Magnetic Analysis, Design, and Experimental Evaluations of ...

IEEJ Journal of Industry ApplicationsVol.5 No.3 pp.276–288 DOI: 10.1541/ieejjia.5.276

Paper

Magnetic Analysis, Design, and Experimental Evaluationsof Integrated Winding Coupled Inductors in Interleaved Converters

Jun Imaoka∗ Member, Kazuhiro Umetani∗∗ Member

Shota Kimura∗ Student Member, Willmar Martinez∗ Student Member

Masayoshi Yamamoto∗ Member, Seikoh Arimura∗∗∗ Non-member

Tetsuo Hirano∗∗∗ Non-member

(Manuscript received July 21, 2015, revised Dec. 25, 2015)

Integrated magnetic components for interleaved converters have been developed in order to fulfill the demand forhigh power density and high efficiency in power conversion systems. The close-coupled inductor and the loosely cou-pled inductor methods for interleaved converters are well known as attractive techniques to downsize magnetic compo-nents or improve the power conversion efficiency. Moreover, the integrated winding coupled inductor has already beenproposed. However, the advantages of the interleaved converter with the integrated winding coupled inductor over theother methods have not been fully elucidated. Consequently, this paper analyzes and evaluates the integrated wind-ing coupled inductor, specifically, the characteristics of the inductor ripple current and the magnetic flux in the core.The analysis shows that the integrated winding coupled inductor provides attractive features compared with the othermethods. The effectiveness of the integrated winding coupled inductor is discussed from theoretical and experimentalpoints of view.

Keywords: integrated winding coupled inductor, interleaved converter, high power density

1. Introduction

In order to reduce the energy consumption and decreasethe use of metal resources for inductors and transformers inpower converters (1), high-power density and high-efficiencyinterleaved power converters have been required in vari-ous industries; such as renewable energies (2)–(4), automotivedrives (5)–(8), railway applications (9), power supply for digitalequipment (10)–(13), electric home applications (14)–(17), etc. In thiscontext, interleaved circuit topology is widely applied be-cause this topology can distribute the power losses and thethermal stresses of each active/passive device by dividing theinput current into each phase and allowing the use of smallcapacitances for the smoothing capacitor (17)–(19).

Moreover, magnetic design techniques for interleaved con-verters are also one of the important key factors to realize fur-ther high-power-density, high efficiency or performance im-provement. Several design methods of magnetic componentsfor interleaved power converters have been proposed from theviewpoints of winding connection, magnetic integration andwinding arrangements.

In the case of the connection techniques of interleaved con-verters, a three-phase interleaved isolated half (or full) bridge

∗ Shimane University1060, Nishikawatsu, Matsue, Shimane 690-8504, Japan

∗∗ Okayama University3-1-1, Tsushimanaka, Okayama, Kita-ku, Okayama 700-0082,Japan

∗∗∗ DENSO CORPORATION1-1, Syowa, Kariya, Aichi 448-8661, Japan

LLC resonant converters with Y connected windings on theprimary or secondary side are proposed to balance the powertransmission of each phase (20) (21). By these winding connec-tions, the problems of unbalanced resonant currents, causedby the unbalanced resonant tank gain and the parasitic resis-tance of power devices in each phase, are solved.

Additionally, magnetic integration techniques for inter-leaved converters have gained attention due to its attractivefeatures. Usually, integrated magnetic components, consistedof multiple windings installed on a single magnetic core, areknown as effective to miniaturize magnetic components onthe basis of the following reasons:

1) DC fluxes generated by DC current can be canceled bythe inversely magnetic coupling of the phase windings. Thus,the sectional area of a magnetic core can be miniaturized un-der the same maximum flux density compared with the con-ventional non-coupled method.

2) AC fluxes can be shared between the multiple phases ofthe transformer. Accordingly, it is possible to partially reducethe peak-peak magnetic flux.

3) Due to the mutual induction, the inductor ripple currentis affected by the other phase current. Therefore, the inductorripple current is affected not only the switching condition ofthe own phase, but also the switching conditions of the otherphases. Therefore, the inductor current of the integrated mag-netic components presents a higher frequency in comparisonwith converters with non-coupled inductors.

For these reasons, integrated magnetic components havebeen applied to several interleaved topologies including iso-lated and non-isolated converters (22)–(29).

c© 2016 The Institute of Electrical Engineers of Japan. 276

Interleaved Converter with Integrated Winding Coupled Inductor（Jun Imaoka et al.）

(a) CCI method (b) LCI method

Fig. 1. Configuration of integrated magnetic compo-nents in the two phase interleaved converter

In case of two-phase interleaved boost converters, inte-grated magnetic components are mainly classified into twomethods: Close-Coupled Inductor (CCI) and Loosely Cou-pled Inductor methods (LCI). The CCI method shown inFig. 1(a) is known as one of the good approaches that are di-vided into a transformer and an inductor (5) (6). Advantages ofthis method come out by the proper core material selectionon inductors for energy storage and transformers. However,this method requires two magnetic components in the case oftwo phase interleaved converters.

On the other hand, Loosely Coupled Inductors (LCI)which integrate a transformer and an inductor are proposedin (7) (9) (11)–(15) (22) (27). The LCI method is shown in Fig. 1(b). Theadvantages of this method are: only one magnetic core isneeded; and a thermal equilibrium between the transformerand the inductor is easy to achieve because these magneticcomponents are integrated. This feature of thermal equi-librium contributes to reduce the time of design and ther-mal evaluation because in the CCI case, the temperaturerise of the inductor and the close-coupled inductor must bechecked. In addition, the concern for the magnetic core struc-ture of the LCI is increasing in recent years. For example,a low-profile coupled inductor (11) is suitable for the three-dimensional structural circuit, or a multilayered coupled chipinductor is suitable for small converter such as point of loadapplication (13). Furthermore, EIE core structure for gettingany coupling coefficient (22); split-winding structure for reduc-ing parasitic capacitance between windings (7); and air-corecoupled inductor suitable for high power application havebeen reported (9).

In addition, the Integrated Winding Coupled Inductor(IWCI) has already been proposed (8) (16). This coupled induc-tor has three windings installed in a single core, and it hassome magnetic coupling including inversely and directly cou-plings. However, the fundamental characteristics and the ad-vantages of this method are still unclear in comparison withthe other integrated magnetic methods.

In order to clarify the advantages of the IWCI, the inter-leaved converter with IWCI is analyzed and evaluated fromthe electrical and magnetic viewpoints. As a result of thisanalysis, the IWCI method can reduce the inductance valueand the total number of winding turns, as well as, miniatur-ize the sectional area of the core in comparison with the LCI.Additionally, we propose the design method for the IWCI,and evaluate the downsizing performance of the core consid-ering the current density of the windings and the flux densityof the core. The validity of these results is discussed from thetheoretical and experimental viewpoints.

Fig. 2. Circuit configuration of the interleaved boostconverter with integrated winding coupled inductor

Fig. 3. Winding arrangement and magnetic core struc-ture of the IWCI

2. Magnetic Structure of the Integrated WindingCoupled Inductor

The circuit configuration of the interleaved converter withIWCI is shown in Fig. 2. Where Vi and Vo are the input andoutput voltage, respectively; iL1, iL2 and iin are the inductorcurrent of each phase and the input current respectively; Co

is the output smoothing capacitor; D1 and D2 are the out-put diodes; S1 and S2 are the main switches. S1 and S2 areswitched with a 180◦ phase shift and operate as the same dutyratio.

Regarding the IWCI, the magnetic core structure and thewinding arrangement are described in Fig. 3. This coupledinductor has three windings, one in the central leg and two inthe outer legs of EI or EE cores. The input current iin and theinductor currents iL1, iL2 flow into the central winding N1 andthe two outer windings N2, respectively. There is an inverselymagnetic coupling between each outer winding N2, and it is adirectly coupling between the outer winding N2 and the cen-tral windings N1. In the circuit diagram, L1 and L2 show theself-inductances on N1 and N2, respectively. M1 and M2 arethe mutual inductances among N1 and N2, and between eachN2, respectively. In this way, several magnetic couplings oc-cur in the cores. By the additional central winding, the to-tal number of winding turns can be reduced in comparisonwith the LCI because both phases can share the current inthe central winding. Regarding the magnetic core structure,an air gap for storing energy and reducing DC fluxes is notinstalled on the outer legs, in order to obtain high mutual in-ductance M2. High mutual inductance M2 is effective for re-ducing the inductor ripple currents because this inductanceshows the current sharing performance between each phaseinductor ripple current. In addition, the DC flux generatedby the inductor average currents in N2 is effectively canceledby the inversely coupling between the outer windings even ifthere are no air gaps in the outer legs. Due to this effect, thesectional area of the core can be miniaturized. From thesefeatures, the reduction of the inductor ripple current and thedownsizing magnetic components can be achieved.

277 IEEJ Journal IA, Vol.5, No.3, 2016


Table 1. Analysis result of the relationship between the inductor ripple current and each inductance

Fig. 4. The concept of separation of the inductor currentcomponents

3. Electrical Characteristic Analysis

In this section, the electrical characteristics are investigatedto show the effectiveness of the IWCI. In this paper, theelectrical characteristics are analyzed focusing on Continu-ous Current Mode (CCM) condition. This is because mag-netic components are usually designed at maximum ratings,and Discontinuous Current Mode (DCM) are not effective inhigh power application because conduction losses rather in-crease (14). Therefore, the characteristics of IWCI are analyzedunder CCM condition.

3.1 Modeling of Inductor Ripple Current First ofall, the relationship between the inductor ripple currents andeach inductance is analyzed. The relationships between theapplied voltages to the inductor windings and the slope of theinductor ripple current of each phase are given by:⎧⎪⎪⎨⎪⎪⎩

vL1 = L1d(iL1+iL2)

dt + 2M1d(iL1+iL2)

dt + L2diL1dt − M2

diL2dt

vL2 = L1d(iL1+iL2)

dt + 2M1d(iL1+iL2)

dt − M2diL1dt + L2

diL2dt

· · · · · · · · · · · · · · · · · · · · (1)

where vL1 and vL2 are the applied voltage to the phase wind-ings between the input terminal of the central winding andone of the output terminals of the outer windings as shown inFig. 3. The applied voltage varies depending on the operat-ing modes; and there are four operating modes in all rangesof duty ratio. Thus, the inductor ripple current is analyzedfor each operating mode, respectively. The definition of theoperating modes and the analysis results in relation to the in-ductor ripple currents are shown in Table 1.

As seen in Eqs. (2)–(5), the inductor currents iL1, iL2 canbe separated in a common current icom and a wheeling modecurrent iwh as shown in Fig. 4. Furthermore, inductor currentsiL1 and iL2 are shown as icom and iwh that are defined by thefollowing equations on the basis of Eqs. (2)–(5):⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎩

diL1dt =

dicomdt +

diwhdt

diL2dt =

dicomdt − diwh

dtdicom

dt =1

(2L1+L2+4M1−M2) ·(Vi − (sl1 + sl2) · Vo

2

)diwhdt =

1(L2+M2) · (sl2 − sl1) · Vo

2

· · · (6)

(a) d ≤ 0.5

(b) d > 0.5

Fig. 5. Inductor current waveforms of the integratedwinding coupled inductor

where sl1 and sl2 are logic functions that indicate the switch-ing conditions of S1 and S2, respectively. The following de-fines sl1 and sl2:{

sl1 = 0 (S1: ON) , sl1 = 1 (S1: OFF)sl2 = 0 (S2: ON) , sl2 = 1 (S2: OFF)

· · · · · · · · · (7)

Based on (6), Figs. 5(a) and (b) illustrate the inductor cur-rent waveforms for duty ratios lower and greater than 0.5,respectively. As seen in these figures, the inductor current iL1

can be expressed as the sum of icom and iwh. On the otherhand, iL2 can be expressed as the difference of the icom andiwh. The mutual inductances M1 and M2 are understood from(6) that these are effective for reducing ripple current of icom

and iwh, respectively.Then, in order to investigate the low inductance charac-

teristics of the IWCI, the inductances related to each currentcomponent are compared with the CCI and the LCI methods.The comparison results of the inductances related to each cur-rent component in cases of each magnetic coupling method



Table 2. Inductances related to each current component

are summarized in Table 2. In this table, Licom and Liwh

show the inductances related to icom and iwh, respectively.Due to the additional central winding, the ripple current oficom rather decreases because the mutual inductance M1 (be-tween N1 and N2) influences with a factor of four. Therefore,if these magnetic coupling methods are designed under thesame condition of inductor ripple current, the inductance ofthe integrated winding coupled inductor can be reduced incomparison to other methods. Furthermore, higher mutualinductance M2 is effective for higher frequency operation ofinductor current because iwh is significantly reduced.

Based on the above results, the peak-to-peak amplitude ofthe ripple current is theoretically derived. The design of rip-ple current is important in order to decide the load range ofthe Continuous Current Mode (CCM), and it is also one ofthe factors to decide power losses in power device and pas-sive components.

As seen in Figs. 5(a), (b), the peak-peak amplitude of theripple current of phase 1 is shown in mode 1 (S1: ON, S2:OFF) in the range of d ≤0.5. On the other hand, in the rangeof d > 0.5, the ripple current is shown in mode 2 (S1: OFF,S2: ON). Therefore, if the transition time of these modes, dtshown in Figs. 5(a), (b) and the voltage gain between inputand output voltage Vo = (1/1 − d)Vi are substituted into theEq. (6), the peak-peak amplitude of the inductor ripple cur-rent is obtained as:

ILpp =

⎧⎪⎪⎨⎪⎪⎩(

1Licom·(

1−2d2·(1−d)

)+ 1

Liwh· 1

2·(1−d)

)· Vi · d · Ts [d ≤ 0.5](

1Licom·(

2d−12d

)+ 1

Liwh· 1

2d

)· Vi · d · Ts [d > 0.5]

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

where d is the duty ratio, and Ts is the switching period. If wesubstitute the value of Licom and Liwh into (8), inductor ripplecurrent can be derived by each magnetic coupling method.

3.2 Derivation of Equivalent Circuit Model Theequivalent circuit model for the IWCI needs evaluation by acircuit simulation. Figure 6 shows one of the equivalent cir-cuit models for the IWCI. The validity of this equivalent cir-cuit model had already been proven by both the Lagrangianmethod based on the analytical dynamics and the inductancematrix method (29). The equivalent circuit is composed of twotransformers connected by directly coupling, and a trans-former connected by inversely coupling and three parasiticleakage inductances. In the equivalent circuit model, eachinductance is defined as follows:

Llk1: the parasitic leakage inductances of the central wind-ing N1.

Llk2: the parasitic leakage inductances of the outer wind-ings N2.

Lm1: the magnetizing inductance between N1 and each N2.M2(Lm2): the mutual inductance between N2 and other

Fig. 6. An equivalent circuit model for the IWCI

Table 3. Evaluation circuit parameters

Table 4. Evaluation magnetic parameters

phase N2.Due to the symmetry between the outer windings, the magne-tizing inductance Lm2 is equal to the mutual inductance M2.In addition, each inductance has the following relationships.⎧⎪⎪⎪⎨⎪⎪⎪⎩

L1 = Llk1 + 2Lm1

L2 = Llk2 + (N2/N1)2 · Lm1 + M2

M1 = (N2/N1) · Lm1

· · · · · · · · · · · · · · · (9)

From the equivalent circuit model shown in Fig. 6 and Eq. (9),the circuit simulation can be carried out.

3.3 Experimental Evaluation to Confirm the Resultsof the Electrical Analysis In order to verify the theo-retical analysis of the inductor ripple current and the equiva-lent circuit model of the IWCI, an experimental evaluation ofthe interleaved boost converter with the prototype of IWCIis conducted. Tables 3 and 4 show the circuit parametersand the magnetic parameters of the prototype, respectively.



Fig. 7. Comparison results regarding the inductor ripplecurrent among the simulated value, the theoretical value,and the measured value

(a) Experimental waveforms (b) Simulated waveforms

Fig. 8. Inductor current waveforms in phase 1 (d = 0.8)

The output voltage is fixed at 200 V. The input voltage is var-ied between 20 V–180 V to investigate the duty ratio influ-ence. Figure 7 shows the comparison result of the inductorripple current among the simulated, the theoretical and themeasured values. As seen in Fig. 7, the theoretical value andthe simulated value are identical with the measured value. Inaddition, the experimental waveforms except for the currentsurge are consistent with the simulated waveforms as shownin Fig. 8. The measured and the theoretical values are con-sistent with 95% on average. Therefore, the analysis of theinductor ripple current and the equivalent circuit model wereverified by experiment. Moreover, the inductor ripple currentcan be reduced at a duty ratio around 0.5 because the com-mon current ripples are significantly reduced. This is becausevoltages across of the two transformers with directly couplingand leakage inductor of the windings are almost zero at dutyratio 0.5 if high mutual inductance M2. Therefore, commoncurrent can be significantly reduced.

4. Magnetic Characteristic Analysis

In this section, magnetic flux characteristics of the IWCIare investigated in order to design the flux density in the core.Magnetic characteristics are analyzed using a magnetic cir-cuit model. A magnetic circuit model for the IWCI is shownin Fig. 9. Rmo is the magnetic reluctance of the outer leg ofeach phase. Rmc is the magnetic reluctance of the central leg.φo1, φo2 and φc are the magnetic fluxes in the outer leg of eachphase and the magnetic flux in the central leg, respectively.

In this magnetic model, the external leakage fluxes in eachwinding are neglected in order to simplify the discussion onthe effect of the additional central winding. The magneticfluxes in the core can be separated into DC and AC fluxes.Therefore, the magnetic flux characteristics are separately an-alyzed for each element of the flux.

Fig. 9. Magnetic circuit model for the integrated wind-ing coupled inductor

(a) Magnetic fluxes in the core (b) Flux separation concept

Fig. 10. Relationship among the applied voltage and themagnetic fluxes

4.1 Modeling of DC, AC and Maximum FluxesFirstly, DC flux generated by the inductor average currents

is analyzed. For the analysis of the DC components, the av-erage inductor current and the DC fluxes in the outer legs andthe central leg are denoted as ILave, Φo, and Φc, respectively.From the magnetic circuit model, the following relationshipscan be obtained:{

N2ILave + 2N1ILave = Φo · Rmo + Φc · Rmc

Φc = 2Φo· · · · · · (10)

Thus, the DC flux in the outer legs and central leg are givenby the following equations, respectively:

Φo =ILave · (2N1 + N2)

Rmo + 2Rmc· · · · · · · · · · · · · · · · · · · · · · · · (11)

Φc = 2Φo =2ILave · (2N1 + N2)

Rmo + 2Rmc· · · · · · · · · · · · · · · · (12)

Then, the characteristics of the AC flux are investigated.The AC flux induces a voltage on the windings, on the basisof Faraday’s law. Figure 10(a) shows the relationship be-tween the applied voltage and the direction of the magneticfluxes. From the relationship, the following state equation isobtained.

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

vL1 = N1dφc

dt+ N2

dφo1

dt

vL2 = N1dφc

dt+ N2

dφo2

dtdφc

dt=

dφo1

dt+

dφo2

dt

· · · · · · · · · · · · · · · · · · · · (13)

Substituting the inductor voltage vL1, vL2 of each operatingmode into (13) yields equations for the AC flux. As theo-retical results of Eq. (13), φo1, φo2 and φc can be separatedin the common flux φcom and the wheeling flux φwh similarlyas in the analytical result of the inductor current. φo1 is ex-pressed as the sum of φcom and φwh; and φo2 is expressed asthe difference of the φcom and φwh. These relationships canbe summarized by the following equation:



(a) LCI method

(b) CCI method

Fig. 11. Magnetic core structure and fluxes of LCImethod and CCI method

Table 5. Effective number of turns related to dφcom/dtand dφwh/dt in each integrated magnetic method

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

dφo1

dt=

dφcom

dt+

dφwh

dtdφo2

dt=

dφcom

dt− dφwh

dtdφc

dt= 2 · dφcom

dt

· · · · · · · · · · · · · · · · · · · · · (14)

In addition, dφcom/dt and dφwh/dt are expressed as:

⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩

dφcom

dt=

12N1 + N2

·(Vi − (sl1 + sl2) · Vo

2

)

dφwh

dt=

1N2· (sl2 − sl1) · Vo

2· · · · · · · · · · · · · · · · · · · (15)

According to (14)–(15), the magnetic fluxes φo1, φo2, φc andits components φcom, φwh have the flux paths illustrated inFigs. 10(a) and (b).

Then, to indicate the feature of IWCI with fewer wind-ing turns, the windings related to dφcom/dt and dφwh/dt areseparately compared with both the LCI and the CCI meth-ods shown in Figs. 11(a) and (b), respectively. The numberof winding turns related to the slopes of the common fluxdφcom/dt and the wheeling flux dφwh/dt in IWCI, LCI andCCI is summarized in Table 5. From this table, IWCI methodincreases the effective number of winding turns for dφcom/dtby the additional central winding N1 in comparison with theother methods. In addition, on the basis of the analysis re-sults, Figs. 12(a) and (b) illustrate the magnetic flux wave-forms of IWCI for a duty ratio lower and greater than 0.5respectively. These figures are derived by substituting boththe transition time of each mode, dt shown in Fig. 12 andlogic functions sl1, sl2 into the Eqs. (14) and (15). As seenin Fig. 12, the peak-to-peak amplitude of the AC flux in thecentral leg and in the outer leg of phase 1 can be obtained atmode 1 in the range of d ≤ 0.5. Similarly, the peak-to-peakamplitude of AC flux is obtained at mode 2 in case of therange of d > 0.5. Therefore, the peak-to-peak amplitude of

(a) d ≤ 0.5

(b) d > 0.5

Fig. 12. Magnetic flux waveforms of the integratedwinding coupled inductor

the AC fluxes in the central and the outer legs is obtained asfollows:

Φopp =

⎧⎪⎪⎨⎪⎪⎩N2·Vi+N1·VoN2·(2·N1+N2) · d · Ts [d ≤ 0.5](N1+N2)·Vo−N2·Vi

N2·(2·N1+N2) · (1 − d) · Ts [d > 0.5]

· · · · · · · · · · · · · · · · · · · (16)

Φcpp =

⎧⎪⎪⎨⎪⎪⎩2 Vi−Vo2·N1+N2

· d · Ts [d ≤ 0.5]Vo−2 Vi2·N1+N2

· (1 − d) · Ts [d > 0.5]· · · · · (17)

Then, the maximum fluxes in each leg are analyzed to designthe maximum flux density of the magnetic core. The maxi-mum fluxes are shown by the sum of DC flux and half of ACflux as shown in Fig. 12. Therefore, maximum fluxes can beobtained by using Eqs. (11)–(12), (16)–(17).

Φop=

⎧⎪⎪⎪⎨⎪⎪⎪⎩ILave·N2·(1+2β)

Rmo(1+2α) +12 · Vi

N2·(1+2β) ·(1+ β

1−d

)· d · Ts [d ≤ 0.5]

ILave·N2·(1+2β)Rmo(1+2α) +

12 · Vi

N2·(1+2β) ·(1+ βd)· d · Ts [d > 0.5]

· · · · · · · · · · · · · · · · · · · · · · · · (18)

Φcp =

⎧⎪⎪⎪⎨⎪⎪⎪⎩2ILave·N2·(1+2β)

Rmo(1+2α) +12 · Vi

N2·(1+2β) ·(

1−2d1−d

)· d · Ts [d ≤ 0.5]

2ILave·N2·(1+2β)Rmo(1+2α) + 1

2 · ViN2·(1+2β) ·

(2d−1

d

)· d · Ts [d > 0.5]

· · · · · · · · · · · · · · · · · · · · · · · · (19)



Fig. 13. Ratio of magnetic fluxes in the central leg andin the outer leg

In (18)–(19), α shows the ratio of magnetic reluctance (α =Rmc/Rmo), and β is the ratio of winding turns (β = N1/N2). Byusing these equations and core sectional areas Ao and Ac inthe outer leg and the central leg, the maximum flux densitiesBop, Bcp in the outer leg and the central leg can be designedby Bop = Φop/Ao or Bcp = Φcp/Ac.

Then, the relationships among each inductance, the wind-ing turns and the magnetic reluctances can be obtained fromthe magnetic circuit model:⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

L1 = N21 ·

2Rmo + 2 · Rmc

Lm1 = N21 ·

1Rmo + 2 · Rmc

L2 = N22 ·

Rmo + Rmc

R2mo + 2 · Rmo · Rmc

M2 = N22 ·

Rmc

R2mo + 2 · Rmo · Rmc

· · · · · · · · · · · · · · · · (20)

From Eq. (20), the inductance values can be calculated fromcore from geometric viewpoints.

4.2 Ratio of Maximum Flux in the Central Leg toMaximum Flux in the Outer Leg In the coupled in-ductor, there are two maximum fluxes in the central leg andin the outer leg, respectively. Therefore, it is necessary to in-vestigate the relationship between these maximum fluxes, inorder to avoid the magnetic saturation in the core. As a studycase, the ratio of the maximum flux in the central leg to themaximum flux in the outer leg (Φcp/Φop) is shown in Fig. 13.The conditions for Fig. 13 are defined as follows: The ratioof the inductor ripple current is ILpp/ILave = 0.5; the ratio ofmagnetic reluctance is α = 10. In addition, β is varied be-tween 0-2 to investigate the influence on the central windingN1.

From Fig. 13, Φcp is found to be smaller than twice themaximum flux Φop in the all ranges of duty ratio. If sectionalarea Ac in the central leg has twice sectional area in compar-ison with sectional area Ao in the outer legs, the flux densityis highest at outer legs. Therefore, flux density should be de-signed at the outer leg because general cores such as EE orEI cores has twice sectional area at central leg in comparisonwith outer legs.

5. Design Process of the Integrated WindingCoupled Inductor

This section discusses a design method for the IWCI. Ta-ble 6 shows the designed circuit parameters. The PC40EC70

Table 6. Circuit parameters for the experimental evalu-ation

Table 7. Magnetic core parameters of the IWCI

(TDK Corporation) is used for the IWCI prototype. The mag-netic core parameters are shown in Table 7.

5.1 Design Considerations The design considerationof the IWCI focuses on the following three points:

1) Maximum flux density: The maximum flux density mustmeet the designed value to avoid magnetic saturation. In thiscase, the magnetic core for the IWCI uses the ferrite core withlow losses in high frequency condition. Designed flux den-sity is 250 mT considering the temperature rise and a residualmagnetic flux density. In addition, the highest flux density inthe core is presented in the outer legs as it is understood fromthe relationship among Fig. 13 and the sectional areas in thecentral leg and in the outer leg shown in Table 7.

2) Inductor ripple current: Inductor ripple current is oneof the important design parts to decide the converter perfor-mance. In this case, the ratio of the inductor ripple current(ILpp/ILave) is 0.4 considering a CCM at 40% of maximumload. For the magnetic circuit model, the inductor ripple cur-rent can be designed by the following equations.

ILpp=

⎧⎪⎪⎪⎨⎪⎪⎪⎩Rmo ·

(1+α · 1−2d

1−d +2β·(β+1)

1−d

)· Vi

(1+2β)2·N22· d · Ts [d≤0.5]

Rmo ·(1+α · 2d−1

d +2β·(β+1)

d

)· Vi

(1+2β)2·N22· d · Ts [d>0.5]

· · · · · · · · · · · · · · · · · · · · · · · · (21)

These equations are useful to design the magnetic parametersfrom the number of winding and geometric structure.

3) Air gap location: the location of the air gap in magneticcore is important to exploit the performance of integratedmagnetic components. The proposed IWCI is provided withair gap only on the central leg. As the reasons for the lo-cation of the air gap, firstly, the DC fluxes on the magneticpath between the outer windings is effectively canceled, andDC fluxes of each winding flow into the central leg. Sec-ondly, high mutual inductance M2 is the major remedy forreducing the peak-peak inductor currents according to (6). In



order to get the highest value of the mutual inductance M2

in the selected core, an air gap on the outer legs should notbe installed. Therefore, the magnetic reluctance Rmo shouldbe minimized to realize the highest mutual inductance fromelectrical viewpoint.

5.2 A Novel Design Method of IWCI A novel de-sign process of the IWCI is through three steps. The threesteps are shown as follows:

1) Measurement of the minimum magnetic reluctance ofRmo: As it was mentioned above, the minimum magneticreluctance Rmo of the PC40EC70 is measured and calcu-lated. Firstly, some winding turns with the same numberare wounded at each outer leg as shown in Fig. 14. Then,self-inductance, leakage inductance and mutual inductanceare measured.

As seen in Figs. 14(a) and (b), the measured inductance La

and Lb are described by the following relationships:{La = 2L2 − 2M2 = 2Llk2

Lb = 2L2 + 2M2 = 2Llk2 + 2M2· · · · · · · · · · · · · · · (22)

From this relationship, M2 can be calculated as follows.

M2 =Lb − La

4· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (23)

Then, Rmo can be calculated by using (20) as follows:

Rmo =N2

2

L2 + M2· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (24)

Using a PC40EC70 and wound 16 turns, a minimum mag-netic reluctance is measured and calculated as 0.216 A/μWb.

2) The decision of the number of winding turns: Then, thenumber of turns of the IWCI is decided by using a simulta-neous equation. The both inductor ripple current and max-imum flux need to fulfill the designed specification. As itcan be seen from (18)–(19) and (21), the magnetic fluxes andthe inductor ripple currents depend on the winding turns andthe magnetic reluctances. In case of the range of d > 0.5,the number of winding turns is determined by (25), whichis obtained by substituting (21) into (18) to eliminate α andcomply the relationship Φop ≤ Φmax. If we substitute the cir-cuit parameters and the measured Rmo and the ratio of wind-ing turns β into (25), the function graphic can be obtainedas shown in Fig. 15. As seen in Fig. 15, three results on N2

exist. Results 1 and 2 are not valid because Rmc is negative.Therefore, only result 3 can simultaneously satisfy the de-signed magnetic flux density and inductor ripple current. Inthis case, the following relationships can be obtained.

−4.36 ≤ N2 ≤ 3.29, N2 ≥ 11.9 · · · · · · · · · · · · · · · · (26)

According to (26), the number of turns N2 is decided as 12turns to reduce the copper loss of the windings.

3) Calculation of the magnetic reluctance in the central legand the inductances: The magnetic reluctance value of Rmc isdecided. From Eq. (21) of d > 0.5 and α = Rmc/Rmo, Rmc is

2 ·{ ILpp·Φmax

Vi ·d·Ts· d

2·d−1

}· (1 + 2β)3 · N3

2 −{ILave + ILpp ·

(1 + βd

)· d

2·d−1

}· (1 + 2β)2 · N2

2

+{1 −(1 + 2β·(β+1)

d

)· 2d

2·d−1

}· Φmax · Rmo · (1 + 2β) · N2 +

{(1 + 2β(β+1)

d

)· d

2·d−1 − 12

}·(1 + βd

)· Rmo · Vi · d · Ts ≥ 0

· · · · · (25)

(a) Winding connection A (b) Winding connection B

Fig. 14. Winding connection for measuring Rmo

Fig. 15. Function graph of the Eq. (25)

Table 8. Magnetic core parameters of IWCI

given by:

Rmc =

⎛⎜⎜⎜⎜⎝ILpp ·(1 + 2β)2 · N2

2

Vi · d · Ts− 2β · (β + 1)

d· Rmo − Rmo

⎞⎟⎟⎟⎟⎠ · d2d − 1

· · · · · · · · · · · · · · · · · · · (27)

If the decided number of winding turns N2 is substituted intothis equation, the designed value of Rmc is 8.32 A/μWb. Ac-cording to (20), the designed inductance values for IWCI arecalculated as shown in Table 8. If these inductance values areused in simulation using the equivalent circuit model shownin Fig. 6, Fig. 16 can be obtained. As seen in this figure, the



Fig. 16. Simulated waveforms using the designed in-ductance values at 1 kw of output power condition

Fig. 17. Experimental waveforms of the 1kw outputcondition

inductor ripple current is confirmed as 4.02 A, and this valuecoincides with the designed inductor ripple current.

4) Installation of an air gap into the central leg: In order toget the designed inductance values of the IWCI, an air gap isinstalled into the central leg. In this case, the length of the airgap is set at 4.5 mm into the central leg to obtain the designedvalues in the measurements. The measured inductance valuesare shown in Table 8. The measured values of the magnetiz-ing inductance Lm1 of each phase are slightly smaller thanthe designed values. The error is 21.2%. As this cause, thereis some parasitic leakage inductance of the outer windings.These leakage inductances are caused by the external leak-age flux.

As a type of windings, Litz wires with low AC resistancesare used to reduce additional winding losses caused by fring-ing fluxes close to the air gap. Some reduction methods forthe additional winding losses at the central winding of theIWCI are shown in the Appendix. These methods are usefulto reduce additional winding losses.

6. Experimental Results

To confirm the validity of the design method, experimen-tal evaluation is carried out by using the condition of Ta-ble 6. The switching devices selected for the prototype of theinterleaved converter, SiC-MOSFETs (STW48NM60N) andSiC-Schottky Diodes (C3D20060D) are used in each phase.Figure 17 shows the experimental waveforms at 1 kW outputpower condition. From this figure, the inductor ripple cur-rents are almost the same as the 4 A of the designed value.The error is less than 0.01%.

In addition, the magnetic saturation has not occurred. Ifthe flux density reaches the saturation flux density, the induc-tor ripple current rapidly increases because the inductancevalue rapidly decreases in the case of ferrite cores. However,the experimental waveforms of the inductor currents are lin-early changed. Therefore, the validity of the design methodis confirmed. Although Fig. 18 gives the power conversion

Fig. 18. Efficiency of the interleaved converter with in-tegrated winding coupled inductor

(a) Estimated core for IWCI or loosely coupled inductor

(b) Estimated core for a non-coupled inductor

Fig. 19. Definitions of core size for the estimated core

efficiency, this result is only advisory.

7. Estimated Downsizing Effect of the IntegratedWinding Coupled Inductor

Because the validity of the design method for the IWCI isconfirmed in the experimental evaluation, the size compari-son between the integrated magnetic components is carriedout by estimation. The purpose of this section is to show thepotential performance of the IWCI from the theoretical view-points. In this section, core size calculation method is alsoproposed if the number of winding turns is decided.

The specifications are determined according to the boostconverter in automotive propulsion systems. The switchingfrequency is set at 30 kHz considering SiC power devices.

The definitions of the size of the estimated core are shownin Fig. 19. The shape of the sectional area, Ao, and the wind-ing area, Aw are defined as the square for analytical conve-nience. In case of this structure, the magnetic reluctancesRmo and Rmc can be obtained by (28) from the geometricalviewpoints.⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩

Rmo �3 · √Aw + 3 · √Ao

μ0 · μr · Ao

Rmc =

√Aw +

√Ao − lg

μ0 · μr · Ac+

lgμ0 · Ac

· · · · · · · · · · · · · (28)

where μ0, μr are the space permeability and the relative per-meability of magnetic material, respectively. From this equa-tion, an air gap length of the central leg is calculated as



follows:

lg =

√Ao +

√Aw − Ac · Rmc · μ0 · μr

1 − μr· · · · · · · · · · · · (29)

In addition, the window area is calculated as:

Aw =(2N1 + N2) · ILave

kw · Jw· · · · · · · · · · · · · · · · · · · · · · · · (30)

where kw is a space factor which shows the ratio of the totalwinding sectional area to the winding area. In this case, kw

is 0.8 considering the insulating film of the windings or thedistance between the windings corresponding to insulation.

Then, substituting (28), (30) into (25) yields the quarticequation related to sectional area Ao in the outer leg. Substi-tuting any number of winding turns N2 and the ratio of wind-ing turns β determines Ao. In addition, Rmc is calculated by(27).

Then, the sectional area Ac in the central leg is calculated

Table 9. Specifications for inductor core size estimation

Table 10. Theoretical inductor core size comparison between the integrated magnetic com-ponents and non-coupled inductor

so as to design the same flux density as the outer leg. Thesectional area in central leg is decided by the following equa-tions:

Ac =Φcp

Bmax· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (31)

In this equation, the value of Φcp can be calculated by sub-stituting the circuit parameter and winding turns into (19).The width of central leg, Wc, is decided by the followingequations:

Wc =Ac√Ao· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (32)

The air gap length in central leg is calculated on the ba-sis of (29). Finally, the inductor core volume and weight arecalculated as follows:{

Volcore = 2 · Ao ·(3√

Aw + 2√

Ao

)+ Ac

(2√

Ao +√

Aw − lg)

Wtcore = db · Volcore

· · · · · · · · · · · · · · · · · · · (33)

Furthermore, the design method for the loosely coupledinductor shown in (22) is applied to calculate the core size.The inductor core volumes of IWCI are compared with non-coupled inductor and LCI. The calculated results are shownin Table 10. As seen in this table, IWCI can be reduced sec-tional area of the core in comparison with the other meth-ods. As a result, the volume of magnetic core, which includesmany rare metals or base metals, can be reduced. The reduc-tion effect of the core volume is about 20% in comparisonwith the conventional LCI. The main reason why the IWCIcan be reduced the core volume, is that common flux φcom

can be effectively reduced by the additional central windingsbecause the common flux φcom is usually large in high dutyratio. Therefore, IWCI can be reduced the core volume un-der the same maximum flux density and this circuit condi-tion. Furthermore, the input current ripple of the LCI andthe IWCI are 39.75 A and 38.95 A at this circuit condition,



respectively. Although this difference is small, IWCI can re-duce the input side stress on the batteries in comparison withthe LCI method. These values can be calculated the equationshown in Appendix.

As the effective range of the IWCI, if the operating dutyratio in the converter fixed at the duty ratio 0.5, LCI is betterthan the proposed method because there are only a wheel-ing flux and a wheeling current, and these components arenot affected by the central windings. However, in the case ofthe high duty ratio condition like this experimental condition,IWCI can be reduced the volume of the core. However, it is amatter of concern that high power integrated magnetic com-ponents increase the heat generation density decided fromthe relationship the losses, the volume and surface area ofthe winding and the magnetic core. As a future work, wetry to propose the integrated magnetic components with flatstructure with low thermal resistance (31) or water cooling formagnetic components (32).

8. Conclusion

This paper analyzed and evaluated the electric and mag-netic characteristics as well as the advantages of the inte-grated winding coupled inductor in interleaved converters.Furthermore, a novel design procedure of the IWCI was pro-posed. As a conclusion, we could obtain some knowledge forthe integrated winding coupled inductor, as follows;

1) From the electrical analysis in section 3, the inductorripple current can be divided into common and wheeling cur-rents. Especially, the mutual inductance M1, between the ad-ditional central winding and the outer windings are effectivefor reducing the common ripple current. Furthermore, the va-lidity of the inductor ripple current analysis is confirmed fromthe experimental results. This result contributes to electricaldesign in order to fulfill the specifications.

2) Magnetic analysis in section 4 revealed that the addi-tional central winding N1 can reduce the common fluxes,which flow into the central leg of the core. The analysismethod introduced in section 4 is useful to apprehend clearlythe behavior of magnetic fluxes in the case of integrated mag-netic, especially. In addition, maximum flux can be designedfrom derived equations.

3) In section 5, a novel design method of IWCI is proposed.By applying this proposed design method, the inductor ripplecurrent and the flux density can be designed if the magneticcore size is decided from the reason of space amount. Thevalidity of the design method is confirmed experimentally insection 6.

4) In section 7, core size design method was proposedwhen the shape of the sectional area, Ao, and the windingarea, Aw are defined as the square. Under the same maximumflux condition, the volume of the estimated core of the inte-grated winding coupled inductor can be miniaturized in com-parison with the loosely coupled inductor and non-coupledinductor. The downsizing effect of the IWCI is about 20% incomparison with the LCI.

Therefore, we concluded that this method is one of thepromising approaches for miniaturizing magnetic compo-nents in interleaved converters.

References

( 1 ) National Institute for Materials Science (NIMS): “The wall of resource con-straints worldwide by 2050”, URL: http://www.nims.go.jp/news/press/2007/02/200702150/p200702150.pdf (in Japanese)

( 2 ) S.V. Araujo, R.P.T. Bascope, G.V.T. Bascope, and L. Menezes: “Step-UpConverter with High Voltage Gain Employing Three-State Switching Celland Voltage Multiplier”, in Proc. IEEE Power Electron. Specialists Conf.(PESC), pp.2271–2277 (2008)

( 3 ) S.Y. Tseng, C.L. Ou, S.T. Peng, and J.D. Lee: “Interleaved Coupled-inductorBoost Converter with Boost Type Snubber for PV system”, in Proc. IEEEEnergy Conver. Cong. and Expo. (ECCE), pp.1860–1867 (2009)

( 4 ) K. Tseng and C. Huang: “High Step-Up High-Efficiency Interleaved Con-verter With Voltage Multiplier Module for Renewable Energy System”, IEEETrans. on Industrial Electronics, Vol.61, No.3, pp.1311–1319 (2014)

( 5 ) M. Hirakawa, M. Nagano, Y. Watanabe, K. Andoh, S. Nakatomi, andS. Hashino: “High Power Density DC/DC Converter using the Close-Coupled Inductors”, in Proc. IEEE Energy Conver. Cong. and Expo. (ECCE),pp.1760–1767 (2009)

( 6 ) M. Pavlovsky, G. Guidi, and A. Kawamura: “Assessment of Coupled andIndependent Phase Designs of Interleaved Multiphase Buck/Boost DC-DCConverter for EV Power Train”, IEEE Trans. on Power Electron., Vol.29,No.6, pp.2693–2704 (2014)

( 7 ) K.J. Hartnett, J.G. Hayes, M.G. Egan, and M.S. Rylko: “CCTT-Core Split-Winding Integrated Magnetic for High-power DC-DC Converters”, IEEETrans. on Power Electron., Vol.28. pp.4970–4984 (2013)

( 8 ) J. Imaoka, M. Yamamoto, K. Umetani, S. Arimura, and T. Hirano: “Char-acteristics Analysis and Performance Evaluation for Interleaved Boost Con-verter with Integrated Winding Coupled Inductor”, in Proc. IEEE EnergyConver. Cong. and Expo. (ECCE), pp.3711–3718 (2013)

( 9 ) T. Nakamura, Y. Taguchi, and M. Ogasa: “Reduction in the Loss from RippleCurrent with Electromagnetic Coupling of Air-core Reactor”, IEEJ Trans.IA, Vol.133, No.6, pp.609–617 (2013) (in Japanese)

(10) E.A. Burton, G. Schrom, F. Paillet, J. Douglas, W.J. Lambert, K.Radhakrishnan, and M.J. Hill: “FIVR—Fully Integrated Voltage Regulatorson 4th Generation Intel R© CoreTM SoCs”, in Proc. IEEE Applied Power Elec-tron. Conf. and Expo (APEC), pp.432–439 (2014)

(11) Q. Li, Y. Dong, F.C. Lee, and D.J. Gilham: “High-Density Low-Profile Cou-pled Inductor Design for Integrated Point-of-Load Converters”, IEEE Trans.on Power Electron., Vol.28, No.1, pp.547–554 (2012)

(12) P. Wong, P. Xu, B. Yang, and F.C. Lee, “Performance Improvements of Inter-leaving VRMs with Coupling Inductors”, IEEE Trans. on Power Electron.,Vol.16, No.4, pp.499–507 (2001)

(13) J. Imaoka, S. Kimura, Y. Itoh, W. Martinez, M. Yamamoto, M. Suzuki, andK. Kawano: “Feasible Evaluations of Coupled Multilayered Chip Inductorfor POL Converters”, IEEJ Journal of IA, Vol.4, No.3, pp.126–135 (2015)

(14) F. Yang, X. Ruan, Y. Yang, and Z. Ye: “Interleaved Critical Current ModeBoost PFC Converter with Coupled Inductor”, IEEE Trans. on Power Elec-tron., Vol.26, No.9, pp.2404–2413 (2011)

(15) J. Imaoka, Y. Ishikura, T. Kawashima, and M. Yamamoto: “Optimal DesignMethod for Interleaved Single-phase PFC Converter with Coupled Induc-tor” In Proc. IEEE Energy Conver. Cong. and Expo. (ECCE), pp.1807–1812(2011)

(16) W. Wen and Y. Lee: “A Two-Cannel Interleaved Boost Converter with Re-duced Core Loss and Copper Loss”, in Proc. IEEE Annual Power Electron.Specialists Conf. (PESC), pp.1003–1009 (2004)

(17) J. Zhu and A. Pratt: “Capacitor Ripple Current in an Interleaved PFC Con-verter”, IEEE Trans. on Power Electron., Vol.24, No.6, pp.1506–1514 (2013)

(18) J. Imaoka, M. Yamamoto, Y. Nakamura, and T. Kawashima: “Analysis ofOutput Capacitor Voltage Ripple in Mulit-phase Transformer-Linked BoostChopper Circuit”, IEEJ Journal of IA, Vol.2, No.5, pp.252–260 (2013)

(19) W. Kim, M.S. Gupta, G. Wei, and D. Brooks: “System level analysis of fast,per-core DVFS using on-chip switching regulators”, in Proc. IEEE Interna-tional Symp. on High Performance Computer Architecture (HPCA), pp.123–134 (2008)

(20) H. Kim, J. Baek, M. Ryu, J. Kim, and J. Jung: “The High-Efficiency IsolatedAC-DC Converter Using the Three-Phase Interleaved LLC Resonant Con-verter Employing the Y-Connected Rectifier”, IEEE Trans. on Power Elec-tron., Vol.29, No.8, pp.4017–4028 (2014)

(21) E. Orietti, P. Mattavelli, G. Spiazzi, C. Adragna, and G. Gattavari: “CurrentSharing in Three-Phase LLC Interleaved Resonant Converter”, in Proc. IEEEEnergy Conv. Cong. and Expo. (ECCE), pp.1145–1152 (2009)

(22) J. Imaoka, S. Kimura, W. Martinez, and M. Yamamoto: “A Novel integratedMagnetic Core Structure Suitable for Transformer-Linked Interleaved BoostChopper Circuit”, IEEJ Journal of IA, Vol.3, No.5, pp.395–404 (2013)



(23 ) T. Qian and B. Lehman: “Coupled Input-Series and Output-Parallel DualInterleaved Flyback Converter for High Input Voltage Application”, IEEETrans. on Power Electron., Vol.23, No.1, pp.88–95 (2008)

(24) F. Forest, E. Laboure, T.A. Meynard, and J. Huselstein: “Multicell Inter-leaved Flyback Using Intercell Transformers”, IEEE Trans. on Power Elec-tron., Vol.22, No.5, pp.1662–1671 (2007)

(25) L. Wong, Y. Lee, D.K. Cheng, and M.H.L. Chow: “Two-Phase Forward Con-verter using an Integrated Magnetic Component”, IEEE Trans. on Aerospaceand Electronic Systems, Vol.40, No.4, pp.1294–1310 (2004)

(26) L. Wong, D.K. Cheng, M.H.L. Chow, and Y. Lee: “Interleaved Three-PhaseForward Converter Using Integrated Transformer”, IEEE Trans. on PowerElectron., Vol.52, No.5, pp.1246–1260 (2005)

(27) E. Laboure, A. Cuniere, T.A. Meynard, F. Forest, and E. Sarraute, “A Theo-retical Approach to Inter Cell Transformers, Application to Interleaved Con-verters”, IEEE Trans. on Power Electron., Vol.23, No.1, pp.464–474 (2008)

(28) T. Jin, K. Zhang, K. Zhang, and K. Smedley: “A New Interleaved Series In-put Parallel Output (ISIPO) Forward Converter With Inherent DemagnetizingFeatures”, IEEE Trans. on Power Electron., Vol.23, No.2, pp.888–895 (2008)

(29) K. Umetani, J. Imaoka, M. Yamamoto, S. Arimura, and T. Hirano: “Evalua-tion of the Lagrangian Method for Deriving Equivalent Circuits of IntegratedMagnetic Components: A Case Study Using the Integrated Winding CoupledInductor”, IEEE Trans. on Ind. Appl., Vol.51, No.1, pp.547–555 (2015)

(30) H. Kawamura, A. Sakamoto, T. Imazawa, and T. Watanabe: “Development ofthe high frequency boost converter”, in Proc. the 2015 IEEJ Annual Meeting,Vol.4, p.153 (2015) (in Japanese)

(31) Y. Nakabayashi, S. Fujisaki, K. Terazono, H. Hara, and K. Ide: “Developmentof High Power Density AC-AC Converter”, in Proc. IEEJ Industry Applica-tions Society Conference, pp.I51–I56 (2012) (in Japanese)

(32) Y. Hasuke, H. Sekine, K. Katano, and Y. Nonobe: “Development of BoostConverter for MIRAI”, SAE Technical Paper, p.6 (2015)

(33) T. Tera, H. Taki, and T. Shimizu: “Loss Reduction of Laminated Core In-ductor using in On-bord charge for EVs”, IEEJ Journal of IA, Vol.4, No.5,pp.626–633 (2015)

(34) N. Takahashi, T. Nakau, D. Miyagi, S, Nogawa, and M. Kuwata: “3-D EddyCurrent Analysis of Bevel Edge Core Reactor using Modeling Technique ofLaminated Steel”, IEEJ Trans. on PE, Vol.128, No.1, pp.277–283 (2008) (inJapanese)

Appendix

1. A Reduction Method of the Additional Losses inthe Central Winding Produced by Fringing Fluxesin the Air Gap

This section introduces the reduction method of the addi-tional winding losses by the Eddy current caused by fring-ing fluxes in the air gap. If the Eddy current losses pro-duced by the fringing fluxes become a problem from the ef-ficiency or thermal viewpoints, there are two solutions fromthe winding or the airgap structure viewpoints. App. Fig. 1shows the methods to reduce the additional winding losses

(a) Split-winding method

(b) Air-gap structure (Refs. (33) (34))

app. Fig. 1. Methods to reduce the additional windingloss at near the airgap in the central leg

close to the air gap in the central leg. App. Fig. 1(a) showsa split-winding method which can avoid the fringing fluxes.This structure can reduce the additional winding losses be-cause there are almost no interlinking fluxes into the wind-ings. However, if the split-winding cannot be realized dueto the windings N1 or the space factor, an air gap with ex-ponential or bevel edge is well known to restrain the occur-ring fringing fluxes (33) (34). App. Fig. 1(b) shows the air gapwith exponential edge (33) which can restrain the expansion offringing fluxes to the windings. Therefore, additional wind-ing losses or local heating near the airgap can be avoided.

2. Input Current Ripple Characteristic of IWCIThe input current ripple of IWCI can be calculated by the

following equation derived from the Eq. (6).

Iin iwci = 2Icompp

=

⎧⎪⎪⎪⎨⎪⎪⎪⎩(

2(2L1+L2+4M1−M2) ·

(1−2d

2·(1−d)

))· Vi · d · Ts [d < 0.5](

2(2L1+L2+4M1−M2) ·

(2d−1

2d

))· Vi · d · Ts [d ≥ 0.5]

· · · · · · · · · · · · · · · · · (A1)

In this case, the input current ripple is calculated by twiceof the common current ripple shown in Figs. 4 and 5. If L1,M1 in this equation are eliminated, the input current of LCImethod can be also calculated.

Jun Imaoka (Member) received his M.S. and Ph.D. degrees in elec-tronic function and system engineering from ShimaneUniversity in 2013 and 2015 respectively. Since Oct.2015, he has been with Kyushu University, Fukuoka,Japan. His research interests include design of in-tegrated magnetic components, modeling for highpower density power converters, EMI of switchingpower supply.

Kazuhiro Umetani (Member) received a Ph.D. degree in geophysi-cal fluid dynamics from Kyoto University, Japan, in2007. From 2007 to 2008, he was a circuit design en-gineer at Toshiba Corporation, Japan. From 2008 to2014, he was with the power group in DENSO COR-PORATION, Japan. He is currently an assistant pro-fessor at Okayama University, Japan. His researchinterests include new circuit configurations in powerelectronics and power magnetics for vehicular appli-cations.

Shota Kimura (Student Member) received his B.S. and M.S. degreeelectrical and electronic system engineering fromShimane University, Shimane, Japan, in 2013 and2015 respectively. Since 2015, he is currently Ph.D.degree in electronic function and system engineeringShimane University. He is interested in magnetic de-sign and core losses analysis for high power densityDC/DC converter.



Wilmar Martinez (Student Member) received B.S. degree in elec-tronic engineering and the M.Sc. degree in electricalengineering from Universidad Nacional de Colom-bia in 2011 and 2013, and is currently pursuing thePh.D. degree in electronic function and system engi-neering with Shimane University, Japan. His currentresearch interests include losses estimation in powerconverters and high power density DC-DC convertersfor Electric Vehicles.

Masayoshi Yamamoto (Member) received his M.S. and Ph.D. degreein science and engineering from Yamaguchi Univer-sity, Yamaguchi, Japan in 2000 and 2004 respectively.From 2004 to 2005, he was with Sanken Electric Co.,Ltd., Saitama, Japan. Since 2006, he has been withShimane University, Shimane, Japan. His researchinterests include power supply for HEV (boost con-verter, buck converter, 3-phase inverter, digital con-trol), charging system for EV, LED illumination sys-tem for a tunnel, EMI of switching power supply, and

wireless power transfer.

Seikoh Arimura (Non-member) received his M.S. and Ph.D. degreesin Astrophysics from Nagoya University, in 1999 and2003, respectively. From 2003 to 2005, he was aresearch assistant with the Japan Aerospace Explo-ration Agency (JAXA). Since 2005, he has been withDENSO CORPORATION, Aichi, Japan. His re-search interests include power electronics for boostconverter and inverter in HV/EV system.

Tetsuo Hirano (Non-member) received his M.S. degree in electronicengineering at Shizuoka University, Japan. Since1984, he has been with DENSO CORPORATION,Japan. His research interests include semiconductorcircuit topologies and power electronics for vehicularapplications.


Date post:	08-Apr-2022
Category:	Documents
Upload:	others
View:	1 times
Download:	0 times

Magnetic Analysis, Design, and Experimental Evaluations of ...

Documents