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Power Electronics Technology March 2005 www.powerelectronics.com14

Using finite element analysis (FEA) techniques, a

simulation tool generates frequency-dependentmodels of integrated magnetic components,accounting for the materials and winding layoutof the magnetic component.

T

he use of integrated magnetics is apromising technique to help reduce thesize of the magnetic components,

achieve higher power density and im-prove the behavior of the circuit. [3, 4, 5, 6]

As more power electronics are uti lized within the automo-tive, aerospace/defense and power supply industries, thedrive to further reduce the size and profile and increase

the performance and reliability of these componentscontinues at a rapid pace. However, the design of thesecomponents is not a trivial task because the selection of

the core, air gaps and winding setup is not evident.The availability of a valid electrical model allows the

designer to select the appropriate constructive parametersin order to obtain the expected behavior. Ansofts PExprtsoftware is capable of creating accurate models for thesecomplex components, letting the designer select theappropriate winding strategy without time-consumingprototyping iterations. PExprt uses powerful finite elementanalysis (FEA) techniques to generate frequency-depen-dent models of integrated magnetic components, whichinclude the materials and winding layout of the magneticcomponent.

Model BasisThe use of virtual models aids the designer in selecting

the appropriate constructive parameters to obtain theexpected behavior without the time and expense of build-test iterations. PExprt provides a straight-forward designprocedure for generating a model from the FEA fieldsolut ion. While a 3D simulation is preferred, 3D FEA solv-ers are not as efficient as 2D FEA solvers in terms of com-putation time for devices with a high number of turns. Asan alternative, PExprt uses a novel 2D approach based onthe application of the Double 2D technique [1] to increasecomputation speed yet preserve accuracy.

The model structure is based on the one presented in [1]Fig. 1.The m odel structure for a 3-w inding compon ent consists ofthe w indings mo del (a) and core mo del (b) show n here.

(a)

(b)

By Robert Prieto, Associate Professor, UniversidadPolitcnica de Madrid, Madrid, Spain, andJ. Mark Christini,Senior Application Engineer, Ansoft Corp., Pittsburgh

d d d

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MAGNETIC COMPONENTS

and [7]. The structure of the model isshown in Fig. 1 for a 3-winding com-ponent (assuming one winding ineach core leg). There is an electricsubmodel (top) coupled with a mag-netic submodel (bottom).

In Fig. 1, the impedance Z11 repre-sents the windings impedance (mag-netic energy and power losses) whenthe net current is only flowing thoughwinding 1. Therefore, the impedanceZ

11is not the self-impedance of wind-

ing 1, because losses and energy at thewhole component (except the core

area) are considered in this imped-ance value. The meaning of imped-ances Z22 and Z33 is equivalent to theone of impedance Z11 when netcurrent flows through windings2 and 3, respectively.

Z12represents the windings imped-ance (magnetic energy and powerlosses) factor due to the simultaneousconduction of net current throughwinding 1 and winding 2. In otherwords, the energy and the losses in thewindings when the current is flowingsimultaneously through windings

Fig. 2.The Do uble 2D procedure app lication depicts the 3D struct ure and t he associat ed 2Dsimulations.

Fig. 3.An EI core shape an d size is selected fro m th e PExprt librar y.

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Fig. 4.After w indin g setu ps are defined, a cross-sectional view of th e com pon ent is created byPExprt.

MAGNETIC COMPONENTS

Fig. 5.A menu in PExprt enables users to d efine the pc-bo ard con ducto rs.

1 and 2 (transformer mode) are notthe addition of the ones obtainedwhen current is flowing throughwinding 1 and winding 2 alternatively(inductor mode). This effect is takeninto consideration by Z12. The rest ofthe impedances, Zij, are analogous toZ12, describing the windings imped-ance due to simultaneous conduction

of net current through the other pairsof windings.

The core part of the magnetic com-ponent is represented by a set of re-luctances and mmf sources. There isa reluctance for each core column (C)and another for each gap (G). It ispossible to replace the core reluctancewith a nonlinear core model (such asthe Jiles-Atherton model) to representhysteresis and eddy current losses.

The simulation procedure pro-posed in this work is based on theDouble 2D approach presented in [2].

This approach is based on the divi-sion of the windings of the magneticcomponent in two parts. Each partproduces field distribution in differ-ent planes of the space. In this way, itis possible to use 2D FEA solvers tostudy these structures.

Fig. 2 shows the actual 3D struc-ture and the double 2D simulations

needed to simulate it. The double 2Dprocess requires simulation of four2D structures. However, the simula-tions that account for the field distri-bution in the air for each leg (sideviews) are very simple. Therefore, thesolution time for these three cases isextremely short.

The FEA model offers several ad-vantages. Because it is based on FEAcalculations, it is accurate (error be-low 10% for most of the applicationrange) and 2D effects (such as thefr inging flux effect around the air gap)

are considered. The model also is fre-quency dependent and is valid fornonsinusoidal waveforms. Anotherbenefit is that the couplings betweeneach pair of windings are accuratelycalculated.

Speed is another advantage. Thesolution time is fastthe average timefor common components is less than15 min. Furthermore, the model gen-eration is completely implemented inPExprt, so the user does not need tolearn how to use the FEA solver.PExprt creates the FEA project auto-matically and solves the fields.

Generating the ModelDefi ni ng the core shape, size and

material. The selection of the coreshape and size is simple. PExprt pro-vides libraries containing most of thecommercially available cores. The ap-propriate core shape for an integratedstructure can be directly selected fromthe library. An EI shape is selected forthis example, as shown in Fig. 3.

Defining the winding setup. Oncethe core is selected, the winding setupfor each core leg should be defined.PExprt provides a flexible user inter-

face that allows the user defining anywinding connection. The turns can beconnected either in parallel or series,creating any possible interleavingstructures. A different winding strat-egy can be defined and assigned foreach core leg. Once the winding set-ups are created and assigned to eachcore leg, a cross-section view of thecomponent can be visualized, asshown in Fig. 4. For this device allwindings are on the outer core legs

only.Defining the pc-board conductors.

The thickness and width of each pla-nar track can be defined easily to ob-tain the real behavior (resistance, cou-pling, leakage and magnetizing induc-tances, and capacitive effects) of thecomponent. The pc-board conductorsare defined through easy-to-usemenus such as that shown in Fig. 5.

Exploring the ResultsPExprt contains a model genera-

tion engine that connects the FEA

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Fig. 6.The tool can p lot para m eters such as resistance versus frequency.

solver wi th the equivalent circuit model.Once the model is obtained, it canbe exported to a circuit simulator(Simplorer, PSpice) or it can be used inPExprt to explore the small-signal be-havior of the component.

The resistance and leakage induc-tance as a function of frequency can beplotted using the tool. The dc resistance,magnetizing inductance and parasiticcapacitive effects also can be obtained.Fig. 6 shows the resistance as a functionof the frequency.

Once the integrated magnetic modelis generated with PExprt Modeler, youcan use that circuit model in Simplorerto explore the performance of your en-tire circuit. The resulting schematic is

represented in Fig. 7.

Validating ResultsTo demonstrate how to use PExprt,

we model a push-pull forward converterwith integrated magnetics for a voltageregulator module (VRM) that producesa 1.2-V, 70-A output from a 48-V input.

MAGNETIC COMPONENTS

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a

aQ2

Vin

Cs

Q1 b

q

p

p

q

b

c

d

e

Co Vo

SR1

SR2_

++

a

p

q

b

Q1

Cs

Q1

b

q

p

a e

d

Lo2

c SR2

Co Vo

+

Lo1

SR1

n:n:1

n:n:1Vin+

Fig. 7.A circuit m odel of the m agnetic compon ent generated in PExprt M odeler can be port ed in Simp lorer forsimu lation of th e entire circuit.

Fig. 8.The design exam ple consists of a push-pu ll converter wit h int egrated m agn etics. Show n

here are the actual imp lementation (a) and th e equivalent electrical circuit (b).

The example is based on the paper,Design of 48-V Voltage RegulatorModules with a Novel IntegratedMagnetics. [3] In this structure, all themagnetic components, including in-put filter inductor, step-down trans-former and output fi lter inductors, areintegrated into a single EI or EE core.

The transformer windings (primary1 and primary 2) as well as the induc-tor winding (secondary) are woundon the two outer legs. The interleav-ing winding technique is used tominimize the leakage inductance ofthe integrated transformer. The corestructure has an air gap in the center

MAGNETIC COMPONENTS

leg and no air gap in thetwo outer legs. Fig. 8 showsthe topology selected forthis example. The validityof the integrated magnet-ics component model

was confirmed in the labwhere the measured resultsfor the device closelymatched those simulatedby PExprt. PETech

References1. Asensi, R.; Cobos, J.A.;Garcia, O.; Pri eto, R.; and

Uceda, J. A Full Procedure

to Model H igh Frequency

Transformer Windings.

Power Electronics SpecialistConference (PESC) 1994.

2. Prieto, R.; Cobos, J.A.;Garcia, O.; Alou, P.; and Uceda, J.

M odel of Integrated M agneti cs by

Means of Double 2D Finite Element

Analysis Techniques. Power Electron-

ics Specialist Conference (PESC) 1994.

3.Xu, P; Ye, M ; Wong, P; Lee, F.C. De-sign of 48-V Voltage Regulator Modules

wi th a Novel In tegrated Magneti cs.

Power Electronics IEEE Transactions,

Vol. 17, No. 6 (November 2002), pp.990-998.

4.Wei, J.; Xu, P.; Lee, F.C. A High Effi -ciency Topology for 12-V VRM-Push-

Pull Buck and Its Integrated M agneti cs

Implementations. Applied Power Elec-

t ron ics Conference and Exposi t i on

2002. Seventeenth Annual IEEE, Vol. 2,

2002, pp. 679-685.

5.Xu, P. and Lee, F.C. Design of H igh-Input Voltage Regulator M odules wi th

a Novel Integrated Magnetics. Appl ied

Power Electronics Conference and Ex-

position 2001. Sixteenth Annual IEEE,

Vol.1, 2001, pp. 262-267.

6. Chen, W.; Hua, G.; Sable, D.; Lee, F.Design of H igh-Efficiency, Low-Profile,

Low-voltage Converter wi th Integrated

Magnetics. Applied Power Electronics

Conference and Exposition, 1997. 12th

Annual , Vol. 2, Feb. 23-27, 1997, pp.

911-917.

7. Prieto, R; Asensi, R; Cobos, J; andUceda, J. A Full Procedure to Model

Integrated M agneti cs based on FEA.

APEC 2004 Conference Proceedings.