FINAL MANUSCRIPT FOR IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 1

Megahertz Multiple-Receiver Wireless PowerTransfer Systems With Power Flow Management

and Maximum Efficiency Point TrackingMinfan Fu, Member, IEEE, He Yin, Student Member, IEEE, Chengbin Ma, Member, IEEE

Abstract—This paper presents systematic analysis and designof a megahertz multiple-receiver wireless power transfer (WPT)system driven by a Class E power amplifier. Both circuit-level andsystem-level analysis are conducted to discuss the characteristicsof the WPT system. In order to simultaneously manage thepower flow and maximize the overall system efficiency, a newcontrol scheme is proposed that combines maximum efficiencypoint tracking (MEPT) and time-division multiplexing (TDM).Through the proposed scheme, receivers with different loadingand coupling conditions can be charged by the same transmitterwith simplified design and control strategy. Finally, the proposedcontrol scheme is validated using an example 6.78 MHz three-receiver WPT system. The experimental results show that variouspower requirements can be quickly and stably satisfied, and theoverall average system efficiency can reach as high as 71.7%.

Index Terms—Wireless power transfer, multiple receivers,analysis and design, time-division multiplexing, maximum effi-ciency point tracking

I. INTRODUCTION

Wireless power transfer (WPT) through inductive couplingbecame increasingly popular during the past years [1]. Besidesthe non-contacting power delivery, another unique advantageof WPT is the possibility to charge multiple receivers (RXs)such as wearable devices, cellphones, and household appli-ances, namely multiple-RX WPT systems. There are funda-mental works focusing on the analysis of multiple couplingcoils under basic compensations [2]–[4]. Meanwhile, variouscoil configurations and circuits have been developed to im-prove the transfer characteristics, such as multiple transmitters(TXs) [5], impedance matching networks [6]–[8], and relaycoils [9], [10]. Using dual-band or multiple-band concept, itis possible to charge multiple devices with different resonantfrequencies [11]–[13]. Several recently published papers dis-cuss the three-dimensional charging by using orthogonal coils

c⃝ 2017 IEEE. Personal use of this material is permitted. Permission fromIEEE must be obtained for all other uses, including reprinting/republishingthis material for advertising or promotional purposes, collecting new collectedworks for resale or redistribution to servers or lists, or reuse of any copyrightedcomponent of this work in other works.

Manuscript received September 27, 2016; revised December 23, 2016;accepted March 6, 2017 (Corresponding author: Chengbin Ma). This workwas supported by the Shanghai Natural Science Foundation under Grant16ZR1416300.

M. Fu is with the Center for Power Electronics Systems, Virginia Poly-technic Institute and State University, Blacksburg, VA 24061, USA (e-mail:minfanfu@vt.edu).

H. Yin and C. Ma are with the University of Michigan-Shanghai Jiao TongUniversity Joint Institute, Shanghai Jiao Tong University, Shanghai 200240,China (e-mail: yyy@sjtu.edu.cn; chbma@sjtu.edu.cn).

or cavities [14]–[16]. A new technology called MultiSpot caneven charge the devices which are worn or carried by theusers [17]. All the above works help to speed up the transitionfrom laboratory systems to real multiple-RX applications.However, there are still many unsolved challenges for apractical multiple-RX systems, particularly the system con-trollability and stability under variations in load and coupling.It is important to specifically develop a suitable configurationand control scheme for multiple-RX systems.

In the conventional design, usually all the receivers arepowered at the same time. The control methods implementedat the TX side (frequency tracking, load-independent source,and automatic impedance matching, etc.) can hardly be usedto manage the power flow among receivers because they onlyaffect the overall performance [18]–[20]. In a multiple-RXWPT system, uncertainties caused by the loading and couplingvariations may dramatically increase due to the varied numberof RXs. The interactive relationships among receivers, such asthe cross coupling, also further affect the coil efficiency andmake the power distribution unpredictable [4]. New designand control schemes are required to achieve power flowmanagement and maintain high overall system efficiency atthe same time in multiple-RX systems.

In order to simplify the system design and control, a well-known communication technology, time-division multiplexing(TDM), has been introduced in WPT applications [21]. TheTDM-based WPT system does not require all the receiversto be simultaneously powered. This significantly reduces thesystem uncertainties and totally avoids the adverse effects ofthe cross coupling [4]. TDM can be directly combined with theexisting control approaches originally developed for the one-RX systems. In high-power applications, an early example isthe combination of frequency tuning and TDM to maintainsystem stability [22]. TDM-based WPT systems have alsobeen developed to charge low-power devices. A real TDM-based WPT system is briefly explained in [23] without detailsin analysis and implementation. Through having differentresonant frequencies, one designated device among multipledevices can be selectively and exclusively charged [24]. Mean-while, the discussion mainly focuses on the coupling coils inthe multiple-RX system. A TDM-based transmitter was built tocharge arbitrarily distributed devices in a medical applicationwith a power level of several mW and an average efficiencyof 5.8% at the worst case of 90 coil misalignment [25]. ATDM-based power control is applied in a three-orthogonal-coil transmitter [16]. The purpose is to focus the power flow

FINAL MANUSCRIPT FOR IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 2

directionally towards the targeted areas. The improvement ofefficiency is not fully discussed.

This paper proposes a systematic design methodology anddevelops a new control scheme by combining maximumefficiency point tracking (MEPT) with TDM, which is shownto be particularly suitable for low-power megahertz (MHz)multiple-RX WPT systems. The use of high operating fre-quency at MHz is attractive for having improved spatialfreedom. However, the high operating frequency is challengingwhen using the conventional hard-switch inverters due to thehigh switching losses. Therefore, in this paper a Class Epower amplifier (PA) is specifically used, which is able toachieve high peak efficiency (theoretically 100%) at MHz [26].To fully utilize this advantage, the well-known technology,MEPT, is applied to achieve high system efficiency throughimproving the loading condition of the Class E PA [27].In addition, via TDM the charging time becomes a newdegree of control freedom. Through the on-off control, thetransmitter can always work at its preferred power levelwhen charging various receivers with quite different powerrequirements. This new possibility further improves the overallsystem efficiency. The TDM-based control also helps to reducethe system complexity and thus improve the stability. To thebest of authors’ knowledge this paper is among one of thefirst works to achieve power and efficiency control (fromdc to dc) in a multiple-RX MHz WPT system. In order topower different RXs with the same TX, a systematic designmethodology is developed to optimize the PA circuit andcompensation capacitors of RXs. The input reactance of therectifier, which is usually ignored, is particularly consideredin the circuit parameters optimization. The proposed designmethodology enables optimized system efficiency and powertransfer capability when charging different RXs. This uniqueadvantage is useful to enhance the functionality and adaptivityof the multiple-RX WPT systems.

II. CIRCUIT-LEVEL ANALYSIS

A. System Configuration

The proposed multiple-RX system consists of one transmit-ter and n receivers. As shown in Fig. 1, the transmitter includesa Class E PA and a TX coil. Each receiver includes a RXcoil, a rectifier, a buck converter, an energy buffer (optional),and a final load. At any time, the TDM-based control canonly enable the charging of at most one RX. Generally,the TX is expected to be able to efficiently charge variousRXs that may have quite different power requirements. Thisobjective can be partly achieved by optimizing the parametersof PA and compensations of the RXs based on the impedancecharacteristics of the rectifiers. The below circuit analysisprovides the basis for discussing the following design andcontrol aspects.

B. Transmitter

As shown in Fig. 2, the transmitter consists of a classicalClass E PA and a TX coil. In the circuit of the PA, there is atransistor STX , a shunt capacitor CS , a radio frequency (RF)choke LF , and a series tuned resonance tank L0C0. Lt, Ct,

Class E

PA

RX1RectifierBuck

converterLoad

TX

Buffer

RX2RectifierBuck

converterLoadBuffer

RXnRectifierBuck

converterLoadBuffer

Fig. 1. System configuration.

Rt are the inductance, compensated capacitance, and parasiticresistance of the TX coil. ZR is the reflected impedance ofthe receivers. The input impedance of the TX coil, ZTX ,is the load of the PA. Given the opreating frequency ω, theresonance of TX coil is achieved by letting ωLt = 1/(ωCt).PPA, PTX and PZR are the PA input power, PA output power,and transferred power. ηPA and ηT are the efficiencies of thePA and TX coil, respectively.

VPA

IPA

STX Cs

LF

L0 C0

j*X ZTX

PTX

PPA

ZRCt

Lt

Rt

Class E PA TX Coil

PZR

ηPA Tη

Fig. 2. Circuit topology of the transmitter.

It is well known that the Class E PA can achieve zero-voltage switching (ZVS) operation under a single optimal load,ZOPT . The circuit parameters of the PA can then be optimizedtargeting this optimal load,

B = ωCS = 8π(π2+4)ZOPT

≈ 0.184ZOPT

X = ωL0 − 1ωC0

= π(π2−4)16 ZOPT ≈ 1.15ZOPT

, (1)

where B is the susceptance of CS , and X is the net reactanceof L0 and C0 [28]. With ZOPT , PA output power PTX andefficiency ηPA can be analytically derived for any PA load,i.e., ZTX (=RTX + jXTX ),

PTX =V 2PAg2RTX

2R2PA

ηPA = g2RTX

2RPA

, (2)

where

g =π sinϕ1 + 2 cosϕ1

2 cosϕ sinϕ1 + π/2 cosψ, (3)

RPA =π2/4− g[π/2 cosϕ+ sinϕ]

πB, (4)

ψ = tan−1 [(X +XTX)/RTX ] , (5)

ϕ = tan−1

[(π2/2−4)−πBRTXρ(2 cosψ+π sinψ)

π+πBRTXρ(π cosψ−2 sinψ)

], (6)

ϕ1 = ϕ+ ψ, (7)

ρ =

√1 + [(X +XTX)/RTX ]

2. (8)

FINAL MANUSCRIPT FOR IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 3

All the above variables, g, RPA, ψ, ϕ, ϕ1 and ρ, relate to theinput impedance of the TX coil, ZTX . As the load of the PA,the TX coil is usually modeled by series-connected Lt, Ct,Rt, and ZR. Under resonance, the below characteristics of theTX coil can be straightforwardly derived, ZTX = ZR +Rt

ηT = (RTX −Rt)/RTX

PZR = PTXηT

. (9)

The above analytical derivations, (1)–(9), show that thecomplexity of the transmitter is mainly caused by the loadsensitive Class E PA. Theoretically, the behavior of the PA canbe analytically predicted for any ZTX when VPA and ZOPT

are known. With normalized parameters (VPA=1 V and ZOPT

= 1 Ω) in (2), Fig. 3(a) and (b) show the influences of RTX

and θTX (i.e., the phase of ZTX ) on ηPA and PTX . Note thatthe calculation errors will become large when RTX is smalldue to the parasitic resistances of the components. It is knownthat ηPA can theoretically achieve 100% when ZTX = ZOPT

thanks to the PA’s ZVS operation. In practice, high ηPA can beensured within a region of impedance around ZOPT . Since itis inconvenient to analytically represent the impedance regionusing a constant-efficiency contour, here the high-efficiencyregion is approximated by a rectangle, as shown in Fig. 3.Specifically the region is defined as

−20 ≤ θTX ≤ 40

0.6ZOPT ≤ RTX ≤ 1.2ZOPT. (10)

Within this region, ηPA is high and stable, but PTX can bequite different. Generally, the influence of θTX on PTX islarger than that of RTX , and PTX increases with a decreasingθTX for a fixed RTX [see Fig. 3 (b)].

RTX ( )

TX

()

ZOPT

(a)

RTX ( )

TX

()

ZOPT

(b)

Fig. 3. Characteristics of PA. (a) ηPA. (b) PTX .

From a system-level perspective, it is important to ensure ahigh-efficiency PA in a WPT system. ZTX is expected to bemaintained within the high-efficiency region. In this paper, thisrequirement on ZTX is indirectly fulfilled through trackingthe maximum efficiency at the secondary side, i.e., throughthe MEPT. Thus the high peak efficiency of the Class EPA can always be achieved. Meanwhile, it should be notedthat in the high-efficiency region, the PA output power, PTX ,significantly varies. This shows that the TX output powercapability can actually be modified through tuning ZTX whilethe high PA efficiency can still be maintained. It indicatesthat RXs with different power requirements could be chargedusing the same TX. This possibility is particularly useful to

improve the adaptivity of the multiple-RX WPT system whenit is required to charge different devices.

C. Coupling

The load of the transmitter, ZR, is the reflected impedanceof the receivers [refer to Fig. 2 and (9)]. If all the receiversare turned on and charged at the same time, the belowrelationships exist,

ZR =

n∑i=1

ω2k2tiLtLi

ZRX,i, and PZR =

n∑i=1

PZRX,i (11)

where kti is the coupling coefficient between the TX coiland RXi coil, ZRX,i is the overall impedance of RXi, andPZRX,i is the power received by ZRX,i [2]. Equation (11)shows that the coupling and loading variations of receiverscan lead to a complicated ZR, and in turn make the behaviorof the PA unpredictable [refer to (2)-(9)]. The possible crosscoupling among RX coils can even lead to a more complicatedimpedance transformation relationship and adversely affect thepower transfer characteristics [4]. Through TDM, i.e., at mostone receiver is turned on, (11) is simplified as

ZR =ω2k2tiLtLi

ZRX,i, and PZR = PZRX,i, (12)

which is straightforward and naturally eliminates the adverseinfluences of the cross coupling. The inactivated RXs haveinfinite resistance as loads (i.e., open circuit), namely zeroinduced current in their RX coils. Thus the inactivated RXs donot disturb the power transfer between the TX and activatedRX. Adopting TDM largely simplifies the system modelingand reduces the complexity in design and control.

D. Receiver

Fig. 4 shows a simplified receiver that includes a RX coiland a rectifier. The circuits after the rectifier are representedby a resistive load RDC,i, i.e., the input resistance of thebuck converter [refer to Fig. 1]. Li, Ci, and Ri are theinductance, compensated capacitors, and parasitic resistanceof the i-th RX coil. ZREC,i (= RREC,i + jXREC,i) is therectifier input impedance, namely the load of the RX coil. Inthe existing design, ZREC,i is usually assumed to be pureresistive. However, this assumption is not valid any morefor a WPT system working at Megahertz. The followingdiscussion considers the influence of XREC,i and optimizesthe compensation capacitors in order to achieve the desirablepower transfer characteristics.

The characteristics of the receiver can be described asZRX,i = jXi +Ri + ZREC,i

Xi = ωLi − 1/(ωCi)ηR,i = RREC,i/(RREC,i +Ri)PREC,i = ηR,iPZRX,i

ηREC,i = PDC,i/PREC,i

, (13)

where Xi is the net reactance of LiCi, ηR,i and ηREC,i arethe efficiencies of the RX coil and rectifier, PREC,i and PDC,i

are the input power and output power of the rectifier. Withconventional secondary compensation, Xi is simply designed

FINAL MANUSCRIPT FOR IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 4

ZREC,i

Vi

Li Ci

RDC,iCF,i

Ri

j*Xi

RX Coil Rectifier

PZRX,i

PREC,i

PDC,i

ηREC,iR,iη

Fig. 4. Circuit topology of the RX coil and rectifier.

to be zero to enhance the RX power receiving capability. How-ever, ZREC,i actually contains obvious reactive componentsin a MHz WPT system. Thus a proper Xi is expected tocompensate the non-zero XREC,i [29]. The influence of Xi

can be analytically explained by the impedance relationshipbetween ZTX and Xi. Combining (9), (12), and (13) gives

ZTX = Rt +ω2kti

2LtLr

(RREC,i +Ri) + j(XREC,i +Xi), (14)

which shows Xi affects the performance of PA through ZTX

[refer to Fig. 3]. Considering the interactive relationshipsamong the above analyzed circuits, system-level discussionand design are required to properly determine the parametersof the circuits.

III. SYSTEM-LEVEL DESIGN AND CONTROL

A. Design of Transmitter

The output power capability and efficiency of the transmitterare mostly determined by the Class E PA. According to theanalysis in section II-B, VPA and ZOPT can serve as twodesign parameters for the PA [refer to (1)-(9)]. All the otherparameters can then be calculated. In a multiple-RX WPTsystem, the transmitter is expected to be able to efficientlypower various kinds of receivers instead of any specific one.A detailed discussion on the PA output power and efficiencyis provided as follows.

The output power of PA, PTX , is proportional to VPA

[refer to (2)]. Thus increasing VPA can enhance the outputcapability of the transmitter. However, large VPA should beavoided to lower the voltage stress on STX (≈ 3.6VPA whenZTX = ZOPT ) [28]. Considering the breakdown voltage ofSTX (150 V) and possible deviation of ZTX from ZOPT ,VPA is chosen as 30 V to fully utilize the capability of theswitch and ensure a safe margin. Another important parameteris ZOPT that determines the high-efficiency impedance region[refer to Fig. 3]. At the same power level a small ZOPT lowersηPA and ηT because the influences of parasitic resistancesof the PA components become obvious. Thus large ZOPT isusually preferred in terms of efficiency. On the other hand,large ZOPT lowers PTX when VPA is given. In this paper,PTX is approximately estimated as 24 W in order to provide20 W for the final loads. Then a 15 Ω ZOPT is calculatedby using the specified PTX and VPA in (2). All the circuitparameters of the transmitter are summarized in Table I. L0 is

a high-Q (310) inductor to ensure the optimal PA operation,and the other parameters of the PA (i.e., X , C0, and CS) canthen be calculated by (1). The inductance (Lt) and parasiticresistance (Rt) of the TX coil are measured by a VectorNetwork Analyzer (VNA). Lt is completely compensated byCt.

TABLE IPARAMETERS OF TRANSMITTER

Frequency VPA ZOPT LF STX CS

6.78 MHz 30 V 15 Ω 68 µH SUD15N15 287 pF

L0 C0 X Lt Ct Rt

1.47 µH 523 pF 17.3 Ω 5.40 µH 104 pF 1.50 Ω

B. Design of Receiver

In the receiver, given the RX coil and rectifier, the onlyunknown parameter that should be properly designed is Xi

[see Fig. 4]. According to the above circuit-level analysis,Xi can adjust the power receiving capability of RXi bycompensating the reactive ZREC,i and thus affecting ZTX

[refer to (14)]. This is because the PA’s characteristics stronglydepend on ZTX , i.e., its load [refer to Fig. 3]. The influenceof Xi is not straightforward and closely relates to ZREC,i (afunction of RDC,i). It is challenging to analytically derive theimpedance relationship between ZREC,i and RDC,i for a full-bridge rectifier working at MHz. For investigation purposes,system-level simulation is conducted using well-known RFcircuit analysis software, the Advanced Design System (ADS)from Keysight Technologies. The parameters in Table I and IIare applied in the simulation.

TABLE IIPARAMETERS OF RX COILS AND RECTIFIERS

Li Ri CF,i Diode1.89 µH 0.65 Ω 10 µF STPSC406

ηPA2REC,i , kti = 0.12ηPA2REC,i , kti = 0.16ηPA2REC,i , kti = 0.20

, kti = 0.12

, kti = 0.16

, kti = 0.20

PDC,i

PDC,i

PDC,i

RDC,i

Pow

er

W

Eff

icie

ncy

RDC,OPT

Fig. 5. ηPA2REC,i and PDC,i under different kti when Xi = 0.

Before designing Xi, the system-level characteristics arefirst discussed under the conventional secondary compensa-tion, i.e., Xi = 0. The efficiency from the PA to rectifier is

ηPA2REC,i = ηPA · ηT · ηR,i · ηREC,i. (15)

FINAL MANUSCRIPT FOR IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 5

Fig. 5 evaluates the influences of RDC,i on ηPA2REC,i andPDC,i under different kti. The figure shows that ηPA2REC,i

can be maximized with an optimal load RDC,OPT for eachkti. By tracking these peak efficiencies, namely the optimalloads, such as through the MEPT, the WPT system can alwayswork along the red envelope curve when the coupling varies.The corresponding PDC,i under RDC,OPT is also close to thepeak power for a specific kti. Although Fig. 5 only showsthe efficiency-power characteristics from the PA to rectifier,the observation itself can be applicable to the overall systembecause the buck converter is much less sensitive to the loadvariation compared to the circuits of the PA, coupling coils,and rectifier [see Fig. 1].

Xi

Eff

icie

ncy

Pow

er Wη PA2REC,i

PDC,i

0.7

XOPT

Fig. 6. Maximized ηPA2REC,i and corresponding PDC,i under differentXi when kti = 0.16 and RDC,i = RDC,OPT .

Under different Xi, the maximum efficiency can be trackedin the same manner. These maximized ηPA2REC,i’s and corre-sponding PDC,i’s are summarized in Fig. 6 when kti = 0.16.The purpose of Fig. 6 is to evaluate the influences of Xi underMEPT. The figure shows the maximized ηPA2REC,i can beimproved by having an optimal Xi (= XOPT = 10 Ω). Thisresult can be explained by the relationship between ZTX andXi, as shown in Fig. 7 [refer to (14)]. The high-efficiencyimpedance region of the Class E PA defined by (10) is alsoplotted. When XOPT is applied, ZTX is closest to the targetZOPT (=15 Ω), and thus the maximized ηPA2REC,i in Fig. 6is achieved. Note that ZTX can be kept within the definedhigh-efficiency region of PA when Xi ∈ [−20 Ω, 40 Ω].This shows the high ηPA2REC,i (> 70%) in Fig. 6 is mostlydue to the high-efficiency operation of PA. Under differentXi, even though the maximum efficiency can be tracked, theoptimal operation of the overall system does not necessarilyguarantee the optimal operation of individual circuits. Forinstance, the Class E PA may not work exactly at its desiredcondition, i.e., the ZVS operation. But it still needs to workclose to the optimal condition in order to improve the overallsystem efficiency. Therefore, the maximized ηPA2REC,i is acompromised solution of the operation of all the circuits.

The influence of Xi on PDC,i in Fig. 6 can also be explainedby Fig. 7 and (14). Fig. 7 shows that RTX is relativelystable but θTX decreases significantly with increasing Xi.This impedance characteristic can lead to increasing PTX andrelatively stable ηPA when Xi increases [refer to Fig. 3 (a)(b)].Within the high-efficiency region of PA, the influences of

RTX

TX

Res

ista

nce

()

Phase (

)

Xi

1.2 ZOPT

0.6 ZOPT

-20

-40

XOPT

Fig. 7. ZTX under different Xi.

RTX and θTX on PTX are quite different. It is interestingto find that PDC,i significantly varies when ηPA2REC,i ishigh, greater than 70% [refer to Fig. 6]. Such characteristicis particularly useful for a high-efficiency multiple-RX systembecause different power receiving capability can be achievedby simply using different secondary compensation in a specificreceiver. This advantage helps to simplify the design of thereceivers and also improves the functionality and adaptivityof the transmitter.

C. Maximum Efficiency Point Tracking

Maximum efficiency point tracking (MEPT) can be appliedbased on the result showing in Fig. 5. The MEPT is now beingwidely used in various electrical systems [27]. It was used inone-RX WPT systems, in which the tracked efficiency does notinclude the efficiency of PA, a standard RF one [30]. A bulkybi-directional coupler is required to measure the input power ofthe TX coil. This paper extends the MEPT of one-RX systemto the proposed TDM-based multiple-RX system, in which thePA efficiency is included. A buck converter is used to achievethe MEPT by controlling RDC,i, as shown in Fig. 8. HereVDC,i, VOUT,i, IDC,i, and IOUT,i are the input and outputvoltages and currents of the buck converter, respectively. Foran ideal buck converter,

Di =VOUT,i

VDC,i=

VOUT,i√RDC,iPDC,i

, (16)

where Di is the duty cycle of the switch SBUCK,i. Foreach specific relative position of coils, i.e., kti, there existsan optimal Di to maximize the overall system efficiency.Meanwhile, the receiver can be turned off by setting Di aszero. Thus the TDM-based control can also be implementedusing the buck converter.

SBUCK,i

IOUT,i

LBUCK,i

DBUCK,i

VOUT,i

VDC,i

IDC,i

PDC,iPOUT,i

RDC,i

Fig. 8. Buck converter.

FINAL MANUSCRIPT FOR IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 6

The MEPT control block diagram is shown in Fig. 9. At anytime, there is at most one receiver being charged. Each receiverhas its own RX controller and communicates with the TXcontroller through WiFi. The controllers obtain the efficiencyηSY S,i (from the PA to the buck converter) by measuring VPA,IPA, VOUT,i and IOUT,i, i.e.,

ηSY S,i = ηPA2REC,i · ηBUCk,i =VOUT,iIOUT,i

VPAIPA, (17)

where ηBUCK,i is the efficiency of the buck converter. Notethat the tracked efficiency is ηSY S,i instead of ηPA2REC,i.Because a high ηBUCK,i, usually greater than 90%, can beachieved over a wide range of load [30], it has a limitedinfluence on the value of RDC,OPT . In this paper, a simpleperturbation and observation (P&O) based method is appliedto track the maximum ηSY S,i. The tracking algorithm has beenreported in [30].

VOUT,i IOUT,i

on/off

TX

controller

PADC

source

PWM

VPA, IPA

PPA PL,iPOUT,iTX coil RXi coil

RXi

controller

RectifierBuck

converter

UC

bankLoad

Wifi

ηPA

ηT

ηR,i

ηREC,i

ηBUCK,i

ηPA2BUCK,i

Fig. 9. Control block diagram of MEPT.

D. TDM-Based Power Flow Management

In real applications, there always exist various uncertain-ties such as in the required power levels, types of power,and coupling conditions. The possibilities of involving thoseuncertainties can significantly increase when the number ofthe receivers is varying. As discussed in section II-C, theTDM-based scheme simplifies the analysis of the multiple-RXsystem, and thus helps to reduce the difficulties in the designand control caused by the complicated coupling conditionsamong RXs. With TDM, the charging time can be utilizedas a new degree of freedom in control. The power flow isstraightforwardly managed among the receivers by controllingthe charging time of each RX. Thus most of the existing con-trol approaches developed for one-RX systems can be directlyapplied. This paper explores a new control scheme by applyingthe MEPT in a TDM-based multiple-RX WPT system, inwhich the efficiency control and power control are simultane-ously achieved. Through introducing load-independent sourcesor proper control on TX side, it is possible to manage theinput power and maintain high efficiency of the TX side. Butit is still difficult to guarantee the overall system efficiencywithout TX-RX communication. Therefore, feedback-basedcontrol is attractive for achieving high efficiency in a dynamicenvironment, where the above uncertainties exist.

Besides, for most power converters, their efficiency usuallydecreases significantly at light load condition. This issuebecomes even worse in a multiple-RX system because itsload range is n time wider than that of a one-RX system.

With the control scheme of combining MEPT and TDM,the transmitter does not require any adjustment or control.Both its dc input voltage and operating frequency are fixed.The WPT system can always work at its desired power levelwith the peak efficiency. Therefore, the transmitter is able tocharge receivers under quite different load conditions withoutsacrificing the power transfer capability. The design of RXs byhaving different Xi’s also achieves different power receivingability. In terms of hardware complexity, only the dc inputand output are used as feedback signals, which can both beeasily measured. The above advantages largely simplify thedesign and control efforts for multiple-RX WPT systems, andimprove the functionality and adaptivity of the systems.

As shown in Fig. 9, a UC bank can be added after thebuck converter as an energy buffer in order to continuouslypower the final load. The UC banks are optional and couldbe removed if continuous charging is not required. Anotheradvantage of the UC banks is that they can decouple PL,i

(the final power requirement) from POUT,i (the actual outputpower of the WPT system). Thus both the stability of MEPTand power response time can be improved. This advantageis particularly useful for the systems using load-sensitiveresonant converters such as the Class E PA.

A voltage range for the UC bank needs to be first defined(i.e., VOUT,i ∈ [VOUT,MIN , VOUT,MAX ]) to ensure sufficientpower storage capability and avoid overcharge. The upper andlower limits should be determined based on a specific targetapplication. This paper focuses on the initial discussion onthe TDM-based multiple-RX WPT systems. Here a straight-forward TDM-based charging strategy is developed involvingthe below two basic rules.

• Rule 1: If all the VOUT,i’s are within the range of[VOUT,MIN , VOUT,MAX ], turn off the transmitter.

• Rule 2: If one or more than one VOUT,i’s are lower thanVOUT,MIN , charge the receiver with the lowest VOUT,i

until this specific VOUT,i reaches VOUT,MAX .Through the above two rules, the system can automatically

turn on and off different RXs according to the UC bankvoltages. Note that the TDM-based strategy can be modifiedfor a system without energy buffer. A simple strategy is toassign the charging time ti for RXi proportional to its power

requirement in a period T , i.e., ti : T = PL,i :n∑

i=1

PL,i. In the

proposed system, VPA is designed to make sure that all theRXs can receive sufficient power when the number of RXsreaches its upper limit. When the number of RXs decreases,VPA is kept to be fixed in order to maximize the output powercapability of TX, which in turn minimizes the charging timeof RXs.

IV. EXPERIMENTAL VERIFICATION

A three-receiver WPT system is built up, as shown inFig. 10. The system includes one transmitter and three identi-cal receivers. On the TX side, a dc source is used to providea constant VPA (=30 V) to a 6.78 MHz Class E PA; a TXcoil is driven by the PA; and a computer is used as the TXcontroller which directly reads the system input power PPA

FINAL MANUSCRIPT FOR IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 7

PA

TX coil

20 cm × 10 cm

DC source

RX coil

10 cm × 6 cm

Buck converter

Rectifier

UC bank

NI myRIO

Electronic load

1

2

3

PL,1

5 W

PL,2 10 W

1 s 4 s

3 W

PL,3

Time

2 W

(Average: 3.4 W)

PL,3 PL,2 PL,1

Time

Time

Fig. 10. Experimental setup.

from the dc source. Each receiver consists of a RX coil, arectifier, a buck converter, a RX controller (NI myRIO), aUC bank and an electronic load. VOUT,i and IOUT,i can bemeasured and read by the RX controller. All the RX controllerscommunicate with the TX controller through WiFi. Althoughthe control circuits cause additional power losses, these losseshave quite limited influence on the whole system efficiencyconsidering the output power level of the WPT system (> 20W). The programmable electronic load is also controlled toemulate various power levels and types of the load, PL,i. Allthe RX coils are fixed and placed right above the TX coil. Thevertical distance between RX coils and TX coil is 20 mm withcoupling coefficients, kt1 = 0.16, kt2 = 0.15, and kt3 = 0.15.The system parameters are given in Table I-III.

TABLE IIIPARAMETERS OF UC BANK

Cell Capacitance VOUT,MIN , VOUT,MAX

BCAP0100 16.7 F [10 V, 15 V](Maxwell) (6 cells in series) (bank)

A. Influences of RDC,i and Xi

First the electronic load is directly connected to the rec-tifier without including the buck converter and UC bank.Thus the system-level characteristics in section III-B can beverified under different RDC,i and Xi. Here only RX2 isactivated for verification purpose. Fig. 11 gives ηPA2REC,2

and PDC,2 under different RDC,2. It validates the existence ofthe maximum efficiency point, which matches the simulationresults in Fig. 5. Fig. 12 shows the influence of X2 onthe maximized ηPA2REC,2 and corresponding PDC,2. Thebasic trend is consistent with that in Fig. 6. An optimal X2

exists (XOPT =10 Ω) to maximize ηPA2REC,2. The measuredPDC,2 is slightly different with the simulated result. This ismainly due to the parasitic resistances of the components andmeasurement errors in the coupling coefficient. It can be seenthat the efficiency and power vary with different Xi. Thisresult validates that the power receiving capability of RXs can

be properly designed through the single parameter of RX, Xi.In the following experiments, all RXs are designed targetingthe same power level and with Xi=XOPT (=10Ω).

RDC,2

Eff

icie

ncy

Pow

er W

ηPA2REC,2

PDC,2

RDC,OPT

Fig. 11. Measured ηPA2REC,2 and PDC,2 under different RDC,2.

Eff

icie

ncy

Pow

er Wη

PA2REC,2

PDC,2

X2

0.7

XOPT

Fig. 12. Influence of X2.

B. Dynamic Characteristics

All the circuits in Fig 10 are included to verify the dynamicresponse of the TDM-based three-RX system. The receivershave the same parameters but with quite different load power

FINAL MANUSCRIPT FOR IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 8

profiles. As shown in Fig. 10, PL,1 and PL,3 are fixed at 5 Wand 2 W, respectively; PL,2 is a pulsed one with two powerlevels of 3 W and 10 W. The proposed TDM-based controldetermines which receiver should be charged. MEPT is thenimplemented in the chosen receiver [refer to section III-C andIII-D].

The system is initialized with VOUT,1 = VOUT,2 =VOUT,3 = VOUT,MAX = 15V . Fig. 13 and Fig. 14 show thedynamic responses of the voltages of the UC banks (VOUT,i’s),output power of the buck converters (POUT,i’s), and inputpower of the PA (PPA). From t0 to t1, all VOUT,i’s stay withinthe range of [VOUT,MIN , VOUT,MAX ], and thus the TX isturned off. Different voltage drop rates are observed due to thedifference in PL,i’s [see Fig. 10]. At t1, VOUT,1 first reachesVOUT,MIN (=10 V) and RX1 is turned on accordingly. TheMEPT is implemented until VOUT,1 reaches VOUT,MAX (=15V) at t2. Then RX2 is turned on rightly after RX1 is turned offbecause VOUT,2 has dropped below 10 V. A similar chargingprocess is repeated after t3.

Time s

Vo

ltag

e V

VOUT,1 VOUT,2 VOUT,3

t1

t2

t3

t4

t5

t7

t8

t0

t6t2

t7

Fig. 13. Voltages of UC banks.

Time s

Po

wer

W

PPA POUT,1 POUT,2 POUT,3

t0 t1 t2 t3 t4 t5 t6 t7 t8

ηSYS,AVG

71.7%

Fig. 14. PA input power and output power of buck converters.

Both Fig. 13 and Fig. 14 show that the receivers can bestably charged under various load power profiles (PL,i’s).Because the UC banks decouple PL,i from the WPT system,each receiver can be charged at the maximized ηSY S,i. Evenunder the pulsed PL,2, only small fluctuations in VOUT,2 isobserved [see the blue curve in Fig. 13]. The stable PPA

and POUT,2 in Fig. 14 indicate that the pulsed PL,2 almosthas no influence on MEPT. This result also shows that thepower response of the system is sufficiently fast even underthe pulsed PL,2. A stable PPA but slightly increasing POUT,i

are observed in Fig. 14. It is because a higher UC voltageresults in a higher efficiency of the buck converter. During thetime interval [t0, t8], the average system efficiency ηSY S,AV G

is 71.7%. This high efficiency validates the benefit of applyingMEPT in a TDM-based multiple-RX WPT system.

V. CONCLUSION

This paper provides a comprehensive discussion on the char-acteristics of a MHz multiple-RX WPT system. Through thecombination of TDM and MEPT, the power flow managementand maximum efficiency can be simultaneously achieved. TheClass E PA is introduced to fully utilize its high efficiencyand the advantage of MEPT. Based on the circuit models, thesystem parameters are designed and optimized at a systemlevel. Experimental results show that the example multiple-RX system quickly tracks the maximum efficiency and meetsvarious power requirements (both constant and pulsed ones).With the proposed design and control scheme, the uncertaintiesin the multiple-RX WPT systems are significantly reduced.This helps to simplify the design and control of the system,and also improve the functionality and adaptivity. Further workcould include the charging time optimization of the TDM-based control.

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Minfan Fu (S’13-M’16) received the B.S., M.S.,and Ph.D. degrees in electrical and computer engi-neering from University of Michigan-Shanghai JiaoTong University Joint Institute, Shanghai Jiao TongUniversity, Shanghai, China in 2010, 2013, and2016, respectively.

He is currently a postdoctoral researcher at theCenter for Power Electronics Systems, VirginiaPolytechnic Institute and State University, Blacks-burg, VA, USA. His research interests include mega-hertz wireless power transfer, resonant converters,

and circuit design optimization.

He Yin (S’13) received the B.S. degree in elec-trical and computer engineering from Universityof Michigan-Shanghai Jiao Tong University JointInstitute, Shanghai Jiao Tong University, Shanghai,China in 2012, where he is currently working towardthe Ph.D. degree.

His research interests include optimization anddecentralized control of hybrid energy systems andwireless power transfer systems.

Chengbin Ma (M’05) received the B.S. (Hons.)degree in industrial automation from East ChinaUniversity of Science and Technology, Shanghai,China, in 1997, and the M.S. and Ph.D. degrees inelectrical engineering from The University of Tokyo,Tokyo, Japan, in 2001 and 2004, respectively.

He is currently an associate professor of elec-trical and computer engineering at University ofMichigan-Shanghai Jiao Tong University Joint In-stitute, Shanghai Jiao Tong University, Shanghai,China. Between 2006 and 2008, he held a postdoc-

toral position with the Department of Mechanical and Aeronautical Engineer-ing, University of California Davis, California, USA. From 2004 to 2006, hewas a R&D researcher with Servo Laboratory, Fanuc Limited, Yamanashi,Japan. He is an associate editor of the IEEE Transactions on IndustrialInformatics. His research interests include networked energy systems, wirelesspower transfer, and mechatronic control.