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Introduction toAC/DC Module

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Introduction to the AC/DC Module

1998–2011 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 Soft-ware License Agreement (www.comsol.com/sla) and may be used or copied only under the terms of the license agreement.

COMSOL, COMSOL Desktop, COMSOL Multiphysics, and LiveLink are registered trade-marks or trademarks of COMSOL AB. Other product or brand names are trademarks or regis-tered trademarks of their respective holders.

Version: May 2011 COMSOL 4.2

Part No. CM020104

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acdc_introduction.book Thursday, April 28, 2011 12:33 PM

The AC/DC ModuleThe AC/DC Module enables you to model and simulate electric and magnetic fields in statics and low frequency applications. It also includes electromagnetic formulations with full or partial (quasi-statics) coupling between electric and magnetic fields. Examples of applications you can successfully simulate and design with the AC/DC Module include resistors, capacitors, inductors, electromagnetic sensors and actuators as well as multiphysics applications such as resistive (Joule) heaters or induction heaters. The Module allows you to model electric and magnetic fields in the frequency domain and in the time domain. Electrical circuit modeling is included and circuits can be connected to field models for excitation and impedance matching purposes. The AC/DC Module physics interfaces are fully multiphysics enabled, which means you can couple any simulation in this module to an arbitrary simulation defined in any of the COMSOL Multiphysics interfaces.

The AC/DC Module includes ECAD import via the ODB++(X), GDS-II and NETEX-G file formats. The results and analysis capabilities include visualization of field distributions as well as calculations of lumped parameters, for example, resistance, capacitance, inductance, impedance, and scattering matrices (S-parameters). Lumped parameters can be exported in the Touchstone file format.

This manual guides you through an example that gives you a quick introduction to the Module and some of its tools and features.

The AC/DC Module | 3


Tutorial example: Modeling of a 3D InductorInductors 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 available for calculating impedances, computer simulations or measurements are necessary in the design of inductors. Inductor modeling is in general more complex than the modeling of resistors and capacitors, but similar principles apply. This model uses a design drawn in an external CAD software and is imported for static and frequency domain analysis in the AC/DC Module. The inductor geometry is shown below.

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 series with an ideal resistor. The inductance and the resistance are both computed in the magnetostatic simulation. At high frequency, capacitive effects cannot be ignored. The equivalent circuit model involves connecting an ideal capacitor in parallel with the DC circuit. The circuit parameters can be obtained by analysis of the frequency dependent impedance obtained from a frequency domain simulation. In this tutorial, we perform the AC analysis up to computing the frequency dependent impedance.

4 | Tutorial example: Modeling of a 3D Inductor


The AC/DC Module also provides a physics interface for Electrical Circuits modeling which is briefly demonstrated in the magnetostatic part of this model.

MODEL WIZARD

These step-by-step instructions guide you through the modeling of an inductor in 3D. First a magnetostatic simulation and inductance calculation is performed with and without using infinite elements to truncate the geometry at the open boundaries. The infinite elements are introduced merely as a demonstration. The magnetic flux is effectively confined within the core so there is no need to accurately model the open boundary. After that, a frequency domain simulation is performed in the range 1-10 MHz.

1 Double-click the COMSOL Multiphysics icon on the desktop.

2 In the Model Wizard window, click the 3D button and click Next .

3 In the Add Physics tree, select, select AC/DC>Magnetic and Electric Fields (mef) .

4 Click Add Selected .

5 Click Next .

6 In the Studies tree, select Preset Studies>Stationary .

7 Click Finish .

GEOMETRY 1

The main geometry is imported from a file. Air domains are typically not part of a CAD geometry, so these are added to the model. For convenience three additional domains are defined in the CAD file. These are used to define a narrow feed gap where an excitation is applied.

Import 1 (imp1)1 Under Model 1 (mod1) node, right-click Geometry 1 and select Import .

2 In the Settings window under Import, click Browse. Then navigate to your COMSOL Multiphysics installation folder, localize the subfolder \models\ACDC_Module\Tutorial_Models, select the file inductor_3d.mphbin and click Open.

Tutorial example: Modeling of a 3D Inductor | 5


3 Click Import.

Sphere 1 (sph1)1 In the Model Builder, right-click Geometry 1 and choose Sphere .

2 Go to the Settings window for Sphere.

3 Locate the Size and Shape section. In the Radius edit field, enter 0.2.

4 Click to expand the Layers section.

5 In the associated table, enter the following settings:

6 Click the Build All button.

Form Union (fin)1 In the Model Builder, click Form Union .

2 In the Settings window, click Build All .

3 Click the Zoom Extents button on the Graphics toolbar.

4 Click the Wireframe Rendering button on the Graphics toolbar.

The geometry should now look like in the figure below.

THICKNESS (M)

0.05



DEFINITIONS

Next, define selections to be used when setting up materials and physics. Star t by defining the domain group for the inductor winding and continue by adding other useful selections.

Explicit 11 In the Model Builder, right-click Model 1 (mod1)>Definitions and choose

Selections>Explicit .

2 Select Domains 7, 8, and 14 only.

3 Right-click Explicit 1 and choose Rename .

4 Go to the Rename Explicit dialog box and enter winding in the New name edit field.

5 Click OK.

Explicit 21 Right-click Definitions and choose Explicit .

2 Select Domain 9 only.


4 Go to the Rename Explicit dialog box and enter gap in the New name edit field.

5 Click OK.


2 Select Domain 6 only.


4 Go to the Rename Explicit dialog box and enter core in the New name edit field.

5 Click OK.


2 Select Domains 1–4 and 10–13 only.


4 Go to the Rename Explicit dialog box and enter infinite_elements in the New name edit field.

5 Click OK.




2 Select Domains 1–6 and 9–13 only.


4 Go to the Rename Explicit dialog box and enter non_conducting in the New name edit field.

5 Click OK.


2 Select Domains 5,6, and 9 only.


4 Go to the Rename Explicit dialog box and enter non_cond_wo_IE in the New name edit field.

5 Click OK.

MATERIALS

Now define the material settings.

Copper1 In the Model Builder, right-click Model 1 (mod1) >Materials and choose Open

Material Browser .

2 Go to the Material Browser window.

3 Locate the Materials section. In the Materials tree, select AC/DC>Copper.

4 Right-click and choose Add Material to Model from the menu.

5 In the Model Builder, click Copper.

6 Go to the Settings window for Material.

7 Locate the Geometric Entity Selection section. From the Selection list, select winding.

Air1 Go to the Material Browser window.

2 Locate the Materials section. In the Materials tree, select Built-In>Air.


4 In the Model Builder, click Air.


6 Locate the Geometric Entity Selection section. From the Selection list, select non_conducting.



Material 3The core material is not part of the material library so it is entered as a user-defined material.

1 In the Model Builder, right-click Materials and choose Material .


3 Locate the Geometric Entity Selection section. From the Selection list, select core.

4 Locate the Material Contents section. In the Material contents table, enter the following settings:

5 Right-click Material 3 and choose Rename .

6 Go to the Rename Material dialog box and enter Core in the New name edit field.

7 Click OK.

MAGNETIC AND ELECTRIC FIELDS (MEF)

The model is solved everywhere, except in the feed gap region. Keeping this void is necessary as its boundaries then will support surface currents closing the current loop.

1 In the Model Builder, click Model 1 (mod1) >Magnetic and Electric Fields (mef) .

2 Select Domains 1–8 and 10–14 only (all domains except 9).

Ampère's Law 1The current conservation equation for the electric potential only applies to the conducting parts of the geometry. In the air domain it suffices to solve Ampère’s Law.

1 In the Model Builder, expand the Magnetic and Electric Fields (mef) node.

2 Right-click Model 1 (mod1) >Magnetic and Electric Fields (mef) and choose Ampère's Law .

3 Go to the Settings window for Ampère's Law.

4 Locate the Domain Selection section. From the Selection list, select non_conducting.

PROPERTY NAME VALUE

Electrical conductivity sigma 0

Relative permittivity epsilonr 1

Relative permeability mur 1e3



Infinite Elements 1To emulate an infinite open space surrounding the inductor, infinite elements are employed.

1 In the Model Builder, right-click Magnetic and Electric Fields (mef) and choose Infinite Elements .

2 Go to the Settings window for Infinite Elements.

3 Locate the Domain Selection section. From the Selection list, select infinite_elements.

4 Locate the Geometric Settings section. From the Type list, select Spherical.

Ampère's Law 11 Right-click Infinite Elements 1 and choose Ampère's Law .


3 Locate the Domain Selection section. From the Selection list, select infinite_elements.

Next, add features for excitation and ground.

Terminal 11 In the Model Builder, right-click Magnetic Insulation 1 and choose Terminal .

2 Select Boundary 58 only.

3 Go to the Settings window for Terminal.

4 Locate the Terminal section. In the I0 edit field, enter 1.

Ground 11 In the Model Builder, right-click Magnetic Insulation 1 and choose Ground .

2 Select Boundary 79 only.

MESH 1

The steep radial scaling of the infinite elements region requires a swept mesh to maintain a reasonably good effective element quality.

Free Triangular 11 In the Model Builder, right-click Model 1 (mod1) >Mesh 1 and choose More

Operations>Free Triangular .

2 Select Boundaries 9–12, 68, 69, 73, and 76 only.



Size1 In the Model Builder, click Size .

2 Go to the Settings window for Size.

3 Locate the Element Size section. From the Predefined list, select Coarser.

Free Triangular 1In the Model Builder, right-click Free Triangular 1 and choose Build Selected .

Swept 11 Right-click Mesh 1 and choose Swept .

2 Go to the Settings window for Swept.

3 Locate the Domain Selection section. From the Geometric entity level list, select Domain.

4 From the Selection list, select infinite_elements.

Distribution 11 Right-click Swept 1 and choose Distribution .

2 Go to the Settings window for Distribution.

3 Locate the Distribution section. In the Number of elements edit field, enter 4.

Swept 1In the Model Builder, right-click Swept 1 and choose Build Selected .

Free Tetrahedral 11 Right-click Mesh 1 and choose Free Tetrahedral .

2 In the Model Builder, right-click Free Tetrahedral 1 and choose Build Selected .

STUDY 1

The magnetostatic model is now ready to solve.

1 In the Model Builder, right-click Study 1 and choose Compute .



RESULTS

Data SetsThe default plot group shows the magnetic flux density norm and helps in detecting possible modeling errors.

Better looking plots can be obtained by manipulating the data sets.

1 In the Model Builder, expand the Results >Data Sets node.

2 Right-click Solution 1 and choose Duplicate .

3 Right-click Solution 2 and choose Add Selection .

4 Go to the Settings window for Selection.

5 Locate the Geometric Entity Selection section. From the Geometric entity level list, select Domain.

6 From the Selection list, select winding.

7 In the Model Builder, right-click Solution 1 and choose Duplicate .

8 Right-click Solution 3 and choose Add Selection .

9 Go to the Settings window for Selection.

10Locate the Geometric Entity Selection section. From the Geometric entity level list, select Domain.



11From the Selection list, select core.

3D Plot Group 21 In the Model Builder, right-click Results and choose 3D Plot Group .

2 Right-click Results >3D Plot Group 2 and choose Volume .

3 Go to the Settings window for Volume.

4 Locate the Data section. From the Data set list, select Solution 2.

5 Locate the Coloring and Style section. From the Color table list, select Thermal.

6 In the Model Builder, right-click 3D Plot Group 2 and choose Volume .

7 Go to the Settings window for Volume.


9 In the upper-right corner of the Expression section, click Replace Expression .

10From the menu, choose Magnetic and Electric Fields (Magnetic Fields)>Magnetic flux density norm (mef.normB).

11Click the Plot button.

12Click the Zoom In button twice on the Graphics toolbar.

Derived ValuesNext, evaluate the coil inductance and resistance.



1 In the Model Builder, right-click Results >Derived Values and choose Global Evaluation .

2 Go to the Settings window for Global Evaluation.


4 From the menu, choose Magnetic and Electric Fields (Electric Currents)>Inductance (mef.L11).

5 Click the Evaluate button.

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

7 Go to the Settings window for Global Evaluation.


9 From the menu, choose Magnetic and Electric Fields (Electric Currents)>Resistance (mef.R11).

10Click the Evaluate button.

You should get about 0.11mH and 0.29m respectively.


Now, solve the model without the infinite elements. This should make no difference as almost all of the magnetic flux resides inside the core region.

1 In the Model Builder, click Model 1 (mod1) >Magnetic and Electric Fields (mef) .

2 Select Domains 5–8 and 14 only.

STUDY 1

In the Model Builder, right-click Study 1 and choose Compute .



RESULTS

Derived Values1 In the Model Builder, click Results > Derived Values > Global Evaluation 1 .


3 In the Model Builder, click Global Evaluation 2 .


Next, connect a simple circuit to the model.

MODEL WIZARD

1 In the Model Builder, right-click Model 1 (mod1) and choose Add Physics .

2 Go to the Model Wizard window.

3 In the Add physics tree, select AC/DC>Electrical Circuit (cir) .

4 Click Add Selected .

5 Click Finish .


Change the field excitation so that it can connect to the circuit part of the model.

Terminal 11 In the Model Builder, click Model 1 (mod1) >Magnetic and Electric Fields (mef)

>Magnetic Insulation 1 >Terminal 1 .

2 Go to the Settings window for Terminal.

3 Locate the Terminal section. From the Terminal type list, select Circuit.



ELECTRICAL CIRCUIT (CIR)

Voltage Source 1In the Model Builder, right-click Model 1 (mod1) >Electrical Circuit (cir) and choose Voltage Source .

Resistor 11 In the Model Builder, right-click Electrical Circuit (cir) and choose Resistor .

2 Go to the Settings window for Resistor.

3 Locate the Node Connections section. In the Node names table, enter the following settings:

4 Locate the Device Parameters section. In the R edit field, enter 100[mohm].

External I Vs. U 1This is a special feature for connecting the circuit to the finite elements model.

1 In the Model Builder, right-click Electrical Circuit (cir) and choose External I Vs. U .

2 Go to the Settings window for External I Vs. U.

3 Locate the External Device section. From the V list, select Terminal voltage (mef/term1).

4 Locate the Node Connections section. In the Node names table, enter the following settings:

STUDY 1

Step 1: StationaryIn the Model Builder, right-click Study 1 and choose Compute .

1

2

2

0



RESULTS

3D Plot Group 2The current is now limited to approximately 10A by the external resistor which has a much larger resistance than that of the winding.

MODEL WIZARD

Now, it is time to set up the model for computing the frequency dependent impedance. For this purpose, the magnetic fields interface is an alternative approach.

1 In the Model Builder, right-click Model 1 (mod1) and choose Add Physics .

2 Go to the Model Wizard window.

3 In the Add physics tree, select AC/DC>Magnetic Fields (mf) .

4 Click Add Selected and Next .

5 In the Studies tree, select Preset Studies>Frequency Domain .

6 Click Finish .



DEFINITIONS

At high frequencies, the skin depth of the conductor cannot be resolved and the fields do not penetrate into the interior. Therefore, the interior is replaced by a lossy boundary condition. For this purpose a selection and a surface material are added.

Explicit 71 In the Model Builder, right-click Model 1 (mod1)>Definitions and choose

Selections>Explicit .

2 Select Domains 7, 8, and 14 only.

3 Go to the Settings window for Explicit.

4 Locate the Output Entities section. From the Output entities list, select Adjacent boundaries.


6 Go to the Rename Explicit dialog box and enter conductor_boundaries in the New name edit field.

7 Click OK.

MATERIALS

Copper (2)1 Go to the Material Browser window.

2 Locate the Materials section. In the Materials tree, select AC/DC>Copper.


4 In the Model Builder, click Copper (2).


6 Locate the Geometric Entity Selection section. From the Geometric entity level list, select Boundary.

7 From the Selection list, select conductor_boundaries.



MAGNETIC FIELDS (MF)

1 In the Model Builder, click Model 1 (mod1)>Magnetic Fields (mf) .

2 Go to the Settings window for Magnetic Fields.

3 Locate the Domain Selection section. From the Selection list, select non_cond_wo_IE.

Apart from the surface loss in the copper conductor, there will also be 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.

Ampère's Law 21 In the Model Builder, expand the Magnetic Fields (mf) node.

2 Right-click Magnetic Fields (mf) and choose Ampère's Law .


4 Locate the Domain Selection section. From the Selection list, select core.

5 Locate the Electric Field section. From the r list, select User defined. In the associated edit field, enter 1-5e-4*j.

Impedance Boundary Condition 11 In the Model Builder, right-click Magnetic Fields (mf) and choose Impedance Boundary

Condition .

2 Go to the Settings window for Impedance Boundary Condition.

3 Locate the Boundary Selection section. From the Selection list, select conductor_boundaries.

The electric potential is not available in this physics interface, so to excite the model a different boundary feature that is more appropriate for high frequency modeling must be used.

Lumped Port 11 In the Model Builder, right-click Magnetic Fields (mf) and choose Lumped Port .

2 Select Boundaries 59–62 only.

The geometrical parameters of the boundary set need to be entered manually.

3 Go to the Settings window for Lumped Port.

4 Locate the Port Properties section. From the Type of port list, select User defined.

5 In the hport edit field, enter 0.024.

6 In the wport edit field, enter 0.046.



7 Specify the ah vector as

8 From the Terminal type list, select Current.

STUDY 1

The newly added physics is by default solved for in all studies. This is not desired here so some manual corrections must be applied.

Step 1: Stationary1 In the Model Builder, click Study 1 >Step 1: Stationary .

2 Go to the Settings window for Stationary.

3 Locate the Physics Selection section. In the associated table, enter the following settings:

STUDY 2

Step 1: Frequency Domain1 In the Model Builder, expand the Study 2 node, then click Step 1: Frequency Domain .

2 Go to the Settings window for Frequency Domain.

3 Locate the Physics Selection section. In the associated table, enter the following settings:

Set up a frequency sweep from 1-10 MHz in steps of 1MHz.

4 Locate the Study Settings section. Click the Range button.

5 Go to the Range dialog box.

1 x

0 y

0 z

PHYSICS INTERFACE USE

Magnetic fields (mf) ×

PHYSICS INTERFACE USE

MAGNETIC AND ELECTRIC FIELDS (MEF) ×

ELECTRICAL CIRCUIT (CIR) ×



6 In the Start edit field, enter 1e6.

7 In the Stop edit field, enter 1e7.

8 In the Step edit field, enter 1e6.

9 Click the Replace button.

The problem becomes ill-conditioned near the resonance frequency. If there were no loss, it would even become singular as the field solution then would approach infinity. Thus for a high Q factor, the iterative solver may fail to converge and then a direct solver must be used. Here it is sufficient to tweak the iterative solver to use a more robust preconditioner.

10 In the Model Builder, right-click Study 2 and choose Show Default Solver.

11Expand the Study 2 >Solver Configurations node.

Solver 212 In the Model Builder, expand the Study 2 >Solver Configurations >Solver 2 node.

13 In the Model Builder, expand the Stationary Solver 1 node.

14 In the Model Builder, click Stationary Solver 1 >Iterative 1 .

15Go to the Settings window for Iterative.

16Locate the General section. From the Preconditioning list, select Right.

17 In the Model Builder, right-click Study 2 and choose Compute .

RESULTS

Finish the modeling session by plotting the real and imaginary parts of the coil impedance.


2 Go to the Settings window for 1D Plot Group.


4 Right-click Results>1D Plot Group 4 and choose Global .

5 Go to the Settings window for Global.

6 In the upper-right corner of the y-Axis Data section, click Replace Expression .

7 From the menu, choose Magnetic Fields>Lumped port impedance (mf.Zport_1).



8 Locate the y-Axis Data section. In the y-axis data table, change to the following settings:

9 Click the Plot button.

The resistive part of the coil impedance peaks at the resonance frequency.


2 Go to the Settings window for 1D Plot Group.


4 Right-click Results>1D Plot Group 5 and choose Global .

5 Go to the Settings window for Global.

6 In the upper-right corner of the y-Axis Data section, click Replace Expression .

7 From the menu, choose Magnetic Fields>Lumped port impedance (mf.Zport_1).

EXPRESSION DESCRIPTION

real(mf.Zport_1) Lumped port impedance



8 Locate the y-Axis Data section. In the y-axis data table, change to the following settings:

9 Click the Plot button.

1D Plot Group 4

The reactive part of the coil impedance changes sign when passing through the resonance frequency, going from inductive to capacitive.

As a final step, pick a nice plot to use as a model thumbnail.

1 In the Model Builder, click Results >3D Plot Group 2 .

2 From the File menu, choose Save Model Thumbnail.

This concludes this introduction.

EXPRESSION DESCRIPTION

imag(mf.Zport_1) Lumped port impedance


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