right-click lution 1 and choose Duplicate . Study 1/Solution 1 (2) and choose Selection.

3 Go to the Settings window for Selection. Under Geometric entity selection:- From the Geometric entity level list, select Domain. - From the Selection list, select Winding.

4 Right-click 5 Right-click S

is added to

6 Go to the S- From the- From the

3D Plot Grou1 On the Resu

An additionwhen the 3D

2 On the 3D | 29

Study 1/Solution 1 (1) and choose Duplicate .tudy 1/Solution 1 (3) and choose Selection. A Selection node

the Model Builder.

ettings window for Selection. Under Geometric Entity Selection: Geometric entity level list, select Domain. Selection list, select Core.

p 2lts toolbar, click 3D Plot Group .

al toolbar containing Plot Tools for the 3D Plot Group appears Plot Group is selected in the Model Builder.

Plot Group 2 toolbar, click Volume .

30 |

3 Go to the Settings window for Volume. Under Data from the Data set list, select Study 1/Solution 1 (2).

4 Click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Model>Component 1>Magnetic Fields>Coil parameters>mf.VCoil - Coil potential.

5 Under Coloring and Style, from the Color table list, select Thermal.

6 Right-click A Volume 2

7 Go to the SUnder DataStudy 1/So

8 Click the Pl

On the GrapZoom In 3D Plot Group 2 and choose Volume . node is added to the Model Builder.

ettings window for Volume. from the Data set list, select lution 1 (3).ot button.

hics window toolbar, click the button twice.

Derived V

The coil inducdisplayed as fo1 On the Resu2 In the Settin3 In the Expr4 Click the Ev

The results the COMSO

5 On the Resu | 31

alues

tance and resistance are available as predefined variables, which are llows.lts toolbar click Global Evaluation . gs window for Global Evaluation, locate the Expression section.

ession text field, enter mf.VCoil_1/mf.ICoil_1.aluate button.

are available in the Table window located in the lower-right side of L Desktop.lts toolbar, click Global Evaluation .

32 |

6 In the Settings window for Global Evaluation, in the Expression text field, enter 2*mf.intWm/mf.ICoil_1^2.

7 Click the doto control in

Compare th0.12 mH, r

Magnetic

As shown in ththe core. ThusSolve the mod1 In the Modwn arrow next to the Evaluate button on the Settings window what table to evaluate.

e results in the Table window. You should get about 0.29 m and espectively. Below, both evaluations are shown in the same table.

Fields (mf)

e Magnetic Flux Density plot, this is effectively contained within , there should be little need to use infinite elements in this model. el without the infinite elements to test this hypothesis.el Builder click Magnetic Fields .

2 In the Settings window for Magnetic Fields, select domains 58 and 14 only.

Study 1

1 On the Stud

Derived V

1 In the ModEvaluation 1

2 In the SettinThe Inducta

3 In the Mod4 In the Settin

The Resistanlittle. | 33

y toolbar click Compute .

alues

el Builder under Results>Derived Values, click Global .

gs window for Global Evaluation, click the Evaluate button. nce value displays in the Table window.

el Builder, click Global Evaluation 2 .gs window for Global Evaluation, click the Evaluate button. ce value displays in the Table window. The results change very

34 |

Model Wizard

Next, add a simple circuit to the model.1 On the Physics toolbar click Add Physics .2 Go to the Add Physics window. In the tree under AC/DC, click Electrical

Circuit (cir) and click Add to Component.3 Close the Add Physics window.

Magnetic

Change the fie1 In the Mod

Boundary F

2 In the SettinCircuit (cur

Electrical

Add a resistorFields (MF)

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

gs window for Boundary Feed under Single-Turn Coil, choose rent) from the Coil excitation list.

Circuit (cir)

and a voltage source in series with the inductor.

Voltage Source 11 In the Model Builder select the Electrical

Circuit (cir) node.2 On the Electrical Circuit toolbar click

Voltage Source .

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

Resistor 11 On the Elec

Resistor 2 Go to the S

Under Nodethe Node nathe right.

3 Under Devifield, enter 1

External I Vs.There is a spec | 35

trical Circuit toolbar click .ettings window for Resistor. Connections enter 1 and 2 in mes table as in the figure to

ce Parameters in the R text 00[mohm].

U 1ial feature for connecting the circuit to the finite elements model.

36 |

1 On the Electrical Circuit toolbar click External I Vs. U .2 In the Settings window for External I Vs.

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

3 Under External Device, from the Electric potential V list choose Coil voltage (mf/stcd1/stcdp1).

The sequence of nodes under Electrical Circuit should

Study 1

1 On the Stud

Results

The current ishas a much larcurrent of 1A drop over the match this figure.

y toolbar click Compute .

now limited to approximately 10A by the external resistor which ger resistance than that of the winding. In the previous step, a was applied. Thus, both the magnetic flux density and the potential winding are10 times larger in the latest solution.

Model Wi

Now, set up th1 On the Hom

Study .2 In the Add

Frequency D3 In the Physi

under Solvemark , wCircuit (cir)

4 Click Add S5 Close the A | 37

zard - Add a Second Study

e model for computing the frequency-dependent impedance.e toolbar click Add

Study window click omain .

cs interfaces in study table, , click to clear the check hich removes the Electrical interface.tudy.dd Study window.

38 |

A Study 2 node with a Frequency Domain study step is added to the Model Builder.

Definit ion

At high frequebecomes difficdomain from tcondition, whFor this purpo

Conductor Bo1 On the Def2 Select Dom3 Go to the S

Output enti

4 In the Labes

ncies, the skin depth of the copper conductor in the winding ult to resolve. The solution is to exclude the interior of the copper he simulation and instead represent the winding by a boundary ich introduces surface losses via an equivalent surface impedance. se add a boundary selection and an associated surface material.

undariesinitions toolbar click Explicit .ains 7, 8, and 14 only.ettings window for Explicit. Under Output Entities from the ties list, select Adjacent boundaries.

l text field enter Conductor Boundaries.

Materials

Copper 11 On the Home toolbar click Add Material .2 Go to the Add Material window. In the

Materials tree under AC/DC, right-click Copper and choose Add to Component 1 from the menu.

3 Close the A4 In the Mod

5 Go to the S- From the- From the | 39

dd Material window.el Builder, click Copper 1.

ettings window for Material. Under Geometric Entity Selection: Geometric entity level list, select Boundary. Selection list, select Conductor Boundaries.

40 |

Magnetic Fields (mf)

1 In the Model Builder click Magnetic Fields .

2 Go to the Sethe Selectio

Ampre's LawApart from thecore. The losspurpose an ex1 On the Phy

A second Am2 Go to the S

the Selectio3 Under Elect

the text fieldttings window for Magnetic Fields. Under Domain Selection from n list, select Non-conducting without IE.

2 surface loss in the copper conductor, there are also AC losses in the

in the core is introduced as an effective loss tangent. For this tra equation/constitutive relation is required.sics toolbar click Domains and choose Ampre's Law .

pre's Law node is added to the Model Builder.ettings window for Ampre's Law. Under Domain Selection, from n list, select Core.ric Field from the r list, select User defined and enter 1-5e-4*j in .

Impedance Boundary Condition 11 On the Physics toolbar click Boundaries and choose Impedance Boundary

Condition .2 Go to the Settings window for Impedance Boundary Condition. Under

Boundary Selection from the Selection list, select Conductor Boundaries.

Disable the SThe Single Tube disabled. 1 In the Mode

and choose

Lumped Port The electric pomodel a differemodeling, mu1 On the Phy

A Lumped P | 41

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

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

1tential is not available in this physics interface, so to excite the nt boundary feature, which is more appropriate for high frequency

st be used.sics toolbar click Boundaries and choose Lumped Port . ort node is added to the sequence in the Model Builder.

42 |

2 Go to the Settings window for Lumped Port. Select boundaries 5962 only. The geometrical parameters of the boundary set need to be entered manually.

3 Under Port Properties from the Type of port list, select User defined.- In the hport text field, enter 0.024.- In the wp

4 Specify the aright.

5 From the TCurrent.

The Model BuMagnetic Fieldort text field, enter 0.046.

h vector as in the figure to the

erminal type list, select

ilder node sequence under s 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 Start text field, enter 1e6. - In the Ste- In the Sto

4 Click Replac

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

Solver 21 On the Stud2 In the Mod

Study 2>Solas in the figuclick the Ite

3 Go to the SIterative. Unfrom the Pr

4 On the StudCompute | 43

p text field, enter 1e6.p text 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.

y toolbar click Show Default Solver .el Builder expand the ver Configurations nodes re to the right and then

rative 1 node. ettings window for der General select Right

econditioning list.y toolbar click .

44 |

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 Sets1 In the Mod

Study 2/So2 Right-click

3 Go to the Sfrom the Ge

4 From the See current distribution at the lowest frequency solved for. This elow resonance and the device is of an inductive nature.

el Builder under Results>Data Sets, right-click lution 2 and choose Duplicate .Study 2/Solution 2 (5) and choose Selection.

ettings window for Selection. Under Geometric Entity Selection ometric entity level list, choose Boundary.lection list, choose Conductor Boundaries.

3D Plot Group 41 On the Results toolbar click 3D Plot Group .

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

2 Go to the Slist, choose

3 From the Pa4 Right-click 5 Go to the S

Expression s

6 From the mcharge>mf.nname, as in Expression t

7 Click the Pl | 45

ettings window for 3D Plot Group. Under Data from the Data set Study 2/Solution 2 (5).

rameter value (freq) list, choose 1.0000E6.3D Plot Group 4 and choose Surface . ettings window for Surface. In the upper-right corner of the ection, click Replace Expression .

enu, choose Model>Component 1>Magnetic Fields>Currents and ormJs - Surface current density norm (when you know the variable

this exercise, you can also enter mf.normJs directly in the ext field).ot button.

46 |

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

Change to themodeling sess

1D Plot Grou1 On the Resu2 In the Settin

Study 2/So3 On the 1D 4 Go to the S

column, entport impe

Note: In generare available indirectly into th highest frequency solved for and compare the results. Finish the ion by plotting the real and imaginary parts of the coil impedance.

p 5lts toolbar click 1D Plot Group . gs window for 1D Plot Group under Data, select

lution 2 (4) from the Data set list.Plot Group 5 toolbar click Global .ettings window for Global. Under y-Axis Data in the Expression er real(mf.Zport_1). In the Description column, enter Lumped dance.

al, 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 On the Resu2 In the Settin

Study 2/So3 On the 1D 4 Go to the S

column, entport imped | 47

of the coil impedance peaks at the resonance frequency.

p 6lts toolbar click 1D Plot Group . gs window for 1D Plot Group under Data, select

lution 2 (4) from the Data set list.Plot Group 6 toolbar click Global .ettings window for Global. Under y-Axis Data in the Expression er imag(mf.Zport_1). In the Description column, enter Lumped ance.

48 |

5 Click the Plot button.

The reactive part going from inducti

As a final step,1 In the Mod2 Click the Ro

for Root un

Make adjustmuntil the imagThis concludeof 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 .ot node (the first node in the model tree). On the Settings window der Presentation>Thumbnail, click Set from Graphics Window.

ents to the image in the Graphics window using the toolbar buttons e is one that is suitable to your purposes.s this introduction.

ContentsIntroductionThe Use of the AC/DC Module

The AC/DC Module Physics InterfacesPhysics Interface Guide by Space Dimension and Study Type

Tutorial 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