Modeling and characterization of PCB coils for inductive wireless charging [original]

research articles

Modeling and characterization of PCB coils

for inductive wireless charging

brian curran

, uwe maaß

, gerhard fotheringham

, nobby stevens

, ivan ndip

and klaus-dieter lang

1,2

Wireless charging is emerging as a viable technology in many industries, including consumer, medical, and sensor electronics.

An investigation of design principles is conducted for a wireless charging platform that is designed to charge devices of different

sizes and technologies, using only through vias. It is shown that at a 5 mm separation distance, a coupling coefﬁcient can be

achieved which varies from 0.12 to 0.37 when staggered hexagonal transmitter coils (approximately 5 cm across) are used with

an unstaggered square receiver coil, which declines to 0.06–0.11 at 2 cm separation. Without design measures, the coupling

coefﬁcient will approach zero at certain positions. The quality factors of the coils can be improved by stacking the coils in

parallel, enabling the use of only through-vias, while the inductance can be controlled horizontally by increasing the

number of turns in the inductor.

Keyword: Wireless power transfer

Received 23 April 2015; Revised 8 September 2015; Accepted 8 September 2015; ﬁrst published online 22 October 2015

I. INTRODUCTION

In recent years, the number of wireless charging devices has

increased in the electronics market. Wireless charging has

many applications, including in medical electronics [1], wire-

less communication [2], as well as consumer and sensor

applications [3]. This technology has the advantage that

there are no sparks, which eliminates risks in environments

where explosive materials are present. It enables devices to

be hermetically sealed. It allows different objects to be

recharged with a single charger at different orientations.

Wireless charging allows objects to be charged during use

and while moving, for example a sensor on a moving piece

of machinery.

Wireless power transfer traditionally uses inductive coup-

ling between a transmitter and receiver inductor coil.

Various research have been done on coil design for wireless

power systems. For example, in litz wire coils, losses in induct-

or coils were examined in [4,5]. Coils in printed circuit boards

(PCBs) have also been widely used for wireless charging appli-

cations [6,7]. Multiple layer coils in ﬂex substrates have also

been studied in [8]. Bond-wires on a PCB substrate arranged

as coils have also been suggested in [9].

In order to increase the coupling coefﬁcient, and thereby

the efﬁciency, of a wireless power link, there have been

efforts to achieve a more homogeneous coupling factor for

wireless charging platforms. For example, Casanova has

done a simulation analysis of a square-shaped planar coil,

where the windings have a staggered separation distance to

achieve a more homogeneous magnetic ﬁeld above the coil

[10]. Waffenschmidt has conducted a similar study using cir-

cular coils in litz wire technologies [11]. These papers have

shown that is it possible to arrive at a very homogeneous mag-

netic ﬁeld distribution by carefully staggering the distance

between the windings of the coil.

Various papers have also investigated placing coils in an

array conﬁguration, so that the transmitter coil can achieve

a much larger charging area. Square coils were used by

Matsumoto et al. [12], where the coils were excited with

three different phases. Square coils were also used by

Yinliang et al.[13], where two coils, with staggering to

improve magnetic ﬁeld homogeneity, were placed adjacently

or overlapping. Matsumoto limited his research to coils in a

straight line and Yinliang limited his research to only two par-

allel or overlapping square coils. Therefore, these papers have

neglected the case where four square coils are arranged in an

array and come to a corner. Ahn et al.[14] investigate this

case, where it is shown that, in general, a very homogeneous

ﬁeld distribution can be achieved but only with exceptions.

An array of four square transmitter coils introduces areas

where the ﬁelds cancel each other, resulting in areas where

the coupling coefﬁcient between the transmitter and receiver

coils is nearly zero.

Circular coils, usually overlapping, have also been used in

wireless charging platforms. Ma and Ma in [15], use circular

planar PCB coils, overlapping in three different layers, to

achieve a charging platform with no areas where the magnetic

ﬁeld is cancelled out. However, the ﬁeld strength is much

Corresponding author:

B. Curran

Email: [email protected]nhofer.de

TU Berlin, Straße des 17, Juni 135, 10623 Berlin, Germany. Phone:

+4903046403757

Fraunhofer Institute for Reliability and Microintegration, Gustav-Meyer Allee 25,

13355, Berlin

Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgien

127

Wireless Power Transfer, 2015, 2(2), 127–133. #Cambridge University Press, 2015

doi:10.1017/wpt.2015.14

stronger in the middle. This would be an advantage for certain

applications but a disadvantage for others. In [16], circular

coils were simulated by Sun et al. in an array form. In a

simple single-layer array conﬁguration, Sun et al. achieve a

magnetic ﬁeld across the entire platform; however, little atten-

tion is given to the homogeneity of the coupling coefﬁcients.

Shen et al.[17] and Zhong et al.[18] have also built arrays

of circular coils using litz wire and ferrite cores, respectively.

Like Sun et al., they achieve a link over a large area platform,

but little attention is made to homogeneity and the resulting

transmitters are much thicker, due to the integration of the

ferrite cores.

Hexagonal coils offer the advantage that they ﬁt better in

an array conﬁguration but, unlike square coils, do not neces-

sarily have magnetic ﬁeld cancellation spots. Overlapping

hexagons, for example, have been presented by Jow and

Ghovanloo in [19] for a sensor application. Very signiﬁcant

research has been conducted by Liu and Hui in a series of

papers [20–23] regarding hexagonal wireless charging plat-

forms. Additionally, Achterberg presents a mixed approach

with square and hexagonal coils stacked in different layers

[24]. Although this research is very signiﬁcant and represents

the most advanced approach, it also has certain disadvan-

tages. For example, the approach places hexagonal coils over-

lapping in different layers. This makes it difﬁcult to

implement the cheapest manufacturing technologies such

as through-vias. And while the research improves the homo-

geneity of the ﬁelds on the platform to improve the

efﬁciency, it pays little attention to the resistance of the

coil. Waffenschmidt [11] has presented a charging platform

with staggered coils in a single layer that requires the receiver

coil to be less than half the size of the transmitter coil.

Although this is an excellent advancement that would allow

for reduced cost charging platforms, it poses a signiﬁcant

challenge for small devices because the transmitter coils

must remain so small.

Creating a magneti-inductive waveguide, with multiple

coils resonating has been another approach for creating

large area wireless power transfer platforms. Shamonina

et al. has proposed a magneto-inductive waveguide that uses

many elements as a magnetic guide for magnetic resonance

imaging [24]. Stevens [25] has designed and modeled a mag-

netic relay system which generates a magneto-inductive wave,

which provides 58% efﬁcient power transfer to any point on

its length. Puccetti et al. has designed and built a similar

array of spiral resonators that are used to transfer power

from a transmitter to a receiver [26]. In [27], Puccetti et al.

conduct an analysis to improve the performance of a multiple

inductively coupled resonator coil system.

The goal of this paper is to propose a charging platform

that uses a staggering of the windings of a coil to achieve a sat-

isfactory coupling coefﬁcient homogeneity, using square and

hexagonal coils without overlapping. By not overlapping

coils, one eliminates interaction between the coils on different

layers. Resistance of the coils can be signiﬁcantly decreased by

connecting coils on different layers in parallel with through-

via technology, thereby offering a higher degree of control

over the efﬁciency, power-handling capability, and heat dissi-

pation of the charging platform. The charging platform should

be suitable for different receiver coils, of different sizes and

shapes, representing different device sizes. The platform

should also accommodate receiver coils of different heights,

representing different coil integration in devices.

II. MODELING OF HOMOGENEITY IN

SQUARE COILS

Publications have shown that planar coils, with evenly spaced

turns, show a much stronger magnetic ﬁeld above the center

of the coil. By increasing the turn density toward the outside

of the coil, one can increase the homogeneity of the magnetic

ﬁeld. In this section, we will focus on the homogeneity of the

magnetic ﬁeld when two square coils are adjacent to each

other and how that translates into a coupling coefﬁcient.

Two adjacent square transmitter coils were simulated with

Ansys Maxwell 3D with a third receiver coil placed some

distance above, as shown in Fig. 1.Inthissection,noferrites

were used in the simulation. Three different coils, each with

5 cm edges and ten turns, but with different spacing between

the coils (different staggering) were compared as transmitter

coils, which are shown in Fig. 2. The evenly spaced coil has

Fig. 1. Diagram of the simulation model.

Fig. 2. Three different coil geometries for comparison.

128 brian curran et al.

conductor widths of 2 mm and gaps of 0.5 mm. The staggered I

coil has gaps of 0.25 mm and widths of 0.75, 0.75, 0.75, 1, 1.25,

2, 2.5, 4.75 and 4.75 mm. The staggered III coil had gaps of

0.25 mm and widths of 0.5, 0.5, 0.5, 0.75, 0.75, 1.5, 1.5, 3 and

9 mm. Each coil has nine turns. The receiver coil remains an

evenly spaced rectangular coil, which represents a generic

device with a coil that the designers of the charging platform

likely cannot control.

The receiver coil is shifted across the transmitter coils in

the X-direction, where X¼0 mm means that the center of

the receiver coil lies directly in the gap between the two

coils and X¼+/225 mm means that the receiver coil is

exactly centered over one of the receiver coils. Figure 3

shows the sum of the coupling coefﬁcients of the receiver

coil and each of the two transmitter coils. In this case, we

are deﬁning the coupling coefﬁcient as the fraction of the

ﬂux generated by the ﬁrst coil that ﬂows through the second

coil and vice versa [28]. When we examine, in Fig. 3(a), the

evenly spaced square transmitter coils, we see that there is

an excellent coupling when the coils are aligned but almost

a zero point when the receiver coil lies at X¼0 mm. For

the staggered transmitter coils, there is a signiﬁcantly higher

coupling at X¼0 mm, with a coupling coefﬁcient above

0.25 for the most staggered coil. There is still a strong

maximum when the coils are aligned but there are no longer

any dead spots, where the coupling is nearly zero.

Figure 3(b) shows that, when the separation distance

between the receiver and transmitter increases, the coupling

coefﬁcient becomes more homogeneous. The two curves,

one that represents the maximum coupling coefﬁcient and

on that represents the smallest, nearly converge as the separ-

ation distance increases from 1 to 20 mm.

Based on these simulations, one can see that it is possible to

achieve a coupling coefﬁcient everywhere over two square

transmitter coils .0.2, even at a very small separation dis-

tance. This coupling coefﬁcient becomes more and more

homogeneous as the distance between the receiver and trans-

mitter increases.

III. INFLUENCE OF FERRITES ON

COUPLING COEFFICIENT

Adding ferrites to the structure, usually below the transmitter

or above the receiver coil, was tested in the same simulation to

see their effects on the coupling coefﬁcient. When a ferrite is

placed between the transmitter and receiver coils, then it

acts as a shield leading to almost no coupling between the

coils. When it is placed above the receiver coil only, it slightly

reduces the coupling coefﬁcient. Only when the ferrite is

placed below the transmitter coil (with or without a ferrite

above the receiver coil), is there a slight improvement in the

coupling coefﬁcient. That improvement, however, is ,10%,

for example an increase from 0.65 to 0.70 when the coils are

in alignment, which is shown in Fig. 4.

IV. MODELING OF RESISTANCE

AND INDUCTANCE

The link efﬁciency is not only dependent on the coupling coef-

ﬁcient, but also dependent on the quality factors of the coils.

When the radius of the coil remains constant and the

number of turns changes, while the maximum width of the

turn remains the same, the inductance and resistance

change exponentially. This occurs because, when the radius

is constant, the inductance will be dependent on the square

of the number of turns. Resistance increases exponentially

because it will be dependent on the total length of the coil,

which increases linearly with the number of turns, and

inversely proportionally to the width of the conductor,

which decreases approximately linearly with the number of

turns.

What this means that the quality factor, which is propor-

tional to the inductance and inversely proportional to the

resistance, changes little when the inductance changes, for a

given radius. This stability can be used to design coils for

Fig. 3. Comparison of coupling coefﬁcients for (a) three different coils as a

receiver coil shifts across and (b) as a receiver coil is lifted above. Fig. 4. Inﬂuence of ferrite placement on coupling coefﬁcient.

modeling and characterization of pcb coils 129

only through vias, which is a less expensive technology. The

inductance for a given size coil can be determined by the

number of coils and the resistance can be decreased by

placing additional coils in parallel on additional layers in the

PCB. Because they are all in parallel, they can easily be con-

nected without blind or buried vias.

Ferrites can also be applied to a coil to increase its induct-

ance and quality factor. Figure 6 shows an investigation of the

inductance and resistance of the coils with and without ferrites

underneath. The study shows that ferries raise the inductance

by approximately 50%, with only a slight variation when add-

itional coils are stacked in parallel. DC resistance with and

without ferrites is also nearly identical. However, in the kHz

frequency range, due to skin-effect and ferrite conductivity,

there is an additional increase in the losses, especially in the

cases where coils are stacked. In fact, despite the increase in

the inductance from the ferrites, the quality factor of the

coils in the kHz frequency range may see no improvement

when ferrites are added because of the increase in losses.

For example, the quality factor of a coils with four layers

stacked in parallel, at 80 kHz, is approximately 10 with and

without ferrites.

V. MODELING OF HOMOGENEITY IN

HEXAGONAL COILS

In order to create a larger charging platform, more than two

coils need to be placed in the array. When four-square coils

are placed in an array conﬁguration, there is an area in the

center of the array where the magnetic ﬁeld cancels out, as

shown in Fig. 7. Therefore, it is more practical for a charging

array to use hexagonal coils.

New staggered coils were constructed, as shown in Fig. 8,

with a hexagonal proﬁle. The coils have conductor widths of

1, 2, 3, 4, 5 and 6 mm for staggered I. Staggered II has con-

ductor widths of 0.5, 0.5, 0.5, 2, 3, 4 and 5 mm. Staggered

III has conductor widths of 0.5, 0.5, 0.5, 4, 4, 6 and 6 mm.

In this case, the receive coil remains square and is not stag-

gered but has approximately the same area as one transmitter

coil, in order to examine a realistic scenario where the receiver

coil and charging platform have not been optimized for each

other.

Two paths were simulated for the receiver coils to cross an

array of four hexagonal coils. The ﬁrst route crosses through

the middle of the coils and the other route crosses over the

Fig. 5. Inductance and resistance for a 5 cm coil, with maximum line width, for a given number of turns.

Fig. 6. Inductance and resistance for up to four coils stacked in parallel with and without ferrites.

130 brian curran et al.

edges, including the corner where three coils meet. The paths

are shown in Fig. 9.

One sees in Fig. 10 that the amount that the hexagon is

staggered changes the homogeneity of the magnetic ﬁeld,

but there is still a strong dependence on the position of the

receiver coil. That being said, one can increase the

minimum coupling coefﬁcient by more than 50%.

When we compare the two different paths, at different dis-

tances, in Fig. 11, we can also see that the minimums remain

relatively close to each other. The coupling coefﬁcient dips to

0.1 at a minimum, at 5 mm separation distances, and vary

between the two paths by about 30%. The maximum coupling

coefﬁcients vary by more than 100%; however, the maximum

is only achieved when the receiver and transmitter coils are

exactly aligned. When the distance between the transmitter

and receiver is increased to 20 mm, the coupling coefﬁcient

becomes much more homogeneous, varying from approxi-

mately 0.07 to 0.11 across the region where the receiver coil

lies completely on top of the charging platform, and decaying

slowly as it is shifted off.

VI. MEASUREMENT RESULTS

To measure the coupling coefﬁcients, the input inductance of

the transmitter coils was measured twice with the receiver coil

at the given position. It was measured once with a short circuit

at the receiver coil output and again with an open circuit at the

receiver coil output. One can then use equations (1)–(7), based

on Fig. 12, to calculate the mutual inductance and the coup-

ling coefﬁcient of the two coils.

Fig. 7. Magnetic ﬁeld for an array of four transmitter coils.

Fig. 8. Staggered hexagonal coils.

Fig. 9. Crossing paths of the receiver coils.

Fig. 10. Coupling coefﬁcient over Path 2 for three different hexagonal coil

geometries for a 5 mm coil separation distance.

Fig. 11. Comparison of the coupling coefﬁcients of two receiver coil paths at

5 mm separation distance (top) and 20 mm (bottom).

modeling and characterization of pcb coils 131

We begin by using Kirchoff’s voltage law for both the trans-

mitter and receiver coil sides, resulting equation (1) (transmit-

ter side) and equation (2) (receiver side).

U1=j

L1i1+j

Mi2,(1)

U2=j

L2i2+j

Mi1.(2)

Then, when the receiver is open-circuited, we can assume

that no current ﬂows on the receiver side, equation (3).

Then, equation (2) can be simpliﬁed to equation (4):

i2=0,(3)

U2=j

L1i1.(4)

Oppositely, when the receiver is short-circuited, equation

(5), then equation (2) is simpliﬁed to equation (6):

U2=0,(5)

L1i1=−i

Mi2.(6)

We can solve equations (6) and (4) simultaneously:

ZMeas =j

L1L1−M2



.(7)

This allows us to determine the coupling coefﬁcient from

impedance measurements at the coil inputs. The measure-

ments and the simulations show an excellent correlation, as

shown in Fig. 13.

VII. CONCLUSIONS

Based on simulation data, validated by measurements, it has

been shown that a transmission coefﬁcient can be achieved

that varies by approximately 50% from the average value at

a separation distance of 5 mm and 10% at a separation dis-

tance of 20 mm. Although the transmission coefﬁcient is not

as homogeneous as other published research, the receiver

coil is not limited to being larger than the transmitter coil.

The approach could be used to achieve a homogeneous char-

ging platform for use with arbitrary-sized receiver coils, for

example different consumer products on the same platform.

The approach can also be used when the receiver coil must

be contained in a small housing, medical devices, and

implants, for example.

ACKNOWLEDGEMENTS

This research was supported by the German Federal Ministry

for Economic Affairs and Energy, the Zentralverband

Elektrotechnik- und Elektronikindustrie e.V. (ZVEI) and the

German Federation of Industrial Research Associations (AIF).

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Brian Curran received his B.S. in elec-

trical engineering from the University

of Rochester, New York, his M.S. from

the University of Kassel, Germany and

his doctor of engineering from the

Technical University of Berlin. He has

worked at the Fraunhofer Institute for

Reliability and Microintegration since

2008. His research includes signal and

power integrity, antenna design and integration and electro-

magnetic compatibility.

modeling and characterization of pcb coils 133