model of the capacitive effects in magnetic components

8/6/2019 Model of the Capacitive Effects in Magnetic Components

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MODEL OF THE CAPACITIVE EFFECTS IN MAGNETIC COMPONENTSR . Pricto, R. Asensi , J .A . Cohos, 0 . Garcka and J . Uceda

Universidad Politk nica de Madrid. E.T.S.I.I.Div. de Ingenieria ElectrBnicaJo& Gutidrrez Abascal, 2

28006 Madrid SPAINTel: 34-1-411 75 17 Fax: 34-1-564 59 66 E-mail: [email protected]

Abstract: A model Jk lie capacitive efects in magneticcomponents fo r Switch M ode Power Supplies (SMPS) as beendeveloped. It can be upplied to multiwinding transformers. A FiniteElement Anabsis (FEA) tool is used ta compure the frequencybehavior of the magnetic component, taking into account geometryam i materials. The param eters ofthe model can be calculated belfi,rethe magnetic component isbuilt. A n acciirute capacitance smodelingis expected to be crucia l j ) r common-mode EM1 transini,s.rionmodeling. The model take s into a ccount winding Jloating voltagesand the ca pacitance among each winding. Several model leveb withdiyerent degrees offreedom are proposed. Some experimental resiiltscumparing the actual m ugneric component results with the beliavioralsimulator resulrs, are presen ted.

I .INTRODUCTIONMagnetic components arewidely used in pnwer supplies. They are

i n d d one of the most important coinponents in pnwer electronicdevices. Accurate models are necessary to ohtain accurate coinputersimulations. It is necessary to obtain the actual wavefonns of thecircuit to control cotnp'nent stresses and ElectroMagneticInterferences (EM I).

The classic model of the transformer capacitive effects is notenough to obtain accura te waveforms. Furthe rinore, the calculationof their parameters is only po ssible onc e the m agnetic component hasbeen built.

This work presents a procedure to calculate a model of thecapacitive effects in a magnetic component, inlcuding multiwindingtransfon ners. T he inodel is hased on the physical description(geometry and materials) of the magnetic cotnpnnent.

Th e parameters of the model are calculated by tntfans of a FiniteElecrnent Analysis (FEA) Tool, so it is not necessary to huild thetnangetic coinponent, which ineaiis time and money in the designprocess.The re are only few references o f the capacitive effects descriptionin high frequency transformer [ I]-[4]. The use of FEA tools in thecapacitive effects modeling has lieen studied in [51 for high powertransfon ners, but it is necessary to build the transfon ner to obtain anexperirnental constant that is necessary Rir the capacitancescalculation. Some authors present capacitive effect tnodels based onreference [6], ut these tnodels are only accurate for high voltagetransfimners and cylindric windings.Th e present work propnses a theoretical inodel that coinpleinentsthe High Frequency T ransfnr iner Windings M odel presented iii [ I ] ,so a full model of the magnetic cimponent hased on he coinponentgmmetry (it is not necessary to build it) is ohtained.An accurate inodel helps tc) ihtain accura te simula tims o f theelectrical waveforms and the electroinagnetic interferences ( EM I ) . s o

the design procedure o f the whole power electronic circuit (SMPS)is itnprovect.2.THEORETICAL DESCRIPTION OF THEMODELS

Depending on the degree of accuracy desired, it is pssbile to usedifferent tnodels with several degrees of f r d o m to model thecapacitive effects in the magnetic cotnponent. Four different levelsare presented in this paper. The accuracy level depends on thedegrees t ) f freedom taken into account in each level.2. I . Level I Model

T he first level model assumes only two degree s of freedom, whichare tlic voltage applied to tlie first winding and the offset voltageamong the different windings.

All voltages are referred to o ne of the firstwinding terminals, andthe rest o f the winding voltages are ohtained by means of the turnsrat c ).

2.1. I . Two winding transformersThe electric energy stored in a volume can be obtained by means

o f ( 1 ) :

The t i n t level has only two degrees of f r d o m ( va ri ab le s) .Ther cfi)re, using only two variables, voltage applied to the firstwinding ( V , ) and offset voltage hetween first and second winding(V


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One capacitor to store part of the offset energ y and part of theglobal energy ( C l @) .

O ne of the possibilities to place these capacitors in the model isshown in figure I :

Fig. 1 . Level 1 Model for two winding transformerTh e energy associated to this inodel is represented in (3):

I = - c , v : + - c o f f ~ f f + - c ~ ~ v l - v o b ) ~1 1 == - (C, Cl0$ v: +5 C O f f C,& vof42 2 21 12 - CiMVi V& = 11+ III + IIII

(3)

Comparing (2) an d (3) the parameters o f the no del can heobtained. Th e resulting parameters a re given by equations (4), ( 5 )and (6):

Puramrtrrs rxtructionTh e three capacitors can h e calculated h y means of two differentsimulations in the FEA tool, and applying the superposition theorem.

One o f the de grees of freedom (voltages) has to be zero in eachsimulation.Siiniclution 1A voltage is applied to the priinary winding. The voltage in the

secondary winding is given by the turns ratio. The offset voltage hasto be zero (see figure 2). ( V I # 0; y f l= 0 )

775-Fig. 2 . First siniulation for the extraction of the parameters of the

modelTh e energy in this sirnulation is given by equation (7):

Sitnicktion 2The same voltage is applied to all the turns of the secondary

winding. All primary winding tum s a re grounded (see figure 3).cv, = 0; o , 0)

;7TFip. 3. Second simulation for the extraction of the

parameters of the niodelTh e energy o f this system is given by equation (8):

I t ca n be seen that:z, = Ii I, = li i

The FEA tool post processor can save the value of the field E,,D,, Eta and Do,, so I,,,(see equation (2)) can be obtained applying htesuperposition theorein. C,, CO, and C , , can be obtained usingequation (4) . ( 5 ) and (6).2.1.2. Thre e w inding t r a ns fo rm e r

Fig. 4. Level 1 niodel fo r three windingtransfomier

I n n three winding transformer there ar e three degrees of freedomVoltage applied to the primary winding (V,)Offset v ol ~ ig e etween primary and secondary winding ( V m JOffset voltage between primary and third winding (Vm3)

The energy in this transforiner is given by (9):

fo r the level 1 no del:

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----1+ - [ [ l ( D o f f l Z . E 0 f f1 3 + D 0 / f 1 3 . E 0 f / 1 3 ) d v == I , + II 1+ I,,, + I ,, + I , + I",

There are six terms of the energy to consider, so six capacitorsshould be placed in the model to store the energies. Figure 4represents the level 1 model for a three winding transformer. Theenergy stored in those capacitors is given by (10):

I = -ceqe T c 0 f f l 2 + 3'0ffl3V 2f f1 3 +21 12-c12(v1 - o f f1 2 I 2 + TCl,("l - ' 0 f f I 3 ) ~ +

+ , ~ o f p 3 ( " o f f l z - V O f f l J - 5' ,, + C t z+ C I 3 ) * +1 (10)

+ 5COfflZ + Cl, + C0fy23"&2 +1

+ Z ( ' o f l l 3 + '13 + ' o f y 2 3 . ?ff13 -- - c 1 2 v l v o f f l Z - c 1 3 v l v o f f 1 3 - c o f f L 3v o f f 1 2 vo f f 1 3 =1

= II + 111+ 1111 I, , + I , + I, ,The model presents the same structure as the two windings one:

On e cap acitor referred to the primary winding , that stores partOn e capacitor that stores part o f the offset energies in each pairOne capacitor that stores part o f the offset energy and part o f

So it is necessary to add additional offset capacitors tc) obtain theThe parameters extraction has the same process than in the two

Energies are calculated by means of the F E A toolThe energies a re asociated to the capacitorsThe superposition theorem is applied

of the global energy C,.ci f windings (CO,,).the global energy (Cy).

desired n uinlxr of parameters.winding transform er.

Puruinrtrrs rxtructinnThree simulations are enough to cil,tain all the paraineters o f th e1. Applying voltage t o the primary winding. The rest 11f the

model:winding voltages are given by the turns ratio:Al l the windings are referred ti) ground. D, and E, arecalculated.

VI f 0 ; V,,? = 0 ; VC,ff,? 0

2 . Applying the same voltage to all the turns of the secondarywinding. The rest of the windings are grounded.DrCf12nd EdfI2are calculated.The rest of the windings a re grounded.D an d E,+f,, are calculated.

VI = 0; ,,, ;r 0; vw, = 03. Applying the sa me voltage to all the turns of the third winding.

V I = 0; ,,, = 0 ; V&IJ # 0Each o f these simulations tnakes zero all the degrees of freedom

except one o f them.

Fig. 5 . Sin d o l io n s n ccd id for [hi, xrraction of the parameters foro rhrw winding tronsfomrer or level I model

2.2. Level 2 modelA model with higher accuracy is obtained by add ing a new degree

of freedom to the Level 1 model. In the level 2 model, the voltagein all the windings is a new degree of freedom , so it is no t given bythe turns ratio. This way, the effect of the leakage inductances ismodelled with mi)re accuracy in the who le model of the m agneticcomponent. All the volhges are referred to one of the primarywinding terminalsFor siinplicity, only two winding transf orm er is described in level3, mc)del.

The electric energy, using three deg rees of freedom, is given by(1 ) :

There art) SIX terms i i f the energy, so six capacitor are needed tostore thebe eiiergic5. A six parameters tnodel is obtained for a twowinding tr.insf)riner (see figure 6):

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LV0Zp5WRj2 4c24volfFQ. 6. Level 2 model for two winding transformer

The energy associated to the system of figure 6 s given hy (12):

1 12 2+ - C , , ( V , - v0,y + - C 2 , ( - vo,,- V2)2 =

Puroineters rxtructionFor a two winding transformer, three simulations are enough to

obtain all the parameters of the level 2 model (applying thesuperposition theorem):1. Applying voltage to the primary winding (refe rred to ground)

and grounding the second winding.D, an d E , ar e calculated.and grounding the primary winding.D, an d E, are calculated.winding and grounding the primary winding.D,#f and E are calculated.

V I # 0; v, = 0; v, = 03. Applying voltage to the secondary winding (referred to gro und)

v, = 0; v, = 0; VI # 03. Applying the same voltage to all the turns of the secondary

v , = 0; v2= 0; V& # 0

.----Fig. 8. LtveI 3 model for two winding tramformer

Th e voltage in the secondary winding is given by the turns ratio.There ar e three degrees of freedom in this model: V I, V, an d V,.Voltage applied to the primary winding (VI)

Floating voltage of the primary winding (Val)Floating voltage of the secondary winding (Vo2)

The electric energy associated to this system is given by (13):

There are six terms o f the energy to be stored in six capacitors(figure 8). Th e electric ener gy stored in th ese capacitors is given by(14):

P u r a n i r t m rxtrciction

The way to extract the parameters of th e model is the same as ina) b) c) For a two windinc tra nsform er three siinulations ar e needed (one

p llevel I and level 2 models.-o f the degrees o f freedom should he zero in each simulation).

The ground reference should be chosen in the core.2.3. Level 3 model 2.4. Lev el4 model

Level 3 model is similar to level I tnodel. For simplicity, for two ~ 1 ~ i ~h cOlnp~ex This all thewinding transformer is de scr ihd fo r level 3 model. The difference voltages t~l ,n t i l lg , the in the windings are no t givenis that the voltage of the windings a re not referred to ground hut theyare floating voltages. Figure 8 shows the iinpleinentation o f this is shown inmodel for a two winding transfixiner

I , ~figure 9

tLlrll\ rat l , l hut they are also a degree of freedom.TI^^ resulting Inodel f i l r a two winding

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C1 3

Fw. . Lcvd 4 ntocicdfor two wincirng tmnsfonnerThis model considers four degrees ( i f freedom fo r a two winding

Voltage applied to the primary winding (V,)Voltage applied to the secondary winding (V2)Floating voltage of the primary winding (Vo,)Floating voltage of the secondary winding (V,)

Th e electric energy is given hy (15):

transformer:

+ i I I / , ( q . q + q . q ) d v+ i / / l ( & . q + q + G ) d v == I I + 4 1 + 4 , + 4 v + I v + I, , + I,,, + I,,, + 4 , + I ,

(15)There are ten tenns o f the energy t o compute. ThereRlre. tencapacitors should be included in to the inodel to store the energies

(figure 9) . Th e energy stored in these capacitors is given by (16):1I = -(C +c, + c, + Cb + cc c,>e,+ - ( C , + c, + c, + c,,v: +

+ -(CA t c, +ca c, + cc C,)G2 t2 '1

212

3 .EXPERIMENTAL RESULTSSeveral magnetic components have been tested to validate theThe model has been tested with:Different core sizes: RM 2 and RM 14Different core inaterink: Philips 3F3 an d Philips 3C85

accuracy of the presented model.

Air gap inclusionDifferent rnagnetic coinponents: transformer and inductorsTh e different tests developed are small signal ones. The use of

higher accuracy levels (level 2, 3 an d 4) should have great advantagein large signal tests, bw au se of the EM1 conduction modeling.Therefore. all the tests have been developed using level 1 model.Future developinents will include EM1 tests with level 2, 3 an d 4niodels t o coin pare the difference am ong all the presented m odels.Level I intldel has I x e n tested with different magneticcom]>l Ilcllts.

TEST1 : Two winding t ransformer . RM12 core Philips 3F3material. Primary with 37 turns in two layers andsecondary with 18 turns in one layer. Solid wire of0 , 7 1 n i n 0 .Induc t or . RM12 core. Philips 3F3 material. 18 turnsin one layer . Sol id wire of 0.7 51 nm 0.Indu ctor wi th air gap of 1 .Sinin. RM14 core. Phflips3C85 material. 24 turns in one layer. Solid wire of0.71n1n0.

TEST?:T E S T 3:

3,+%

le+05

k + 3 '

iero:

Fig. 10. Trnnsfomier TEST 1. Open circuit

Fix. 11. Iruliumr TEST 2. Frequency hehnvior


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1t+04

1 ~ 0 3

3w02

Ti. 13. Trancformer TEST4. Open circuit

TEST4: Two winding t ransformer. RM12 ore. Philips 3F3material. Primary 36 turns i n two layers andsecondary with 35 urns in two layers. Solid wire of0 . 7 m i n 0 .

Figure 10 si1ciws tlie open circuit test in TEST1 transformer.Figure 1 1 shows tlie frequency behavior of TEST2 inductor. Figure17- slinws the fryu cncy I~eha viorof EST3 inductor . Figure 13showtlie open circuit test in TES T4 transformer. All figures show thecoinparistin between ineasured (using an HP4195 impedanceanalyzer) an d simulated (using ELDO behavioral simulator) results.

4.CONCLUSIONSA new theoretical model to take into account the capacitive effects

in high frequbncy magnetic cnin pn en ts has been presented. Th eprocedure allows calculate the parameters of themodel using onlytlie geoinetrical description and materials of the magneticcomponents. The model considers a distributed representation of thecapacitive effects by means of n set of lumped capacitances. Theadvaiit:ige cif this models in EM1 conduction analysis will be studiedi n future developinents. Experimental results show the accuracy ofthe level I inodel.

REFERENCES[ 11 "A It111 procedure to model high frequency transfonner

windings", R . Asensi, J.A. Cohos, 0. Garcia, R. Prieto andJ . Uceda, Power Electronics Speciulists Conference, 1994."Entian c d C r( ss-Co upled-SwondariesModel forMultiwindingTransfirmers", H.A. Owen j r . . V.A. Niemela and T.G.Wilson, P o w r Electronics Speciulists Conference, 1992.

131 "Issues Regarding the Capacitance of 1-10 MHzTra us fmne rs " , L.F. Casey, A.F. Goldberg and M.F.Schlecht, A p p h f Power Electrc>nic.sConference, 1988."At1 accurate method fo r inodeling transforenner windingcapacitances" , .A . Collins, Iruircsrriul Electronics Conference,1990."Transient overvoltage study and model for shel-type powertransformers", V. Woivre, J .P. Arthaud, A. Ahmad and N.Burais, IEEE Trurrsuctionson Power Delivery, vol. 8 , no. 1,January 1993.161 "Einfaclie Niherungsftmneln fur die Eigenkapazitiitmzlirlngigen Spuleri", Von Harry Zuhrt, Elekrrorec/inische

[21

(41

I S ]

Zc~if.vc./rri$,5 , July 1934.

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model of the capacitive effects in magnetic components

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