! 奈良先端科学技術大学院大学 情報科学研究科 ネットワークシステム学研究室

イノベーション・ジャパン２０１３

左図のように電力源と給電線をインピーダンス整合器を介して接続し、給電線近傍にある２次インダクタ回路と磁界結合する構成となっています。一次側二次側ともに設計周波数で共振するように回路定数を定め、アンテナとして動作します。

ワイヤレス給電技術の応用

EV普及の加速

生活インフラの再構築

安全・安心社会

近年、ワイヤレス給電技術は非常に注目されており、スマートフォンを置くだけで充電できる充電器が出現しました。現在主流となっている磁界共鳴を用いたワイヤレス給電方式は、回路を共振させて離れて配置した２つのコイルの間を電力

を伝送します。効率よく電力を伝送するには、コイル形状、配置、インピーダンスの整合条件を成立させる必要があります。本研究ではコイルを用いずに広域な給電エリアを展開可能な新方式を提案しています。

平行二線の周囲に発生する磁界を二次インダクタで結合する

バッテリレスでモバイル機器の軽量化を目指す

広域ワイヤレス給電

スマートフォン

電気自動車

電動アシスト付自転車

�����

����������

�����������

���

�� �

�����

! 奈良先端科学技術大学院大学 情報科学研究科 ネットワークシステム学研究室

イノベーション・ジャパン２０１３

磁気結合時の等価回路を用いて負荷に供給する電力が最大となる最適負荷抵抗値の値を導出できます。また電磁界シミュレーションによって一次回路と空間を隔てた二次回路の間の相互インダクタンスを評価しました。

MHz以上の高周波を電力搬送波とすることで、二次側回路の小型化・軽量化が可能です

平行二線で一次側を構成するため、柔軟なレイアウト変更が可能です。

通過電力、反射電力、電力消費中のインピーダンスのリアルタイム測定が可能です。

高速自動整合による無効電力の低減が可能です。

一次側を高周波給電線とすることで、放射電磁界はほとんどありません。

波長と線路長との関係で一次側は分布定数線路となり、２次側の場所によってインピーダンスが変化します。

☢⏺⤖

ଵ

ܯ ଵݔଶݔ

➼౯ᅇ㊰

Ԣଵ ଶ

ଵ ଶ

ଵ ଶ ଵ ଶ ଵ ଶ ଵ

ଶ

ଶ

ଶଵ

等価回路解析、電磁界シミュレーション

一次回路と二次回路を共振させ、相互インダクタンスが求まれば、反射電力を最小化できます。

電車模型を用いたデモンストレーション

共同研究企業

株式会社ダイヘン 技術開発本部

電力源の回路のインピーダンス

Z0 =

!L

C[!] (1)

Z1 = jZ0 tan !x1[!] (2)Z2 = jZ0 tan !x2[!] (3)

1

特性インピーダンス

Z0 =

!L

C[!] (1)

Z1 = jZ0 tan !x1[!] (2)Z2 = jZ0 tan !x2[!] (3)

1

V0 10 20 30 40 50

0

0.5

1

1.5

2

2.5

3

3.5

4

Frequency, f [MHz]

RL op

t [Ω]

50[nH]100[nH]500[nH]

M=

0 0.5 1 1.5 2 2.5 3 3.5 4−55

−50

−45

−40

−35

−30

RL [Ω]

Rel

ativ

e po

wer

leve

l [dB

]

50[nH]100[nH]500[nH]

M=

二次側負荷抵抗値にかかる相対電圧値の関係(電力搬送波周波数:13.56MHz)

電力搬送波周波数に対する二次側回路の最適負荷抵抗値の関係。

Parallel line responses as distributed constant circuit for highfrequency signals, and its parameters are given by

L =

µ

⇡cosh

�1

✓d

2r

◆, [H/m] (1)

C =

⇡✏

cosh

�1 �d2r

� , [F/m] (2)

R =

1

r

rµf

⇡✏, [⌦/m] (3)

Z0 =

rL

C, [⌦] (4)

where L, C, R, and Z0 is inductance, capacitance, resistance,and characteristics impedance, respectively. When d, 2r are 4[mm] and 1 [mm], respectively, the Z0 = 525.46 [⌦] is derivedat the frequency of 13.56MHz.

B. Equivalent Circuit ☢⏺⤖

ଵ

ܯ ଵݔଶݔ

Fig. 3. Model of magnetic coupling

Figure 3 shows the model of magnetic coupling betweenparallel line feeder and the receiver. The receiver has certainvalue of impedance, ZL. The Z1, ZL, x1, x2, and M aresource impedance, load impedance, load positions and mutualinductance, respectively. Magnetic coupling can be presented

➼౯ᅇ㊰

Ԣଵ ଶ

ଶ ଶ ଶ

ଶ ଶ↓ᦆኻ䛺䜙

ଶ ଶ

ଵଶ

Fig. 4. Equivalent circuit of Fig. 3

by using inductors with mutual inductance. Figure 4 showsthe equivalent circuit shown in Fig. 3[4]. The Z 0

1 = R1 + jX1

is combined impedance, power source circuit, Z1, and feederline with its length of x1.

The Z2 can be represented as follows,

Z2 = Z0tanh ↵x2 + j tan�x2

1 + j tanh ↵x2 tan�x2(5)

where ↵, � are attenuation and phase constant, respectively.If parallel line is lossless media, Z2 can be represented asZ2 = jZ0 tan�x2,

➼౯ᅇ㊰

Ԣଵ ଶ

ଵ

ଶ

Fig. 5. Equivalent circuit transformed from Fig. 4➼౯ᅇ㊰

Ԣଵ ଶ

ଵ ଶ

ଵ ଶ ଵ ଶ ଵ ଶ ଵ

ଶ

ଶ

ଶଵ

Fig. 6. Equivalent circuit transformed from Fig.5

Figure 5 shows the equivalent circuit that is transformedfrom Fig. 4. Figure 6 shows the equivalent circuit that is trans-formed from Fig. 5. As a result of these transformations, therelationship between source voltage, V , and I2 is representedas

V =

(Z 01+Z2+j!L1)(j!(L2�M)+ZL)+j!M(Z 0

1+Z2+j!(L1�M))

j!MI2.

(6)It is assumed that the load impedance, ZL, is described as

RL + jXL. When the imaginary part of Z 01 + Z2 + jwL1

is cancelled out by tuning X1, and jwL2 is canceled out bytuning XL, Eq. (6) is

V =

(R1RL + w2M2)

2

jwMI2. (7)

Eq. (7) shows the relationship between source voltage andthe load current when reactance components of primary andsecondary coils are cancelled out at not magnetic coupling,but coils are completely isolated.

III. SUPPLIED POWER TO THE LOAD

The supplied power to the load, PL, can be presented by|I2|2RL,

PL = |V |2 !2M2RL

|R1RL + !2M2|2 . (8)

In Eq.(8), coefficient of |V |2 depends on frequency, mutualinductance, load resistance, and source impedance. Figure7 shows the relationship between RL and relative powerlevel without impedance matching. The parameter is mutualinductance, M . It is found that the coefficient of V 2 has apeak value at a certain value of load resistance, RL.

Parallel line responses as distributed constant circuit for highfrequency signals, and its parameters are given by

L =

µ

⇡cosh

�1

✓d

2r

◆, [H/m] (1)

C =

⇡✏

cosh

�1 �d2r

� , [F/m] (2)

R =

1

r

rµf

⇡✏, [⌦/m] (3)

Z0 =

rL

C, [⌦] (4)

where L, C, R, and Z0 is inductance, capacitance, resistance,and characteristics impedance, respectively. When d, 2r are 4[mm] and 1 [mm], respectively, the Z0 = 525.46 [⌦] is derivedat the frequency of 13.56MHz.

B. Equivalent Circuit ☢⏺⤖

ଵ

ܯ ଵݔଶݔ

Fig. 3. Model of magnetic coupling

Figure 3 shows the model of magnetic coupling betweenparallel line feeder and the receiver. The receiver has certainvalue of impedance, ZL. The Z1, ZL, x1, x2, and M aresource impedance, load impedance, load positions and mutualinductance, respectively. Magnetic coupling can be presented

➼౯ᅇ㊰

Ԣଵ ଶ

ଶ ଶ ଶ

ଶ ଶ↓ᦆኻ䛺䜙

ଶ ଶ

ଵଶ

Fig. 4. Equivalent circuit of Fig. 3

by using inductors with mutual inductance. Figure 4 showsthe equivalent circuit shown in Fig. 3[4]. The Z 0

1 = R1 + jX1

is combined impedance, power source circuit, Z1, and feederline with its length of x1.

The Z2 can be represented as follows,

Z2 = Z0tanh ↵x2 + j tan�x2

1 + j tanh ↵x2 tan�x2(5)

where ↵, � are attenuation and phase constant, respectively.If parallel line is lossless media, Z2 can be represented asZ2 = jZ0 tan�x2,

➼౯ᅇ㊰

Ԣଵ ଶ

ଵ

ଶ

Fig. 5. Equivalent circuit transformed from Fig. 4➼౯ᅇ㊰

Ԣଵ ଶ

ଵ ଶ

ଵ ଶ ଵ ଶ ଵ ଶ ଵ

ଶ

ଶ

ଶଵ

Fig. 6. Equivalent circuit transformed from Fig.5

Figure 5 shows the equivalent circuit that is transformedfrom Fig. 4. Figure 6 shows the equivalent circuit that is trans-formed from Fig. 5. As a result of these transformations, therelationship between source voltage, V , and I2 is representedas

V =

(Z 01+Z2+j!L1)(j!(L2�M)+ZL)+j!M(Z 0

1+Z2+j!(L1�M))

j!MI2.

(6)It is assumed that the load impedance, ZL, is described as

RL + jXL. When the imaginary part of Z 01 + Z2 + jwL1

is cancelled out by tuning X1, and jwL2 is canceled out bytuning XL, Eq. (6) is

V =

(R1RL + w2M2)

2

jwMI2. (7)

Eq. (7) shows the relationship between source voltage andthe load current when reactance components of primary andsecondary coils are cancelled out at not magnetic coupling,but coils are completely isolated.

III. SUPPLIED POWER TO THE LOAD

The supplied power to the load, PL, can be presented by|I2|2RL,

PL = |V |2 !2M2RL

|R1RL + !2M2|2 . (8)

In Eq.(8), coefficient of |V |2 depends on frequency, mutualinductance, load resistance, and source impedance. Figure7 shows the relationship between RL and relative powerlevel without impedance matching. The parameter is mutualinductance, M . It is found that the coefficient of V 2 has apeak value at a certain value of load resistance, RL.

負荷に供給される電力

0 0.5 1 1.5 2 2.5 3 3.5 4−55

−50

−45

−40

−35

−30

RL [Ω]

Rela

tive

pow

er le

vel [

dB]

50[nH]100[nH]500[nH]

Fig. 7. Relationship between RL and relative power level without impedancematching. (f=13.56 MHz, R1=Z0)

The maximum value of coefficient is obtained by solving@PL/@RL = 0,

RLopt

=

!2M2

R1. (9)

0 10 20 30 40 500

0.5

1

1.5

2

2.5

3

3.5

4

Frequency, f [MHz]

R L opt [Ω

]

50[nH]100[nH]500[nH]

Fig. 8. Relationship between RL and frequency (R1 = Z0)

An example of tuning of R1 is to equal to the characteristicimpedance of the parallel line feeder, R1 = Z0. Figure 8shows the relationship between RL

opt

and frequency with theparameter of mutual inductance. If the mutual inductance ishigh, the load resistance is increased drastically. For example,optimum load resistance is 0.0345[⌦] in case of M = 50 [nH]and f = 13.56 [MHz].

IV. SIMULATION AND PERFORMANCE EVALUATION

A. Setup and Parameter

Figure 9 shows the configuration of two parallel line forcomputer simulation[10]. Parallel line is located at 1-st layer.Small secondary coil simulated the load circuit, and it islocated at 3-rd layer. The 2-nd layer is filled by the air. Table

I shows the parameters used in the simulation. Copper is usedto the material of the coils. Coil length is defined as shownin Fig. 9. The length of primary coil is longer than secondaryone. Once the primary and secondary coils are setup at certainposition and certain length, mutual inductance between twocoils, M , can be evaluated by the computer simulation. Itis obtained by the k

pL1L2, where k is magnetic coupled

coefficient.

Distance between primary and secondary�

Length of secondary�

Input port�Output port�

Fig. 9. Configuration and location of feeder and secondary circuit

TABLE IPARAMETERS

d [mm] 402r [mm] 1f [MHz] 13.56

Conductivity [S/m] 5.9 ⇥ 107

Characteristic impedance [⌦] 525Length of secondary [mm] 100

Distance between primary and secondary [mm] 10

B. Mutual Inductance

Figure 10 shows the relationship among mutual inductance,length ratio, and RL

opt

. The ”Length ratio” is defined as a ratioof primary coil length and secondary one. Mutual inductanceis reversely proportional to length ratio. In this figure, mutualinductance is a function of length ratio, then optimum loadresistance, RL

opt

, is obtained from the mutual inductance. Forexample, when length ratio is 15, M of 50 [nH] is found.

0 50 100 150 2000

5

10

15

20

25

Mutual Inductance, M[nH]

Leng

th ra

tio

0 50 100 150 200

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

R L opt

Fig. 10. Relationship between length ratio, M , and RLopt

to achievemaximum power

0 0.5 1 1.5 2 2.5 3 3.5 4−55

−50

−45

−40

−35

−30

RL [Ω]

Rel

ativ

e po

wer

leve

l [dB

]

50[nH]100[nH]500[nH]

Fig. 7. Relationship between RL and relative power level without impedancematching. (f=13.56 MHz, R1=Z0)

The maximum value of coefficient is obtained by solving@PL/@RL = 0,

RLopt

=

!2M2

R1. (9)

0 10 20 30 40 500

0.5

1

1.5

2

2.5

3

3.5

4

Frequency, f [MHz]

RL op

t [Ω]

50[nH]100[nH]500[nH]

Fig. 8. Relationship between RL and frequency (R1 = Z0)

An example of tuning of R1 is to equal to the characteristicimpedance of the parallel line feeder, R1 = Z0. Figure 8shows the relationship between RL

opt

and frequency with theparameter of mutual inductance. If the mutual inductance ishigh, the load resistance is increased drastically. For example,optimum load resistance is 0.0345[⌦] in case of M = 50 [nH]and f = 13.56 [MHz].

IV. SIMULATION AND PERFORMANCE EVALUATION

A. Setup and Parameter

Figure 9 shows the configuration of two parallel line forcomputer simulation[10]. Parallel line is located at 1-st layer.Small secondary coil simulated the load circuit, and it islocated at 3-rd layer. The 2-nd layer is filled by the air. Table

I shows the parameters used in the simulation. Copper is usedto the material of the coils. Coil length is defined as shownin Fig. 9. The length of primary coil is longer than secondaryone. Once the primary and secondary coils are setup at certainposition and certain length, mutual inductance between twocoils, M , can be evaluated by the computer simulation. Itis obtained by the k

pL1L2, where k is magnetic coupled

coefficient.

Distance between primary and secondary�

Length of secondary�

Input port�Output port�

Fig. 9. Configuration and location of feeder and secondary circuit

TABLE IPARAMETERS

d [mm] 402r [mm] 1f [MHz] 13.56

Conductivity [S/m] 5.9 ⇥ 107

Characteristic impedance [⌦] 525Length of secondary [mm] 100

Distance between primary and secondary [mm] 10

B. Mutual Inductance

Figure 10 shows the relationship among mutual inductance,length ratio, and RL

opt

. The ”Length ratio” is defined as a ratioof primary coil length and secondary one. Mutual inductanceis reversely proportional to length ratio. In this figure, mutualinductance is a function of length ratio, then optimum loadresistance, RL

opt

, is obtained from the mutual inductance. Forexample, when length ratio is 15, M of 50 [nH] is found.

0 50 100 150 2000

5

10

15

20

25

Mutual Inductance, M[nH]

Leng

th ra

tio

0 50 100 150 200

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

RL op

t

Fig. 10. Relationship between length ratio, M , and RLopt

to achievemaximum power

最適負荷抵抗値

short

0 50 100 150 2000

5

10

15

20

25

Mutual Inductance, M[nH]

Leng

th ra

tio

0 50 100 150 200

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

RL op

t

一次側回路サイズと相互インダクタンスの関係(@13.56MHz)

0 0.5 1 1.5 2 2.5 3 3.5 4−55

−50

−45

−40

−35

−30

RL [Ω]

Rela

tive

pow

er le

vel [

dB]

50[nH]100[nH]500[nH]

Fig. 7. Relationship between RL and relative power level without impedancematching. (f=13.56 MHz, R1=Z0)

The maximum value of coefficient is obtained by solving@PL/@RL = 0,

RLopt

=

!2M2

R1. (9)

0 10 20 30 40 500

0.5

1

1.5

2

2.5

3

3.5

4

Frequency, f [MHz]

R L opt [Ω

]

50[nH]100[nH]500[nH]

Fig. 8. Relationship between RL and frequency (R1 = Z0)

An example of tuning of R1 is to equal to the characteristicimpedance of the parallel line feeder, R1 = Z0. Figure 8shows the relationship between RL

opt

and frequency with theparameter of mutual inductance. If the mutual inductance ishigh, the load resistance is increased drastically. For example,optimum load resistance is 0.0345[⌦] in case of M = 50 [nH]and f = 13.56 [MHz].

IV. SIMULATION AND PERFORMANCE EVALUATION

A. Setup and Parameter

Figure 9 shows the configuration of two parallel line forcomputer simulation[10]. Parallel line is located at 1-st layer.Small secondary coil simulated the load circuit, and it islocated at 3-rd layer. The 2-nd layer is filled by the air. Table

I shows the parameters used in the simulation. Copper is usedto the material of the coils. Coil length is defined as shownin Fig. 9. The length of primary coil is longer than secondaryone. Once the primary and secondary coils are setup at certainposition and certain length, mutual inductance between twocoils, M , can be evaluated by the computer simulation. Itis obtained by the k

pL1L2, where k is magnetic coupled

coefficient.

Distance between primary and secondary�

Length of secondary�

Input port�Output port�

Fig. 9. Configuration and location of feeder and secondary circuit

TABLE IPARAMETERS

d [mm] 402r [mm] 1f [MHz] 13.56

Conductivity [S/m] 5.9 ⇥ 107

Characteristic impedance [⌦] 525Length of secondary [mm] 100

Distance between primary and secondary [mm] 10

B. Mutual Inductance

Figure 10 shows the relationship among mutual inductance,length ratio, and RL

opt

. The ”Length ratio” is defined as a ratioof primary coil length and secondary one. Mutual inductanceis reversely proportional to length ratio. In this figure, mutualinductance is a function of length ratio, then optimum loadresistance, RL

opt

, is obtained from the mutual inductance. Forexample, when length ratio is 15, M of 50 [nH] is found.

0 50 100 150 2000

5

10

15

20

25

Mutual Inductance, M[nH]

Leng

th ra

tio

0 50 100 150 200

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

R L opt

Fig. 10. Relationship between length ratio, M , and RLopt

to achievemaximum power

シミュレーション諸元