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IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 57, NO. 8, AUGUST 2022

A 6.78-MHz Multiple-Transmitter Wireless Power
Transfer System With Efficiency Maximization
by Adaptive Magnetic Field Adder IC
Hao Qiu , Member, IEEE, Takayasu Sakurai, Life Fellow, IEEE, and Makoto Takamiya , Senior Member, IEEE
Abstract— A 6.78-MHz multiple-transmitter (TX) wirelesspower transfer (WPT) system was presented. An adaptive magnetic field adder (AMFA) IC was proposed, for the first time,to enable the maximization of the system efficiency (ηSYS ) byadaptively optimizing the amplitude and phase of the current
in each TX coil on the basis of the coupling coefficient (k)between each TX coil and the receiver (RX) coil. Under the
optimal condition, the current in each TX coil is proportional
to k between the TX coil and the RX coil. For the independent
control of the current in each TX coil, a selectively activatedshared-half-bridge (HB) power amplifier (PA) together with analternate TX coil array was proposed. To sense a small k, dutyratio control was proposed in the integrated k sensor. The AMFA
IC was fabricated by a 0.18-μm CMOS process with 1.8-V
devices. The peak power conversion efficiency of the proposed
PA reached 74%. The k sensor could accurately measure k witha percentage error within ±2.5%. A WPT system consisting of a
4×4 TX coil array driven by four AMFA ICs and a single RX coil
was implemented. Experimental results showed that, comparedwith the conventional system, ηSYS was increased from 0.11%
to 51% with a load power of 576 mW when the RX coil wasperpendicular to the TX coils. When the RX coil was parallelto the TX coils, a ηSYS of 63%, which is higher than those inprevious works, was also achieved.
Index Terms— Adaptive magnetic field adder (AMFA), alternate coil array, amplitude and phase control, coupling coefficientsensor, double-off control, duty-ratio control, efficiency maximization, magnetic resonance coupling, multiple transmitter (TX)
coils, near field, power amplifier (PA) topology for multiple TX
coils, shared topology, wireless power transfer (WPT).

I. I NTRODUCTIONW

IRELESS power transfer (WPT) based on magnetic
resonance coupling is a promising technology for the
charging of mobile devices, including mobile phones, smart
watches, and so on [1]. Instead of inserting the charging cableand leaving the devices in a corner every time, we would be
able to operate them and move freely if they could be wirelessly charged; this would greatly improve the user experience.
Manuscript received 13 March 2021; revised 25 September 2021; accepted
3 June 2022. Date of publication 23 June 2022; date of current version 25 July 2022. This article was approved by Associate Editor
Wing-Hung Ki. (Corresponding author: Hao Qiu.)
Hao Qiu is with the School of Electronic Science and Engineering, and theEngineering Research Center of Opto-Electro Materials and Chip Techniques,
Nanjing University, Nanjing 210023, China (e-mail: haoqiu@nju.edu.cn).
Takayasu Sakurai and Makoto Takamiya are with the Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan (e-mail:mtaka@iis.u-tokyo.ac.jp).
Color versions of one or more figures in this article are available athttps://doi.org/10.1109/JSSC.2022.3183174.
Digital Object Identifier 10.1109/JSSC.2022.3183174

Fig. 1. WPT scenario where a mobile device with the RX coil is wirelessly
charged by the TX coil array placed on a table.

To realize this vision where the receiver (RX) can change its
position and sometimes be perpendicular to the transmitter(TX), many related works have been published. In a WPTsystem, the most important target has been the improvementof its efficiency and robustness against the variation in theposition of the RX relative to the TX.
In a system using a single TX coil, the power transferredthrough the magnetic field is highly directional and its value
drops very rapidly with distance and misalignment between the
TX and RX coils. As a result, it is always required that the RX
coil be perfectly aligned with the TX coil, which degrades theuser experience. To alleviate this problem, several methods,
such as coil design [2]–[4], new compensation topologies[5]–[7], new circuit topologies [8]–[12], and impedance matching techniques [13]–[16], have been proposed. However, when
the coupling coefficient (k) between the TX and RX coils is
small, the benefits that these methods yield can be limited.
Under an extreme condition where k is zero, no power can betransferred to the RX coil. Physically, this case corresponds
to the RX coil being perpendicular to the TX coil with thecenter of the TX coil being on the plane of the RX coil [17].
Rather than using a single TX coil, the system in which
multiple TX coils [18]–[27] are used has gathered muchattention, owing to its increased design freedom. Fig. 1 shows
an application scenario in which a mobile phone is charged
using multiple TX coils on a table. The conventional methods
include selectively driving one of the multiple TX coils[18], [19], as shown in Fig. 2(a), and driving all TX coilswith the same current [20], as shown in Fig. 2(b). On theother hand, as shown in Fig. 2(c), with the optimal control of
the amplitude and phase of the current in each TX coil, themagnetic fields from multiple TX coils can be constructively
added at the position of the RX coil to maximize the system0018-9200 © 2022 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See https://www.ieee.org/publications/rights/index.html for more information.

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QIU et al.: 6.78-MHz MULTIPLE-TX WPT SYSTEM WITH EFFICIENCY MAXIMIZATION BY AMFA IC

Fig. 2.

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Schematic of a WPT system using (a) and (b) conventional methods and (c) proposed method.

efficiency (ηSYS ). We refer to this concept as adaptive magnetic
field adder (AMFA) and its effectiveness has been theoreticallydemonstrated in [21]. There are two basic requirements: 1) the
amplitude and phase of the current in each TX coil should be
able to be independently controlled and 2) k between each
TX coil and the RX coil should be adaptively measured inaccordance with the position of the RX coil.
There have been several attempts to implement AMFA.
It has been demonstrated that ηSYS can be improved [22] andthe load power can be adjusted [23], [24] through the phase
control of the current in each TX coil. However, no amplitudecontrol has been discussed. In [25], it was concluded that
ηSYS is affected by the amplitude and phase of the current
in each TX coil. However, the optimal condition for attaining
the maximum ηSYS has not been discussed. In all previous
works [26]–[28], AMFA has been implemented with discrete
components, which makes the system bulky and costly. Moreover, the number of power amplifiers (PAs) equals that of TX
coils, which leads to a large form factor and high cost of theentire system. Furthermore, k sensing was performed using avector network analyzer (VNA) during the experiment in [22]or even before the experiment [25], [28], which is difficult toaccomplish in real applications.
Our major contributions in this work are summarized asfollows.
1) For the first time, we proposed an AMFA IC in a
multiple-TX WPT system that enables maximizationof ηSYS by optimizing the amplitude and phase of thecurrent in each TX coil.
2) The independent control of the current in each TX coil isachieved with the proposed selectively activated sharedhalf-bridge (HB) PA together with an alternate TX coilarray. The PA topology significantly reduces the form
factor.
3) In the integrated k sensor, duty-ratio control is proposed
to guarantee its correct operation when measuring asmall k.
Compared with our earlier work [29], herein, we added a
detailed analysis as well as simulation results of the proposed
PA topology and integrated k sensor, measurement results of
the integrated k sensor, and a comprehensive measurement of
the WPT system for different positions of the RX coil.

Fig. 3.
(a) Equivalent circuits of the WPT system shown in Fig. 2(c).
(b) Corresponding k between each pair of coils in the WPT system.

The rest of this article is organized as follows. In Section II,
the multiple-TX WPT system and the control algorithm for
the AMFA in it are presented. Section III shows the circuit
implementation of the proposed AMFA IC. In Section IV,
measurement results are presented and discussed. Finally,
conclusions are given in Section V.
II. P ROPOSED M ULTIPLE -TX WPT S YSTEM
A. Control Algorithm for AMFA
Fig. 3(a) shows the equivalent circuit of the WPT system
shown in Fig. 2(c). The TX side consists of four TX coils (TX
coils 1–4). TX coil i (i = 1 − 4) is represented by an inductor(L i ) with a parasitic resistance (ri ) connected to a compensation capacitor (Ci ) in series. The voltage source is represented
by VSi with an internal resistance (R Si ). The current flowing
in TX coil i is Ii . L RX and rRX , respectively, represent
the inductance and parasitic resistance of the RX coil. CRX

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is the value of the compensation capacitor. R L is the load
resistance. The current flowing in the RX coil is IRX . All TX
and RX coils resonate at the same resonance frequency ( f 0 ).
Fig. 3(b) shows k between each pair of coils. kmn represents
k between TX coils m and n, where m and n range from 1 to
4 and m = n. ki represents k between TX coil i and the
RX coil.
Applying Kirchhoff’s law to the circuit, we can obtain (1),as shown at the bottom of the page. As is pointed out
theoretically [21], the maximal coil-to-coil efficiency can beobtained by optimizing the amplitude and phase of the current
in each TX coil. In this work, the polarity (POL) of k is also
considered [30]. Under the optimized condition, for TX coili , Ii is proportional to ki . For example, if a positive k1 has
twice the amplitude of a negative k2 , it is required that theamplitude of I1 is twice that of I2 and these two currents are
in antiphase. Under the optimized condition, the maximal coilto-coil efficiency is derived as (2), shown at the bottom of thepage. k between TX coils is not shown in (2) and thus does
not affect the system performance.
On the other hand, if only a single TX coil, such as TX
coil 1, is driven to transfer power wirelessly to the RX coil,the coil-to-coil efficiency is expressed asηsingle-TX =Fig. 4. Calculated coil-to-coil efficiency using a single TX coil and multiple
TX coils with control.

recently published works [26], [27], it is claimed that thecontrol can be realized by equalizing the input impedance ofeach TX coil, whereby their system implementation becomesmuch simpler. This conclusion is arrived at under the assumption that no coupling occurs among TX coils [26] or that an
LCC inverter is used on the TX side [27], which does not
represent the usual situation in WPT systems. Thus, to covermost multiple-TX WPT systems, it is still necessary to know
k between each TX coil and the RX coil.

R L ω02 k12 L 1 L RX
. (3)(R L + rRX ) r1 + (R L + rRX )ω02 k12 L 1 L RX
2

To compare the coil-to-coil efficiency of a WPT systemusing multiple TX coils and that using a single TX coil,
we performed a simple calculation. The results for (2) and (3)are shown in Fig. 4. In our calculation, for s implicity,
we assume that all TX coils and the RX coil are the same.
This means that all the inductances, parasitic resistances, andcompensation capacitances, represented by L 0 , r0 , and C0 ,respectively, are the same. The values used for the calculation
are shown in Fig. 4 (table inset). In addition, all k values
between each TX coil and the RX coil are the same. Here,it is represented by k0 . According to the calculation results,
under all coupling conditions, the coil-to-coil efficiency canbe improved by using multiple TX coils compared with using
a single TX coil.
As is discussed in [21], it is important to know k between
each TX coil and the RX coil. On the other hand, in two⎛⎞⎛

R S1 + r1
VS1⎜ j ω k √L L
⎜VS2 ⎟ ⎜
0 12
1 2
⎜ ⎟ ⎜
√
⎜ VS3 ⎟ = ⎜ j ω0 k13 L 1 L 3⎜ ⎟ ⎜√⎝VS4 ⎠ ⎜⎝ j ω0 k14 L 1 L 4
0√− j ω0 k1 L 1 L RX√j ω0 k12 L 1 L 2
R S2 + r2√
j ω0 k23 L 2 L 3√
j ω0 k24 L 2 L 4√− j ω0 k2 L 2 L RX

B. System Architecture and Its Operation
The overall architecture of the proposed multiple-TX WPTsystem is shown in Fig. 5. It consists of four AMFA ICs,
16 TX coils, one RX coil, and a LabVIEW control block. All
coils resonate at the same f0 . Each AMFA IC is connected tofour TX coils, among which a single TX coil is selected tobe driven. Thus, with four AMFA ICs, four TX coils in total
are driven simultaneously to transfer power wirelessly to the
RX coil. In this work, since the focus is put on the design of
the TX side, we choose to implement the RX side in a simple
way without adding a rectifier.
The operation of the WPT system has the following threesteps. First, the AMFA ICs operate in the k-sensing mode.
Take AMFA IC TX1 as an example. The k values between TX
coils 1A–1D and the RX coil are measured, and the TX coil√j ω0 k13 L 1 L 3√
j ω0 k23 L 2 L 3
R S3 + r3√
j ω0 k34 L 3 L 4√− j ω0 k3 L 3 L RX√j ω0 k14 L 1 L 4√
j ω0 k24 L 2 L 4√
j ω0 k34 L 3 L 4
R S4 + r4√− j ω0 k4 L 4 L RX√⎞
− j ω0 k1 L 1 L RX ⎛ ⎞I1√− j ω0 k2 L 2 L RX ⎟⎟⎜ I2 ⎟⎜⎟⎟√⎜ I3 ⎟ (1)− j ω0 k3 L 3 L RX ⎟
⎟
⎜
⎟
√
⎟⎝ ⎠
− j ω0 k4 L 4 L RX ⎠ I4
IRX
R L + rRX

where j is the imaginary unit and ω0 is the resonant angular frequency and equals 2π f 0 .

ηmultiple-TX =R L ω02(R L + rRX )24
2
i=1 k i L i L RX

2

4
2
2
i=1 ri k i L i L RX + (R L + rRX )ω0

4
2
i=1 k i L i L RX

2

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(2)

QIU et al.: 6.78-MHz MULTIPLE-TX WPT SYSTEM WITH EFFICIENCY MAXIMIZATION BY AMFA IC

Fig. 5.

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Proposed WPT system consisting of AMFA ICs, TX coils, the RX coil, and a LabVIEW controller. SIPO stands for serial-in parallel-out.

with the maximum k is selected to transfer power wirelessly
to the RX coil later. AMFA ICs TX2–TX4 repeat the similar
procedures. Second, the k values corresponding to the selectedfour TX coils are transmitted to the LabVIEW block for
information processing. After the information processing, theLabVIEW block generates the required control signals for the
AMFA ICs and these ICs operate in the WPT mode. As will
be discussed in Section III-A, the current in each TX coilis adjusted by controlling the phases of signals driving HBs
in the AMFA ICs. As a result, the current in each TX coilis optimized to be proportional to k between the TX coiland the RX coil, and the coil-to-coil efficiency is maximized.
Third, in a real wireless charging scenario, k can changewith the change in the position of the RX coil. To adapt tothis process, steps 1 and 2 are repeated at a certain interval
to update the amplitude and phase of the current in each
TX coil.
III. P ROPOSED AMFA IC
As shown in Fig. 5, one AMFA IC consists of five HBs,
an integrated k sensor, and digital control blocks. In thissection, we describe the circuit implementation in detail.
A. PA Topology for Independent Current Control in Multiple
TX Coils
In a WPT system, to reduce the power loss in PAs,
one of the most important points in the design is to use
power transistors with low ON resistance. Thus, the integrated
power transistors in PAs are usually designed with largegate widths, resulting in occupying a large die area. This
problem is considerable when we discuss the multiple-TX
WPT system, in which the number of PAs equals that of TX

coils. The use of an N-legged converter [31] or a multileg
converter [32] has been proposed to reduce the number of
power transistors. However, none of the previous methods cansatisfy the requirement of our multiple-TX WPT system thatthe amplitude and phase of the current in each TX coil becontrolled independently.
On the other hand, the current in each TX coil can be controlled independently using the proposed AMFA IC operatingin the WPT mode, as is shown in Fig. 6. Fig. 6(a) shows
the schematic of the proposed selectively activated sharedHB PA. Four HBs, that is, HB1–HB4, are connected to one
terminal of TX coils 1A–1D, respectively. The other terminalsof the four TX coils are commonly connected to a shared
block, which consists of HB0 and the k sensor. Thus, the total
number of HBs is five. This is a 38% reduction comparedwith the conventional design in which eight HBs are necessary
for four TX coils. The number of k sensors is also reducedby 75%.
Among TX coils 1A–1D, only one of them is driven,
whereas the other three remain idle to eliminate any possible
power loss, which will be discussed later. For example, if TX
coil 1A is driven, HB0 and HB1 are activated, whereas
HB2–HB4 are deactivated. The amplitude and phase of thecurrent through TX coil 1A are controlled by the phases of thesignals driving HB0 and HB1 [33]. Fig. 6(b) shows the patternof the proposed alternate TX coil array and four AMFA ICs.
By combining them, we can realize the required independent
control of the current in each TX coil. For example, when
the RX coil is within the region indicated by the dashedsquare in case 1, TX coils 1A–4A are driven by AMFA ICs
TX1–TX4, respectively. The same principle applies in case 2.
That is, TX coils 1B, 2A, 3B, and 4A are driven by AMFAICs TX1–TX4, respectively.

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Fig. 6. AMFA IC operating in the WPT mode. (a) Proposed selectively activated shared-HB PA for the independent control of current in multiple TX coils.
(b) Proposed alternate TX coil array. (c) Schematic of double-off control block.

Fig. 7. (a) Schematic of PA topology obtained using the conventional control. (b) Schematic of gate drive signals to HBs. Simulated results of power losses(c) I and (d) II obtained using the conventional control and double-off control. The RX coil is assumed to be absent in the simulation.

Regarding the activation or deactivation of TX coils,
Fig. 6(c) shows the schematic of the double-off control block.
If the signal EN is “0,” the signals connected to PMOS andNMOS in the HB are locked at “1” and “0,” respectively,
deactivating the HB. On the other hand, if the signal EN is“1,” the HB is activated. The other way to deactivate the TX
coil is to use the conventional control [31], in which the twocomponent HBs connected to the TX coil are activated andthe corresponding gate drive signals are synchronized.
Fig. 7(a) and (b) shows an example in which TX coils
1B, 1C, and 1D are deactivated by synchronizing the corresponding gate drive signals of HB2–HB4 with that of HB0.

However, two types of power loss may occur. First, the power
loss can occur in deactivated TX coils, including TX coils
1B, 1C, and 1D. Take TX coil 1B as an example. The large
current through TX coil 1A causes the output voltage of HB0
different from that of HB2, even when the gate drive signals of
the two HBs are synchronized. The voltage difference between
two terminals of TX coil 1B results in power loss, which wecall power loss I. Second, all HBs are activated, resulting in
power loss in the gate drivers of HB2–HB4, that is, power
loss II. Different from that in the kHz range, the gate driverloss, which is proportional to the operating frequency, cannot
be neglected in the MHz range.

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Fig. 8. Schematic of (a) AMFA IC operating in the k-sensing mode and (b) its equivalent circuit with the integrated k senor. (c) Simulated k dependenceof R on the basis of (4).

Fig. 7(c) and (d), respectively, shows simulated power
losses I and II obtained using the conventional control [31]and double-off control. In the simulation, the RX coil isassumed to be absent for simplicity. Power loss I obtainedusing the double-off control is reduced to 15.7 μW, 1/612 of
the conventional value. Similarly, power loss II is reduced to33.9 μW, 1/83.5 of the conventional value. Thus, by simply
adding an additional enable signal to the conventional control,
the double-off control can greatly reduce unnecessary power
loss and achieve a high power conversion efficiency in the PA
topology for multiple TX coils. This will be discussed again
in Section IV-A. Note that the possible cause of power loss
in Fig. 6(a) is the induced eddy current in TX coils otherthan TX coil 1A. However, this has been demonstrated to be
negligible [4].
B. Integrated k Sensor and Duty-Ratio Control
The AMFA IC can also be configured to operate in the
k-sensing mode to measure k between each TX coil andthe RX coil. Take TX coil 1A as an example. As shownin Fig. 8(a), HB1 and the k sensor are activated by setting
EN1 to “1” and all other enable signals to “0.” Fig. 8(b)shows the equivalent circuit. L and r, respectively, represent
the inductance and parasitic resistance of TX coil 1A. C isthe value of the compensation capacitor. R is the equivalent
impedance looking into TX coil 1A and equals [34]√2
ω0 k L L RX
.
(4)
R=r +
rRX + R L
Since f 0 , L, r , L RX , rRX , and R L are constants and theirvalues are known, on the basis of (4), k can be obtained bymeasuring R on the TX side. Fig. 8(c) shows the simulated
k dependence of R. k equals 0 when the RX coil is absent
and reaches around 0.2 when the RX coil is closely coupledwith the TX coil. Corresponding R values are 2.2 and 100 ,
respectively.
This method makes k sensing much easier because thewireless communication link from the RX coil to the TX
coil used in [8] is eliminated. In addition, since R is apure resistance, rather than using a VNA [22] or a gain
and phase detector [35], which is impossible to integrate,
we used a simple transimpedance amplifier (TIA) for k sensor
implementation.
As shown in Fig. 8(b), the current (I ) supplied by HB1
flows through R, and R f , and finally sinks in the TIA. The
following equation can be derived:|I | =|VIN ||VOUT |
=
R
βRf

(5)

where β is the voltage gain of the source follower, R f is
the feedback resistance of the operational amplifier (op-amp)
in the TIA, and VIN and VOUT are the voltages indicatedin Fig. 8(b). For small-signal analysis, |VIN | and |VOUT |,respectively, represent the peak amplitudes of the components
of VIN and VOUT at f0 . |I | represents the peak amplitude of I .
Thus, by substituting (5) into (4), we can obtain k as
k=

(RRX + R L )(β R f |VOUT |/|VIN | − r )√.
ω0 L L RX(6)

To guarantee the correct operation of the k sensor, two main
requirements are listed for the design of the op-amp. One isthat its unity-gain bandwidth should be much higher than f 0 .
In our design, its value is designed to be greater than ten
times f 0 . The other one is that the op-amp should always
operate within its linear region [36]. When k is large, in otherwords, R is large, |I | is small according to (5). Under thiscondition, the op-amp can operate within its linear region.
On the other hand, as k decreases, R also decreases and theincreased |I | requirement may cause the op-amp to operate
outside of its linear region [36].

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IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 57, NO. 8, AUGUST 2022

Simulated dependence of the amplitude of current on D.
Fig. 11.
(a) Photograph of AMFA IC. (b) Photograph and measured
specifications of coil.

R = 10 . As is expected, |I | can be decreased by reducing
D. When D is smaller than 20%, |I | decreases linearly with
D. Fig. 10(a) and (b) shows the simulated waveforms of
VIN and VOUT when D equals 15% and 2%, respectively.
In simulations, k and R f are assumed to be 0.058 and 10 ,
respectively. As was discussed before, the op-amp operates
outside of its linear region and results in a distorted waveformof VOUT at D = 15%. On the other hand, when D becomes
small, such as 2%, |I | is reduced and the op-amp returns
to its linear region. Fig. 10(c) shows the design window of
D when using our proposed D control. When k is less than
0.12, D smaller than 50% is necessary to guarantee the correct
operation of the k sensor. The black line indicates the upper
limit of D as a function of k and any D within the design
window can be selected. For simplicity, in this work, we selectD = 2% for the k sensor. Therefore, our proposed D control
guarantees correct k sensing when k is small in this work.
Utilizing the k sensor, the POL of k can also be determined.
The details can be referred to in the Appendix.
IV. M EASUREMENT R ESULTS

Fig. 10. Proposed duty-ratio control in the integrated k sensor. Simulated
waveforms when (a) D = 15% and (b) D = 2%. (c) Design window of D.

To ensure that the op-amp operates in the linear region, it isnecessary to decrease |I |. There have been several methodsof PA power control, as is reviewed in [37]. Since only asingle HB is activated, the phase shift control method [38]is inapplicable. Pulse frequency modulation [39] does notcomply with the requirement of the industrial, scientific, andmedical (ISM) band. Instead of using pulse density modulation [40], we propose duty ratio (D) control to decrease |I |when measuring a small k; this is much easier to design.
To demonstrate the capability of the proposed D control, Fig. 9 shows the simulated dependence of |I | on D,
in which k is assumed to be 0.058, which corresponds toFig. 11(a) shows the photograph of the proposed AMFA IC.
Fabricated by a 1.8-V, 0.18-μm CMOS process, it occupies
7.02 mm2 . Both TX coils and the RX coil have the same
parameters, as shown in Fig. 11(b). To minimize their parametric differences, we carefully tuned their f 0 to 6.78 MHz
using a VNA. Fig. 12 shows the measurement setup of the
proposed multiple-TX WPT system, in which four AMFA ICs(TX1–TX4) are connected to 16 TX coils, the same as shownin Fig. 6(b). The RX coil with R L = 10  is perpendicular
to TX coils.
A. AMFA IC in Two Operation Modes
We start with the measurement of the AMFA IC operatingin the WPT mode. Fig. 13 (inset) shows its equivalent circuit.
The phases of the signals driving HB0 and HB1 are ϕ0 and ϕ1 ,respectively. By changing their phase difference, the corresponding power conversion efficiency and output power of the
AMFA IC were measured. During measurement, the supply

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QIU et al.: 6.78-MHz MULTIPLE-TX WPT SYSTEM WITH EFFICIENCY MAXIMIZATION BY AMFA IC

Fig. 12.

Photograph of the measurement setup.

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Fig. 14. Measured performance of the AMFA IC operating in the k-sensing
mode.

calibration, for each position of the RX coil, the waveforms of
VIN and VOUT were measured and their amplitude components
at f 0 were extracted by fast Fourier transform (FFT) analysis
for k calculation in (6). Fig. 14 compares k measured by
the k-sensor with that measured with a VNA. A good correspondence with a small percentage error within ±2.5% isdemonstrated. Thus, owing to our proposed D control, k canbe accurately measured by the AMFA IC.
B. System Measurement

Fig. 13. Measured performance of the AMFA IC operating in the WPTmode with its equivalent circuit shown in the inset.

voltage is 1.8 V, and k between TX coil 1A and the RX coil
is 0.058. The results are shown in Fig. 13.
With the four-bit control of the phase difference, theamplitude and phase of the current through TX coil 1A
can be adjusted [33]. The output power shows a sinusoidal
relationship with the phase difference, which is ascribed tothe amplitude of the current through TX coil 1A having asinusoidal relationship with half the phase difference [33].
When the phase difference approaches 180◦ , the output powershows a maximum of 167 mW. With an increase in the phasedifference, the power conversion efficiency first increases andthen shows a plateau where the maximum value is 74%
followed by a slight decrease. The high power-conversion efficiency is owing to the double-off control in our PA topology,
which is in accordance with the analysis in Section III-A.
The slight decrease in power conversion efficiency when the
output power approaches its maximum value is the same as
the simulation results (not shown), and it may be ascribed to alarger quiescent current with respect to the output current [41].
After evaluating the AMFA IC in the WPT mode, we measured it in the k-sensing mode. As discussed previously, D was
set as 2% through the entire measurement. First, we calibrated
the value of ßR f in (5) when the RX coil was absent. After

The performance of the WPT system is evaluated in bothcases shown in Fig. 6(b). In case 1, Fig. 15(a) shows the detailsof the coil setup, in which the RX coil is perpendicular to the
TX coils. The distance from the center of the RX coil to the
TX coil plane is 25 mm. Starting from the origin, the RX coil
is moved along the x-direction in 12.5-mm steps.
For each position of the RX coil, as described in
Section II-B, the AMFA ICs first operate in the k-sensing
mode. Take AMFA IC TX1 as an example. In the k-sensing
mode, this IC has two main functions. One is to detect whichof the TX coils (1A–1D) has the best coupling condition
with the RX coil, and the other is to know its value. Here,TX coil 1A is selected by AMFA IC TX1. Similarly, TX coils
2A–4A are selected by AMFA IC TX2–TX4, respectively.
Fig. 15(b) shows the measured k between the selected TX
coils (1A–4A) and the RX coil. The results for all other
TX coils and the RX coil are not shown, since they are notimportant to the following system control. The details of how
to determine the POL of k are referred to in the Appendix.
After k-sensing, the AMFA ICs operate in the WPT mode.
Fig. 15(c) and (d) shows the measured amplitudes and phasesof the current in each TX coil, respectively. The current wasmeasured using a current probe (Tektronix P6021).
The measurement setup is symmetric about the x-axis, andit can be expected that the coupling coefficient (k1A ) between
TX coil 1A and the RX coil equals that (k3A ) between TX
coil 3A and the RX coil and that the coupling coefficient (k2A )between TX coil 2A and the RX coil equals that (k4A ) between
TX coil 4A and the RX coil. In the following analysis, k3A and

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Fig. 15. (a) Coil setup of case 1 in Fig. 6(b). Measured (b) k, (c) current amplitude, (d) current phase, (e) ηSYS , and (f) load power with different lateral
misalignments. Two conventional methods and the proposed method are compared.

k4A are discussed and the same conclusion can be drawn for
k1A and k2A .
When x = 0 mm, as shown in Fig. 15(b), k3A and k4A havenearly the same amplitude. According to the control algorithm
in Section II-A, the current (I3A ) through TX coil 3A and that
(I4A ) through TX coil 4A should have the same amplitudes;
this is confirmed in Fig. 15(c). k3A is positive, whereas k4A is
negative. Thus, it is required that I3A and I4A be in antiphase.
This is also confirmed in Fig. 15(d). When x = 12.5 mm,
as shown in Fig. 15(b), the ratio of amplitudes of k3A and k4A
is 0.53, which is also the required ratio of amplitudes of I3A
and I4A . This requirement is confirmed by the measured value(0.56), as shown in Fig. 15(c). In Fig. 15(d), I3A and I4A are
in antiphase, which is in accordance with the polarities of k3A
and k4A .
More discussions about k1A and k2A are given for
x = 12.5 mm. In Fig. 15(b), k2A shows some difference from
k4A , which is ascribed to the fact that the experimental setup
is not perfectly symmetrical. However, that does not affectthe operation of the AMFA ICs. From Fig. 15(b) and (c),the ratio of amplitudes of the current (I1A ) through TX coil
1A and the current (I2A ) through TX coil 2A is 0.72, which
is approximately equal to the ratio of k1A to k2A (0.67).
In addition, I1A and I2A are in antiphase, which is determinedby the polarities of k1A and k2A .
Thus, the current through each TX coil is proportional to k
between the TX coil and the RX coil. Our experiment copeswith the analysis in Section II-A, which guarantees a good
performance of our WPT system. Fig. 15(e) and (f) shows
ηSYS (the ratio of the load power to the input power fromdc supply) and load power measured using different WPT
methods. The power consumption of all on-chip digital control
is also included. The black curve shows the measured resultsof driving a single TX coil as shown in Fig. 2(a). TX coils
1A, 2A, and 1A are driven when x = 0, 12.5, and 25 mm,
respectively. The blue curve shows the measured results bydriving four TX coils with the same current, in other words,
without control, as shown in Fig. 2(b). Compared with thesetwo conventional methods, the proposed method of driving
four TX coils with control, as shown in Fig. 2(c) can significantly improve both ηSYS and load power. Take x = 0 mm as
an example. Compared with the conventional WPT methods,
ηSYS is improved from 0.02% to 48% and load power is also
improved from 0.11 to 458 mW.
Case 2 in Fig. 6(b) is also considered. The experimental
results are shown in Fig. 16. After the k-sensing mode,
AMFA ICs TX1–TX4 select TX coils 1B, 2A, 3B, and 4A,
respectively, and operate in the WPT mode. The same as incase 1, the current through each TX coil is proportional to k
between the TX coil and the RX coil. As a result, the WPTperformance can be greatly improved by using the proposed
method of driving four TX coils with control, compared withthe two conventional methods in Fig. 2. Take x = 0 mm
as an example. ηSYS is improved from 0.11% to 51% andload power is also improved from 0.85 to 576 mW. Throughcases 1 and 2, it is demonstrated that an independent control
can be realized by the selectively activated shared-HB PA
topology together with an alternate TX coil array in our WPT
system.
Furthermore, to comprehensively evaluate the performanceof the proposed WPT system, further analysis is performed.
Different representative positions of the RX coil relative to the
TX coils are summarized in Fig. 17. Besides the condition that
the RX coil is perpendicular to the TX coils, another condition
that the RX coil is parallel to the TX coils is also considered.
For both conditions, the distance is defined as that from the

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QIU et al.: 6.78-MHz MULTIPLE-TX WPT SYSTEM WITH EFFICIENCY MAXIMIZATION BY AMFA IC

2399

Fig. 16. (a) Coil setup of case 2 in Fig. 6(b). Measured (b) k, (c) current amplitude, (d) current phase, (e) ηSYS , and (f) load power with different lateral
misalignments. Two conventional methods and the proposed method are compared.

Fig. 18. Measured (a) ηSYS and (b) load power corresponding to different
positions of the RX coil in Fig. 17.
Fig. 17. Top-view schematic of TX (black) and RX (red) coils for different
positions of the RX coil.

center of the RX coil to the TX coils. Its value is 25 mm, thatis, half the diameter of coils.
Fig. 18 summarizes ηSYS and load power measured using
three different WPT methods for different positions of the
RX coil. The supply voltage was 1.8 V. For all positions,the increase in ηSYS by the adoption of the proposed AMFAIC has been demonstrated. More discussions are given for
positions (iii) and (v)–(vii). At these positions, the absolutevalue of k is small and results in a low coil-to-coil efficiency.
This is the reason why low values of ηSYS and load power are
shown even with the adoption of the proposed AMFA IC. For
the position (x), in our proposed method, the amplitude of thecurrent in TX coils 1A, 3A, and 4A is smaller than that in TX
coil 2A. Thus, compared with driving four TX coils without
control, the input power is smaller in our proposed method.
This is the reason why a smaller load power but a higher ηSYS
are shown.

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IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 57, NO. 8, AUGUST 2022

TABLE IC OMPARISONS W ITH P REVIOUS W ORKS ON C HARGING S INGLE
RX C OIL U SING M ULTIPLE TX C OILS

Fig. 19. Equivalent circuits of TX coils 1 and 2, and the RX coil. All coils
resonate at the same f 0 .

Table I shows the performance characteristics of our method
and those in previous works on charging a single RX coilusing multiple TX coils. Our design realizes the implementation of the AMFA IC for the first time. With our proposed
AMFA IC, compared with the conventional WPT methods, themultiple-TX WPT system achieves ηSYS improvement from
0.11% to 51% when the RX coil is perpendicular to the TX
coils. When the RX coil is parallel to the TX coils, ηSYS also
compares favorably with those in previous works. One may becurious about why the parallel case shows a higher ηSYS but
with a smaller load power compared with the perpendicularcase. In the parallel case, a high k results in a high R according
to (4), that is also the output impedance of a PA. This limits
the output power of the PA [16], which results in a small load
power shown in the parallel case though with a high ηSYS .
More discussions are given. First, on the basis of all
measurement results, it can be concluded that the significant
performance improvement in the multiple-TX WPT system
is worth the effort expended in optimizing the current ineach TX coil. Second, the algorithm described in Section II-A
was realized using the LabVIEW control block. In future
work, the integration of this algorithm is expected to further
improve the integration level and bring the WPT system closer
to real applications. Third, the load power in this work is
below 1 W but enough for the wireless charging of a smart
watch. We would like to emphasize that the load power is
not limited by our design but by VDD . By choosing another
implementation technology with a higher VDD , the load poweris expected to be increased to the order of 10 W that can alsosatisfy the charging requirement for a mobile phone.
V. C ONCLUSION
The AMFA IC was implemented, for the first time, in a
6.78-MHz multiple-TX WPT system to enable the controlof the amplitude and phase of the current in each TX coil
to maximize ηSYS . The selectively activated shared-HB PA
topology together with an alternate TX coil array was proposed

for independent current control in each TX coil. Duty-ratio
control guaranteed correct k sensing in the integrated k sensor
when k was smaller than 0.12. A WPT system consisting offour AMFA ICs, a 4 × 4 TX coil array, and a single RX coil
was implemented. Measurement results showed that, comparedwith the conventional system, ηSYS was improved from 0.11%
to 51% with a load power of 576 mW when the RX coil wasperpendicular to the TX coils. A ηSYS of 63%, which is higher
than those in previous works, was also achieved when the RX
coil was parallel to the TX coils. Moreover, ηSYS improvementfor different positions of the RX coil upon the adoption of the
AMFA IC was demonstrated.
A PPENDIX
A. POL of k
To make the analysis simple, we consider a WPT system
consisting of TX coils 1 and 2, and the RX coil, as shownin Fig. 19. Since k12 is constant and does not change overtime, its value can be measured offline prior to the experiment.
We pick TX coil 1 as the reference and its POL is positiveby definition. Note that its POL could be defined as negative,
in which case, the POL of k2 would flip without any change inpower delivered to the RX coil. We assume all k amplitudes
were determined by the procedure described in Section III-B.
By applying Kirchhoff’s law to the circuit, we can obtain
VS1 = I1 r1 − j ω0 k1 L 1 L RX IRX + j ω0 k12 L 1 L 2 I2
VS2 = I2 r2 − j ω0 k2 L 2 L RX IRX + j ω0 k12 L 1 L 2 I1
j ω0 k1 L 1 L RX I1 + j ω0 k2 L 2 L RX I2 = IRX (R L + rRX )(7)through which we can derive√√
ω02 k1 L 1 L RX k2 L 2 L RX
r +R
 RX  Lω02 k22 L 2 L RX
= VS2 − r2 +I2 − j ω0 k12 L 1 L 2 I1 /I1 .
rRX + R L
(8)

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QIU et al.: 6.78-MHz MULTIPLE-TX WPT SYSTEM WITH EFFICIENCY MAXIMIZATION BY AMFA IC
POL(k1 k2 ) = POL

2401



 
ω02 k22 L 2 L RX
I2 − j ω0 k12 L 1 L 2 I1 /I1
VS2 − r2 +rRX + R L

In the above equation, ω0 , L 1 , L 2 , L RX , r1 , r2 , rRX , and R L
correspond to the experimental setup and have been known.
By measuring VS2 , I1 , and I2 , we can determine the POL of
k1 k2 as (9), shown at the top of the page, and thus know thePOL of k2 .
After explaining how to determine the POL of k, we explain
the details in the experiment as follows. Take TX coils 1Aand 2A as examples. Both AMFA ICs TX1 and TX2 operate
in the k-sensing mode and the equivalent circuit is the sameas that in Fig. 8(b). VS1 and VS2 in Fig. 19 correspond to
the amplitude component of VIN at f 0 . I1 and I2 can beobtained by substituting the measured VOUT in (5). The phasedifference between the current and VOUT is calibrated when
the RX coil is absent. Thus, in our experimental setup, thepolarities of k1 and k2 can be determined and the same
principle can apply to a WPT system consisting of more
TX coils.

(9)

into (8), we can obtain POL(k1 k2 ) = POL VS2 − R2 I2 − j ω0 k12 L 1 L 2 I1 /I1 .
(12)
Through (12), the POL of k1 k2 does not require the information of R L and can be known. Thus, the POL of k2 canalso be determined.
From the above analysis, we have demonstrated that an
unknown R L does not affect the operation of our system. Here,we consider the change of R L during the charging process,which is common in practice. As discussed in Section II-B,
to adapt to the change of the position of the RX coil, oursystem divides the whole charging process to different timeintervals. For each time interval, it is acceptable that R L is
considered a constant. When it goes to the next time interval,
R L changes and our system also adapts to it.
R EFERENCES

B. Unknown R L
In this work, we implemented the WPT system using R L =10 . Someone may be concerned whether the system cantake care of the case where R L is unknown or changes during
the charging process.
In this section, we first demonstrate that an unknown R L
does not affect the operation of the WPT system.
As discussed in Section II-A, as long as the ratio of
optimized I1 and I2 equals that of k1 and k2 , the systemefficiency can be maximized. According to (4), R1 and R2
can be measured through the k sensor, and their values arecorrelated with k1 and k2 , respectively,
ω02 k12 L 1 L RX
rRX + R L
ω2 k22 L 2 L RX
R2 = r 2 +rRX + R L
R1 = r 1 +(10)where R1 and R2 are the equivalent impedances looking into
TX coils 1 and 2, respectively.
Through (10), the ratio of the amplitudes of k1 and k2 canbe determined as k1
L 2 R1 − r 1
=
.
(11)
k2
L 1 R2 − r 2
In (11), L 1 , L 2 , r1 , and r2 are the parameters of coils andhave been determined prior to the experiment. R1 and R2 canbe measured by the k sensor in the experiment. Thus, although
R L is not known to the system, the ratio of optimized I1 andI2 can be determined as (11). Thus, whether R L is known or
not does affect the operation of our system.
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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, respectively, and the Ph.D.
degree in electrical engineering from The Universityof Tokyo, Tokyo, Japan, in 2016.
He joined the School of Electronic Science andEngineering, Nanjing University, in 2021, where
he is currently an Associate Professor. He wasa Researcher with The University of Tokyo from2017 to 2020. His research interests include integrated power management circuits for wireless powering and energy harvesting and nano-systems based on low-dimensional materials.
Dr. Qiu received the National Science Fund for Excellent Young Scholars in
2021, the First Prize of Science and Technology Award of Jiangsu Province
in 2016, and the IEEE Electron Devices Society (EDS) Japan Chapter
Student Award in 2016. He was selected as one of the Highly Cited Chinese
Researchers by Elsevier in 2021. He served as a Research Fellow for theJapan Society for the Promotion of Science (JSPS) from 2015 to 2017 and a
Representative for the Japan Society of Applied Physics (JSAP) from 2016
and 2018.

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QIU et al.: 6.78-MHz MULTIPLE-TX WPT SYSTEM WITH EFFICIENCY MAXIMIZATION BY AMFA IC

Takayasu Sakurai (Life Fellow, IEEE) received the
Ph.D. degree in electrical engineering (EE) from The
University of Tokyo, Tokyo, Japan, in 1981.
In 1981, he joined Toshiba Corporation, Tokyo,
where he designed CMOS DRAM, SRAM, RISC
processors, DSPs, and SoC Solutions. He has
worked extensively on interconnect delay and capacitance modeling known as Sakurai model andalpha power-law MOS model. From 1988 to 1990,
he was a Visiting Researcher with the University ofCalifornia 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, working on low-power high-speed
VLSI, memory design, interconnects, ubiquitous electronics, organic IC’s,
and large-area electronics. He is currently a Professor Emeritus. He was a
Domain Research Supervisor for nano-electronics area with the Japan Scienceand Technology Agency, Kawaguchi, Japan. He has published more than
700 technical publications, including 200 invited presentations and several
books, and filed more than 200 patents.
Dr. Sakurai is an IEICE Fellow. He was a recipient of the 2010 IEEE
Donald O. Pederson Award in Solid-State Circuits, the 2009 and 2010
IEEE Paul Rappaport Award, the 2010 IEICE Electronics Society Award,
the 2009 IEICE Achievement Award, the 2005 IEEE ICICDT Award,
the 2005 P&I Patent of the Year Award, the 2004 IEEE Takuo SuganoAward, and four product awards. He is also the Executive Committee Chair ofIEEE VLSI Symposia and the Steering Committee Chair of IEEE A-SSCC.
He served as the Conference Chair for the Symposium on VLSI Circuits
and ICICDT, the Vice Chair for ASPDAC, the TPC Chair for A-SSCC and
VLSI Symposium, an Executive Committee Member for ISLPED, and a
Program Committee Member for the IEEE International Solid-State Circuits
Conference (ISSCC), CICC, A-SSCC, DAC, ESSCIRC, ICCAD, ISLPED,
and other international conferences. He delivered keynote speech at morethan 50 conferences, including ISSCC, ESSCIRC, and ISLPED. He was anelected Administration Committee Member for the IEEE Solid-State Circuits
Society and an IEEE CAS and SSCS Distinguished Lecturer.

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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, Minato,
Japan, where he was engaged in the circuit designof high-speed digital LSIs. He joined The University of Tokyo in 2005, where he is currently aProfessor with the Institute of Industrial Science.
From 2013 to 2014, he stayed at the University ofCalifornia at Berkeley, Berkeley, CA, USA, as a
Visiting Scholar. His research interests include the digital gate driver andsensor ICs for power electronics and the integrated power management circuits
for automotive and industrial applications.
Dr. Takamiya is a member of the Technical Program Committee of theIEEE Symposium on VLSI Circuits and the IEEE Asian Solid-State Circuits
Conference. He received the 2009 and 2010 IEEE Paul Rappaport Awards andthe Best Paper Award at the 2013 IEEE Wireless Power Transfer Conference.
He served on the technical program committees of the IEEE International
Solid-State Circuits Conference (ISSCC) from 2015 to 2020 and the IEEE
Custom Integrated Circuits Conference from 2006 to 2011. He was the Far
East Regional Chair of ISSCC 2020. He was a Distinguished Lecturer of theIEEE Solid-State Circuits Society from 2019 to 2020.

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