Antennas in Wireless Charging Systemsapplications is the space solar power system (SPS), which is a big project to collect sunlight in geostationary orbit, convert it to electromagnetic

Antennas in Wireless Charging Systems

Qiang Chena* and Qiaowei YuanbaTohoku University, Sendai, JapanbNational Institute of Technology, Sendai College, Sendai, Japan

Abstract

The antenna is one of the most critical components in wireless charging systems since the power transferefficiency of the system is largely dependent on the antenna performance. In this chapter, the modelingand analysis of antennas are introduced with a focus on increasing the power transfer efficiency. Therelationship between wireless power transfer efficiency and antenna parameters like antenna geometry,ohmic loss, impedance matching circuits, and distance between transmitting and receiving antennas isstudied analytically and numerically by using circuit theory and full-wave electromagnetic analysis, inorder to provide some fundamental and theoretical knowledge to develop antennas for highly efficientwireless charging systems. Finally, challenges and recent studies of antennas for wireless power transfersystems, as well as standards on this field, are briefly introduced.

Keywords

Near-field coupling; Wireless power transfer; Wireless charging; Wireless power transmission; Antenna;Impedance matching; Efficiency; Equivalent circuit; Scattering parameters; Scattering matrix; Impedancematrix

Introduction

Research on wireless power transfer (WPT) started more than 100 years ago. Nikola Tesla developed thefirst practicalWPTsystem in 1989 (Tesla 1904) and revealed the system configuration in his U.S. patent in1914 (Tesla 1914). Reinhold Rudenberg described the fundamental theory of electric power absorption byantennas early in 1908 (Reinhold 1908). Since then, there have been numerous researches of bothfundamental and application studies on the WPT. This technology has been widely applied to manyapplications from wirelessly charging electronic devices to the solar power satellite (SPS) system(McSpadden and Mankins 2002). However, this technology still faces challenges. One of the biggestchallenges is keeping high power transfer efficiency (PTE) over a long transmission distance.

Wireless power transfer can be classified into two categories based on how the electromagnetic field isused to transfer power. One is far-field radiation, and the other is the near-field coupling. The near-fieldcoupling approach is also called the inductive coupling method or induction method. This method iseffective for a short-range power transfer with a relatively high power transfer efficiency. The near-fieldcoupling approach has already been applied to many practical applications such as wireless charging forcordless phone, electric toothbrush, and passive radio-frequency identification (RFID) tags. On the otherhand, the far-field radiation approach is applicable to power transfer over a long distance. But the powertransfer efficiency is extremely low, depending on the transmission distance. One of the most well-known

*Email: [email protected]

Handbook of Antenna TechnologiesDOI 10.1007/978-981-4560-75-7_91-1# Springer Science+Business Media Singapore 2015

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applications is the space solar power system (SPS), which is a big project to collect sunlight ingeostationary orbit, convert it to electromagnetic power, and transfer the power to the earth in the formof electromagnetic waves. This method requires directive antennas with high gain to increase the powertransfer efficiency, as well as a direction tracking system to track the movements of the antennas.Therefore, the far-field radiation approach is usually limited to the applications in the environment ofline-of-sight propagation.

A very efficient near-field power transfer was experimentally demonstrated by introducing a conceptcalled evanescent resonant coupling (Kurs et al. 2007). In the paper, two self-resonant coils were used asreceiving and transmitting antennas, and a power transfer for lighting up a 60-W light bulb with 40 %efficiency over distances in excess of 2 m was demonstrated experimentally. This magnetically resonantsystem was critical to realize power transfer over a relatively long distance while keeping a good powertransfer efficiency compared with the conventional induction coupling method. There have been manyresearch papers and reports soon after this publication (for example, Karalis et al. 2008; Cannonet al. 2009; Tak et al. 2009; Ishizaki et al. 2010; Yuan et al. 2010). It was shown that the evanescentresonant coupling method can transmit the energy for longer distance than the previous near-fieldinduction method (Murakami et al. 1996; Hatanaka et al. 2002) and was more efficient than thefar-field radiation method where the vast majority of energy was wasted due to the transmission loss(Brown 1984; Matsumoto 2002; Rodenbeck and Chang 2005). It was also found that the electric couplingwas effective in wireless power transfer with a high efficiency (Kim and Ling 2007). It was stated in Chenet al. (2012) that the conjugate impedance matching for both transmitting and receiving antennas couldbring about the maximum power transfer efficiency instead of using the concept of antenna resonance ormagnetic resonance. It was demonstrated in the paper that an efficiency up to 100 % could be achieved inthe near-field region when the antennas were perfectly conducting and electrically small if the conjugate-matching condition was satisfied. It was also described that, in practice, loop antennas were superior to thedipole antennas in achieving high efficiency, if the conducting losses of both the antennas and thematching circuits were considered.

In this chapter, modeling and analysis of antennas in wireless charging systems based on the near-fieldcoupling approach by using circuit theory and full-wave model electromagnetic analysis is introducedfrom a viewpoint of increasing wireless power transfer efficiency for the wireless charging systems.Circuit theory can provide a clear image of how electromagnetic power is coupled through the antennas,and it can give some basic knowledge on finding the key factors to increase power transfer efficiency.Full-wave analysis can give an electromagnetic simulation in a practical situation where antennacharacteristics including antenna impedance, radiation, and conducting loss can be evaluated accurately.Because these antenna characteristics play an important role in determining the power transfer efficiency,the full-wave analysis is required to design antennas for a practical wireless charging system. Full-waveanalysis of conical models where two types of antennas, dipole antennas and loop antennas, are used fornear-field coupling show some general principles for antenna design to achieve the maximum powertransfer efficiency for the wireless charging systems. Finally, some recent application developments andstandards of the wireless charging technology are introduced.

Configuration of Wireless Charging System and Definition of Power TransferEfficiency

A typical wireless charging system is generally composed of a source, impedance matching circuits,transmitting and receiving antennas, a rectifier, and a load impedance, as shown in Fig. 1. At thetransmitting side, the electromagnetic power is generated by a voltage source V0 with internal impedance


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rs and is transferred through the impedance matching circuit to the transmitting antenna. The electromag-netic field is wirelessly coupled to the receiving side through the receiving antenna, impedance matchingcircuit, rectifier circuit, and is finally consumed by the resistance r. This configuration is also valid for thefar-field radiation approach if the antennas are located in the far-field region.

Because antennas are the main topic in this chapter, it is adequate to consider a more simplifiedconfiguration model shown in Fig. 2. In this model, Zs is the equivalent impedance looking toward thematching circuit and power source, and Zl is the impedance looking to rectifier circuit and load. Althoughrectifier is a nonlinear circuit, it is assumed to be a linear parameter which is independent of the receivedpower in this chapter. It is important to note that characteristics of a single antenna, such as the resonantfrequency, input impedance, and gain, are useless for evaluating the antenna performance in the wirelesscharging system based on the near-field coupling approach, because the transmitting and receivingantennas are coupled strongly with each other.

The power transfer efficiency, one of the most important parameters to evaluate performance of thewireless charging system, is defined as the ratio of the absorbed power in the load impedance Zl to theincident power into the transmitting antenna:

� ¼ Pl

Pinc; (1)

In this case, Pinc is the incident power and Pl is the absorbed power. The incident power is the maximumpower available to the transmitting antenna when the condition of impedance matching is satisfied at Port1 of Fig. 2.

It will be shown that the power transfer efficiency � reaches the maximum value when the impedancesZs and Zl are complex conjugate matching to the input impedance of Port 1 and Port 2, respectively. Thatis,

Zin ¼ Z�s ; (2)

Zin Zout

Fig. 2 Transmitting and receiving antennas in wireless charging system

Fig. 1 Configuration of a typical wireless charging system


Page 3 of 24

at Port 1, and

Zout ¼ Z�l ; (3)

at Port 2, where Zin is the input impedance looking into Port 1 and Zout is the input impedance looking intoPort 2. It should be noted again that Zin is not equal to the input impedance of the transmitting antenna andZout is not the input impedance of the receiving antenna because the mutual coupling cannot be ignoredbetween the transmitting and the receiving antennas when the near-field power coupling is discussed.

In the following sections, the relationship between the impedance matching condition and the conditionfor obtaining the maximum power transfer efficiency as well as the relationship between wireless powertransfer efficiency and antenna parameters are investigated theoretically and numerically by using circuittheory and full-wave electromagnetic analysis.

Circuit Theory

When wireless charging systems operate at lower frequencies, the radiation from the system can beignored, and antennas in the system can be approximately modeled using lumped circuit elements.Analysis using lumped circuit elements can be carried out based on circuit theory, which is very simpleand provides a straightforward model demonstrating the operating principle of antennas in wirelesscharging systems.

At low frequency, the electromagnetic field can be assumed to be a quasistatic field, and electromag-netic coupling can be classified into induction through the magnetic field and coupling through the electricfield. In this section, the power charge system using the magnetic induction is focused on and discussed.

Magnetic induction can be performed using two inductors, also called coils, as a transmitting antennaand a receiving antenna because coils can produce strong magnetic fields in the near-field area. The coilcan be either a single-turn coil or a multiturn coil, but the total length of the wire should be much smallerthan the wavelength. Otherwise, electromagnetic power would be radiated from the system, and the powercharging efficiency, or power transfer efficiency, would be largely degraded.

An equivalent circuit for describing the basic phenomena of magnetic field induction is shown in Fig. 3.Two inductors for transmitting and receiving are equivalent to two inductors L1 and L2 and are coupled toeach other with mutual inductanceM. r1 and r2 represent the ohmic loss of the transmitting and receivingcircuits, respectively, mainly caused by the inductors. A voltage source with voltage V0 is fed to thetransmitting circuit. Zl is the load impedance where the power provided by the voltage source is absorbed.

L1L2

Mr1 r2

Zl

I1 I2

V0

Transmitting side Receiving side

Fig. 3 Equivalent circuit for magnetic field coupling


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In the following, it is shown how to obtain the maximum power transfer efficiency by optimizing thevalue of Zl. This analysis provides a fundamental knowledge to develop a highly efficient wirelesscharging system by designing the load impedance.

When Kirchhoff’s voltage law is applied to the electric circuit in Fig. 3, the equations

r1 þ joL1ð ÞI1 þ joMI2 ¼ V 0 (4)

joMI1 þ Zl þ r2 þ joL2ð ÞI2 ¼ 0 (5)

are obtained. By solving Eqs. 4 and 5 simultaneously, current at the transmitting side becomes

I1 ¼V 0 joM0 Zl þ r2 þ joL2

��

r1 þ joL1 joMjoM Zl þ r2 þ joL2

��¼ Zl þ r2 þ joL2ð ÞV 0

r1 þ joL1ð Þ Zl þ r2 þ joL2ð Þ þ o2M2 : (6)

The relationship betweenmagnitude of the currents at the transmitting and receiving sides can be derived as

jI2j2 ¼ o2M2

r22 þ X 2 þ oL2ð Þ2 jI1j2: (7)

The input impedance looking into the circuit from the voltage source is derived from Eq. 6 as

Zin ¼ V 0

I1¼ r1 þ joL1 þ o2M 2

Zl þ r2 þ joL2: (8)

Then, the real part of Zin becomes

Rin ¼ r1 þ o2M 2 Rl þ r2ð ÞRl þ r2ð Þ2 þ X l þ oL2ð Þ2 ; (9)

where Rl and Xl are the real and imaginary parts of Zl, respectively.The total power consumed in the circuit generated by voltage V0 is

Pin ¼ 1

2RinjI1j2; (10)

and the power consumed in the load Zl is

Pl ¼ 1

2RljI2j2: (11)

Therefore, the power transfer efficiency is evaluated as


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� ¼ Pl

Pin(12)

o2M2Rl

r1 Rl þ r2ð Þ2 þ X l þ oL2ð Þ2� �

þ o2M2 Rl þ r2ð Þ: (13)

Now, the load resistance Rl and the load reactance Xl are optimized to achieve maximum power transferefficiency. For this purpose, the partial derivatives of the efficiency with respect to Rl and Xl should satisfythe conditions

@�

@X l¼ 0; (14)

and

@�

@Rl¼ 0: (15)

The optimized value of Rl is obtained by solving the above two equations as

Rlm ¼ r2ffiffiffiffiffiffiffiffiffiffiffi1þ a

p; (16)

and the optimized value of Xl is also obtained as

X lm ¼ �oL2; (17)

where a is defined as

a ¼ o2M2

r1r2: (18)

Therefore, when the load impedance Zl satisfies both Eqs. 16 and 17, the power transfer efficiency �reaches to the maximum, expressed as

�m ¼ 1� 2

1þ ffiffiffiffiffiffiffiffiffiffiffi1þ a

p ¼ 1� ffiffiffiffiffiffiffiffiffiffiffi1þ a

p� �2a

: (19)

This analysis indicates that the maximum power transfer efficiency can be achieved by the loadimpedance which satisfies both Eq. 16 for real part and Eq. 17 for imaginary part. Because Eq. 17 isthe condition of resonance in receiving circuit, this analysis indicates that the maximum power transferefficiency can be achieved if both Eqs. 16 and 17 are satisfied simultaneously, while the resonancecondition is necessary but not enough. It is also noted that the optimized load resistance is related not onlywith the resistance of inductor in the receiving side but also with that in the transmitting side through theparameter a which indicates the mutual coupling effect between these two inductors. a can be alsoexpressed as


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a ¼ k2Q1Q2;

where k is the coupling coefficient,

k ¼ M

L1L2; (20)

and Q1 and Q2 are the quality factors

Q1 ¼oL1r1

; (21)

and

Q2 ¼oL2r2

: (22)

Therefore, the maximum power transfer efficiency can be expressed as

�m ¼ 1� 2

1þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ k2Q1Q2

q ; (23)

which shows that the maximum power transfer efficiency is dependent on coupling factor k and the qualityfactors Q1 and Q2. A large quality factor and a strong coupling between the coupled inductors willincrease the value of the maximum efficiency.

The condition for obtaining the maximum efficiency is not given in the transmitting circuit in the abovediscussion. It is because the power transfer efficiency is normalized by the input power to the circuit,rather than the incident power in this section. If the efficiency is defined as the absorbed power over theincident power, the efficiency optimization should be made by defining an internal impedance of thepower source and then optimizing the internal impedance in the same way as discussed for the receivingcircuit.

As a numerical example, a wireless power transfer by two solenoid coils is analyzed by using circuittheory. The analysis model is shown in Fig. 4. Two solenoid coils are used as the antennas for wirelesspower transfer. The solenoid coils have a length l, N turns per meter, and radius a. The coils are made ofconducting wire with radius Ra and conductivity s. The two coils are separated over a distance d.

d

2a

l

2a

Zl

l

V0

Transmitting solenoid coil Receiving solenoid coil

Fig. 4 Analysis model of wireless charging system by using two solenoid coils


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When the solenoid coil is extremely small compared with wavelength, it can be assumed the current onthe solenoid coil is uniformly in-phase distributed on the surface of the conducting wire. The inductanceL of the solenoid coil is then given in a closed form as

L ¼ m0n2pa2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffia2 þ l2

p� a

� �; (24)

where m0 is permeability in vacuum. The resistance r of the coil is derived as

r ¼ 2paN2pRads

¼ aN

Rads; (25)

where d is skin depth of the wire expressed as

d ¼ffiffiffiffiffiffiffiffiffiffiffi2

om0s

s: (26)

It is difficult to give a closed form to express exactly the mutual inductance M between the coils. Forsimplicity, it is assumed here that the distance between coils is small enough that the coupling factorbecomes k = 1. Therefore, the mutual inductance M is equal to L.

Consider the case that f = 85 kHz, l = 100 cm,N = 100,Ra = 1mm, and s = 5.8 � 107 S/m. Figure 5shows the equivalent inductance and resistance of the solenoid coils which are calculated using Eqs. 24and 25. As the radius of the solenoid coil increases, both the inductance and resistance increase as well.Corresponding to the change of radius, the optimized load impedance to achieve the maximum powertransfer efficiency can be obtained by using Eqs. 16 and 17, as shown in Fig. 6. The maximum powertransfer efficiency, when the load impedance is optimized, is shown in Fig. 7, which is calculated by usingEq. 23. It is shown that the maximum power transfer efficiency is as high as nearly 100 % because thecoupling factor between coils is assumed to be 1. Based on this assumption, the maximum power transferefficiency is independent of the distance between coils. Therefore, the numerical analysis using the circuittheory is limited to simple analysis models where the lumped circuit elements can be accurately evaluated.In practice, because geometry of both transmitting and receiving antennas would be very complicated, it isusually impossible to obtain the exact characteristics of those lumped circuit elements such as the

0 10 20 30 40 50 60

1

2

3

4

5

0

1

2

3

4

5

f = 85kHz

l = 100cm

N = 100

Ra = 1mm

Circuit Theory

L

r

r [Ω

]L [m

H]

a [cm]

Fig. 5 Equivalent resistance and inductance of the solenoid coils


Page 8 of 24

inductance and resistance of the coils, as well as the mutual coupling factor in the equivalent circuit. In thefollowing sections, some approaches based on a full-wave electromagnetic analysis are introduced whichis capable of accurately analyzing the antennas with complicated geometry and moderate electrical size inthe wireless charging system.

Impedance Matrix Approach

In this section, the near-field coupling is modeled by using the impedance matrix approach. The wirelesscharging system can be expressed in a form of two-port network shown in Fig. 8. Here, Zs is the internalimpedance of the voltage source and Zl is the load impedance. Both of them have a complex value,expressed as Zs = Rs + jXs and Zl = Rl + jXl, respectively. The relation between the port currents I1, I2and port voltages V1, V2 is given in terms of the impedance matrix,

0 10 20 30 40 50 60

1

2

3

4

5

−5

−4

−3

−2

−1

0

f = 85kHz

l = 100cm

N = 100

Ra = 1mm

d = 50cm

k = 1

Circuit Theory

RIm

[kΩ

]

XIm

RIm

XIm

[kΩ]

a [cm]

Fig. 6 Optimized load impedance to achieve the maximum power transfer efficiency

0 10 20 30a [cm]

40 50 6099

99.2

99.4

99.6

99.8

100

h m [%

] f = 85kHz

l = 100cm

N = 100

Ra = 1mm

d = 50cm

k = 1

Circuit Theory

Fig. 7 The maximum power transfer efficiency when the optimized impedance is loaded


Page 9 of 24

V 1

V 2

� ¼ Z11 Z12

Z21 Z22

� I1I2

� (27)

If the geometry of the wireless charging system is known, the matrix impedance in Fig. 8 can be obtainedby using some numerical methods based on full-wave electromagnetic analysis.

If Zin is the impedance looking into Port 1 and Zout is the impedance looking into Port 2, they areexpressed in the form of impedance parameters (Z-parameters) as

Zin ¼ Z11 � Z12Z21

Zl þ Z22; (28)

and

Zout ¼ Z22 � Z12Z21

Zs þ Z11: (29)

The condition of conjugate impedance matching applied to both ports is expressed as

Zin ¼ Z�s ; (30)

and

Zout ¼ Z�l : (31)

By solving these two equations simultaneously, the matched load impedance becomes

Rlmat ¼ R22

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� a1ð Þ 1þ a2ð Þ

p; (32)

X lmat ¼ R22ffiffiffiffiffiffiffiffiffia1a2

p � X 22: (33)

The matched internal impedance becomes

Rsmat ¼ R11

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� a1ð Þ 1þ a2ð Þ

p; (34)

X smat ¼ R11ffiffiffiffiffiffiffiffiffia1a2

p � X 11; (35)

where a1 ¼ R212= R11R22ð Þ and a2 ¼ X 2

12= R11R22ð Þ.When the power transfer efficiency is definted as the absorbed power by the load impedance over the

input power (not incident power!) to the Port 1, it can be expressed as

ZlZs

I1 I2

V2V1Zin Zout

[Z] =Z11

Z12

Z21

Z22V0

Port 1 Port 2

Fig. 8 Two-port network for modeling WPT using magnetic field coupling


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� ¼ RljI2j2RinjI1j2 : (36)

By using relation between currents |I2|2 and |I1|

2

jI2j2 ¼ jZ12j2jZl þ Z22j2 jI1j

2; (37)

the power transfer efficiency can be calculated as

� ¼ RljZ12j2RinjZl þ Z22j2 : (38)

If impedance matching condition is satisfied at Port 2, substituting the matched load impedance Rlmat inEq. 32 and Xlmat in Eq. 33 for Zl, the power transfer efficiency in terms of the input power becomes

�mat ¼a1 þ a2ffiffiffiffiffiffiffiffiffiffiffiffiffi

1� a1p þ ffiffiffiffiffiffiffiffiffiffiffiffiffi

1þ a2p� �2 : (39)

When the impedance matrix approach is applied to the analysis model in Fig. 3 in section “CircuitTheory,” as shown in Fig. 9, the impedance matrix for the two-port network becomes

Z½ � ¼ r1 þ joL1 joMjoM r2 þ joL2

� : (40)

Then, a1 = 0 and a2 = o2M2/(r1r2) = a. If it is assumed that the impedance matching condition issatisfied at Port 2, the load impedance can be derived by using Eqs. 32 and 33 as

Rlmat ¼ r2ffiffiffiffiffiffiffiffiffiffiffi1þ a

p; (41)

and

X lmat ¼ �oL2: (42)

L1 L2

Mr1 r2

Rl

I1 I2

V0

[Z ] =r1 + jwL1

r2 + jwL2

jwM

jwM

Fig. 9 Two-port impedance matrix network for modeling wireless charging system using magnetic field coupling


Page 11 of 24

The power transfer efficiency in terms of the input power can be derived as

�mat ¼1� ffiffiffiffiffiffiffiffiffiffiffi

1þ ap� �2a

: (43)

Equations 41, 42, and 43 agree completely with Eqs. 16, 17, and 19, demonstrating the fact that theimpedance matching condition is nothing but the condition to achieve the maximum power transferefficiency. Therefore, in developing a wireless charging system based on the near-field coupling approach,the biggest challenge is to keep the impedance matching condition being satisfied when the transmittingantenna and receiving antenna are moving relative to each other. It is required in the practical systemdesign to adaptively change the antenna geometry or the impedance matching network to keep satisfyingthe impedance matching condition at both transmitting and receiving ports.

Here, the analysis model shown in Fig. 4 is again solved by using the impedance matrix approach, butthe impedancematrix is numerically calculated by using the method of moments, one of the most effectivefull-wave electromagnetic analysis methods.

Corresponding to radius of the solenoid coils, the optimized load impedance to achieve the maximumpower transfer efficiency can be obtained by using Eqs. 41 and 42, as shown in Fig. 10. Compared with theresults shown in Fig. 6, the reactance is almost the same, but the resistance is very different. The maximumpower transfer efficiency, which is calculated by using Eq. 43 under the impedance match condition, isshown in Fig. 11. Efficiency drops greatly when radius of the coil becomes small, which is very differentfrom that obtained in the previous section. The reason for these large differences in calculated efficiency isdue to the fact that mutual coupling between coils, radiation loss, as well as conducting loss of the coils areapproximately calculated by using the analytical forms in section “Circuit Theory” but accuratelycalculated by the method of moments in this section. When the distance between the coils changes, thematched load impedance is shown in Fig. 12, and the maximum efficiency under the condition ofimpedance matching is shown in Fig. 13. These analysis results provide important knowledge to designantenna load impedance and evaluate the maximum power transfer efficiency of the wireless chargingsystem.

010 20 30 40 50 60

0.2

0.4

0.6

0.8

1

–5

–4

–3

–2

–1

0

f = 85kHz

l = 100cm

N = 100

Ra = 1mm

d = 50cm

Full-wave

RIm

at [k

Ω]

XImat

RImatX

Imat [kΩ

]

a [cm]

Fig. 10 Matched load impedance versus coil radius for the model using two solenoid coils


Page 12 of 24

0 10 20 30 40 50 60

20

40

60

80

100

f = 85kHzl = 100cmN = 100Ra = 1mmd = 50cm

Full-wave

a [cm]

h mat

[%]

Fig. 11 Maximuam power transfer efficiency versus coil radius when load impedance is matched

f = 85kHzl = 100cmN = 100Ra = 1mma = 20cm

Full-wave

r Imat

[kΩ

]

rImat

XImat

XIm

at [Ω]

d [cm]0 20 40 60 80 100

10

20

30

40

50

–700

–650

–600

Fig. 12 Matched load impedance versus coil distance

20

40

60

80

100

d [cm]

Full-wave

0 20 40 60 80 100

h mat

[%]

f = 85kHzl = 100cmN = 100Ra = 1mma = 20cm

Fig. 13 Maximum power transfer efficiency versus coil distance when load impedance is matched


Page 13 of 24

Scattering Matrix Approach

The antennas in wireless charging system can be also analyzed by using the scattering matrix approach asshown in Fig. 14, where the system consisting of transmitting port and receiving port is again expressed asa two-port network as in the last section. Port 1 is the transmitting port including the transmitting antennaand its load impedance Zs, and Port 2 is the receiving port including receiving antenna and its loadimpedance Zl. Here, instead of impedance matrix, the scattering matrix S is used to express the two-portnetwork properties. The scattering parameters are very effective in evaluating the performance ofmultiport network, which are easily measured using a vector network analyzer and calculated by manycommercial full-wave electromagnetic simulators.

The reflection coefficients of the internal impedance Zs and load impedance Zl are

Gs ¼ Zs � Z0

Zs þ Z0; (44)

and

Gl ¼ Zl � Z0

Zl þ Z0; (45)

respectively, where Z0 represents the reference impedance of 50 Ω, the same with that in the scatteringmatrix. The condition of conjugate impedance matching becomes

Gs ¼ G�in; (46)

Gl ¼ G�out; (47)

where Gin and Gout are the reflection coefficient at Port 1 and Port 2, respectively, and are expressed as

Gin ¼ S11 þ S12S21Gl

1� S22Gl(48)

and

Gout ¼ S22 þ S12S21Gs

1� S11Gs(49)

The optimal reflection coefficients for maximum power transfer efficiency can be obtained by solvingEquations 46 and 47 as

Zs

ZlV0 Port 1 Port 2

a1

S11

S21 S22

S12

a2

b2b1

Fig. 14 Two-port network for modeling antennas in wireless charging systems


Page 14 of 24

Gsm ¼ B1 �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiB1

2 � 4jC1j2p

2C1; (50)

and

Glm ¼B2 �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiB22 � 4jC2j2

q2C2

; (51)

where

B1 ¼ 1þ jS11j2 � jS22j2 � jDj2; (52)

C1 ¼ S11 � DS�22; (53)

B2 ¼ 1þ jS22j2 � jS11j2 � jDj2; (54)

C2 ¼ S22 � DS�11; (55)

D ¼ S11S22 � S12S21: (56)

The optimal impedance of the voltage source and load impedance can be obtained using Eqs. 44 and 45from those optimal reflection coefficients given by Eqs. 50 and 51.

On the other hand, the power transfer efficiency can be expressed in terms of the S parameters and thereflection coefficients at the input and output port,

� ¼ jb2j2 � ja2j2ja1j2 ¼

1� Glj j2� �

1� Gsj j2� �

S21j j2

1� S11Gsð Þ 1� S22Glð Þ � S12S21GsGlj j2 (57)

where the efficiency can be calculated if the values of Zs and Zl are given while the maximum efficiency isavailable when Zs and Zl are the optimal impedance, namely, complex conjugate matched impedance.

Antenna Modeling and Analysis Using Scattering Matrix Approach

Antenna ModelsTwo kinds of antennas are studied; dipole antenna and loop antenna. When these antennas are used fornear-field coupling, a small dipole antenna is used for electric field coupling while a small loop antenna isused for magnetic field coupling. Although these conical models of the antennas are used in the study,these results and observations from the numerical simulations provide theoretical insight into how todesign antennas for wireless charging systems based on the near-field coupling approach.

Figure 15 shows a dipole–dipole model. The length of the wire dipole is 2l; the antenna distance is d.The two antennas are located parallel with the z axis. The internal impedance of the voltage source is Zs,and the load impedance connected with the receiving antenna is Zl. Figure 16 gives a loop–loop model.The circular loop antenna has a diameter of D separated at distance of d. The axes of two loop antennascoincide with x axis. All the antennas are made of conducting wire of radius a.


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In this chapter, the method of moments is used to numerically analyze the antennas to calculate theS parameters of the two-port network.

Maximum Power Transfer Efficiency Without Consideration of Loss in Antennas andMatching CircuitsWhen the antenna size is fixed, the maximum power transfer efficiency under the condition of conjugateimpedance matching at the two ports is shown by changing the antenna distance d. The numerical resultsare shown in Fig. 17. Here, the dipole length 2l and loop diameter D are 0.1l, and it is assumed that theantenna is made of electrically perfect conductor. It is found that the power transfer efficiency rises up to100 %when transmitting and receiving antennas are coming close to each other. However, in the practicalwireless charging system, the power transfer efficiency is degraded by the power loss which includesantenna conducting loss, radiation loss, and return loss of antennas. When the antennas are electricallysmall and antenna distance is electrically small, the radiation power is much less than the coupled power.Therefore, if the condition of impedance matching at the two ports is satisfied and antenna conducting lossis not considered, it is reasonable that the power transfer efficiency should approach to 100 %. Theefficiency decreases when the distance becomes large because the radiation power from the transmittingand receiving antennas increases when the two antennas are moved far away from each other.

In Fig. 18, the relationship between the maximum power transfer efficiency and antenna size is shown.It is found that the maximum power transfer efficiency could be increased by reducing the antenna size todecrease the radiation power. Theoretically speaking, the result is true if the conducting loss is ignored.However, as shown in the following discussion, the conducting loss of the antenna, as well as the

Fig. 16 Loop–loop model for wireless charging system

Fig. 15 Dipole–dipole model for wireless charging system


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conducting loss in the matching circuits of antennas, may dominate the loss when the antenna sizebecomes extremely small and decrease the maximum power transfer efficiency on the contrary. Theefficiency of loop–loop drops more than that of dipole–dipole because the loop has a larger antennaeffective aperture and radiates more power than the dipole in the case of D = 2l.

Maximum Power Transfer Efficiency with Consideration of Loss in Antennas andMatching CircuitsIt was known that antennas in the wireless charging system should be electrically small to reduce theradiation loss as discussed above. However, the conducting loss of the antennas cannot be ignored anymore as the antenna is electrically small. Furthermore, the ohmic loss in the matching circuit should beconsidered in analyzing the maximum power transfer efficiency. The following numerical results showthe importance of considering ohmic loss in antennas as well as in impedance matching circuits.

0 0.05 0.1 0.15 0.2 0.25

20

40

60

80

100

Dipole - Dipole2l = 0.1λ

Loop - LoopD = 0.1λ

h [%

]

d [λ]

Fig. 17 The maximum power transfer efficiency as a function of antenna distance for dipole–dipole and loop–loop models

0 0.1 0.2 0.3 0.4 0.5

20

40

60

80

100

2l [λ] for DipolesD [λ] for Loops

d = 0.1λ

Loop - Loop

Dipole - Dipole

h [%

]

Fig. 18 The maximum power transfer efficiency as a function of antenna size for dipole–dipole and loop–loop models withoutconducting loss in antennas


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The impedance matching networks are added into the two-port network to change the optimalimpedance to 50 Ω at both sides as shown in Fig. 19. There are many types of the impedance matchingnetworks such as L-section matching, quarter wave transformer, and single-stub tuning. L-sectionmatching uses two reactive elements to match an arbitrary impedance to an arbitrary desired impedance.This technique is very effective in low-frequency application. In this chapter, the L-section matchingnetworks as shown in Fig. 20 are used to match the optimized impedance Zopt, which is required tomaximize the efficiency. In this case, the internal impedance of voltage source and the load impedance areassumed to be 50 Ω. There are two configurations for an L-section matching network as shown in Fig. 20.Assume that Zopt has a real part of Ropt. If the normalized value of Ropt[O]/50 is larger than unit, theconfiguration (a) should be selected while if the Ropt[O]/50 is smaller than unit, the configuration(b) should be used. The reactive elements X and B may be either an inductance L or a capacitance C,depending on the value of normalized Zopt. In the wireless charging applications, because the frequency isusually very low and the matching circuit size is electrically small, lumped element inductors andcapacitors can be used. The analytic solutions for the reactive elements X and B are available in reference(Pozar 1998).

The ohmic loss of these lumped elements in the impedance matching circuits is expressed in terms ofQ value. It is found that the Q value of a capacitor is generally higher than that of an inductor. A typicalQ value of a commercial inductor and capacitor is assumed to be QL = 100 and QC = 200, respectively,in this chapter. The antenna conductor is assumed to be copper with its conductivity of sCu = 5.8 � 107

S/m.Figures 21 and 22 show the relationship between the maximum efficiency and antenna distance when

antenna size is fixed for cases of dipole–dipole and loop–loop transmission, respectively. In these figures,the results are compared when only copper loss is considered and when both copper loss and loss ofmatching circuits are considered. It is found that the copper loss does not degrade the efficiency much,while loss of matching network degrades the efficiency significantly. When transmission distance is thesame and the two types of antennas have approximately the same electrical size, the maximum efficiencyof loop–loop transmission is larger than that of dipole–dipole transmission. Therefore, the loop–loop

Zs = 50Ω

Zl = 50ΩV0 Port 1

Matching Networks Matching Networks

Port 2

S11

S21 S22

S12

Fig. 19 Two-port network combined with impedance matching circuits for modeling WPT system

50ΩZopt

jX

jB 50ΩZopt

jX

jB

Matching Networks

a b

Matching Networks

Fig. 20 L-section impedance matching circuits


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transmission is usually superior to the dipole–dipole transmission in terms of efficiency if the impedancematching condition is satisfied.

Figures. 23 and 24 show the relationship between the maximum efficiency and antenna size whenantenna distance is fixed to be 0.1 l for dipole–dipole and loop–loop transmission, respectively. When theohmic loss of impedance matching circuits is considered, the efficiency of the dipole system decreasesrapidly as the antenna size becomes small. However, for the loop–loop configuration, there is an optimalloop size, in the range ofD = 0.1 l to 0.15 l. This is because the efficiency is reduced due to the increaseof the radiation loss when D becomes large but is also reduced due to the increase of the ohmic losseswhenD is small. Thus, an optimal loop size exists in the middle. Numerical results of investigation on theloss of power transfer system are shown in Figs. 25 and 26, which give the fraction of loss as a function ofantenna size for dipole–dipole and loop–loop models, respectively. Here, a little mismatch loss isobserved because the impedance matching circuit was designed when ohmic loss in the matching circuitswas omitted. It is found that the loss in the matching circuits dominates the loss and is the most important

0 0.05 0.1 0.15 0.2 0.25

20

40

60

80

100Dipole - Dipole2l = 0.1 λf = 3 MHz

Only σCu

σCu + (QL = 100,Qc =200)

h [%

]

d [λ]

Fig. 21 The maximum power transfer efficiency as a function of antenna distance d for dipole–dipole model when ohmic lossof antennas and impedance matching circuits are considered

0 0.05 0.1 0.15 0.2 0.25

20

40

60

80

100Loop - LoopD = 0.1 λf = 3 MHz

Only σCu

σCu + (QL = 100, QC =200)

h [%

]

d [λ]

Fig. 22 The maximum power transfer efficiency as a function of antenna distance d for loop–loop model when ohmic loss ofantennas and impedance matching circuits are considered


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factor degrading the power transfer efficiency when antennas are electrically small. When antenna sizebecomes large, the radiation loss increases rapidly and becomes a dominant factor to decrease theefficiency.

Recent Application Developments, Standards, and Challenges

Development and Challenges on Antenna Technology for WPTAs described above, the impedance matching for both transmitting and receiving antennas is required toobtain the maximum value of efficiency of the WPT. However, it is not easy to keep the impedancematching condition for mobile devices where the transmitting antenna and receiving antenna are movingrelative to each other. In near-field WPT, because the transmitting antennas and receiving antennas arestrongly coupled with each other, a little variation of antenna positions and direction of antenna

0 0.1 0.2 0.3 0.4 0.25

20

40

60

80

100

Diploe - Dipoled = 0.1 λf = 3 MHz

Only σCu

σCu + (QL = 100, QC =200)

h [%

]

2l [λ]

Fig. 23 The maximum power transfer efficiency as a function of antenna size for dipole–dipole model when ohmic loss ofantennas and impedance matching circuits are considered

0 0.05 0.1 0.15 0.2 0.25

20

40

60

80

100

Loop - Loopd = 0.1 λf = 3 MHzOnly σCu

σCu + (QL = 100, QC =200)

h [%

]

D [λ]

Fig. 24 The maximum power transfer efficiency as a function of antenna size for loop–loop model when ohmic loss ofantennas and impedance matching circuits are considered


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polarization may cause a large variation of input impedance of these antennas, significantly decreasing theefficiency. Therefore, there are some researches focused on how to solve the problem of antennamisalignment.

There are two technical approaches to solve this problem. One is to use an impedance matching circuitto adaptively change the impedance at the input and output ports to compensate the impedancemismatching. For example, in Lee et al. (2014), a WPT system with a switchable capacitor array circuithas been presented, for compensating the variation of mutual coupling between two coils. It wasdemonstrated that the return loss can be improved greatly due to the operation of the capacitor arraycircuit when the distance between the two coils is changed. This approach was also introduced in Leeet al. (2012) and Aldhaher et al. (2014).

Another technical solution is to design an antenna that performs well even if it is misaligned. Forexample, a 3D loop with orthogonal polarizations is proposed as a WPT antenna to compensate the

Radiation Loss

0.10

10

20

30

40

50

Fra

ctio

n of

Los

s [%

]

60

70

80

90

100

0.15 0.2 0.25 0.3

2l [λ]

0.35 0.4 0.50.45

Mismatch Loss Loss in Matching Circuits

Fig. 25 Fraction of loss as a function of antenna size for dipole–dipole model when ohmic loss of antennas and impedancematching circuits are considered

Radiation Loss

0.050

10

20

30

40

50

Fra

ctio

n of

Los

s [%

]

60

70

80

90

100

0.075 0.1 0.125 0.15

D [λ]

0.175 0.2 0.250.225

Mismatch Loss Loss in Matching Circuits

Fig. 26 Fraction of loss as a function of antenna size for loop–loop model when ohmic loss of antennas and impedancematching circuits are considered


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efficiency drop due to the angular and lateral misalignment (Jonah et al. 2013). Also, a coil array wasapplied to a secondary coil instead of typical single coil to secure a stable power transmission efficiencyfor implantable devices (Ahn et al. 2014).

It is a big challenge to design antennas and AC-DC conversion circuits with high transmissionefficiency for mobile devices. More studies and researches are expected to make a practical near-fieldWPT system.

Some WPT StandardsIt is very important to the wireless charging industry to create a wireless power charging standard on aglobal scale that can allow electronic products and charging stations to be universally compatible witheach other. Currently, several global standards for wireless power transfer have been developed. Some ofthem are introduced in the following.

Wireless Power Consortium (WPC) developed a standard for wireless charging technology, called “Qi”(Hui 2013). The WPC, established in 2008, is an open-membership cooperation of Asian, European, andAmerican companies in diverse industries, including electronics manufacturers and original equipmentmanufacturers. The WPC published the Qi for products with an output power of 5 Wor less in 2009. TheWPC began to extend Qi specifications for medium power-consuming devices delivering power less than120 W. The Qi specifications are available as free public download from the WPC website.

The Alliance for Wireless Power (A4WP) developed an interface standard called Rezence for wirelesselectrical power transfer based on the near-field coupling. The A4WP was formed in May 2012 with agoal to create a WPT system using Rezence technology, which consists of a single power transmitter unitand one or more power receiver units for wireless power transfer. The A4WP announced an expansion ofthe Rezence standard up to 50 W in June 2014, which is expected to expand the range of wireless powertransfer for those products including laptops, tablets, and other consumer electronics.

The Power Matters Alliance (PMA), founded in March 2012, is a trade association whose mission is tocreate a better power paradigm for battery-equipped devices using wireless charging technology. Themembership of the PMA is made up of companies across a diverse set of industries including telecom-munication, consumer devices, automotive, retail, furniture, surfaces, and more, in order to guaranteeconsumers interoperable devices that employ wireless power technology. The PMA interface standarddescribes analog power transfer (inductive and resonant), digital transceiver communication, cloud-basedpower management, and environmental sustainability. The IEEE established the Wireless Power andCharging SystemsWorking Group (WPCS-WG) in October 2013, to develop the IEEE P2100.1 StandardSpecifications for Wireless Power and Charging Systems following the creation of the PMA. The A4WPand the PMA have signed an agreement aimed at establishing global interoperability of the two standardsin February 2014.

Activities of WPT standardization are also very active in Japan in recent years. IEICE TechnicalCommittee on Wireless Power Transfer provides a platform for exchanging new ideas at the frontier ofWPT researches. A consortium called Wireless Power Transfer Consortium for Practical Application(WiPoT) was founded in 2013 to accelerate the development of practical applications from the funda-mental studies of WPT.

Summary

It was described how to investigate antenna parameters from the viewpoint of antenna theory to obtain themaximum power transfer efficiency in the wireless charging system based on the near-field couplingapproach. The antenna parameters include geometry of transmitting and receiving antennas, electrical size


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of antennas, impedance matching for antennas, distance between transmitting and receiving antennas,conductor loss (ohmic loss) of antennas, ohmic loss of matching circuits, and so on, in order to clarify therelationship between the maximum efficiency and these parameters. The approaches introduced in thischapter would be helpful to design and develop antennas in the wireless charging systems, and thesimulation results can provide theoretical insight to how to optimize antenna design to improve the powertransfer efficiency.

Acknowledgments

Authors are grateful for assistance given by Mr. Brock Delong of Ohio State University and Mr. ShunMaruyama of Tohoku University.

Cross-References

▶Antennas in Microwave Wireless Power Transmission▶Near-Field Antenna Measurement Techniques▶Numerical Modeling in Antenna Engineering▶ Small Antennas (PIFA/PILA/Loading Antenna/etc)

References

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Documents

Antennas in Wireless Charging Systemsapplications is the space solar power system (SPS), which is a big project to collect sunlight in geostationary orbit, convert it to electromagnetic