Highly-Efficient Multi-Coil Wireless Power Transfer … 1 Mehdi Kiani GT-Bionics Lab, School of...

www.GTBionics.org 1

Mehdi Kiani

GT-Bionics Lab, School of Electrical and Computer Engineering

Georgia Institute of Technology, Atlanta, GA

Highly-Efficient Multi-Coil Wireless

Power Transfer

(WPT)

May 31, 2014

www.GTBionics.org 2

WPT Applications

2

Charging mobile electronics Implantable Medical Devices

(IMDs)

Charging electric cars

RFID

www.GTBionics.org 3

Coupled-mode Magnetic Resonance-based Power Transmission

A. Kurs, et. al, Science 2007

• Proposed by physicists at MIT based on coupled-mode theory (CMT)

• An alternative wireless power-transfer technique using typically four coils

• Goal: Increase the power transfer efficiency (PTE) at large coupling distances

60-W is

transferred

from 2-m

away

www.GTBionics.org 4

Questions?

• A need for a comprehensive circuit theory for coupled-mode magnetic resonance-based links

• A need for circuit theory based on the reflected-load theory (RLT) for multi-coil links

• Are coupled-mode magnetic resonance-based links always the optimal choice?

• A need for a new figure-of-merit (FoM) for high performance multi-coil design

vs.

Resonant-magnetic coupling Inductive coupling

www.GTBionics.org 5

Calculating Power Transfer Efficiency (PTE) based on RLT

• PTE is highly dependent

on: k23, Q2, and Q3

• Secondary R3L3C3 can be

reflected onto the primary:

LLref QLkRR QLLkR 320

2

233

2

332

2

23 )||)(/(

)/(1)/)(/( 2

232

2

0

2

23323 kLkCLLCref

Q3L = Q3QL / (Q3+QL)

R.R. Harrison, ISCAS 2007

Lref

ref

RRQ

RQ

RR

RPTE

3

2

3

3

2

3

2

L

L

L

L

Q

Q

QQk

QQk 3

32

2

23

32

2

23 .1

QL = RL / ω0L

M.W. Baker and R. Sarpeshkar, TBioCAS 2007

www.GTBionics.org 6

Maximizing PTE in 2-Coil Link

• PTE is highly dependent on RL

• RL is often predefined by the application

Impedance

Transformation

1) Matching circuits 2) Multiple coils

L

L

L

Lcoil

Q

Q

QQk

QQk 3

32

2

23

32

2

232 .

1

2/1

32

2

23

3,

)1( QQk

QQ PTEL

• For a given set of Q2, Q3 and k23 values, there is an

optimal load, RL,PTE, which can maximize the PTE at that

particular arrangement, such as the coupling distance.

L,PTEL,PTE QLR 30

M. Kiani and M. Ghovanloo, TBCAS 2011

www.GTBionics.org 7

PTE and Delivered Power (PDL) in Multi-coil Inductive Links based on RLT

)/( 1,0 iirefiiiL RRLQ

• In an m-coil link with negligible coupling between non-

neighboring coils

Rref from (i+1)th coil to the ith coil:

Loaded Q of the ith coil:

PTE between ith and (i+1)th coils:

m-coil link PTE:

PDL:

Four-coil link (m = 4)

Liiiiiiref QLkR )1(0

2

1,1,

)/( 1,1,1, iirefiiirefii RRR

LmL

m

i

iicoilm QQ /1

1

1,

mLmL L = RQ 0/ LmmL RL = Q /0

coilm

L

scoilmL

QQkR

VP

21

2

121

2

,1

1

2

Parallel load: Series load:


www.GTBionics.org 8

PTE in Multi-coil Inductive Links based on CMT

• In m-capacitively loaded resonators:

Four-coil link (m = 4)

Resonance width:

)()()()()(

212111 tFtajKtajdt

tdaS

)()()()(

1,1 tajKtajdt

tdammmmLm

m

)()()()()(

11,1,1 tajKtajKtajdt

tdaiiiiiiii

i

21

1

m

i m

iiLm

L

S

Lcoilm

A

AP

P

tj

ii eAta 0)(

22 iii AP

ii Q2/0

Coupling rate: 2/1,01, iiii kK

PTE from CMT is identical to the one from RLT!

M. Kiani and M. Ghovanloo, TCAS-I 2012

www.GTBionics.org 9

Resonant Magnetic Coupling vs. Inductive Coupling (Transient)

CMT transient response is accurate when

coils coupling is weak and coils quality

factor is very high!

1) Mid-range high-Q condition 2) Short-range low-Q condition


www.GTBionics.org 10

3-Coil Inductive Link

• L3-L4 inductive link provides designers with a DoF (M34) to adjust the reflected load on to L3 to be the optimal value: RL,PTE

• Loosely coupled L2-L3 link is designed for optimal RL,PTE

• Inductive link optimization is decoupled from RL

• L3-L4 inductive link PTE is high as their coupling distance is small

L,PTEL,PTE QLR 30 2/1

32

2

23

3,

)1( QQk

QQ PTEL

L

L

LL

Lcoil

Q

Q

QQkQQkQQk

QQkQQk 4

43

2

3443

2

3432

2

23

43

2

3432

2

2334233 .

)]1)(1[(

))((

L2

L3

L4



Maximizing PTE in the 3-Coil Link

By changing k34

(and Rref,3), the

3-coil PTE can be

kept at maximum

for a wide range

of RL.

A 2-coil link does not provide this flexibility, and PTE maximizes

only for a specific RL value.



4-Coil Inductive Link

• 4-Coil link adds an additional DoF for impedance matching on the source side

• If k12 is large, the reflected load onto L1 increases dramatically, which helps maximize the PTE at the cost of reducing PDL

L

L

LL

Lcoil

Q

Q

QQkQQkQQkQQkQQk

QQkQQkQQk 4

43

2

3432

2

2332

2

2343

2

3421

2

12

43

2

3432

2

2321

2

123423124

]1].[)1).(1[(

))()((..



PTE and PDL in 3-Coil Link

Maximizing PTE should

not be at the cost of

decreasing PDL

L

L

L

LscoilL

Q

Q

QQkQQk

QQkQQk

R

VP 4

2

43

2

3432

2

23

43

2

3432

2

23

2

2

3,)1(

))((

2

2/1

32

43

2

34,23

1

QQ

QQkk L

PDL

2/1

43

32

2

23,34

1

L

PDLQQ

QQkk

The optimal design maximizes

both PTE and PDL



PTE and PDL in 4-Coil Link

• If k12 is large enough, 4-

coil can tolerate

variations in coil

separation (k23) and

maintain a large PTE

• Large k12 reduces the

available power from the

source

• Small overlap between

high PTE and PDL

areas



3-Coil vs. 4-Coil Link (Measurements)

4-coil link (PDL = 4.4 mW)

3-coil link (PDL = 260 mW) Vs = 1 V



Resonant-Magnetic Coupling vs. Inductive Coupling (PTE)

Calculated PTEs were similar from CMT and RLT and matched very

well with measurements!

Four-coil link measurement

setup. Three and two-coil

links used similar coils except

L1 and L4, respectively.



A New Figure of Merit (FoM) for Inductive Power Transmission

• Conventional design merits are either PTE or PDL

• How to balance PTE and PDL?

• How to choose between 2-, 3-, and 4-coil links?

2

,

s

coilmL

n

coilm

V

PFoM

n: PTE weight, which

depends on the application

• FoM effect on PTE and PDL drop:

max,max , LP

: FoM is maximized FoMLFoM P ,,2

2

max,

,max,

,

max

max

)2(

,2

1

n

n

P

PPP

n

L

FoMLL

LossL

FoMLoss

: PTE and PDL are

maximized

M. Kiani and M. Ghovanloo, TIE 2013


PTE vs. PDL Loss based on FoM for 2-, 3-, and 4-coil Links

n = 2 results in

similar PTE and

PDL drops = 25%

2

,

s

coilmL

n

coilm

V

PFoM

n = 0 FoM ~ PDL

n → ∞ FoM ~ PTE



Optimal 2-coil Link for IMDs based on FoM

• 2-coil Link for

IMDs

• Rx coil dia. =

10 mm

• Vs = 1 V

• Rs = 0.5 Ω

• RL = 100 Ω

• f0 = 13.56 MHz

• d23 = 10 mm

At d23 = 10 mm, FoM-optimized link provides 47% more PTE than the PDL-optimized link and 16 times larger PDL than the PTE-optimized link.



Comparing 2- 3- & 4-Coil Links for IMDs

• At d23 = 10 mm, 4-coil link provides 4.9% more PTE and 11 times less PDL than an equivalent 3-coil. At d23 = 20 mm, PTE difference is 7.7%, while PTE of 3-coil is 192 times larger than an equivalent 4-coil

• For large Rs, 4-coil is optimal

An FoM including both PTE and PDL is needed to differentiate between 2-,3-, and 4-coil links!



Optimal Multi-coil Link for Charging Handheld Mobile Devices based on FoM

Rx coil dia. = 4 cm, Rs = 0.5 Ω, RL = 5 Ω, f0 = 13.56 MHz, d23 = 10 cm

The 4-coil link has superior FoM at d23 = 10 cm at the cost of much lower PTE, and consequently the FoM, at shorter coupling distances.



Optimal Multi-coil Link based on FoM

2-Coil Link 3-Coil Link 4-Coil Link

Strong coupling (k)

Weak coupling (k)

Large PDL (small Rs)

Small PDL (large Rs)

Coupling variations &

small Rs

Coupling variations &

large Rs


Highly-Efficient Multi-Coil Wireless Power Transfer … 1 Mehdi Kiani GT-Bionics Lab, School of...

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