IEEE PEDS 2017, Honolulu, USA12 – 15 December 2017

Highly Efficient Power Inductors forHigh-Frequency Wide-Bandgap Power Converters

Arne Hendrik Wienhausen, Alexander Sewergin, Stefan P. Engel, Rik W. De DonckerInstitute for Power Electronics and Electrical Drives

RWTH Aachen University, Aachen, GermanyEmail: post@isea.rwth-aachen.de

Abstract—Highly efficient power inductors for high switchingfrequencies are required to take full advantage of modern wide-bandgap (WBG) semiconductors in terms of power densityand efficiency. However, appropriate inductors are usually notavailable from stock. In this paper a new design approachfor high-frequency power inductors is presented using planarcores, 3D printed spiral bobbins and copper foil in verticalorientation. Even though the presented approach is based on low-cost copper foil instead of expensive litz wire, it does not sufferthe typical drawbacks at high-frequency operation. It reducesthe required amount of copper significantly and shows excellentcopper utilization. The new design approach is presented indetail, key design parameters are discussed and simulation aswell as measurement results are shown and analyzed.

I. INTRODUCTION

Modern WBG power transistors based on silicon carbide(SiC) and gallium nitride (GaN) gain more and more popular-ity in power electronics. Their superior switching characteris-tics and low conduction losses result in high power densities ofpower electronic systems that cannot be covered by classic sili-con (Si) power semiconductors. To fully utilize the outstandingcharacteristics of SiC and GaN power transistors suitableinductive components for high-frequency operation are neededsince classic approaches limit the switching frequency due tohigh losses [1], [2], [3].

The design approach for highly efficient power inductorspresented in this paper is based on low-cost copper foil insteadof expensive litz wire. Nevertheless, it exhibits excellent high-frequency characteristics. A vertical copper foil orientation isused for an improved copper utilization. The copper thicknessof the used copper foil is a crucial design parameter and needsto be chosen according to the applied switching frequency.

Fig. 1 shows rendered images of the proposed inductordesign. While Fig. 1(a) shows the completely assembledinductor, the internal structure of the proposed inductor designis depicted in Fig. 1(b).

A 3D printed spiral bobbin serves as spatial separator foreach turn of the copper foil winding, ensuring a low parasiticcapacitance and providing insulation between each turn ofthe winding. A low parasitic capacitance is mandatory forhigh-frequency operation as it directly affects the resonantfrequency of the inductor which should be much higher thanthe switching frequency. Uninsulated copper foil can be usedif spacing is sufficient. The used copper foil is very thin andcan easily be cut and be placed inside the spiral.

(a) Completely assembled inductor

(b) Internal inductor structure

Fig. 1. Rendered images of the proposed inductor design

Iteration steps during the prototyping and optimization pro-cess can rapidly be applied and fabrication tolerances can bekept very small using high-precision 3D printers. The neededplastic parts for the design can be printed within a few hourson a modern 3D printer. Different laboratory prototypes havebeen built and characterized in the lab.

The key aspects of the new approach and measurement

978-1-5090-2364-6/17/$31.00 c©2017 IEEE442

Fig. 2. Transparently printed inductor prototype according to the presenteddesign approach (PLT ferrite plate removed for a clear view on the windingstructure)

results are presented and analyzed in the following. A transpar-ent version of a E43 E-PLT design according to the presentedapproach is depicted in Fig. 2.

II. COPPER ORIENTATION

Planar core shapes are typically used with horizontallyorientated copper traces as depicted in Fig. 3(a) and Fig. 4(a).This type of construction has various advantages compared toclassic wire-wound approaches [4]. The conductors may forexample also be integrated in a printed circuit board (PCB).

The horizontal copper orientation suffers one major draw-back. In the area where the magnetic field hits the coppernear the center leg of the inductor it shows an orientation iny-direction (see Fig. 3, marker A). Current flows through thecopper traces in z-direction. This leads to a concentration ofcurrent in x-direction towards the center leg of the inductordue to Lorentz force [5].

Ax

y

z(a) Horizontal copper orientation

x

y

z A

(b) Vertical copper orientation

Fig. 3. Cross section of a planar inductor including the magnetic field

J FL

FL

H

Jx

y

z

(a) Horizontal copper orientation

x

y

z

J FL

FL

H

J

(b) Vertical copper orientation

Fig. 4. Copper trace cross-section in horizontal orientation showing poorcopper utilization (a) and in vertical copper orientation resulting in superiorconduction characteristics (b)

In the presence of the magnetic field ~H = Hy · ~ey eachpositive charge e with a velocity ~vh = vh,z · ~ez in z-directionexperiences a force ~FL in x-direction according to (1).

~FL = e · ~vh × µ · ~H = e · µ · vh,z ·Hy · ~ex (1)

This phenomenon is depicted in Fig. 4 for the horizontal andthe vertical approach. While the current is concentrated in thearea facing the center leg of the inductor the area facing theoutside is hardly used for current conduction resulting in a highequivalent resistance and virtually unused copper, which forexample can result in additional losses as shown later in thispaper. Compared to the horizontal layout the vertical layoutfeatures superior copper utilization due to a significantly largercopper surface facing the center leg of the inductor.

In the horizontal layout this phenomenon can be observedon every copper trace in a similar fashion so that very highcurrents (winding turns times inductor current) are concen-trated in the center area forcing the magnetic field to changedirection abruptly. In the vertical approach the outer tracesare less affected than the inner traces as the magnetic fieldstrength continuously decreases with growing distance to theair gap due to less current concentrated in the center regionof the inductor (see Fig. 3).

III. COPPER THICKNESS

When designing power inductors for high-frequency opera-tion, the copper thickness wCu is a crucial design parameter asit significantly affects copper losses. Copper traces thicker thanthe skin depth should be avoided as they allow reverse currentsto be induced in the same copper trace, which can significantlyincrease the losses. These reverse currents can clearly be seenin simulation. Fig. 5 shows the current distribution inside thewinding for two different copper thicknesses. While the copperfoil with wCu = 100 µm shows only a small area conducting

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zoomarea

(a) wCu = 100 µm

zoomarea

(b) wCu = 200 µm

+ +

_

_

_

_

+ +

+

+

+

+

_

+

(c) Zoom on thecenter copper tracefor wCu = 100 µm

+

+

+

+

+

+

+

+

_

_

_

_

_

_

_

_

(d) Zoom on thecenter copper tracefor wCu = 200 µm

Fig. 5. Resulting current density inside the copper traces for copper thicknessof 100 µm (a, c) and 200 µm (b, d) (Ipeak = 10A, f = 500 kHz)

reverse current in the center trace (Fig. 5(c)), wCu = 200 µmresults in reverse current in nearly half of the cross-section(Fig. 5(d)).

In the calculation of the RMS value of the current Irms

according to (2) a significant amount of loss-generating currentis not taken into account as a part of the current is canceledout if positive and negative local current densities Jz both arepresent in one conductor.

Irms =

√√√√√ 1

T

t0+T∫t0

(∫∫ACu

Jz(t) dA

)2

dt (2)

Losses are generated everywhere in the conductor where

the current denstity differs from zero and conduction lossesin copper are independent of the current direction. Based on(3) - (5), Itot is introduced according to (6). Itot representsthe total RMS current in the cross-section ACu of one coppertrace regardless of the sign of the local current density Jz. Asa consequence, the amount of current which is canceled outin (2) due to different signs of Jz is fully taken into accountin the calculation of Itot according to (6).

Ptot = R · I2tot (3)

=1

T

t0+T∫t0

(∫lCu

(∫∫ACu

ρ(Jz(t))2 dA

)dl

)dt (4)

= ρlCu

ACu︸ ︷︷ ︸R

· ACu

T

t0+T∫t0

(∫∫ACu

(Jz(t))2 dA

)dt

︸ ︷︷ ︸I2tot

(5)

Itot =

√√√√√ACu

T

t0+T∫t0

(∫∫ACu

(Jz(t))2 dA

)dt (6)

Dependent on the copper thickness Itot and Irms can differwidely because of the reverse currents shown in Fig. 5.According to (7), Irel is defined as the ratio of Itot to Irms.

Irel =ItotIrms

=

√√√√√√ACu

t0+T∫t0

∫∫ACu

(Jz(t))2 dA(∫∫ACu

Jz(t) dA)2 dt (7)

Irel is presented in Fig. 6 for different copper traces as afunction of copper thickness. Increasing the copper thicknessreduces efficiency because additional reverse currents areinduced (Fig. 5). For a copper width wCu = 250 µm, the totalcurrent Itot in the center copper trace is 13 times higher thanthe RMS current Irms. These high currents result in very highcopper losses.

50 100 150 200 250Copper thickness w

cuin µm

0

5

10

15

20

Rel

ativ

e R

MS

cur

rent

Ire

l

Fig. 6. Irel for different copper traces as a function of copper thickness(Ipeak = 10A, f = 500 kHz)

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35 50 70 100 150 200 250Copper thickness w

cuin µm

0

2

4

6

8

10

12P

(wcu

) / P

vert

ical

(wcu

= s

kin

dept

h) Horizontal layoutVertical layout

skin depth(f = 500 kHz)

Fig. 7. Relative copper losses referenced to the copper losses of the verticallayout with wCu equal to the skin depth (Ipeak = 10A, f = 500 kHz, samewinding area for vertical and horizontal design)

The simulated relative copper losses pCu are depicted inFig. 7 for different copper thicknesses. The relative copperlosses are normalized to the copper losses of a vertical layoutwhere wCu is equal to the skin depth. For a copper thicknesshigher than the skin depth a strong rise in copper losses canbe observed. Thicker copper traces simply add losses Fig. 7also shows the normalized copper losses for the horizontallayout as a comparison. The same winding area was usedfor the horizontal as well as the vertical design. As predictedin the previous chapter, the vertical layout features superiorefficiency. It is shown that the copper losses are reduced atleast by a factor of two.

IV. PARALLEL CONDUCTORS

Parallel conductors are often used in order to lower theseries resistance of power inductors. If the areas spanned bythe parallel conductors differ in size (like in the proposeddesign), the use of parallel traces should be avoided, as asignificant reverse current is induced (Fig. 8). Copper lossesare not reduced but increased with additional conductors inparallel. According to Fig. 8(b), the current in the innerconductor i2 is even higher than the inductor current iL.This phenomenon has been verified in the lab with differentinductor prototypes. In designs with two conductors in parallel,connecting only one of the conductors significantly improvesinductor performance as not only the additional current in thedisconnected conductor can be avoided but also the currentin the remaining conductor is reduced to the total inductorcurrent.

A special case of parallel windings is litz wire where manyinsulated conductors are packed together. The single conductorpositions are transposed frequently to distribute the currentequally. The distance in which the positions are completelytransposed ltranspose is an important design parameter butoften unknown.

For high-frequency designs, inductors may become verysmall in size so that this distance is not neglectable. The strandcount in a litz wire design for applications with a nominalpower in the kilowatt range can easily reach a few hundreds

iL

i1i2

(a)

iL

i1

i2

t

i

(b)

Fig. 8. Iinductor consruction with parallel copper traces (a) and resultingcurrent waveforms for a triangular inductor current (b)

which makes ltranspose a critical parameter. On the other hand,keeping ltranspose short increases the total winding lengthsignificantly due to more changes of conductor positions perlength. This also increases copper losses. Thus, a single copperfoil winding is advisable for high frequency operation.

V. EXPERIMENTAL RESULTS

Various prototypes have been build, characterized in the laband used for successful validation of the simulation results.Besides the effects of the copper orientation and the copperthickness, very high resonant frequencies could be observedon the proposed design due to the low parasitic capacitance.This makes the proposed layout an excellent choice for high-frequency power electronics.

Fig. 9 shows measurement results for E43 and E58 gappedplanar E cores made from 3F36 ferrite material with 9 turns.The separator between each turn as well as the slot for thecopper foil both have a width of 0.5mm resulting in oneturn per millimeter. For the prototype with two conductorsin parallel, the turn per millimeter ratio is reduced by 50% asthe design also features a separator between parallel traces.

The designs with two E cores (E-E) allow to use a twotimes larger copper cross-section and, therefore, show goodperformance for applications with a dc offset (e.g. buck orboost converters) and frequencies below approx. 1MHz. Forhigh-frequency resonant power converters with no dc offsetin the inductor current the designs with an E-PLT core

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100 kHz 1 MHz 10 MHzFrequency

0

50

100

150L

in µ

H

0

1

2

3

4

5

6

7

8

Rs

in O

hm

E43 E-PLT 100µm copper foilE43 E-PLT 250µm copper foilE43 E-E 100µm copper foil

(a) E43/10/28 Core

100 kHz 1 MHz 10 MHzFrequency

0

50

100

150

Lin

µH

0

1

2

3

4

5

6

7

8

Rs

in O

hm

E58 E-PLT 1x100µm copper foilE58 E-PLT 2x100µm copper foilE58 E-PLT 630x100µm litz wireE58 E-E 1x100µm copper foil

(b) E58/11/38 Core

Fig. 9. Inductance L and series resistance Rs measurement results fordifferent winding strategies (measurements conducted with Agilent 4294A)

combination represent a promising layout as it shows superiorhigh-frequency characteristics (see Fig. 9).

The reasons for the superior high-frequency characteristicsof the E-PLT core designs are the lower parasitic capacitanceof the winding and the position of the air-gap which is locatedat one end of the center leg. This leads to a lower exposure ofthe winding to the fringing flux. In the E-E designs the air-gapis located in the middle of the center leg, which increases theexposure to the fringing flux.

For the E43 core (Fig. 9(a)), the series resistance of the in-ductor prototype with 250 µm copper thickness at a frequencyof 500 kHz is 5 times higher compared to the prototype with100 µm copper thickness. This clearly shows the significanceof the copper thickness wCu as a critical design parameter.

For the E58 core (Fig. 9(b)), the litz wire winding showsthe lowest resonant frequency and the highest series resistanceat a frequency of 430 kHz and above. If the design with twocopper foils in parallel (which should not be used as shownearlier in this paper) is excluded, this frequency even dropsto less than 150 kHz. Below this frequency litz wire with adiameter of 100 µm represents a reasonable choice. For higherfrequencies even thinner litz wires can be used, but this makesthe production process of the inductor extremely vulnerable tocracks in the litz wire. At a frequency of 500 kHz, the series

100 kHz 1 MHz 3 MHzFrequency

0

10

20

30

40

50

60

Rel

ativ

e co

pper

uti

liza

tion

Fig. 10. Improved copper utilization of the E58 E-PLT inductor design with100 µm copper foil winding referenced to the equivalent 630x100 µm litzwire design

resistance of the E58 litz wire prototype is 3.3 times higherthan the series resistance of the E58 E-PLT vertical copperfoil prototype with a copper thickness of 100 µm.

The proposed design reduces the required amountof copper significantly. The cross-section of the usedcopper foil is ACu,foil = 0.1mm · 5.0mm = 0.5mm2 andACu,litz = 630 · π · (0.1mm/2)

2= 4.95mm2 for the used

litz wire, which is nearly ten times as high.For the E58 E-PLT inductor with 100 µm thick vertical

copper foil, this leads to a more than 32 times higher copperutilization compared to the litz wire design at a frequencyof 500 kHz and above. A comparison for frequencies up to3MHz is given in Fig. 10. For higher frequencies the litz wiredesign begins to resonante. Because of the large cross-sectionof the litz wire, the copper utilization of the 100 µm copperfoil design is even 6.4 times higher at a frequency of 100 kHz.

In order to verify reverse currents in parallel windings,a full-SiC boost converter [6] has been equipped with theinductor prototype with two copper foils in parallel shown inFig. 12(b). The resulting current wave forms for a switchingfrequency of 150 kHz are presented in Fig. 11.

40 A20 A

20 A20 A

Parallel copper foil 2 Parallel copper foil 1

Total inductor current

Fig. 11. Measured current wave forms for the E58 inductor prototypewith 2x100 µm copper foil in parallel (Fig. 12(b)) showing excessive reversecurrent in green (f = 150 kHz, total inductor current in yellow)

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(a) (b)

(c) (d)

Fig. 12. E58 inductor prototypes (E58 E-PLT 100 µm copper foil (a), E58E-PLT 2x100 µm copper foil in parallel (b), E58 E-PLT 630x100 µm litz wire(c), E58 E-E 100 µm copper foil (d))

The single conductor currents are shown in magenta andgreen while the resulting total inductor current is depicted inyellow. It can be observed that the reverse current has the sameamplitude as the overall inductor current in this application.This results in an amplitude of twice the total inductor currentin the inner winding. Losses can be reduced significantly ifonly one single copper foil is used.

Photos of a selection of built prototypes are shown inFig. 12.

VI. CONCLUSION

A new design approach for high-frequency power inductorswith superior characteristics has been presented. The proposedsetup is based on copper foil which makes it very cost efficientwhile not suffering high copper losses. It has been shown thatthe orientation as well as the thickness of the used copper foilis a crucial design parameter. The proposed design outperformseven litz wire designs especially at high frequencies whilekeeping inductor costs low. At frequencies of 500 kHz andabove, the copper utilization is increased by a factor of morethan 32 compared to an equivalent litz wire design.

It has been shown that adding copper to the design doesnot automatically reduce copper losses. Parallel conductorsand copper foil which are thicker than the skin depth add asignificant amount of losses and, therefore, should be avoided.

For mass production the required plastic parts can be madeusing injection molding, which reduces the production coststo a minimum.

REFERENCES

[1] A. H. Wienhausen and D. Kranzer, 1 MHz Resonant DC/DC-ConverterUsing 600 V Gallium Nitride (GaN) Power Transistors, in Silicon Carbideand Related Materials 2012, ser. Materials Science Forum, vol. 740. TransTech Publications, 3 2013, pp. 1123–1127.

[2] C. Armbruster, A. Hensel, A. H. Wienhausen and D. Kranzer, Applicationof GaN power transistors in a 2.5 MHz LLC DC/DC converter forcompact and efficient power conversion, in 2016 18th European Con-ference on Power Electronics and Applications (EPE’16 ECCE Europe),Karlsruhe, 2016, pp. 1-7.

[3] G. Sarriegui, S. Beushausen and R. W. De Doncker, Comparison ofhigh frequency inductors for bidirectional DC-DC converters for electricvehicles, in 2016 18th European Conference on Power Electronics andApplications (EPE’16 ECCE Europe), Karlsruhe, 2016, pp. 1-8.

[4] L. L. Jenkins, J. M. Aggas, B. K. Rhea, W. E. Abell, C. G. Wilsonand R. N. Dean, Design and implementation of planar inductors forlow voltage GaN-based power converters, in 2015 IEEE Applied PowerElectronics Conference and Exposition (APEC), Charlotte, NC, 2015, pp.1381-1387.

[5] P. A Tipler and G. P. Mosca, Physics for Scientists and Engineers, NewYork: W. H. Freeman, 2003

[6] A. Sewergin, A. H. Wienhausen, K. Oberdieck, and R. W. De Doncker,Modular bidirectional full-SiC dc dc converter for automotive application,Accepted for PEDS 2017 in Honolulu, Hawaii, 2017.

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