Loss Reduction of Laminated Core Inductor used in On-board

IEEJ Journal of Industry ApplicationsVol.4 No.5 pp.626–633 DOI: 10.1541/ieejjia.4.626

Paper

Loss Reduction of Laminated Core Inductorused in On-board Charger for EVs

Takahiro Tera∗ Member, Hiroshi Taki∗ Member

Toshihisa Shimizu∗∗ Senior Member

(Manuscript received Aug. 7, 2014, revised April 15, 2015)

A laminated core has advantages such as low iron loss, high permeability, and high saturation flux density. Forinductor applications, an air gap has to be inserted into the magnetic circuit to avoid saturation at lower magnetic fieldstrengths. However, when an air gap is inserted, fringing flux leaks out of the air gap and concentrates on the surfaceof the core. As a result, the iron loss increases to 292% as compared with an ungapped core, and the inductancecharacteristic deteriorates. Although a core with chamfered edges is known as a prior art that reduces the iron loss to147%, there is scope for improvement. In this paper, we propose a core with curved edges for loss reduction of thelaminated core inductor. Consequently, the proposed shape reduces the iron loss to 113% and improves the inductancecharacteristic. Thus, the proposed method increases the efficiency and reduces the size of the on-board charger.

Keywords: laminated core, fringing flux, iron loss, inductor

1. Introduction

With regard to the issue of global warming and fossil fueldepletion, the regulation of CO2 emission has been tight-ened. In the automotive industry, vehicles with a combus-tion engine are converted into electric vehicles (EVs) orplug-in hybrid vehicles (PHVs) with a battery (1). As forthe battery charger for EVs/PHVs, there exist an on-boardcharger. The on-board charger has a power factor correction(PFC) converter and a DC-DC converter. The switched-modepower supply(SMPS) technology is used for these convert-ers (2). SMPS is becoming more important particularly in au-tomotive applications such as the on-board charger for EVs.SMPS relies on the magnetic components for power conver-sion. SMPS works at frequencies much higher than the util-ity frequency, and increasing the frequency is crucial for re-ducing the size of the on-board SMPS. For reducing lossesoccurring in magnetic components, it is important to elimi-nate eddy currents. Therefore, powder cores including dustcores and laminated cores using amorphous and nanocrys-talline materials have been proposed.

Powder cores have low permeability and are distributed-gap magnetic components in nature owing to their low den-sity. There is a tendency to increase the core size becausea reduction in the permeability of the core directly leads toa reduction in the inductance. They have a low iron loss athundreds of kHz. The iron loss for the powder cores canbe practically and accurately calculated, as described in (3)–(8),aiding design optimization.

On the other hand, laminated cores have a higher

∗ DENSO CORPORATION1-1, Showacho, Kariya, Aichi 448-8861, Japan

∗∗ Tokyo Metropolitan University1-1, Minami-Osawa, Hachioji-shi, Tokyo 192-0397, Japan

permeability than powder cores. The high permeability ne-cessitates air gaps in the magnetic circuit when they are usedfor inductors. It is easy to downsize the core because the in-ductance relies on the air gap. If having no air gaps, thesecores have a low iron loss at dozens of kHz. However, themagnetic flux crossing the air gap expands its cross sectionalarea, thereby causing fringing flux that induces in-plane eddycurrent and magnetic flux concentration on the surface of thecore. As a result, the iron loss increases, and the inductancecharacteristic deteriorates.

As a well-known prior art, a core with chamfered edges hasbeen proposed (9), which reduces the iron loss by suppressingthe fringing flux. However, it is insufficient to disperse themagnetic flux concentration for laminated cores owing to thehigh permeability of amorphous and nanocrystalline mate-rials. A loss reduction method involving slitting of the coresheets has been proposed (10), which reduces the in-plane eddycurrent. However, it has no effect on dispersion of the mag-netic flux.

The objective of this study is to clarify the behavior of thefringing flux, reduce the iron loss, and improve the induc-tance characteristics under DC-biased magnetization. In thispaper, we propose a method for loss reduction of laminatedcore inductors. In Sect. 2, the specifications of the on-boardcharger and inductor are stated. In Sect. 3, the loss calcula-tion of the laminated core is explained, and the loss mecha-nism is determined using the model. In Sect. 4 we proposean iron loss reduction method on the basis of the dispersionof magnetic flux. In Sect. 5, the proposed method is analyzedby simulation to verify the reduction of the iron loss and im-provement of the inductance characteristic. In Sect. 6, theeffect of the loss reduction is verified through an experiment,and it is confirmed that the proposed method is valuable forthe loss reduction of the laminated core inductor used in the

c© 2015 The Institute of Electrical Engineers of Japan. 626

Loss Reduction of Laminated Core Inductor（Takahiro Tera et al.）

Fig. 1. Charging system with on-board charger

Fig. 2. Circuit configuration of the on-board charger

Table 1. Specifications of circuit and PFC inductor

AC input voltage 100/200 VAC input current 15 ADC output power 3.0 kW

Inductance at 15 A 470 μHSwitching frequency 20 kHz

Table 2. Core characteristicsRelative permeability at 20 kHz 30000

Electric conductivity 8.3× 105 S/mSaturation flux density 1.23 T

Stacking factor 78 %Thickness 18 μm

on-board charger for EVs. The conclusion of this study isstated in the final section.

2. Circuit Configuration of the On-board Charger

Figure 1 shows the charging system with an on-boardcharger. Figure 2 shows the circuit configuration of the on-board charger. Although inductors are used in both the PFCconverter and DC-DC converter, in this study, we have fo-cused on the PFC inductor. The specifications of the circuitand the PFC inductor are listed in Table 1. Figure 3 showsimulation results of the input and inductor waveforms. ThePFC converter controls the input current to be in-phase withthe input voltage. The voltage frequency is the utility fre-quency of 50 Hz. The current waveform represents the sumof the sinusoidal current at 50 Hz and ripple current owing toconverter switching at 20 kHz. It is sufficiently higher than50 Hz, thus, the current at 50 Hz can be practically regardedas DC. The smaller the inductance, the larger is the ripplecurrent, therefore, the switching loss and conduction loss ofthe switching devices increase. The target inductance valueat 15 A is set to 470 μH.

The structure of the designed inductor is shown in Fig. 4.The core characteristics are summarized in Table 2. We use alaminated core made of nanocrystalline soft magnetic mate-rial, which is called FINEMET R©. The laminated core is fabri-cated on machines which wind insulated sheet onto a mandrelunder controlled tension. Because of the very thin sheet, or-thogonal eddy current loss occuring in the sheet is very small.Generally, edges near the air gap are right-angled.

Fig. 3. Input and inductor waveforms

Fig. 4. Structure of the inductor

3. Loss Calculation of the Laminated Core

3.1 Method for Calculating the Iron Loss We ana-lyze the laminated core inductor by using the JMAG, whichis finite element analysis software. Figure 5 shows the one-eighth section model for the analysis of the iron loss. A coil ismodeled as one block, thereby simplifying the actual strandsof the magnet wire. The AC losses in the coil are not consid-ered.

Modeling within a single sheet of lamination is difficultowing to the limited computing power. Thus, several homog-enization methods, which model the laminated core by a solidone with anisotropic permeability and conductivity, are pro-posed (11)–(13). In Ref. (11), orthogonal eddy current in the sheetis neglected, therefore, the method can be applied to analysiswhere the effect of orthogonal eddy currents is very low. Inthis paper, we use FINEMET R© with sheet thickness in 18 μm,and the skin depth of the core is about 22 μm at 20 kHz.Because an increase in the iron loss owing to non-uniformmagnetic flux density is less than 1%, we select the homog-enization method in Ref. (13). When we use FINEMET R© at100 kHz or more, we need to apply homogenization methodsin Refs. (12), (13), which consider the effect of orthogonaleddy currents.

In Ref. (11), by using the relative permeability μ and elec-tric conductivity σ of the single laminated core, the relativepermeability μ′ and electric conductivity σ′ of the homoge-nized model are expressed as,

1/μ′x = α/μμ0 + (1 − α)/μ0

μ′yz = αμμ0 + (1 − α)μ0

σ′x = 0, σ′yz = ασ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (1)

627 IEEJ Journal IA, Vol.4, No.5, 2015


Fig. 5. Analysis model for iron loss

where α is the stacking factor of the laminated core, μ0 is thespace permeability, subscript x indicates the direction orthog-onal to the core sheets, and subscript yz indicates the direc-tion in-plane with the core sheets. Here, the in-plane eddycurrent is calculated using (1). To model the eddy currentaccurately, we select hexahedron mesh.

In actual PFC converter, magnetic flux waveform of induc-tors is closer to a triangular wave than a sinusoidal wave. Inaddition, minor B-H loops in the major B-H loop vary un-der DC-biased magnetization. However, currently availablemeasuring equipment and software can only consider the ironloss by sinusoidal magnetic flux, and not consider DC-biasedmagnetization. Therefore, we apply a sinusoidal wave to theiron loss simulation to verify the effect of proposed structureshown in Sect. 4.2. The current for the analysis is selected sothat the peak of average magnetic flux density in the core is150 mT.

It is known that the absolute value of the iron loss varieswith the difference of the magnetic flux waveform and DC-biased magnetization. With regard to the difference betweenthe sinusoidal wave and triangular wave, it is known that theiron loss is determined by the rate of change of the magneticflux density, dB/dt (6)–(8). Even if each amplitude of the sinu-soidal wave and triangular wave is the same, each iron lossis not the same. With regard to DC-biased magnetization, itis expected that the iron loss varies with the size of minorB-H loops (3)–(5) (8). In future, we will measure the iron loss ofFINEMET R© core under DC-biased magnetization.

As described above, the iron loss by sinusoidal magneticflux and that by actual magnetic flux are different. How-ever, the magnetic flux distribution hardly tends to dependon the magnetic flux waveform. Therefore, we suppose thatif the iron loss reduction and improvement of the inductancecharacteristics are obtained with simulation using sinusoidalmagnetic flux, a similar effect can be obtained with actualmagnetic flux.

After the magnetic analysis, the orthogonal eddy currentloss and hysteresis loss are calculated by the following for-mula,

Wi = KeB2 f 2 + KhBβ f (2)

where Wi is the total iron loss per unit volume, Ke is the eddycurrent loss coefficient, Kh is the hysteresis loss coefficient, βis the fitting parameter, and B is the peak value of the mag-netic flux density for sinusoidal excitation at the switchingfrequency f .3.2 Loss Mechanism Caused by the Fringing FluxFigure 6(a) shows the magnetic flux density distribution

of the model, where Bsur f ace is the maximum value of the

(a) Magnetic flux density distribution (b) Magnetic flux lines

Fig. 6. Magnetic flux of the gapped core

(a) Eddy current loss (in-plane)

(b) Eddy current loss (orthogonal) (c) Hysteresis loss

Fig. 7. Iron loss distribution of the gapped core

Fig. 8. Iron loss of the gapped core

magnetic flux density within the range of 1 mm from the sur-face, and Binner is the maximum value in the inner regiondeeper than 1 mm from the surface. It shows that Bsur f ace ishigher than Binner. This implies that the fringing flux shownin Fig. 6(b) flows close to the surface because μ′x is usuallyhigher than μ′yz. The result is particularly noticeable in theFINEMET R© core because of the magnetic anisotropy with μ′x6,000 times higher than μ′yz. As shown in Fig. 6(a), the con-centrated magnetic flux at the surface leads to the increase inthe iron loss.

Figure 7 shows the the iron loss distribution. It shows thatthe in-plane eddy current flows on the surface of the core, andthe orthogonal eddy current loss and hysteresis loss concen-trate on the surface. Figure 8 shows the result of the iron losssimulation in comparison with an the ungapped core. Insert-ing an air gap increases the iron loss from 0.75 W to 2.21 W.



The results indicate that it is necessary to minimize the in-plane eddy current on the surface of the core and disperse themagnetic flux evenly in the core.

4. Iron Loss Reduction based on Dispersion ofthe Magnetic Flux

4.1 Conventional Method with Chamfered EdgesFigure 9 shows the effect of the conventional method with

chamfered edges known as a prior art of the iron loss reduc-tion . We designed the x-dimension as 1 mm and the chamferangle from the x-axis as 74 degrees. The iron loss is reducedto 1.1 W as shown in Fig. 10. This design is merely one ex-ample, and there is a little scope for improvement. However,the magnetic flux is not completely dispersed, and the effectof the fringing flux is not eliminated.4.2 Derivation of Method for Iron Loss ReductionIn this paper, we have proposed an exponential curved

shape as shown in Fig. 11 and the following equation,

y1 = ygabx+yg xo f f set1−xwidth

yg + yg(1 − a)

(x ≥ xwidth − ygxo f f set1)

(a) Magnetic density distribution (b) Comparison of magnetic flux density

Fig. 9. Effect of the conventional method with cham-fered edges

Fig. 10. Comparison of iron loss of right-angled shapeand chamfered shape

Fig. 11. Proposed core with exponential curved edges

y2 = ygab−x+yg xo f f set2−xwidth

yg + yg(1 − a)

(x ≤ ygxo f f set2 − xwidth) · · · · · · · · · · · · · · · · · · · · (3)

where, a and b are the design parameters, xo f f set1 and xo f f set2

are offsets in the x-direction, yg is half of the gap, xwidth ishalf of the core width. The reference point in the x-directionis the center of the core width. The reference point in they-direction is the center of the air gap. We select a = 0.008,b = 5.21, xo f f set1 = 5.44, and xo f f set2 = 5. The differencebetween xo f f set1 and xo f f set2 is because of the difference inthe magnetic resistance between the inner perimeter and theouter perimeter, thus the fringing flux tends to leak out fromthe shorter magnetic path. As a result of introducing a curvededge, the magnetic resistance increases, therefore, the air gapis adjusted from 1.1 mm to 0.9 mm to maintain the inductanceat the same value. Figure 12 shows the difference betweenthe magnetic flux densities of the right-angled shape and theexponential curved shape. It shows that the Bsur f ace in the y-direction at 15 mm reduces from 753 mT to 177 mT and Binner

increases owing to the reduced air gap.We explain the effect of this shape by a simplified

schematic shown in Fig. 13. Only six layers at the surfaceof the lamination are shown. In our simulation, approxi-mately 480 sheets are modeled, where, i and B shown in the

(a) Right-angled shape (b) Exponential curved shape

Fig. 12. Effect of the proposed structure

(a) (b) (c)

Fig. 13. Dispersion of the magnetic flux and minimiza-tion of the eddy current



(a) Magnetic flux density distribution(yg = 0.25)

(b) Comparison of magnetic flux density

Fig. 14. Effect of the parameter yg

(a) Magnetic flux density distribution (b) Comparison of magnetic flux density

Fig. 15. Effect of the parameter xo f f set

figure represent the in-plane eddy current and the magneticflux density up to the sixth layer, respectively. Figure 13(a)shows the right-angled shape with a right-angled edge fac-ing the air gap, ieddy1 and B1 being the largest owing to theflux concentration in the first layer as discussed in Sect. 3. Asshown n Fig. 13(b), the core edge is chamfered to minimizeieddy1. The dimensions dx and dy are selected to cover thearea where the fringing flux accumulates. As a result, ieddy

is spread over the top five layers to form five small eddies,thereby reducing the ieddy1 loss considerably. Further, B1 inthe core is dispersed evenly, and B1, B2, B3, and B4 are sub-stantially uniform. Therefore, the orthogonal eddy current isreduced. However, the still-remaining edge between the fifthand sixth layer of the core increases B5 owing to the smallmagnetic resistance in this location, which results in an in-crease in the iron loss.

Further, the edge is altered to a curved form, as shownin Fig. 13(c). Here i and B up to the sixth layer are moreevenly dispersed. For fully implementing the concept de-scribed above, we chose the exponential curved shape, asshown in Fig. 11.4.3 Effect of the Parameters The proposed Eq. (3)

provides the optimal curve for the yg, therefore, the changein yg or xo f f set lead to the concentration of the magnetic flux.Figure 14 shows the simulation result obtained by changingthe yg to 0.25 mm, or 0.65 mm. The current value of eachsimulation is adjusted in order to maintain the magnetic fluxdensity. When compared with the result of 0.45 mm, Binner

at 0.25 mm increases to 171 mT, and Bsur f ace at 0.65 mm in-creases to 237 mT. In both the cases, the concentration ofthe magnetic flux leads to an increase in the iron loss. Inparticular, the increase in Bsur f ace causes the in-plane eddycurrent. Figure 15 shows the simulation result obtained bychanging xo f f set1 to 1.75 mm. Bsur f ace increases to 440 mT,and causes an increase in the iron loss. On the other hand,

(a) Magnetic flux density distribution (b) Comparison of magnetic flux density

Fig. 16. Effect of the parameter xwidth

(a) Eddy current loss (in-plane)

(b) Eddy current loss (orthogonal) (c) Hysteresis loss

Fig. 17. Iron loss distribution of the exponential curvedshape

for the parameter xwidth, the proposed equation is applied as itis. Figure 16 shows the simulation result obtained by chang-ing the xwidth twice. It is found that Bsur f ace and Binner are thesame. From the above, it is intended to provide an optimalcurve for yg. Further, it is applicable to the condition thatxwidth and yg xo f f set match.

5. Simulation Results

5.1 Reduction of the Iron Loss The loss reductioneffect of the exponential curved shape is presented here. Fig-ure 17 shows the iron loss distribution of the exponentialcurved shape. It shows that the in-plane eddy current lossis almost eliminated and the remaining 1% occurs at the un-processed flat surface. The orthogonal eddy current loss andhysteresis loss are equalized in the distribution. The loss re-duction effect of the exponential curved shape is presented inFig. 18. The loss owing to the air gap reduces to 0.76 W. Inthis paper, the edges of the core are reshaped to equalize themagnetic flux density in the xy plane, thus, the magnetic fluxconcentration in the yz plane is still unabated. The remain-ing edges can be reshaped in the same way to reduce the lossfurther.5.2 Improvement of the Inductance CharacteristicWe then proceed to the improvement of the inductance

characteristic under DC-biased magnetization. The currentfor the analysis is derived as the sum of the AC current rip-



Fig. 18. Iron loss of the proposed structure

Fig. 19. Inductance characteristics under DC-biasedmagnetization

(a) Right-angled shape (b) Exponential curved shape

Fig. 20. Magnetic flux density at 23 A

ple ΔI and the specified DC current. The inductance L iscalculated by the following equation,

L =Δφ

ΔI· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (4)

where, Δφ is the fluctuation in the flux linkage. Figure 26shows the inductance characteristics under DC-biased mag-netization. Figure 20 shows the magnetic flux density at 23 A.The inductance of the right-angled shape decreases graduallybecause the magnetic flux saturates gradually from wherethe magnetic flux is concentrated. While the inductance ofthe exponential curved shape is improved under higher DC-biased currents because the magnetic flux saturates simulta-neously owing to the effect of the dispersion of the magneticflux. If an overcurrent protection is sufficient, the exponentialcurved shape using the FINEMET R© core is suitable for induc-tor. This result contributes to the reduction of the switchingloss and conduction loss, and downsizing.

Fig. 21. Prototype of the exponential curved shape

Fig. 22. Configuration of iron loss measurement

6. Experimental Results

In this section, the reduction of iron loss and improvementof inductance is confirmed experimentally. Figure 21 showsa prototype of the exponential curved shape. The prototypeis processed by grinding with a machining center.6.1 Iron Loss Measurement Figure 22 shows a con-

figuration of iron loss measurement. The iron loss is mea-sured with B-H analyzer SY-8219 manufactured by IwatsuTest Instruments Corp. The excitation winding and pickupwinding are wound around the core. The iron loss is calcu-lated with the following equation,

Pi =N1

N2

1T

∫ T

0i1(t)v2(t)dt · · · · · · · · · · · · · · · · · · · · · · · (5)

where, i1 is the exciting current, v2 is the pickup voltage, N1

is the number of turns of the excitation winding, and N2 isthe number of turns of the pickup winding. The measure-ment condition is similar to the simulation condition, and si-nusoidal current is applied.

Figure 23 shows the experimental result of the iron loss,and both the simulation result and experimental result aresummarized in Table 3. The percentage of the iron loss ofeach gapped core to that of the ungapped core is also shown.The right-angled shape increases the iron loss to 2.19 W whenthe air gap is inserted, and it is consistent with the simulationresult. The exponential curved shape reduces the iron loss to0.85 W, and there is a small error between the experimentalresult and the simulation result. The effect of the exponential



Fig. 23. Experimental result of iron loss

Table 3. Summary of results

Ungapped Right-angled Chamfered Exponentialcore shape shape curved shape

Simulation 0.75 W 2.21 W 1.10 W 0.76 W(100%) (295%) (147%) (101%)

Experiment 0.75 W 2.19 W Unmeasured 0.85 W(100%) (292%) (113%)

Fig. 24. Comparison of results

curved shape is confirmed.Figure 24 shows a comparison of the simulation result and

experimental result. As seen in Fig. 24, the experimentalvalue of the exponential curved shape is slightly higher thanthe calculated value. We assume that the reason for the differ-ence is an increase of the orthogonal eddy current by partialshorting on the processed surface. In future, we will revealappropriate processing conditions.6.2 Inductance Measurement Figure 25 shows a

configuration of inductance measurement. Voltage is appliedto the inductor for a period of time. The inductance L is cal-culated by the following equation,

L =VL

dIL/dt· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (6)

where, VL is inductor voltage, and IL is inductor current, t isthe time. The frequency characteristic of relative permeabil-ity and the minor loop under DC-biased magnetization arenot considered. The inductance in the initial magnetizationcurve are measured. Figure 26 shows the inductance charac-teristics under DC-biased magnetization. As with simulationresult, the inductance under higher DC-biased currents is im-proved. Therefore, this result indicates that the exponentialcurved shape disperses the magnetic flux.

Fig. 25. Configuration of inductance measurement

Fig. 26. Inductance characteristics under DC-biasedmagnetization

7. Conclusion

In the present work, we proposed a method for optimizingthe core shape near the air gap in order to evenly dispersethe magnetic flux in the core and minimize the in-plane eddycurrent. We found that an exponential curved shape is suit-able. The effect of loss reduction is confirmed through anexperiment. Inserting the air gap increases the iron loss to292%. While the conventional core with chamfered edgesreduces the iron loss to 147%, the exponential curved shapereduces the iron loss to 113%. Furthermore, the exponentialcurved shape improves the inductance characteristic underDC-biased magnetization. The proposed method helps in-crease efficiency and reduce the size of the on-board charger.

In this study, the effect of the exponential curved shapewas confirmed under the assumption that a sinusoidal currentflows. In the actual PFC operation, the ripple current is al-most a triangular wave, and the duty of the voltage changes.In addition, the iron loss changes under DC-biased magne-tization. However, it is obvious that the proposed shape iseffective. In the future work, we will verify the effect of lossreduction by considering the actual operation.

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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.

Hiroshi Taki (Member) received the B.S. degree in electrical engi-neering from Shizuoka University, Japan in 1984.Since 1984, he has been working as a research en-gineer at DENSO CORPORATION, Japan. His re-search interests include engine control system, powerelectronics, and EMI design.

Toshihisa Shimizu (Senior Member) received the B.E., M.E. andDr.Eng. degrees all in electrical engineering fromTokyo Metropolitan University in 1978, 1980, and1991, respectively. He has been a visiting professor atVPEC, Virginia Polytechnic Institute and State Uni-versity, Virginia, USA, in 1998. In 1980, he joinedFuji Electric Corporate Research and Development,Ltd. as a research engineer. Since 1993, he has beenwith Department of Electrical Engineering, TokyoMetropolitan University, Tokyo, Japan. Now he is

a full professor. His research interests include power converters, high fre-quency inverters, photovoltaic power generations, modeling and reductionof EMI in Power Electronics, high power density converter design, inductorloss analysis, etc. He is a senior member of IEEE, and a senior member ofthe Institute of Electrical Engineers of Japan.


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Loss Reduction of Laminated Core Inductor used in On-board