High-Frequency Model of the Coupled Inductors Used in EMI Filters

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 27, NO. 6, JUNE 2012 2805

High-Frequency Model of the Coupled InductorsUsed in EMI Filters

Jean-Luc Kotny, Xavier Margueron, Member, IEEE, and Nadir Idir, Member, IEEE

Abstract—This paper deals with a high-frequency modelingmethod of the coupled inductors used in electromagnetic interfer-ence (EMI) filters. These filters are intended to reduce conductedemissions generated by power static converters towards the powergrid. To model the EMI filters, it is necessary to identify the variousparameters of the passive elements: inductors and capacitors. Be-cause of their major impact on filter efficiency, these elements mustbe identified with accuracy. In this study, high-frequency model ofcommon-mode-coupled inductors is proposed. The identificationof the model parameters is based on the experimental approach.Simulation results of the proposed model are compared to the ex-perimental data obtained using the specific experimental setup.These results made it possible to validate the EMI filter model andits robustness in a frequency range varying from 9 kHz to 30 MHz.The proposed high-frequency inductor models will be very helpfulfor design and optimization of EMI filters, since the high-frequencybehavior of the filter mainly depends on magnetic materials usedand on the geometrical characteristics of winding.

Index Terms—Electromagnetic interference, equivalent circuits,filters, inductors, modelling, parameter extraction.

I. INTRODUCTION

NOWADAYS, the increase of power converter numberis very problematic for electromagnetic compatibility

(EMC). Indeed, each power static converter generates a lot ofhigh-frequency (HF) interferences toward the power networkthat becomes more and more polluted [1]. The main solution toreduce these conducted emissions is based on the utilization ofEMI filters [2], [3]. It can also be combined with other solutionslike slowing down the dv/dt and di/dt during the transitions ofthe power semiconductor components and/or by acting on theconverter controls [4], [5].

THE EMI filters are made of coupled inductors combinedwith capacitors; the choice of the topology depends on networkand load impedances. A typical differential mode (DM) andcommon mode (CM) filter used for power converter is shown inFig. 1.

Manuscript received May 8, 2011; revised August 8, 2011; accepted October22, 2011. Date of current version March 16, 2012. This paper was presentedat the 2009 IEEE Energy Conversion Congress and Exposition. Recommendedfor publication by Associate Editor J.-L. Schanen.

J.-L. Kotny and N. Idir are with the Laboratory of Electrical Engineering andPower Electronics, University of Lille 1, F-59650 Villeneuve d’Ascq, France(e-mail: [email protected]; [email protected]).

X. Margueron is with the Laboratory of Electrical Engineering and PowerElectronics, Ecole Centrale de Lille, F-59650 Villeneuve d’Ascq, France(e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2011.2175452

Fig. 1. Typical EMI Filter topology.

It is well known that magnetic components have a strong im-pact on filter efficiency [6], [7]. They are typically made withcopper wiring on high-permeability ring ferrite. These chokesare traditionally designed by a “cut and try” process, which isvery expensive and time consuming because of the high num-ber of prototypes that are needed. Wires specifications and theirplacement, printed circuit board (PCB) characteristics, or mag-netic core performances introduce parasitic effects that can re-duce drastically the filter’s efficiency [8], [9].

The stray elements of the passive components, such as equiv-alent series inductor of capacitors and equivalent parallel capac-itor of inductors, degrade the performances of the EMI filters.While for a lot of cases, their influence is less important thanthe couplings among components and layouts [10].

In order to design and optimize the performance of the filterby simulation, a high-frequency model, including parasitic el-ements, must be used. These elements must be identified witha good accuracy [11]. In this paper, a high-frequency modelingmethod of the coupled inductors of EMI filter is presented. Thenew equivalent circuit is detailed and its characterization pro-cess is described. The obtained model is tested with differentmagnetic material and gives good results on a large frequencyrange from 1 kHz to 30 MHz. In order to validate the proposedmodel and to test its reliability, CM inductors and capacitorsare used to realize EMI filters. The simulation results usingthe high-frequency model of the filter are validated by experi-mental measurements. In the following section, high-frequencymodeling method of the coupled inductors is detailed.

II. HIGH-FREQUENCY MODEL OF COUPLED INDUCTORS

In this study, a prototype of the coupling inductors has beenrealized with EPCOS ferrite material N30 [12]. The core shapeis a ring R58.3/40.8/17.6 and each winding is made of 15 turnsof copper (diameter 1.5 mm). At first, we will propose an equiv-alent circuit model of the coupled inductors. Then, we propose

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2806 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 27, NO. 6, JUNE 2012

Fig. 2. High-frequency model of the coupled inductors. (a) Common-modeinductors. (b) High-frequency equivalent circuit.

an experimental method of characterization of the passive com-ponent, which will enable us to identify the model parameters.

A. Equivalent Circuit of the Coupled Inductors

Coupled inductors used in EMI filters are a specific case oftraditional n-windings magnetic components [13], [14] becausethey are made with two identical windings around a magneticcore [see Fig. 2(a)]. The objective is to have a model of coupledinductors based on equivalent electrical circuit, which enablesus to describe the various physical phenomena (magnetic andelectrostatic) that appear in high frequency. In order to have amore precise model, a symmetrical equivalent circuit of theseinductors, is used [see Fig. 2(b)]. The proposed model is alumped model; it uses only R, L, and C elements to describeits behavior in a large frequency range. Half of the equivalentcircuit is made of three impedances Z1 (×2) and Z2 , ideallycoupled inductors and four different capacitors CS , Ce , CP , andCC .

It is known that for a two-winding transformer model, witha strong magnetic coupling, only three capacitors are necessaryto describe its electrostatic behavior [14]. In the case of thecoupled inductors and in order to have a symmetric model (foreach winding), a supplementary capacitor CS has been added tothe circuit as shown in Fig. 2(b).

B. Parameters Identification Method

In order to determine the parameters of the CM inductormodel [see Fig 2(b)], impedance measurements realized in dif-ferent test configurations are necessary. An impedance analyzer(Agilent 4294A) is then used and it enables to obtain impedancemeasurements (modulus and phase) on a large frequency rangefrom 1 kHz to 100 MHz [15].

To identify the various impedances of magnetic component,different test configurations can be carried out [17]. Due tothe geometrical symmetry of coupled inductors and using theequivalent circuit presented in the Fig. 2(b), only five well-chosen measurements, as shown in Fig. 3, should be sufficientfor determining all the magnetic and electrostatic parts of themodel.

In order to determine all the parameters of the coupled in-ductor model, different kinds of impedance are necessary. Forexample, subtracting flux or additional flux measurements arerealized and only one open circuit measurement is used forthe magnetizing inductance identification. Fig. 3 describes thefive main measurement configurations (T0–T4) that are cho-sen to identify the equivalent circuit elements of the coupledinductors.

In the determination process of the model parameters, thefirst configuration T0 is used to identify the leakage impedanceZ1 . Then, T0 , T1 , T2 , and T3 are combined to calculate thefour capacitances and finally T4 enables us to identify the mag-netizing part of the component. Table I sums up the variousmeasurement configurations that allow us to identify the modelparameters. The five impedances measured on the prototypeusing the impedance analyzer are shown in Figs. 4 and 5.

The impedance measured in configuration T3 is quite differentfrom the others because it corresponds to a capacitive behaviorfrom 1 kHz to 30 MHz. Indeed, this impedance is measuredbetween both windings short circuited, so the measurement isequivalent to a capacitance.

III. DETERMINATION OF THE MODEL PARAMETERS

All impedances are modeled by one or more combination ofRLC circuit. The aim of this section is to propose equivalentcircuits which allow us to model the frequency variation ofleakage impedance (Z1), magnetizing impedance (Z2) and thefour capacitors (CC , Ce , CP , and CS ) of the coupled inductorsshown in Fig. 2(b).

A. Leakage Impedance

The leakage impedance parameters are obtained from themeasurement configuration T0 because windings are connectedin a subtracting flux topology (cancellation of magnetizing flux).The impedance obtained from T0 corresponds to parallel RLCimpedance which the equivalent circuit is shown in Fig. 6. Theinductance L1 is identified in frequency band (between 1 kHzand 3.7 MHz) when the impedance measured in this config-uration increases (and phase equals to 90◦). The inductancevariation (with frequency) is due to eddy current effects in thecopper wires. Until the resonance frequency, the error betweenthe model and the measurement is still lower than 5%. The ob-tained model is quite simple, but can be improved using ladderRL circuits in order to model correctly the eddy current ef-fects [14]. The value of the resistance R1 is measured at the res-onance frequency (fr = 19.9MHz) of the impedance obtainedfrom T0 as shown in Fig. 4. The capacitance of the equivalentcircuit of the coupled inductor in configuration T0 is given byC0 = 2 (Ce + CP ).

KOTNY et al.: HIGH-FREQUENCY MODEL OF THE COUPLED INDUCTORS USED IN EMI FILTERS 2807

Fig. 3. Impedance measurement configurations. (a) Parallel windings subtracting flux (T0 ). (b) Series windings subtracting flux (T1 ). (c) Parallel windingsadditional flux (T2 ). (d) Between e1 and e2 with two short circuits (T3 ). (e) Open circuit (T4 ).

TABLE IMODEL PARAMETERS IDENTIFICATION

Fig. 4. Impedance (modulus) measurement configurations (T0 , T1 , T4 ).

Fig. 5. Impedance (modulus) measurement configurations (T2 , T3 ).

Fig. 6. Equivalent circuit of the measurement configuration (T0 ).

TABLE IILEAKAGE PARAMETERS

Fig. 7. Equivalent circuit of three measurement configurations: (a) configura-tion (T1 ); (b) configuration (T2 ); (c) configuration (T3 ).

From the curve (T0) shown in Fig. 4, the capacitance C0is computed from the resonance frequency (fr = 19.9MHz)using (1). This capacitance corresponds to the combination ofboth capacitances Ce and Cp . Table II sums up these leakageparameter values

C0 =1

(2π fr )2L1. (1)

B. Parasitic Capacitances

The capacitance value C0 is identified from the leakageimpedance measured in configuration T0 . However, it remainsthree other capacities to calculate. With three more equations,the system can be solved. These equations are given by mea-surements carried out in configurations T1 , T2 , and T3 . Theirequivalent circuits are presented in Fig. 7.

The impedance measured in configuration T1 is quite similarto T0 . Thus, the model used is also a parallel RLC circuit [seeFig. 7(a)]. The measured values of R and L are four times higherthan the leakage parameters. The capacitance value C1 is alsodetermined from the resonance frequency. The value of thiscapacitance is given by the following relation:

C1 = CS + CP +CC + Ce

2= 6.8 pF. (2)

The equivalent circuit of the impedance measured in config-uration T2 cannot use only one RLC series circuit. Indeed, onewill show, in the next section, that the magnetizing impedancewill require three RLC circuits to describe its high frequencybehavior. Because the focus is on the electrostatic part of theimpedance, for frequency upper than 50 MHz, a tangent of the


TABLE IIICAPACITOR VALUES

impedance curve is plotted. The obtained equivalent capacitanceis equal to

C2 = 2(Ce + CC ) = 8 pF. (3)

The last needed equation is given by impedance measuredin the configuration T3 . Its equivalent representation is an RLCseries circuit shown in the Fig. 7(c). The capacitance is easilyevaluated between 1 kHz and 4 MHz using the imaginary partof the measured impedance. The equivalent capacitance is equalto

C3 = 2(CP + CC + CS ) = 19.2 pF. (4)

Finally, these measurements lead us to a four unknown equa-tions system (5) that can be easily solved, and the obtainedresults are given in (6)

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

2Ce + 2CP = C0

Cc

2+

Ce

2+ CP + CS = C1

2Ce + 2CC = C2

2CC + 2CP + 2CS = C3

(5)

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

CC = −C1 +C2

4+

C3

2

Ce = C1 +C2

4− C3

2

CP =C0

2− C1 −

C2

4+

C3

2

CS = −C0

2+ 2C1 −

C3

2.

(6)

Table III sums up the obtained values for the fourcapacitances.

One can note that the value of the capacity Ce is negative.This can be justified by the simplicity of the proposed behaviormodel of the impedances and also to the measurement errorsrelated to the accuracy of the impedance analyzer (measurementequipment).

C. Magnetizing Impedance

The impedance measured in configuration T4 enables to char-acterize the magnetizing part Z2 of the component. Thus, suchimpedance, shown in Fig. 8, cannot be described by only oneRLC circuit. Three different circuits have to be used in order todescribe the three areas.

1) The first area, from low frequency to F1 = 670 kHz, cor-responds to the proper inductance traditionally calculatedusing the following relation:

L = N 2AL (7)

where N is the winding turns and AL is the inductancefactor.

Fig. 8. Impedance modulus in open circuit [configuration (T4 )].

Fig. 9. Modeling of the magnetizing impedance. (a) Equivalent circuit of themagnetizing impedance. (b) Comparison of the impedance modulus in config-uration (T4 ).

The inductance factor of the ferrite material N30, usedto realize a prototype of the coupling inductors, is equalto AL = 5400 ± 20%. Thus, it is well known that thecharacteristics of magnetic materials used in the design ofthe EMI filters depend on the levels and frequency rangesof the conducted disturbances to be attenuated.

2) The second area, from F1 to F2 = 11 MHz, correspondsto high frequency effects of the magnetic material. Thisfrequency band is divided into two parts 2a and 2b. At thefrequency F ′

2 , one can note a slope break of the impedancemodulus; thus, the magnetic material effect is masked byan electrostatic effect.

3) In the third area, a resonance appears which can be linkedto the inductive leakage phenomena combined with elec-trostatic effects.


Fig. 10. Model of the magnetizing impedance. (a) Influence of R2 and RC 2 .(b) Influence of L’2 and C’2 .

Fig. 11. High-frequency model of the coupled inductors.

The magnetizing impedance evolution measured in config-uration T4 is shown in Fig. 8. The equivalent circuit at thisimpedance, which corresponds only to the areas 1 and 2, isshown Fig. 9(a). In this frequency band (area 1 and 2), the influ-ence of the leakage inductances and the parasitic capacitancesis negligible.

The value of L2 is calculated using the imaginary part of theimpedance (L2 = Z2 sin θ/ω) in the frequency band between 1

TABLE IVEQUIVALENT CIRCUIT COMPONENT VALUES

Fig. 12. Impedance measurement configurations. (a) Short-circuit of onewinding (T5 ). (b) Open circuit with e1 -s2 connected (T6 ).

and 370 kHz as shown in the Fig. 8 [or using relation (7)]. Theobtained value of this inductance is equal to L2 = 1.32 mH.

The elements R′2 and C2 are obtained from the first resonance

frequency F1 = 670 kHz (see Fig. 8). The resistance value isequal to R′

2 = 7340Ω. The capacitance C2 is calculated withthe following relation:

C2 =1

2L2 (2π F1)2 = 21.4 pF. (8)

The elements R2 and RC 2 fix the impedance slope betweenthe frequencies F1 and F ′

2 (area 2a). The value of the resistanceRC 2 = 4980 Ω is obtained from the impedance slope in this area.However, the resistance R2 is calculated using the equivalentresistance at the frequency F ′

2 = 3MHz. Its value is equal toR2 = 2026 Ω.

The last equivalent circuit L′2 and C ′

2 is used to model theevolution of the impedance between F ′

2 and F2 (area 2b). Thevalues of these parameters are obtained by a fitting method usinganalysis program linear active circuit (APLAC) software. In or-der to show the influence of the various elements on the accuracyof the proposed model, we present in Fig. 10(a) the comparisonbetween a simulation of the equivalent circuit of the magnetizingimpedance without elements R2 and RC 2 . However, Fig. 10(b)shows the simulation of the same circuit without elements L′

2and C ′

2 .The comparison between simulation results and measure-

ment data [see Fig. 9(b)] shows that the proposed equivalentcircuit allows to model, with a good accuracy, the evolution of


Fig. 13. Impedance evolution of the coupled inductors in four configuration tests (simulation and experimental). (a) Configuration T5 . (b) Configuration T2 . (c)Configuration T0 . (d) Configuration T6 .

Fig. 14. EMI filter characterization.

the magnetizing impedance Z2 . Fig. 11 presents the final highfrequency coupled inductor model. Its parameter values arelisted in Table IV. The obtained model uses only electrical equiv-alent circuits that enable us to make simulations in frequency andtime domains using simulator software such as SPICE. How-ever, for time domain simulation, negative capacitances must beremoved to positive one using inverse perfect couplers [14].

Fig. 15. Experimental EMI filter characterization for CM.

To complete the equivalent circuit, supplementary resistorRC is added in series with impedance Z1 in order to modelthe low-frequency winding resistance, which is measured withimpedance analyzer. The validity of the obtained model will bediscussed in the following section.

IV. MODEL VALIDATION

To validate the proposed model, different configuration testsare considered. To study the robustness of the model, two otherconfigurations, short circuit measurements T5 and open circuitT6 as shown in Fig. 12, are used. The comparison betweenexperimental data and simulation results, using SPICE software,is shown in Fig. 13. The obtained results show a good accuracy


Fig. 16. Measurement method of the CM and DM filters attenuations: (a) common-mode filter; (b) differential-mode filter.

Fig. 17. CM filter response. Tracking generator power level (output) is equalto 3 dB·m.

of the coupled inductor model up to 100 MHz. These resultsprove the validity and robustness of the proposed model. Thenext step consists of using the proposed model to study bysimulation the design of the EMI filter that is made from CMand DM filters.

V. EMI FILTER APPLICATION

The coupled inductors are associated with capacitors toachieve a complete EMI filter. Components are connected to-gether on the PCB and placed inside a metallic box as shown inFig. 14. Fig. 15 shows the interior of the box, which contains theCM inductors and four capacitors CY = 4.7 nF. The two smallboxes are the resistive dispatchers, which are used to divide thepower injected in an equal way on the two input ports of thefilter. For simulation, the capacitors “CY ” have been character-ized using the impedance analyzer. The equivalent circuit usedis an RLC series circuit: C = 4.9 nF,R = 0.18Ω, R = 6.4 nH.The connection wires were also modeled [18], [19].

Both CM and DM filters have been tested according to exper-imental setup shown in Fig. 16. A spectrum analyzer (HP ESAL1500A) is used to characterize the CM and the DM filters. Inthe DM configuration test, a high-frequency balun (transformer)is added in order to obtain a balanced system. The tracking RFgenerator power level (output side) is equal to 3 dB·m for theCM characterization and 0 dB·m for the DM characterization.

Fig. 18. DM filter response. Tracking generator power level (output) is equalto 0 dB·m.

The filters are characterized with input/output impedances equalto 50 Ω/50 Ω.

Both configuration filter attenuations are calculated by sim-ulation using the different components models (coupled induc-tors, capacitor CY , wires, etc.). Figs. 17 and 18 show compar-ison between measured and calculated attenuation for CM andDM filters. For both configurations, these results show a lowdifference (3 dB) between measurement and simulation up to30 MHz.

The filter attenuation depends mainly on the magnetic mate-rial and capacitor’s characteristics [19]–[21]. On the other hand,the maximum attenuation strongly depends on the filter realiza-tion (L and C positioning, coaxial wire lengths, connectionslengths, etc.). In conclusion, filter efficiency mainly depends onits component characteristics and their relative positioning, soa particular care must be taken while realizing an EMI filter forreducing these parasitic effects.

VI. CONCLUSION

In this paper, an electrical equivalent circuit of coupled induc-tors used in EMI filters is detailed. The symmetric model pro-posed takes into account the high-frequency phenomena whichappear when the frequency increases. The identification methodof the model parameters using impedance measurements


in different configurations tests has been proposed. The ob-tained model has been tested and validated for CM inductors.The proposed model of the coupled inductors is used in thesimulation of EMI filter. The obtained results show very goodagreement between simulation results and experimental data upto 30 MHz. The next work consists of optimizing the EMI fil-ters (weight, dimensions, etc.) by simulation using the proposedEMI filter model associated with the high-frequency models ofthe power converters and line impedance stabilization network.

REFERENCES

[1] S. Wang, Y. Y. Maillet, F. Wang, D. Boroyevich, and R. Burgos, “In-vestigation of hybrid EMI filters for common-mode EMI suppression ina motor drive system,” IEEE Trans. Power Electron., vol. 25, no. 4,pp. 1034–1045, Apr. 2010.

[2] H. Akagi, H. Hasegawa, and T. Doumoto, “Design and performance ofpassive EMI filter for use with a voltage-source PWM inverter havingsinusoidal output voltage and zero common-mode voltage,” IEEE Trans.Power Electron., vol. 19, no. 4, pp. 1069–1076, Jul. 2004.

[3] W. Xiaofeng, X. Dehong, Z. Yanjun, C. Yi, O. Yasuhiro, and M. Kazuaki,“Integrated EMI filter design with flexible PCB structure,” in Proc. IEEEPower Electron. Soc., Jun.15–19, 2008, pp. 1613–1617.

[4] N. Idir, R. Bausiere, and J. J. Franchaud, “Active gate voltage control ofturn-on di/dt and turn-off dv/dt in insulated gate transistors,” IEEE Trans.Power Electron., vol. 21, no. 4, pp. 849–855, Jul. 2006.

[5] A. Videt, P. Le Moigne, N. Idir, P. Baudesson, and X. Cimetiere, “Anew carrier-based PWM providing common-mode-current reduction andDC-bus balancing for three-level inverters,” IEEE Trans. Ind. Electron.,vol. 54, no. 6, pp. 3001–3011, Dec. 2007.

[6] H. Chen, Z. Qian, Z. Zeng, and C. Wolf, “Modeling of parasitic induc-tive couplings in a Pi-shaped common mode EMI filters,” IEEE Trans.Electromagn. Compat., vol. 50, no. 1, pp. 71–79, Feb. 2008.

[7] R. Chen, J. D. Van Wyk, S. Wang, and W. G. Odendaal, “Improving thecharacteristics of integrated EMI filters by embedded conductive layers,”IEEE Trans. Power Electron., vol. 20, no. 3, pp. 611–619, May 2005.

[8] X. Wu, D. Xu, Z. Wen, Y. Okuma, and K. Mino, “Design, modeling, andimprovement of integrated EMI filter with flexible multilayer foils,” IEEETrans. Power Electron., vol. 26, no. 5, pp. 1344–1354, May 2011.

[9] F. Leferink, H. Bergsma, B. Ferreira, and W. Van Etten, “High performanceEMI filter for frequency converters,” presented at the EMC Eur. 2004,Eindhoven, The Netherlands.

[10] S. Wang, F. C. Lee, D. Y. Chen, and W. G. Odendaal, “Effects of para-sitic parameters on the performance of EMI filters,” IEEE Trans. PowerElectron., vol. 19, no. 3, pp. 869–877, May 2004.

[11] S. Wang, F. C. Lee, and W. G. Odendaal, “Characterization and parasiticextraction of EMI filters using scattering parameters,” IEEE Trans. PowerElectron., vol. 20, no. 2, pp. 502–510, Mar. 2005.

[12] (2008). [Online]. Available: http://www.epcos.com/web/generator/Web/Sections/ProductCatalog/Ferrites/

[13] X. Margueron and J.-P. Keradec, “Design of equivalent circuits and char-acterization strategy for n-input coupled inductors,” IEEE Trans. Ind.Appl., vol. 43, no. 1, pp. 14–22, Jan./Feb. 2007.

[14] X. Margueron and J.-P. Keradec, “Identifying the magnetic part of theequivalent circuit of n-winding transformer,” IEEE Trans. Instrum. Meas.,vol. 56, no. 1, pp. 146–152, Feb. 2007.

[15] Agilent 4294A Precision Impedance Analyzer-Operation Manual, AgilentTechnol., Santa Clara, CA, 2009.

[16] S. Wang, F. Lee, W. Odendaal, and J. van Wyk, “Improvement of EMI filterperformance with parasitic coupling cancellation,” IEEE Trans. PowerElectron., vol. 20, no. 5, pp. 1221–1228, Sep. 2005.

[17] G. Grandi, I. Montanari, and U. Reggiani, “Effects of power converter par-asitic components on conducted EMI,” in Proc. Int. Symp. Electromagn.Compat. (EMC Zurich), 1997, pp. 499–504.

[18] H. Zhu, A. Hefner, Jr., and J. Lai, “Characterization of power electronicssystem interconnect parasitics using time domain reflectometry,” IEEETrans. Power Electron., vol. 14, no. 4, pp. 622–628, Jul. 1999.

[19] T. C. Neugebauer and D. J. Perreault, “Parasitic capacitance cancellationin filter inductors,” IEEE Trans. Power Electron., vol. 21, no. 1, pp. 282–288, Jan. 2006.

[20] M. C. Caponet, F. Profumo, and A. Tenconi, “EMI filters design for powerelectronics,” in Proc. IEEE 33rd Annual Power Electron. Spec. Conf.,2002, Jun.23–27, 2002, vol. 4, pp. 2027–2032.

[21] Y. Maillet, L. Rixin, W. Shuo, W. Fei, R. Burgos, and D. Boroyevich,“High-density EMI filter design for DC-fed motor drives,” IEEE Trans.Power Electron., vol. 25, no. 5, pp. 1163–1172, May 2010.

Jean-Luc Kotny received the Ph.D. degree from theUniversity of Lille 1, Villeneuve d’Ascq, France, in1984.

He is currently an Associate Professor at the Uni-versity of Lille 1. His main research interests includepower electronics and electromagnetic compatibility.

Xavier Margueron (M’09) was born in Chambery,France, in 1980. He received the Diploma in electri-cal engineering from the Ecole Nationale Superieured’Ingenieurs Electriciens de Grenoble, Grenoble,France, in 2003, and the Doctorat de Genie Elec-trique from the Universite Joseph Fourier, Grenoble,in 2006. His principal fields of research are related topassive components and HF modeling.

Since September 2007, he has been an AssociateProfessor at the Ecole Centrale de Lille, Villeneuved’Ascq, France, where he carries out research in the

Laboratory of Electrical Engineering and Power Electronics . His research in-terests include HF power electronics and passive component modeling andoptimization.

Nadir Idir (M’93) received the Ph.D. degree in elec-trical engineering from the University of Lille 1, Vil-leneuve d’Ascq, France, in 1993.

He is currently a Full Professor with IUT A ofthe University of Lille 1, where he teaches powerelectronics and electromagnetic compatibility . Since1993, he has been with the Laboratory of Electri-cal Engineering and Power Electronics, University ofLille 1. His research interests include design method-ologies for HF switching converters, power devices(SiC and GaN), electromagnetic interference (EMI)

in static converters, HF modeling of the passive components, and EMI filterdesign methodologies for switching converters.

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High-Frequency Model of the Coupled Inductors Used in EMI Filters