Research ArticleParameters Optimization for Magnetic Resonance CouplingWireless Power Transmission
Changsheng Li He Zhang and Xiaohua Jiang
ZNDY of Ministerial Key Laboratory Nanjing University of Science and Technology Nanjing 210094 China
Correspondence should be addressed to Changsheng Li lichangsheng1984163com
Received 3 April 2014 Accepted 28 April 2014 Published 13 May 2014
Academic Editor Guojie Zhang
Copyright copy 2014 Changsheng Li et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Taking maximum power transmission and power stable transmission as research objectives optimal design for the wireless powertransmission system based onmagnetic resonance coupling is carried out in this paper Firstly based on themutual couplingmodelmathematical expressions of optimal coupling coefficients for the maximum power transmission target are deduced Whereaftermethods of enhancing power transmission stability based on parameters optimal design are investigated It is found that thesensitivity of the load power to the transmission parameters can be reduced and the power transmission stability can be enhanced byimproving the system resonance frequency or coupling coefficient between the drivingpick-up coil and the transmissionreceivingcoil Experiment results are well conformed to the theoretical analysis conclusions
1 Introduction
Wireless power transmission technology using magneticresonance coupling offeringwirelessmid-range power trans-mission was originally proposed by a research group led byMarin Soljacic from MIT in 2007 They used a self-madewireless power device to power a 60-watt bulb from a distanceof 2m with an efficiency of 40ndash50 [1] The appearanceof this technology breaks the traditional model of electro-magnetic induction transmission for which efficiency strictlydepended on the coupling coefficient of coils wireless powertransmission distances were extended from the millimeter tothe meter range [2ndash7] This represented a breakthrough inwireless power transmission technology
With the development and application of wireless powertransmission technology based on magnetic resonance cou-pling parameters optimal design and optimal control forthe power transmission process have become the focusof research [8ndash16] To maximize transmission power ortransmission efficiency [9ndash11] analyzed the influence lawsof operating parameters on the transmission performanceoptimized load value coil size and quality factor of thesystem However with coupling coefficients between coils askey parameters in system design no optimal conclusion wasdrawn Furthermore influence laws of operating parameters
on the transmission stability were not investigated On theother hand although magnetic resonance has significantadvantage in transmission distance compared with electro-magnetic induction this technology has intrinsic limitationas the load absorption power is sensitive to variations in theoperating parameters and small differences in operating andresonance frequency will reduce transmission performancesignificantly To solve this problem an optimal controlmethod of frequency-adaptive adjustment was proposedin [12 13] By applying modules for state detection RFcommunication and tracking adjustment in the transmissionand receiving terminals combined with optimization controlalgorithm this method detects the systemrsquos working state inreal time and dynamically adjusts the system working at theoptimum stateThismethod is a good solution for applicationwhen transmission and receiving terminals are in a static orquasi-static state However as this method needs extra circuitmodules in hardware and calculating time in software it isunsuitable for situationswith strict requirements in space andtime A typical example is high-speed dynamic cartridge linksetting for projectiles in a weapon system In terms of spacethere has been strictly space limitation to accommodateelectronic devices in projectiles In terms of time there is notime to adjust to and there is relative high-speed movementbetween transmission and receiving terminals (for a type of
Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 321203 8 pageshttpdxdoiorg1011552014321203
2 The Scientific World Journal
M12
R1 R2 R3
RLL1 L2L3 L4C2 C3
M23
M34
V1
Figure 1 Equivalent circuit model of a resonant system
projectile the setting rate is 5000 bulletsmin) One possiblesolution could be to improve power transmission stability andreduce the sensitivity of power transmission performanceto the variations in the operating parameters by optimalparameter design
Based on the circuit model of magnetic resonance systemthat has been established in [17] using the theoretical analysismethod of impedance mapping the coupling coefficientsof coils are optimized to maximize power transmissionThenmethods of improving power transmission stability anddecreasing transmission performance sensitivity to variationsin operating parameters are discussed
2 Circuit Model
The equivalent circuit model of this resonant system basedon mutual inductance theory is shown in Figure 1 [17]There 119871
1 1198712 1198713 and 119871
4are the self-inductance of the
driving transmission receiving and pick-up coils respec-tively 119862
2and 119862
3the respective resonance capacitances of the
transmission and receiving coils 1198772and 119877
3the equivalent
resistances of the transmission and receiving coils1198771the sum
of the power amplifier output resistance and the equivalentresistance of the driving coil 119877
119871the equivalent load of the
system including the resistance of the pick-up coil 1the
excitation voltage source and 119872119894119895and 119896
119894119895the respective
mutual inductance and coupling coefficient of any pair ofcoils with119872
119894119895= 119896119894119895radic119871 119894119871119895 and 0 le 119896119894119895 le 1
For a resonant system the transmission performanceis not always increasing with the decreasing of separationbetween coils which has been proved by experiment [9]There is an optimal value for the coupling coefficient atwhich the load gets the maximum power In order to avoidmathematical calculation of the four equations establishedaccording the Kirchhoff rsquos law when solving the optimalvalues of coupling coefficient 119896
12 11989623 and 119896
34 the analysis
method of impedance mapping is adopted in this paper [18]Through this method the electric parameters of coils aremapped into the adjacent coils and the four-coil systemcan be equivalent to a double-coil or a single-coil systemwhich will significantly reduce the difficulty of mathematicalanalysis
The electric parameters of driving and pick-up coils aremapped into the transmission and receiving coils respec-tively and the results are as follows
1198851198911=
(12059611987212)2
1198771+ 119895120596119871
1
= 1198771015840
1+
1
1198951205961198621015840
1
V2
I2 I3
R2 R3
L2 L3
C2 C3
M23
R9984001
C9984001
C9984004
R998400L
Figure 2 Double-coil equivalent circuit of a resonant system
In (4) and (5) 120596119903is the self-resonating angular frequency
of the transmission and receiving coils under the influence ofthe drive and pick-up coils respectively when the system isoperating at undercoupled state By solving 119883
22asymp 11988333asymp 0
120596119903can be expressed as follows
120596119903asymp ( [radic(119871
2
1+ 1198772
111987121198622)2
minus 41198962
121198712
11198772
111987121198622
+1198712
1minus 1198772
111987121198622]
05
)
times ([2 (1 minus 1198962
12) 1198712
111987121198622]05
)
minus1
asymp ( [radic(1198712
4+ 1198772
411987131198623)2
minus 41198962
341198712
41198772
411987131198623
+1198712
4minus 1198772
411987131198623]
05
)
times ([2 (1 minus 1198962
34) 1198712
411987131198623]05
)
minus1
(6)
For the solution of the optimal value 11989612 the electric
parameters of the pick-up coil the receiving coil and thetransmission coil are mapped into the adjacent loops in turnand the resonant system can be equivalent to a single-coilsystem eventuallyThemapping process is shown in Figure 3
In Figure 3(a)
11987710158401015840
33=11987733(12059611987223)2
1198772
33+ 1198832
33
11987110158401015840
33=
1198722
23
11986233(1198772
33+ 1198832
33)
11986210158401015840
33=1198772
33+ 1198832
33
119871312059641198722
23
11986233=
11986231198621015840
4
1198623+ 1198621015840
4
(7)
In Figure 3(b)
11987710158401015840
22=119877222(12059611987212)2
1198772
222+ 1198832
222
11987110158401015840
22=
1198722
12
119862222
(1198772
222+ 1198832
222)
11986210158401015840
22=1198772
222+ 1198832
222
11987122212059641198722
12
119877222
= 1198772+ 11987710158401015840
33
119871222
= 1198712+ 11987110158401015840
33 119862
222=
119862211986210158401015840
33
1198622+ 11986210158401015840
33
119883222
= 120596119871222
minus1
120596119862222
(8)
The mapping resistance of load 119877119871at the driving coil is
119877101584010158401015840
119871=
1198771015840
11987111987710158401015840
33(12059611987212)2
(1198772
222+ 1198832
222) 11987733
(9)
From Figure 3(b) the transmission power of system canbe written as
1198750=
051198812
1119898119877101584010158401015840
119871
(1198771+ 11987710158401015840
22)2
+ [120596 (1198711+ 11987110158401015840
22) minus (1120596119862
10158401015840
22)]2 (10)
Optimal value 11989612can be derived from (10) using calculus
as follows
11989612-opt = radic
radic1205762 + 4120575120585 minus 120576
212057511987111198712
(11)
In (11) 120576 = 21198772221198622
2221205962
1199031198771120591 120575 = 3119877
2
2221198622
2221205964
119903+ 1205892 120585 =
1205902+ 1198622
2221198772
11205912 120591 = 119877
2
222+ 1198832
222 and 120589 = 120596
119903minus 1198712221198622221205963
119903
120590 = 1205961199031198711119862222120591
From (4) (5) and (11) the optimal values of couplingcoefficients are closely related to the resonance angularfrequency120596
119903 In the condition of undercoupling and near the
critical coupling 120596119903can be approximated as a constant as
(6) But in the overcoupling region the resonance frequencyappears as splitting phenomena and the values vary sharplywith increasing of 119896
23 Therefore the formulas developed in
this paper can only be used in the condition of undercouplingand near the critical coupling On the other hand the sig-nificant advantage of resonance technology compared with
4 The Scientific World Journal
Powersource
Drivingcoil
Transmissioncoil coil
Receivingcoil
Pick-up
A
V1
d1 d2d3
V2
RL
(a) Schematic diagram of the experimental system (b) Experimental setup
Figure 4 Experimental system
electromagnetic induction technology is the farther distanceof wireless transmission Therefore the optimal design forlarge distance (nonovercoupling region) has good practicalengineering valueThe coupling status of the resonant systemis determined by 119896
23 the value of the coupling coefficient 119896
23
at critical coupling status is called critical coupling coefficientdenoted as 119896
119888 If 11989623gt 119896119888 the coupling status is overcoupling
whereas if 11989623
lt 119896119888 the status is undercoupling Referring
the solving method of 119896119888to double-coil system in [19] from
Figure 2 the critical coupling coefficient of this four-coilsystem can be written as
119896119888= [
[
(1198771015840
1+ 1198772)2
+ (1198771015840
119871+ 1198773)2
212059621199031198712
2
]
]
05
(12)
To verify the above optimization theory experimentalanalysis for a resonant system is performedThe experimentalsystem is shown in Figure 4 The coil is 75mm in diameterand is wound with 09 mm diameter enameled copper wireand the load resistance is 50Ω The power source used inthe experiment is a signal generator (Tektronix AFG3102peak value of output voltage 5V and output impedance50Ω) Power measurements are performed using a currentprobe (Tektronix TCP312 with TCPA300) with oscilloscopes(Tektronix TDS2022) The transmission and the receivingterminals are placed coaxially and are able to be displacedalong the axis The separations between driving and trans-mission coils transmission and receiving coils and receivingand pick-up coils are denoted as 119889
1 1198892 and 119889
3 respectively
The number of turns in driving and pick-up coils is 2 and intransmission and receiving coils is 5
The key parameters of coils in Table 1 are measured by theLCR meter (HIOKI 3532-50)
Figure 5 is the experiment curves of variations in trans-mission power with separation between coils Optimal valuesof coupling coefficients are listed in Tables 2 3 and 4
From Tables 2ndash4 we can see that the optimal valuesobtained from theoretical calculation and experiment arewell consistent Error is mainly caused by the following tworeasons one is the resonance angular frequency taken intheoretical calculation that is an approximation as (6) andthe other is the that separation between coils can only bechanged step by step The experimental results showed that
Table 2 Theoretical and experimental values of 11989612-opt
Experiment conditions Theory Experiment11989623(1198892mm) 119896
34(1198893mm) 119896
1211989612(1198891mm)
0101 (35) 0600 (0) 0451 0414 (3)0019 (100) 0414 (3) 0179 0176 (20)0050 (60) 0414 (3) 0320 0367 (5)0153 (25) 0353 (5) 1000lowast 1000lowastlowastThe separation between coils is as close as possible the same meaning as inTable 3
Table 3 Theoretical and experimental values of 11989634-opt
Experiment conditions Theory Experiment11989612(1198891mm) 119896
the optimization formulas are correct and can be used toeffectively optimize the power transmission characteristics inthe nonovercoupling region for resonant systems
The Scientific World Journal 5
0 5 10 15 20 25 305
15
25
35
45
55Po
wer
(mW
)
d3 (mm)
(a) 1198892 = 35mm
0 5 10 15 20 25 305
15
25
35
45
Pow
er (m
W)
d3 (mm)
(b) 1198892 = 60mm
0 5 10 15 20 25 305
10
15
20
Pow
er (m
W)
d3 (mm)
d1 = 0mmd1 = 3mm
d1 = 5mmd1 = 20mm
(c) 1198892 = 100mm
Figure 5 Variations in transmission power with separation between coils
3 Methods for Enhancing PowerTransmission Stability
The power transmission performance of the resonant systemis determined by the synthesis of different transmissionparameters Peak power output is acquired at the resonancefrequency point and the absorption power of the loaddeclines sharply when the operating frequency deviates fromthe resonance frequency In engineering applications thetransmission performance may decline for the differences inactual and design resonance frequency caused by fabricationprocess of coils relativemovement between transmission andreceiving terminals interference of environmental factorsand other reasons The possible solution for this problem isto improve the pass bandwidth of the system to reduce thesensitivity of the transmission power to operating frequencyvariations by optimal design for parameters That is tosay when the deviation in the operating frequency fromthe resonance frequency is small even without frequency-adaptive adjustment the system can still output high powerwith efficiency
Simulation analysis and experimental results all showthat by improving the system resonance frequency orcoupling coefficient 119896
12 11989634
can effectively improve thepower transmission stability under conditions that affect less
negatively other transmission performances The followingintroduces these two methods and analyzes what negativeinfluence these may introduce
(1) Increasing Values of the Coupling Coefficients 11989612and 119896
34
The degree of sharpness in the frequency response curve ofthe load power reduces as the coupling coefficients 119896
12and
11989634increase By reducing the axial distance between the driv-
ing coil (pick-up coil) and the transmission coil (receivingcoil) values of the coupling coefficients 119896
12and 119896
34can be
increased This will play an active role in reducing the degreeof sharpness in the frequency response curve of the loadpower On the other hand from the angle ofmaximumpowertransmission it is not the larger of coupling coefficients thebetter By increasing 119896
12 11989634 to enhance power transmission
stability may reduce the amplitude of power transmissionsimultaneous As illustrated by the experiment curves inFigure 5 transmission power may increase as 119889
1and 119889
3
increase This phenomenon is even more apparent when thevalue of 119889
2is larger Figure 6 shows the experimental curve of
the normalized load power at various excitation frequenciessettings 119889
1= 0 and 119889
2= 60mm 119875max is the load absorption
power at resonance Clearly the system pass bandwidthincreases 33 KHz when 119889
3is decreased from 12mm to 0
6 The Scientific World Journal
1
08
06
04
02
008 09 1 11 12
ffr
P0P
max
d3 = 0mmd3 = 5mmd3 = 12mm
Figure 6 Variation of load power with frequency at various 1198893values
20 30 40 50 60 70 80 90 100 110 1200
10
20
30
40
50
60
Pow
er (m
W)
d2 (mm)
fr = 1MHzfr = 2MHzfr = 5MHz
(a) 119877119871 = 50Ω
20 30 40 50 60 70 80 90 100 110 1200
10
20
30
40
50
60
fr = 1MHzfr = 2MHzfr = 5MHz
Pow
er (m
W)
d2 (mm)
(b) 119877119871 = 150Ω
Figure 7 Variations in power transmission characteristics with various resonance frequencies
(2) Increasing the Resonance Frequency The resonance fre-quency is a key parameter in system design whose value canbe changed by adjusting the number of turns or the externallymatched capacitance of the transmission and receiving coilsThe degree of sharpness in the frequency response curve ofload power reduces as resonance frequency increases There-fore enhancing power transmission stability can be obtainedby properly reducing the value of the external matchedcapacitance Transmission systems with a high resonancefrequency can produce high power transmission over shortdistancesHowever transmission performance attenuates fastas the separation between transmission and receiving termi-nals increasesTherefore it is not appropriate for the wirelesstransmission of power over long distance The attenuationof transmission power for systems with small resonancefrequencies is relatively slow as the separation between trans-mission and receiving terminals increase This is shown inFigure 7 Figure 8 gives the normalized experimental curve ofload power for various excitation frequencies at 119889
2= 60mm
and 119877119871= 50Ω It shows that when 119891
119903= 5MHz the pass
bandwidth is 236KHz and 285KHz wider than that at 2MHzand 1MHz respectively In addition along with increasingthe resonance frequency difficulties of circuit implementingincrease and inversion losses in the driving circuit alsoincrease These factors will cause further degradation in totaltransmission efficiency
To illustrate the effect of optimization both Figures 6 and8 show normalized curves of the resonant system with onlya single resonance frequency When the separation betweentransmission and receiving terminals is small and the systemshows splitting in the resonance frequency the optimizationmethod is still applicable
In summary by appropriate readjustment of the trans-mission parameters the sharpness in the frequency responsecurve of load power can be effectively reduced Simulta-neously transmission power might be reduced when thepower transmission stability is improved In contrast wirelesspower transmission technology based onmagnetic resonancecoupling relies on a strong coupling between transmissionand receiving terminals to produce high efficiency power
The Scientific World Journal 7
1
08
06
04
02
007 08 09 1 11 12 13
ffr
fr = 1MHzfr = 2MHzfr = 5MHz
P0P
max
Figure 8 Variations in frequency response curve of load powerwithvarious resonance frequencies
transmission The transmission theory is established basedon resonance which in principle determines the sensitivity ofthe power transfer characteristics to the working frequencyTherefore the sensitivity cannot be totally eliminated Dur-ing engineering-design stages the transmission parametersshould be set appropriately by accommodating with thetransmission performance of the system
4 Conclusion
In this paper power transmission characteristics of magneticresonance coupling wireless power transmission system areoptimized Based on themutual couplingmodel of a resonantsystem optimization formulas of coupling coefficient in thecondition of maximum power transmission are deduced andexperimental results show that the optimization formulasare correct and can be used to effectively optimize powertransmission characteristics in the nonovercoupling regionOn the other hand by improving the system resonancefrequency or coupling coefficient 119896
12 11989634 the power trans-
mission stability can be improved while power transmissionperformance sensitivity to variations in operating parameterscan be decreasedThe conclusions obtained in this paper willenrich the theory of wireless power transmission based onmagnetic resonance and provide a reference for engineeringapplications
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National Natural ScienceFoundation of China under Grant no 61104185
References
[1] A Kurs A Karalis R Moffatt J D Joannopoulos P Fisherand M Soljacic ldquoWireless power transfer via strongly coupled
magnetic resonancesrdquo Science vol 317 no 5834 pp 83ndash862007
[2] C A Tucker KWarwick andW Holderbaum ldquoA contributionto the wireless transmission of powerrdquo International Journal ofElectrical Power amp Energy Systems vol 47 pp 235ndash242 2013
[3] A Karalis J D Joannopoulos and M Soljacic ldquoEfficient wire-less non-radiativemid-range energy transferrdquoAnnals of Physicsvol 323 no 1 pp 34ndash48 2008
[4] T Chan and C Chen ldquoA primary side control method for wire-less energy transmission systemrdquo IEEE Transactions on Circuitsand Systems I Regular Papers vol 59 no 8 pp 1805ndash1814 2012
[5] C K Lee W X Zhong and S Y R Hui ldquoEffects of magneticcoupling of nonadjacent resonators on wireless power domino-resonator systemsrdquo IEEE Transactions on Power Electronics vol27 no 4 pp 1905ndash1916 2012
[6] D Ahn and S Hong ldquoEffect of coupling between multipletransmitters or multiple receivers on wireless power transferrdquoIEEE Transactions on Industrial Electronics vol 60 no 7 pp2602ndash2613 2013
[7] Y Li Q Yang Z Yan et al ldquoCharacteristic of frequency in wire-less power transfer system via magnetic resonance couplingrdquoElectric Machines and Control vol 16 no 7 pp 7ndash11 2012
[8] J Wang Z Zhu C Li J Huangfu and L Ran ldquoPLL-based self-adaptive resonance tuning for a wireless-powered potentiome-terrdquo IEEE Transactions on Circuits and Systems II Express Briefsvol 60 no 7 pp 392ndash396 2013
[9] Y-H Kim S-Y Kang M-L Lee B-G Yu and T ZyungldquoOptimization ofwireless power transmission through resonantcouplingrdquo in Proceedings of the Compatability and Power Elec-tronics (CPE rsquo09) pp 426ndash431 Badajoz Spain May 2009
[10] JHuhW Lee S ChoiGCho andCRim ldquoFrequency-domaincircuit model and analysis of coupled magnetic resonancesystemsrdquo Journal of Power Electronics vol 13 no 2 pp 275ndash2862013
[11] O Jonal S V Georgakopoulos and M M Tentzeris ldquoOptimaldesign parameters for wireless power transfer by resonancemagneticrdquo IEEE Antennas andWireless Propagation Letters vol11 pp 1390ndash1393 2012
[12] A P Sample D A Meyer and J R Smith ldquoAnalysis experi-mental results and range adaptation of magnetically coupledresonators for wireless power transferrdquo IEEE Transactions onIndustrial Electronics vol 58 no 2 pp 544ndash554 2011
[13] N Y Kim K Y Kim and C W Kim ldquoAutomated frequencytracking system for efficient mid-range magnetic resonancewireless power transferrdquo Microwave and Optical TechnologyLetters vol 54 no 6 pp 1423ndash1426 2012
[14] J W Kim H-C Son K-H Kim and Y-J Park ldquoEfficiencyanalysis of magnetic resonance wireless power transfer withintermediate resonant coilrdquo IEEE Antennas andWireless Propa-gation Letters vol 10 pp 389ndash392 2011
[15] L L Tan X L Huang H Huang Y Zou and H Li ldquoTransferefficiency optimal control of magnetic resonance coupled sys-tem of wireless power transfer based on frequency controlrdquoScience China Technological Sciences vol 54 no 6 pp 1428ndash1434 2011
[16] R Xue K Cheng and M Je ldquoHigh-efficiency wireless powertransfer for biomedical implants by optimal resonant loadtransformationrdquo IEEE Transactions on Circuits and Systems IRegular Papers vol 60 no 4 pp 867ndash874 2013
[17] Y Y Ko S L Ho W N Fu and X Zhang ldquoA novel hybrid res-onator for wireless power delivery in bio-implantable devicesrdquo
8 The Scientific World Journal
IEEE Transactions OnMagnetics vol 48 no 11 pp 4518ndash45212012
[18] J Huang Cirruits China Machine Press Beijing 2003[19] W Q Niu W Gu J X Chu and A D Shen ldquoCoupled-mode
analysis of frequency splitting phenomena in CPT systemsrdquoElectronics Letters vol 48 no 12 pp 723ndash724 2012
Figure 1 Equivalent circuit model of a resonant system
projectile the setting rate is 5000 bulletsmin) One possiblesolution could be to improve power transmission stability andreduce the sensitivity of power transmission performanceto the variations in the operating parameters by optimalparameter design
Based on the circuit model of magnetic resonance systemthat has been established in [17] using the theoretical analysismethod of impedance mapping the coupling coefficientsof coils are optimized to maximize power transmissionThenmethods of improving power transmission stability anddecreasing transmission performance sensitivity to variationsin operating parameters are discussed
2 Circuit Model
The equivalent circuit model of this resonant system basedon mutual inductance theory is shown in Figure 1 [17]There 119871
1 1198712 1198713 and 119871
4are the self-inductance of the
driving transmission receiving and pick-up coils respec-tively 119862
2and 119862
3the respective resonance capacitances of the
transmission and receiving coils 1198772and 119877
3the equivalent
resistances of the transmission and receiving coils1198771the sum
of the power amplifier output resistance and the equivalentresistance of the driving coil 119877
119871the equivalent load of the
system including the resistance of the pick-up coil 1the
excitation voltage source and 119872119894119895and 119896
119894119895the respective
mutual inductance and coupling coefficient of any pair ofcoils with119872
119894119895= 119896119894119895radic119871 119894119871119895 and 0 le 119896119894119895 le 1
For a resonant system the transmission performanceis not always increasing with the decreasing of separationbetween coils which has been proved by experiment [9]There is an optimal value for the coupling coefficient atwhich the load gets the maximum power In order to avoidmathematical calculation of the four equations establishedaccording the Kirchhoff rsquos law when solving the optimalvalues of coupling coefficient 119896
12 11989623 and 119896
34 the analysis
method of impedance mapping is adopted in this paper [18]Through this method the electric parameters of coils aremapped into the adjacent coils and the four-coil systemcan be equivalent to a double-coil or a single-coil systemwhich will significantly reduce the difficulty of mathematicalanalysis
The electric parameters of driving and pick-up coils aremapped into the transmission and receiving coils respec-tively and the results are as follows
1198851198911=
(12059611987212)2
1198771+ 119895120596119871
1
= 1198771015840
1+
1
1198951205961198621015840
1
V2
I2 I3
R2 R3
L2 L3
C2 C3
M23
R9984001
C9984001
C9984004
R998400L
Figure 2 Double-coil equivalent circuit of a resonant system
In (4) and (5) 120596119903is the self-resonating angular frequency
of the transmission and receiving coils under the influence ofthe drive and pick-up coils respectively when the system isoperating at undercoupled state By solving 119883
22asymp 11988333asymp 0
120596119903can be expressed as follows
120596119903asymp ( [radic(119871
2
1+ 1198772
111987121198622)2
minus 41198962
121198712
11198772
111987121198622
+1198712
1minus 1198772
111987121198622]
05
)
times ([2 (1 minus 1198962
12) 1198712
111987121198622]05
)
minus1
asymp ( [radic(1198712
4+ 1198772
411987131198623)2
minus 41198962
341198712
41198772
411987131198623
+1198712
4minus 1198772
411987131198623]
05
)
times ([2 (1 minus 1198962
34) 1198712
411987131198623]05
)
minus1
(6)
For the solution of the optimal value 11989612 the electric
parameters of the pick-up coil the receiving coil and thetransmission coil are mapped into the adjacent loops in turnand the resonant system can be equivalent to a single-coilsystem eventuallyThemapping process is shown in Figure 3
In Figure 3(a)
11987710158401015840
33=11987733(12059611987223)2
1198772
33+ 1198832
33
11987110158401015840
33=
1198722
23
11986233(1198772
33+ 1198832
33)
11986210158401015840
33=1198772
33+ 1198832
33
119871312059641198722
23
11986233=
11986231198621015840
4
1198623+ 1198621015840
4
(7)
In Figure 3(b)
11987710158401015840
22=119877222(12059611987212)2
1198772
222+ 1198832
222
11987110158401015840
22=
1198722
12
119862222
(1198772
222+ 1198832
222)
11986210158401015840
22=1198772
222+ 1198832
222
11987122212059641198722
12
119877222
= 1198772+ 11987710158401015840
33
119871222
= 1198712+ 11987110158401015840
33 119862
222=
119862211986210158401015840
33
1198622+ 11986210158401015840
33
119883222
= 120596119871222
minus1
120596119862222
(8)
The mapping resistance of load 119877119871at the driving coil is
119877101584010158401015840
119871=
1198771015840
11987111987710158401015840
33(12059611987212)2
(1198772
222+ 1198832
222) 11987733
(9)
From Figure 3(b) the transmission power of system canbe written as
1198750=
051198812
1119898119877101584010158401015840
119871
(1198771+ 11987710158401015840
22)2
+ [120596 (1198711+ 11987110158401015840
22) minus (1120596119862
10158401015840
22)]2 (10)
Optimal value 11989612can be derived from (10) using calculus
as follows
11989612-opt = radic
radic1205762 + 4120575120585 minus 120576
212057511987111198712
(11)
In (11) 120576 = 21198772221198622
2221205962
1199031198771120591 120575 = 3119877
2
2221198622
2221205964
119903+ 1205892 120585 =
1205902+ 1198622
2221198772
11205912 120591 = 119877
2
222+ 1198832
222 and 120589 = 120596
119903minus 1198712221198622221205963
119903
120590 = 1205961199031198711119862222120591
From (4) (5) and (11) the optimal values of couplingcoefficients are closely related to the resonance angularfrequency120596
119903 In the condition of undercoupling and near the
critical coupling 120596119903can be approximated as a constant as
(6) But in the overcoupling region the resonance frequencyappears as splitting phenomena and the values vary sharplywith increasing of 119896
23 Therefore the formulas developed in
this paper can only be used in the condition of undercouplingand near the critical coupling On the other hand the sig-nificant advantage of resonance technology compared with
4 The Scientific World Journal
Powersource
Drivingcoil
Transmissioncoil coil
Receivingcoil
Pick-up
A
V1
d1 d2d3
V2
RL
(a) Schematic diagram of the experimental system (b) Experimental setup
Figure 4 Experimental system
electromagnetic induction technology is the farther distanceof wireless transmission Therefore the optimal design forlarge distance (nonovercoupling region) has good practicalengineering valueThe coupling status of the resonant systemis determined by 119896
23 the value of the coupling coefficient 119896
23
at critical coupling status is called critical coupling coefficientdenoted as 119896
119888 If 11989623gt 119896119888 the coupling status is overcoupling
whereas if 11989623
lt 119896119888 the status is undercoupling Referring
the solving method of 119896119888to double-coil system in [19] from
Figure 2 the critical coupling coefficient of this four-coilsystem can be written as
119896119888= [
[
(1198771015840
1+ 1198772)2
+ (1198771015840
119871+ 1198773)2
212059621199031198712
2
]
]
05
(12)
To verify the above optimization theory experimentalanalysis for a resonant system is performedThe experimentalsystem is shown in Figure 4 The coil is 75mm in diameterand is wound with 09 mm diameter enameled copper wireand the load resistance is 50Ω The power source used inthe experiment is a signal generator (Tektronix AFG3102peak value of output voltage 5V and output impedance50Ω) Power measurements are performed using a currentprobe (Tektronix TCP312 with TCPA300) with oscilloscopes(Tektronix TDS2022) The transmission and the receivingterminals are placed coaxially and are able to be displacedalong the axis The separations between driving and trans-mission coils transmission and receiving coils and receivingand pick-up coils are denoted as 119889
1 1198892 and 119889
3 respectively
The number of turns in driving and pick-up coils is 2 and intransmission and receiving coils is 5
The key parameters of coils in Table 1 are measured by theLCR meter (HIOKI 3532-50)
Figure 5 is the experiment curves of variations in trans-mission power with separation between coils Optimal valuesof coupling coefficients are listed in Tables 2 3 and 4
From Tables 2ndash4 we can see that the optimal valuesobtained from theoretical calculation and experiment arewell consistent Error is mainly caused by the following tworeasons one is the resonance angular frequency taken intheoretical calculation that is an approximation as (6) andthe other is the that separation between coils can only bechanged step by step The experimental results showed that
Table 2 Theoretical and experimental values of 11989612-opt
Experiment conditions Theory Experiment11989623(1198892mm) 119896
34(1198893mm) 119896
1211989612(1198891mm)
0101 (35) 0600 (0) 0451 0414 (3)0019 (100) 0414 (3) 0179 0176 (20)0050 (60) 0414 (3) 0320 0367 (5)0153 (25) 0353 (5) 1000lowast 1000lowastlowastThe separation between coils is as close as possible the same meaning as inTable 3
Table 3 Theoretical and experimental values of 11989634-opt
Experiment conditions Theory Experiment11989612(1198891mm) 119896
the optimization formulas are correct and can be used toeffectively optimize the power transmission characteristics inthe nonovercoupling region for resonant systems
The Scientific World Journal 5
0 5 10 15 20 25 305
15
25
35
45
55Po
wer
(mW
)
d3 (mm)
(a) 1198892 = 35mm
0 5 10 15 20 25 305
15
25
35
45
Pow
er (m
W)
d3 (mm)
(b) 1198892 = 60mm
0 5 10 15 20 25 305
10
15
20
Pow
er (m
W)
d3 (mm)
d1 = 0mmd1 = 3mm
d1 = 5mmd1 = 20mm
(c) 1198892 = 100mm
Figure 5 Variations in transmission power with separation between coils
3 Methods for Enhancing PowerTransmission Stability
The power transmission performance of the resonant systemis determined by the synthesis of different transmissionparameters Peak power output is acquired at the resonancefrequency point and the absorption power of the loaddeclines sharply when the operating frequency deviates fromthe resonance frequency In engineering applications thetransmission performance may decline for the differences inactual and design resonance frequency caused by fabricationprocess of coils relativemovement between transmission andreceiving terminals interference of environmental factorsand other reasons The possible solution for this problem isto improve the pass bandwidth of the system to reduce thesensitivity of the transmission power to operating frequencyvariations by optimal design for parameters That is tosay when the deviation in the operating frequency fromthe resonance frequency is small even without frequency-adaptive adjustment the system can still output high powerwith efficiency
Simulation analysis and experimental results all showthat by improving the system resonance frequency orcoupling coefficient 119896
12 11989634
can effectively improve thepower transmission stability under conditions that affect less
negatively other transmission performances The followingintroduces these two methods and analyzes what negativeinfluence these may introduce
(1) Increasing Values of the Coupling Coefficients 11989612and 119896
34
The degree of sharpness in the frequency response curve ofthe load power reduces as the coupling coefficients 119896
12and
11989634increase By reducing the axial distance between the driv-
ing coil (pick-up coil) and the transmission coil (receivingcoil) values of the coupling coefficients 119896
12and 119896
34can be
increased This will play an active role in reducing the degreeof sharpness in the frequency response curve of the loadpower On the other hand from the angle ofmaximumpowertransmission it is not the larger of coupling coefficients thebetter By increasing 119896
12 11989634 to enhance power transmission
stability may reduce the amplitude of power transmissionsimultaneous As illustrated by the experiment curves inFigure 5 transmission power may increase as 119889
1and 119889
3
increase This phenomenon is even more apparent when thevalue of 119889
2is larger Figure 6 shows the experimental curve of
the normalized load power at various excitation frequenciessettings 119889
1= 0 and 119889
2= 60mm 119875max is the load absorption
power at resonance Clearly the system pass bandwidthincreases 33 KHz when 119889
3is decreased from 12mm to 0
6 The Scientific World Journal
1
08
06
04
02
008 09 1 11 12
ffr
P0P
max
d3 = 0mmd3 = 5mmd3 = 12mm
Figure 6 Variation of load power with frequency at various 1198893values
20 30 40 50 60 70 80 90 100 110 1200
10
20
30
40
50
60
Pow
er (m
W)
d2 (mm)
fr = 1MHzfr = 2MHzfr = 5MHz
(a) 119877119871 = 50Ω
20 30 40 50 60 70 80 90 100 110 1200
10
20
30
40
50
60
fr = 1MHzfr = 2MHzfr = 5MHz
Pow
er (m
W)
d2 (mm)
(b) 119877119871 = 150Ω
Figure 7 Variations in power transmission characteristics with various resonance frequencies
(2) Increasing the Resonance Frequency The resonance fre-quency is a key parameter in system design whose value canbe changed by adjusting the number of turns or the externallymatched capacitance of the transmission and receiving coilsThe degree of sharpness in the frequency response curve ofload power reduces as resonance frequency increases There-fore enhancing power transmission stability can be obtainedby properly reducing the value of the external matchedcapacitance Transmission systems with a high resonancefrequency can produce high power transmission over shortdistancesHowever transmission performance attenuates fastas the separation between transmission and receiving termi-nals increasesTherefore it is not appropriate for the wirelesstransmission of power over long distance The attenuationof transmission power for systems with small resonancefrequencies is relatively slow as the separation between trans-mission and receiving terminals increase This is shown inFigure 7 Figure 8 gives the normalized experimental curve ofload power for various excitation frequencies at 119889
2= 60mm
and 119877119871= 50Ω It shows that when 119891
119903= 5MHz the pass
bandwidth is 236KHz and 285KHz wider than that at 2MHzand 1MHz respectively In addition along with increasingthe resonance frequency difficulties of circuit implementingincrease and inversion losses in the driving circuit alsoincrease These factors will cause further degradation in totaltransmission efficiency
To illustrate the effect of optimization both Figures 6 and8 show normalized curves of the resonant system with onlya single resonance frequency When the separation betweentransmission and receiving terminals is small and the systemshows splitting in the resonance frequency the optimizationmethod is still applicable
In summary by appropriate readjustment of the trans-mission parameters the sharpness in the frequency responsecurve of load power can be effectively reduced Simulta-neously transmission power might be reduced when thepower transmission stability is improved In contrast wirelesspower transmission technology based onmagnetic resonancecoupling relies on a strong coupling between transmissionand receiving terminals to produce high efficiency power
The Scientific World Journal 7
1
08
06
04
02
007 08 09 1 11 12 13
ffr
fr = 1MHzfr = 2MHzfr = 5MHz
P0P
max
Figure 8 Variations in frequency response curve of load powerwithvarious resonance frequencies
transmission The transmission theory is established basedon resonance which in principle determines the sensitivity ofthe power transfer characteristics to the working frequencyTherefore the sensitivity cannot be totally eliminated Dur-ing engineering-design stages the transmission parametersshould be set appropriately by accommodating with thetransmission performance of the system
4 Conclusion
In this paper power transmission characteristics of magneticresonance coupling wireless power transmission system areoptimized Based on themutual couplingmodel of a resonantsystem optimization formulas of coupling coefficient in thecondition of maximum power transmission are deduced andexperimental results show that the optimization formulasare correct and can be used to effectively optimize powertransmission characteristics in the nonovercoupling regionOn the other hand by improving the system resonancefrequency or coupling coefficient 119896
12 11989634 the power trans-
mission stability can be improved while power transmissionperformance sensitivity to variations in operating parameterscan be decreasedThe conclusions obtained in this paper willenrich the theory of wireless power transmission based onmagnetic resonance and provide a reference for engineeringapplications
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National Natural ScienceFoundation of China under Grant no 61104185
References
[1] A Kurs A Karalis R Moffatt J D Joannopoulos P Fisherand M Soljacic ldquoWireless power transfer via strongly coupled
magnetic resonancesrdquo Science vol 317 no 5834 pp 83ndash862007
[2] C A Tucker KWarwick andW Holderbaum ldquoA contributionto the wireless transmission of powerrdquo International Journal ofElectrical Power amp Energy Systems vol 47 pp 235ndash242 2013
[3] A Karalis J D Joannopoulos and M Soljacic ldquoEfficient wire-less non-radiativemid-range energy transferrdquoAnnals of Physicsvol 323 no 1 pp 34ndash48 2008
[4] T Chan and C Chen ldquoA primary side control method for wire-less energy transmission systemrdquo IEEE Transactions on Circuitsand Systems I Regular Papers vol 59 no 8 pp 1805ndash1814 2012
[5] C K Lee W X Zhong and S Y R Hui ldquoEffects of magneticcoupling of nonadjacent resonators on wireless power domino-resonator systemsrdquo IEEE Transactions on Power Electronics vol27 no 4 pp 1905ndash1916 2012
[6] D Ahn and S Hong ldquoEffect of coupling between multipletransmitters or multiple receivers on wireless power transferrdquoIEEE Transactions on Industrial Electronics vol 60 no 7 pp2602ndash2613 2013
[7] Y Li Q Yang Z Yan et al ldquoCharacteristic of frequency in wire-less power transfer system via magnetic resonance couplingrdquoElectric Machines and Control vol 16 no 7 pp 7ndash11 2012
[8] J Wang Z Zhu C Li J Huangfu and L Ran ldquoPLL-based self-adaptive resonance tuning for a wireless-powered potentiome-terrdquo IEEE Transactions on Circuits and Systems II Express Briefsvol 60 no 7 pp 392ndash396 2013
[9] Y-H Kim S-Y Kang M-L Lee B-G Yu and T ZyungldquoOptimization ofwireless power transmission through resonantcouplingrdquo in Proceedings of the Compatability and Power Elec-tronics (CPE rsquo09) pp 426ndash431 Badajoz Spain May 2009
[10] JHuhW Lee S ChoiGCho andCRim ldquoFrequency-domaincircuit model and analysis of coupled magnetic resonancesystemsrdquo Journal of Power Electronics vol 13 no 2 pp 275ndash2862013
[11] O Jonal S V Georgakopoulos and M M Tentzeris ldquoOptimaldesign parameters for wireless power transfer by resonancemagneticrdquo IEEE Antennas andWireless Propagation Letters vol11 pp 1390ndash1393 2012
[12] A P Sample D A Meyer and J R Smith ldquoAnalysis experi-mental results and range adaptation of magnetically coupledresonators for wireless power transferrdquo IEEE Transactions onIndustrial Electronics vol 58 no 2 pp 544ndash554 2011
[13] N Y Kim K Y Kim and C W Kim ldquoAutomated frequencytracking system for efficient mid-range magnetic resonancewireless power transferrdquo Microwave and Optical TechnologyLetters vol 54 no 6 pp 1423ndash1426 2012
[14] J W Kim H-C Son K-H Kim and Y-J Park ldquoEfficiencyanalysis of magnetic resonance wireless power transfer withintermediate resonant coilrdquo IEEE Antennas andWireless Propa-gation Letters vol 10 pp 389ndash392 2011
[15] L L Tan X L Huang H Huang Y Zou and H Li ldquoTransferefficiency optimal control of magnetic resonance coupled sys-tem of wireless power transfer based on frequency controlrdquoScience China Technological Sciences vol 54 no 6 pp 1428ndash1434 2011
[16] R Xue K Cheng and M Je ldquoHigh-efficiency wireless powertransfer for biomedical implants by optimal resonant loadtransformationrdquo IEEE Transactions on Circuits and Systems IRegular Papers vol 60 no 4 pp 867ndash874 2013
[17] Y Y Ko S L Ho W N Fu and X Zhang ldquoA novel hybrid res-onator for wireless power delivery in bio-implantable devicesrdquo
8 The Scientific World Journal
IEEE Transactions OnMagnetics vol 48 no 11 pp 4518ndash45212012
[18] J Huang Cirruits China Machine Press Beijing 2003[19] W Q Niu W Gu J X Chu and A D Shen ldquoCoupled-mode
analysis of frequency splitting phenomena in CPT systemsrdquoElectronics Letters vol 48 no 12 pp 723ndash724 2012
In (4) and (5) 120596119903is the self-resonating angular frequency
of the transmission and receiving coils under the influence ofthe drive and pick-up coils respectively when the system isoperating at undercoupled state By solving 119883
22asymp 11988333asymp 0
120596119903can be expressed as follows
120596119903asymp ( [radic(119871
2
1+ 1198772
111987121198622)2
minus 41198962
121198712
11198772
111987121198622
+1198712
1minus 1198772
111987121198622]
05
)
times ([2 (1 minus 1198962
12) 1198712
111987121198622]05
)
minus1
asymp ( [radic(1198712
4+ 1198772
411987131198623)2
minus 41198962
341198712
41198772
411987131198623
+1198712
4minus 1198772
411987131198623]
05
)
times ([2 (1 minus 1198962
34) 1198712
411987131198623]05
)
minus1
(6)
For the solution of the optimal value 11989612 the electric
parameters of the pick-up coil the receiving coil and thetransmission coil are mapped into the adjacent loops in turnand the resonant system can be equivalent to a single-coilsystem eventuallyThemapping process is shown in Figure 3
In Figure 3(a)
11987710158401015840
33=11987733(12059611987223)2
1198772
33+ 1198832
33
11987110158401015840
33=
1198722
23
11986233(1198772
33+ 1198832
33)
11986210158401015840
33=1198772
33+ 1198832
33
119871312059641198722
23
11986233=
11986231198621015840
4
1198623+ 1198621015840
4
(7)
In Figure 3(b)
11987710158401015840
22=119877222(12059611987212)2
1198772
222+ 1198832
222
11987110158401015840
22=
1198722
12
119862222
(1198772
222+ 1198832
222)
11986210158401015840
22=1198772
222+ 1198832
222
11987122212059641198722
12
119877222
= 1198772+ 11987710158401015840
33
119871222
= 1198712+ 11987110158401015840
33 119862
222=
119862211986210158401015840
33
1198622+ 11986210158401015840
33
119883222
= 120596119871222
minus1
120596119862222
(8)
The mapping resistance of load 119877119871at the driving coil is
119877101584010158401015840
119871=
1198771015840
11987111987710158401015840
33(12059611987212)2
(1198772
222+ 1198832
222) 11987733
(9)
From Figure 3(b) the transmission power of system canbe written as
1198750=
051198812
1119898119877101584010158401015840
119871
(1198771+ 11987710158401015840
22)2
+ [120596 (1198711+ 11987110158401015840
22) minus (1120596119862
10158401015840
22)]2 (10)
Optimal value 11989612can be derived from (10) using calculus
as follows
11989612-opt = radic
radic1205762 + 4120575120585 minus 120576
212057511987111198712
(11)
In (11) 120576 = 21198772221198622
2221205962
1199031198771120591 120575 = 3119877
2
2221198622
2221205964
119903+ 1205892 120585 =
1205902+ 1198622
2221198772
11205912 120591 = 119877
2
222+ 1198832
222 and 120589 = 120596
119903minus 1198712221198622221205963
119903
120590 = 1205961199031198711119862222120591
From (4) (5) and (11) the optimal values of couplingcoefficients are closely related to the resonance angularfrequency120596
119903 In the condition of undercoupling and near the
critical coupling 120596119903can be approximated as a constant as
(6) But in the overcoupling region the resonance frequencyappears as splitting phenomena and the values vary sharplywith increasing of 119896
23 Therefore the formulas developed in
this paper can only be used in the condition of undercouplingand near the critical coupling On the other hand the sig-nificant advantage of resonance technology compared with
4 The Scientific World Journal
Powersource
Drivingcoil
Transmissioncoil coil
Receivingcoil
Pick-up
A
V1
d1 d2d3
V2
RL
(a) Schematic diagram of the experimental system (b) Experimental setup
Figure 4 Experimental system
electromagnetic induction technology is the farther distanceof wireless transmission Therefore the optimal design forlarge distance (nonovercoupling region) has good practicalengineering valueThe coupling status of the resonant systemis determined by 119896
23 the value of the coupling coefficient 119896
23
at critical coupling status is called critical coupling coefficientdenoted as 119896
119888 If 11989623gt 119896119888 the coupling status is overcoupling
whereas if 11989623
lt 119896119888 the status is undercoupling Referring
the solving method of 119896119888to double-coil system in [19] from
Figure 2 the critical coupling coefficient of this four-coilsystem can be written as
119896119888= [
[
(1198771015840
1+ 1198772)2
+ (1198771015840
119871+ 1198773)2
212059621199031198712
2
]
]
05
(12)
To verify the above optimization theory experimentalanalysis for a resonant system is performedThe experimentalsystem is shown in Figure 4 The coil is 75mm in diameterand is wound with 09 mm diameter enameled copper wireand the load resistance is 50Ω The power source used inthe experiment is a signal generator (Tektronix AFG3102peak value of output voltage 5V and output impedance50Ω) Power measurements are performed using a currentprobe (Tektronix TCP312 with TCPA300) with oscilloscopes(Tektronix TDS2022) The transmission and the receivingterminals are placed coaxially and are able to be displacedalong the axis The separations between driving and trans-mission coils transmission and receiving coils and receivingand pick-up coils are denoted as 119889
1 1198892 and 119889
3 respectively
The number of turns in driving and pick-up coils is 2 and intransmission and receiving coils is 5
The key parameters of coils in Table 1 are measured by theLCR meter (HIOKI 3532-50)
Figure 5 is the experiment curves of variations in trans-mission power with separation between coils Optimal valuesof coupling coefficients are listed in Tables 2 3 and 4
From Tables 2ndash4 we can see that the optimal valuesobtained from theoretical calculation and experiment arewell consistent Error is mainly caused by the following tworeasons one is the resonance angular frequency taken intheoretical calculation that is an approximation as (6) andthe other is the that separation between coils can only bechanged step by step The experimental results showed that
Table 2 Theoretical and experimental values of 11989612-opt
Experiment conditions Theory Experiment11989623(1198892mm) 119896
34(1198893mm) 119896
1211989612(1198891mm)
0101 (35) 0600 (0) 0451 0414 (3)0019 (100) 0414 (3) 0179 0176 (20)0050 (60) 0414 (3) 0320 0367 (5)0153 (25) 0353 (5) 1000lowast 1000lowastlowastThe separation between coils is as close as possible the same meaning as inTable 3
Table 3 Theoretical and experimental values of 11989634-opt
Experiment conditions Theory Experiment11989612(1198891mm) 119896
the optimization formulas are correct and can be used toeffectively optimize the power transmission characteristics inthe nonovercoupling region for resonant systems
The Scientific World Journal 5
0 5 10 15 20 25 305
15
25
35
45
55Po
wer
(mW
)
d3 (mm)
(a) 1198892 = 35mm
0 5 10 15 20 25 305
15
25
35
45
Pow
er (m
W)
d3 (mm)
(b) 1198892 = 60mm
0 5 10 15 20 25 305
10
15
20
Pow
er (m
W)
d3 (mm)
d1 = 0mmd1 = 3mm
d1 = 5mmd1 = 20mm
(c) 1198892 = 100mm
Figure 5 Variations in transmission power with separation between coils
3 Methods for Enhancing PowerTransmission Stability
The power transmission performance of the resonant systemis determined by the synthesis of different transmissionparameters Peak power output is acquired at the resonancefrequency point and the absorption power of the loaddeclines sharply when the operating frequency deviates fromthe resonance frequency In engineering applications thetransmission performance may decline for the differences inactual and design resonance frequency caused by fabricationprocess of coils relativemovement between transmission andreceiving terminals interference of environmental factorsand other reasons The possible solution for this problem isto improve the pass bandwidth of the system to reduce thesensitivity of the transmission power to operating frequencyvariations by optimal design for parameters That is tosay when the deviation in the operating frequency fromthe resonance frequency is small even without frequency-adaptive adjustment the system can still output high powerwith efficiency
Simulation analysis and experimental results all showthat by improving the system resonance frequency orcoupling coefficient 119896
12 11989634
can effectively improve thepower transmission stability under conditions that affect less
negatively other transmission performances The followingintroduces these two methods and analyzes what negativeinfluence these may introduce
(1) Increasing Values of the Coupling Coefficients 11989612and 119896
34
The degree of sharpness in the frequency response curve ofthe load power reduces as the coupling coefficients 119896
12and
11989634increase By reducing the axial distance between the driv-
ing coil (pick-up coil) and the transmission coil (receivingcoil) values of the coupling coefficients 119896
12and 119896
34can be
increased This will play an active role in reducing the degreeof sharpness in the frequency response curve of the loadpower On the other hand from the angle ofmaximumpowertransmission it is not the larger of coupling coefficients thebetter By increasing 119896
12 11989634 to enhance power transmission
stability may reduce the amplitude of power transmissionsimultaneous As illustrated by the experiment curves inFigure 5 transmission power may increase as 119889
1and 119889
3
increase This phenomenon is even more apparent when thevalue of 119889
2is larger Figure 6 shows the experimental curve of
the normalized load power at various excitation frequenciessettings 119889
1= 0 and 119889
2= 60mm 119875max is the load absorption
power at resonance Clearly the system pass bandwidthincreases 33 KHz when 119889
3is decreased from 12mm to 0
6 The Scientific World Journal
1
08
06
04
02
008 09 1 11 12
ffr
P0P
max
d3 = 0mmd3 = 5mmd3 = 12mm
Figure 6 Variation of load power with frequency at various 1198893values
20 30 40 50 60 70 80 90 100 110 1200
10
20
30
40
50
60
Pow
er (m
W)
d2 (mm)
fr = 1MHzfr = 2MHzfr = 5MHz
(a) 119877119871 = 50Ω
20 30 40 50 60 70 80 90 100 110 1200
10
20
30
40
50
60
fr = 1MHzfr = 2MHzfr = 5MHz
Pow
er (m
W)
d2 (mm)
(b) 119877119871 = 150Ω
Figure 7 Variations in power transmission characteristics with various resonance frequencies
(2) Increasing the Resonance Frequency The resonance fre-quency is a key parameter in system design whose value canbe changed by adjusting the number of turns or the externallymatched capacitance of the transmission and receiving coilsThe degree of sharpness in the frequency response curve ofload power reduces as resonance frequency increases There-fore enhancing power transmission stability can be obtainedby properly reducing the value of the external matchedcapacitance Transmission systems with a high resonancefrequency can produce high power transmission over shortdistancesHowever transmission performance attenuates fastas the separation between transmission and receiving termi-nals increasesTherefore it is not appropriate for the wirelesstransmission of power over long distance The attenuationof transmission power for systems with small resonancefrequencies is relatively slow as the separation between trans-mission and receiving terminals increase This is shown inFigure 7 Figure 8 gives the normalized experimental curve ofload power for various excitation frequencies at 119889
2= 60mm
and 119877119871= 50Ω It shows that when 119891
119903= 5MHz the pass
bandwidth is 236KHz and 285KHz wider than that at 2MHzand 1MHz respectively In addition along with increasingthe resonance frequency difficulties of circuit implementingincrease and inversion losses in the driving circuit alsoincrease These factors will cause further degradation in totaltransmission efficiency
To illustrate the effect of optimization both Figures 6 and8 show normalized curves of the resonant system with onlya single resonance frequency When the separation betweentransmission and receiving terminals is small and the systemshows splitting in the resonance frequency the optimizationmethod is still applicable
In summary by appropriate readjustment of the trans-mission parameters the sharpness in the frequency responsecurve of load power can be effectively reduced Simulta-neously transmission power might be reduced when thepower transmission stability is improved In contrast wirelesspower transmission technology based onmagnetic resonancecoupling relies on a strong coupling between transmissionand receiving terminals to produce high efficiency power
The Scientific World Journal 7
1
08
06
04
02
007 08 09 1 11 12 13
ffr
fr = 1MHzfr = 2MHzfr = 5MHz
P0P
max
Figure 8 Variations in frequency response curve of load powerwithvarious resonance frequencies
transmission The transmission theory is established basedon resonance which in principle determines the sensitivity ofthe power transfer characteristics to the working frequencyTherefore the sensitivity cannot be totally eliminated Dur-ing engineering-design stages the transmission parametersshould be set appropriately by accommodating with thetransmission performance of the system
4 Conclusion
In this paper power transmission characteristics of magneticresonance coupling wireless power transmission system areoptimized Based on themutual couplingmodel of a resonantsystem optimization formulas of coupling coefficient in thecondition of maximum power transmission are deduced andexperimental results show that the optimization formulasare correct and can be used to effectively optimize powertransmission characteristics in the nonovercoupling regionOn the other hand by improving the system resonancefrequency or coupling coefficient 119896
12 11989634 the power trans-
mission stability can be improved while power transmissionperformance sensitivity to variations in operating parameterscan be decreasedThe conclusions obtained in this paper willenrich the theory of wireless power transmission based onmagnetic resonance and provide a reference for engineeringapplications
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National Natural ScienceFoundation of China under Grant no 61104185
References
[1] A Kurs A Karalis R Moffatt J D Joannopoulos P Fisherand M Soljacic ldquoWireless power transfer via strongly coupled
magnetic resonancesrdquo Science vol 317 no 5834 pp 83ndash862007
[2] C A Tucker KWarwick andW Holderbaum ldquoA contributionto the wireless transmission of powerrdquo International Journal ofElectrical Power amp Energy Systems vol 47 pp 235ndash242 2013
[3] A Karalis J D Joannopoulos and M Soljacic ldquoEfficient wire-less non-radiativemid-range energy transferrdquoAnnals of Physicsvol 323 no 1 pp 34ndash48 2008
[4] T Chan and C Chen ldquoA primary side control method for wire-less energy transmission systemrdquo IEEE Transactions on Circuitsand Systems I Regular Papers vol 59 no 8 pp 1805ndash1814 2012
[5] C K Lee W X Zhong and S Y R Hui ldquoEffects of magneticcoupling of nonadjacent resonators on wireless power domino-resonator systemsrdquo IEEE Transactions on Power Electronics vol27 no 4 pp 1905ndash1916 2012
[6] D Ahn and S Hong ldquoEffect of coupling between multipletransmitters or multiple receivers on wireless power transferrdquoIEEE Transactions on Industrial Electronics vol 60 no 7 pp2602ndash2613 2013
[7] Y Li Q Yang Z Yan et al ldquoCharacteristic of frequency in wire-less power transfer system via magnetic resonance couplingrdquoElectric Machines and Control vol 16 no 7 pp 7ndash11 2012
[8] J Wang Z Zhu C Li J Huangfu and L Ran ldquoPLL-based self-adaptive resonance tuning for a wireless-powered potentiome-terrdquo IEEE Transactions on Circuits and Systems II Express Briefsvol 60 no 7 pp 392ndash396 2013
[9] Y-H Kim S-Y Kang M-L Lee B-G Yu and T ZyungldquoOptimization ofwireless power transmission through resonantcouplingrdquo in Proceedings of the Compatability and Power Elec-tronics (CPE rsquo09) pp 426ndash431 Badajoz Spain May 2009
[10] JHuhW Lee S ChoiGCho andCRim ldquoFrequency-domaincircuit model and analysis of coupled magnetic resonancesystemsrdquo Journal of Power Electronics vol 13 no 2 pp 275ndash2862013
[11] O Jonal S V Georgakopoulos and M M Tentzeris ldquoOptimaldesign parameters for wireless power transfer by resonancemagneticrdquo IEEE Antennas andWireless Propagation Letters vol11 pp 1390ndash1393 2012
[12] A P Sample D A Meyer and J R Smith ldquoAnalysis experi-mental results and range adaptation of magnetically coupledresonators for wireless power transferrdquo IEEE Transactions onIndustrial Electronics vol 58 no 2 pp 544ndash554 2011
[13] N Y Kim K Y Kim and C W Kim ldquoAutomated frequencytracking system for efficient mid-range magnetic resonancewireless power transferrdquo Microwave and Optical TechnologyLetters vol 54 no 6 pp 1423ndash1426 2012
[14] J W Kim H-C Son K-H Kim and Y-J Park ldquoEfficiencyanalysis of magnetic resonance wireless power transfer withintermediate resonant coilrdquo IEEE Antennas andWireless Propa-gation Letters vol 10 pp 389ndash392 2011
[15] L L Tan X L Huang H Huang Y Zou and H Li ldquoTransferefficiency optimal control of magnetic resonance coupled sys-tem of wireless power transfer based on frequency controlrdquoScience China Technological Sciences vol 54 no 6 pp 1428ndash1434 2011
[16] R Xue K Cheng and M Je ldquoHigh-efficiency wireless powertransfer for biomedical implants by optimal resonant loadtransformationrdquo IEEE Transactions on Circuits and Systems IRegular Papers vol 60 no 4 pp 867ndash874 2013
[17] Y Y Ko S L Ho W N Fu and X Zhang ldquoA novel hybrid res-onator for wireless power delivery in bio-implantable devicesrdquo
8 The Scientific World Journal
IEEE Transactions OnMagnetics vol 48 no 11 pp 4518ndash45212012
[18] J Huang Cirruits China Machine Press Beijing 2003[19] W Q Niu W Gu J X Chu and A D Shen ldquoCoupled-mode
analysis of frequency splitting phenomena in CPT systemsrdquoElectronics Letters vol 48 no 12 pp 723ndash724 2012
(a) Schematic diagram of the experimental system (b) Experimental setup
Figure 4 Experimental system
electromagnetic induction technology is the farther distanceof wireless transmission Therefore the optimal design forlarge distance (nonovercoupling region) has good practicalengineering valueThe coupling status of the resonant systemis determined by 119896
23 the value of the coupling coefficient 119896
23
at critical coupling status is called critical coupling coefficientdenoted as 119896
119888 If 11989623gt 119896119888 the coupling status is overcoupling
whereas if 11989623
lt 119896119888 the status is undercoupling Referring
the solving method of 119896119888to double-coil system in [19] from
Figure 2 the critical coupling coefficient of this four-coilsystem can be written as
119896119888= [
[
(1198771015840
1+ 1198772)2
+ (1198771015840
119871+ 1198773)2
212059621199031198712
2
]
]
05
(12)
To verify the above optimization theory experimentalanalysis for a resonant system is performedThe experimentalsystem is shown in Figure 4 The coil is 75mm in diameterand is wound with 09 mm diameter enameled copper wireand the load resistance is 50Ω The power source used inthe experiment is a signal generator (Tektronix AFG3102peak value of output voltage 5V and output impedance50Ω) Power measurements are performed using a currentprobe (Tektronix TCP312 with TCPA300) with oscilloscopes(Tektronix TDS2022) The transmission and the receivingterminals are placed coaxially and are able to be displacedalong the axis The separations between driving and trans-mission coils transmission and receiving coils and receivingand pick-up coils are denoted as 119889
1 1198892 and 119889
3 respectively
The number of turns in driving and pick-up coils is 2 and intransmission and receiving coils is 5
The key parameters of coils in Table 1 are measured by theLCR meter (HIOKI 3532-50)
Figure 5 is the experiment curves of variations in trans-mission power with separation between coils Optimal valuesof coupling coefficients are listed in Tables 2 3 and 4
From Tables 2ndash4 we can see that the optimal valuesobtained from theoretical calculation and experiment arewell consistent Error is mainly caused by the following tworeasons one is the resonance angular frequency taken intheoretical calculation that is an approximation as (6) andthe other is the that separation between coils can only bechanged step by step The experimental results showed that
Table 2 Theoretical and experimental values of 11989612-opt
Experiment conditions Theory Experiment11989623(1198892mm) 119896
34(1198893mm) 119896
1211989612(1198891mm)
0101 (35) 0600 (0) 0451 0414 (3)0019 (100) 0414 (3) 0179 0176 (20)0050 (60) 0414 (3) 0320 0367 (5)0153 (25) 0353 (5) 1000lowast 1000lowastlowastThe separation between coils is as close as possible the same meaning as inTable 3
Table 3 Theoretical and experimental values of 11989634-opt
Experiment conditions Theory Experiment11989612(1198891mm) 119896
the optimization formulas are correct and can be used toeffectively optimize the power transmission characteristics inthe nonovercoupling region for resonant systems
The Scientific World Journal 5
0 5 10 15 20 25 305
15
25
35
45
55Po
wer
(mW
)
d3 (mm)
(a) 1198892 = 35mm
0 5 10 15 20 25 305
15
25
35
45
Pow
er (m
W)
d3 (mm)
(b) 1198892 = 60mm
0 5 10 15 20 25 305
10
15
20
Pow
er (m
W)
d3 (mm)
d1 = 0mmd1 = 3mm
d1 = 5mmd1 = 20mm
(c) 1198892 = 100mm
Figure 5 Variations in transmission power with separation between coils
3 Methods for Enhancing PowerTransmission Stability
The power transmission performance of the resonant systemis determined by the synthesis of different transmissionparameters Peak power output is acquired at the resonancefrequency point and the absorption power of the loaddeclines sharply when the operating frequency deviates fromthe resonance frequency In engineering applications thetransmission performance may decline for the differences inactual and design resonance frequency caused by fabricationprocess of coils relativemovement between transmission andreceiving terminals interference of environmental factorsand other reasons The possible solution for this problem isto improve the pass bandwidth of the system to reduce thesensitivity of the transmission power to operating frequencyvariations by optimal design for parameters That is tosay when the deviation in the operating frequency fromthe resonance frequency is small even without frequency-adaptive adjustment the system can still output high powerwith efficiency
Simulation analysis and experimental results all showthat by improving the system resonance frequency orcoupling coefficient 119896
12 11989634
can effectively improve thepower transmission stability under conditions that affect less
negatively other transmission performances The followingintroduces these two methods and analyzes what negativeinfluence these may introduce
(1) Increasing Values of the Coupling Coefficients 11989612and 119896
34
The degree of sharpness in the frequency response curve ofthe load power reduces as the coupling coefficients 119896
12and
11989634increase By reducing the axial distance between the driv-
ing coil (pick-up coil) and the transmission coil (receivingcoil) values of the coupling coefficients 119896
12and 119896
34can be
increased This will play an active role in reducing the degreeof sharpness in the frequency response curve of the loadpower On the other hand from the angle ofmaximumpowertransmission it is not the larger of coupling coefficients thebetter By increasing 119896
12 11989634 to enhance power transmission
stability may reduce the amplitude of power transmissionsimultaneous As illustrated by the experiment curves inFigure 5 transmission power may increase as 119889
1and 119889
3
increase This phenomenon is even more apparent when thevalue of 119889
2is larger Figure 6 shows the experimental curve of
the normalized load power at various excitation frequenciessettings 119889
1= 0 and 119889
2= 60mm 119875max is the load absorption
power at resonance Clearly the system pass bandwidthincreases 33 KHz when 119889
3is decreased from 12mm to 0
6 The Scientific World Journal
1
08
06
04
02
008 09 1 11 12
ffr
P0P
max
d3 = 0mmd3 = 5mmd3 = 12mm
Figure 6 Variation of load power with frequency at various 1198893values
20 30 40 50 60 70 80 90 100 110 1200
10
20
30
40
50
60
Pow
er (m
W)
d2 (mm)
fr = 1MHzfr = 2MHzfr = 5MHz
(a) 119877119871 = 50Ω
20 30 40 50 60 70 80 90 100 110 1200
10
20
30
40
50
60
fr = 1MHzfr = 2MHzfr = 5MHz
Pow
er (m
W)
d2 (mm)
(b) 119877119871 = 150Ω
Figure 7 Variations in power transmission characteristics with various resonance frequencies
(2) Increasing the Resonance Frequency The resonance fre-quency is a key parameter in system design whose value canbe changed by adjusting the number of turns or the externallymatched capacitance of the transmission and receiving coilsThe degree of sharpness in the frequency response curve ofload power reduces as resonance frequency increases There-fore enhancing power transmission stability can be obtainedby properly reducing the value of the external matchedcapacitance Transmission systems with a high resonancefrequency can produce high power transmission over shortdistancesHowever transmission performance attenuates fastas the separation between transmission and receiving termi-nals increasesTherefore it is not appropriate for the wirelesstransmission of power over long distance The attenuationof transmission power for systems with small resonancefrequencies is relatively slow as the separation between trans-mission and receiving terminals increase This is shown inFigure 7 Figure 8 gives the normalized experimental curve ofload power for various excitation frequencies at 119889
2= 60mm
and 119877119871= 50Ω It shows that when 119891
119903= 5MHz the pass
bandwidth is 236KHz and 285KHz wider than that at 2MHzand 1MHz respectively In addition along with increasingthe resonance frequency difficulties of circuit implementingincrease and inversion losses in the driving circuit alsoincrease These factors will cause further degradation in totaltransmission efficiency
To illustrate the effect of optimization both Figures 6 and8 show normalized curves of the resonant system with onlya single resonance frequency When the separation betweentransmission and receiving terminals is small and the systemshows splitting in the resonance frequency the optimizationmethod is still applicable
In summary by appropriate readjustment of the trans-mission parameters the sharpness in the frequency responsecurve of load power can be effectively reduced Simulta-neously transmission power might be reduced when thepower transmission stability is improved In contrast wirelesspower transmission technology based onmagnetic resonancecoupling relies on a strong coupling between transmissionand receiving terminals to produce high efficiency power
The Scientific World Journal 7
1
08
06
04
02
007 08 09 1 11 12 13
ffr
fr = 1MHzfr = 2MHzfr = 5MHz
P0P
max
Figure 8 Variations in frequency response curve of load powerwithvarious resonance frequencies
transmission The transmission theory is established basedon resonance which in principle determines the sensitivity ofthe power transfer characteristics to the working frequencyTherefore the sensitivity cannot be totally eliminated Dur-ing engineering-design stages the transmission parametersshould be set appropriately by accommodating with thetransmission performance of the system
4 Conclusion
In this paper power transmission characteristics of magneticresonance coupling wireless power transmission system areoptimized Based on themutual couplingmodel of a resonantsystem optimization formulas of coupling coefficient in thecondition of maximum power transmission are deduced andexperimental results show that the optimization formulasare correct and can be used to effectively optimize powertransmission characteristics in the nonovercoupling regionOn the other hand by improving the system resonancefrequency or coupling coefficient 119896
12 11989634 the power trans-
mission stability can be improved while power transmissionperformance sensitivity to variations in operating parameterscan be decreasedThe conclusions obtained in this paper willenrich the theory of wireless power transmission based onmagnetic resonance and provide a reference for engineeringapplications
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National Natural ScienceFoundation of China under Grant no 61104185
References
[1] A Kurs A Karalis R Moffatt J D Joannopoulos P Fisherand M Soljacic ldquoWireless power transfer via strongly coupled
magnetic resonancesrdquo Science vol 317 no 5834 pp 83ndash862007
[2] C A Tucker KWarwick andW Holderbaum ldquoA contributionto the wireless transmission of powerrdquo International Journal ofElectrical Power amp Energy Systems vol 47 pp 235ndash242 2013
[3] A Karalis J D Joannopoulos and M Soljacic ldquoEfficient wire-less non-radiativemid-range energy transferrdquoAnnals of Physicsvol 323 no 1 pp 34ndash48 2008
[4] T Chan and C Chen ldquoA primary side control method for wire-less energy transmission systemrdquo IEEE Transactions on Circuitsand Systems I Regular Papers vol 59 no 8 pp 1805ndash1814 2012
[5] C K Lee W X Zhong and S Y R Hui ldquoEffects of magneticcoupling of nonadjacent resonators on wireless power domino-resonator systemsrdquo IEEE Transactions on Power Electronics vol27 no 4 pp 1905ndash1916 2012
[6] D Ahn and S Hong ldquoEffect of coupling between multipletransmitters or multiple receivers on wireless power transferrdquoIEEE Transactions on Industrial Electronics vol 60 no 7 pp2602ndash2613 2013
[7] Y Li Q Yang Z Yan et al ldquoCharacteristic of frequency in wire-less power transfer system via magnetic resonance couplingrdquoElectric Machines and Control vol 16 no 7 pp 7ndash11 2012
[8] J Wang Z Zhu C Li J Huangfu and L Ran ldquoPLL-based self-adaptive resonance tuning for a wireless-powered potentiome-terrdquo IEEE Transactions on Circuits and Systems II Express Briefsvol 60 no 7 pp 392ndash396 2013
[9] Y-H Kim S-Y Kang M-L Lee B-G Yu and T ZyungldquoOptimization ofwireless power transmission through resonantcouplingrdquo in Proceedings of the Compatability and Power Elec-tronics (CPE rsquo09) pp 426ndash431 Badajoz Spain May 2009
[10] JHuhW Lee S ChoiGCho andCRim ldquoFrequency-domaincircuit model and analysis of coupled magnetic resonancesystemsrdquo Journal of Power Electronics vol 13 no 2 pp 275ndash2862013
[11] O Jonal S V Georgakopoulos and M M Tentzeris ldquoOptimaldesign parameters for wireless power transfer by resonancemagneticrdquo IEEE Antennas andWireless Propagation Letters vol11 pp 1390ndash1393 2012
[12] A P Sample D A Meyer and J R Smith ldquoAnalysis experi-mental results and range adaptation of magnetically coupledresonators for wireless power transferrdquo IEEE Transactions onIndustrial Electronics vol 58 no 2 pp 544ndash554 2011
[13] N Y Kim K Y Kim and C W Kim ldquoAutomated frequencytracking system for efficient mid-range magnetic resonancewireless power transferrdquo Microwave and Optical TechnologyLetters vol 54 no 6 pp 1423ndash1426 2012
[14] J W Kim H-C Son K-H Kim and Y-J Park ldquoEfficiencyanalysis of magnetic resonance wireless power transfer withintermediate resonant coilrdquo IEEE Antennas andWireless Propa-gation Letters vol 10 pp 389ndash392 2011
[15] L L Tan X L Huang H Huang Y Zou and H Li ldquoTransferefficiency optimal control of magnetic resonance coupled sys-tem of wireless power transfer based on frequency controlrdquoScience China Technological Sciences vol 54 no 6 pp 1428ndash1434 2011
[16] R Xue K Cheng and M Je ldquoHigh-efficiency wireless powertransfer for biomedical implants by optimal resonant loadtransformationrdquo IEEE Transactions on Circuits and Systems IRegular Papers vol 60 no 4 pp 867ndash874 2013
[17] Y Y Ko S L Ho W N Fu and X Zhang ldquoA novel hybrid res-onator for wireless power delivery in bio-implantable devicesrdquo
8 The Scientific World Journal
IEEE Transactions OnMagnetics vol 48 no 11 pp 4518ndash45212012
[18] J Huang Cirruits China Machine Press Beijing 2003[19] W Q Niu W Gu J X Chu and A D Shen ldquoCoupled-mode
analysis of frequency splitting phenomena in CPT systemsrdquoElectronics Letters vol 48 no 12 pp 723ndash724 2012
Figure 5 Variations in transmission power with separation between coils
3 Methods for Enhancing PowerTransmission Stability
The power transmission performance of the resonant systemis determined by the synthesis of different transmissionparameters Peak power output is acquired at the resonancefrequency point and the absorption power of the loaddeclines sharply when the operating frequency deviates fromthe resonance frequency In engineering applications thetransmission performance may decline for the differences inactual and design resonance frequency caused by fabricationprocess of coils relativemovement between transmission andreceiving terminals interference of environmental factorsand other reasons The possible solution for this problem isto improve the pass bandwidth of the system to reduce thesensitivity of the transmission power to operating frequencyvariations by optimal design for parameters That is tosay when the deviation in the operating frequency fromthe resonance frequency is small even without frequency-adaptive adjustment the system can still output high powerwith efficiency
Simulation analysis and experimental results all showthat by improving the system resonance frequency orcoupling coefficient 119896
12 11989634
can effectively improve thepower transmission stability under conditions that affect less
negatively other transmission performances The followingintroduces these two methods and analyzes what negativeinfluence these may introduce
(1) Increasing Values of the Coupling Coefficients 11989612and 119896
34
The degree of sharpness in the frequency response curve ofthe load power reduces as the coupling coefficients 119896
12and
11989634increase By reducing the axial distance between the driv-
ing coil (pick-up coil) and the transmission coil (receivingcoil) values of the coupling coefficients 119896
12and 119896
34can be
increased This will play an active role in reducing the degreeof sharpness in the frequency response curve of the loadpower On the other hand from the angle ofmaximumpowertransmission it is not the larger of coupling coefficients thebetter By increasing 119896
12 11989634 to enhance power transmission
stability may reduce the amplitude of power transmissionsimultaneous As illustrated by the experiment curves inFigure 5 transmission power may increase as 119889
1and 119889
3
increase This phenomenon is even more apparent when thevalue of 119889
2is larger Figure 6 shows the experimental curve of
the normalized load power at various excitation frequenciessettings 119889
1= 0 and 119889
2= 60mm 119875max is the load absorption
power at resonance Clearly the system pass bandwidthincreases 33 KHz when 119889
3is decreased from 12mm to 0
6 The Scientific World Journal
1
08
06
04
02
008 09 1 11 12
ffr
P0P
max
d3 = 0mmd3 = 5mmd3 = 12mm
Figure 6 Variation of load power with frequency at various 1198893values
20 30 40 50 60 70 80 90 100 110 1200
10
20
30
40
50
60
Pow
er (m
W)
d2 (mm)
fr = 1MHzfr = 2MHzfr = 5MHz
(a) 119877119871 = 50Ω
20 30 40 50 60 70 80 90 100 110 1200
10
20
30
40
50
60
fr = 1MHzfr = 2MHzfr = 5MHz
Pow
er (m
W)
d2 (mm)
(b) 119877119871 = 150Ω
Figure 7 Variations in power transmission characteristics with various resonance frequencies
(2) Increasing the Resonance Frequency The resonance fre-quency is a key parameter in system design whose value canbe changed by adjusting the number of turns or the externallymatched capacitance of the transmission and receiving coilsThe degree of sharpness in the frequency response curve ofload power reduces as resonance frequency increases There-fore enhancing power transmission stability can be obtainedby properly reducing the value of the external matchedcapacitance Transmission systems with a high resonancefrequency can produce high power transmission over shortdistancesHowever transmission performance attenuates fastas the separation between transmission and receiving termi-nals increasesTherefore it is not appropriate for the wirelesstransmission of power over long distance The attenuationof transmission power for systems with small resonancefrequencies is relatively slow as the separation between trans-mission and receiving terminals increase This is shown inFigure 7 Figure 8 gives the normalized experimental curve ofload power for various excitation frequencies at 119889
2= 60mm
and 119877119871= 50Ω It shows that when 119891
119903= 5MHz the pass
bandwidth is 236KHz and 285KHz wider than that at 2MHzand 1MHz respectively In addition along with increasingthe resonance frequency difficulties of circuit implementingincrease and inversion losses in the driving circuit alsoincrease These factors will cause further degradation in totaltransmission efficiency
To illustrate the effect of optimization both Figures 6 and8 show normalized curves of the resonant system with onlya single resonance frequency When the separation betweentransmission and receiving terminals is small and the systemshows splitting in the resonance frequency the optimizationmethod is still applicable
In summary by appropriate readjustment of the trans-mission parameters the sharpness in the frequency responsecurve of load power can be effectively reduced Simulta-neously transmission power might be reduced when thepower transmission stability is improved In contrast wirelesspower transmission technology based onmagnetic resonancecoupling relies on a strong coupling between transmissionand receiving terminals to produce high efficiency power
The Scientific World Journal 7
1
08
06
04
02
007 08 09 1 11 12 13
ffr
fr = 1MHzfr = 2MHzfr = 5MHz
P0P
max
Figure 8 Variations in frequency response curve of load powerwithvarious resonance frequencies
transmission The transmission theory is established basedon resonance which in principle determines the sensitivity ofthe power transfer characteristics to the working frequencyTherefore the sensitivity cannot be totally eliminated Dur-ing engineering-design stages the transmission parametersshould be set appropriately by accommodating with thetransmission performance of the system
4 Conclusion
In this paper power transmission characteristics of magneticresonance coupling wireless power transmission system areoptimized Based on themutual couplingmodel of a resonantsystem optimization formulas of coupling coefficient in thecondition of maximum power transmission are deduced andexperimental results show that the optimization formulasare correct and can be used to effectively optimize powertransmission characteristics in the nonovercoupling regionOn the other hand by improving the system resonancefrequency or coupling coefficient 119896
12 11989634 the power trans-
mission stability can be improved while power transmissionperformance sensitivity to variations in operating parameterscan be decreasedThe conclusions obtained in this paper willenrich the theory of wireless power transmission based onmagnetic resonance and provide a reference for engineeringapplications
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National Natural ScienceFoundation of China under Grant no 61104185
References
[1] A Kurs A Karalis R Moffatt J D Joannopoulos P Fisherand M Soljacic ldquoWireless power transfer via strongly coupled
magnetic resonancesrdquo Science vol 317 no 5834 pp 83ndash862007
[2] C A Tucker KWarwick andW Holderbaum ldquoA contributionto the wireless transmission of powerrdquo International Journal ofElectrical Power amp Energy Systems vol 47 pp 235ndash242 2013
[3] A Karalis J D Joannopoulos and M Soljacic ldquoEfficient wire-less non-radiativemid-range energy transferrdquoAnnals of Physicsvol 323 no 1 pp 34ndash48 2008
[4] T Chan and C Chen ldquoA primary side control method for wire-less energy transmission systemrdquo IEEE Transactions on Circuitsand Systems I Regular Papers vol 59 no 8 pp 1805ndash1814 2012
[5] C K Lee W X Zhong and S Y R Hui ldquoEffects of magneticcoupling of nonadjacent resonators on wireless power domino-resonator systemsrdquo IEEE Transactions on Power Electronics vol27 no 4 pp 1905ndash1916 2012
[6] D Ahn and S Hong ldquoEffect of coupling between multipletransmitters or multiple receivers on wireless power transferrdquoIEEE Transactions on Industrial Electronics vol 60 no 7 pp2602ndash2613 2013
[7] Y Li Q Yang Z Yan et al ldquoCharacteristic of frequency in wire-less power transfer system via magnetic resonance couplingrdquoElectric Machines and Control vol 16 no 7 pp 7ndash11 2012
[8] J Wang Z Zhu C Li J Huangfu and L Ran ldquoPLL-based self-adaptive resonance tuning for a wireless-powered potentiome-terrdquo IEEE Transactions on Circuits and Systems II Express Briefsvol 60 no 7 pp 392ndash396 2013
[9] Y-H Kim S-Y Kang M-L Lee B-G Yu and T ZyungldquoOptimization ofwireless power transmission through resonantcouplingrdquo in Proceedings of the Compatability and Power Elec-tronics (CPE rsquo09) pp 426ndash431 Badajoz Spain May 2009
[10] JHuhW Lee S ChoiGCho andCRim ldquoFrequency-domaincircuit model and analysis of coupled magnetic resonancesystemsrdquo Journal of Power Electronics vol 13 no 2 pp 275ndash2862013
[11] O Jonal S V Georgakopoulos and M M Tentzeris ldquoOptimaldesign parameters for wireless power transfer by resonancemagneticrdquo IEEE Antennas andWireless Propagation Letters vol11 pp 1390ndash1393 2012
[12] A P Sample D A Meyer and J R Smith ldquoAnalysis experi-mental results and range adaptation of magnetically coupledresonators for wireless power transferrdquo IEEE Transactions onIndustrial Electronics vol 58 no 2 pp 544ndash554 2011
[13] N Y Kim K Y Kim and C W Kim ldquoAutomated frequencytracking system for efficient mid-range magnetic resonancewireless power transferrdquo Microwave and Optical TechnologyLetters vol 54 no 6 pp 1423ndash1426 2012
[14] J W Kim H-C Son K-H Kim and Y-J Park ldquoEfficiencyanalysis of magnetic resonance wireless power transfer withintermediate resonant coilrdquo IEEE Antennas andWireless Propa-gation Letters vol 10 pp 389ndash392 2011
[15] L L Tan X L Huang H Huang Y Zou and H Li ldquoTransferefficiency optimal control of magnetic resonance coupled sys-tem of wireless power transfer based on frequency controlrdquoScience China Technological Sciences vol 54 no 6 pp 1428ndash1434 2011
[16] R Xue K Cheng and M Je ldquoHigh-efficiency wireless powertransfer for biomedical implants by optimal resonant loadtransformationrdquo IEEE Transactions on Circuits and Systems IRegular Papers vol 60 no 4 pp 867ndash874 2013
[17] Y Y Ko S L Ho W N Fu and X Zhang ldquoA novel hybrid res-onator for wireless power delivery in bio-implantable devicesrdquo
8 The Scientific World Journal
IEEE Transactions OnMagnetics vol 48 no 11 pp 4518ndash45212012
[18] J Huang Cirruits China Machine Press Beijing 2003[19] W Q Niu W Gu J X Chu and A D Shen ldquoCoupled-mode
analysis of frequency splitting phenomena in CPT systemsrdquoElectronics Letters vol 48 no 12 pp 723ndash724 2012
Figure 6 Variation of load power with frequency at various 1198893values
20 30 40 50 60 70 80 90 100 110 1200
10
20
30
40
50
60
Pow
er (m
W)
d2 (mm)
fr = 1MHzfr = 2MHzfr = 5MHz
(a) 119877119871 = 50Ω
20 30 40 50 60 70 80 90 100 110 1200
10
20
30
40
50
60
fr = 1MHzfr = 2MHzfr = 5MHz
Pow
er (m
W)
d2 (mm)
(b) 119877119871 = 150Ω
Figure 7 Variations in power transmission characteristics with various resonance frequencies
(2) Increasing the Resonance Frequency The resonance fre-quency is a key parameter in system design whose value canbe changed by adjusting the number of turns or the externallymatched capacitance of the transmission and receiving coilsThe degree of sharpness in the frequency response curve ofload power reduces as resonance frequency increases There-fore enhancing power transmission stability can be obtainedby properly reducing the value of the external matchedcapacitance Transmission systems with a high resonancefrequency can produce high power transmission over shortdistancesHowever transmission performance attenuates fastas the separation between transmission and receiving termi-nals increasesTherefore it is not appropriate for the wirelesstransmission of power over long distance The attenuationof transmission power for systems with small resonancefrequencies is relatively slow as the separation between trans-mission and receiving terminals increase This is shown inFigure 7 Figure 8 gives the normalized experimental curve ofload power for various excitation frequencies at 119889
2= 60mm
and 119877119871= 50Ω It shows that when 119891
119903= 5MHz the pass
bandwidth is 236KHz and 285KHz wider than that at 2MHzand 1MHz respectively In addition along with increasingthe resonance frequency difficulties of circuit implementingincrease and inversion losses in the driving circuit alsoincrease These factors will cause further degradation in totaltransmission efficiency
To illustrate the effect of optimization both Figures 6 and8 show normalized curves of the resonant system with onlya single resonance frequency When the separation betweentransmission and receiving terminals is small and the systemshows splitting in the resonance frequency the optimizationmethod is still applicable
In summary by appropriate readjustment of the trans-mission parameters the sharpness in the frequency responsecurve of load power can be effectively reduced Simulta-neously transmission power might be reduced when thepower transmission stability is improved In contrast wirelesspower transmission technology based onmagnetic resonancecoupling relies on a strong coupling between transmissionand receiving terminals to produce high efficiency power
The Scientific World Journal 7
1
08
06
04
02
007 08 09 1 11 12 13
ffr
fr = 1MHzfr = 2MHzfr = 5MHz
P0P
max
Figure 8 Variations in frequency response curve of load powerwithvarious resonance frequencies
transmission The transmission theory is established basedon resonance which in principle determines the sensitivity ofthe power transfer characteristics to the working frequencyTherefore the sensitivity cannot be totally eliminated Dur-ing engineering-design stages the transmission parametersshould be set appropriately by accommodating with thetransmission performance of the system
4 Conclusion
In this paper power transmission characteristics of magneticresonance coupling wireless power transmission system areoptimized Based on themutual couplingmodel of a resonantsystem optimization formulas of coupling coefficient in thecondition of maximum power transmission are deduced andexperimental results show that the optimization formulasare correct and can be used to effectively optimize powertransmission characteristics in the nonovercoupling regionOn the other hand by improving the system resonancefrequency or coupling coefficient 119896
12 11989634 the power trans-
mission stability can be improved while power transmissionperformance sensitivity to variations in operating parameterscan be decreasedThe conclusions obtained in this paper willenrich the theory of wireless power transmission based onmagnetic resonance and provide a reference for engineeringapplications
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National Natural ScienceFoundation of China under Grant no 61104185
References
[1] A Kurs A Karalis R Moffatt J D Joannopoulos P Fisherand M Soljacic ldquoWireless power transfer via strongly coupled
magnetic resonancesrdquo Science vol 317 no 5834 pp 83ndash862007
[2] C A Tucker KWarwick andW Holderbaum ldquoA contributionto the wireless transmission of powerrdquo International Journal ofElectrical Power amp Energy Systems vol 47 pp 235ndash242 2013
[3] A Karalis J D Joannopoulos and M Soljacic ldquoEfficient wire-less non-radiativemid-range energy transferrdquoAnnals of Physicsvol 323 no 1 pp 34ndash48 2008
[4] T Chan and C Chen ldquoA primary side control method for wire-less energy transmission systemrdquo IEEE Transactions on Circuitsand Systems I Regular Papers vol 59 no 8 pp 1805ndash1814 2012
[5] C K Lee W X Zhong and S Y R Hui ldquoEffects of magneticcoupling of nonadjacent resonators on wireless power domino-resonator systemsrdquo IEEE Transactions on Power Electronics vol27 no 4 pp 1905ndash1916 2012
[6] D Ahn and S Hong ldquoEffect of coupling between multipletransmitters or multiple receivers on wireless power transferrdquoIEEE Transactions on Industrial Electronics vol 60 no 7 pp2602ndash2613 2013
[7] Y Li Q Yang Z Yan et al ldquoCharacteristic of frequency in wire-less power transfer system via magnetic resonance couplingrdquoElectric Machines and Control vol 16 no 7 pp 7ndash11 2012
[8] J Wang Z Zhu C Li J Huangfu and L Ran ldquoPLL-based self-adaptive resonance tuning for a wireless-powered potentiome-terrdquo IEEE Transactions on Circuits and Systems II Express Briefsvol 60 no 7 pp 392ndash396 2013
[9] Y-H Kim S-Y Kang M-L Lee B-G Yu and T ZyungldquoOptimization ofwireless power transmission through resonantcouplingrdquo in Proceedings of the Compatability and Power Elec-tronics (CPE rsquo09) pp 426ndash431 Badajoz Spain May 2009
[10] JHuhW Lee S ChoiGCho andCRim ldquoFrequency-domaincircuit model and analysis of coupled magnetic resonancesystemsrdquo Journal of Power Electronics vol 13 no 2 pp 275ndash2862013
[11] O Jonal S V Georgakopoulos and M M Tentzeris ldquoOptimaldesign parameters for wireless power transfer by resonancemagneticrdquo IEEE Antennas andWireless Propagation Letters vol11 pp 1390ndash1393 2012
[12] A P Sample D A Meyer and J R Smith ldquoAnalysis experi-mental results and range adaptation of magnetically coupledresonators for wireless power transferrdquo IEEE Transactions onIndustrial Electronics vol 58 no 2 pp 544ndash554 2011
[13] N Y Kim K Y Kim and C W Kim ldquoAutomated frequencytracking system for efficient mid-range magnetic resonancewireless power transferrdquo Microwave and Optical TechnologyLetters vol 54 no 6 pp 1423ndash1426 2012
[14] J W Kim H-C Son K-H Kim and Y-J Park ldquoEfficiencyanalysis of magnetic resonance wireless power transfer withintermediate resonant coilrdquo IEEE Antennas andWireless Propa-gation Letters vol 10 pp 389ndash392 2011
[15] L L Tan X L Huang H Huang Y Zou and H Li ldquoTransferefficiency optimal control of magnetic resonance coupled sys-tem of wireless power transfer based on frequency controlrdquoScience China Technological Sciences vol 54 no 6 pp 1428ndash1434 2011
[16] R Xue K Cheng and M Je ldquoHigh-efficiency wireless powertransfer for biomedical implants by optimal resonant loadtransformationrdquo IEEE Transactions on Circuits and Systems IRegular Papers vol 60 no 4 pp 867ndash874 2013
[17] Y Y Ko S L Ho W N Fu and X Zhang ldquoA novel hybrid res-onator for wireless power delivery in bio-implantable devicesrdquo
8 The Scientific World Journal
IEEE Transactions OnMagnetics vol 48 no 11 pp 4518ndash45212012
[18] J Huang Cirruits China Machine Press Beijing 2003[19] W Q Niu W Gu J X Chu and A D Shen ldquoCoupled-mode
analysis of frequency splitting phenomena in CPT systemsrdquoElectronics Letters vol 48 no 12 pp 723ndash724 2012
Figure 8 Variations in frequency response curve of load powerwithvarious resonance frequencies
transmission The transmission theory is established basedon resonance which in principle determines the sensitivity ofthe power transfer characteristics to the working frequencyTherefore the sensitivity cannot be totally eliminated Dur-ing engineering-design stages the transmission parametersshould be set appropriately by accommodating with thetransmission performance of the system
4 Conclusion
In this paper power transmission characteristics of magneticresonance coupling wireless power transmission system areoptimized Based on themutual couplingmodel of a resonantsystem optimization formulas of coupling coefficient in thecondition of maximum power transmission are deduced andexperimental results show that the optimization formulasare correct and can be used to effectively optimize powertransmission characteristics in the nonovercoupling regionOn the other hand by improving the system resonancefrequency or coupling coefficient 119896
12 11989634 the power trans-
mission stability can be improved while power transmissionperformance sensitivity to variations in operating parameterscan be decreasedThe conclusions obtained in this paper willenrich the theory of wireless power transmission based onmagnetic resonance and provide a reference for engineeringapplications
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by the National Natural ScienceFoundation of China under Grant no 61104185
References
[1] A Kurs A Karalis R Moffatt J D Joannopoulos P Fisherand M Soljacic ldquoWireless power transfer via strongly coupled
magnetic resonancesrdquo Science vol 317 no 5834 pp 83ndash862007
[2] C A Tucker KWarwick andW Holderbaum ldquoA contributionto the wireless transmission of powerrdquo International Journal ofElectrical Power amp Energy Systems vol 47 pp 235ndash242 2013
[3] A Karalis J D Joannopoulos and M Soljacic ldquoEfficient wire-less non-radiativemid-range energy transferrdquoAnnals of Physicsvol 323 no 1 pp 34ndash48 2008
[4] T Chan and C Chen ldquoA primary side control method for wire-less energy transmission systemrdquo IEEE Transactions on Circuitsand Systems I Regular Papers vol 59 no 8 pp 1805ndash1814 2012
[5] C K Lee W X Zhong and S Y R Hui ldquoEffects of magneticcoupling of nonadjacent resonators on wireless power domino-resonator systemsrdquo IEEE Transactions on Power Electronics vol27 no 4 pp 1905ndash1916 2012
[6] D Ahn and S Hong ldquoEffect of coupling between multipletransmitters or multiple receivers on wireless power transferrdquoIEEE Transactions on Industrial Electronics vol 60 no 7 pp2602ndash2613 2013
[7] Y Li Q Yang Z Yan et al ldquoCharacteristic of frequency in wire-less power transfer system via magnetic resonance couplingrdquoElectric Machines and Control vol 16 no 7 pp 7ndash11 2012
[8] J Wang Z Zhu C Li J Huangfu and L Ran ldquoPLL-based self-adaptive resonance tuning for a wireless-powered potentiome-terrdquo IEEE Transactions on Circuits and Systems II Express Briefsvol 60 no 7 pp 392ndash396 2013
[9] Y-H Kim S-Y Kang M-L Lee B-G Yu and T ZyungldquoOptimization ofwireless power transmission through resonantcouplingrdquo in Proceedings of the Compatability and Power Elec-tronics (CPE rsquo09) pp 426ndash431 Badajoz Spain May 2009
[10] JHuhW Lee S ChoiGCho andCRim ldquoFrequency-domaincircuit model and analysis of coupled magnetic resonancesystemsrdquo Journal of Power Electronics vol 13 no 2 pp 275ndash2862013
[11] O Jonal S V Georgakopoulos and M M Tentzeris ldquoOptimaldesign parameters for wireless power transfer by resonancemagneticrdquo IEEE Antennas andWireless Propagation Letters vol11 pp 1390ndash1393 2012
[12] A P Sample D A Meyer and J R Smith ldquoAnalysis experi-mental results and range adaptation of magnetically coupledresonators for wireless power transferrdquo IEEE Transactions onIndustrial Electronics vol 58 no 2 pp 544ndash554 2011
[13] N Y Kim K Y Kim and C W Kim ldquoAutomated frequencytracking system for efficient mid-range magnetic resonancewireless power transferrdquo Microwave and Optical TechnologyLetters vol 54 no 6 pp 1423ndash1426 2012
[14] J W Kim H-C Son K-H Kim and Y-J Park ldquoEfficiencyanalysis of magnetic resonance wireless power transfer withintermediate resonant coilrdquo IEEE Antennas andWireless Propa-gation Letters vol 10 pp 389ndash392 2011
[15] L L Tan X L Huang H Huang Y Zou and H Li ldquoTransferefficiency optimal control of magnetic resonance coupled sys-tem of wireless power transfer based on frequency controlrdquoScience China Technological Sciences vol 54 no 6 pp 1428ndash1434 2011
[16] R Xue K Cheng and M Je ldquoHigh-efficiency wireless powertransfer for biomedical implants by optimal resonant loadtransformationrdquo IEEE Transactions on Circuits and Systems IRegular Papers vol 60 no 4 pp 867ndash874 2013
[17] Y Y Ko S L Ho W N Fu and X Zhang ldquoA novel hybrid res-onator for wireless power delivery in bio-implantable devicesrdquo
8 The Scientific World Journal
IEEE Transactions OnMagnetics vol 48 no 11 pp 4518ndash45212012
[18] J Huang Cirruits China Machine Press Beijing 2003[19] W Q Niu W Gu J X Chu and A D Shen ldquoCoupled-mode
analysis of frequency splitting phenomena in CPT systemsrdquoElectronics Letters vol 48 no 12 pp 723ndash724 2012
