Design of Coupled Inductor for Two-PhaseSynchronous Boost Converters in Automotive

ApplicationsGeorg Tobias Gotz, Alexander Stippich, Arne Hendrik Wienhausen, Rik W. De Doncker

Institute for Power Electronics and Electrical DrivesRWTH Aachen University, Aachen, Germany

Email: post@isea.rwth-aachen.de

Abstract—This paper introduces a design for a coupled in-ductor for a two-phase synchronous boost converter based onsilicon carbide (SiC) MOSFETs. The converter operates ata high switching frequency of 300kHz and is designed fora maximum output power of 32kW. Despite the very highswitching frequency and consequently smaller sizes of passivecomponents, passives remain one of the largest components of theconverter, especially inductors. The magnetic coupling of severalphases of a converter in the form of coupled inductors allows afurther reduction in size and weight of these passive components.Fast switching SiC devices and the high power rating requirea sophisticated design, whose process is described in detail. Forevaluation in an experimental setup, a prototype is manufacturedand the efficiency is compared to the converter operated withuncoupled inductors. The design of the coupled inductor achievessimilar efficiency while requiring less material, which improvesthe power density and decreases costs.

I. INTRODUCTION

Increasing the power density of power electronic convertersfor automotive applications is an ongoing research topic [1].Silicon carbide (SiC) MOSFETs allow increasing the switch-ing frequency of dc-dc converters considerably. As a result,passive components can be reduced in size, which enablesconverters with high power densities. Although passive com-ponents can be downsized considerably due to the increasedswitching frequency, magnetic components still represent oneof the largest components in such converters [2].

Coupled inductors can be used to further decrease thevolume of the inductor and increase the power density of con-verters. However, presented coupled inductor designs are onlydesigned for either high power or high switching frequencyoperation or only operate at low voltages [3]–[8].

In this paper, a design of a coupled inductor for very high-frequency operation with SiC MOSFETs at voltages up to800V with a power up to 32 kW is presented. A sophisticateddesign of the coupled inductor regarding thermal and electricalcharacteristics is developed. A prototype is constructed andcharacterized relating to electrical characteristics. Finally, thedesign is experimentally verified in a synchronous boostconverter setup (see Figure 1). The efficiency in operation with10 kW load is measured and compared to the efficiency of aconverter with comparable uncoupled inductors.

Uin

S1

S2

S3

S4

iini1

i2Uout

iout

u2

u1

Fig. 1. Schematic interleaved synchronous boost converter

II. CORE GEOMETRY

In uncoupled multiphase boost converters, each inductor iscapable of carrying the full phase current of one phase. Withthe interleaved inductor with negative coupling, a cancellationof dc flux in the inductor is achieved. The effective magneticflux in the ferrite core is smaller so that the core requires asmaller cross-sectional area.

In a non-ideal coupled inductor (see Figure 2), flux gener-ated by winding 1 φ11 is not completely linked to winding 2and vice versa. The ratio between linked flux, also called mainflux (φ12, φ21), and generated flux is the coupling factor k:

k =φ12φ11

=φ21φ22

(1)

The part of the generated flux by one winding, which is notlinked to other windings, is called stray flux (φ1σ, φ2σ).

φ2σφ12φ1σ

φ21

u1 u2

i1 i2

Fig. 2. General flux paths

0 0.5 1 1.5 2 2.5 3

0

50

100

150

200

250

normalized time tT

fluxφ

inµW

bφ1 = φ1σ k = 0φ2 = φ2σ k = 0φ1 k = 0, 7φ2 k = 0, 7φ1σ k = 0, 7φ2σ k = 0, 7φσ = φ1σ + φ2σ k = 0, 7

Fig. 3. Magnetic flux in the coupled inductor L = 30 µH, N = 7, uin = 400V, d2 = 0, 59, Pload = 32 kW

Figure 3 shows the flux divided into main and stray fluxfor a coupled inductor (k = 0.7) and uncoupled inductor(k = 0) plotted over three switching cycles with a periodtime T . φ1 and φ2 are the magnetic fluxes in the materialof the leg with winding 1 respectively winding 2. The plottedvalues are simulated for converter operation at an input voltageuin = 400V, a load power Pout of 32 kW and a duty cycled of 0, 59. Each winding of the inductor has N = 7 turns andan inductance L of 30 µH.

The smaller amount of direct (dc) flux in the coupledinductor compared to the uncoupled one leads to a smallermaximum flux in the ferrite material. This allows a smallercross-sectional area which results in a smaller core and savesweight and volume.

A topology analysis based on the method described in [3]is used to determine the design parameters for the coupledinductor (see Table I).

The coupled inductor needs a relatively high stray induc-tance with respect to the main inductance which results in asmall coupling factor in comparison to transformers. Thereare different possibilities to realize coupled inductors with asignificant stray inductance:• addition of external inductors [6]• creating stray flux by geometric separation of wind-

ing [5]• specific design of magnetic stray path filled with perme-

able material [3], [4], [7], [8]

TABLE IREQUIREMENTS OF COUPLED INDUCTOR

parameter value

Inductance L 30 µHCoupling factor k 0.7

Min. resonant frequency fres,min 6MHz

PQ core

bobbin

winding

stray platefoil

spacer

Fig. 4. Exploded view of the inductor

The presented inductor implements the last option with aspecifically designed stray flux path. Figure 4 shows anexploded view of the designed inductor.

III. FLUX LINKAGE IN A COUPLED INDUCTOR

As discussed in the previous section, the magnetic fluxcancellation enables a smaller and lighter coupled inductorcompared to uncoupled inductors. For design purposes, acalculation of the minimum number of turns for coupledinductors based on the saturation flux density is deduced.

Figure 5 shows the equivalent circuit of a coupled induc-tor. The coupled inductor shall have symmetrical properties.

1:1u2σu1σ i1 i2 i2

L2σ

u2um

L1σ

umu1 Lm

im

Fig. 5. Equivalent circuit diagram coupled inductor

Therefore, the inductance of each winding (2) and the numberof turns (3) are similar.

L1 = L2 = L (2)N1 = N2 = N (3)

The stray inductances L1σ, L2σ and main inductance Lm inthe equivalent circuit are deduced depending on the couplingfactor k. This results in the definitions (4) to (6).

L1σ = (1− k) · L1 = (1− k) · L (4)L2σ = (1− k) · L2 = (1− k) · L (5)Lm = k · L (6)

To avoid saturation in the ferrite material, the individualfluxes existing in the core are analyzed. Figure 2 showsconsidered flux paths in a coupled inductor. The definitionsof the used fluxes in Figure 2 are defined in equations (7) to(12) [9].

φ11 =L1

N1· i1 (7)

φ12 =Lm

N2· i1 (8)

φ1σ =L1σ

N1· i1 (9)

φ22 =L2

N2· i2 (10)

φ21 =Lm

N1· i2 (11)

φ2σ =L2σ

N2· i2 (12)

The total flux in the material is φ1, which is calculated byequation (13), and φ2 that results from equation (14).

φ1 = φ11 − φ21= φ12 + φ1σ − φ21 (13)

φ2 = φ22 − φ12= φ21 + φ2σ − φ12 (14)

Further, a formula to calculate the number of turns isdeduced. In equation (13), φ11 and φ22 are substituted withequations (7) and (9). Furthermore, equations (4), (6) and (3)are inserted in (13), which results in equation (15) .

φ1 =Lm

N2· i1 +

L1σ

N1· i1 −

Lm

N1· i2

=k · LN2· i1 +

L · (1− k)N1

· i1 −L · kN1· i2

=L

N· ((k + (1− k)) · i2 − k · i2)

=L

N· (i1 − k · i2) (15)

An equivalent derivation is achieved for flux φ2 and results inequation (16).

φ2 =L

N· (i2 − k · i1) (16)

To avoid saturation in the core, the magnetic flux density mustalways stay below the saturation flux density Bsat. Hence, thefollowing equations (17) and (18) must be valid whereby Acore

is the magnetic cross-sectional area of the core.

|φ1|max

Acore≤ Bsat (17)

|φ2|max

Acore≤ Bsat (18)

F1,m

F2,m

Rgap

4

2 · Rcore2 · Rcore

2 · RstrayRgap

42 · Rstray

2 · Rcore 2 · Rcoreφ2

φ1

φσ

2

φσ

2

Rgap

2Rgap

2

Rgap

2Rgap

2

Fig. 6. Equivalent magnetic circuit of the coupled inductor

By combining equations (15) and (17) a condition for thenumber of turns for winding 1 can be formulated.

L

N ·Acore· |i1 − k · i2|max ≤ Bsat (19)

⇔N ≥ L

Bsat ·Acore· |i1 − k · i2|max (20)

For winding 2 the equation for the number of turns can becalculated equivalently.

N ≥ L

Bsat ·Acore· |i2 − k · i1|max (21)

IV. CALCULATION OF GEOMETRY PARAMETERS

In this section, the calculation of key parameters, e.g. air gaplengths and magnetic resistances, is presented. Figure 6 showsthe equivalent magnetic circuit of the coupled inductor basedon the magnetic structure shown in Figure 4. For an optimizeddesign, the core dimensions and flux splitting between mainand stray flux are deduced in this section. The magneticresistance of the stray plates is neglected because of the shortmagnetic path compared to the magnetic path length of thecore.

A. Calculation of reluctance of air gaps

For magnetic devices, an equivalent magnetic circuit canbe created. The flux φ is equivalent to the current, themagnetomotive force (mmf) F is equal to the voltage andthe reluctance R is equal to a resistor. The definitions ofRmag, φ and Fmag are presented in equations (22) to (24).l is the effective length and A is the cross-sectional area ofthe magnetic path, whereby B is the magnetic flux density inthe path.

Rmag =l

µ ·A (22)

φ = B ·A (23)Fmag = N · i (24)

lgap,inner

lgap,outer

lstray

hplate

lgap

Fig. 7. Air gap lengths

The evaluation of the equivalent magnetic circuit (see Fig-ure 6) allows calculating the flux splitting between the mainand stray flux. This is important for the calculation of the airgap lengths in the inductor. In the equivalent circuit, F1,m

and F2,m are the magnetic voltages generated by windingcurrent i1 respectively i2. The magnetic reluctance Rcore isthe reluctance of one half PQ core. Rgap/2 is the resistanceof the air gap located between one half PQ core and the strayplates. Rstray represents the summarized magnetic resistanceof the two air gaps between the stray plates.

Derived from the magnetic equivalent circuit Rcore, Rgap

andRstray results in equations (25) to (27) whereby lcore is theeffective length of the magnetic path of one half PQ core. Thereluctances of the air gaps correlate with the air gap lengths.

Rcore =lcore

µ0 · µr,core ·Acore(25)

Rgap = 2 ·(

1

1 + k· N

2

L−Rcore

)(26)

Rstray =1

1− k ·(Rcore +

Rgap

2

)(27)

B. Calculation of air gap lengths

Out of the reluctance, the air gap length (lgap) can be cal-culated. The air gap length depends on the required reluctanceand the cross-sectional area of the air gap. Because of fringingflux, the cross-sectional area of the air gap is larger than thecross-sectional area of the core. For rectangle core shapes, agood approximation is based on the assumption, that the sidelengths of the cross-sectional area of the air gap are longer bythe air gap length than the side lengths of the cross-sectionalarea of the core. This results in equation (28), in which aand b are the edge lengths of the cross-sectional area of thecore. Using a similar approach for air gaps with a round cross-sectional area, the assumed cross-sectional area is calculatedwith equation (29). In this equation, r is the radius of thecross-sectional core area.

Aair,rectangle = (a+ lgap) · (b+ lgap) (28)

A1

A2

A1

a

b

r

Fig. 8. Cross-sectional area of the air gaps

Aair,circle =

(r +

lgap2

)2

· π (29)

Combining the equations (22) and (28) results in equa-tion (30) for air gaps with a rectangular cross-sectional area.Equation (31) applies to a round cross-sectional area.

⇔ lgap,rectangle =−a+ b− 1

Rgap·µ0

2

±

√√√√(a+ b− 1Rgap·µ0

2

)2

− a · b (30)

lgap,circle =−2 · r − 1

Rgap·µ0·π

2

±

√√√√(2 · r − 1Rgap·µ0·π

2

)2

− r2 (31)

For the design of the coupled inductor, two different airgap lengths (lgap, lstray) are determined. The air gap lgapcan be calculated at the air gap at the inner leg of the PQcore lgap,inner or at the outer leg lgap,outer. Figure 7 showsthe positions of the air gap lengths (lstray, lgap). Figure 8shows the cross-sectional areas of the PQ core. The cross-sectional area of the inner air gap lgap,inner (labeled with A2)is round and is calculated according to formula (31). Thecross-sectional area A1 is approximated using a rectangularcross-sectional area (see red box in Figure 8). The width b isderived from the depth a and the cross-sectional area Acore ofthe PQ core (see formula (32)).

b =Acore/2

a(32)

The outer air gap length lgap,outer is calculated with theequation (30) using the derived quantities a and b.

The air gap length lstray in the stray flux path is calculatedwith equation (30). For the calculation, b is set to hplate anda remains unchanged because depth of the stray plate is equalto the depth of the PQ core.

V. MINIMUM THICKNESS OF STRAY PLATES

To prevent saturation in the stray plates a condition forminimum stray plate thickness is required. For that purpose,an expression for the stray flux φ1σ and φ2σ is required.

Using the flux definitions from section III, an equation forφ1σ is derived where equations (4) and (7) are inserted inequation (9). The expression is then rewritten to equation (33).

φ1σ =L1σ

N1· i1

= (1− k) · L1

N1· i1

= (1− k) · φ11 (33)

The same approach is used for φ2σ and results in equa-tion (34).

φ2σ =(1− k) · φ22 (34)

The flux φ1σ and φ2σ superpose in the stray plates (seeFigure 6) resulting in φσ (see equation (35)).

φσ =φ1σ + φ2σ

=(1− k) · (φ11 + φ22) (35)

φ1 and φ2 are replaced with equation (7) and equation (10)which results in equation (36).

φσ =L

N· (1− k) · (i1 + i2) (36)

φσ is the total stray flux that is divided equally to the outerstray plates. So each one carries half of the total stray flux φσ.From the flux in the stray plates (equation (36)) and equation(23), the magnetic field strength in the ferrite material of thestray plates is calculated.

Bσ =φσ

2 ·Acore,stray(37)

=L

2 ·N ·Acore,stray· (1− k) · (i1 + i2) (38)

To avoid saturation, the maximum field strength in the platesmust be smaller than the saturation field strength of the ferritematerial Bsat.

With equation (38), this results in a condition for minimumcross-sectional area Acore,stray of the stray plates.

Acore,stray ≥L

N· (1− k) ·max |i1 + i2|

2 ·Bsat(39)

Replacing i1 + i2 with the input current iin, the minimumarea divided by a results in the minimum thickness of thestray plates hplate:

hplate ≥Acore,stray

a(40)

=L · (1− k) ·max |iin|

2 ·N · a ·Bsat(41)

VI. EXPERIMENTAL SETUP

A prototype is set up for validation. A PQ core madeof 3F36 [10] is chosen, because the material has a goodperformance at the required frequency range. A PQ core isa good tradeoff between electrical shielding and heat dissipa-tion. The core size PQ50/50 is selected because the winding

TABLE IIGEOMETRY PARAMETERS OF COUPLED INDUCTOR FOR A PQ50/50 CORE

parameter value

Core manufacturer FerroxcubeMaterial 3F36 [10]Number of turns per Coil 7 8 9lgap,inner 179 µm 242 µm 316 µmlgap,outer 188 µm 255 µm 333 µmlstray 1.15mm 1.65mm 2.35mm

minimum hplate 5.48mm 4.79mm 4.26mm

Volume 0.125L

Switching frequency 300 kHz

window from the next smaller core (PQ50/35) is to small for7 turns. But to avoid saturation in the core, a minimum of 7turns per winding is required for a PQ50/35 as well as fora PQ50/50 core. The saturation flux density for the designprocess was 340mT. Because the thickest plates in 3F36material have a thickness of 5mm (PLT64/50/5 cores [11]),the required minimum plate thickness for 7 turns of 5.48mmcannot be fulfilled. Therefore, the number of turns is chosen to8 turns.The design results for a PQ50/50 core [12] are shownin Table II.

Two foils, one of 100 µm thickness and a second one of150 µm thickness, are used as spacers between the PQ50/50cores and the stray plates. The air gap spacers in the straypath are produced in a three-dimensional printing processand are 5mm wide. The large difference to the calculatedvalue of 1.65mm can be explained with the big gap betweenthe winding and the stray plates. All components are gluedtogether for mechanical stability. Figure 9 shows the inductor

Fig. 9. Prototype of the coupled inductor

weight volume0102030405060708090

100454 g

345 g

182 cm3

125 cm3

rela

tive

size

in%

2x PQ50/35 PQ50/50 coupled inductor

Fig. 10. Savings using the coupled inductor

prototype.To evaluate the coupled inductor in performance two com-

parable uncoupled inductors are used. The reference inductorsare identical to the inductor used in the single-phase converterpresented in [2]. Each uncoupled inductor is based on aPQ50/35 core [13] consisting of 3F36 material. Each inductorhas an inductance L of 30 µH and a number of turns of 11. Thewindings material for the coupled and uncoupled inductors isa 630x0.1mm litz wire.

A. Evaluation of volume and weight

The coupled inductor enables a significant saving in volumeand weight (see Figure 10). In comparison to the describeduncoupled configuration, a volume saving of 20.7% and aneconomy of the weight of 24% is achieved. The reduction inthe number of turns decreases the resistance of the windings.The uncoupled inductor has 36% fewer turns, resulting inlower copper losses and copper costs.

B. Characterization of coupled inductor

The coupled inductor is characterized by an impedanceanalyzer (Agilent 4294A). Table III shows the results of themeasurement. The inductor features a high resonant frequencyabove 9MHz and enables a high switching frequency.

The coupling factor k1 and k2 is calculated from the in-ductance Lshort and Lopen. Lshort is the measured inductancewhere the other winding is shorted. Lopen is the measuredinductance with opened clamps at the other winding. This

TABLE IIICHARACTERIZATION RESULTS OF COUPLED INDUCTOR

parameter value

Inductances L1, L2 29.4 µH, 29.1 µHResonant frequencies fres,1, fres2 9.25MHz, 9.25MHz

Coupling factor k1, k2 0.71, 0.71

Coupled Inductor

Converter

Fig. 11. Converter test setup

results in a coupling factor for the winding 1 (k1) andwinding 2 (k2).

k =

√1− Lshort

Lopen(42)

The inductance and the coupling factor meets the requiredvalues listed in Table I. Hence, the coupled inductor fulfillsall previously defined requirements.

In the design process, the coupled inductor was assumed assymmetric. Comparing the measured inductance values of theprototype, the inductance values of the two windings havea difference in inductance of 0.3 µH. That is 1% absolutedeviation of the mean value of the two inductance values. Sothe assumption of symmetry is valid. The difference can occure.g. from a different length of cable and production tolerancesof the core and the inductor itself. The smaller inductancevalue and the higher coupling factor results in a slightly highercurrent ripple.

C. Test of the coupled inductor in a converter setup

The coupled inductor is evaluated in a synchronous boostconverter setup, which is shown in Figure 11. The converteris published in paper [14].

For the comparison, the efficiency at 10 kW and the effi-ciency at open clamps (no load) are used. For power mea-surements, a precision power analyzer from type LMG500(ZES Zimmer) with current sensors from type IT600-S Ul-trastab (LEM) is used. As load, an ohmic resistor is utilized.For the tests, the converter operates at 300 kHz switchingfrequency, an input voltage of 400V and an output voltageof approximately 800V. Table IV shows the measured inputand output values of the setup with coupled and uncoupledinductor. The efficiency of the uncoupled inductor in com-parison to the coupled inductor is slightly higher, but theno-load losses of the coupled inductor are lower than of theuncoupled inductor. Under load operation at 10 kW, the lossesare slightly increased despite using less ferrite material (16%)and turns (36%), which normally decreases the losses. The

TABLE IVMEASUREMENTS OF THE CONVERTER SETUP - fs = 300 kHz

Inductor Uin Iin Pin Uout Iout Pout efficiency

PQ50/35 (uncoupled) 400V 0.11A 42.8W 798V 0A 0W –395V 28.0A 11.0 kW 796V 13.4A 10.7 kW 96.7%

PQ50/50 400V 0.10A 41.9W 803V 0A 0W –397V 27.9A 11.1 kW 798V 13.4A 11.1 kW 96.5%

0 0.5 1 1.5 2

−10

−5

0

5

10

normalized time tT

curr

enti

inA

i1(t) (simulated)i2(t) (simulated)i1(t) (measured)i2(t) (measured)i1(t) (measured)i2(t) (measured)

Fig. 12. Current waveform of the coupled inductor (Uin = 400V; duty cycle d = 0.3; Pout = 0W; fs = 300 kHz)

peak-to-peak flux in the PQ cores is increased by 25% from215mT to 290mT. The increased peak-to-peak flux generatesadditional losses in the ferrite material. In total, the savingsare compensated by the additional losses caused by the higherflux ripple.

In Figure 12, a comparison between the calculated andmeasured current waveforms is depicted. The waveformsare measured with an oscilloscope from type HDO6104-MS(Teledyne LeCroy) and current probes from type N2783B(Keysight/Agilent). For the measurement, the converter op-erates at no-load, with a switching frequency of 300 kHz,an input voltage of 400V and a duty cycle d of 0.3. Forthe coupled inductor, the measured current waveforms of thephases differ in comparison to simulated waveform in a smalldirect current offset, which results from a slightly asymmetricsetup. This can be settled by a controller in the future.

VII. CONCLUSION

This paper presented a design process of a coupled inductorfor the application in fast-switching high power convertersutilizing SiC devices. Based on the fundamental equations,a reluctance model was developed for the proposed designand the calculation of geometric parameters was presented indetail. With the reluctance model, all required parameters ofthe coupled inductor in a synchronous boost converter werecalculated and the prototype was designed and constructed.

The inductor was successfully operated in a two-phasesynchronous boost converter at a high switching frequency of300 kHz, at a power of 10 kW and a voltage of 400V to 800V.

The comparison between the coupled and the uncoupledinductor during operation shows almost no change regardingefficiency and no-load losses.

When comparing the coupled inductor to two uncoupledinductors designed for the same specifications, a saving inthe volume of 20.7% and in the weight of 24% is achieved.Due to lower material usage, system costs can be reduced.Consequently, the power density of multiphase dc-dc convert-ers can be increased by the utilization of coupled inductors.Thereby, it was demonstrated that coupled inductors provide away to further reduce the size of passive components in fast-switching SiC converters, in which inductors are one of thelargest components.

ACKNOWLEDGMENT

The research was funded by the German Research Foun-dation (DFG) as part of the post graduate program mobilEM(GRK 1856).

REFERENCES

[1] A. Stippich, “Key Components of Modular PropulsionSystems for Next Generation Electric Vehicles,” en,CPSS Transactions on Power Electronics and Appli-cations, vol. 2, no. 4, pp. 249–258, Dec. 2017. DOI:10.24295/CPSSTPEA.2017.00023.

[2] A. Stippich, L. Frager, A. Sewergin, T. Kamp, andR. W. De Doncker, “Design of a High-Frequency Dc-DcConverter with a Custom Power Module and IntegratedCooling Structures,” in International Exhibition andConference for Power Electronics, Intelligent Motion,Renewable Energy and Energy Management (PCIM),Nuremberg: VDE, 2019.

[3] J.-P. Lee, H. Cha, D. Shin, K.-J. Lee, D.-W. Yoo, andJ.-Y. Yoo, “Analysis and Design of Coupled Inductorsfor Two-Phase Interleaved DC-DC Converters,” en,Journal of Power Electronics, vol. 13, no. 3, pp. 339–348, May 2013. DOI: 10.6113/JPE.2013.13.3.339.

[4] K. J. Hartnett, J. G. Hayes, M. G. Egan, and M. S.Rylko, “CCTT-Core Split-Winding Integrated Magneticfor High-Power DC–DC Converters,” IEEE Transac-tions on Power Electronics, vol. 28, no. 11, pp. 4970–4984, Nov. 2013. DOI: 10.1109/TPEL.2013.2240394.

[5] H. Kosai, S. McNeal, B. Jordan, J. Scofield, B. Ray,and Z. Turgut, “Coupled Inductor Characterization fora High Performance Interleaved Boost Converter,” IEEETransactions on Magnetics, vol. 45, no. 10, pp. 4812–4815, Oct. 2009. DOI: 10.1109/TMAG.2009.2024639.

[6] M. Fujimoto and Y. Naito, “Fully Optimized DiscreteCoupled Inductor DC/DC Converter as the TriMagiCConverter TM;” in PCIM Europe 2018; InternationalExhibition and Conference for Power Electronics, In-telligent Motion, Renewable Energy and Energy Man-agement, Jun. 2018, pp. 1–6.

[7] K. J. Hartnett, J. G. Hayes, M. G. Egan, and M. S.Rylko, “Novel CCTT-core split-winding integratedmagnetic for High-Power DC-DC converters,” in 2011IEEE Energy Conversion Congress and Exposition, Sep.2011, pp. 598–605. DOI: 10.1109/ECCE.2011.6063824.

[8] P.-L. Wong, Q. Wu, P. Xu, B. Yang, and F. C. Lee,“Investigating coupling inductors in the interleavingQSW VRM,” in APEC 2000. Fifteenth Annual IEEEApplied Power Electronics Conference and Exposition,vol. 2, Feb. 2000, 973–978 vol.2. DOI: 10.1109/APEC.2000.822807.

[9] L. Stiny, Passive elektronische Bauelemente, de. Wies-baden: Springer Fachmedien Wiesbaden, 2015. DOI: 10.1007/978-3-658-08652-7.

[10] Data Sheet 3f36 Material specification, Ferroxcube,Jun. 2013. [Online]. Available: https://www.ferroxcube.com/upload/media/product/file/MDS/3f36.pdf (visitedon 10/30/2018).

[11] Product specifications PLT64/50/5, 2016. [Online].Available: https : / / www . ferroxcube . com / upload /media/product/file/Pr ds/E64 10 50 PLT64 50 5.pdf(visited on 02/17/2019).

[12] Product specifications PQ50/50 Ferroxcube, 2016. [On-line]. Available: https://www.ferroxcube.com/upload/media / product / file / Pr ds / PQ50 50 . pdf (visited on12/22/2018).

[13] Product specifications PQ50/35 Ferroxcube, 2016. [On-line]. Available: https://www.ferroxcube.com/upload/media / product / file / Pr ds / PQ50 35 . pdf (visited on12/22/2018).

[14] A. Sewergin, A. H. Wienhausen, K. Oberdieck, andR. W. De Doncker, “Modular bidirectional full-SiCDC-DC converter for automotive applications,” en, in2017 IEEE 12th International Conference on PowerElectronics and Drive Systems (PEDS), Honolulu, HI:IEEE, Dec. 2017, pp. 277–281. DOI: 10.1109/PEDS.2017.8289126.