IEEJ Journal of Industry ApplicationsVol.4 No.3 pp.166–173 DOI: 10.1541/ieejjia.4.166

Paper

A Magnetic Structure Integrating Differential-Mode and Common-ModeInductors with Improved Tolerance to DC Saturation

Kazuhiro Umetani∗a)Member, Takahiro Tera∗ Member

Kazuhrio Shirakawa∗ Member

(Manuscript received July 22, 2014)

The integration of differential-mode (DM) and common-mode (CM) inductors onto a single core has been expectedto miniaturize EMC filters. On the other hand, this technique possibly leads to lower tolerance to magnetic saturationcaused by the DC flux, hindering the miniaturization effect due to integration. Particularly, this problem seems to beexacerbated in the previously reported magnetic structure. The reason may lie in the fact that this conventional structuretends to induce a large DC flux because its equivalent number of turns for the DM inductance is restricted to only halfof the total number of turns. This paper addresses this problem by proposing a novel structure that assigns more turnsto the DM inductance to suppress the DC flux more effectively. A theoretical analysis and experiments verified thatthe proposed structure is equivalent to series-connected DM and CM inductors. Additionally, an analytical estimationrevealed that the proposed structure reduced the core volume by 41% compared to the conventional structure for thesame wire length. These results demonstrate effectiveness of the proposed structure for miniaturizing EMC filters.

Keywords: integrated magnetic component, EMC filter, differential-mode inductor, common-mode inductor

1. Introduction

Recently, high power density is intensely required forswitching converters. Accordingly, their circuit componentsare also required to be miniaturized. Particularly, magneticdevices for EMC filters, such as differential-mode (DM) in-ductors and common-mode (CM) inductors, often occupy asignificant volume. Therefore, a number of techniques (1)–(11)

have been proposed to miniaturize DM and CM inductors.A promising approach is to integrate a DM inductor and

a CM inductor into a single device. As well-known exam-ples (1)–(3), highly integrated structures are proposed based onplanar magnetic cores. These structures are beneficial in fur-ther integrating capacitors by inserting a dielectric layer be-tween a pair of planar windings. However, these structurescan suffer from excessive copper loss in high power applica-tions because planar core generally requires long wire lengthfor the windings. The same benefit and problem also tend tooccur in the structures in which conductive foils are used aswindings (4) because the foils tend to have large DC resistancecompared to thick wires. Therefore, high power applications

Based on “Novel Magnetic Structure of Integrated Differential-Mode and Common-Mode Inductors to Suppress DC Satura-tion” by Kazuhiro Umetani, Takahiro Tera, and Kazuhiro Shi-rakawa, which is presented in the proceedings of the 2014 Inter-national Power Electronics Conference, Hiroshima, Japan.

a) Correspondence to: Kazuhiro Umetani. E-mail: umetani@okayama-u.ac.jp∗ DENSO CORPORATION R&D Center

1-1, Showacho, Kariya, Aichi 448-8661, Japan(Kazuhiro Umetani is currently at Okayama University since 1Oct., 2014)

often prefer integration techniques based on bulk core withwindings of thick wire.

This type of techniques has also been reported in a num-ber of studies. These techniques can be classified into twomajor categories. One is the structural integration (5)–(8), whichintegrates DM and CM inductors on separate magnetic corespartly sharing the windings. Techniques of this category arebeneficial in reducing the dead space because the cores canbe closely placed by sharing the windings. The other cate-gory is the magnetic integration (9)–(11), which integrates DMand CM inductors on a single magnetic core. Techniques ofthis category allow sharing not only the windings but also thecore between the DM and CM inductors. Compared to thestructural integration, the magnetic integration can offer fur-ther miniaturization because the total core volume may alsobe reduced by sharing magnetic paths.

On the other hand, the magnetic integration has a drawbackthat the CM inductance, as well as the DM inductance, cansaturate because the DC flux induced by the DM current cancause magnetic saturation in the shared magnetic path. Thismay require expanding the cross-section of magnetic pathsto design necessary tolerance to the magnetic saturation notonly of the DM inductance but also of the CM inductance. Asa result, the miniaturizing effect of the magnetic integrationmay be hindered.

An effective strategy to alleviate the problem is to suppressthe DC flux. This strategy generally requires increasing theequivalent number of turns NDM that link with the flux in-duced by the DM current. Below, we show the reason.

As an analogy to the basic inductor with a single magneticpath, we can define NDM as the ratio (12) of the total flux link-age to the flux, when only DM current is applied. Hence, we

c© 2015 The Institute of Electrical Engineers of Japan. 166

Integrated Differential-Mode and Common-Mode Inductors（Kazuhiro Umetani et al.）

obtain (1), if we assume constant DM inductance LDM .

NDM ≡ LDMIDM

φDM,

∴ φDM =LDMIDM

NDM, · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (1)

where φDM is the flux induced by the DM current IDM .Accordingly, we can express the DC flux φDC induced by

the DC component IDC in IDM as follows:

φDC =LDMIDC

NDM. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (2)

Because LDM and the maximum value for IDC are generallyspecified as requirement, increasing NDM is indispensable tosuppressing φDC .

However, as shown in this paper, NDM is restricted to onlyhalf of the total number of turns on the conventional mag-netic structure employed in the prior works (9)–(11). Therefore,the conventional structure often suffer from large DC flux in-duction. Due to the problem, the conventional structure maynot offer effective miniaturization of DM and CM inductors.

The purpose of this paper is to address the problem byproposing a novel magnetic structure. In the proposed struc-ture, more winding turns can be assigned to NDM than theconventional structure in order to suppress the DC flux in-duction. As a result, further reduction in the core volume canbe expected, if magnetic saturation is a determining factor inthe cross-sectional area of the magnetic paths, as is often thecases when large LDM or large IDC is specified.

This paper investigates the proposed structure in the fol-lowing four sections. Section 2 analyzes the operating prin-ciples of the proposed structure theoretically. Then, Sect. 3verifies the operating principles experimentally. Section 3also verifies that the proposed structure can miniaturize thediscrete DM and CM inductors by the magnetic integration.Section 4 analytically compares the core volume between theproposed and conventional structures to verify the core re-duction effect of suppressing the DC flux. In this compari-son, the core dimensions are estimated under the same wirelength and under the same specifications in which magneticsaturation dominantly determines the cross-sectional area ofmagnetic paths. Finally, Sect. 5 presents the conclusions.

2. Proposed Magnetic Structure

2.1 Operating Principles Figure 1(a) illustrates theproposed magnetic structure. The structure has a core withthree legs. The center leg has a gap and two windings withthe same number of turns. The windings on the center legare both wound so that DM current induce the same directionof flux. Each of the outer legs has a winding connected inseries with one of the windings on the center leg. The wind-ings on the outer legs have the same number of turns and arewound so that DM current induce the flux in the outer leg inthe direction that reinforces the flux in the center leg.

On the other hand, the conventional magnetic structure em-ployed in the prior works (9)–(11) is magnetically equivalent toFig. 1(b). It differs from the proposed structure in the wind-ings on the center leg.

Electrical functions of the proposed structure are equiva-lent to series-connected discrete DM and CM inductors, as

(a) (b)

Fig. 1. Magnetic structures integrating DM and CM in-ductors. (a) Proposed structure (b) Conventional struc-ture

Fig. 2. Magnetic circuit model of the proposed structure

well as the conventional structure. Below, we show the rea-son utilizing the Lagrangian modeling (13) (14).

As discussed previously (13) (14), the Lagrangian modeling of-fers a systematic method to transform an integrated magneticcomponent into an equivalent circuit of basic transformersand inductors, each of which consists of a single closed mag-netic path. In this method, we first translate the physical mag-netic structure into Lagrangian, which can be directly config-ured from their electric and magnetic networks. Then, weapply a point transformation (15) to the Lagrangian, obtaininganother Lagrangian that belongs to a circuit of basic trans-formers and inductors. Finally, we again translate the resul-tant Lagrangian to obtain the equivalent circuit.

Now, we apply this method to the proposed structure. Themagnetic circuit of the proposed structure can be expressedas Fig. 2. NC and NO are the numbers of turns of the centerleg windings and the outer leg windings, respectively. RC

and RO are the reluctance of the center leg and the outerlegs, respectively. The two outer legs are designed to havethe same reluctance RO according to the designing conceptof the proposed structure. We denote the electric charge thatflows through the winding A and B as q1 and q2, respectively.Then, translating Fig. 2 yields the following Lagrangian L:

L = NOq̇1φ1 + NOq̇2φ3 − NCq̇1φ2 − NCq̇2φ2

− ROφ12/2 − RCφ2

2/2 − ROφ32/2

+ λ (φ1 + φ2 + φ3) , · · · · · · · · · · · · · · · · · · · · · · · · · (3)

where λ is a Lagrangian multiplier; φ1, φ2, and φ3 are thefluxes of the left outer leg, the center leg, and the right outerleg, respectively. A dot over a variable indicates its timederivative.

The Lagrangian multiplier can be eliminated by substitut-ing φ3 = −φ1 − φ2 into (3). Then, we have

L = NOq̇1φ1 − NOq̇2 (φ1 + φ2) − NCq̇1φ2 − NCq̇2φ2

− ROφ12/2−RCφ2

2/2−RO (φ1+φ2) 2/2. · · · · · (4)

Next, we apply a point transformation to the result. Thepurpose of this transformation is to convert the magnetic en-ergy terms in (4), i.e. the fifth, sixth, and seventh terms, intoa diagonal form of the fluxes. Then, the resultant Lagrangiancorresponds to a circuit of magnetic components each made

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Integrated Differential-Mode and Common-Mode Inductors（Kazuhiro Umetani et al.）

Fig. 3. Equivalent circuit of the proposed structure

of a single closed magnetic path. Introducing a flux φA de-fined as φA = φ1 + φ2/2 to eliminate φ1, we obtain

L = NO (q̇1 − q̇2) φA − (NC + NO/2) (q̇1 + q̇2) φ2

− ROφA2 − (RC + RO/2) φ2

2/2. · · · · · · · · · · · · · · (5)

Lagrangian obtained in (5) can be translated into a seriesconnection of discrete DM and CM inductors as illustratedin Fig. 3. The flux φ2 constitutes a DM inductor that has twowindings with the number of turns NC + NO/2, whereas φA

constitutes a CM inductor that has two windings with thenumber of turns NO. Note that NC = 0 corresponds to theconventional structure. Because NC = 0 in Fig. 3 gives theequivalent circuit for the conventional structure, the numberof turns on its equivalent DM inductor equals to only half ofthe total number of turns on the conventional structure. Thus,the proposed structure increases the number of turns on theDM inductor by 2NC by adding two windings with the num-ber of turns NC . On the other hand, it keeps the number ofturns on the CM inductor unchanged.2.2 Merits and Drawbacks Now, we examine

whether the proposed structure allows its equivalent DM in-ductor to have greater number of turns than the conventionalstructure. For this purpose, we compare the number of turnson the equivalent DM inductor between the proposed andconventional structures under the same total wire length andthe same core dimensions.

First, we investigate the wire length per turn on the cen-ter and outer legs. As we have seen in the previous subsec-tion, the flux through the center leg φ2 corresponds to the fluxof the DM inductor. On the other hand, the relations φ1 =

φA−φ2/2 and φ3 = −φA−φ2/2 indicate that the fluxes throughthe outer legs are the sum of the flux of the CM inductor andhalf the flux of the DM inductor. Hence, the cross-sectionalarea AO of the outer leg should be designed at least greaterthan half the cross-sectional area AC of the center leg. Ac-cordingly, we have

AC ≤ 2AO. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (6)

If we assume the same cross-sectional shape among thecenter and outer legs, we obtain the following relation be-tween the perimeter lC of the center leg and the perimeter lOof the outer leg using the fact that the perimeter is propor-tional to the square root of the cross-sectional area:

lC ≤√

2lO,

∴ lC < 2lO. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (7)

Equation (7) shows that one turn on the center leg is shorterthan two turns on the outer legs. On the other hand, oneturn on the center leg is equivalent in the DM inductor in

Fig. 3 to two turns on the outer leg. Therefore, the proposedstructure can equip its DM inductor with the same number ofturns using shorter wire than the conventional structure. Inother words, the proposed structure can equip the DM induc-tor with a greater number of turns under the same total wirelength.

This indicates that the proposed structure can effectivelysuppress the DC flux induced by the DC component in theDM current. Because the DC flux flows in both the centerand outer legs, excessive DC flux increases not only RC butalso RO, causing saturation of both the DM and CM induc-tance. Hence, the proposed structure can suppress saturationof both the DM and CM inductance, thus avoiding the cen-ter and outer legs from being designed with expanded cross-section to ensure necessary tolerance to saturation.

On the other hand, the proposed structure has smaller num-ber of turns on the outer legs than the conventional structureunder the same total wire length. Therefore, the proposedstructure has a drawback that its equivalent CM inductor has asmaller number of turns than the conventional structure. Thisindicates that the proposed structure requires smaller RO inorder to keep the same CM inductance as the conventionalstructure.

If reducing RO inevitably requires for expanding the cross-section of the outer legs, for example when we cannot employa core material with higher permeability, the proposed struc-ture may not lead to effective reduction in the core volume.However, the proposed structure can offer effective core re-duction in other conditions, for example when designing nec-essary tolerance to the DC flux determines the cross-sectionalarea rather than designing necessary value for RO. We presenta case study to estimate the core reduction effect under thiscondition in Sect. 4.

3. Experiment

The purpose of this section is to confirm experimentallythe operating principles of the proposed structure. The ex-periment evaluated the following two subjects. One is thefunctional equivalence of the proposed structure to the dis-crete DM and CM inductors. The other is miniaturization ofthe discrete inductors by the magnetic integration using theproposed structure.3.1 Prototypes We developed two prototypes pro-

viding the DM and CM inductance under the same require-ment specifications presented in Table 1. One is the proposedstructure; and the other is the series-connected discrete DMand CM inductors. These specifications were designed as apart of an input filter of a PFC converter, whose maximuminput AC current was set at 16 Arms. In this application,the input current has the frequency far lower than the DMnoise. Hence, the input current can be regarded as the DCcomponent in the DM current. We specified the DM and CMinductance at the instantaneous input current of 16 A. In ad-dition, we required the saturation current of the DM and CMinductance to be greater than the maximum instantaneous in-put current, i.e. 22.5 A.

Both prototypes were made of ferrite cores with similarpermeability and saturation flux density. The prototype ofthe proposed structure is made of PC40 (TDK Corporation),whereas that of the discrete inductors is made of PC47 (TDK

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Integrated Differential-Mode and Common-Mode Inductors（Kazuhiro Umetani et al.）

Table 1. Requirement specifications and evaluation re-sults of the prototypes

Fig. 4. Physical structure of the prototype of the pro-posed structure

(a) (b)

Fig. 5. Photographs of the prototype of the proposedstructure. (a) Front side (b) Rear side

Corporation). PC40 and PC47 have the typical relative per-meability of 2300 and 2400, respectively; and they have thesaturation flux density of 510 mT and 530 mT, respectively.We designed these prototypes to have the same vertical di-mension and the same average height so that the horizontaldimension reflects the volume.

Figure 4 illustrates the physical structure of the prototypeof the proposed structure. In the prototype, we placed theflattened center leg in the front side and the outer legs in therear side. This disposition is beneficial in enhancing the CMinductance by minimizing flux path length through the twoouter legs. Additionally, for easy assembly, we installed twogaps in the top and bottom beams near the center leg, respec-tively, to provide the reluctance RC (corresponding to the gapon the center leg in Fig. 1). Contrarily, we installed no gapon the outer legs. The photographs of the prototype are pre-sented in Fig. 5.

The cross-sectional area of the center leg was designed so

Fig. 6. Photograph of the prototype of the discrete in-ductors

that the maximum instantaneous input current approximatelyinduces the saturation flux density there. Meanwhile, we de-signed the cross-sectional area of the outer leg 1.19 times asgreat as that of the center leg. Because the DC flux in theouter leg is half of that in the center leg, the DC flux den-sity in the outer leg does not exceed 42% of the saturationflux density. Hence, the outer leg was designed with suffi-cient margin of the DC flux to suppress the CM inductancedecrease.

On the other hand, the prototype of the discrete inductorswas made of two basic PQ cores, as shown in Fig. 6. Wedesigned wire of their windings to have the similar cross-sectional area as the prototype of the proposed structure. Inaddition, we designed this prototype to have similar DC re-sistance as the prototype of the proposed structure, as shownin Table 1.3.2 Functional Equivalence Between the PrototypesWe confirmed that the proposed structure is functionally

equivalent to series-connected discrete inductors by eval-uating conversion ratios between DM and CM noise, i.e.CM voltage response to DM noise excitation and DM volt-age response to CM noise excitation. The conversion ratiosmust vanish in series-connected ideal DM and CM inductors.Hence, we need to verify that the prototype of the proposedstructure shows as small conversion ratios as the prototype ofthe discrete inductors.

Evaluation circuits of the conversion ratios are presented inFig. 7. We connected the windings A and B in series as shownin Fig. 7(a) and Fig. 7(b). Then, we applied AC voltage sig-nal with the amplitude of ±5 Vpeak to the series-connectedwindings.

Now, we express the voltage induced in each winding us-ing the DM voltage VDM and the CM voltage VCM. If wedenote the induced voltage in the winding A and B as VA andVB, respectively, we have{

VA = VCM + VDM ,VB = VCM − VDM .

· · · · · · · · · · · · · · · · · · · · · · · · · · · (8)

Note that the AC signal voltage corresponds to VA − VB,i.e. 2VDM , in Fig. 7(a) and to VA + VB, i.e. 2VCM, in Fig. 7(b).Hence, the AC signal is a DM voltage source that excites DMnoise current in Fig. 7(a) and a CM voltage source that excitesCM noise current in Fig. 7(b).

We connected the midpoint between the terminals of the

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Integrated Differential-Mode and Common-Mode Inductors（Kazuhiro Umetani et al.）

(a)

(b)

Fig. 7. Evalution circuits of the conversion ratios be-tween DM and CM noise. (a) Evaluation of CM noiseresponse to DM noise excitation (b) Evaluation of DMnoise response to CM noise excitation

(a)

(b)

Fig. 8. Measured conversion ratios. (a) Ratio of CMnoise response to DM noise excitation (b) Ratio of DMnoise response to CM noise excitation

AC signal to the ground. Then, we measured the voltage po-tential at the connecting point of the windings A and B. Themeasured voltage represents the CM voltage response −VCM

in Fig. 7(a) and the DM voltage response −VDM in Fig. 7(b).We obtained the conversion ratios by normalizing the ampli-tude of the measured voltage by half the amplitude of theAC signal voltage. The normalized voltage in Fig. 7(a) cor-responds to the ratio of CM noise response to DM noise ex-citation, and that in Fig. 7(b) corresponds to the ratio of DMnoise response to CM noise excitation.

We examined the conversion ratios in the frequency rangebelow 500 kHz because the dimensional resonance may dete-riorate the soft-magnetic property of the ferrite core above thefrequency. Figure 8 shows the results. The ratios of the pro-posed structure were found approximately as small as thoseof the discrete inductors. Both the prototypes showed the

(a)

(b)

Fig. 9. Method to evaluate the DM inductance and theDM saturation current. (a) Evaluation circuit (b) Voltageand current waveforms in the evaluation process

ratio of CM noise response smaller than 7% and the ratio ofDM noise response smaller than 1% below 500 kHz.

Consequently, we concluded that the two prototypes areapproximately equivalent each to the other in their electricalfunctions, as expected from the theory.3.3 DM and CM Filtering Capability Next, we con-

firmed that the two prototypes have similar filtering capabil-ity by evaluating the DM and CM inductance as well as theDM and CM saturation current. The evaluation methods areas follows.

Figure 9 illustrates the evaluation circuit of the DM induc-tance and the DM saturation current. The windings A and Bwere connected in series in a similar manner as in Fig. 7(a).Therefore, DM voltage was applied to the prototype duringthe on-state of the switch S1. We held S1 in the on-stateuntil the DM current sufficiently saturated the prototype. Atthe same time, we measured the applied voltage VCOIL andthe DM current ICOIL. The current ICOIL increased mono-tonically during the on-state of S1 as illustrated in Fig. 9(b).Hence, we obtained the DM inductance LDM as the differen-tial inductance (12) defined by

LDM =VCOIL

dICOIL/dt, · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (9)

where t is the time. The DM inductance LDM can be obtainedas a function of ICOIL. The DM saturation current is the DMcurrent ICOIL when LDM decreases to 75% of its value at ICOIL

= 0 A.The method to evaluate the CM inductance is slightly more

complicated than the method for the DM inductance. Fig-ure 10(a) illustrates the evaluation circuit. In this experiment,we further connected the capacitor C1 with the capacitanceof 1 nF between the ground and the connecting point of thewindings A and B. Then, we held the switch S1 in the on-stateuntil the DM current increased to the predetermined level IDC

as illustrated in Fig. 10(b). After the turn-off of S1, the DMcurrent circulated through the diode D1. The circulating DMcurrent maintained itself for a while because no DM voltagewas applied to the prototype.

At the same time, an LC oscillation occurred between thecapacitor C1 and the prototype. This oscillation was excited

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Integrated Differential-Mode and Common-Mode Inductors（Kazuhiro Umetani et al.）

(a)

(b)

Fig. 10. Method to evaluate the CM inductance and theCM saturation current. (a) Evaluation circuit (b) Voltageand current waveforms in the evaluation process

at the turn-off of S1, because the voltage VC of the capacitorC1 was approximately half of the supply voltage of 15 V atthe turn-off of S1 and then VC was going to settle finally tozero as the oscillation was dissipated. As a result, the volt-age and current waveforms can be illustrated as Fig. 10(b).Note that the voltage VC equals to the CM voltage VCM ofthe prototype when the DM current circulates through D1.Therefore, this oscillation corresponds to the LC oscillationbetween C1 and the CM inductance LCM of the prototype.Hence, we obtained LCM according to

LCM =1

C1ωOS C2, · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (10)

where C1 is the capacitance of C1 and ωOS C is the angularfrequency of the oscillation. The CM inductance LCM can beobtained as a function of IDC by determining LCM at variouslevels of IDC . The CM saturation current is the DM currentIDC when LCM decreases to 75% of its value at IDC = 0 A.

The measurement results of LDM and LCM are presentedin Fig. 11. As summarized in Table 1, evaluation results ofboth the prototypes met the requirement specifications. Theyshowed approximately the same DM and CM inductance. Onthe other hand, the proposed structure showed slightly betterDM saturation current than the discrete inductors. As for sat-uration of the CM inductance, only the proposed structurehas the saturation current because the discrete CM inductordoes not saturate by the DM current. Nonetheless, the pro-posed structure showed CM saturation current far above therequirement specification.

Consequently, the prototypes are confirmed to have similarfiltering capability.3.4 Comparison of the Volume Finally, we com-

pared the volume between the prototypes. The result is shownin Fig. 12. Because the prototypes have the same vertical di-mension and the same average height, the horizontal dimen-sion reflects the total volume including the dead space. Com-paring the horizontal dimension between the prototypes, wefound that the proposed structure reduced the total volume by31%.

(a)

(b)

Fig. 11. Measurement results of (a) the DM inductanceLDM and (b) the CM inductance LCM

Fig. 12. Comparison of the volume between the proto-types. (a) Proposed structure (b) Discrete inductors

This reduction effect was contributed not only by eliminat-ing dead space but also by reducing the core. According tocomparison of the net core volume, we found that the pro-posed structure also reduced the core volume by 17%. Con-sequently, we concluded that the proposed structure success-fully miniaturized the discrete inductors.

4. Core Reduction Effect of Suppressing DC Flux

This section analytically estimates the core reduction ef-fect of the proposed structure in comparison with the con-ventional structure shown in Fig. 1(b). For this purpose, weestimates the core dimensions of the conventional structure,when the same specifications as Table 1 is applied and thesame physical core structure as Fig. 4 is employed. We de-termine the core dimensions of the conventional structure bymodifying the prototype of the proposed structure discussedin the previous section. Then, we compare the core volumebetween the estimated conventional structure and the proto-type of the proposed structure.

When estimating the conventional structure, we set the to-tal wire length the same as the prototype of the proposedstructure. Hence, the DC resistance can be kept the samewithout expanding the cross-section of the wire. On the otherhand, we expand the cross-section of magnetic paths to keep

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Integrated Differential-Mode and Common-Mode Inductors（Kazuhiro Umetani et al.）

the DM and CM saturation current the same as the prototypeof the proposed structure. For convenience, we assume thesame cross-sectional shapes of the center and outer legs asthe prototype of the proposed structure, when we expand thecross-section. In addition, we adjust RC and RO to keep theDM and CM inductance the same as the prototype of the pro-posed structure. When we adjust RO, we change the perme-ability of the core material while keeping the saturation fluxdensity unchanged. As for adjusting RC , we assume that re-luctance of the air gaps mainly contributes RC and we adjustthe gap length to obtain appropriate value for RC .

In the first step, we compose the conventional structure di-rectly on the magnetic core employed in the prototype of theproposed structure. Because the total wire length is kept un-changed, this conventional structure has the outer leg wind-ings with the number of turns NO temp set at 16.

Next, we expand the cross-section of the magnetic core.We assume to enlarge the cross-sectional area of the outerleg by a factor α. Then, the number of turns NO mod of theouter leg windings after this modification should be changedaccording to (11) because the perimeter of the cross-sectionis expanded by

√α.

NO mod = NO temp/√α = 16/

√α. · · · · · · · · · · · · · · · (11)

In order to estimate α that provides the same CM saturationcurrent as the proposed structure, we consider the DC flux inφ2 when the DC component in the DM current equals to theCM saturation current. We denote the DC flux in the ex-panded core at the CM saturation current as φ2 mod, and thatin the prototype of the proposed structure as φ2 org. Becausewe require the same DM inductance LDM and the same CMsaturation current, we have the following relation accordingto (2) and Fig. 3:

φ2 mod

φ2 org=

2NC org + NO org

NO mod=

20NO mod

, · · · · · · · · · · (12)

where NC org and NO org are the numbers of turns of the cen-ter leg windings and the outer leg windings in the prototypeof the proposed structure, respectively.

Because the reluctance RO determines the CM inductance,increase rate of RO at the CM saturation current must be thesame as the prototype of the proposed structure in order to ac-complish the same CM saturation current. Accordingly, theDC flux density in the outer legs at the CM saturation cur-rent must be designed to be the same as the prototype of theproposed structure. Hence, we have

α =φ2 mod

φ2 org. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13)

Equations (11)–(13) determine α and NO mod:

α ≈ 1.56, NO mod ≈ 13. · · · · · · · · · · · · · · · · · · · · · · · (14)

The DC flux density in the center leg at the DM saturationcurrent must also be designed to be the same as the prototypeof the proposed structure in order to accomplish the sameDM saturation current. As a result, we also need to expandthe cross-section of the center leg by α, according to similardiscussion to obtain (13). In addition, we need to expand thecross-section of the top and bottom beams by α because the

(a) (b)

Fig. 13. Top view of (a) the core in the prototype of theproposed structure and (b) the estimated core of the con-ventional structure. The solid lines illustrate the outlineof the top beam core; and the dotted lines illustrate theoutline of the center and outer legs

DC flux also flows through the beams.The above discussion also determines the gap length at the

top and bottom beams of the estimated core of the conven-tional structure. Let lg mod and lg org be the gap length of theestimated core and the proposed structure, respectively. Ap-plying Ampere’s law to the closed flux path passing throughthe center leg and one of the outer legs, we obtain the follow-ing equation:

2Bsat

μglg org =

(2NC org + NO org

)Isat, · · · · · · · · · · · (15)

2Bsat

μglg mod = NO modIsat, · · · · · · · · · · · · · · · · · · · · · · (16)

where Bsat is the DC flux density at the DM saturation currentIsat, and μg is the absolute permeability of the gap material.From (15) and (16), we obtain:

lg mod

lg org=

NO mod

2NC org + NO org=

1320. · · · · · · · · · · · · · · · (17)

Substituting lg org = 0.0014 m into (17), we obtain lg mod:

lg mod ≈ 0.00091. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (18)

Finally, we obtain the estimation result of the core dimen-sions as shown in Fig. 13. If we assume the height of thelegs the same as the prototype of the proposed structure, thenet core volume of the conventional structure is estimated as3.5× 104 mm3. On the other hand, the net core volume of theproposed structure is 2.0 × 104 mm3. Consequently, the pro-posed structure is found to reduce the core volume by 41%compared to the conventional structure.

5. Conclusions

The magnetic integration is an attractive technique tominiaturize EMC filters. Prior works have reported EMCfilters that applied this technique to integrate a DM induc-tor and a CM inductor. However, the conventional magneticstructure employed in these works can often suffer from themagnetic saturation of the DM or CM inductance, becausethe equivalent number of turns for the DM inductance is re-stricted to only half of the total number of turns and it can beinsufficient to suppress DC flux induction. This may lead toexpanding the cross-section of magnetic paths to ensure nec-essary tolerance to the magnetic saturation, thus hinderingthe miniaturization effect of the magnetic integration.

To address the problem, this paper proposed a novel struc-ture that allows assigning more turns to the DM inductance

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Integrated Differential-Mode and Common-Mode Inductors（Kazuhiro Umetani et al.）

than the conventional structure. We confirmed that the pro-posed structure is equivalent to series-connected discrete DMand CM inductors both theoretically and experimentally. Fur-thermore, we confirmed experimentally that the proposedstructure can miniaturize the discrete DM and CM inductors.

An analytical estimation was carried out to evaluate corereduction effect of the proposed structure in comparison withthe conventional structure. The result revealed that the pro-posed structure reduced the core volume by 41% under thesame total wire length and under the same specifications, inwhich saturation by the DC flux is a determining factor in thecross-sectional area of magnetic paths.

These results demonstrate effectiveness of the proposedstructure for miniaturizing EMC filters.

References

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Kazuhiro Umetani (Member) was born at Kobe, Japan in 1980. Hereceived the Ph.D. degree in geophysical fluid dy-namics in Kyoto University, Japan. From 2007 to2008, he was a circuit design engineer at Toshiba,Japan. From 2008 to 2014, he was with power elec-tronics group in DENSO CORPORATION, Japan.He is currently an assistant professor at OkayamaUniversity, Japan. His research interests include newcircuit configurations in power electronics and powermagnetics for vehicular applications.

Takahiro Tera (Member) was born at Saitama, Japan in 1981. Hereceived the B.S. and M.S. degrees in electrical en-gineering from Tokyo University of Science, Tokyo,Japan in 2004 and 2006, respectively. Since 2006, hehas been working as a research engineer at DENSOCORPORATION, Japan. His research interests in-clude power electronics, power converters deign, andmagnetic components design.

Kazuhiro Shirakawa (Member) received the B.S. and M.S. degreesin electrical engineering from Tokyo MetropolitanUniversity, Tokyo, Japan in 2003 and 2007, respec-tively. Since 2007, he has been with DENSO COR-PORATION, Japan as a power electronics engineer,where his main responsibility is to develop powerconversion circuits for automotive. His research in-terests include EMI design and high-frequency tech-nique.

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