electronics

Article Output Analysis of Inductive Wireless Power Ttransfer with Series LC and LLC Resonance Operations Depending on Coupling Condition

KangHyun Yi

School of Electronic and Electric Engineering, Daegu University, Gyeongsan 38453, Korea; [email protected]; Tel.: +48-53-850-6652  Received: 6 March 2020; Accepted: 30 March 2020; Published: 31 March 2020 

Abstract: This paper analyzes the output voltage of an inductive (WPT) depending on coupling conditions. When the optimum efficiency and maximum output power are obtained, it is called critical coupling, so the receiving coil and the transmitting coil should be separated by a certain distance. When the distance between the transmitting coil and receiving coil is very short, it is called over coupling, and output power decreases with the optimal operating state of the critical coupling condition. To design the entire circuit system for the inductive WPT depending on the coupling condition, it is beneficial to analyze the output voltage according to a load variation, an input voltage, and an operating frequency. Therefore, the output voltage depending on the coupling condition in the inductive WPT is analyzed in this paper. The output voltage gain in critical coupling condition is greater than one and is not affected by a load variation by a series LC resonant operation. The reduced output power in an over coupling condition can be recovered by a series LLC resonant operation. In addition, the output voltage gain is almost one and is affected by the load variation in the over coupling condition. A 5W prototype is implemented with the wireless power consortium standard coils and experimental results are shown to verify theoretical analysis and operation.

Keywords: inductive coupling wireless power transfer; coupling coefficient; LC resonance; LLC resonance; wireless power consortium (WPC)

1. Introduction Wireless power transfer (WPT) has been researched for a wireless computing environment. WPT uses magnetic coupling or electric coupling to transfer power wirelessly. A general system is composed of an inverter, matching circuit, rectifier, and transmitting coupling medium such as capacitors or coils, as shown in Figure1[ 1]. In particular, an inductive WPT using magnetic coupling was commercialized for charging mobile devices cordlessly, and the wireless power consortium (WPC) has standardized the inductive WPT for a low power application. Many WPT smartphone chargers have been developed with the WPC standard [2]. The inductive WPT has many good features. The inductive WPT used in the WPC standard is a magnetic resonance WPT with a low-quality factor of transmitting and receiving coils. Operation frequency is determined by a resonance between a coil and a lumped capacitor. Since the operation principle of the WPC method is the same as the magnetic resonance WPT, the output power can be obtained in the highest level of coupling without frequency splitting via a critical coupling and output power decreases in very close clearance, via over coupling, between a transmitting coil and a receiving coil [3]. The WPC standard recommends that the distance between two coils be more than 2 mm [4].

Electronics 2020, 9, 592; doi:10.3390/electronics9040592 www.mdpi.com/journal/electronics Electronics 2020, 9, 592 2 of 11 Electronics 2020, 9, x FOR PEER REVIEW 2 of 11

Inverter Matching Matching Rectifier

E DC AC DC Power - - RO Supply AC DC

H

Figure 1. Simple structure of wireless power transfer system with magnetic and electric [1] coupling [1]. Figure 1. Simple structure of wireless power transfer system with magnetic and electric [1] coupling The[1]. prior research has focused on the analysis of the maximum power point of the system [5–7]. The maximum power point in a two-coil structure is inconsistent with the maximum efficiency The prior research has focused on the analysis of the maximum power point of the system [5–7]. point [5,6]. The frequency splitting problem of two coils and three coils was studied, and the influence The maximum power point in a two-coil structure is inconsistent with the maximum efficiency point of frequency splitting on the output power was analyzed [7]. In the conventional WPT system, it has [5,6]. The frequency splitting problem of two coils and three coils was studied, and the influence of been shown that maximum power transfer is possible only by making the resonance frequency and the frequency splitting on the output power was analyzed [7]. In the conventional WPT system, it has operating frequency the same [8–10]. Some studies have found that output power is maximized in the been shown that maximum power transfer is possible only by making the resonance frequency and critical coupling condition [11,12]. Other works have studied maximizing system efficiency [13,14]. It is the operating frequency the same [8–10]. Some studies have found that output power is maximized possible to minimize the loss and maximize the coupling coefficient by designing a magnetic coupling in the critical coupling condition [11,12]. Other works have studied maximizing system efficiency system with high-quality factor [13]. Another way to gain high efficiency is to reduce proximity effect [13,14]. It is possible to minimize the loss and maximize the coupling coefficient by designing a losses by increasing the separation between coil turns or increasing the number of the turns within the magnetic coupling system with high-quality factor [13]. Another way to gain high efficiency is to given area [14]. The other studies have increased the transferring distance or improved efficiency by reduce proximity effect losses by increasing the separation between coil turns or increasing the increasing the number of coils [15,16]. However, in the inductive WPT system, the coupling condition number of the turns within the given area [14]. The other studies have increased the transferring is changed according to the position of the receiver. It is needed to analyze an output voltage and a distance or improved efficiency by increasing the number of coils [15,16]. However, in the inductive circuit operation according to a load condition, an input voltage, and an operating frequency to design WPT system, the coupling condition is changed according to the position of the receiver. It is needed the entire circuit system for the inductive WPT depending on the coupling condition. In particular, for to analyze an output voltage and a circuit operation according to a load condition, an input voltage, low-power wireless charging systems for mobile devices like the WPC standard, the output voltage and an operating frequency to design the entire circuit system for the inductive WPT depending on characteristics help to design the WPT system when the distance between the transmitting and receiving the coupling condition. In particular, for low-power wireless charging systems for mobile devices coils can be very close, or more than 2 mm, as recommended by the WPC. The prior studies lacked the like the WPC standard, the output voltage characteristics help to design the WPT system when the output voltage characteristics for the load variation, the input voltage, and the operating frequency distance between the transmitting and receiving coils can be very close, or more than 2 mm, as depending on the coupling condition. recommended by the WPC. The prior studies lacked the output voltage characteristics for the load Therefore, the output voltage analysis of an inductive WPT using the WPC coils with LC and variation, the input voltage, and the operating frequency depending on the coupling condition. LLC resonance operations according to the distance between transmitter and receiver coils is studied Therefore, the output voltage analysis of an inductive WPT using the WPC coils with LC and in this paper. According to the coupling condition with the commercialized WPC coils, the optimal LLC resonance operations according to the distance between transmitter and receiver coils is studied frequency and operation method are considered to obtain the sufficient output power and the voltage in this paper. According to the coupling condition with the commercialized WPC coils, the optimal in desired applications depending on the coupling condition. When the distance from the transmitter frequency and operation method are considered to obtain the sufficient output power and the voltage to the receiver is more than 2 mm via a critical coupling condition, the output power and voltage can in desired applications depending on the coupling condition. When the distance from the transmitter be obtained by a series LC resonance operation. The output voltage in the critical coupling condition to the receiver is more than 2 mm via a critical coupling condition, the output power and voltage can is greater than one and is not affected by a load variation. In addition, when the distance from the be obtained by a series LC resonance operation. The output voltage in the critical coupling condition transmitter to the receiver is within 2 mm via an over coupling condition, a series LLC resonant is greater than one and is not affected by a load variation. In addition, when the distance from the operation is suitable to recover output power with high efficiency. When there is the over coupling transmitter to the receiver is within 2 mm via an over coupling condition, a series LLC resonant condition, the coils can be modeled with a magnetized , a leakage inductor, and an ideal operation is suitable to recover output power with high efficiency. When there is the over coupling and the series LLC resonance operation can be obtained [17]. The output voltage gain is condition, the coils can be modeled with a magnetized inductor, a leakage inductor, and an ideal about one and is affected by the load change in the over coupling condition. The series LLC resonant transformer and the series LLC resonance operation can be obtained [17]. The output voltage gain is operation obtains higher efficiency in the over coupling condition than in the critical coupling due about one and is affected by the load change in the over coupling condition. The series LLC resonant to low switching loss of semiconductor devices in MOSFEs and diodes. Operation and features are operation obtains higher efficiency in the over coupling condition than in the critical coupling due to verified with a 5W prototype using WPC standard coils. low switching loss of semiconductor devices in MOSFEs and diodes. Operation and features are 2.verifiedLC resonance with a 5W Operation prototype in using Critical WPC Coupling standard coils.

2. LCWhen resonance the distance Operation is about in C 2ritical mm in C theoupling inductive WPT of the WPC standard, it is a critical coupling condition and the operation uses resonance between the transmitter and receiver coils. The circuit When the distance is about 2mm in the inductive WPT of the WPC standard, it is a critical system is shown in Figure2. The WPC standard recommends that operational frequency be about coupling condition and the operation uses resonance between the transmitter and receiver coils. The circuit system is shown in Figure 2. The WPC standard recommends that operational frequency be

Electronics 2020, 9, x FOR PEER REVIEW 3 of 11 Electronics 2020, 9, 592 3 of 11 Electronics 2020, 9, x FOR PEER REVIEW 3 of 11 about 120 kHz. This chapter analyzes simple circuit system operation and output voltage characteristics under the critical coupling condition. 120about kHz. 120 This kHz. chapter This analyzes chapter simple analyzes circuit simple system circuit operation system and operation output voltage and output characteristics voltage under the critical coupling condition. characteristics under the critical coupling condition.WPC Rx Coil M1

WPC Rx Coil M1 D1 D4

C + Vin CT R D + D 4 i 1 Tx C V+ O Vin CT R Co RO

va+ c LT LR iTx VO Co RO ¯ M2 v ¯ac L LR T ¯ M2 ¯ D2 D3

WPC T Coil D2 D3 x WPC T Coil Figure 2. Wireless power consortium (WPC) LCx series resonant circuit in the critical coupling condition.Figure 2. Wireless power consortium (WPC) LC series resonant circuit in the critical coupling condition. Figure 2. Wireless power consortium (WPC) LC series resonant circuit in the critical coupling condition. 2.1.2.1. LC LC resonance resonance O Operationperation 2.1. LCFigFigure resonanceure 33 showsshows Operation operationaloperational waveformswaveforms ofof thethe LC resonanceresonance operation. By By turning turning on on and and turning turning off M and M switches, rectangular voltage is enforced to the transmitter LC resonator and power off M1 and M22 switches, rectangular voltage is enforced to the transmitter LC resonator and power Figure 3 shows operational waveforms of the LC resonance operation. By turning on and turning cancan transfer transfer from from transmitter transmitter to to receiver. receiver. Zero Zero voltage voltage switching switching (ZVS) (ZVS) of of MOSFETs MOSFETs and and zero zero current current off M1 and M2 switches, rectangular voltage is enforced to the transmitter LC resonator and power switchingswitching (ZCS) (ZCS) of of rectifiers rectifiers cannot be achieved. The operation of the circuit is simple. can transfer from transmitter to receiver. Zero voltage switching (ZVS) of MOSFETs and zero current switching (ZCS) of rectifiers cannot be achieved. The operation of the circuit is simple. Vgs_M1 M1 ON M1 ON

Vgs_ M2 ON Vgs_MM21 M1 ON M1 ON

Vgs_M2 M2 ON

iTx

iTx

Vin

vac Vin

vac t0 t t 1 2 t3 t4 t Figure 3. Simple0 operational waveformt1 t2 in the LC resonancet3 t4 operation. Figure 3. Simple operational waveform in the LC resonance operation. 2.2. DC Voltage Gain in the LC Resonance Operation Figure 3. Simple operational waveform in the LC resonance operation. 2.2. DC Voltage Gain in the LC Resonance Operation F F Figure4 shows the equivalent circuit model of an LC resonance operation. Vin and Vo are the first2.2. DCFig harmonic ureVoltage 4 shows ofGain the inthe Fourier the equivalent LC seriesResonance expansioncircuit Operation model of theof a inputn LC andresonance output operation. square , VinF and respectively. VoF are the firstKirchho harmonicff’s voltage of the law Fourier (KVL) series equations expansion for the ofLC theresonance input and operation output square are given voltages, by respectively. Figure 4 shows the equivalent circuit model of an LC resonance operation. VinF and VoF are the Kirchhoff’s voltage law (KVL) equations for the LC resonance! operation are given by first harmonic of the Fourier series expansion1 of the input and output square voltages, respectively. F = + + Kirchhoff’s voltage law (KVL) equationsVin  for1 thej ωLCLT resonanceRp I1 operationjωMI2 are given by (1) VjF jωCT ωL  R I − jωMI in Tp12 (1) jωCT 1 VjF  ω L  R I  jωMI! inF jωC Tp1 12 (1) V =jωMIT 1 + jωL I (2) OVjF ωMI1   jωLIR 2 O 12−jωCR R (2) jωCR F p1 VjωMI   jωLI O M =12k LTLR R (2(3)) M kjω LC LR TR (3) 8RO RMac= k L L (4) 8RπTRO2 (3) Rac  2 (4) 8R R  O (4) ac 2

Electronics 2020, 9, x FOR PEER REVIEW 4 of 11

Electronics 2020, 9, x FOR PEER REVIEW 4 of 11 Electronics 2020, 9, 592 4 of 11

VF MR O ac GV F (5) V 22 in F 11ω CLRR/T  ac  pω ω CL R   F V  TR MR   VO OMR ac ac GV  F (5) GV = =V   22  22    (5) F in ω11RR/ω CLRR/Tω 1 acω C p ω L ω MCL R j V   2ac p TR  T    2  in 1/ ω CT L  Rac + Rp/ωT  1/ ω CR L  − T     − R + 222 + 2 ωω RR/RacacR pp/ωω 1 ω1/C Tω C LT  ML j M j where M is mutual , Rac is− an equivalent AC resistor,T − RTo is a load resistor, Resr is some whereparasiticM is resistor mutual in inductance, the transmitter,Rac is an and equivalent k is a AC coupling resistor, coefficient.Ro is a load The resistor, outputResr is voltage some parasitic can be where M is mutual inductance, Rac is an equivalent AC resistor, Ro is a load resistor, Resr is some determinedresistor in the by transmitter, Rac and switching and k is frequency a coupling given coeffi cient.the coupling The output coefficient voltage as can shown be determined in Equation by (5).Rac parasitic resistor in the transmitter, and k is a coupling coefficient. The output voltage can be Whenand switching the resonant frequency frequency given and the switching coupling frequency coefficient are as shownthe same, in Equationan output (5). voltage When gain the is resonant greater determined by Rac and switching frequency given the coupling coefficient as shown in Equation (5). thanfrequency one and and the switching output voltage frequency is not are affected the same, by anthe outputload variation voltage as gain shown is greater in Figure than 5. one Therefore, and the When the resonant frequency and switching frequency are the same, an output voltage gain is greater theoutput WPC voltage standard is not recommends affected by thethat load operation variation frequency as shown be in determined Figure5. Therefore, by the WPC standard than one and the output voltage is not affected by the load variation as shown in Figure 5. Therefore, recommends that operation frequency be determined11 by the WPC standard recommends that ffoperation  frequency  be determined by sr22π LC π LC (6) 1 11TTRR1 fs fffr= =  (6) ≈ sr2π √L C 2π √L C (6) where fs is switching frequency. This can make22 πit possibleTLCTTRRT toπ determineLCR R an input voltage, an operating frequency, kinds of parts etc. for a low-power WPT system at the critical coupling condition. wherewheref sfs isis switchingswitching frequency.frequency. ThisThis cancan makemake itit possiblepossible toto determinedetermine anan inputinput voltage,voltage, anan operatingoperating frequency,frequency, kinds kinds of of parts parts etc. etc. forfor aa low-powerlow-power WPTWPT system system at at the the critical critical coupling coupling condition. condition.

Figure 4. Equivalent circuit model in LC resonance operation. Figure 4. Equivalent circuit model in LC resonance operation. Figure 4. Equivalent circuit model in LC resonance operation. 3 LT=LR=24μH, CT=CR=103nF, fs=100kHz, Rac=217Ω 3 LT=LR=24μH, CT=CR=103nF, fs=100kHz, Rac=217Ω 2.5 Load = 100% Load = 80% 2.5 LLooaadd = = 6 100%0% LLooaadd = = 4 800%% 2 LLooaadd = = 2 600%% v Load = 10%

G Load = 40% 2 Load = 20% v Load = 10% 1G .5

1.5 1

1 0.5 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1 0.5 fn= fs/fr 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1 Figure 5. Voltage conversion ratiofn= fs according/fr to load variation. Figure 5. Voltage conversion ratio according to load variation. 3. LLC Resonance Operation in Over Coupling 3. LLC resonance OperationFigure 5.in Voltage Over C conversionoupling ratio according to load variation. The operation method is changed to obtain the same output power in the critical coupling condition3. LLC resonance when the O distanceperation is in less Over than C aboutoupling 2 mm. When the distance between the WPC transmitter

Electronics 2020, 9, x FOR PEER REVIEW 5 of 11 Electronics 2020, 9, x FOR PEER REVIEW 5 of 11 ElectronicsThe 2020 ope,ration9, 592 method is changed to obtain the same output power in the critical coupling5 of 11 conditionThe when operation the distance method is is less changed than about to obtain 2 mm. theWhen same the outputdistance power between in the the WPC critical transmitter coupling condition when the distance is less than about 2 mm. When the distance between the WPC transmitter andand receiver receiver coils coils is is within within 2 2 mm, mm, a a coupling coupling coefficient coefficient is is greater greater than than that that of of critical critical coupling, coupling, a andnd and receiver coils is within 2 mm, a coupling coefficient is greater than that of critical coupling, and thisthis state state is is called called an an over over coupl couplinging condition condition.. In In this this condition, condition, a a series series LLCLLC resonantresonant operation operation with with this state is called an over coupling condition. In this condition, a series LLC resonant operation with thethe WPC WPC c coilsoils can can be be obtained obtained with with a a leakage leakage inductance, inductance, a a magnetized magnetized inductor inductor and and the the external external the WPC coils can be obtained with a leakage inductance, a magnetized inductor and the external capacitorcapacitor for for an an inductive inductive WPT WPT system system as as shown shown in in Fig Figureure 66.. Transmitter and receiver can capacitor for an inductive WPT system as shown in Figure 6. Transmitter and receiver inductors can bebe modeled modeled with with a a magnetized magnetized inductor, inductor, a a leakage inductor and an ideal transformer. be modeled with a magnetized inductor, a leakage inductor and an ideal transformer. M 1 WPC Rx Coil M 1 WPC Rx Coil D1 D4

Lr C + Vin iTx R D1 D4

Lr + + C Vin iTx R iLm VO Co RO + iLm VO vLm L Co RO M ¯ vLm M2 CT LM ¯ ¯ M2 CT ¯ D2 D3 D2 D3 WPC Tx Coil WPC Tx Coil FigureFigure 6. 6. EquivalentEquivalent LLCLLC resonantresonant resonance resonance circuit circuit in in the the over over coupling coupling condition. condition. Figure 6. Equivalent LLC resonant resonance circuit in the over coupling condition. 3.1.3.1. LLC LLC resonance Resonance O Operationperation 3.1. LLC resonance Operation AsAs shown shown in in Fi Figuregure 66,, the WPC WPT coilscoils can be regarded as aa transformertransformer and an inductiveinductive WPTWPT Assystem system shown can can in be be Fi driven drivengure 6, by by the a a series seriesWPC LLC LLCWPT resonanceresonance coils can operation operation.be regarded. The The as operation operationa transformer of of the the andproposed proposed an inductive circuit circuit isisWPT similar similar system to to that that can of ofbe the thedriven conventional conventional by a series LLCLLC LLC resonanceresonance resonance DC/DC DC operation/DC converter converter. The operation [17] [17].. The The of proposed proposedthe proposed circuit circuit circuit has has fourfouris similar modes modes to in inthat operation, operation, of the conventional as as shown shown in in LLCF Figureigure resonance 77.. The operation DC/DC converter from modes [17] 1. The to 2 isproposed shown. circuit has four modes in operation, as shown in Figure 7. The operation from modes 1 to 2 is shown.

Vgs_M1 M1 ON M1 ON

Vgs_M1 M1 ON M1 ON Vgs_M2 M2 ON

Vgs_M2 M2 ON

iTx iLm iTx iLm

VO

VO vLm

vLm -VO

-VO

t0 t1 t2 t3t4

t0 t1 t2 t3t4 Figure 7. Operational waveform in LLC resonance operation. Figure 7. Operational waveform in LLC resonance operation. Figure 7. Operational waveform in LLC resonance operation. Mode 1(t0~t1): Mode 1 begins by turning on the M1 switch. Before the switch is turned on, the outputMode capacitor 1(t0~t1) of: Mode the M 1 isbegins discharged by turning and achieves on the theM1 ZVSswitch. of MOSFETs Before the by switch the magnetized is turned inductoron, the Mode 1(t0~t1): Mode 1 begins by turning on the M1 switch. Before the switch is turned on, the outputLM. By capacitor the resonance of the between M1 is discharged the Lr and and the achievescoupling the capacitors, ZVS of C MOSFETsT and CR ,by the the current magnetized of Lr is output capacitor of the M1 is discharged and achieves the ZVS of MOSFETs by the magnetized inductorincreased, LMD. 1Byand theD resonance3 are turned between on, and the the L powerr and the is transferred coupling capacitors, to the load. C TheT and voltage CR, the across current LM of is inductor LM. By the resonance between the Lr and the coupling capacitors, CT and CR, the current of Lther is outputincreased, voltage. D1 and D3 are turned on, and the power is transferred to the load. The voltage across Lr is increased, D1 and D3 are turned on, and the power is transferred to the load. The voltage across LM isMode the output 2(t1~t2 voltage.): When the resonance between the Lr and the coupling capacitors is finished, mode 2 LM is the output voltage. begins.Mode The 2(tD1~t1 and2): WhenD3 are the turned resonance off in between the ZCS andthe L switchr and theM1 couplingis turned ocapacitorsff. The voltage is finished, of the outputmode Mode 2(t1~t2): When the resonance between the Lr and the coupling capacitors is finished, mode 2capacitors begins. The in MD1 and MD32 are dischargedturned off in and the charged ZCS and by switch the resonance M1 is turned with the off. inductors. The voltage When of the the 2 begins. The D1 and D3 are turned off in the ZCS and switch M1 is turned off. The voltage of the outputvoltage capacitors of Lp is V ino, modeM1 and 2 finishes.M2 are discharged and charged by the resonance with the inductors. output capacitors− in M1 and M2 are discharged and charged by the resonance with the inductors. When the voltage of Lp is –Vo, mode 2 finishes. When the voltage of Lp is –Vo, mode 2 finishes.

Electronics 2020, 9, 592 6 of 11 Electronics 2020, 9, x FOR PEER REVIEW 6 of 11

3.2. DC V Voltageoltage G Gainain in the LLC ResonanceResonance OperationOperation FigureFigure8 8 shows shows aa transformertransformer modelmodel forfor thethe WPCWPC transmittertransmitter andand receiverreceiver coils.coils. ThisThis transformertransformer model can be useful in the over coupling condition. Inductance of L and L is larger than that of L model can be useful in the over coupling condition. Inductance of L11 and L22 is larger than that of LTT and L because sheets in transmitter and receiver coils influence the over coupling condition. Lr and LRR because ferrite sheets in transmitter and receiver coils influence the over coupling condition. and L inductor can be given by Lr andM LM inductor can be given by   2 2 Lr =LrL1 L11 nM nMover over =11  kk L L 1 (7(7)) − − 2 LM nM over k L21 (8) LM = nMover = k L 1 (8) r LLN1 NT n 1 T (9) n = LN= (9) L22 NR R s L1L1 k 1 sc sc (10) k = 1 L (10) − 1L1 where kk isis thethe couplingcoupling coecoefficient,fficient, NNTT isis thethe numbernumber ofof turnsturns inin thethe transmittertransmitter coil,coil, NNRR the numbernumber 1 of turns inin thethe receiverreceiver coil,coil, MMoverover is mutualmutual inductance,inductance, andand LLSCSC1 isis an an inductance inductance when when the receiver inductor is short.short. M Lr NT:NR

L1 L2 LM

Figure 8. Equivalent transformer model forfor the WPC coils.

F F FigureFigure9 9 shows shows the the equivalent equivalent circuit circuit model model of of an anLLC LLCresonance resonance operating. operating.V VininF andand VVooF are the firstfirst harmonicharmonic ofof thethe Fourier Fourier series series expansion expansion of of the the input input and and output output square square voltages, voltages, as shownas shown in the in priorthe prior section. section When. WhenNT NandT andNR NareR are the the same, same, an an output output voltage voltage gain gain in in the the overover couplingcoupling condition can be given by

F 2 VO ω LMRacCr G = = (11) V VFF  ω2LRC ! VinO ω2 M ac r ω2 GV  F jω 1 222 LM + Rac 1 2 (11) Vin −ωωo ω− ωp jω 11LR   22M ac  rωo ωp 1  ωo = (12) L1rCr ωo  (12) s LC rr1 ωp = (13) (Lr +1LM )Cr ωp  (13) LLCr M r where Cr is (CTCR)/(CT + CR). The output voltage gain in the over coupling condition is similar to that of the conventional LLC resonant DC/DC converter, as shown in Figure 10[ 17]. Therefore, the where Cr is CC/CCTRTR    . The output voltage gain in the over coupling condition is similar to that switching frequency can be determined by of the conventional LLC resonant DC/DC converter, as shown in Figure 10 [17]. Therefore, the switching frequency can be determined by 1 fS = fo = (14) 2π √1 LrCr ff So (14) 2π LCrr

where fs is switching frequency. If the operating frequency is set as in Equation (14), a constant output voltage can be obtained regardless of the load variation. However, the fo changes due to the deviation

Electronics 2020, 9, 592 7 of 11

Electronics 2020, 9, x FOR PEER REVIEW 7 of 11 where fs is switching frequency. If the operating frequency is set as in Equation (14), a constant output Electronics 2020, 9, x FOR PEER REVIEW 7 of 11 voltage can be obtained regardless of the load variation. However, the fo changes due to the deviation of the coil inductance and resonant capacitance. If the fn is operated less than 1, the output voltage of the coil inductance and resonant capacitance. If the fn is operated less than 1, the output voltage gain gainof the is affectedcoil inductance by the loadand resonantvariation ,capacitance. and at the maximumIf the fn is operatedload, the lessoutput than voltage 1, the gainoutput becomes voltage is affected by the load variation, and at the maximum load, the output voltage gain becomes smaller smallergain is thanaffected one .by W thehen load the loadvariation decreases,, and at the the output maximum voltage load, gain the increases. output voltage These gaincan makebecomes it than one. When the load decreases, the output voltage gain increases. These can make it possible to possiblesmaller tothan design one .an W inputhen the voltage, load decreases, an operating the frequency,output voltage devices gain etc. increases. for a low These power can inductive make it design an input voltage, an operating frequency, devices etc. for a low power inductive WPT system at WPTpossible system to designat the over an input coupling voltage, condition an operating. frequency, devices etc. for a low power inductive theWPT over system coupling at the condition. over coupling condition. Lr Lr CRCT/(CR+CT) + F CRCT/(CR+CT) +F Vin LM Rac VO V F R F in LM ac V-O -

Figure 9. Equivalent circuit model in LLC resonance operation. FigureFigure 9. 9.Equivalent Equivalent circuit circuit model model in inLLC LLCresonance resonance operation. operation. L =39μH,L =7.5μH, C =51.5nF, f =220kHz, R =4.5Ω 1.05 M r r s ac LM=39μH,Lr=7.5μH, Cr=51.5nF, fs=220kHz, Rac=4.5Ω 1.05 Load = 100% LoLaoda =d =80 1%00% Load = 60% Load = 80% LoLaoda d= =4 06%0% 1 Load = 20% Load = 40% 1 LoLaoda d= =1 02%0% Load = 10%

v 0.95 G v 0.95 G

0.9 0.9

0.85 0.805.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1 0.9 0.92 0.94 0.96 0.9f8n= f1s/fo 1.02 1.04 1.06 1.08 1.1 fn= fs/fo Figure 10. Equivalent circuit model in LC resonance operation. Figure 10. Equivalent circuit model in LC resonance operation. 4. Experiment Results Figure 10. Equivalent circuit model in LC resonance operation. 4. Experiment Results 4. ExperimentAn experimental Results prototype for a commercialized WPC 5W charger for a mobile device was implementedAn experimental to verify the prototype proposed for operation, a commercialized as shown inWPC Figure 5W 11 charger. Table1 for shows a mobile the parameters device wa ins An experimental prototype for a commercialized WPC 5W charger for a mobile device was seriesimplementedLC and toLLC verifyresonance the proposed operations. operation As shown, as shown in Figure in Fig 12ure, the 11 maximum. Table 1 shows output the power parameters is 5W implemented to verify the proposed operation, as shown in Figure 11. Table 1 shows the parameters within series a distance LC and of LLC more resonance than 2 mm operations. between two As coils,shown the in operation Figure 12 is, the the maximum series LC resonance output power and the is in series LC and LLC resonance operations. As shown in Figure 12, the maximum output power is switching5W with a frequencydistance of is more about than 120 kHz.2 mm between two coils, the operation is the series LC resonance and5W the with switching a distance frequency of more is than abo ut2 mm 120 kHz.between two coils, the operation is the series LC resonance and the switching frequency is abo ut 120 kHz.

Electronics 2020, 9, x FOR PEER REVIEW 8 of 11

Table 1. Specific Components of the prototype.

Parameters Value/Part

Vin 15V

LT and LR 24μH

L1 and L2 46μH

CT and CR 103nF

M1 and M2 FDMC86116LZ

D1 ~ D4 Electronics 2020, 9, x FOR PEER REVIEW SS1P5L 8 of 11 Lr 7.5μH Table 1. Specific Components of the prototype. LM 39μH Electronics 2020, 9, 592 8 of 11 ParametersPout Value/Part5W

Vin 15V

LT and LR 24μH

L1 and L2 46μH

CT and CR 103nF

M1 and M2 FDMC86116LZ

D1 ~ D4 SS1P5L

Lr 7.5μH

LM 39μH

Pout 5W

FigureFigure 11.11. Experimental set.set. Table 1. Specific Components of the prototype.

Parameters Value/Part

Vin 15 V LT and LR 24 µH L1 and L2 46 µH CT and CR 103 nF M1 and M2 FDMC86116LZ D1~D4 SS1P5L L 7.5 µH r LM 39 µH FigurePout 11. Experimental5W set.

Figure 12. Experimental waveforms in the critical coupling condition.

Figure 13a shows that the output voltage is higher than input voltage and is constant regardless of load variation, as in the theoretical analysis. Efficiency is below 70% at a full load condition and decreases at a light load condition, as shown in Figure 13b, because the current in the transmitter is almost same when the load is small, as shown in Figure 12.

Figure 12. Experimental waveforms in the critical coupling condition. Figure 12. Experimental waveforms in the critical coupling condition. Figure 13a shows that the output voltage is higher than input voltage and is constant regardless Figure 13a shows that the output voltage is higher than input voltage and is constant regardless of load variation, as in the theoretical analysis. Efficiency is below 70% at a full load condition and of load variation, as in the theoretical analysis. Efficiency is below 70% at a full load condition and decreases at a light load condition, as shown in Figure 13b, because the current in the transmitter is decreases at a light load condition, as shown in Figure 13b, because the current in the transmitter is almost same when the load is small, as shown in Figure 12. almost same when the load is small, as shown in Figure 12.

Electronics 2020, 9, 592 9 of 11 Electronics 2020, 9, x FOR PEER REVIEW 9 of 11 Electronics 2020, 9, x FOR PEER REVIEW 9 of 11 70 40 70 4] 0 ] V

[ 35 60

V [ 3e 5 60

g ] e a

g 30 ]

t 50 % l a

30 [

t 50

o % l [ y v

o

25 c t y v 40

25 n c u t

4e 0 n i p u t

20 e c i i p u

f 30 t 20 c f i o u

f 30 E f

o 15 d

e 15 E d

i 20 f e i i 10 20 t f i 1c 0 t

e 10 c e R 5 10

R 5 0 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0.5 1 1.5 O2utp2u.t5 pow3er [3W.5] 4 4.5 5 Output power [W] Output power [W] Output power [W] (a) (b) (a) (b) Figure 13. Output voltage and efficiency according to load variation: (a) output voltage; (b) FigureFigure 13. 13. OutputOutput voltage voltage and and efficiency efficiency according according to to load variation variation:: ( (a)) output voltage; (b) efficiency. efficiency. efficiency. However, the same output power cannot be obtained with the series LC resonance operation in However, the same output power cannot be obtained with the series LC resonance operation in 2 mmHowever, distance the between same output two coils, power as shown cannot in be Figure obtained 14. When with the the series distance LC betweenresonance the operation transmitter in 2mm distance between two coils, as shown in Figure 14. When the distance between the transmitter 2mmand receiverdistance coils between is below two 2 coils, mm, as the shown coupling in Figure coefficient 14. When is about the 0.92 distance by Equation between (10), the and transmitter this is an and receiver coils is below 2 mm, the coupling coefficient is about 0.92 by Equation (10), and this is andover rece couplingiver coils condition. is below 2 mm, the coupling coefficient is about 0.92 by Equation (10), and this is an over coupling condition. an over coupling condition. 5W Load 5W Load vgs_M1 :2V/div. vgs_M1 :2V/div.

iTx :2A/div. iTx :2A/div.

Time base: 5μs/div. Time base: 5μs/div.

Figure 14. Experimental waveforms in the over coupling condition with the LC resonance operation. Figure 14. Experimental waveforms in the over coupling condition with the LC resonance operation. Figure 14. Experimental waveforms in the over coupling condition with the LC resonance operation. However, the 5W output power is recovered by the LLC operation with increasing the switching However, the 5W output power is recovered by the LLC operation with increasing the switching frequency,However, as shown the 5W in output Figure power15. As is shown recovered in Figure by the 15 ,LLC as the operation theoretical with analysis, increasing the outputthe switching voltage frequency, as shown in Figure 15. As shown in Figure 15, as the theoretical analysis, the output frequency,and output as power shown are in aff Figureected by 15. the As load shown variation in Figure in the 15, over as coupling the theoretical condition analysis, and the the current output on voltage and output power are affected by the load variation in the over coupling condition and the voltagethe transmitter and output decreases power asare the affected load decreases. by the load Figure variation 16a showsin the over that thecoupling output condition voltage isand almost the current on the transmitter decreases as the load decreases. Figure 16a shows that the output voltage currentsame with on the a half tran ofsmitt the inputer decreases voltage as in the the load full loaddecreases. condition. Figure Figure 16a 16showsb shows that that the eoutputfficiency voltage above is almost same with a half of the input voltage in the full load condition. Figure 16b shows that is70% almost at the same full load with is a higher half of than the the input critical voltage coupling in the condition full load by condition. low switching Figure loss 16b in the shows MOSFETs that efficiency above 70% at the full load is higher than the critical coupling condition by low switching efficiencyand the diodes, above even70% at though the full the load frequency is higher has than increased. the critical The coupling experimental condition results by demonstrate low switching the loss in the MOSFETs and the diodes, even though the frequency has increased. The experimental lossvalidity in the of MOSFETs the theoretical and analysisthe diodes, of the even output though voltage the gainfrequency when thehas same increased. output The power experimental is obtained results demonstrate the validity of the theoretical analysis of the output voltage gain when the same resultsin the seriesdemonstrateLC and theLLC validityresonant of operationsthe theoretical depending analysis on of the the coupling output voltage conditions. gain when the same output power is obtained in the series LC and LLC resonant operations depending on the coupling output power is obtained in the series LC and LLC resonant operations depending on the coupling conditions. conditions.

Electronics 2020, 9, x FOR PEER REVIEW 10 of 11 Electronics 2020, 9, 592 10 of 11 Electronics 2020, 9, x FOR PEER REVIEW 10 of 11 5W Load 2.5W Load

v :2V/div. vgs_M1 :2V/div. 5W Load gs_M1 2.5W Load

vgs_M1 :2V/div. vgs_M1 :2V/div.

iTx :2A/div. iTx :2A/div. i :2A/div. Tx Time base: 2μs/div. Time base: 2μs/div. iTx :2A/div. 4W Load 0.5W Load Time base: 2μs/div. Time base: 2μs/div. vgs_M1 :2V/div. vgs_M1 :2V/div. 4W Load 0.5W Load

vgs_M1 :2V/div. vgs_M1 :2V/div.

iTx :2A/div. iTx :2A/div.

iTx :2A/div. iTx :2A/div. Time base: 2μs/div. Time base: 2μs/div. Time base: 2μs/div. Time base: 2μs/div. Figure 15. Experimental waveforms in the over coupling condition with the LLC resonance operation. Figure 15.15. Experimental waveformswaveforms inin thethe overover couplingcoupling condition condition with with the the LLC LLC resonance resonance operation.

operation.7 84

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a 82

% 78 t

V 5 [ l

[

6 o y 80 e 76 v ] c

g t 4 n a % e 78 u t 74

5 i [ l

p c o t i y

f 76 v 72 c u 3 f

t o 4 n

E e u 74

i 70 d p c e t 2 i i f

f 72 u 3 68 f i o t

E c 70 d e 1 66 e 2 i R

f 68 i 64 t 0 c 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 e 1 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 66 R Output power [W] 64 Output power [W] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 (a)O utput power [W] (bO)u tput power [W]

FigureFigure 16. 16. OutputOutput voltage voltage(a) and and efficiency efficiency according according to to load load variation variation:: (a ()a output) output(b) voltage; voltage; (b ()b efficiency.) efficiency.

5.5. Conclusion ConclusionsFigure 16.s Output voltage and efficiency according to load variation: (a) output voltage; (b) efficiency.

5. ConclusionInIn this this paper,s anan operation operation method method depending depending on coupling on coupling conditions conditions such as such the distance as the distance between betweenthe WPC the transmitter WPC transmitter and receiver and receiver coils is studied. coils is studied. Theoretical Theoretical output voltage output characteristics voltage characteristics according In this paper, an operation method depending on coupling conditions such as the distance accordingto the coupling to the conditioncoupling arecondition analyzed, are and analyzed the validity, and the is verified validity through is verified experiments through withexperiments the same between the WPC transmitter and receiver coils is studied. Theoretical output voltage characteristics withoutput the power.same output A series power.LC resonance A series LC operation resonance is suitableoperation at is a distancesuitable at of a more distance than o 2f mmmore between than 2 according to the coupling condition are analyzed, and the validity is verified through experiments mmtwo between coils in two the criticalcoils in coupling the critical condition coupling for condition an inductive for an WPT inductive system. WPT A system series LLC. A seriesresonance LLC with the same output power. A series LC resonance operation is suitable at a distance of more than 2 resonanceoperation operation method for method the inductive for the inductive WPT is consideredWPT is considered to obtain to constant obtain constant output poweroutput inpower an over in mm between two coils in the critical coupling condition for an inductive WPT system. A series LLC ancoupling over coupl condition.ing condition The output. The output voltage voltage gain in gain the critical in the critical coupling coupling condition condition is greater is greater than one than and resonance operation method for the inductive WPT is considered to obtain constant output power in onedoes and not does change not change with load with variation. load variation The reduced. The reduced output output power power in over in coupling over coupling condition condition can be an over coupling condition. The output voltage gain in the critical coupling condition is greater than canrecovered be recovered by the by series the LLCseriesresonant LLC resonant operation. operation. In addition, In addition the output, the output voltage voltage gain is almostgain is onealmost and one and does not change with load variation. The reduced output power in over coupling condition oneis a andffected is affected by the load by the variation load variation in the over in the coupling over coupling condition. condition. The LLC Theresonance LLC resonance operation operation can be a can be recovered by the series LLC resonant operation. In addition, the output voltage gain is almost cangood be solution a good to solution compensate to compensate the low effi theciency low in efficiency over coupling in over inductive coupling WPT. inductive The analyzed WPT. results The one and is affected by the load variation in the over coupling condition. The LLC resonance operation analyzedare expected results to beare useful expect ated coupling to be useful conditions at coupling in designing conditions a low in designing power inductive a low power WPT inductive system for can be a good solution to compensate the low efficiency in over coupling inductive WPT. The WPTthe wireless system for charging the wireless of a mobile charging device. of a mobile device. analyzed results are expected to be useful at coupling conditions in designing a low power inductive Acknowledgments:Acknowledgments:WPT system for the ThisThis wireless research research charging was was supported supported of a mobile by by the the Daegudevice Daegu University. University Research Research Grant, Grant, 2018. 2018. Conflicts of Interest: The authors declare no conflict of interest. ConflictsAcknowledgments: of Interest: TheThis authors research declare was supported no conflict by of the interest. Daegu University Research Grant, 2018.

RConflictseferences of Interest: The authors declare no conflict of interest.

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Electronics 2020, 9, 592 11 of 11

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