IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 68, NO. 9, SEPTEMBER 2020

4031

Digital Transmitter Coil for Wireless Power
Transfer Robust Against Variation ofDistance and Lateral Misalignment
Hao Qiu , Member, IEEE, Takayasu Sakurai, Fellow, IEEE, and Makoto Takamiya , Senior Member, IEEE

Abstract— A digital transmitter (TX) coil consisting of several
subcoils connected in parallel is proposed in wireless powertransfer (WPT) systems robust against the variation of distanceand lateral misalignment. According to the position of thereceiver coil, the radius of the digital TX coil can be programed
to its optimal value to achieve the maximum coil-to-coil efficiency.
Moreover, targeting the wireless charging of mobile devices,
we propose a practical design methodology for the digital TX coil.
It is concluded that the digital TX coil consisting of two subcoils isan effective design and that the performance is not significantly
improved by adding more subcoils. The optimal radius ratioof these two subcoils is 0.54. Furthermore, we implement thedesigned digital TX coil in a prototype WPT system, including
a power amplifier and a rectifier. Experimental results showthat within a space with a maximum distance and lateral
misalignment of 100 mm, the system efficiency is improved by
the digital TX coil and reaches a maximum value of 48%.
Compared with using a conventional TX coil with a constantradius, the system efficiency shows an absolute improvement of
up to 7%.
Index Terms— Coil design methodology, coil-to-coil efficiency,
distance, lateral misalignment, magnetic resonance coupling,mutual inductance, optimal radius, wireless power transfer (WPT).

I. I NTRODUCTIONW

IRELESS power transfer (WPT) based on magnetic
resonance coupling has been applied in a wide range ofapplications, such as mobile devices and biomedical implanted
devices [1]–[3]. The variation of the distance and lateral
misalignment of the receiver (RX) coil relative to the transmitter (TX) coil, however, strongly affects the WPT systemefficiency (ηSYS ) and is a critical problem. The discussion ofangular misalignment is out of the scope of this article. During
the wireless charging of mobile devices, it is preferable thatdevices are not placed on a wireless charging pad but can beheld in hand and operated. Therefore, a method robust against
the variation of distance and lateral misalignment is required
for WPT systems.
Manuscript received January 11, 2020; revised March 9, 2020; accepted
April 12, 2020. Date of publication May 14, 2020; date of current version
September 2, 2020. This work was supported by Japan Science and Technology Agency (JST) Exploratory Research for Advanced Technology (ERATO),
Japan, under Grant JPMJER1501. (Corresponding author: Hao Qiu.)
The authors are with the Institute of Industrial Science, The University ofTokyo, Tokyo 153-8505, Japan (e-mail: hqiu@iis.u-tokyo.ac.jp).
Color versions of one or more of the figures in this article are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TMTT.2020.2990976

The previously reported methods are mainly divided into
three categories [1]: control methods [4]–[11], circuit compensation topologies [12]–[14], and coil design [15]–[18].
In the first category, frequency tracking [4]–[6], impedance
matching networks [7], [8], and coil repeaters [9]–[11] havebeen proposed to achieve impedance matching between the
TX coil input impedance and the source impedance over awide range. In the second category, in addition to the traditional compensation topologies (series–series, series–parallel,parallel–series, and parallel–parallel), several new topologies,
such as capacitor–capacitor–inductor [12], inductor–capacitor–
capacitor [13], and hybrid topologies [14], with better misalignment performance have been proposed. However, in theabove-mentioned two categories, the complex circuit topology
makes the system more sensitive to parameter variations [19],affecting its reliability. In addition, coil-to-coil efficiency (η)
cannot be improved.
On the other hand, in the third category, the coil design
can directly maximize η, and thus, maximize ηSYS . Fromthe practical viewpoint, the TX coil design is preferable to
the RX coil design. In [15], the pattern of the TX coil
was designed to realize a relatively uniform magnetic field
distribution under lateral misalignment. However, its tolerance
to the variation of distance is not demonstrated. In [16], theoptimal TX coil layout design with respect to the distance
was proposed, but it was not discussed how to change its
layout adaptively. Volumetric coil structures [17], [18] havebeen proposed to minimize the effects of variation of distanceand lateral misalignment but are not easily implementable inpractice.
Our major contributions in this article are summarized asfollows: 1) we propose a digital TX coil topology, which
consists of several subcoils connected in parallel where thecoil radius can be programed to its optimal value giving the
maximum η. 2) We propose a practical design methodology forthe digital TX coil, including the number of subcoils and theirradii, under the variation of distance and lateral misalignment.
3) We implement the digital TX coil in a prototype anddemonstrate its effectiveness in a WPT system robust against
the variation of distance and lateral misalignment. Comparedwith our earlier work [20], we have added a discussion aboutlateral alignment, proposed a practical design methodology,
and implemented the digital TX coil in a prototype WPTsystem.

0018-9480 © 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See https://www.ieee.org/publications/rights/index.html for more information.

Authorized licensed use limited to: University of Tokyo. Downloaded on September 20,2020 at 12:41:21 UTC from IEEE Xplore. Restrictions apply.

4032

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 68, NO. 9, SEPTEMBER 2020

Fig. 2.

Simplified equivalent circuit of a WPT system.

resistance (R S ), an inductor (L TX ) with a parasitic resistance(RTX ), and a compensation capacitor (CTX ). The RX side iscomposed of an inductor (L RX ) with a parasitic resistance(RRX ), a compensation capacitor (CRX ), and a load resistance(R L ). The currents flowing in the TX and RX sides are ITX
and IRX , respectively. k is the coupling coefficient between
the TX and RX coils. Applying Kirchhoff’s voltage law to
the circuit, we obtain the following equations at the resonancefrequency ( f 0 ):
ω0 = 2π f 0

M = k L TX L RX

Fig. 1. (a) Configuration of the TX and RX coils. A single turn of TX
and RX coils is shown for simplicity. (b) rTX dependence of η. (c) Position
dependence of η using the conventional TX coil with constant rTX and the
proposed TX coil with programmable rTX .

The rest of this article is organized as follows. In Section II,
the optimal radius of the TX coil giving the maximum η isdiscussed. Then, the digital TX coil topology is proposed in
Section III. A practical design methodology for the digital TX
coil under the variation of distance and lateral misalignmentis proposed in Section IV. Experimental results are presented
in Section V. Finally, conclusions are given in Section VI.
II. O PTIMAL T RANSMITTER C OIL R ADIUS FOR M AXIMUME FFICIENCY UNDER THE VARIATION OF D ISTANCE AND
L ATERAL M ISALIGNMENT
Fig. 1 shows the key concept of this article. The configuration of the TX and RX coils is shown in Fig. 1(a). The
radii of the TX and RX coils are denoted by rTX and rRX ,respectively. In this article, the axes of the coils are always
parallel. Distance and lateral misalignment are denoted by z
and x, respectively. As shown in Fig. 1(b), η shows a peakwhen rTX approaches its optimized value (rTX,OPT) and asmaller or larger rTX will degrade η [20], [21]. In our WPT
system design, we first optimize the TX coil to maximize η at
the farthest position (x, z). When the RX coil moves nearerto (x’, z’), with a constant rTX in the conventional (CON)design, η increases to η’CON owing to the enhanced coupling.
On the other hand, if a TX coil with an adjustable rTX isused in the proposed (PPSD) design, η’CON can be further
improved to η’PPSD . Thus, compared with the conventional
design, the proposed design can achieve better misalignment
tolerance. In this section, we derive the relationship between
rTX,OPT and (x, z).

VS = ITX [R S + RTX + j ω0 L TX + 1/( j ω0CTX )]− j ω0 M IRX
j ω0 M ITX = IRX [RL + RRX + j ω0 L RX + 1/( j ω0 CTX )](1)
L TX CTX = L RX CRX = (ω0 )−2where M is the mutual inductance between the TX and RX
coils, ω0 is the resonant angular frequency, and j is theimaginary unit.
η is defined by the ratio of the power output from the RX
coil to the power input into the TX coil [22]. In addition,
when R L is assumed to equal its optimal value (R L,OPT ) of
RRX (1 + k 2 Q TX Q RX )1/2 , η can be expressed asη=

k 2 Q TX Q RX
(1 + 1 + k 2 Q TX Q RX )2

(2)

where
k 2 Q TX Q RX =(ω0 M)2.
RTX RRX(3)

Here, Q TX and Q RX are the quality factors of the TX
and RX coils, respectively. Thus, η can be maximized by
maximizing k 2 Q TX Q RX .
B. Derivation of Optimal Transmitter Coil Radius

A. Equivalent Circuit Analysis

k 2 Q TX Q RX , on the other hand, is correlated with the physical parameters of the coils. First, we discuss the calculationof the coil resistances. For a tightly wound coil, the resistancedepends on both the skin effect and the proximity effect andcan be expressed as follows [23]:


2mrTX
3δ

(4)
+
(1 + G p )
1
+
RTX =
σ2
δ
4


3δ
2nrRX

+
(5)
RRX =
1
+
(1 + G p ).
σ2
δ
4

Fig. 2 shows the equivalent circuit of a WPT system. The
TX side consists of a voltage source (VS ) with an internal

Here, σ is the conductivity of copper (5.96 × 107 S/m), and is the diameter of the copper wire (1 mm). m and n are

Authorized licensed use limited to: University of Tokyo. Downloaded on September 20,2020 at 12:41:21 UTC from IEEE Xplore. Restrictions apply.

QIU et al.: DIGITAL TX COIL FOR WPT4033

the numbers of turns of the TX and RX coils, respectively.
The skin depth (δ) is calculated as (πμ0 f 0 σ )−1/2 , where μ0
is the vacuum permeability (4π × 10−7 H/m). The proximity
effect is included in the proximity factor (G p ) [24].
Second, employing Neumann’s equation [25], M can be
determined by adding all combinations of M pq between the ploop of the TX coil and the q loop of the RX coil
M=

n
m 


M pq

p=1 q=1and π 1 − x cos φ
(β)
rRX
μ0 √
rTXrRXdφ
M pq =
√
π
U3
0
where
x2
x
−2
cos φ
2
rRX
rRX


2
2
− β K (β) − E(β)
(β) =
β
k
U =

β =

1+

4rTXrRX U(rRX + rTX U )2 + z 2pq

(6)

(7)
(8)
(9)

p−1
q−1
tTX +
tRX .
(10)
m
n
Here, φ is the angle in the integration, and K and E are thefirst kind and the second kind of complete elliptic integrals,
respectively [26]. tTX and tRX are the thicknesses of the TX
and RX coils, respectively. z pq denotes the distance of the qloop of the RX coil relative to the p loop of the TX coil, andz is defined as z pq when p = q = 1.
Thus, by substituting (4)–(6) into (3), k 2 Q TX Q RX can beobtained. It is found that when f 0 , m, n, and rRX are constants,
for a specific (x, z), k 2 Q TX Q RX reaches its maximum whenrTX equals rTX,OPT , which is obtained by solving
z pq = z +∂ 2
k Q TX Q RX = 0.
(11)
∂rTX
In this article, we consider our target application as wirelesscharging of mobile devices and select f 0 as 150 kHz. The
maximum z (z max ) and maximum x (x max ) are both set
as 100 mm. Fig. 3(a) shows the calculated dependence ofrTX,OPT on (x, z) obtained from (11) using rRX = 100 mm,
m = n = 10, and tTX = tRX = 13 mm. Starting fromrTX,OPT = 100 mm at (0 mm, 0 mm), rTX,OPT increases withincreasing misalignment and reaches 205 mm at (100 mm,
100 mm). Fig. 3(b) shows the coil configurations at four
selected positions (A, B, C, and D). Compared with the
distance dependence, rTX,OPT is affected more strongly bylateral misalignment.
III. P ROPOSED D IGITAL T RANSMITTER C OIL T OPOLOGY
To implement the TX coil with a programmable rTX according to different positions of the RX coil, a digital TX coil
topology is proposed. Fig. 4 shows a schematic of the WPTsystem. The TX side consists of a power amplifier (PA),the proposed digital TX coil, and a switch (SW) control

Fig. 3. (a) rTX,OPT surface under different misalignment conditions. Bothz max and xmax equal 100 mm. The x and z axes are reversed to clearly show
the data. (b) Coil configurations under four misalignment conditions.

Fig. 4. Schematic of the WPT system in which a PA, the proposed digital
TX coil, the RX coil, and a rectifier are implemented. A single turn of TX
and RX coils is shown for simplicity.

unit. The digital TX coil consists of N concentric subcoils
connected in parallel. The l coil (TXl ) with a radius of rTXl isconnected with the corresponding compensation capacitance(Cl ) and SW (SWl ) in series, where l = 1, 2, . . . , N. The
RX side consists of the RX coil, a rectifier followed by asmoothing capacitor (C L ), and R L . For each specific position

Authorized licensed use limited to: University of Tokyo. Downloaded on September 20,2020 at 12:41:21 UTC from IEEE Xplore. Restrictions apply.

4034

Fig. 5.

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 68, NO. 9, SEPTEMBER 2020

Equivalent circuit of the WPT system.

of the RX coil, one of the subcoils is turned on. Thus,
the radius of the digital TX coil can be adjusted to thecorresponding rTX,OPT electronically rather than mechanically,such as by using motors. In addition, a LabVIEW programis developed to support the automatic operation of the SW
control unit. Details are given in Section V-A.
Fig. 5 shows the equivalent circuit. The l subcoil in thedigital TX coil is denoted by an inductance (L l ) and a parasitic
resistance (Rl ) connected in series. f0 for each subcoil in thedigital TX coil is the same as that of the RX coil. The rectifierconsists of four diodes, D1 –D4 . The dc voltage supply is VDD ,and the dc current flowing into the PA is I D . The input voltage
and current of the digital TX coil are denoted by VIN and IIN ,respectively. The output voltage and current of the RX coil aredenoted by VOUT and IOUT , respectively. The voltage across
R L is denoted by VLoad .

Fig. 6. Flowchart to calculate rTX1,OPT , rTX2,OPT , and the correspondingηmax for N = 2.

IV. D ESIGN M ETHODOLOGY OF D IGITAL T RANSMITTERC OIL U NDER THE VARIATION OF D ISTANCE AND
L ATERAL M ISALIGNMENT
Using the proposed digital TX coil with adjustable rTX ,we can obtain the maximum η at each position. However,
it would be impractical to implement the digital TX coil withan infinite number of subcoils, considering that in the application scenario, the RX coil can move continuously within
the wireless charging space. Thus, in this section, we propose
a practical design methodology that determines the numberof subcoils in the digital TX coil and their radii (rTX1,OPT,
rTX2,OPT , . . . , rTXN,OPT ) under the variation of distance andlateral misalignment.
A. Performance IndicatorFirst, we define the average η (η̄) as the key performanceindicatorη=

x max z max
ηdzd x00

x max z max

.

(12)

A higher η̄ indicates a better performance.
B. Design Methodology of Digital Transmitter CoilIn this part, we calculate and compare η̄ values for different N. As discussed at the beginning of Section II, we firstmaximize η at (x max , z max ) and set rTX1 as 205 mm inaccordance with position D in Fig. 3(b).

Fig. 7.

Calculated rTX2 dependence of η̄ in the case of N = 2.

In the case of N = 1, which corresponds to TX1 with
rTX1,OPT , η̄ can be easily calculated as 87% using (2), (3),and (12). For N = 2, Fig. 6 shows the flowchart to calculate
rTX2,OPT and the corresponding maximum η̄ (ηmax ). Regarding
the selection of x, z, and r , there is a tradeoff between
calculation accuracy and calculation cost. A smaller size
increment gives a more accurate definition of rTX2,OPT , but
is at the cost of longer calculation time. We set the size
increment as 5 mm in our work. There are two calculation
loops. In the first loop, η̄ is calculated for a specific rTX2 .
For each (x, z), TX1 or TX2 is turned ON, depending on
which gives the higher η. After obtaining the η distribution
within the range of (x max , z max ), η̄ is calculated using (12).
In the second loop, rTX2 is changed step by step until ηmax is
obtained. Fig. 7 shows the rTX2 dependence of η̄. When rTX2
equals rTX2,OPT , ηmax is 91%. Thus, for N = 2, rTX1,OPT and

Authorized licensed use limited to: University of Tokyo. Downloaded on September 20,2020 at 12:41:21 UTC from IEEE Xplore. Restrictions apply.

QIU et al.: DIGITAL TX COIL FOR WPT

4035

Fig. 9. Calculated N dependence of (a) ηmax and (b) ratio of rTXl,OPT torTX1,OPT , where l = 1, 2, . . . , N .

Fig. 8. Calculated η surfaces using (a) TX1 , (b) TX2 , and (c) digital TX
coil for N = 2 under different misalignment conditions.

rTX2,OPT equal 205 and 110 mm, respectively, and ηmax
¯ isgreater than that for N = 1.
ηmaxincreases
fromTo
demonstratehow
N = 1 to N = 2, Fig. 8 shows a comparison of η
surfaces using TX1 with rTX1,OPT , TX2 with rTX2,OPT , andthe digital TX coil for N = 2. TX1 and TX2 perform
well far from and near (0 mm, 0 mm), respectively.
Thus, as shown in Fig. 8(c), with TX1 and TX2 turned
ON outside and inside the highlighted black volume,
respectively, the digital TX coil achieves a higher η than TX1
in Fig. 8(a). The boundary on the η surface is defined by
η(rTX = rTX1,OPT ) = η(rTX = rTX2,OPT ).
After obtaining ηmax for N = 1 and 2, the results for
N = 3–6 are calculated and are shown in Fig. 9(a). It isfound that ηmax is improved greatly by using two subcoils but
increases slightly when N exceeds two. This means that thedigital TX coil consisting of two subcoils is a practical design,

and adding any more subcoils only increases the system’s
cost without significantly improving its performance. Fig. 9(b)shows the ratio of rTXl,OPT (l = 1, 2, . . . , N) to rTX1,OPT fordifferent N. In the optimized design (N = 2), the ratio of
rTX2,OPT to rTX1,OPT is 0.54.
When using the digital TX coil with the optimized design,ηmax¯ is 91%, compared with 87% obtained using the conventional TX design, that is, N = 1. In this article, the coilparameters are selected to obtain high-quality factors, and thepossible improvement of the performance is limited. Thus,in real applications where the coil quality factors are usually
lower, the advantage of using the proposed digital TX coilover the conventional TX coil will be greater.

C. Scalability of Proposed Design Methodology
In addition, the scalability of the proposed design methodology is discussed. It has been demonstrated that the ratioof the distance to the coil radius determines η in a WPTsystem [27], [28]. Then, it can be predicted that, under thevariation of distance and lateral misalignment, η is determinedby the ratios of the distance and lateral misalignment with thecoil radius. Thus, if the WPT system is scaled up or down withconstant ratios of x max /rRX and z max /rRX , the same results as
in Fig. 9 can be obtained (data not shown). This indicates that

Authorized licensed use limited to: University of Tokyo. Downloaded on September 20,2020 at 12:41:21 UTC from IEEE Xplore. Restrictions apply.

4036

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 68, NO. 9, SEPTEMBER 2020

Fig. 10. Photograph of the digital TX coil consisting of TX1 and TX2 withthe optimized design and the RX coil.
TABLE IM EASURED P HYSICAL AND E LECTRICAL PARAMETERS
OF D IGITAL TX C OIL AND RX C OIL
Fig. 11. Photograph of the WPT prototype consisting of a PA, the digital
TX coil, the RX coil, and a rectifier with a dc load.

our proposed design methodology is universal and independentof the system size.

to drive a class-D PA (EPC 9511) [29]. The power of theclass-D PA is supplied by TAKASAGO ZX-S-400LAN and
KIKUSUI PMP16-1QU. The PA supplies the power to thedigital TX coil, which is then wirelessly transferred to the
RX coil. The four diodes in the rectifier use a DSEP60-12A
Schottky diode from IXYS Corporation, Milpitas, CA, USA,C L and R L are an FG22 × 7.1H685KRT06 capacitor (6.8 μF)
from TDK Corporation, Tokyo, Japan, and a PF2205-10RF1
resistor (10 ) from Riedon Resistors, Inc., Alhambra, CA,
USA, respectively. For each position of the RX coil, SW1
and SW2 are turned ON one by one, and the corresponding
VDD , I D , VIN , IIN , VOUT , IOUT , and VLoad (shown in Fig. 5)
are monitored using voltage probes (Tektronix P6139B) andcurrent probes (Tektronix P6021A). The results are shownon oscilloscopes (Agilent D5054A and Tektronix TDS3054C).
By measuring VIN , IIN , VOUT , and IOUT , we can calculate η.
ηSYS is defined as the power delivered to R L divided by thedc power supply and is expressed as

V. E XPERIMENTAL R ESULTS
To verify the effectiveness of the designed digital TX coilin a WPT system robust against the variation of distance andlateral misalignment, we implement the digital TX coil in a
prototype WPT system, including a PA and a rectifier. The
experimental results are compared with the calculation results.
A. Prototype WPT System Utilizing Digital Transmitter CoilFig. 10 shows a photograph of the digital TX coil consistingof TX1 and TX2 with the practical design in Section IV. All
coils are made of 18 AWG (RS Pro) wire. Table I shows their
physical dimensions and electrical parameters measured using
a network analyzer (Keysight E5061B). Relays (Panasonic
TQ2-L2-4.5) with an ON-resistance of less than 50 m areused as the SWs.
As is shown in Fig. 11, a signal generator (Tektronix
AFG3252) is used to generate a square wave signal at 150 kHz

ηSYS =

2 /R
VLoad
L
VDD I D(13)

where the digital control power in the class-D PA is also
included.
A LabVIEW control program is then run on a computer toprocess the information and generate the control voltages for
SW1 and SW2 through a digital waveform generator (National
Instruments PXIe-6555). ηSYS is selected as the criterion
for subcoil selection. If ηSYS using TX1 is higher than thatusing TX2 , SW1 is turned ON. Otherwise, SW2 is turned
ON . Another possible criterion is η, which would make theimplementation more feasible. By measuring k between eachsubcoil and the RX coil, k 2 Q TX Q RX and η can be simply
calculated. In addition, k can be obtained by simply monitoring
VIN and IIN [22], [30], without using a directional coupler ora network analyzer to measure S parameters, such as in other

Authorized licensed use limited to: University of Tokyo. Downloaded on September 20,2020 at 12:41:21 UTC from IEEE Xplore. Restrictions apply.

QIU et al.: DIGITAL TX COIL FOR WPTFig. 12. Measured M using (a) TX1 and (b) TX2 under different misalignment conditions.

4037

Fig. 13. Error between calculated M and measured M using (a) TX1 and(b) TX2 under different misalignment conditions.

systems [5], [7], [11]. Thus, a simple switch control is realized.
These two criteria will be compared in Section V-C.
B. Measurement and Comparison of Mutual InductanceTo confirm the accuracy of the calculation results, M ismeasured in 2-D along the x- and z-directions every 20 mmfrom 0 to 100 mm using the method described in [22].
Fig. 12(a) shows the measured M (Mmeas ) between TX1and the RX coil. Starting from 10.6 μH at (0 mm, 0 mm),
Mmeas drops to 6.64 μH at (0 mm, 100 mm), which is a 37%
reduction. On the other hand, it rises to 14.2 μH at (100 mm,
0 mm), a 33% increase, which is ascribed to the asymmetricalradii between TX1 and the RX coil [21]. When the positionof the RX coil is changed to (100 mm, 100 mm) with thelargest misalignment, Mmeas drops to 5.98 μH, which is a 44%
reduction. Fig. 12(b) shows Mmeas between TX2 and the RX
coil. Mmeas shows a maximum of 23.6 μH at (0 mm, 0 mm)
and reductions of 80%, 71%, and 89% at (0 mm, 100 mm),(100 mm, 0 mm), and (100 mm, 100 mm), respectively.
Fig. 13(a) and (b) shows a comparison of Mmeas and the calculated M (Mcal ). The error is defined as (Mmeas −Mcal )/Mmeasand shows different trends for TX1 and TX2 . It is small for
TX1 but large for TX2 when the RX coil is near (0 mm,
0 mm). However, in both cases, the error is less than 10% overthe entire region, which demonstrates the accuracy of (6) incalculating M. In addition, compared with the measurement
results, the calculated RTX and RRX using (4) and (5) also
show an error within 10% (data not shown). All these results

Fig. 14. Measured distribution map showing where TX1 or TX2 in thedigital TX coil is turned ON. When the RX coil is near (0 mm, 0 mm), TX2
is turned ON. Otherwise, TX1 is turned ON. There are two boundaries. One
is a blue solid line determined by whether TX1 or TX2 achieves the higher
system efficiency. The other one is a red dashed line determined by which
whether TX1 or TX2 achieves the higher coil-to-coil efficiency.

verify the accuracy of the calculation results and validate theproposed design methodology of the digital TX coil.
C. System Efficiency Measurement of WPT Prototype
To evaluate the performance of the WPT prototype, startingfrom (0 mm, 0 mm), ηSYS is measured point by point in
2-D along the x- and z-directions every 20 mm from 0 to
100 mm. At each position, the power supply of the class-D PA
is modulated to regulate the power delivered to R L to 0.9 W.

Authorized licensed use limited to: University of Tokyo. Downloaded on September 20,2020 at 12:41:21 UTC from IEEE Xplore. Restrictions apply.

4038

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 68, NO. 9, SEPTEMBER 2020

misalignment is proposed. Its radius can be programed to its
optimal value for the maximum coil-to-coil efficiency for eachposition of the RX coil. A practical design methodology is
proposed, and it is concluded that the digital TX coil consistingof two subcoils is an effective design and that the performance
is not significantly improved by adding more subcoils. The
optimal radius ratio of these two subcoils is 0.54. In the
fabricated WPT prototype, the system efficiency is improvedby the digital TX coil and reaches a maximum value of 48%.
Compared with using a conventional TX coil with a constantradius, the system efficiency shows an absolute improvementof up to 7%.
R EFERENCES

Fig. 15.
(a) Measured ηSYS using the digital TX coil under different
misalignment conditions. (b) Improvement in measured ηSYS using the digital
TX coil compared with the conventional TX coil (TX1 ) under different
misalignment conditions.

Depending on which coil achieves the higher ηSYS , TX1
or TX2 in the digital TX coil is turned ON automatically,
as described in Section V-A. In the measured distribution map
shown in Fig. 14, the boundary indicated by the blue solidline distinguishes the regions where TX1 or TX2 is turned ON.
When the RX coil is near (0 mm, 0 mm), TX2 is turned ON.
Otherwise, TX1 is turned ON.
In addition, the distribution map using η rather than ηSYS as
the criterion is shown for comparison in Fig. 14. The boundaryis indicated by the red dashed line. This line coincides with theblue solid line except at two positions. Take the black arrowas an example. The switching from TX2 to TX1 increases η.
From a systematic viewpoint, a different TX coil results in adifferent k, which will change the reflected impedance fromthe RX coil, and thus, affect ηSYS . However, ηSYS is still
increased. Thus, it can be concluded that η plays an importantrole in determining ηSYS , as mentioned in Section I.
Fig. 15(a) shows the measured ηSYS using the digital TX
coil. It has a maximum value of 48% at (0 mm, 0 mm).
In Fig. 15(b), ηSYS is shown to be improved under the variationof distance and lateral misalignment compared with that forthe conventional TX coil (TX1 ). The maximum absolute
improvement of 7% is at (0 mm, 0 mm), which is the mostcommon position of the RX coil.
VI. C ONCLUSIONA WPT system utilizing a digital TX coil topologythat is robust against the variation of distance and lateral[1] Z. Zhang, H. Pang, A. Georgiadis, and C. Cecati, “Wireless powertransfer—An overview,” IEEE Trans. Ind. Electron., vol. 66, no. 2,
pp. 1044–1058, Feb. 2019.
[2] C.-G. Kim, D.-H. Seo, J.-S. You, J.-H. Park, and B. H. Cho, “Designof a contactless battery charger for cellular phone,” IEEE Trans. Ind.
Electron., vol. 48, no. 6, pp. 1238–1247, Jun. 2001.
[3] T. Campi, S. Cruciani, F. Palandrani, V. De Santis, A. Hirata, and
M. Feliziani, “Wireless power transfer charging system for AIMDs
and pacemakers,” IEEE Trans. Microw. Theory Techn., vol. 64, no. 2,
pp. 633–642, Feb. 2016.
[4] Q. Zhu, Y. Guo, L. Wang, C. Liao, and F. Li, “Improving the misalignment tolerance of wireless charging system by optimizing thecompensate capacitor,” IEEE Trans. Ind. Electron., vol. 62, no. 8,
pp. 4832–4836, Aug. 2015.
[5] A. P. Sample, D. A. Meyer, and J. R. Smith, “Analysis, experimental
results, and range adaptation of magnetically coupled resonators for
wireless power transfer,” IEEE Trans. Ind. Electron., vol. 58, no. 2,
pp. 544–554, Feb. 2011.
[6] J. Park, Y. Tak, Y. Kim, Y. Kim, and S. Nam, “Investigation of adaptive
matching methods for near-field wireless power transfer,” IEEE Trans.
Antennas Propag., vol. 59, no. 5, pp. 1769–1773, May 2011.
[7] T. C. Beh, M. Kato, T. Imura, S. Oh, and Y. Hori, “Automatedimpedance matching system for robust wireless power transfer via
magnetic resonance coupling,” IEEE Trans. Ind. Electron., vol. 60, no. 9,
pp. 3689–3698, Sep. 2013.
[8] Y. Lim, H. Tang, S. Lim, and J. Park, “An adaptive impedance-matching
network based on a novel capacitor matrix for wireless power transfer,”
IEEE Trans. Power Electron., vol. 29, no. 8, pp. 4403–4413, Aug. 2014.
[9] T. P. Duong and J.-W. Lee, “Experimental results of high-efficiency resonant coupling wireless power transfer using a variable coupling method,”IEEE Microw. Wireless Compon. Lett., vol. 21, no. 8, pp. 442–444,
Aug. 2011.
[10] J. Kim and J. Jeong, “Range-adaptive wireless power transfer using
multiloop and tunable matching techniques,” IEEE Trans. Ind. Electron.,
vol. 62, no. 10, pp. 6233–6241, Oct. 2015.
[11] G. Lee, B. H. Waters, Y. G. Shin, J. R. Smith, and W. S. Park, “A reconfigurable resonant coil for range adaptation wireless power transfer,”
IEEE Trans. Microw. Theory Techn., vol. 64, no. 2, pp. 624–632,
Feb. 2016.
[12] J. L. Villa, J. Sallan, J. F. S. Osorio, and A. Llombart, “Highmisalignment tolerant compensation topology for ICPT systems,” IEEE
Trans. Ind. Electron., vol. 59, no. 2, pp. 945–951, Feb. 2012.
[13] W. Li, H. Zhao, S. Q. Li, J. J. Deng, T. Kan, and C. C. Mi, “Integrated LCC compensation topology for wireless charger in electric andplug-in electric vehicles,” IEEE Trans. Ind. Electron., vol. 62, no. 7,
pp. 4215–4225, Jul. 2015.
[14] L. Zhao, D. J. Thrimawithana, and U. K. Madawala, “Hybrid bidirectional wireless EV charging system tolerant to pad misalignment,” IEEE
Trans. Ind. Electron., vol. 64, no. 9, pp. 7079–7086, Sep. 2017.
[15] T.-H. Kim, G.-H. Yun, W. Y. Lee, and J.-G. Yook, “Asymmetric coilstructures for highly efficient wireless power transfer systems,” IEEE
Trans. Microw. Theory Techn., vol. 66, no. 7, pp. 3443–3451, Jul. 2018.
[16] B. H. Waters, B. J. Mahoney, G. Lee, and J. R. Smith, “Optimal coilsize ratios for wireless power transfer applications,” in Proc. IEEE Int.
Symp. Circuits Syst. (ISCAS), Jun. 2014, pp. 2045–2048.
[17] J. Kim, D.-H. Kim, and Y.-J. Park, “Free-positioning wireless powertransfer to multiple devices using a planar transmitting coil and switchable impedance matching networks,” IEEE Trans. Microw. Theory
Techn., vol. 64, no. 11, pp. 3714–3722, Nov. 2016.

Authorized licensed use limited to: University of Tokyo. Downloaded on September 20,2020 at 12:41:21 UTC from IEEE Xplore. Restrictions apply.

QIU et al.: DIGITAL TX COIL FOR WPT[18] D. Liu, H. Hu, and S. V. Georgakopoulos, “Misalignment sensitivity ofstrongly coupled wireless power transfer systems,” IEEE Trans. PowerElectron., vol. 32, no. 7, pp. 5509–5519, Jul. 2017.
[19] F. Lu, H. Hofmann, J. Deng, and C. Mi, “Output power and efficiency sensitivity to circuit parameter variations in double-sided LCCcompensated wireless power transfer system,” in Proc. IEEE Appl.
Power Electron. Conf. Expo. (APEC), Mar. 2015, pp. 507–601.
[20] H. Qiu, Y. Narusue, Y. Kawahara, T. Sakurai, and M. Takamiya, “Digital
coil: Transmitter coil with programmable radius for wireless poweringrobust against distance variation,” in Proc. IEEE Wireless Power Transf.
Conf., Jun. 2018, pp. 1–4.
[21] C. Zheng, H. Ma, J.-S. Lai, and L. Zhang, “Design considerations
to reduce gap variation and misalignment effects for the inductive
power transfer system,” IEEE Trans. Power Electron., vol. 30, no. 11,
pp. 6108–6119, Nov. 2015.
[22] K. Hata, T. Imura, and Y. Hori, “Simplified measuring method of kQ
product for wireless power transfer via magnetic resonance couplingbased on input impedance measurement,” in Proc. 43rd Annu. Conf.
IEEE Ind. Electron. Soc. (IECON), Oct. 2017, pp. 6974–6979.
[23] J. Kim and Y.-J. Park, “Approximate closed-form formula for calculating
ohmic resistance in coils of parallel round wires with unequal pitches,”
IEEE Trans. Ind. Electron., vol. 62, no. 6, pp. 3482–3489, Jun. 2015.
[24] G. Smith, “The proximity effect in systems of parallel conductors
and electrically small multiturn loop antennas,” Div. Eng. Appl. Phys.,
Harvard Univ., Cambridge, MA, USA, Tech. Rep. 624, 1971.
[25] C. Akyel, S. I. Babic, and M.-M. Mahmoudi, “Mutual inductancecalculation for non-coaxial circular air coils with parallel axes,” Prog.
Electromagn. Res., vol. 91, pp. 287–301, Jan. 2009.
[26] R. H. Good, “Elliptic integrals, the forgotten functions,” Eur. J. Phys.,vol. 22, no. 2, pp. 119–126, Mar. 2001.
[27] C. Nagai et al., “Scaling law of coupling coefficient and coil size inwireless power transfer design via magnetic coupling,” Electr. Eng. Jpn.,
vol. 202, no. 4, pp. 21–30, Mar. 2018.
[28] J. P. K. Sampath, A. Alphones, L. Y. Y. Kenneth, andD. M. Vilathgamuwa, “Analysis on normalized distance and scalability
in designing wireless power transfer,” in Proc. IEEE PELS Workshop
Emerg. Technol., Wireless Power (WoW), Jun. 2015, pp. 1–6.
[29] 10 W Multi-Mode Wireless Power Amplifier EPC9511 Datasheet, EPC,
Chennai, India, 2016.
[30] H. Qiu, Y. Narusue, Y. Kawahara, T. Sakurai, and M. Takamiya, “Distance detection system for digital transmitter coil achieving distancevariation-tolerant wireless power transfer,” in Proc. IEEE 15th Brazilian Power Electron. Conf., 5th IEEE Southern Power Electron. Conf.
(COBEP/SPEC), Dec. 2019, pp. 830–835.
Hao Qiu (Member, IEEE) received the B.S. degree
in materials science and the M.Eng. degree in electrical engineering from Nanjing University, Nanjing,
China, in 2010 and 2013, and the Ph.D. degree inelectrical engineering from The University of Tokyo,
Tokyo, Japan, in 2016, respectively.
He has been a Researcher with The Universityof Tokyo. His research interests cover materials,
devices, and circuits. His present focus is circuitdesign for wireless power transfer and wireless communication systems for IoT applications.
Dr. Qiu served as a Research Fellow with the Japan Society for the
Promotion of Science from 2015 to 2017 and a Representative with the Japan
Society of Applied Physics from 2016 and 2018. He received the 2016 IEEE
Electron Devices Society (EDS) Japan Chapter Student Award and the 2017
Chinese Government Award for Outstanding Self-Finance Students Abroad.

4039

Takayasu Sakurai (Fellow, IEEE) received the
Ph.D. degree in electrical engineering from The
University of Tokyo, Tokyo, Japan, in 1981.
In 1981, he joined Toshiba Corporation, Tokyo,
where he designed CMOS DRAM, SRAM, andRISC processors, DSPs, and SoC Solutions. He has
worked extensively on interconnect delay and capacitance modeling, known as the Sakurai model andthe alpha power-law MOS model. From 1988 to
1990, he was a Visiting Researcher with the University of California at Berkeley, Berkeley, CA, USA,
where he conducted research in the field of VLSI CAD. Since 1996, he has
been a Professor with The University of Tokyo, Tokyo, where he is involved
in low-power high-speed VLSI, memory design, interconnects, ubiquitouselectronics, organic IC’s, and large-area electronics. He is also a Domain
Research Supervisor for nano-electronics area with the Japan Science andTechnology Agency, Kawaguchi, Japan. He has filed more than 200 patents.
He has authored or coauthored more than 600 technical publications, including
100 invited presentations and several books.
Dr. Sakurai is an IEICE Fellow. He was an Elected AdCom Member
for the IEEE Solid-State Circuits Society and an IEEE CAS and SSCS
Distinguished Lecturer. He was a recipient of the 2004 IEEE Takuo SuganoAward, the 2005 IEEE ICICDT Award, the 2005 P\&I Patent of the YearAward, the 2009 IEICE Achievement Award, the IEEE Paul Rappaport Awardin 2009 and 2010, respectively, the 2010 IEEE Donald O. Pederson Awardin Solid-State Circuits, the 2010 IEICE Electronics Society Award, and four
product awards. He served as the Conference Chair for the Symposium on
VLSI Circuits and ICICDT, the Vice Chair for ASPDAC, the TPC Chair
for the IEEE A-SSCC and the VLSI Symposium, an Executive Committee
Member for ISLPED, and a Program Committee Member for the International
Solid-State Circuits Conference (ISSCC), CICC, A-SSCC, DAC, ESSCIRC,
ICCAD, ISLPED, and other international conferences. He is the Executive
Committee Chair of the VLSI Symposia and a Steering Committee Chair of
the IEEE A-SSCC. He delivered keynote speech at more than 50 conferences,including ISSCC, ESSCIRC, and ISLPED.

Makoto Takamiya (Senior Member, IEEE) received
the B.S., M.S., and Ph.D. degrees in electronicengineering from The University of Tokyo, Tokyo,
Japan, in 1995, 1997, and 2000, respectively.
In 2000, he joined NEC Corporation, Tokyo,
where he was engaged in the circuit design ofhigh-speed digital LSI’s. In 2005, he joined The
University of Tokyo, where he is currently a Professor with the Institute of Industrial Science. From2013 to 2014, he was a Visiting Scholar with the
University of California at Berkeley, Berkeley, CA,
USA. His research interests include the integrated power management circuits
for wireless powering and energy harvesting for wearable and IoT applications
and the digital gate driver IC for power electronics.
Dr. Takamiya is a member of the Technical Program Committee of the IEEE
International Solid-State Circuits Conference (ISSCC). He received the IEEE
Paul Rappaport Award in 2009 and 2010, respectively, and the Best Paper
Award in the 2013 IEEE Wireless Power Transfer Conference. He served on
the technical program committees of the IEEE Custom Integrated Circuits
Conference from 2006 to 2011 and the IEEE Symposium on VLSI Circuits
from 2009 to 2017. He is the Far East Regional Chair in ISSCC 2020. He isa Distinguished Lecturer of the IEEE Solid-State Circuits Society.

Authorized licensed use limited to: University of Tokyo. Downloaded on September 20,2020 at 12:41:21 UTC from IEEE Xplore. Restrictions apply.