Wireless Power Transfer Using Class E Inverter with ... · as a coil driver in a wireless power...

0093-9994 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. Seehttp://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI10.1109/TIA.2014.2300200, IEEE Transactions on Industry Applications

1

Wireless Power Transfer Using Class E Inverterwith Saturable DC-Feed InductorSamer Aldhaher, Patrick C. K. Luk Senior Member, IEEE, Akram Bati

School of Engineering, Cranfield University, Bedford, [email protected]

Abstract—Resonant converters used as coil drivers in inductivelinks generally operate efficiently at optimum switching con-ditions for constant load values and ranges. Changes in loadand range can shift the operation of the coil driver to a non-optimum switching state which results in higher switching lossesand reduced output power levels. This paper presents a methodto adapt to variations in range for a Class E inverter usedas a coil driver in a wireless power transfer (WPT) systembased on inductive coupling. It is shown that by controllingthe duty cycle of the inverter’s switch and the value of its DC-feed inductance, the Class E inverter can be tuned to operate atoptimum switching conditions as the distance between the coilsof the WPT system changes. Mathematical analysis is presentedbased on a linear piecewise state-space representation of theinverter and the inductive link. Extensive experimental resultsare presented to verify the performed analysis and validity ofthe proposed tuning procedure.

Index Terms—Inductive power transmission, Coupling circuits,Resonant inverters, Tunable circuits and devices

I. INTRODUCTION

The weak coupling of the coils in an inductive link requiresa strong magnetic field to be created to deliver high powerlevels at large ranges. To achieve this, it requires the use ofcoil drivers that can generate large currents at frequenciesoften in the kilohertz and megahertz ranges. The Class Einverter is a suitable type of DC/AC inverters to meet sucha requirement. Invented by the Sokals [1] in 1975, it has beenstudied extensively and its analysis is well documented inliterature [2]–[10]. The Class E inverter is simple to construct,and consists of a single switching element and has a largepower handling capability compared to other inverters. Itcan achieve a theoretical 100% power efficiency by zero-voltage switching (ZVS) and zero-voltage derivative switching(ZVDS). It is considered as a resonant converter and operatesat optimum switching conditions for a fixed value of loadand switching frequency. Due to this operating constraint, theuse of the Class E inverter as the coil driver in an inductivelink means that the wireless power transfer (WPT) system canonly operate efficiently for fixed values of load, range andresonant frequency. As a result, novel WPT applications wheremobility and dynamic range are required, cannot benefit fromthe features of the Class E inverter.

The effect of displacement and misalignment of the coilsin a WPT system on the performance of Class E inverters areinvestigated in [11], [12]. It is shown that the displacement ofthe coils from their optimum position shifts the operation ofthe Class E inverter to a non-optimum switching condition. As

a result, the overall efficiency of the WPT system is degradedand the power delivered to the load is reduced. In addition,large voltages and current spikes can develop in the Class Einverter and may result in permanent damage to the inverter’sswitching element. Therefore, the Class E inverter will haveto be tuned to operate at optimum switching conditions asthe displacements in the coils occur. A tuning method hasbeen presented in [12] to allow the Class E inverter to operateoptimally by replacing a capacitor and adjusting the switchingfrequency. This tuning method may not be a practical solutionsince the inverter has to be powered off before physicalreplacements and adjustments can be then performed. In [13],adaptive frequency tuning is used at the primary coil driverand an adaptive impedance matching circuit is included at thesecondary coil side. The received power is regulated as therange of the coils changes. Although this solution allows formaximum power efficiency to be achieved over a certain coilseparation range, it requires complex circuitry and powerfulsignal processing microcontrollers and does not necessaryallow the coil driver to operate at its optimum conditions. Inthis paper, we extend on our previous work presented in [11]in order to achieve optimum switching conditions of the coildriver by using duty cycle control and saturable reactors.

This paper is organised as follows. Section II provides abrief review on the operation of inductive links. Section IIIanalyses the Class E inverter including the inductive linkusing a piecewise linear state-space representation. Section IVpresents the tuning method of the Class E inverter and dis-cusses how the values of the duty cycle of the switching signaland DC-feed inductance are calculated to achieve optimumswitching conditions. Section V presents extensive experimen-tal results to verify the analysis of the Class E inverter and toconfirm the successful operation of the tuning method. Finally,Section VII includes the conclusion and future work.

II. RESONANT INDUCTIVE LINKS REVIEW

This section provides a brief review of inductive links,further details can be found in [12], [14]–[23]. An inductivelink consists of a primary coil driven by a power currentsignal at a certain frequency and a secondary coil tunedto that frequency. The secondary coil, to which the load isconnected to, can be tuned by using an external capacitor.The secondary coil can also be designed with a self-resonantfrequency that is equal to the frequency of the power currentsignal of the primary coil. Both coils are separated by a certain

e101466

Text Box

IEEE Transactions on Industry Applications, Volume 50 , Issue 4, 2014, Pages 2710 - 2718



2

rS

CS RL

rP

LP LS

M

Fig. 1. Resonant coupled coils circuit representation.

distance, may or may not be aligned with each other andmay be designed with different dimensions. A dimensionlessparameter, referred to as the coupling coefficient k, is oftenused in inductive links to describe the amount of magneticflux linkage between the two coils as follows

k ≡ M√LPLS

(1)

where LP and LS are the self inductances of the primary andsecondary coils respectively and M is the mutual inductanceof the two coils. Fig. 1 shows the equivalent circuit of aninductive link. Capacitor CS is connected in parallel with thesecondary coil to create resonance. Resistances rP and rSare the equivalent series resistances (ESR) of the primary andsecondary coils respectively. The resonant frequency of thesecondary coil can be calculated and is given by [14]

f =1

2π

√1

LSCS− 1

C2SR

2L

. (2)

III. ANALYSIS

The circuit of the Class E inverter along with an inductivelink and their equivalent circuit are shown in Fig. 2. TheMOSFET drain channel is represented by resistances rON andrOFF for the ON and OFF intervals respectively. The equivalentcircuit is a piecewise linear system an can be described by thefollowing general state-space representation for each ON andOFF intervals

X(ωt) = AX(ωt) +Bu(ωt) (3)

where X = [x1, x2, x3, x4, x5, x6]T is the state vector. The

state variables x1, x2, x3 represent the voltage across the shuntcapacitor C1, the voltage across the series capacitor C2 andthe voltage across the parallel capacitor CS for both ON andOFF intervals respectively. The states x4, x5, x6 represent thecurrent of the DC-feed inductance Lf , the current of theprimary coil Lp and the current of the secondary coil Ls

for both ON and OFF intervals respectively. Resistance rfrepresents the ESR of the DC-feed inductor. The input vector uis equal to the unit step function. The ON interval’s domain isdefined as 0 ≤ ωt ≤ 2πD, whereas the domain for the OFFinterval is defined as 0 ≤ ωt ≤ 2π(1 −D). Using KVL and

KCL, the following equations can be obtained

V = x4rf + x4Lf + x1 (4)x5 = C2x2 (5)

x6 = x3CS +x3

RL(6)

V = x4rf + x4Lf + x1 (7)

x4 =x1

rON/OFF+ x1C1 + x5 (8)

x1 = x2 + x5rp + x5Lp − x6M (9)x5M = x6LS + x6rs + x3. (10)

Using Equ. 9-10, the derivative states x5 and x6 can be writtenas

x5 =1

LpLs −M2

(x1Ls − x2Ls − x3M − x5Lsrp − x6Mrs

)(11)

x6 =1

LpLs −M2

(x1M − x2M − x3Lp − x5Mrp − x6Lprs

).

(12)

Based on Eqs. 4-7 and Eqs. 11-12, the matrices A, B, C andD for both ON and OFF intervals are given by

AON/OFF =

−1

rON/OFFC10 0

0 0 0

0 0−1

RLCS−1

Lf0 0

Ls

LpLs −M2

−Ls

LpLs −M2

−M

LpLs −M2

M

LpLs −M2

−M

LpLs −M2

−Lp

LpLs −M2

...

...

1

C1

−1

C10

01

C20

0 01

CS−rfLf

0 0

0−Lsrp

LpLs −M2

−MrsLpLs −M2

0−Mrp

LpLs −M2

−LprsLpLs −M2

(13)

BON = BOFF = B =

[0 0 0

V

Lf0 0

]T. (14)

The solution to Eq. 3 for the ON and OFF intervals can bewritten in the form

xON(ωt) = eAONωtxON(0) +A−1ON(e

AONωt − I)B (15)

xOFF(ωt) = eAOFFωtxOFF(0) +A−1OFF(e

AOFFωt − I)B(16)

where xON(0) and xOFF(0) are the initial conditions for theON and OFF states respectively and I is a 6×6 identity



3

VG

Lf

V

C2

rLP

LP

C1

LS

rLS

CS RL

Q

M

(a) Class E inverter with an inductive link

+− V

x4

rf Lf

rON/rOFF C1

+

−

x1

C2

+ −

x2

rp

LP

x5

LS

rs x6

CS

+

−

x3

RL

M

(b) Equivalent circuit

Fig. 2. Class E inverter and the inductive link for both ON and OFF intervals

matrix. The initial conditions are determined by applying thecontinuity conditions of the voltages across C1, C2 and CS andthe currents of Lf , Lp and Ls when the circuit transitions fromthe ON state to the OFF state, hence the following equationsare obtained

xON(0) = xOFF(ωt)

∣∣∣∣ωt=2π(1−D)

(17)

xOFF(0) = xON(ωt)

∣∣∣∣ωt=2πD

. (18)

By evaluating the above equations, the initial conditions areequal to the following[

xON(0)xOFF(0)

]=

[−eAON2πD I

I −eAOFF2π(1−D)

]−1

.[A−1

ON(eAON2πD − I)

A−1OFF(e

AOFF2π(1−D)− I)

]B. (19)

For optimal switching conditions, i.e. ZVS and ZVDS, thefollowing states should be equal to the following

xON1(0) = 0 (20)xON3(0)− xON4(0) = 0. (21)

The average DC current I to the inverter is equal to theaverage value of the DC-feed inductor’s current

I =1

2π

(∫ 2πD

0

xON4(ωt)dωt+

∫ 2π(1−D)

0

xOFF4(ωt)dωt

).

(22)

IV. OPTIMISATION AND TUNING

The variation of the coupling coefficient between the pri-mary and the secondary coils of the inductive link, due to

a change of the distance between the coils, will alter theoperation of the Class E inverter from its optimal switchingconditions. It is therefore necessary to recalculate the values ofits components as the coupling coefficient changes to ensureoptimum switching operation.

Due to practical considerations, it is not desirable to replacethe components of the Class E inverter for every change thatoccurs in the coupling coefficient. Achieving the two optimumswitching conditions, ZVS and ZVDS, implies that at leasttwo operating parameters and/or component values should becontrolled. The simplest parameters that can be controlledare the duty cycle of the MOSFET gate switching signaland its frequency. However, controlling the frequency maynot be a viable solution since that might reduce the powertransfer efficiency of the inductive link. As a result, the valueof either Lf , C1 or C2 should be controlled in addition tothe duty cycle of the MOSFET gate drive signal. We chooseto control the value of Lf since it is practically possible toimplement by using magnetic amplifiers or saturable reactors.Using Eqs. 19, 20 and 21, the values of the duty cycle andLf can be numerically solved. Fig. 3 shows solutions of theduty cycle and Lf as the coupling coefficient varies from 0.2to 0.45 for a WPT system. The complete specifications of theWPT system, including the Class E inverter and the inductivelink, are summarised in Table I.

V. HARDWARE SETUP

To verify the performed analysis and the proposed tuningmethod, a WPT system consisting of a Class E inverter andan inductive link is implemented as shown in Fig. 4. Thecomplete specifications are summarised in Table I. A functiongenerator is connected to the MOSFET driver to vary theduty cycle of the MOSFET’s switching signal. The control



4

0.2 0.25 0.3 0.35 0.4 0.45 0.50.46

0.47

0.48

0.49

0.5

k

D

(a) duty cycle

0.2 0.25 0.3 0.35 0.4 0.45 0.51

1.25

1.5

1.75

2

2.25

2.5

2.75

3

k

Lf(µH)

(b) DC-feed inductance Lf

Fig. 3. Solutions of the duty cycle and the DC-feed inductance.

of the DC-feed inductance is achieved by using a saturablereactor. The saturable reactor consists of two windings, aprimary winding which represents the DC-feed inductance tobe controlled and a control winding which is connected toa variable DC current source. Both windings are wound ona 3C90 ferrite core from Ferroxcube. Ferrite cores generallyhave lower eddy current and hysteresis than other magneticcores, such as iron powder. By varying the DC current source,the amount of magnetic flux that is injected into the magneticcore via the control windings is altered, which in turn alters theinductance of the primary windings that represent the DC-feedinductor. Detailed description about the operation of saturablereactors and their applications can be found in [24]. The DC-feed inductance is at a maximum when the control DC currentis zero and decreases as the control DC current is increased.Two saturable reactors are used with their primary windingsconnected in phase and their control windings connected inantiphase manner to cancel the induced voltage in the controlwindings.

The ESR of the saturable DC-feed inductors is not constant,but varies according to frequency, temperature, the DC biasoperating point and the intensity of the AC flux due to thecurrent in the primary windings. The total losses in an inductorincrease as it saturates since its inductance is lower and itscurrent increases. This leads to higher ohmic losses in thewindings and higher hysteresis losses in the core. However, aconstant ESR value had been assumed to simplify the analysisand to obtain the solutions of the duty cycle and the DC-feedinductance in Fig. 3. An ESR value of 0.3Ω was obtainedduring initial measurements. In this setup, the temperature ofthe inductors is monitored to provide an indication of howsignificant the losses of the saturable DC-feed inductors are.

The primary coil of the inductive link consists of two layers

VG

V

C2

rLP

LP

C1

LS

rLS

CS RL

Q

M

Lf

f

Fig. 4. The implemented circuit of the Class E inverter and the inductivelink.

TABLE IVALUES AND RANGES OF SEVERAL PARAMETERS OF THE CLASS E

INVERTER AND THE INDUCTIVE LINK MEASURED AT 800 KHZ

Indu

ctiv

eL

ink

Component/Parameter ValueLP / rP 5.76 µH / 0.17ΩLS / rS 5 µH / 0.28Ω

CS 5.92 nFResonant Frequency fo 750 kHz

RL 47Ω

Mutual Inductance (M ) Range 1.37 - 2.23 µHCoupling Coefficient (k) Range 0.25 - 0.45

Coils Separation Dist. Range 0.5 - 2.5 cm

Cla

ssE

Inve

rter

Component/Parameter ValueMOSFET STP40NF10

Gate Driver TC1412rON/rOFF 0.15Ω/∞

Input Voltage 8VC1 22 nFC2 7.9 nF

Switching Frequency fs 800 kHzDuty Cycle Range 40 - 50%

Satu

rabl

eR

eact

ors

Component/Parameter ValueCore Type 3C90

No. of Cores 2

Primary turns per core 2.5

Control turns per core 70

Control winding’s resistance per core 0.23Ω

rf 0.3Ω

Control Current Range I 0.00 - 1.50ALf Range 3 - 1 µH

each having four turns of 18 AWG magnetic wire and a radiusof 8 cm. The secondary coil consists of a single layer offour turns of 20 AWG magnet wire with a radius of 7 cm.The mutual inductance was measured using the PSM1700PsimetriQ phase sensitive multimeter. The coupling coefficientof the coils is calculated using Eq. 1 and is plotted in Fig. 5.A photograph of the complete experimental setup is shown inFig. 6.

VI. EXPERIMENTAL RESULTS AND DISCUSSION

The validation process was performed as follows. The coilswere kept at an initial separation distance of 2.5 cm and werebrought closer to each other in steps of 0.25 cm to a distance



5

0 0.5 1 1.5 2 2.5 3 3.50.1

0.15

0.2

0.25

0.3

0.35

0.4

Distance (cm)

CouplingCoeffi

cien

tk

Fig. 5. The calculated coupling coefficient as the coils of the inductive linkare displaced while maintaining alignment.

0.5 cm. The duty cycle and the control current of the saturablereactors were varied according to Fig. 3 to achieve optimumswitching conditions over the entire distance range. Fig. 7shows several measured parameters over the entire separationrange of the coils. In Fig. 7a, the measured values of the dutycycle required to achieve optimum switching conditions arecompared with the theoretical values shown in Fig. 3. Thediscrepancies are due to the finite rise and fall times of theMOSFET and the MOSFET driver. Fig. 7b shows the valuesof the DC control current of the saturable reactors. The valuesof the DC-feed inductance cannot be measured accuratelysince several factors could affect the inductance such as theamplitude of the input current, the switching frequency andinput voltage. The temperature of the saturable reactors wasbelow 50C over the entire distance range which indicates thatthe losses in the saturable reactors are not significant.

Figs. 7c-g show the variation of voltages and currentsthroughout the inverter over the entire distance range. Theinput power and the transmitted power are plotted in Fig. 7h.A peak occurs at a distance of 1.25 cm corresponding to acoupling coefficient value of 0.3. The measured overall systemefficiency, i.e. DC-to-load, and the measured efficiency of theinductive link are shown in Figs. 7h and 7i respectively. Theoverall system efficiency covers the losses of the primarywindings of the saturable reactors, the switching losses in theClass E inverter and the losses in the inductive link. The powerloss in the control windings of the saturable reactors was notincluded in the overall system efficiency. It is noted that thepower loss in the control windings can be calculated fromFig. 7b and its peak is 0.911W at a maximum control currentof 1.35A. The efficiency of the inductive link increases asthe coils are brought closer to each other since the reflectedimpedance of the load becomes more significant than that ofthe ESR of the coils. The overall efficiency increases as thecoils are brought closer and remains relatively constant at 80%for larger coupling coefficient values.

Figs. 8 and 9 show the experimental waveforms of thevoltages and currents throughout the Class E inverter and theinductive link respectively. In Fig. 8a and Fig. 9a, the inverteris operating at optimum switching conditions achieving ZVSand ZVDS. The separation distance is 1.25 cm correspondingto a coupling coefficient of 0.3, the DC control currentis 0.85A, the duty cycle of the switching signal is 49.5%and the power delivered to the load is 11.75W. Theoretical

Fig. 6. Photograph of the experimental setup.

waveforms are also plotted and are in good agreement with theexperimental waveforms. In Fig. 8b and Fig. 9b, the coils arebrought closer to each other to a separation distance of 0.75 cmcorresponding to a coupling coefficient of 0.35 while main-taining the same DC control current and duty cycle. Sincethe coupling coefficient has now changed, the Class E inverterno longer operates at optimum switching conditions since theMOSFET is being switched ON at a non-zero voltage as canbe seen in the figures. The non-optimum switching conditionsresult in distortion of the voltage and current waveforms. Thiscauses excessive losses in the form of heat and reduces theamount of power that can be delivered over the load which inthis case is now 7.70W. In Fig. 8c and Fig. 9c, the inverter isretuned and is now operating at optimum switching conditionsby decreasing the duty cycle of the switching signal to 48.0%and increasing the DC control current to 1.35A. Theoreticalwaveforms are also plotted and are found to match the newexperimental waveforms. The power delivered to load has nowincreased to 8.92W. Therefore, the proposed tuning method ofcontrolling the duty cycle of the switching frequency and DC-feed inductance has been successfully demonstrated allowingthe Class E inverter to operate safely and efficiently over acertain coil displacement range.

VII. CONCLUSION AND FUTURE WORK

A novel method has been presented to tune Class E invertersthat are used as primary coil drivers in WPT systems basedon inductive coupling. By varying the inductance of the DC-feed inductor via a DC current source and the duty cycleof the MOSFET’s switching signal, the Class E invertercan operate at optimised switching conditions achieving ZVSand ZVDS as the coupled coils of the inductive link aredisplaced. This tuning method may be applied to certain WPTapplications such as inductive charging for electric vehiclesand mobile devices where displacements and misalignments ofthe coils are likely to occur. Mathematical analysis has beenperformed to derive the voltage and current relationships ofthe Class E inverter and the inductive link using a piecewiselinear state-space representation. The equations derived areused to numerically calculate the required duty cycle andthe DC-feed inductance for tuning as the coupling coefficientof the inductive link changes. Extensive experimental results



6

0.2 0.25 0.3 0.35 0.40.4

0.42

0.44

0.46

0.48

0.5

k

D

Measured

Calculated

(a) Measured duty cycle.

0.2 0.25 0.3 0.35 0.40

0.25

0.5

0.75

1

1.25

1.5

k

IC(A

)

Measured

(b) Measured control current.

0.2 0.25 0.3 0.35 0.41

1.2

1.4

1.6

1.8

2

k

ID

C(A

)

Measured

(c) Measured input DC current.

0.2 0.25 0.3 0.35 0.40

1

2

3

4

5

6

k

ILf(A

)peak-to-peak

Calculated

(d) Calculated DC-feed induc-tor’s current.

0.2 0.25 0.3 0.35 0.43

3.5

4

4.5

5

5.5

6

k

IL

P(A

)peak-to-peak

Measured

(e) Measured primary coil cur-rent.

0.2 0.25 0.3 0.35 0.425

26

27

28

29

30

k

VD

S(V

)

Measured

(f) Measured MOSFET peakvoltage.

0.2 0.25 0.3 0.35 0.460

80

100

120

140

160

k

VC

2(V

)peak-to-peak

Calculated

(g) Calculated voltage of C2.

0.2 0.25 0.3 0.35 0.4

6

8

10

12

14

k

Pow

er(W

)

Measured Transmitted Power

Measured Load Power

(h) Measured power.

0.2 0.25 0.3 0.35 0.475

80

85

90

95

k

Pow

er(W

)

Overall Efficiency

Inductive Link Efficiency

(i) Measured efficiencies

Fig. 7. Measured and calculated parameters, voltages and currents over acertain coupling coefficient range.

are presented which verify the performed analysis and thesuccessful operation of the proposed tuning method.

Since only manual feedback has been used in tuning thecurrent system, future work should include designing con-trollers to achieve automatic tuning. Moreover, improving themodelling of the Class E inverter can be further improvedby including the saturable reactor instead of a single inductorrepresentation. In addition, investigation into high frequency,efficient rectifiers such as Class E rectifiers could be performedto produce a DC voltage output in the secondary coil circuitryof the inductive link.

− 2

0

2

4

6

8

10

time (0.5µs/ div)

VGS(V

)

Measured

0

5

10

15

20

25

30

time (0.5µs/ div)

VDS(V

)

Theory

Measured

− 60

− 40

− 20

0

20

40

60

time (0.5µs/ div)

VC2(V

)

Theory

Calculated

− 60

− 40

− 20

0

20

40

60

time (0.5µs/ div)

VLP(V

)

Theory

Measured

− 60

− 40

− 20

0

20

40

60

time (0.5µs/ div)

VR(V

)

Theory

Measured

− 60

− 40

− 20

0

20

40

60

time (0.5µs/ div)

Vsat(V)

Measured

(a) Tuned optimum opera-tion at k = 0.25.

− 2

0

2

4

6

8

10

time (0.5µs/ div)

VGS(V

)

Measured

− 5

0

5

10

15

20

25

time (0.5µs/ div)

VDS(V

)

Measured

− 60

− 40

− 20

0

20

40

60

time (0.5µs/ div)

VC2(V

)

Calculated

− 60

− 40

− 20

0

20

40

60

time (0.5µs/ div)

VLP(V

)

Measured

− 60

− 40

− 20

0

20

40

60

time (0.5µs/ div)

VR(V

)

Measured

− 60

− 40

− 20

0

20

40

60

time (0.5µs/ div)Vsat(V)

Measured

(b) Untuned non-optimumoperation at k = 0.35.

− 2

0

2

4

6

8

10

time (0.5µs/ div)

VGS(V

)

Measured

0

5

10

15

20

25

30

time (0.5µ/ s)

VDS(V

)

Theory

Measured

− 80

− 60

− 40

− 20

0

20

40

60

80

time (0.5µs/ div)

VC2(V

)

Theory

Calculated

− 80

− 60

− 40

− 20

0

20

40

60

80

time (0.5µs/ div)

VLP(V

)

Theory

Measured

− 60

− 40

− 20

0

20

40

60

time (0.5µs/ div)

VR(V

)

Theory

Measured

− 60

− 40

− 20

0

20

40

60

time (0.5µs/ div)

Vsat(V)

Measured

(c) Retuned optimum op-eration at k = 0.35.

Fig. 8. Voltage waveforms of the implemented WPT system at differentcoupling coefficients demonstrating the proposed tuning method. The wave-forms represent the MOSFET’s gate driving signal VGS , the MOSFET’s drainvoltage VDS , the voltage across the series capacitor VC2 , the voltage acrossthe primary coil VLP

, the output voltage at the load VR and the voltagedeveloped across the control windings of one of the saturable reactors Vsat.

− 2

− 1

0

1

2

3

4

5

time (0.5µs/ div)

I Lf(A

)

Theory

Calculated

− 3

− 2

− 1

0

1

2

3

4

time (0.5µs/ div)

I C1(A

)

Theory

Calculated

− 2

− 1.5

− 1

− 0.5

0

0.5

1

1.5

2

time (0.5µs/ div)

I LP(A

)

Theory

Measured

(a) Tuned optimum opera-tion at k = 0.25.

− 2

− 1

0

1

2

3

4

5

time (0.5µs/ div)

I Lf(A)

Calculated

− 3

− 2

− 1

0

1

2

3

4

time (0.5µs/ div)

I C1(A)

Calculated

− 2

− 1.5

− 1

− 0.5

0

0.5

1

1.5

2

time (0.5µs/ div)

I LP(A)

Measured

(b) Untuned non-optimumoperation at k = 0.35.

− 2

− 1

0

1

2

3

4

5

time (0.5µs/ div)

I Lf(A

)

Theory

Calculated

− 3

− 2

− 1

0

1

2

3

4

time (0.5µ/ s)

I C1(A

)

Theory

Calculated

− 3

− 2

− 1

0

1

2

3

time (0.5µ/ s)

I LP(A

)

Theory

Measured

(c) Retuned optimum op-eration at k = 0.35.

Fig. 9. Current waveforms of the implemented WPT system at different cou-pling coefficients demonstrating the proposed tuning method. The waveformsrepresent the DC-feed inductor’s current ILf

, the shunt capacitor’s currentIC1 and the primary coil’s current ILP

.



7

REFERENCES

[1] N. O. Sokal and A. D. Sokal, “Class E-a new class of high-efficiencytuned single-ended switching power amplifiers,” IEEE J. Solid-StateCircuits, vol. 10, no. 3, pp. 168 – 176, Jun. 1975.

[2] A. Grebennikov and N. O. Sokal, Switchedmode RF Power Amplifiers.Oxford, UK: Newnes, 2007.

[3] M. Kazimierczuk and K. Puczko, “Exact analysis of Class-E tunedpower amplifier at any Q and switch duty cycle,” IEEE Trans. CircuitsSyst., vol. 34, no. 2, pp. 149–159, Feb. 1987.

[4] M. K. Kazimierczuk, RF Power Amplifiers. Chichester, UK: John Wiley& Sons, 2008.

[5] M. K. Kazimierczuk and D. Czarkowski, Resonant Power Converters,2nd ed. New Jersey, USA: John Wiley & Sons, 2011.

[6] M. Kazimierczuk and X. Bui, “Class E DC/DC converters with aninductive impedance inverter,” IEEE Trans. Power Electron., vol. 4,no. 1, pp. 124–135, Jan. 1989.

[7] D. Kessler and M. Kazimierczuk, “Power losses and efficiency of Class-E power amplifier at any duty ratio,” IEEE Trans. Circuits Syst. I, Reg.Papers, vol. 51, no. 9, pp. 1675–1689, Sep. 2004.

[8] T. Suetsugu and M. Kazimierczuk, “Design procedure of Class-Eamplifier for off-nominal operation at 50% duty ratio,” IEEE Trans.Circuits Syst. I, Reg. Papers, vol. 53, pp. 1468–1476, Jul. 2006.

[9] ——, “Off-nominal operation of Class-E amplifier at any duty ratio,”IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 54, no. 6, pp. 1389–1397,Jun. 2007.

[10] ——, “Analysis and design of Class-E amplifier with shunt capacitancecomposed of nonlinear and linear capacitances,” IEEE Trans. CircuitsSyst. I, Reg. Papers, vol. 51, no. 7, pp. 1261–1268, Jul. 2004.

[11] S. Aldhaher, P. C. K. Luk, and J. F. Whidborne, “Tuning Class invertersapplied in inductive links using saturable reactors,” IEEE Trans. PowerElectron., vol. to be published, 2013.

[12] M. Pinuela, D. C. Yates, S. Lucyszyn, and P. D. Mitcheson, “MaximizingDC-to-load efficiency for inductive power transfer,” IEEE Trans. PowerElectron., vol. 28, no. 5, pp. 2437 – 2447, May 2013.

[13] A. Sample, B. Waters, S. Wisdom, and J. Smith, “Enabling seamlesswireless power delivery in dynamic environments,” Proc. IEEE, vol.101, no. 6, pp. 1343–1358, Apr. 2013.

[14] B. Lenaerts and R. Puers, Inductive Link Design, ser. Analog Circuitsand Signal Processing. Springer Netherlands, 2009.

[15] J. P. C. Smeets, T. T. Overboom, J. W. Jansen, and E. A. Lomonova,“Comparison of position-independent contactless energy transfer sys-tems,” IEEE Trans. Power Electron., vol. 28, no. 4, pp. 2059–2067,Apr. 2013.

[16] K. Fotopoulou and B. Flynn, “Wireless power transfer in loosely coupledlinks: Coil misalignment model,” IEEE Trans. Magn., vol. 47, no. 2, pp.416–430, Feb. 2011.

[17] R. Jegadeesan, Y.-X. Guo, and M. Je, “Overcoming coil misalignmentusing magnetic fields of induced currents in wireless power transmis-sion,” in IEEE Int. Microwave Symp. Dig. (MTT),, Jun. 2012, pp. 1–3.

[18] T. P. Duong and J.-W. Lee, “Experimental results of high-efficiencyresonant coupling wireless power transfer using a variable couplingmethod,” IEEE Microw. Wireless Compon. Lett., vol. 21, no. 8, pp. 442– 444, Aug. 2011.

[19] W. Zhong, C. K. Lee, and S. Hui, “General analysis on the use of Tesla’sresonators in domino forms for wireless power transfer,” IEEE Trans.Ind. Electron., vol. 60, no. 1, pp. 261 – 270, Jan. 2013.

[20] H. Wu, G. Covic, J. Boys, and D. Robertson, “A series-tuned inductive-power-transfer pickup with a controllable AC-voltage output,” IEEETrans. Power Electron., vol. 26, no. 1, pp. 98–109, Jan. 2011.

[21] S.-H. Lee and R. Lorenz, “Development and validation of model for95%-efficiency 220-W wireless power transfer over a 30-cm air gap,”IEEE Trans. Ind. Appl., vol. 47, no. 6, pp. 2495–2504, 2011.

[22] Z. Pantic and S. Lukic, “Wireless power transfer in loosely coupledlinks: Coil misalignment model,” IEEE Trans. Power Electron., vol. 27,no. 11, pp. 4503–4513, Nov. 2012.

[23] K. Schuylenbergh and R. Puers, Automatic link tuning. SpringerNetherlands, 2009.

[24] “Magnetic amplifiers: A rising star in naval electronics,” ElectronicsDesign and Development Division, Bureau of Ships, U. S. Navy, 1951.

Samer Aldhaher received the B.Sc. degree in elec-trical engineering from the University of Jordan,Amman, Jordan in 2010. He is currently workingtowards the Ph.D. degree at Cranfield University,Bedford, UK.

His current research interests include the designof high frequency DC/AC inverters, wireless powertransfer applications based on resonant inductivelinks and switched-mode circuits.

Patrick Chi-Kwong Luk (M’92-SM’08) is a nativeof Hong Kong. He received the High Diploma withmerits (BSc) from Hong Kong Polytechnic Uni-versity (PolyU), Hong Kong, in 1983, the M.Phil.degree from Sheffield University, U.K., in 1989, andthe Ph.D. degree from the University of South Wales,U.K., in 1992, all in electrical engineering.

He started his career first in industry as an Assis-tant Engineer at GEC (H.K.) and then ApplicationEngineer at Polytek Engineering Co. (H.K.). In1986, he began his academic career as a Researcher

at PolyU. Since 1988, he had held academic positions at the Universityof South Wales, U.K., Robert Gordon University, U.K., and University ofHertfordshire, U.K. In 2002, he joined Cranfield University, U.K., where heis currently Chair Professor in Electrical Engineering and Head of the ElectricPower and Drives Group, School of Engineering. He is the Chairman ofthe IEEE UK&RI Young Professionals and Professional Activities AffinityGroups, and is an Associate Editor for IEEE Transactions in Power Electron-ics. He has over 140 technical publications in electrical machines and drives.His main current research interests include electrical machines and convertersfor future transport and renewable energy applications. He has been invitedas keynote speaker at international conferences.

A Senior Member of the IEEE, he won the 2011 IET Premium Award inElectric Power Applications.

Akram Bati Akram Bati received the BSc in Elec-trical Engineering from Baghdad University , Iraq in1980, the MSc and the PhD in Electrical Power Sys-tems from Cranfield Institute of Technology (CIT)in 1985 and 1988 respectively. He started his careerfirst in industry as O&M Engineer. In 1984 he beganhis academic research as assistant lecturer in theUniversity of Technology, Baghdad, Iraq and thenjoined CIT to do his MSc and PhD degrees. Since1988, he had held academic positions at the Uni-versity of Technology, Iraq, and Mutah University,

Jordan, and Kwazulu Natal University, Durban, South Africa. In 2011 hejoined Cranfield University as academic visitor and then in 2013 as a memberof staff in the group of Electric Power and Drives. He has over 30 technicalpublications in the area of Power Systems and he is a member of IEEE PES.

He served as TCP of many IEEE conferences on smart grids and PowerEngineering and he is a regular peer reviewer for IEEE Transactions andEPSRC proposals. His main current research is on smart grids stability andoptimized load flow.

Wireless Power Transfer Using Class E Inverter with ... · as a coil driver in a wireless power...

Documents

Transcript of Wireless Power Transfer Using Class E Inverter with ... · as a coil driver in a wireless power...