design of a double-sided lclc compensated capacitive power

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JESTPE.2020.3030657, IEEE Journalof Emerging and Selected Topics in Power Electronics

1

Design of a Double-Sided LCLC CompensatedCapacitive Power Transfer System with Predesigned

Coupler Plate Voltage StressesJing Lian, Xiaohui Qu, Senior Member, IEEE, Xi Chen, Senior

Member, IEEE, and Chunting Chris Mi, Fellow, IEEE

Abstract—A high-performance capacitive power transfer (CP-T) system is expected to achieve the load-independent constantoutput, near-zero reactive power, and soft switching of powerswitches simultaneously, resulting in a reduced power stage,simple control circuitry, and minimum component ratings. How-ever, a well-compensated CPT system still suffers very highvoltage stresses among not only the main coupled plates butalso the leakage coupled plates due to the small coupling andedge emission, which increase the risk of air breakdown anddeteriorate the electromagnetic interference (EMI) issue. Tosolve this problem, the voltage stresses among such couplerplates should be predesigned at an acceptable level. This papersystematically analyzes characteristics of a double-sided LCLCcompensated CPT converter, which is proved to have enoughdesign freedom providing predesigned voltage stresses for twokinds of coupled plates. Also, three operating frequencies withload-independent constant current (CC) output and input zero-phase angle (ZPA) are found. Without reactive power in thecircuit, a parameter design method is proposed for the double-sided LCLC compensated CPT converter at each frequencyto satisfy the desired CC output and the predesigned voltagelimitations. In this way, the breakdown and EMI issues can bewell mitigated by the intended design and this method can also beextended to other CPT circuits. Finally, a CPT prototype is builtto verify the theoretical analysis with the predesigned voltagestresses among the coupler plates.

Index Terms—Capacitive power transfer, voltage stresses, L-CLC compensation, design freedom, parameter design.

I. INTRODUCTION

Nowadays, the wireless power transfer technology includinginductive power transfer (IPT) and capacitive power transfer(CPT) techniques has found many applications due to advan-tages of convenience, safety, and isolation [1]–[6]. The CPTsystems use metal plates as couplers, rather than expensiveLitz wires and heavy magnetic cores in IPT converters, whichcould reduce the cost and weight of the whole system. Also,the power transfer medium of CPT systems, i.e., electric fields,can effectively avoid eddy currents and corresponding losses

This work is supported in part by the National Natural Science Foundationof China (52077038), the Natural Science Foundation of Jiangsu Province(BK20181280), and Fundamental Research Funds for Central Universities ofChina.

J. Lian and X. Qu are with the School of Electrical Engineering, SoutheastUniversity and Jiangsu Key Laboratory of Smart Grid Technology andEquipment, Nanjing, 210096, China. Email: [email protected].

X. Chen is with GEIRI North America, San Jose, CA 95134 USA.C. C. Mi is with the Department of Electrical and Computer Engineering,

San Diego State University, San Diego, CA 92182 USA.

High Low

P1 P2

P3 P4

Fig. 1. Electric field emission around the coupler plates, where P1 and P2

are placed at the primary side and P3 and P4 are placed at the secondaryside. P1 with P3 and P2 with P4 are main coupled plates while P1 with P2

and P3 with P4 are leakage coupled plates.

in the nearby metals [7], [8]. Thus, CPT systems are superiorto IPT systems in some applications [9].

The coupled metal plates actually behave as capacitorsin the CPT system [10], which generate significant reactivepower in the circuit. The large reactive power will increasecomponent ratings and degrade the power transfer capability.Therefore, compensation networks are necessary to improvethese performances. Similar to a compensated IPT system [11],a well-compensated CPT system should desirably achieve thefollowing characteristics:

1) Zero phase angle (ZPA) between the input voltage andinput current: The realization of input ZPA can eliminatethe reactive power in the circuit and then minimize thecomponent volt-ampere (VA) ratings. Thus, the powertransfer capability can be improved effectively.

2) Soft switching of the driver circuit: When the inputZPA is permitted, the input impedance can be easilymodulated to be from purely resistive to slightly induc-tive for zero-voltage switching (ZVS) of MOSFETs orslightly capacitive for zero-current switching (ZCS) ofIGBTs. Soft switching can further reduce power lossesand switching noises.

3) Load-independent constant output: Constant current (C-C) or constant voltage (CV) output is required in manypractical applications, such as battery or super-capacitorcharging, LED lighting, and so on. A single-stage CP-T converter is expected to provide the desired load-independent output so that the front-end or back-endDC/DC regulator can be saved.

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2

LR Ou

1fL 2L

2fC1fC

ri

DCU

1Q

2Q

3Q

4Q

A

B

ABiABu ru

1D

2D

3D

4D

Oi

OC

RECi

1exC 2exC

1L 2fL1

P3P

2P

4P

Fig. 2. Schematic of a double-sided LCLC compensated CPT converter.

To satisfy the above requirements, some compensation cir-cuits in CPT systems have been proposed and analyzed, suchas a double-sided LC circuit [12], [13], a double-sided LCLCcircuit [14], [15], a four-coil compensation circuit [16], and soon. Some circuit design methods are given to improve transferefficiency [17]–[19]. Unlike the loosely coupled transformerin IPT systems, coupler plates in CPT systems behave asvery small coupling capacitances due to the low dielectriccoefficient in the air. Therefore, a large amount of electricfield emission is released around the plates, especially onthe edge of plates as shown in Fig. 1 [21]. Usually, theplates on the same primary or secondary side are placedclosely. From Fig. 1, the edge emission is more serious inthe region close to P1 and P2 or close to P3 and P4. Inthis way, there are high voltage stresses on the main couplingcapacitors formed by P1 and P3 or P2 and P4 and the leakagecapacitors formed by P1 and P2 or P3 and P4, which canreadily exceed the breakdown voltage limitation of 3 kV/mmin the coupler plates [22], and cause a large leakage electricfield radiation [23]. To solve the above issues, prior work[24] tries to maximize the coupling capacitance and thendecrease voltages on the main capacitors. Reference [16] usesresonant networks and an isolated transformer to regulate inputand output voltages of coupler plates, and then voltages onthe main coupled capacitors are decreased. Reference [25]reallocates voltage stresses of all compensation componentsand capacitive couplers by a mathematic calculation based ona double-sided CL compensation circuit.

However, the aforementioned works usually optimize thevoltage stresses only on the main coupled plates. From Fig. 1,the voltage stresses on the leakage coupled plates are alsocritical to be optimized [26]. Reference [27] identifies therelationship of voltage stresses between the main couplerplates and the leakage coupler plates based on a simple double-sided LC compensated CPT system. With a desired load-independent CC output and input ZPA, the double-sided LCcompensated CPT system has no freedom to optimize suchtwo kinds of voltage stresses. Therefore, a higher-order com-pensation circuit is needed here for the voltage optimizationof two kinds of coupled plates.

In this paper, a higher-order double-sided LCLC compensat-ed CPT converter with enough design freedom is systematical-ly analyzed to fulfill the predesigned voltage stresses amongthe coupled plates. Meanwhile, three operating frequencieswith load-independent constant current (CC) output and inputZPA are found in Section II. Without reactive power in the

(a) Structure of the coupler (b) Equivalent Π-type model

MC

P MC C−

S MC C−

x

y

z

P1 P2

P3 P4

l

d1

d

l

Fig. 3. Coupler structure and equivalent circuit model in the shadow areaof Fig. 2.

circuit, a parameter design method is proposed to satisfy therequired CC output and predesigned voltage stresses for bothmain coupled plates and leakage coupled plates, as detailedin Section III. This method can be readily extended to theother CPT systems. Finally, a 40 W double-sided LCLC CPTsystem is built and experimental results agree well with thetheoretical analysis in Section IV. Section V concludes thepaper.

II. CHARACTERISTIC ANALYSIS FOR INPUT ZPA ANDLOAD-INDEPENDENT CONSTANT OUTPUT

Fig. 2 shows the schematic of a double-sided LCLC com-pensated CPT system where the full-bridge inverter generatesthe high-frequency AC voltage uAB to power the resonantcircuit and two pairs of coupler plates P1, P2, P3, and P4.Lf1, Cf1, L1, and Cex1 construct the primary LCLC networkwhile Lf2, Cf2, L2, and Cex2 construct the secondary LCLCnetwork. The structure and dimensions of the coupler areshown in Fig. 3(a) where l is the plate length, d is the airdistance, and d1 is the distance between two plates on the sameside. A Π-type model with the equivalent primary capacitorCP , secondary capacitor CS , and mutual capacitor CM can beused in the metal plates, as shown in Fig. 3(b) [28]. The nativecoupling coefficient kC is defined as CM√

CPCS. With Cex1 and

Cex2 parallel to equivalent capacitors CP −CM and CS−CM

respectively, it defines that

C1 = Cex1 + CP and C2 = Cex2 + CS . (1)

Then the equivalent coupling coefficient k becomes

k =CM√C1C2

. (2)

And k < kC .To facilitate the analysis, the double-sided LCLC compen-

sated CPT converter in Fig. 2 can be driven by a purelysinusoidal AC voltage source Uin, i.e., the vector of the




3

rU

1fL 2L

2fC1fC 1 MC C−

2 MC C−

1L 2fL

inU

ER2u

1u1Cfu

1Lfu 1Lu 2Lu 2Lfu

MC

2Cfu

CMu

inI

rI

Fig. 4. Equivalent circuit of double-sided LCLC compensated CPT circuitusing Π-type model.

inU ER

1fL

1fC

AC

BC

CC

2fC

2fLinI

rI11

L12L

13L

21L

22L

23L

rU1

L 2L

A1 A2 A3

Fig. 5. Equivalent circuit of double-sided LCLC compensated CPT circuitusing T-type model. Each shadow denotes a T network.

fundamental component of uAB and delivers power to anequivalent load RE , as shown in Fig. 4. With the C filter,RL = π2RE

8 . Based on the reciprocity principle, Fig. 4 can befurther derived as an equivalent T-type network with CA, CB ,and CC , as shown in Fig. 5. Here, CA, CB , and CC satisfy

CA =C1C2 − C2

M

C2 − CM=

C1(1− k2)

1− k√

C1

C2

CB =C1C2 − C2

M

CM=

1− k2

k2CM

CC =C1C2 − C2

M

C1 − CM=

C2(1− k2)

1− k√

C2

C1

. (3)

A. One Frequency for Input ZPA and Load-independent Out-put

From Fig. 5, the primary compensation inductor L1 can bedivided into three parts in series, i.e., L11, L12, and L13 whilethe secondary L2 can be divided as L21, L22, and L13 in series.Then three T networks are given in different color shadows.To find a working angular frequency ω0 for the CPT converterhaving properties of input ZPA and load-independent output,every T network should satisfy Z1 = −Z2 = Z3 at ω0 inFig. 6 where

ω0 =1√

Lf1Cf1

=1√

Lf2Cf2

=1√

L11Cf1

=1√

L12CB

=1√

L13CA

=1√

L23Cf2

=1√

L22CB

=1√

L21CC

. (4)

Then, the output current Ir1 and the input impendence ZIN1

at ω0 are given by

Ir1 = jω0k

2Cf1Cf2Uin

(1− k2)CMand (5)

ZIN1 =1

RE

[CM

ω0Cf1Cf2

(1

k2− 1

)]2. (6)

1Z

2Z

3Z

Fig. 6. A typical T network.

in1U ER

1fL

1fC

AC

BC

CC

2fC

2fLinI r

I11'L

12'L

13'L

21'L

22'L

23'L

rU1

L

2L

Fig. 7. Equivalent circuit of Fig. 5 operating at ω1, not ω0.

in2U ERBC

2fC

2fL rI12 'L 22 'L 23 'L

(a)

in1U ERBC 2fC

2fL

rI12 'L 22 'L 23 'L

1I ER2fC

2fL rI

(b)

(c) (d)

2I ER

2fL rI

rU

rUrU

rU

Fig. 8. Derivation circuits (a)-(d) of Fig. 7.

A load-independent CC output and input ZPA are realized atω0 which is consistent with the result in [14].

B. Other ZPA Frequencies for Load-Independent Output

With the parameter constraints in (4), the CPT convertermay not work at ω0, but at another frequency ω1. Then theequivalent circuit in Fig. 5 can be transformed as that in Fig. 7by Thevenin’s theorem. The primary L1 can still be dividedinto three parts, i.e., L′

11, L′12, and L′

13 and the secondary L2

is divided as L′21, L′

22, and L′13. If L′

11 is designed to resonatewith Lf1 parallelled by Cf1 at ω1, a load-independent voltagesource Uin1 drives the following circuit, as shown in Fig. 8(a).Design that L′

13 resonates with CA and L′21 resonates with CC ,

Fig. 8(a) has two typical T networks. There are two cases forfurther derivation.

1) If L′12 resonates with CB at ω1, Uin1 can be transformed

to a load-independent current source I1 as shown inFig. 8(b). By (4), Lf2 cannot resonate with Cf2 at ω1.Thus, it is impossible to realize CC or CV output forRE in Fig. 8(b).

2) If L′12 cannot resonate with CB at ω1, Fig. 8(a) can be

converted to Fig. 8(c) by Thevenin’s theorem with a newload-independent voltage source Uin2 in series with theparallel connection of L′

12 and 1jω1CB

. Design that L′22

resonates with L′12 paralleled by CB and L′

23 resonateswith Cf2. Then a load-independent current I2 can drivethe load RE directly as shown in Fig. 8(d).




4

Following the above analysis, we have

ω1 =

√Lf1 + L′

11

L′11Lf1Cf1

=

√L′12 + L′

22

L′12L

′22CB

=1√

L′13CA

=1√

L′21CC

=1√

L′23Cf2

(7)

Under the constraint of the same set of compensation param-eters,

L1 = L11 + L12 + L13 = L′11 + L′

12 + L′13 and

L2 = L21 + L22 + L23 = L′21 + L′

22 + L′23. (8)

Substituting (4) and (7) into (8), we have

ω1 =

ω0

√√√√√√1±

√√√√√ 1 + ( 1k2 − 1) C1

Cf1+ ( 1

k2 − 1)2C2

M

Cf1Cf2

1k2 + ( 1

k2 − 1)( C1

Cf1+ C2

Cf2) + ( 1

k2 − 1)2C2

M

Cf1Cf2

.

(9)

Although a new load-independent CC output can be foundat ω1 in Fig. 8(d), the input impedance cannot be guaranteedto be resistive. To ensure the input ZPA, a transmission matrixAT of the CPT system is introduced here, which satisfies[

Uin

Iin

]= AT

[Ur

Ir

]=

[a11 ja12ja21 a22

] [Ur

Ir

]. (10)

The CPT converter can still be divided into three T networkswith matrixes A1, A2, and A3 as shown in Fig. 5 whereL11,12,13,21,22,23 should be L′

11,12,13,21,22,23. By the basictheory of two-port network,

AT=A1A2A3=

[a′11 a′12a′13 a′14

] [a′21 a′22a′23 a′24

] [a′31 a′32a′33 a′34

]. (11)

Matrices A1, A2, and A3 are given by

A1 =

[1− ω2

1Lf1Cf1 0jω1Cf1 1− ω2

1L′11Cf1

],

A2 =

[1− ω2

1L′12CB 0

jω1CB 1− ω21L

′22CB

], and

A3 =

[0 jω1L

′23

jω1Cf2 1− ω21Lf2Cf2

]. (12)

By solving (11) and (12), a11 = a′31(a′11a

′21 + a′12a

′23) +

a′33(a′11a

′22 + a′12a

′24) = 0. Then the input impedance of the

CPT circuit can be expressed as

ZIN =Uin

Iin=

ja12a22 + ja21RE

=a21a12RE + ja12a22

a222 + a221R2E

.

(13)

If ZIN is purely resistive, a12a22 = 0 from (13). If a12 = 0,the input impedance is always zero, which is not practical.Therefore, a22 = 0. By (11),

a22 = a′32(a′13a

′21 + a′14a

′23) + a′14a

′24a

′34

= (Cf1C2 − C1Cf2)ω21 − ω2

0

CMCf2ω20

= 0. (14)

So, a ZPA design constraint is obtained as

Cf1C2 − C1Cf2 = 0 (15)

Substituting (15) into (9), the other two frequencies ω1H,1L

with input ZPA and load-independent CC output can be givenas

ω1H = ω0

√1 + α and ω1L = ω0

√1− α, (16)

where α =

√(1−k2)2

(C2Cf2

)2+

C2Cf2

(1−k2)+k2

1+(1−k2)C2Cf2

.

The load-independent CC current Ir2 and the input impen-dence ZIN2 at ω1H and ω1L are identical and given by

Ir2 = −jω1CM

k2

(1− k2 +

1

β

)Uin and (17)

ZIN2 =k4β2

[(1− k2)β + 1]2ω21C

2MRE

(18)

where β = C1

Cf1= C2

Cf2.

In summary, with so many compensation components, i.e.,Cf1,f2, Lf1,f2, C1,2 and L1,2, the double-sided LCLC com-pensated CPT converter has three ZPA frequencies with load-independent CC output and may have enough design freedomto optimize the voltage stresses among coupler plates, whichwill be analyzed in the next Section.

III. DESIGN AND IMPLEMENTATION OF CPT CONVERTERWITH VOLTAGE STRESS OPTIMIZATION

A. Design Freedom and Optimization Theory

As analyzed in Section II, the double-sided LCLC compen-sated CPT converter can be designed at ω0 or ω1 to realizeinput ZPA and output load-independent constant current. Asshown in Fig. 2, the input DC voltage UDC can be modulatedby Q1,2,3,4 with D being the duty cycle of uAB in one halfcycle. The fundamental component of uAB, denoted as uIN,is given as

uIN(t) =4UDC

πsin

πD

2sinωt. (19)

By (5) and (17), the output current IO1 at ω0 and IO2 at ω1

under C filter should be given asIO1 =

8

π2

ω0k2Cf1Cf2

CM (1− k2)UDC sin

πD

2

IO2 =8

π2

ω1CM

k2

(1− k2 +

Cf2

C2

)UDC sin

πD

2

. (20)

From (20), with the given UDC, coupler parameter CM ,and operating frequency, both IO1 and IO2 are functions ofCf1, Cf2, C1, and C2. Meanwhile, it should be noticed thatLf1, Lf2, L1, and L2 are also the functions of Cf1, Cf2,C1, and C2 by (4) and (7). Therefore, with one constraintof (20), the double-sided LCLC compensated CPT converterhas the design freedom to optimize uCM, u1, and u2 withfour independent control variables Cf1, Cf2, C1, and C2. Itis the reason why the low order compensation circuit can notoptimize all voltages among the coupler plates. For example,the double-sided LC compensated CPT converter only has two




5

independent variables C1 and C2, so that voltage stresses ofu1 and u2 can not be designed below the given values in [27].

For any CPT system, the key coupler plates can be modeledas a Π-type network as shown in Fig. 4. Assuming all reactivecomponents are lossless, the transferred real power P of theCPT converter is actually the power transferred via the Π-typenetwork. Therefore, we haveP =

1

2ωCMU1U2 sinφ

U2CM = U2

1 + U22 − 2U1U2 cosφ ≥ 2U2(1− cosφ)

(21)

where P = I2ORL, U1,2 is the magnitude of u1,2 and φ is thephase angle between u1 and u2. The minimum UCM occurswhen U1 = U2 = U . By solving (21), it can be written as

UCM =√2U

√√√√1±

√1−

(2P

ωCMU2

)2

(22)

where ± is decided by φ with − for [−π2 ,

π2 ] and + for

[−π,−π2 ] or [π2 , π] in one period. If (22) makes sense,

ω ≥ 2P

CMU2≥ 2P

CMU2max

(23)

where Umax is the given maximum voltage of u1 or u2.Besides, the maximum voltage UCMmax of uCM is usuallygiven to avoid the air breakdown and EMI issue. From (22),with the given output power P , coupler parameter CM , Umax,and UCMmax , the operating frequency ω should be consideredcarefully besides the constraint of (23).

With the above consideration, (22) can be rewritten as

ω =4P

CMUCM

√4U2 − U2

CM

. (24)

The relationship of ω to U and UCM can be judged by

∂ω

∂U= − 16PU

CMUCM(√4U2 − U2

CM)3and (25)

∂ω

∂UCM=

8P (U2CM − 2U2)

CMU2CM(

√4U2 − U2

CM)3. (26)

According to (25) and (26), ∂ω∂U < 0 while ∂ω

∂UCMdepends on

the relationship between UCM and√2U .

1) If φ ∈ [−π2 ,

π2 ], UCM <

√2U in (22). From (26),

∂ω∂UCM

< 0. Therefore, with the given Umax and UCMmax ,the minimum ω can be readily determined by

ω ≥ 4P

CMUCMmax

√4U2

max − U2CMmax

. (27)

2) If φ ∈ [−π,−π2 ] or [π2 , π], UCM >

√2U . From (26),

∂ω∂UCM

> 0. It is hard to determine a minimum ω by (24).So we should check the relationship between UCM andU . From (22) with +, it is evident that ∂UCM

∂U > 0, and

then we have UCM ≥√2U . Substitute U ≥

√2P

ωCMby

(23) into UCM ≥√2U , and we have

ω ≥ 4P

CMU2CM

≥ 4P

CMU2CMmax

. (28)

Summarily, for any CPT converter with enough independentvariables, the operating angular frequency ω can be designedby (23) and (27) for φ ∈ [−π

2 ,π2 ] or by (23) and (28) for

φ ∈ [−π,−π2 ] or [π2 , π], satisfying the requirement of output

power, given coupler plates and given coupler plate voltagestresses. The range of φ should be analyzed for the detailedCPT topology.

B. Phase Angle for Different Angular Frequencies

The phase angle φ between u1 and u2 for a double-sidedLCLC compensated CPT converter as shown in Fig. 2 can bedetermined by the expressions of vectors U1 and U2, as givenin (29) at ω0 and (30) at ω1, i.e., ω1H,1L.

U1|ω0 =

(1− L1

Lf1+

1

jω0Cf1ZIN1

)Uin

U2|ω0 =

[RE

(1− L2

Lf2

)− 1

jω0Cf2

]Ir1

. (29)

From (4), L1 > Lf1 and L2 > Lf2. From (6), ZIN1 > 0.Substituting (5) into (29), we have ℜ(U1) < 0, ℑ(U1) < 0,ℜ(U2) < 0 and ℑ(U2) < 0. Thus, both U1 and U2 are locatedat the third quadrant at ω0 as shown in Figs. 9(a) and (b) whereφ ∈ [−π

2 ,π2 ].

Similarly, if the CPT converter operates at ω1,U1|ω1 =

[γ − jω1Lf1

ZIN2

(γ +

ω20

ω21

(1− γ)

)]Uin

U2|ω1 =

[γRE + jω1Lf2

(γ +

ω20

ω21

(1− γ)

)]Ir2

(30)

where γ = 1− ω21

ω20

(1 + 1

(1−k2)β

). If the CPT converter works

at ω1H, ω21

ω20

= 1 + α by (16) and α > 0. So γ < 0. The

expression of γ +ω2

0

ω21(1 − γ) can be derived to be always

negative. From (18), ZIN2 > 0. Substituting (17) into (30),we have ℜ(U1) < 0, ℑ(U1) > 0, ℜ(U2) < 0 and ℑ(U2) >0. Then, both U1 and U2 at ω1H are located at the secondquadrant with φ ∈ [−π

2 ,π2 ], as shown in Figs. 9(c) and (d). If

the CPT converter works at ω1L, ω21

ω20= 1−α. The expression

of γ +ω2

0

ω21(1− γ) can be derived to be always positive. Thus,

ℑ(U1) < 0 and ℜ(U2) > 0. But the polarity of γ can not beuniquely determined by

γ|ω1L =

√(1− k2)2β2 + (1− k2)β + k2 − 1

(1−k2)β. (31)

There are two cases for γ.1) If β <

√5−4k2−12(1−k2) , γ < 0. Then ℜ(U1) < 0 and

ℑ(U2) > 0. Thus, U1 is located at the third quadrantand U2 is located at the first quadrant at ω1L, as shownin Figs. 9(e) and (f). So φ ∈ [−π,−π

2 ] or [π2 , π].2) If β >

√5−4k2−12(1−k2) , γ > 0. Then ℜ(U1) > 0 and

ℑ(U2) < 0. Thus, U1 and U2 are both located at thefourth quadrant with φ ∈ [−π

2 ,π2 ], as shown in Figs. 9(g)

and (h).From Section III-A, in the double-sided LCLC compensated

CPT converter, the operating angular frequencies ω0 and ω1H




6

+j

+1

l2U

2U

lf2U

cf2U

cf2I

rI

rU

l2I

+j

+1

l2U

2U

lf2U

cf2U

cf2I

rI

rU

l2I

+j

+1

If1U

l1U

cf1U1U

l1I

cf1I

inI inU

+j

+1

lf1U

cf1U

1U

inI inU

cf1I

l1U

o

o

l1I

o

+1

+jlf1U

l1U

cf1U1U

l1I

inUo

+j

+1

cf2I2U

l2U

lf2U

cf2U

l2IrI

rU

o

(a) (b)

(c) (d)

o

(e) (f)

+j

+1

l2U

2U

lf2U

cf2U

cf2I

rI

rU

l2I

+j

+1

If1U

l1U

cf1U

1U

l1I

cf1I

inI inU

o o

(g) (h)

Fig. 9. Vector voltages and currents of the double-sided LCLC compensatedCPT converter at ω0 for (a) and (b), at ω1H for (c) and (d) or at ω1L for (e),(f), (g) and (h).

should be designed by (23) and (27) due to φ ∈ [−π2 ,

π2 ]. The

operating angular frequency ω1L can be designed by (23) and(27) for φ ∈ [−π

2 ,π2 ] or by (23) and (28) for φ ∈ [−π,−π

2 ]or [π2 , π]. But it should be noticed that the operation range ofφ is determined by the relationship between β and

√5−4k2−12(1−k2) .

Therefore, if the CPT converter is designed at ω1L, β and k canbe solved by the next Section III-C, and φ must be recheckedto satisfy the predesigned range.

C. Parameter Design Process

From Section III-B, the phase angle φ of the double-sidedLCLC compensated CPT converter has two cases. With thepredesigned UCMmax , Umax, IO, CM , UDC, and full output

Given UDC, CP, CS, CM, IO, P, UCMmax and Umax

Calculate range of ω0, ω1H,

and ω1L by (21) & (25)

Calculate range of ω1L

by (21) & (26)

Choose U by (30) & (32) Choose U by (30) & (33)

Calculate

C1, C2, Cf1, Cf2

if 2

πϕ < if 2

π ϕ π< <

Calculate L1, L2, Lf1, Lf2, Cex1 and Cex2 by (1), (4), (7), (8) & (14)

Complete

YES YESNo Solution

NO

Choose the operating frequency ω

ω = ω0

SolveU1 = U by (27)

U2 = U by (27)

IO1 = IO by (18)

Choose C1 = C2

ω = ω1L

SolveU1 = U by (28)

U2 = U by (28)

IO2 = IO by (18)

C1Cf2 = C2Cf1 by (13)

SolveU1 = U by (28)

U2 = U by (28)

IO2 = IO by (18)

C1Cf2 = C2Cf1 by (13)

ω = ω1H,1L

Calculate

C1, C2, Cf1, Cf2

ω = ω0 ω = ω1Lω = ω1H

Calculate

C1, C2, Cf1, Cf2

Fig. 10. Parameter design chart of a double-sided LCLC compensated CPTconverter.

power P , the operating angular frequencies ω0, ω1H, and ω1L

can be calculated in a range by (23) and (27) or by (23) and(28). Select ω as the operating angular frequency, (23) can berewritten as √

2P

ωCM≤ U ≤ Umax. (32)

Meanwhile, UCM ≤ UCMmax . With (22), two cases of φ shouldbe considered.

1) If φ ∈ [−π2 ,

π2 ], substitute UCMmax into (22) with − and

solve U as Usolu1. The relationship between U and UCM

can be determined by

∂UCM

∂U=

√2√

1−√

1− 4P 2

ω2C2MU4

·

1− 1√1− 4P 2

ω2C2MU4

< 0. (33)

Thus,

U ≥ Usolu1. (34)

2) If φ ∈ [−π,−π2 ] or [π2 , π], substitute UCMmax

into (22)with + and solve U as Usolu2. Due to ∂UCM

∂U > 0 at this




7

0.98 1 1.02-20

-10

0

10

20

Phase Angle(deg

)

(d)1.010.99

0.9 1 1.10.8

0.9

1

1.1

1.2

(e)

Norm

alized

Curren

t Output

0.9 1 1.10.8

0.9

1

1.1

1.2

Norm

alized

Curren

t Output

(c)

Norm

alized

Curren

t Output

0.9 1 1.10.8

0.9

1

1.1

1.2

(a)

0.98 1 1.02-20

-10

0

10

20

Phase Angle(deg

)

(f)1.010.99

0.98 1-20

-10

0

10

20

Phase Angle(deg

)

(b)1.010.99 1.02

L1

Lf2

L1 L2 C1 C2

Lf1 Lf2 Cf1 Cf2

L1 L2 C1 C2

Lf1 Lf2 Cf1 Cf2

L1 L2 C1 C2

Lf1 Lf2 Cf1 Cf2

Lf2

Lf2

Fig. 11. Normalized output current and phase angle versus normalizedparameters at ω0 with (a) and (b), ω1H with (c) and (d), and ω1L with(e) and (f).

case,

U ≤ Usolu2. (35)

From (32) and (34) or (35), U can be selected to guaranteeUCM ≤ UCMmax . Then we can combine four equations to solvefour independent parameters Cf1, Cf2, C1, and C2, whichinclude U1 = U2 = U by (29) or (30), IO = IO1 or IO = IO2

by (20) and (15) for ω1. Here, it should be noted that thereare only three equations for ω0 case. Therefore, one parameteramong Cf1, Cf2, C1, and C2 can be predesigned, for example,C1 = C2. The detailed design process is given in Fig. 10. FromFig. 10, φ must satisfy one case of |φ| < π

2 or π2 < |φ| < π at

least. Thus, if one case is not satisfied, there is no solution andφ can satisfy the other case to find the solution. The operatingfrequency could be selected according to the requirements ofapplications, product volume, cost, efficiency, and EMI issues.

D. Soft Switching Realization

Fig. 11 shows the normalized output current and phase angleversus normalized parameters at ω0, ω1H and ω1L respectively.From Figs. 11 (a) and (b), it can be seen that the output currentis not sensitive to L1 and Lf2 variations at ω0. Then thesmaller L1 and Lf2 will permit the ZVS of CPT converters,which is consistent with the results in [15]. Similarly, theoutput current is not sensitive to the variation of Lf2 at bothω1H and ω1L from Figs. 11 (c) and (e). A small decrement ofLf2 can ensure ZVS from Figs. 11 (d) and (f).

Inverter RectifierL1 L2Cex2Lf1 Lf2Cex1Cf1 Cf2Coupler Plates

Fig. 12. Experimental prototype of the double-sided LCLC compensatedCPT converter.

TABLE ICALCULATED PARAMETERS FOR CPT CONVERTER AT DIFFERENT

FREQUENCIES UNDER UCM OF 750 V.

Parameter f0 = 500 kHz f1H = 500 kHz f1L = 1.5 MHzU 1041 V 1041 V 495 VCf1 1.98 nF 3.18 nF 0.92 nFCf2 2.73 nF 3.69 nF 1.1 nFCex1 44 pF 251 pF 234 pFCex2 44 pF 296 pF 287 pFLf1 51.25 µH 41.52 µH 6.3 µHLf2 42.71 µH 35.85 µH 5.3 µHL1 1647 µH 510 µH 28.4 µHL2 1638 µH 441 µH 23.7 µH

IV. EXPERIMENT VERIFICATION

To verify the above analysis, a 40 W double-sided LCLCcompensated CPT prototype is built to provide a constantcurrent of 2 A, as shown in Fig. 12. The length l of eachcoupler plate is 200 mm and the air distance d is 6 mm.The distance d1 between two plates in the same primary orsecondary side is 10 mm. The equivalent parameters can bemeasured as CM = 35 pF and CP = CS = 40 pF. The inputDC voltage is 24 V and the duty cycle is set as 0.95. Thepredesigned maximum voltage stress UCMmax is 800 V andUmax is 1200 V.

From Fig. 10, the operating frequency can be calculated asf ≥ 402 kHz for f0, f1H,1L and φ ∈ [−π

2 ,π2 ], while f ≥ 1.14

MHz for f1L and φ ∈ [−π,−π2 ] or [π2 , π]. If f is designed

at 500 kHz as f0, f1H,1L for φ ∈ [−π2 ,

π2 ], the calculated U

belongs to [994 V, 1200 V] and UCM belongs to [629 V, 800V]. If f is designed as 1.5 MHz as f1L for φ ∈ [−π,−π

2 ]or [π2 , π], U belongs to [493 V, 502 V] and UCM belongsto [697 V, 800 V]. We choose UCM = 750 V with a designmargin and the calculated U , Cf1,2, Cex1,2, L1,2, Lf1,2 aregiven in Table I. It should be noted there is no solution forf1L when φ ∈ [−π

2 ,π2 ]. The CPT converter can be designed

to work at f0 or f1H of 500 kHz in the consideration ofthe implementation of the inventor, efficiency, and EMI issues[29]. Comparing the inductor sizes at two frequencies listedin Table I, f1H of 500 kHz is used here. A microcontrollerTMS320F28335 and the gate driver 1EDI20N12AF are used todrive Q1,2,3,4. Q1,2,3,4 use IPA180N10N3 while the secondaryrectifier diodes D1,2,3,4 use VB30100S.

Fig. 13 shows the experimental waveforms of gate-sourcevoltage uGS1 for MOSFET Q1, modulated voltage uAB, input




8 uGS1uAB iINIO(a) RL = 5 ΩuGS1uAB iINIO(b) RL = 10 Ω

Fig. 13. Experimental waveforms of uGS1, uAB, iIN, and IO at (a) halfload and (b) full load. uGS1uC13 u1u2Fig. 14. Experimental waveforms of uGS1, uC13, u1, and u2 at full load.

600

800

1000

UCM U1 U2

2% 4% 6% 8% 10%0%X-axis misalignment

1200

1400

Voltage (V)

6002% 4% 6% 8% 10%

800

1000

1200

1400

0%

Voltage (V)

Y-axis misalignment

UCM U1 U2

(a) (b)

Fig. 15. Voltages UCM, U1 and U2 under (a) X-axis misalignment and (b)Y-axis misalignment.

current iIN and output current IO for half load of RL = 5Ω and full load of RL = 10 Ω. It is found that the outputcurrent keeps at the required 2 A independent of the load. Thesmall phase angle of iIN lagging uAB facilitates ZVS of thefull-bridge switches. To verify the voltage stress optimization,voltage waveforms of uGS1, uC13, u1, and u2 at full load aregiven in Fig. 14. From Fig. 14, the measured U1 and U2 are1030 V and 985 V, which are close to the theoretical valuesand the small difference is caused by the capacitor tolerance.UC13 is measured as 380 V where UCM ≈ 2UC13, which isalso consistent with the value in Table I. The experimental

Voltage stresses (V)

Voltage stresses (V)

Time (µs) Time (µs) (a) (b)

-1200-800-4000

4008001200-400

0

400

0 1 2 3

uC13

u2

u1

-200

0

200

-2000

-1000

0

1000

2000

0 1 2 3

u2

u1

uC13

Fig. 16. Comparison of uC13, u1, and u2 at full load with (a) conventionalsymmetric parameters and (b) proposed parameters in a double-sided LCLCcompensated CPT converter.

0 200 400(mm)

(a) with conventional symmetric parameters

0 200 400(mm)

(b) with proposed parameters

Fig. 17. Electric field emissions around the coupler plates at two cases ofparameter design.

results show good agreement with the calculated values. Ifthe plate misalignment happens, the secondary plates of P3

and P4 may move in X-axis or Y-axis direction as shownin Fig. 3 (a). Fig. 15 gives the maximum voltage variationsof calculated UCM (i.e., 2UC13), U1, and U2 under the X-axis and Y-axis misalignment percentages to the plate length.It can be seen that a small misalignment for X-axis or Y-axis is permitted with the predesigned voltage stresses. Theefficiency of the CPT converter is measured around 83% atfull load and the losses mainly distribute in the coupler plates,magnetic inductors, and rectifier diodes, which is not the keyand omitted in this paper.

To further show the electric field emission reduction withthe proposed design method, Fig. 16 (a) gives the voltagewaveforms of uC13, u1 and u2 at the same output currentand full load for the double-sided LCLC CPT circuit usingconventional symmetric parameters, i.e., Cex1 = Cex2 = 145pF, Cf1 = Cf2 = 6 nF, L1 = L2 = 731 µH, and Lf1 = Lf2 =21 µH. Compared to Fig. 16 (b) with the proposed parameter




9

design, the voltage stresses of U1 and U2 are much largeralthough UC13 decreases. Thus, the electric field emissionsaround the coupler plates are much larger than those in theproposed design, as shown in Fig. 17.

V. CONCLUSION

To reduce the risk of air breakdown and mitigate theelectromagnetic interference (EMI) issue in a capacitive powertransfer (CPT) system, the voltage stresses among both themain coupled plates and the leakage coupled plates should beoptimized in the acceptable levels. In this paper, a double-sidedLCLC compensated CPT circuit is proved to have enoughdesign freedom to optimize the voltage stresses among thecoupler. Meanwhile, three frequencies are found in the double-sided LCLC compensated CPT circuit to realize input zero-phase angle (ZPA) and load-independent constant current (CC)output simultaneously, which can facilitate a reduced powerstage, simple control circuitry, and high transfer efficiency.Also, a parameter design method is proposed to realize therequired load-independent CC output and the predesignedvoltage stresses at each frequency. The method can be readilyextended to the other CPT systems. Experimental results havevalidated the theoretical analysis well.

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[6] Y. Chen, Z. Kou, Y. Zhang, Z. He, R. Mai, and G. Cao, “Hybrid topologywith configurable charge current and charge voltage output-based WPTcharger for massive electric bicycles,” IEEE J. Emer. Sel. Topics PowerElectron., vol. 6, no. 3, pp. 1581-1594, Sept. 2018.

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[9] R. H. W. Liang, C. K. Lee, and S. Y. R. Hui, “Design, analysis andexperimental verification of a ball-joint structure with constant couplingfor capacitive wireless power transfer,” IEEE J. Emer. Sel. Topics PowerElectron., to appear. DOI: 10.1109/JESTPE.2019.2938226.

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[12] F. Lu, H. Zhang, H. Hofmann, and C. C. Mi, “A double-sided LC-compensation circuit for loosely coupled capacitive power transfer,”IEEE Trans. Power Electron., vol. 33, no. 2, pp. 1633-1643, Feb. 2018.

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[27] J. Lian and X. Qu, “Design of a double–sided LC compensated capac-itive power transfer system with capacitor voltage stress optimization.,”IEEE Trans. Circuits Syst. II, Exp. Briefs., vol. 67, no. 4, pp. 715-719,Apr. 2020.

[28] L. Huang and A. P. Hu, “Defining the mutual coupling of capacitivepower transfer for wireless power transfer,” Electron. Let., vol. 51, no.22, pp. 1806-1807, Oct. 2015.

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Jing Lian received the BEng degree in electricalengineering from China University of Mining andTechnology, Xuzhou, China, in 2015. She is cur-rently working toward the PhD degree in electricalengineering in Southeast University, Nanjing, Chi-na.

Her current research interest mainly includeswireless power transfer.




10

Xiaohui Qu (M’10–SM’19) received the BEng andMEng degrees in electrical engineering from theNanjing University of Aeronautics and Astronautics,Nanjing, China, in 2003 and 2006, respectively, andthe PhD degree in power electronics from the HongKong Polytechnic University, Hong Kong, in 2010.

From February to May 2009, she was engaged as aVisiting Scholar at the Center for Power ElectronicsSystems, Virginia Tech, VA, USA. Since 2010, shejoined the School of Electrical Engineering, South-east University, China, where she is currently a full

Professor with research focus on power electronics. From January 2015 toJanuary 2016, she was a Visiting Scholar with the Center of Reliable PowerElectronics (CORPE), Aalborg University, Denmark. Her current researchinterests include LED lighting systems, wireless power transfer, and powerelectronics reliability.

Dr. Qu received the Outstanding Reviewer Award and the Prize Paper Awardfrom IEEE TRANSACTIONS ON POWER ELECTRONICS in 2017 and 2018.

Xi Chen (S’07-M’13-SM’16) received BEng fromBeijing Technology and Business University, Bei-jing, China, MSc from Kings College London, U-niversity of London, London, U.K. and PhD fromthe Hong Kong Polytechnic University, Hong Kong,SAR, in 2003, 2005 and 2009, respectively.

He was a Postdoctoral Research Fellow at theInstitute of Software, Chinese Academy of Science.He was a Visiting Student at the University ofFlorida in 2008. In 2014, he joined GEIRI NorthAmerica, San Jose, CA, USA, where he currently is

the Chief Information Officer. From 2009 to 2014, he was with State GridCorporation of China, Beijing, China. His research interests include nonlineardynamics, Internet of Things, smart grids, and electric vehicle charging.

He servers as Associate Editor of IEEE Systems Journal. He served as GuestEditor of IEEE Transactions on Intelligent Transportation System: EnablingExtreme Fast Charging Technology for Electric Vehicles.

Chunting Chris Mi (S00–A01–M01–SM03–F12)received the BSEE and MSEE. degrees in electricalengineering from Northwestern Polytechnical Uni-versity, Xian, China, and the PhD degree in elec-trical engineering from the University of Toronto,Toronto, Ontario, Canada, in 1985, 1988, and 2001,respectively.

He is a Professor and the Chair of electricaland computer engineering and the Director of theDepartment of Energy-funded Graduate AutomotiveTechnology Education Center for Electric Drive

Transportation, San Diego State University (SDSU), San Diego, CA, USA.Prior to joining SDSU, he was with with the University of Michigan,Dearborn, MI, USA, from 2001 to 2015.

Dr. Mi received the Distinguished Teaching Award, the DistinguishedResearch Award of University of Michigan, Dearborn, the 2007 IEEE Region4 Outstanding Engineer Award, the IEEE Southeastern Michigan SectionOutstanding Professional Award, and the SAE Environmental Excellence inTransportation (E2T). He has also served as a Panelist in major IEEE andSAE conferences.


design of a double-sided lclc compensated capacitive power

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