Modeling and Experimentation of Loosely-Coupled Coils with Transmitter Having Orthogonally-Placed

Windings

Jeff Po Wa Chow*, Student Member, IEEE, Henry Shu Hung Chung*†, Senior Member, IEEE, Chun Sing Cheng*, Abdulmecit Gungor*, Sai Chun Tang‡, Senior Member, IEEE, and

Leanne Lai Hang Chan*, Member, IEEE

*Centre for Smart Energy Conversion and Utilization Research, City University of Hong Kong, Hong Kong † Research Institute of Electronic Automation, Shanghai Maritime University, Shanghai, China

‡ Department of Radiology, Harvard Medical School, Brigham and Women’s Hospital, Boston, MA, USA

Abstract - It is sometimes unavoidable to use loosely-coupled coils in applications, such as biomedical devices, for transferring electric energy wirelessly. However, coil misalignment would cause unwanted degradation of the power transfer efficiency. A coil structure that consists of two orthogonally-placed windings in the transmitter is investigated in this paper. Such structure lessens the variation of the coupling between the transmitting and receiving coil sets under the misalignment situations. A driving mechanism for maximizing the power transfer efficiency will be discussed. An experimental prototype has been built and evaluated under lateral and angular misalignments. Experimental results confirm the merits and are in close agreement with the theoretical predictions.

I. INTRODUCTION Wireless inductive links have been widely used in many

applications, such as cochlear implants, retinal prostheses, and battery chargers [1]-[3]. Fig. 1 illustrates a simplified diagram of a wireless inductive link system made of a single parallel transmitting coil and receiving coil. The transmitter consists of a coil driving circuit and a transmitting coil, and the receiver consists of a receiving coil and an end-use device (load). However, in the reality, the energy coupling coils are often misaligned, deteriorating the energy transfer capability and efficiency. The two coils are thus loosely coupled. Implantable spinal-cord stimulator (SCS) is a typical application that can take advantage of the wireless power transfer technology. SCS is a device that generates an electrical current to treat patients suffered from chronically neuropathic pain [4]-[5]. Fig. 2 illustrates the location of the implanted SCS device. The device is powered up externally through inductive power transfer. Although many improved transmitter and receiver designs have been developed, the

link efficiency is still constrained by a fundamental “bottleneck” – fluctuations of the power transfer efficiency due to the coil misalignment. When the coils are coaxially orientated, the coils are well coupled and thus the link efficiency is maximized. However, if the two coils are misaligned, the magnetic coupling and the overall link efficiency will drop and increase possible radiation exposure.

Fig. 1 Wireless inductive link with loosely-coupled coils [7].

Fig. 2 Implantable spinal-cord stimulation (SCS) device.

Spinal cord

Implantable device

This work was supported by a grant from the Research Grants Councilof the Hong Kong Special Administrative Region, China, through ProjectCityU 112613 and also under the program for professor of specialappointment (Eastern Scholar) at Shanghai Institutions of Higher learning.

978-1-4673-7151-3/15/$31.00 ©2015 IEEE 4927

According to the prior-art investigations [6]-[7], maximum transfer efficiency is primarily determined by the quality factors of the coils and the coupling coefficient between the two coils. It has also been demonstrated in [7] that degradation of the power transfer efficiency, due to coil misalignment, cannot be overcome effectively by simply changing the number of turns in the receiving coil.

In order to attain better magnetic coupling under misaligned conditions, a detailed investigation into the use of parallel and orthogonal windings in the receiving coil set for loosely-coupled link is presented in [7]. As discussed in [7], the concept of using an orthogonal winding is not limited to apply for the receiving coil set but also for the transmitting coil set. This paper extends the investigation by carrying out a scientific analysis on the performance characteristics of using an orthogonal winding in the transmitting coil.

Fig. 3 Proposed transmitting coil structure with a parallel winding and an

orthogonal winding.

II. MUTUAL INDUCTANCE BETWEEN COILS In order to study the effect of misalignment on affecting

the power transfer efficiency, the following investigations start with calculating the mutual inductance between the coils. The mutual inductance is defined as the amount of flux linked with the receiving coil due to unit current in transmitting coil. It is determined by the double integral Neumann formula [7]-[8]. The T-shaped transmitting coil structure shown in Fig. 3 is used to tackle the reduction of the mutual inductance under coil misalignments. One end of the added orthogonal winding is aligned on the same plane of the parallel winding, so that the space between the receiving coil and the proposed transmitting coil is the same as the structure with the parallel coil (Fig. 1). Without loss of generality, the two transmitting windings are assumed to have the same physical dimensions. Let M1 be the mutual inductance between the parallel winding and the receiving winding, and M2 be the mutual inductance between the orthogonal winding and the receiving coil. It should be noted that there is no inductive coupling between the parallel winding and the orthogonal winding as the two windings are spatially orthogonal. and represent the angular and lateral misalignments, respectively. Figs. 4(a) and 4(b) show

the profiles of M1 and M2 when = 0o and = 0%, respectively. The lateral misalignment is normalized by the dimension of the transmitting coil. When the transmitting coil is perfectly aligned with the receiving coil, M1 is maximized and M2 is zero. When the transmitting coil is displaced, M1 decreases but M2 increases. It should be noted that the polarity of the orthogonal windings is interchanged when or is negative. Therefore, when the misalignment increases, the coupling between the parallel winding and receiving coil will be imparted. Conversely, the coupling between the orthogonal winding and receiving coil will be improved.

(a) Lateral misalignment.

(b) Angular misalignment.

Fig. 4 Mutual inductance under lateral and angular misalignments.

III. MAGNETIC FIELD DISTRIBUTION The magnetic field distributions of the parallel, orthogonal,

and proposed structures are simulated by COMSOL Multiphysics [9], and visualized in Fig 5. Fig 5(a) shows the field pattern of the single parallel transmitting winding with an excitation current of 1A and the receiving coil being laterally misaligned. The generated magnetic field, represented by the streamlines, is perpendicular to the plane of the parallel winding.

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(a)

(b)

(c)

Fig. 5 Magnetic field profiles generated by the three transmitting coil sets.

Fig. 5(b) shows the flux pattern of the magnetic field generated by the orthogonal winding with an excitation current of 0.5A. Fig. 5(c) shows the flux pattern when the parallel and orthogonal windings are excited by 1A and 0.5A in-phase currents, respectively. Under this excitation condition, the resultant field pattern is orientated towards the receiving coil. Thus, most of the field flux generated by the transmitting coil is coupled to the receiving coil, being stronger than the ones shown in Figs. 5(a) and 5(b). As will be discussed in Sec. IV, with the added orthogonal winding, the strength of the coupling between the two coils is determined by the excitation currents on the two windings.

IV. MATHEMATICAL MODELING

A. Modeling and Optimization In order to achieve maximum power transfer efficiency,

the transmitting windings should be driven by two independent sources. Fig. 6 shows the transformer model of the proposed coil structure together with the series-type matching capacitors [7]. The subscripts “o” and “1” and “2” denote the receiving coil, parallel winding and orthogonal winding in the transmitting coil, respectively.

L and r represent the self-inductance and ac resistance of the windings. The series resonant capacitors C1, C2 and Co are connected to the corresponding winding for eliminating the effect of the self-inductance and hence, increasing the input power and efficiency.

Fig. 6 Equivalent circuit of the proposed winding structure.

Two independent sources vin1 and vin2 are connected to

the parallel winding and orthogonal winding, respectively. However, as the transmitting windings have high quality factors (> 200 in the experimental prototype) and are designed to operate at series resonance condition, the input impedances are low. Thus, the excitation should be of current mode. Thus, i1 and i2 should be controlled and regulated. As it will be discussed below, the ratio between the two excitation currents has to satisfy a relationship determined by the mutual inductances and the ac resistances of the windings.

Parallel winding

Receiving Coil

Magnetic Field

Orthogonal winding

Receiving Coil

Magnetic Field

Orthogonal winding

Receiving Coil

Magnetic Field

Parallel winding

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The mathematical model for describing the inductive energy transfer system shown in Fig. 6 is given in (1). The ratio between the two transmitting winding currents is given in (2), where δ denotes the phase shift between the currents. By substituting (2) into (1), the power transfer efficiency η is expressed in (3). Detailed derivation of (3) is given in Appendix A. The maximum efficiency is achieved by optimizing the transmitting winding current ratio.

1 1 11

1 1

2 2 2 2 22

1 2

1 0

10

1( )

in

in

o o

o oo

r j L j Mj C

v iv r j L j M i

j Cv i

j M j M r j Lj C

+ ω + − ωω

= + ω + − ωω

ω ω − + ω +ω

(1)

11

2 2

iii i

= ∠δ (2)

22 2

1 1 2 2

( ) ( )

L

oL o

RZ

R r r i r iU

η=+ + +

(3)

where 1/ ( )o L o o oZ R r j L j C= + + ω + ω

2 22 2 21 1 1 2 1 2 2 2( ) 2 cos( ) ( )U M i M M i i M i= ω + ω δ + ω

The optimized parameters and conditions, which are

given in (4)-(5), are determined by differentiating η with respect to δ and the current magnitude ratio. From (3)-(5), the maximum efficiency is given in (6).

2

1

0 , with 0

, otherwise

opt

opt

MM

δ = ≥

δ = π (4)

2 2 1

1 1 2,opt

i M ri M r

= (5)

2 21 2

1 2max 2 2

2 1 2

1 2

( ) ( )

( ) ( )( )[ ]

L

o L o

M Mr r

RM MZ R rr r

ω ω+η =

ω ω+ + + (6)

B. Mutual Inductances Ratio Estimation The optimized current ratio and maximum efficiency can

be achieved by determining the ratio between M2 and M1. The mutual inductance ratio is given in (7) while the derivation is detailed in Appendix B. An online algorithm for estimating the mutual inductance ratio is proposed as follows.

2

2 2 222

1 1 1 1

in

in

P i rMM P i r

−=

− (7)

where 1 1 1 1cos( )in inP v i= ρ and 2 2 2 2cos( )in inP v i= ρ . The mutual inductance ratio is obtained by (7) under the

required conditions that δ = 0 and |i1| = |i2|. Pin1 and Pin2 represent the peak input power to the two windings in the transmitting coil. ρ1 and ρ2 are the phase differences between the corresponding input voltages and currents. It should be noted that (7) reveals the polarity of the mutual inductance ratio to determine the optimized phase difference between the two input currents given in (4). A flowchart showing the algorithm for achieving maximum power transfer efficiency is shown in Fig. 7.

Fig. 7 Flowchart for ηmax .

The ac winding resistance, r1 and r2, are measured at the

beginning. The input currents to the two transmitting windings are regulated to have the same phase and magnitude, in order to satisfy the required conditions given in (7). Then, the input voltage and current are sampled to determine the input power. The mutual inductance ratio can therefore be estimated by using (7). Based on (4) and (5), the optimized input current ratio is determined and the currents are adjusted accordingly to achieve maximum power transfer efficiency.

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C. Comparison on the efficiency The power efficiency improvement contributed by the

orthogonal winding is studied by comparing the maximum efficiency ηmax of the proposed coil structure given in (6) to the efficiency ηs of the single parallel transmitting coil structure given in (8), where the single transmitting coil structure is shown in Fig. 1. From (6) and (8), the power efficiency ratio is obtained and given in (9). Based on (9), the maximum efficiency of the proposed winding structure is always higher than that of the single parallel winding because M2

2 > 0.

21

12

2 1

1

( )

( )( )[ ]

s L

o L o

Mr

RMZ R rr

ω

η =ω+ +

(8)

Dividing (6) by (8),

2 22 1 2

max 1 22

2 1

1

( ) ( )[ ]

( )

o

so

M MZ Kr r

MZ Kr

ω ω+ +η =

ωη + (9)

where 2 2 2

1 1 2

1 1 2

( ) ( ) ( )( ) [ ]L oM M MK R rr r r

ω ω ω= + + .

V. CIRCUIT IMPLEMENTATION

Fig. 8 Schematic of driving circuit

To realize the mutual inductances ratio estimation, two

power converters for driving the transmitting coil windings are built. A schematic of the power transfer system is shown in Fig. 8. The parallel and orthogonal windings are driven by Driver 1 and Driver 2, respectively. The two driver circuits are identical. Each one is composed of two power conversion stages. The first stage is a buck DC-DC converter, which regulates the DC-link voltage (i.e., Vdc1 and Vdc2). The second stage is a half-bridge series-resonant-parallel-loaded inverter. Each half-bridge is made of two GaN transistors, EPC2012. They are switched at the resonant frequency of 2.2MHz and their duty cycle is slightly less than 0.5. The magnitudes of voltages, vin1 and vin2, and currents, i1 and i2, and their phase difference

between the corresponding voltage and current waveforms are sampled. Moreover, the phase difference between the currents, i1 and i2, are sampled. The program shown in Fig. 7 is implemented in a microcontroller (STM32F4).

VI. EXPERIMENTAL VERIFICATIONS

A. Testing Setup The performances of the single parallel transmitting coil

and the proposed T-shaped winding structure are investigated on a test bed shown in Fig. 9. Such a setup allows altering and measuring the degree of lateral and angular misalignments. The receiving coil has 16 turns, and each of the transmitting windings has 10 turns. The parameters of the transmitting and receiving coils are given in Tables I and II. All electrical parameters are measured by an impedance analyzer, Agilent Impedance Analyzer 4294A. The two transmitting windings are individually driven by two RF amplifiers, Amplifier Research 75A250A and 25A100. The operating frequency is 2.2MHz. Two synchronized function generators, Wavetek 81, are connected to the RF amplifiers to regulate the phase angle between i1 and i2. Fig. 10 shows the waveforms of vin1, i1, vin2 and i2. Both input current magnitude and phase difference are individually adjustable.

Table I – Parameters of the transmitting coils

a (cm)

N1 , N2*

L1 (μH)

r1 ( )†

C1 (pF)

L2 (μH)

r2 ( )†

C2 (pF)

Litz Wire

(AWG/ Strands)

4 10, 0

9.47 0.65 553 -- -- -- 46 / 300

4 10, 10

9.47 0.65 553 9.91 0.63 526 46 / 300

Table II – Parameters of the receiving coil

b (cm) No‡ Lo (μH)

ro ( )†

Co (pF)

RL ( ) d (cm) Wire size

(AWG)

2.1 16 10.5 2.74 493 12 2 28 * N1 and N2 are the numbers of turns of parallel and orthogonal windings, respectively. † The ac resistance of the coil at the operating frequency of 2.2MHz ‡ No is the number of turns of receiving coil.

B. Efficiency Fig. 11 shows the calculated and measured power

efficiency of the energy transfer system prototype with the proposed transmitting coil under three different lateral misalignment conditions and with different transmitting coil current ratios when δ = 0. The efficiency is calculated based on (3) and consistent with the measured results. The formula given in (6) is applied and the calculated values are marked in the figure with corresponding colors.

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(a) Aligned condition.

(b) Lateral misalignment.

(c) Angular misalignment. Fig. 9 Experiment Setup

Fig. 10 Waveforms [Ch1: (5V/div), Ch2: (500 mA/div), Ch3: (5V/div),

Ch4: (500 mA/div)] (Timebase: 200 ns/div)

Fig. 11 Efficiency versus input current magnitude ratio under three lateral

misalignment conditions.

Fig. 12 shows the measured (ηmax,mea) and calculated (ηmax,cal) efficiency of the proposed T-shaped winding structure and that of the single parallel coil structure (ηs,mea and ηs,cal). Fig. 12(a) shows the efficiency under different lateral misalignment conditions when θ = 0°. Both calculated and measured results are consistent and show that the proposed coil structure can improve the efficiency for more than 10% when the lateral misalignment is more than 60%. Fig. 12(b) shows the efficiency profile under different angular misalignment conditions when Δ = 0cm. The efficiency of the proposed structure is always higher than 58% and the efficiency improvement is up to 40% at the angular misalignment of 80º.

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(a)

(b)

Fig 12 Maximized power transfer efficiency of two coil sets under misalignments.

C. Estimation of the Mutual Inductance Ratio Fig. 13 illustrates the wireless power transfer system

prototype and the experimental setup. Each transmitting coil winding is connected to an individual driver. The coil waveforms vin1, i1, vin2 and i2 are shown in Fig. 14. Again, both input current magnitude and phase difference are individually adjustable. Fig. 15 shows the mutual inductance ratio values calculated by the Neumann formula and estimated in real-time by a microcontroller under different misalignment conditions. Fig. 15(a) shows the results under different lateral misalignment conditions when θ = 0°. Both calculated and estimated values are consistent. The input current i1 magnitude increases while the misalignment increases and the magnetic coupling decreases. The designed operating range allows a lateral misalignment of ±60%. Fig. 15(b) shows the ratio under different angular misalignment conditions when Δ = 0cm. Both calculated and estimated values are in close agreement.

Fig. 13 Driving circuit for the windings.

Fig. 14 Waveforms [Ch1: (5V/div), Ch2: (500 mA/div), Ch3: (5V/div),

Ch4: (500 mA/div)] (Timebase: 200 ns/div)

(a)

13.6%

vin1

i1

vin2

i2

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(b)

Fig. 15 Mutual inductance ratio (M2/M1) estimation under misalignments.

VII. CONCLUSIONS A comprehensive investigation into the use of an

orthogonal winding added to the transmitting coil for enhancing the power transfer efficiency under different coil misalignment conditions has been presented. The criteria for driving the windings so as to ensure maximum power transfer efficiency are formulated. Both theoretical and experimental results show that the power transfer efficiency under both lateral and angular misalignment conditions can be effectively increased by the added orthogonal winding. The analysis method discussed in this paper is generic and can be extended to study complex structures.

APPENDIX

A. Derivations of (3)

1 1 2 2o

o

j M i j M ii

Zω + ω= (A1)

2 2

1 1 1 1 2 21

[ ( ) ]oin

o

Z Z M i M M ivZ

+ ω + ω= (A2)

2 2

2 2 2 1 2 12

[ ( ) ]oin

o

Z Z M i M M ivZ

+ ω + ω= (A3)

where

1 1 11

1Z r j L

j C= + ω +

ω

2 2 22

1Z r j L

j C= + ω +

ω

1

o L o oo

Z R r j Lj C

= + + ω +ω

21 2 1 2

1 2

2221 1

1 12

1[( ) cos( ) ( ) sin( )]

( )( )

L o oo

in

o

L o

o

M M R r L i iCP

ZR r M i

r iZ

ω + δ − ω − δω=

+ ω+ +

(A4)

21 2 1 2

2 2

2222 2

2 22

1[( )cos( ) ( )sin( )]

( )( )

L o oo

in

o

L o

o

M M R r L i iCP

Z

R r M ir i

Z

ω + δ + ω − δω=

+ ω+ +

(A5)

1 2

out

in in

PP P

η=+

(A6)

B. Derivations of (7) When 0δ= ,

21 2 2 1 1 11 1 12

( )( )L oin

o

M R r M i M i iP r i

Z

ω + ω + ω= + (B1)

22 1 1 2 2 22 2 22

( )( )L oin

o

M R r M i M i iP r i

Z

ω + ω + ω= + (B2)

2

21 1 1 1

2 2 1 1 1

( )( ) ( )

oin

L o

ZM P r i

R r M i M i i= −

ω + ω + ω (B3)

2

22 2 2 2

1 1 2 2 2

( )( )( )

oin

L o

ZM P r i

R r M i M i i= −

ω + ω + ω (B4)

When 1 2i i= , the ratio between M2 and M1 is equal to (7).

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