wide-range voltage gain and high-efficiency of isolated...

© 200● The Institute of Electrical Engineers of Japan. 1

電気学会論文誌●（●●●●●●●部門誌）

IEEJ Transactions on ●●●●●●●●●●●●●●●

Vol.●● No.● pp.●-●● DOI: ●.●●/ieejeiss.●●.●

Wide-Range Voltage Gain and High-Efficiency of Isolated LLC

Converter using Six-Switch and Two Asymmetric Transformers

Yuki Kinoshita＊ Student member, Hitoshi Haga＊a) Senior member

(Manuscript received Jan. 00, 20XX, revised May 00, 20XX)

This paper proposes a circuit configuration of LLC converter a wide voltage range and high efficiency. The proposed LLC

overcomes the narrow voltage gain range of conventional full-bridge (FB) LLC converters. Owing to the switching patterns of the

primary side, two resonant tanks operate in half-bridge and FB modes. The two resonant tanks are designed with different

parameters, and the proposed LLC has six operating modes. These modes enable a squeezed switching frequency span, which is

close to the resonance frequency. The proposed control method achieves seamless transition between the operating modes and a

wide voltage gain range. First, the operating principles and characteristics of the proposed converter are analyzed. The transitions

between modes are determined based on the analyzed theory. In addition, the design guidelines for the two resonant tanks are

describe. The parameters of the two resonant tanks are designed using the first harmonic approximation method, and each is

determined to achieve a wide voltage range and high efficiency. A prototype rated to 1.0-kW is designed to convert the input of

360 V to an output of 100-420 V, and the proof of concept is validated. Experimental results confirm that the proposed circuit

achieves a voltage gain of less than 0.5 to more than 2.0 under different load conditions. Furthermore, the proposed mode transition

method achieves seamless transition between modes without complicated calculations. Experiments confirm a maximum efficiency

of 96.5%.

Keywords: LLC converter, wide output voltage range, high efficiency, onboard charger,

1. Introduction

Recently, there has been a growing interest in plug-in hybrid

electric vehicles (PHEVs), owing to the support of national policies

and the interest in environmental issues. Consequently, the demand

for on-board chargers has been increasing rapidly. Most of today’s

PHEVs are equipped with Li-ion battery packs (1)–(2). A typical

charging profile of a deeply depleted Li-ion battery pack is plotted

in Fig. 1. In PHEV battery packs, the Li-ion cell voltage range is

mapped to a wide voltage range, typically 100-420 V (3)–(5).

Consequently, the on-board battery charger must be compatible

with this wide voltage range of the battery packs. A typical PHEV

onboard charger consists of two stages. The first stage comprises a

boost-type AC-DC converter for active power factor correction,

while the second stage is an isolated DC-DC converter (6)–(7). The

characteristics of this type of onboard charger are mainly dependent

on the DC-DC converter, because the output voltage and output

current are regulated in the second stage.

One of the most popular DC-DC converters for battery chargers

is the full-bridge LLC (FB-LLC) resonant converter. The LLC

resonant converter is topologically attractive for its features of wide

soft switching range and high power density (8)–(10). FB-LLC

converters are usually controlled by pulse frequency modulation

(PFM) of the primary switches. However, to be adapted to a wide

output voltage range, the switching frequency (fs) of the LLC

converter must swing in a wide span and deviates from the resonant

frequency (fr) (5), (11). Furthermore, when fs is higher than fr, the

primary switches of the FB-LLC converter suffer from a high turn-

off current. In addition, it loses its main advantages such as low

switching loss (12)–(13). As a result, it becomes less efficient.

Therefore, it is desirable that the LLC converter be designed to

always operate in the fs ≤ fr region. When fs ≤ fr, zero voltage

switching (ZVS), zero current switching, and good regulation of

output voltage can be achieved easily. However, it is still difficult

to achieve both a wide voltage range and high efficiency (14). This

is because of the increased circulating current of the resonance tank

when fs is far away from fr.

To achieve a wide voltage regulation range and narrow fs range

simultaneously, many control strategies and modifications to the

circuit structure have been studied (5), (15)–(18). In (15), the interleaved

configuration and phase shift control of a FB-LLC are used. The

proposed LLC resonant converters always operate in the fs ≤ fr

region and the switching frequency range can be narrowed

significantly. However, the circulating current caused by the phase

shift control leads to a decrease in efficiency (19). In (5), a voltage

doubling rectifier circuit structure was proposed for charging a

deeply depleted Li-ion battery. This proposed method can achieve

an output voltage from 100 to 420 V by PFM control. However, the

switching frequency range is wide and the range is not limited to fs

≤ fr. In (16), a DC link follows the battery voltage and an LLC

converter is operated around fr. Although, this approach reduces the

conduction loss, a wide voltage variation is required at the AC/DC

stage. In (17), a modified LLC converter with two transformers was

proposed. A bidirectional switch adjusts the equivalent turn ratio of

the two transformers connected in series. Therefore, four operation

modes with different voltage gain ranges can be realized. However,

the transformer utilization rate is low, because one transformer is

not used for power transmission in two of the operation modes. In

(18), primary bridge structure consisting of five switches was

proposed. The primary bridge circuit can realize four operation

modes with different voltage gain ranges. However, the fs range

a) Correspondence to: Hitoshi Haga. E-mail: [email protected]

＊ Nagaoka University of Technology.

1603-1, Kamitomioka-machi, Nagaoka, Niigata, Japan 940-2188

Paper

Wide Range Operation and High Efficiency of On-board Charger (Yuki Kinoshita et al.)

2 IEEJ Trans. ●●, Vol.●●, No.●, ●●●

extends from 50 to 150 kHz. Furthermore, the range of fs is not

limited to fs ≤ fr.

The originality of this paper is the variable topology of the

primary bridge depending on the state of the battery. With the

transition of the proposed six operating modes, output voltages

from 100 to 420 V can be achieved in the range of fs ≤ fr. The

transition of the operation mode is performed according to the

theoretical formula of each operation mode. In addition, by using

two resonant tanks designed with different parameters, high

efficiency is achieved near the nominal battery voltage. The two

resonant tanks with different parameters allow the design of large

magnetizing inductances and small leakage inductances. This

allows for reductions in the circuit circulating current and

conduction losses.

This paper is organized as follows: first, the proposed circuit

configuration and six operation modes with different voltage gain

ranges are introduced. Second, the theory and output voltage of the

proposed operation modes are described. Next, the design

guidelines for the resonance tank to achieve a wide voltage range

and the transition between operating modes are described. Finally,

experimental results show that the proposed circuit achieves a wide

range of voltage gains as well as seamless transitions.

2. Proposed LLC and Six Operation Modes

2.1 Circuit Configuration of the Proposed LLC The

schematic of the proposed LLC converter is illustrated in Fig. 2.

The primary side is consists of six MOSFETs. The parameters of

leakage inductance (Lr1, Lr2), resonance capacitance (Cr1, Cr2), and

magnetizing inductance (Lm1, Lm2) are different. Tr1 and Tr2 are

asymmetric isolated transformers with turn ratios n1 and n2.

Therefore, the two resonant tanks show different voltage

characteristics. On the secondary side, six diodes share the

transformer’s secondary windings. By controlling the primary-side

MOSFETs, the inputs of the resonant tanks can be configured as FB

or half-bridge (HB) and series or parallel. Therefore, these

combinations provide six operating modes. The primary-side

circuits of the six operation modes are shown in Fig. 3. Furthermore,

Table 1 shows the bridge configuration and the connection status of

the transformer in the six operation modes. Fig. 3 shows the bridge

configuration and the ON/OFF status of the switches. The output

voltage is controlled by each operation mode and PFM.

2.2 Six Operation Modes of the Proposed LLC Fig. 3 (a)

shows operation mode 1. In mode 1, S1, S4 S5 and S2, S3, S6 are

driven complementarily with a certain dead time. Tr1 and Tr2 are in

series and integrated into one resonant tank. The input of the

resonance tanks operates in the FB configuration. Fig. 3 (b) shows

operation mode 2. In mode 2, S1, S4 and S2, S3 are driven

complementarily with a certain dead time. S5 and S6 are constantly

ON. In this mode, only transformer Tr1 contributes to power

transmission. Therefore, operation mode 2 is equivalent to the

conventional FB-LLC. Fig. 3 (c) shows operation mode 3. In this

mode, S3, S6 and S4, S5 are driven complementarily with a certain

dead time. S1 and S2 are constantly ON. The input of Tr2 is in the FB

configuration and only transformer Tr2 contributes to power

transmission. Therefore, operation mode 3 also has the same

characteristic as the conventional FB-LLC. Mode 2 and mode 3

have different output characteristics, owing to the different

parameters of the resonance tanks. Fig. 3 (d) shows operation mode

4. In mode 4, S1, S6 and S2, S3 are driven complementarily with a

certain dead time. S4 and S5 are constantly ON. The input of Tr1 is

FB and the input of Tr2 is HB. Fig. 3 (e) shows operation mode 5.

In this mode, S1, S6 and S4, S5 are driven complementarily with a

certain dead time. S2 and S3 are constantly ON. The input of Tr1 is

HB and the input of Tr2 is FB. The output characteristics of mode 4

and mode 5 are also different. Fig. 3 (f) shows operation mode 6. In

mode 6, S1, S6 and S2, S5 are driven complementarily with a certain

dead time. S3 and S4 are constantly ON. The inputs of Tr1 and Tr2

are FB, and this mode exhibits the highest voltage gain.

In mode 1, Tr1 and Tr2 are connected in series, thereby achieving

Fig.1 Charging profile of a Li-ion battery

Fig.2 Proposed LLC converter

(a) mode 1 (b) mode 2 (c) mode 3

(d) mode 4 (e) mode 5 (f) mode 6

Fig.3 Six operation modes of the proposed LLC

Table 1. Bridge configuration and connection status

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Curr

ent

rate

Bat

tery

Volt

age

Vo

Voltage

Current

Vo=420V

Vo=100V

Vo=250V

CC1 CC2 CV

Time

S1

Vin

S2

S3 S4

S5 S6

vab

vcd

iLr1

iLr2

Lr1

Cr1

Lm1

Lr2

Cr2

Lm2

Tr1

n1:1

Tr2

n2:1

D1 D2 D3

D4 D5 D6

Co RLVo

Coss Io

S1 S2

S3 S4

S5 S6

S1 S2

S3 S4 S3 S4

S5 S6

FB

FB

FB

FB

S1

S4

S5 S6

S1 S2

S3

S6

S1 S2

S5 S6

FB

HB

HB

FB

FB

FB

mode Tr1 operating Tr2 operating connection status

1 FB FB Series

2 FB - Independence

3 - FB Independence

4 FB HB Parallel

5 HB FB Parallel

6 FB FB Parallel



lower gain than the conventional FB-LLC. In modes 2 and 3, the

transformers operate independently. These modes show the same

characteristics as the conventional FB-LLC. In modes 4, 5, and 6,

the transformers are connected in parallel. In these modes, a higher

voltage gain can be obtained compared to the conventional FB-LLC.

3. Theoretical Analysis of each Operation Mode

3.1 Output voltage gain characteristics Fig. 4 shows

typical output voltage gain characteristics of the LLC converter.

The output voltage gain Go is expressed as follows:

in

oo

V

VnG

1 (1).

The output characteristics of the LLC converter depend on the load

conditions. Under no-load conditions, the LLC peak gain is high.

However, at full load, the LLC peak gain is low. Therefore, it is

difficult to realize a wide output voltage gain under various load

conditions. Fig. 5 shows a schematic diagram of the gain

characteristic of the proposed LLC converter. However, the turns

ratio of the transformer is n1> n2. To normalize the voltage gains in

different modes, the output voltage gain in mode 2 at fs = fr is

defined as Go = 1.0 (Eq. (1)). The six operation modes enable a

narrow fs span and a wide voltage gain range. Furthermore,

according to (16), the efficiency is also improved because the

squeezed fs range is close to fr. This is due to the reduction in the

circuit circulating current and root mean square (rms) current. To

realize a wide range of output voltage gain, transitions between the

different operation modes are required, as shown in Fig. 5.

3.2 Operation mode 1 Fig. 6 shows a steady

waveform in at fs = fr mode 1. The input of Tr1, vab is a two-level

square wave. In the steady state, rms value is given by Eq. (2).

21

2_

nn

nVv in

rmsab

(2)

where n1 and n2 are the turn ratios of the transformers, and Vin is the

input voltage. Similarly, the rms value of vcd is given by Eq. (3).

21

1_

nn

nVv in

rmscd

(3)

Fig. 7 shows a current path when the switches S1, S4, and S5 are ON.

In mode 1, the primary windings of the transformers Tr1 and Tr2 are

connected in series, as shown in Fig. 7. Hence, the amplitudes of

the resonance currents iLr1 and iLr2 flowing through the circuit are

equal. Furthermore, when switches S1, S4, and S5 are ON, diodes D1,

D3, and D5 conduct. Thus, in mode 1, the secondary windings of the

transformer are connected in parallel. Mode 1 is an input series

output parallel (ISOP) configuration, in which the primary side is

connected in series and the secondary side is connected in parallel.

The output voltage at fs = fr is given by Eq. (4), and the output

voltage in mode 1 is lower than those in modes 2 and 3, which are

the conventional FB-LLC configuration.

21 nn

VV in

o

(4)

3.3 Operation mode 2 Fig. 8 shows a steady waveform

at fs = fr in mode 2. In this mode, S5 and S6 are constantly ON; S1,

S4 and S2, S3 are driven complementarily with a certain dead time.

Therefore, vab is a two-level (−Vin to Vin) square wave. Transformer

Tr1 operates in the FB configuration. In mode 2, because

transformer Tr2 does not contribute to power transmission, the

Fig.4 Typical FB-LLC gain characteristics

Fig.5 Proposed LLC gain characteristics

Fig.6 Steady-state waveform at fs=fr in mode 1

Fig.7 Current path in mode 1


0.6 0.7 0.8 0.9 1.01.0

1.2

1.4

1.6

1.8

Ou

tpu

t V

olt

age G

ain

Go

Normalized Frequency fn (fs/fr)

Full Load Gain

No Load Gain

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.7 0.8 0.9 1.0Normalized Frequency fn (fs/fr)

Outp

ut V

olt

age G

ain

Go mode6

mode5mode4

mode2 mode3

mode1

Gate-Source Signal[V]


Transformer Input Voltage vab[V]

Transformer Input Voltage vcd[V]

Resonant Current[A]iLr1 = iLr2

S1,S4,S5

S2,S3,S6

S1

Vin

S2

S3 S4

S5 S6

vab

vcd

iLr1

iLr2

Lr1

Cr1

Lm1

Lr2

Cr2

Lm2

Tr1

n1:1

Tr2

n2:1

D1 D2 D3

D4 D5 D6

Co RLVo





Resonant Current[A]

S1,S4

S2,S3

Vin

-Vin

iLr1 iLr2



output voltage at fs = fr is given by Eq. (5). The input of Tr2, vcd, is

zero. Furthermore, the resonance current iLr2 is also zero.

1n

VV in

o (5)


waveform at fs = fr in mode 3. In this mode, S1 and S2 are constantly

ON; S3, S6 and S4, S5 are driven complementarily with a certain dead

time. Therefore, vcd is a two-level (−Vin to Vin) square wave. The

input of Tr1, vab, is zero. Furthermore, the resonance current iLr1 is

also zero. In this mode, the output voltage at fs = fr is given by Eq.

(6). This is the same characteristic as that of the conventional FB-

LLC.

2n

VV in

o (6)

In the proposed circuit, Tr1 and Tr2 are designed with different

parameters, such that the output voltages of Eq. (5) and Eq. (6) are

different.




time. The input of Tr1, vab, is a two-level (−Vin to Vin) square wave.

However, the input of Tr2, vcd, is a two-level (−Vin to 0) square wave.

vab and vcd are two different two-level square waves, which shows

that Tr1 operates in FB and Tr2 operates in HB. Therefore, in this

mode, the output voltage at fs = fr is given by Eq. (7).

21 2n

V

n

VV inin

o (7)

Fig. 11 shows the current path at S1, S6 in this mode. The primary

windings of transformers Tr1 and Tr2 are connected in parallel.

However, the secondary windings are connected in series. The

diodes D2 and D5 are always OFF. Therefore, the output voltage Vo

is expressed by the sum of Tr1 operating in FB and Tr2 operating in

HB, as shown in Eq. (7).





Fig.11 Current path in mode 4


time. The input of Tr1, vab, is a two-level (0 to −Vin) square wave.

However, the input of Tr2, vcd, is a two-level (−Vin to Vin) square

wave. vab and vcd are two different two-level square waves, which

shows that Tr1 operates in HB and Tr2 operates in FB. Therefore, in

this mode, the output voltage at fs = fr is given by Eq. (8). The output

voltage Vo is expressed by the sum of Tr1 operating in HB and Tr2

operating in FB, as shown in Eq. (8).

212 n

V

n

VV inin

o (8)

As in operation mode 4, the primary windings of transformers Tr1

and Tr2 are connected in parallel. Further, the secondary windings

are connected in series.




time. vab and vcd are two-level (−Vin to Vin) square waves. The inputs

of the two transformers operate in FB. Therefore, the output voltage

Vo at fs = fr is given by Eq. (9). ir1 is unequal to ir2, owing to the

different transformer parameters.

21 n

V

n

VV inin

o (9)

The output voltage Vo is the sum of Eq. (5) and Eq. (6). This mode

exhibits the highest voltage gain. This indicates that the two

resonant tanks transfer different power to the load because n1 and n2

are different.







Resonant Current[A]

S3,S6

S4,S5

Vin

-ViniLr2 iLr1

S1,S6

S2,S3

Vin

-Vin

-ViniLr2 iLr1





Resonant Current[A]

0

S1

Vin

S2

S3 S4

S5 S6

vab

vcd

iLr1

iLr2

Lr1

Cr1

Lm1

Lr2

Cr2

Lm2

Tr1

n1:1

Tr2

n2:1

D1 D2 D3

D4 D5 D6

Co RLVo





Resonant Current[A]

S1,S6

S2,S3

0

-Vin

Vin

-ViniLr2 iLr1





Resonant Current[A]

S1,S6

S2,S5

Vin

-Vin

Vin

-ViniLr2 iLr1



4. Design Guidelines and Transition Control

4.1 Output Voltage Range and Design Guidelines As

shown in Fig. 1, the charging range of a Li-ion battery is classified

into constant current (CC) and constant voltage (CV) charging. The

CC region is further classified into a deeply discharged region

(CC1) and a normally discharged region (CC2). The CC2 and CV

regions are used when the battery operates in normal SOC

conditions. On the other hand, the CC1 region is used when the cell

is not charged in advance or when returning from an over

discharged state. In this study, the charging current is 1.00 A in

region CC1 and 2.38 A in region CC2. In the CV charging region,

the voltage is kept constant and the current is reduced gradually.

The maximum voltage of the battery is 420 V, the nominal voltage

is 250 V, and the minimum voltage when deeply discharged is 100

V. Thus, the proposed converter should be designed by considering

all these current and voltage ranges of the Li-ion battery.

In this study, the minimum output voltage of the converter is

given by Eq. (4). This is because the proposed LLC is always

designed to operate in the fs ≤ fr region. The input voltage Vin is

constant at 360V. Therefore, the turn ratio of each transformer must

satisfy Eq. (10).

6.321 nn (10)

The primary purpose of this study is to achieve high efficiency at

nominal battery operation. According to (16), the highest efficiency

of LLC is achieved around the primary resonance frequency of the

resonant tank. The second purpose is to achieve a wide range of

output voltage. To compensate between the lowest battery voltage

and the nominal voltage, an output voltage gain of 2.5 is required.

This means that the conversion efficiency deteriorates. Therefore,

the nominal voltage is achieved in mode 3, and mode 2 is designed

to complement between the minimum battery voltage and the

nominal voltage. The turn ratio of the resonance tank Tr2 is given

by Eq. (11).

44.1250

3602

norm

in

V

Vn (11)

where Vnorm is the nominal voltage. The turn ratio of the resonance

tank Tr1 is given by Eq. (12) to narrow the switching frequency

range.

16.26.3 21 nn (12)

Therefore, at fs = fr in mode 1, the output voltage is the minimum

voltage of the battery. Table 2 shows the output voltage range for

each of the proposed LLC modes and the peak gain required to

transition to the next operating mode. The peak gain of each

operation mode in Table 2 is normalized using the gain obtained at

fn = 1.0 of each operation mode. To achieve the transition between

modes, the peak output voltage of each mode should be higher than

Table 2. Voltage operating range and required gain

the minimum voltage of the next mode. In order to transition from

mode1 to moe2, the peak output voltage of mode1 needs to be

higher than the voltage obtained by Eq. (5). The minimum output

voltage for mode1 is expressed by Eq. (4), which is 100V from Eq.

(11) and (12). On the other hand, the minimum voltage in mode2 is

166V according to Eq. (5). Therefore, in order to transit from mode1

to mode2, the peak gain of mode1 must be 1.66 or more. The

required peak gain can be obtained similarly for other operation

modes. As shown in Table 2, the peak gain of the proposed LLC is

much lower than that of the conventional FB-LLC. Thus, the

efficiency over a wide output voltage range can be enhanced and

the design complexity can be reduced.

In this study, the parameters are designed based on the first

harmonic approximation (FHA) method (20)–(22). The equivalent

circuit model of the proposed LLC based on the FHA method is

shown in Fig. 14. Re is the equivalent load resistance. The FHA

method provides acceptable accuracy when fs is in the vicinity of fr,

because the first harmonic part of the resonant current dominates.

Using the FHA method, the voltage gains of resonance tanks Tr1 and

Tr2 can be expressed as

2

2

2

2

111

11

1

nnx

nx

ox

ffQ

fk

G (13)

rx

mxx

L

Lk (14)

Lx

rxrx

Rn

CLQ

2

1 (15)

r

sn

f

ff (16).

where x = 1 or 2. Furthermore, the two resonance tanks are designed

to have the same resonance frequency. Therefore, this relationship

is given by Eq. (17).

2211 2

1

2

1

rrrr

rCLCL

f

(17)

The total voltage gain of the proposed LLC depends on the gains

Go1 and Go2 of each resonant tank, and is given by Eq. (18).

2

2

1

1

n

Gv

n

GvV ocdoab

o

(18)

where vab and vcd are equal to the input voltage when operating in

FB, and half of the input voltage when operating in HB.

To determine the parameters Lm1 and Lm2, it is necessary to find

the upper limits of Lm1 and Lm2, such that ZVS is maintained within

Fig.14 Equivalent circuit model of the proposed LLC

mode output voltage range peak gain

1 Eq.(4) ≦ Vo 100V ≦ Vo 1.66

2 Eq.(5) ≦ Vo 166V ≦ Vo 1.51

3 Eq.(6) ≦ Vo 250V ≦ Vo 1.16

4 Eq.(7) ≦ Vo 291V ≦ Vo 1.14

5 Eq.(8) ≦ Vo 333V ≦ Vo 1.25

6 Eq.(9) ≦ Vo≦Vmax 417V ≦ Vo≦420 1.01

Lr1

Cr1

Lm1

Lr2

Cr2

Lm2

Re

vab

vcd



the given dead time. According to (23), the charging and

discharging of Coss in an FB-LLC is accomplished within a time

period t, as follows:

ossmxs CLft 16 (19)

To ensure the ZVS of the MOSFETs is maintained, the dead time

must be longer than the period in Eq. (19). According to Eq. (19),

the upper limit of Lmx could be obtained as

soss

dm

fC

tL

16 (20).

The proposed LLC operates by a combination of FB and HB.

Therefore, the magnetizing inductance of the proposed LLC is also

determined according to Eq. (20).

4.2 Transition between operation modes Fig. 15 shows

the voltage/current control block. The state of charge (SOC)

management block estimates the SOC of the battery and selects the

charging mode. The charging mode is selected by detecting the

output voltage and output current. When the detected output voltage

is 420V or less, the controller operates in CC mode. In CC mode,

the current controller is activated to maintain a constant charging

current. Furthermore, when the output voltage is 250 V or less, the

converter operates at CC1, therefore the output current command

value is Io_ref = 1.0A. When the detected value exceeds 250V, it

operates with CC2, the output current command value Io_ref is 2.38A.

On the other hand, when the output voltage reaches 420V, it

operates in CV mode. In CV mode, the voltage controller is

activated to maintain a constant charging voltage. The MUX is used

to determine between the CC mode and the CV mode. The output

of the PI controller is converted from a voltage reference to a

frequency reference by using gain K. The generated frequency

information is converted into a triangle wave. The duty cycle of the

switch that performs switching is 0.5.

Furthermore, the transition between the operation modes is

performed using the mode selection. The mode is selected by using

the output voltage obtained from Eq. (4)–(9) as a threshold. For

example, the output voltage Vo immediately after the transition from

mode 1 to mode 2 is represented by Eq. (5). Therefore, the

switching frequency after performing the mode transition is fs = fr

in all operating modes. To realize a seamless transition when a

mode transition is detected, the switching frequency fs changes to

be equal to the resonance frequency fr. The switching frequency fs

is feed-forward-compensated, and the compensation amount f’ is

given by Eq. (21). After the transition, the output of PI controller

reset to suppress the divergence of the controller.

sr fff ' (21)

Further, chattering occurs when the output voltage fluctuates near

the threshold value when the mode is selected. To prevent this, there

is hysteresis in the operation mode switching operation. As shown

in Fig. 4, the voltage gain at fs = fr of the LLC converter is Go = 1.0.

This characteristic does not depend on the state of the load.

Therefore, no special design is required for transition between

operation modes in the proposed control method. The switching

pattern changes according to the mode.

5. Experimental Verification

5.1 Experimental Conditions A 1.0-kW converter

prototype has been built. Table 3 lists the detailed prototype

parameters. td is 150 ns. To achieve a wide range of output voltage

gain and a high efficiency, the parameters of the two resonant tanks

are asymmetric. From Table 2, comparing modes 2 and 3, the peak

gain of mode 2 is larger than that of mode 3. Therefore, the

parameters constituting the resonance tank Tr1 are designed such

that the k1 value becomes small to realize a wide range of voltage

gain. On the contrary, k2 is 7.5, which is a large design. This means

that high efficiency is obtained near the nominal voltage of the

battery, that is, in mode 3. The lower limit of the switching

frequency is 70 kHz, and the converter operates near the resonance

frequency. The switching frequency range of the proposed circuit is

designed to be narrow compared to certain other designs (5), (18).

5.2 Steady-State Waveforms The steady-state

waveforms in mode 1 to mode 6 are captured in Fig. 16. As shown

in Fig. 16(a), the voltage levels of vab and vcd are different square

waves. The waveform in mode 1 is a light load condition. Mode 1

allows lower output voltages to be achieved compared to the

conventional FB-LLC, owing to the ISOP structure.

Fig. 16(b) shows a steady waveform in mode 2. As shown, vab is a

two-level (−360 to 360 V) square wave in FB. However, vcd is zero.

Hence, Tr1 supplies power to the load, whereas Tr2 does not supply

power to the load.

Fig. 16(c) demonstrates the steady-state waveforms of the

proposed circuit when it operates in mode 3. As shown, vcd is a two-

level (−360 to 360V) square wave in FB. iLr1 is almost zero, which

Fig.15 Voltage /Current control block and operation mode transition

+

-

K

mo

de selectio

n

Freq

uen

cy

com

pen

sation

+

+

Trian

gle w

ave

gen

erator

+

－

logic

Io_ref

Io

fs f_ref

f’=fr-fs

S1

S2

S3

S4

S5

S6

S

mode

+

-

Vo_ref

Vo

+

-

Io

M

U

X

v

d=0.5

PI

PI PI

Vo SOC

management

Vo

Io

S

Io_ref

Vo_ref

Current control loop

Voltage control loop

mode

0

1

mode threshold

1 Eq.(4) ≦ Vo<Eq.(5)

2 Eq.(5) ≦ Vo<Eq.(6)

3 Eq.(6) ≦ Vo<Eq.(7)

4 Eq.(7) ≦ Vo<Eq.(8)

5 Eq.(8) ≦ Vo<Eq.(9)

6 Eq.(9) ≦ Vo≦Vmax

mode sector



Table. 3 Converter parameters

indicates that Tr1 does not contribute to power transmission. The

experimental result agrees with the theoretical analysis.

Fig. 16(d) shows a steady-state waveform in mode 4. It can be seen

that vab and vcd are two different two-level square waves. The

voltages are −360 to 360 V and 0 to −360 V, respectively. These

different square waves indicate that the two resonant tanks operate

in FB and HB, respectively. ir2 is smaller than ir1, and Tr1 delivers a

higher power than Tr2.

Fig. 16(e) shows a steady-state waveform in mode 5. It can be seen

that vab and vcd are two different two-level square waves. The

voltages are -360 to 0 V, and −360 to 360 V, respectively. This

implies that Tr1 operates in HB and Tr2 operates in FB.

Fig. 16(f) demonstrates the steady-state waveforms of the

proposed circuit when it operates in mode 6. As shown in Fig. 16(f),

vab and vcd are two identical two-level square waves. The same

voltage range, from −360 to 360 V, indicates that the two resonant

tanks both operate in FB. However, ir1 is unequal to ir2. This

indicates that the two resonant tanks deliver different powers to the

load, because the parameters that constitute Tr1 and Tr2 are different.

5.3 Output Voltage Gain Characteristics Fig. 17

shows the measured results of output voltage gain characteristics of

the proposed LLC. The output voltage gain is normalized by Eq. (6).

It can be confirmed that the output voltage gain of the proposed

LLC can be achieved from less than 0.5 to more than 2.0 under

different load conditions. The voltage gain of fn = 0.7 in each

operation mode is expressed by the approximate expression of Eq.

(13). The gain characteristic of mode 3 is flat as compared with

other operation modes. The gain at fn = 0.7 in mode3 of Fig.17 (a)

is Go = 1.16 from the Eq. (13). The gain at fn = 0.7 in mode3 of (b)

is Go = 1.19. The experimental values are Go = 1.16 and Go = 1.17,

respectively, which satisfies the gain condition for transition to the

next operation mode. Similarly, the output voltage gain obtained at

the lowest switching frequency of each mode exceeds that obtained

at fs = fr of the next mode. Therefore, the design requirements

necessary for the operation mode transition are satisfied.

Comparing the gain curves of modes 2 and 3, it can be seen that

mode 2 covers a wider voltage gain range under the same load

conditions. This is because the inductor ratio k1 is smaller than the

inductor ratio k2. Similarly, comparing modes 4 and 5, the voltage

gain range of mode 4 is wider than that of mode 5. In mode 4, Tr1

operates in FB and Tr2 operates in HB. However, in mode 5, Tr1

operates in HB and Tr2 operates in FB. Therefore, in mode 4, Tr1

and Tr2 deliver more and less power to the load, respectively. In

mode 4, the parameter of Tr1 is dominant, and in mode 5, the

parameter of Tr2 is dominant. The mode 1 gain is lower than those

of other modes, and the mode 6 gain is higher. The output voltage

gain of mode 1 at fs = fr is less than half of that of mode 3. The

output voltage gain of mode 6 at fs = fr is more than twice that of

mode 3. In general, under load conditions with a large Q value, the

LLC peak gain is low. The peak gain of each mode in Fig. 17 (a) is

lower than the peak gain in Fig. 17 (b). Nevertheless, a wide range

of output voltage gain is obtained. Therefore, the proposed LLC can

realize a wide range of voltage gain for loads with various load

states such as a Li-ion battery.

5.4 Operation mode transition Fig. 18 shows the

transition waveforms in each operation mode. Fig. 18(a)

description symbol parameter

input voltage Vin 360V

output voltgae range Vo 100V-420V

leakage inductanceLr1 100

Lr2 40

resonance capacitanceCr1 25.3

Cr2 63.3

magnetizing inductanceLm1 250

Lm2 300

turn ration1 2.1

n2 1.5

switching frequency range fs 70kHz-100kHz

resonance frequency fr 100kHz

primary switch S1-S6 FMW79F60S1

output capacitance Coss 180pF

secondary diode D1-D6 TRS12A65C

(a) mode1 Vo=100V Po=100W (b) mode2 Vo=170V Po=170W (c) mode3 Vo=245V Po=600W

(d) mode4 Vo=290V Po=690W (e) mode5 Vo=330V Po=780W (f) mode6 Vo=415V Po=987W

Fig.16 Steady-state waveforms

vab 500V/div

vcd 500V/div

iLr1 5.0A/div

iLr2 5.0A/div

5.0μs/div vab 1000V/div

vcd 1000V/div

iLr1 10.0A/div

iLr2 5.0A/div


vcd 1000V/div

iLr1 5.0A/div

iLr2 10.0A/div

5.0μs/div


vcd 1000V/div

iLr1 5.0A/div

iLr2 5.0A/div


vcd 1000V/div

iLr1 10.0A/div

iLr2 10.0A/div


vcd 1000V/div

iLr1 10.0A/div

iLr2 10.0A/div



demonstrates a smooth transition from mode 1 to mode 2. Before

the transition, the operation mode is mode 1. The operation mode

after the transition is mode 2. According to Fig. 3(b), switch S5 in

mode 2 is always ON. As shown in Fig. 18(a), the gate–source

voltage VGS5 of switch S5 after the transition is constant and ON. It

can be seen that there is no large deviation in the output voltage

before and after the transition. The output voltage immediately after

the transition is given by Eq. (5). The switching frequency fs after

the transition is equal to the resonance frequency fr, and is 100 kHz.

Fig. 18(b) shows a transition from mode 2 to mode 3. In mode 2,

iLr2 is almost zero. In mode 3, iLr1 is almost zero. This experimental

result agrees with the theoretical analysis. According to Fig. 3(c),

switch S1 in mode 3 is always ON. The same characteristic can be

confirmed from Fig. 18 (b). It can be seen that there is no large

deviation in the output voltage before and after the transition. The

output voltage immediately after the transition is given by Eq. (6).

Fig. 18(c) demonstrates a smooth transition from mode 3 to 4.

Before the transition, the operation mode is mode 3. The operation

mode after the transition is mode 4. According to Fig. 3(d), switch

S5 in mode 4 is always ON. The output voltage immediately after

the transition is given by Eq. (7). iLr1 before the transition is almost

zero. There is no large deviation in the output before and after the

transition. In summary, the designed prototype demonstrates a

robust dynamic response over the entire working range.

5.5 Efficiency Fig. 19 provides the measured

efficiency data in the CC1 and CC2 charging stages. In CC1, when

Vo increases, the operation mode changes from mode 1 to 2, and

from mode 2 to 3. In CC2, when Vo increases, the operation mode

changes from mode 3 to 4, mode 4 to 5, and mode 5 to 6.

(a) RL=100Ω

(b) RL=300Ω

Fig.17 Measured output voltage gain characteristics

Fig. 19(a) shows the efficiency characteristics in the CC1 mode.

In this charging mode, the output current Io is a constant current of

1.0 A and the battery voltage varies from 100 to 250 V. The

transition from mode 1 to 2 occurs near Vo = 170 V. The transition

from mode 1 to 2 improves the efficiency by 1.2%. This is because

the latter mode enables fs closer to fr. Similarly, the transition from

mode 2 to 3 occurs near Vo = 250 V. The transition from mode 2 to

3 improves the efficiency by 3.7% and greatly improves the

efficiency compared to the transition from mode 1 to 2. This is

because the inductor ratio k2 constituting Tr2 is designed to be a large

value, in addition to the fact that the latter mode enables fs closer to

fr.

Fig. 19(b) shows the efficiency characteristics in the CC2 mode.

In this charging mode, the output current Io is a constant current of

2.38 A and the battery voltage varies from 250 to 420 V. Similarly,

in CC2, the latter mode demonstrates higher efficiency than the

former mode. In particular, by transitioning from mode 5 to 6 at the

operating point near the rated load, the efficiency is improved by

1.3%. The converter demonstrates 96.5% peak efficiency and good

overall efficiency in CC mode. Therefore, the operation mode

(a) mode1 to mode2

(b) mode2 to mode3

(c) mode3 to mode4

Fig.18 Operation mode transition waveform

0.7 0.8 0.9 1.00

0.5

1.0

1.5

2.0

2.5mode1 mode2

mode3 mode4

mode5 mode6

Outp

ut V

olt

age G

ain

Go


0.7 0.8 0.9 1.00

0.5

1.0

1.5

2.0

2.5

Outp

ut V

olt

age G

ain

Go


mode1 mode2

mode3 mode4

mode5 mode6

VGS5 10V/div

Vo 10V/div

iLr1 5.0A/div

iLr2 5.0A/div

500us/div

mode1 mode2

VGS1 10V/div

Vo 10V/div

iLr1 10.0A/div

iLr2 10.0A/div

500us/div

mode2 mode3

500us/div

VGS5 10V/div

Vo 10V/div

iLr1 5.0A/div

iLr2 5.0A/div

mode3 mode4



transition at fs = fr achieves seamless transition and high efficiency.

In summary, the proposed circuit topology and control method

combine wide voltage gain and high efficiency.

(a) CC1

(b) CC2

Fig.19 Efficiency characteristics in CC mode

6. Conclusions

In this paper, an asymmetric Dual-LLC resonant converter is

proposed for wide voltage gain applications such as Li-ion batteries.

Owing to the modulation of the six switches, the switching

frequency operates in a range close to the resonance frequency. The

two asymmetric transformers provide a wide voltage range (from

100 to 420 V) and high efficiency. The theoretical analysis of the

proposed six operating modes enables transitions between the

operating modes. The proposed control method achieves seamless

transitions between the operating modes without a complicated

design. The proposed topology, operation principles, design

guidelines, equivalent model, and output voltage gains analysis are

presented. To validate the effectiveness of this topology and the

theoretical analysis, a 1.0-kW laboratory prototype with an input of

360 V and an output of 100-420 V is designed. Experimental results

confirm that the proposed LLC provides a wide range of voltage

gain over a narrow switching frequency range (fs: 70-100 kHz).

Furthermore, it is confirmed that the proposed control method

achieves seamless transitions, and the converter shows good

characteristics at all charging states. The overall experimental

performance is good and the peak efficiency is 96.5%. This

proposed LLC is suitable for applications with wide output voltage

ranges, including electrical vehicle onboard chargers.

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100 150 200 25070

75

80

85

90

95

Eff

icie

ncy η

[%]

Output Voltage Vo[V]

mode3

fs=fr

mode2

mode1CC1

Io=1.0A

3.7%

1.2%

fs=fr

fs=fr

250 300 350 40092

93

94

95

96

97

98

CC2

Io=2.38A

Eff

icie

ncy

η[%

]

Output Voltage Vo[V]

mode3

mode4mode5

mode6

1.3%

fs=fr

fs=fr fs=frfs=fr


10 IEEJ Trans. ●●, Vol.●●, No.●, ●●●

for LLC resonant converter," 2010 Twenty-Fifth Annual IEEE Applied

Power Electronics Conference and Exposition (APEC), Palm Springs, CA,

2010, pp. 1770-1777.

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design methodology for LLC resonant converter," Twenty-First Annual IEEE

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Dallas, TX, 2006, pp. 6

Yuki Kinoshita (Student member) received the B.E. degree in

electrical, electronics and information engineering

from Nagaoka University of Technology, Niigata,

Japan in 2019. Presently, he has been in Master's

Program Nagaoka University of Technology. He is

the student member of IEEJ. His main research

isolated DC/DC converter.

Hitoshi Haga (Senior member) received the B.E., M.E. and D. Eng.

degrees in energy and environmental science from

the Nagaoka University of Technology, Nagaoka,

Japan, in 1999, 2001, and 2004, respectively. From

2004 to 2007, he was a Researcher with Daikin

Industries, Ltd., Osaka, Japan. From 2007 to 2010,

he was an Assistant Professor with The Sendai

National College of Technology, Sendai, Japan.

Since 2010, he has been with the Nagaoka University

of Technology, where he became an Associate Professor in 2016. His

research interests include power electronics.

wide-range voltage gain and high-efficiency of isolated...

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