Article

Control of Dual-Output DC/DC Converters Using
Duty Cycle and Frequency
Yoshinori Matsushita 1,2, *, Toshihiko Noguchi 1 , Kazuki Shimizu 3 , Noritaka Taguchi 2 andMakoto Ishii 2
1
2
3

*

Graduate School of Science and Technology, Shizuoka University, Hamamatsu 432-8561, Japan;
noguchi.toshihiko@shizuoka.ac.jp
Yazaki Research and Technology Center, YAZAKI Corporation, Susono, Shizuoka 410-1194, Japan;
noritaka.taguchi@jp.yazaki.com (N.T.); makoto.ishii@jp.yazaki.com (M.I.)
Graduate School of Integrated Science and Technology, Shizuoka University, Hamamatsu 432-8561, Japan;
shimizu.kazuki.16@shizuoka.ac.jp
Correspondence: yoshinori.matsushita@jp.yazaki.com

Received: 28 September 2020; Accepted: 10 November 2020; Published: 13 November 2020


Abstract: As part of the integration process of the auxiliary power systems of electric vehicles,
plug-in hybrid vehicles and fuel cell vehicles, this study proposes a method to control two different
voltage types using two control factors of the rectangular alternating waveforms contained in DC/DC
converters, namely the duty cycle and frequency. A prototype circuit consisting of an H-bridge
inverter, a transformer, two series resonant filters and two diode bridge circuits was constructed.
The H-bridge inverter was connected to the primary side of the transformer and the diode bridge
rectifier circuit was connected to the secondary side in parallel. Series resonant filters were inserted
between one of the diode bridge circuits and the transformer. Thereafter, the proposed control method
was applied to the transformer voltage of the prototype circuit. Although the circuit operation became
complex owing to the circulating current flowing between the ground (GND) of the two output
circuits, it exhibited ideal static and dynamic characteristics, thereby confirming the possibility ofcontrolling two voltages with the duty cycle and frequency control factors. The results of the efficiency
evaluation and loss analysis demonstrated a minimum efficiency of 68.3% and a maximum efficiencyof 88.9%. As the output power of the circuit containing the resonant filters increased, the current peakvalue increased and the circuit became less efficient.
Keywords: dual output; DC/DC converter; pulse width and frequency control; auxiliary powersource; duty cycle; frequency

1. Introduction
1.1. Research Motivations
Considering that the transportation field is estimated to be responsible for 26% of all CO2
emissions globally [1], the reduction of CO2 emissions from vehicles is an effective measure to curb
global warming. In an attempt to reduce CO2 emissions, the vehicle market is switching from gasoline
cars to electric vehicles (EVs), plug-in hybrid vehicles (PHVs) and fuel cell vehicles (FCVs), which areequipped with high-voltage sources that enable motor driving. The market for such vehicles is
expected to grow continually in the coming years [2]. The auxiliary power sources of EVs, PHVs and
FCVs use isolated DC/DC converters with input that provides high-voltage power for driving [3,4].
With the electrification of conventional functions (drive by wire) and the sophistication of internal
environments, the number and types of auxiliary loads are increasing continually. That is, the power

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capacity required for the auxiliary power supply is increasing and, depending on the use conditionsof the car, the power consumption of the auxiliary load may have a significant impact on the total
vehicle power consumption [5,6]. One factor that increases the power consumption is the additional
conduction losses caused by the large current that flows when a heavy load is driven with a 12 V
power supply. An option for reducing these conduction losses is to set the power supply voltageof the auxiliary system to 48 V and to reduce the current value [7,8]. However, owing to the costs,
part supplies and maintenance service involved, it is difficult to make all loads for a 12 V power supply
compatible with a 48 V power supply and, as a result, the demand for loads requiring a 12 V power
supply remains. For this reason, the auxiliary power supply requires a dual system that supports both
48 V and 12 V.
The configuration known as the 48-V mild hybrid, standardized as LV148 in Europe, supplies adual system of 48 V and 12 V by generating a direct current of 48 V in the alternator of engine-powered
vehicles and producing a 12 V power supply with a non-isolated bidirectional DC/DC converter of
48 V and 12 V [9]. However, the fact that two power conversions are required to generate 12 V makes
this system inefficient. Moreover, the system contains two sets of power supply equipment, making it
expensive and bulky.
1.2. Literature Review
To overcome these issues, numerous studies have been conducted on single-input, dual-output
DC/DC converters that input high voltages for driving and output 48 V and 12 V, as well as bidirectional
multiport converters that make use of a power supply from renewable energy sources installed in cars
and V2X [10–16]. On the other hand, studies have been carried out on mastering GaN devices since
GaN devices provide a high switching speed that enable operations at higher frequencies than those of
conventional Si and SiC devices, which makes power converters more compact and efficient [17–21].
The studies of the auxiliary power sources of cars have exhibited functions such as bidirectional
power transmission and four or more inputs/outputs. However, as a result of the multiple functions,the number of switching devices sending control signals has increased, thereby increasing the total
wiring length of the control signals. As control signals are vulnerable to noise, they are incompatible withthe high frequencies resulting from the use of GaN devices or increases in the power capacity of auxiliary
equipment. Furthermore, when the total wiring length of the control signal increases, the layout
becomes more complex to prevent induction noise from the power section. However, few studies havefocused on the issue.
1.3. Contribution
To attenuate this problem, the authors have proposed a method for controlling single-input,
dual-output DC/DC converters as integrated auxiliary power sources for EVs, PHVs and FCVs,
with fewer control signals and a shorter wiring length [16]. The method has novel characteristics
switching devices on input port are able to control two output voltages, which is not shared by
References [10–15]. However, Reference [16] only had demonstrated the efficacy of the method withsimulation. In this paper, therefore, the validity of the method is verified using an actual circuit with
1 kW output.
2. Overview of Proposed Control Method and Main Circuit Configuration
2.1. Overview of Proposed Control Method and Main Circuit Configuration
Figure 1 presents the concept of the proposed control method. The two output voltages Vout1
and Vout2 are controlled by two control factors, namely the duty cycle and frequency (period) withrectangular alternating voltage. This control method requires the main circuit to contain waveforms
with a duty cycle and frequency, as well as elements with output voltages that vary according to
the changes in the duty cycle and frequency. Therefore, in this study, the isolated DC/DC converter

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depicted in Figure 2 was adopted as a simple main circuit to validate the proposed control method.
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The isolation approach used consists of a transformer, the primary side of which is an input capacitor(C
and an H-bridge
inverterthat is formedby the switching
devices S1,and S4.
Theinputgatein ) isolation
The
approachused consistsof a transformer,
the primary
sideS2,
ofS3
which
is an
signals
G1,
G2,
G3
and
G4
are
input
to
each
switch,respectively.
G1
toG4
generatearectangularcapacitor (Cin) and an H-bridge inverter that is formed by the switching devices S1, S2, S3 and S4.
alternating
voltagewithandfrequency
controlfactors
and this G1
voltageapplied toThegate signals
G1,
G2,theG3dutyand cycle
G4 areinput
to eachswitch,respectively.
to G4is generateathe primaryalternatingside of the voltage
transformer.
Ondutythe secondaryside of thecontrol
transformer,
rectifiercircuit ofrectangularwith thecycle and frequency
factorsaand
this voltage
isoutput voltage
Vout1 consistingof diodes
D11, D12,
D14, Lout1 sideand C
similarly, aa rectifier
rectifierappliedto the primaryside of thetransformer.
On D13,the secondary
ofout1
theand,transformer,
circuit ofof output
outputvoltage
voltageVV
consistingof D21,D11,
D22,D12,
D23,
D24,
Lout2
and
connected
out2
circuitout1
consistingof diodes
D13,
D14,
Lout1
andCout2
Cout1areand,similarly,inaparallel.
A
seriesofresonant
filters
consisting
of
L
,
C
,
L
and
C
are
inserted
between
the
srA
srA
srB
srB
rectifier circuit of output voltage Vout2 consisting of D21, D22, D23, D24, Lout2 and Cout2 are connectedlatterdiode Abridgeand thefilterstransformer.
Thisofseries
resonant
filter changes the impedance to aninparallel.
seriescircuitof resonantconsisting
LsrA, CsrA, LsrB and CsrB are inserted between thearbitraryvalue
by operatingthefrequency
and thereby
controls
the output
voltage.theToimpedance
maintain thelatterdiode
bridgecircuit andthetransformer.
This series
resonant
filter changes
tosymmetryoftheoperation,theparameters
of
the
two
seriesresonant
filters
must
have
the
same
values.
an arbitrary value by operating the frequency and thereby controls the output voltage. To
maintain
Impedancechanges
by frequency
affect ofthetheimpedances
both theseriesmust
resonant
andthesymmetryof the caused
operation,
the parameters
two series ofresonant
filters
have filter
the same
the subsequentsmoothing
In thiscase, if Lsr1affect= Lsr2the=L
Csr , series
the impedance
sr and Csr1 =sr2 = thevalues.
Impedancechangesfilter.
causedby frequency
impedancesofCbothresonantoftheseriesresonant
filter(Z)
tothefrequencyofthetransformer
voltage
(f
)
and
the
impedancesrtx Csr1 = Csr2
filter and the subsequent smoothingfilter. In this case, if Lsr1 = Lsr2 = Lsr and= Csr, thefollowing thefilter of the
Vout2
(Zsm2
) can respectively
be expressedas (ftx) and theimpedanceof smoothing
the series resonant
filter
(Zsrside) to thefrequencyof the transformer
voltage out2 side (Zsm2) can respectively be expressed as
impedance following the smoothing filter of the V1
Zsr ( ftx ) = j ωLsr − 1,(1)
Zsr f = j ωLsr − ωC,sr
(1)
ωCsr





2ω2 𝐶)𝑜𝑢𝑡2
Rout2 2 Cout2 Rout2 Rout2


2𝜔 (
𝑅𝑜𝑢𝑡2
(
)
+
j
(2)
2ω
L
−
Zsm2 ( ftx ) =Z


ftx =
+j
2𝜔
𝐿
−
,
(2)
out2
𝑜𝑢𝑡2

,
2
2
2 1+ 2ω 22 R𝑜𝑢𝑡2 𝐶𝑜𝑢𝑡2
2 2
1+ 2𝜔 2 𝑅𝑜𝑢𝑡2 2 𝐶𝑜𝑢𝑡22
2
2
1 + (2ω) Rout2 Cout2
1 + (2ω) Rout2 Cout2 tx and Rout2 is the load resistance value of the Vout2-side circuit. Considering that thewhere ω
ω=
= 2πf
2πftx
where
and Rout2 is the load resistance value of the Vout2 -side circuit. Considering that thefrequencyofthewaveforms doubles
bridge full-wave
full-wave rectification,
frequency of the waveforms
doubles after
after thethe diode
diode bridge
rectification, thethe frequency
frequency ininZ
sm2 is doubled. With these values, Zout2, which is the impedance of the Vout2-side circuit for ftx, can be
Zsm2 is doubled. With these values, Zout2 , which is the impedance of the Vout2 -side circuit for ftx , can beapproximatedasapproximated as
Z|𝑍(3)tx ) |=
out2 ( f𝑓(3)|Z sr|| ++|Z|Zsm2|.. |.
= 22|Z

out2

sr

sm2

If the condition is satisfied whereby |Z)| decreases or increases monotonically within thetx)||Zout2out2 (ftx
operating frequency range,
f
and
|Z
|
exhibitaone-to-one
can bebe controlledcontrolled
range, ftx
tx|Zout2out2| exhibit a one-to-onerelationshiprelationshipand
andVVout2
out2 canMoreover, as the side circuit
isaa typical
typical diode
diode bridge rectifier
can bebe changed
changedby fftx
tx.. Moreover,circuit V
Vout1
out1 isrectifier circuit,
circuit,VVout1
out1 canby the duty cycleofthesecondaryside
voltageofthetransformer(D).
Therefore,Vistxtx). Therefore, Vout1
cycle of the secondary side voltage of the transformer (Dout1 is mainly
by D
Dtxtxand
andVVout2
mainlycontrollable
ftx butchanges
as as
well
as,
out2
tx affect
out1
controllable byis ismainlycontrollable
byby
ftx butchangesin Dintx D
affectVout1Vas
well
Vout2
V
changesin ftx affect
Vout2
as as
well
as. V
it ispossible
not possible
to control
andout2 , whereas
out1 . Thus,
out1 V
Vout2 as
well
Vout1
Thus,
it is notto control
Vout1 Vand
out2
whereaschangesin ftx affectV
Dtx andftx , respectively.
However,addinga gap
theresponse
responsespeed
speed ofout2 independently
independently
usingusing
Dtx andftx, respectively.
However,by byaddinga gap
inintheboth output voltages, it is possible to prevent interference
interference inin thethe control
control by
by D
Dtxtx and ftx
tx and to adjust
both output voltages to the target values.

Figure 1.
1. Concept
Concept ofof dual-output
dual-output control.
control.
FigureWorld Electric Vehicle Journal 2020, 11, 72
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4 of 21
4 of 21

Figure 2. Circuit configuration for applying proposed control method.
Figure 2. Circuit configuration for applying proposed
proposed control
control method.
method.

Althoughthe proposed
control method
requires theincorporation ofa circuit suchas aa series
seriesAlthough
Although thethe proposed
proposed control
control method
method requires
requires thethe incorporation
incorporation ofof aa circuit
circuit such
such asas a series
resonant
filtertolinkthefrequency
andcontroltarget,itispossibletocontroltwo
outputvoltagesresonant
resonant filter
filter to
to link
link thethe frequency
frequency andand control
control target,
target, itit isis possible
possible toto control
control two
two output
output voltages
voltages
using
only
the
switchingdevicesnecessarytogenerateanACrectangular
waveform
voltageusing
voltage (that(that is,is,using only
only thethe switchingswitching devices
devices necessary
necessary toto generate
generate anan AC
AC rectangular
rectangular waveform
waveform voltage
(that
is,
without
addingnewswitchingdevicesfordual-output
control).
This
reducesthelayoutrestrictions
without
addingnewswitchingdevicesfordual-output
control).
This
reducesthelayoutrestrictions
towithout adding new switching devices for dual-output control). This reduces the layout restrictions
to prevent
inductivenoise
the large
currentof themainresulting
circuit, resulting
greaterprevent
inductivenoise
fromfrom
the large
part ofpart
the maincircuit,in greaterin
flexibility
to prevent
inductive
noise
from
the current
large current
partof themain circuit, resulting
ingreater
flexibility
in thecircuitMaterials
design. Materials
and Methods
shouldbe describedwith sufficientdetailstointhecircuitdesign.
andMethods
shouldbedescribed
withsufficientdetails
toallow
flexibility in the circuit design. Materials and Methods should be described with sufficient details
toallowotherstoreplicate
and
build
on
publishedresults.
Pleasenotethatpublicationof
yourothersreplicateand buildon build
publishedresults. Please
notethat publicationof your manuscript
allow toothersto replicate
andon publishedresults.
Pleasenote that publicationof yourmanuscript
implicatesthat
youallmust
make data,
all materials,
codeassociatedand protocols
implicatesyou must
makematerials,
computerdata,code computerand protocols
withmanuscriptthat
implicatesthat
you must
make all materials,
data,
computercode and protocols
associatedwiththepublication
available
toreaders.
Pleasediscloseatthesubmission
stage
the
publication
to readers.
Pleasetodiscloseat Pleasethe submission
stage
restrictions
on anytheassociatedwithavailable
the publication
available
readers.
disclose at
the anysubmission
stage
any
restrictions
ontheavailabilityofmaterials
orinformation.
New
methods
andprotocols
shouldbeavailabilityofmaterials
orinformation.
New
methods
andprotocols
shouldbedescribed
indetailrestrictions on the availability of materials or information. New methods and protocols should be
described
in detail while
well-establishedmethods
can bebriefly
describedcited.
and appropriately cited.
while
well-establishedmethods
can be briefly
described
andappropriately
described
in detail while
well-establishedmethods
can bebriefly
described and appropriately cited.
2.2. Operating Principles of Proposed Control Method
2.2. Operating Principles of Proposed Control Method
Figure 3 presents a block diagram of the proposed control method. The calculation is conducted
Figure 3 presents a block diagram of the proposed control method. The calculation is conductedby a Field Programmable Gate Array (FPGA)(FPGA) and the signals input into the FPGA are the feedback
by a Field Programmable Gate Array (FPGA) and the signals input into the FPGA are the feedback
signals V
Vfb1 and Vfb2
obtained bybydividing
dividingby
byVV
out1andandVVout2
out2, respectively.
respectively.VVfb1
fb1 andand V
Vfb2
fb2 arewhich are obtained
out1
fb2, , which
signals Vfb1
fb1 and Vfb2, which are obtained by dividing by Vout1 and Vout2, respectively. Vfb1 and Vfb2 are
input into the FPGA via the AD converter andand thethe differences
differencesfrom
fromthetherespective
respectivetarget
targetvalues
valuesVVout1
out1*
input into the FPGA via the AD converter and the differences from the respective target values Vout1*
and
V
out2
*
are
input
into
the
PI
calculation
part
(PI
1
and
PI
2
).
The
outputsignalfromPI
1contains
theand Vout2 * are input into the PI calculation part (PI1 and PI2 ). The output signal from PI1 contains
and Vout2* are input into the PI calculation part (PI1 and PI2). The output signal from PI1contains theinformationof thephase
shiftamountδ (δα(αδ) required
Dtx,,
the informationof thephase
shiftamount) requiredbybythe
thepulse
pulsewidth
widthcontrol
control toto definedefine D
information of the phase shift amount δ (αδ) δrequired by the pulse width control to define Dtxtx,
whereastheoutputsignalfromPI
2
contains
the
informationnecessary
todefine
f
tx
(
α
T
).
These
signals
whereas the output signal from PI2 contains the information necessary to define ftx (αT ). These signals
whereas the output signal from PI2 contains the information necessary to define ftx (αT). These signals
areinput into
into thethe pulse
pulse width
width andand frequency
frequency control
control (PWFC)(PWFC) section
section andare converted
converted into
into thetheare input
and areare input into the pulse
widthand frequency control (PWFC) section and are converted into the00switchingsignals G1
G1′ toto G4G4′,, which
the information
information ofof D
Dtx andswitching signals
which containcontain theand fftx neededneeded forfor thethe transformer
transformer
switching signals G1′ to G4′, which contain the information of Dtxtx and ftx
tx needed for the transformer
0 tovoltagetocontrol
V
out1
and
V
out2
.
Thereafter,asignalwithacertaindead
time
providedto
G1′
G4′
voltage to control Vout1 and Vout2 . Thereafter, a signal with a certain dead time provided to G1to
G4is0
voltage to control Vout1 and Vout2. Thereafter, a signal with a certain dead time provided to G1′ to G4′ is
output
from
the
FPGA
and
gate
is output
from
the
FPGA
andit itisissubsequently
subsequentlyoutput
outputtotothe
thegatesgatesofofS1
S1to
to S4
S4 viavia thethe isolated
isolated gate
output from the FPGA and it is subsequently output to the gates of S1 to S4 via the isolated gate
driver
(G1 toto G4).
G4).
driver (G1driver (G1 to G4).

FPGA
FPGA

Vfb1
Vfb1

Vfb2
Vfb2

Vout1** PI1
Vout1
+ PI1
+
+
Vout2** + Vout2
-

PI2
PI2

G1'
G1'
G2'
Pulse width andG2'
Pulse width andfrequency controller G3'
frequency controller G3'(PWFC)T(PWFC)
G4'
T
G4'

G1
G1
G2
G2
G3
G3
G4
G4

FigureFigure 3.
3. Control
Control block
block diagram
diagram ofof proposed
proposed circuit.
circuit.
Figure 3. Control block diagram of proposed circuit.

Figure 4 shows the PWFC principle of switching the signal generation. The output signals from
Figure 4 shows the PWFC principle of switching the signal generation. The output signals fromthe PWFC part are G1′, with a variable frequency and a constant duty cycle of 0.5; G3′, which is
the PWFC part are G1′, with a variable frequency and a constant duty cycle of 0.5; G3′, which isWorld Electric Vehicle Journal 2020, 11, x

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5 of 20phase-shifted from G1′ by δ; and G2′ and G4′, which are inverted versions of G1′ and G3′,
respectively. A sawtooth wave with an upper limit of the crest value set by αT is generated by a
Figure4 shows
the PWFC
principleof signals.
switchingthesawtooth
signal generation.
The output
signals
counter
insidethe PWFC
to generate
these
This
wave counter
decreases
fromfrom
the0 , with a variable frequency and a constant duty cycle of 0.5; G30 , which is
the
PWFC
part
are
G1
upper limit defined by αT and when the counter reaches zero it is set to the upper limit again. As
0 by δ; and G20 and G40 , which are inverted versions of G10 and G30 , respectively.
phase-shifted
fromofG1thethedecrease ratio
counter corresponds to the clock period (TCLK) of the FPGA and remainsAsawtooth
wave
with
an
limitwaveof thecrest
value setfsawby) α
is generated
a counter
inside theconstant, the period of the upper
sawtoothTsaw(frequency
isTdefinedby αTby. Thisis the period
Ttx
PWFC
to
generatethesesignals.
This
sawtoothwave
counterdecreases
from
the
upper
limit
(frequency ftx) that is necessary for the control. Furthermore, ftx is the switching frequency ofdefinedG1′ toby αandwhen the ascounter reaches zero it is set to the upper limit again. As the decrease ratio of
G4′
is expressedT and
the counter corresponds to the clock period (TCLK ) of
the FPGA and remains constant, the period of
1
𝑓
=
(4)is
the sawtooth wave Tsaw (frequency fsaw ) is definedbyα, . This is the period Ttx (frequency ftx ) that𝑇 TCLK T
00necessary for the control. Furthermore, ftx is the switching frequency of G1 to G4 and is expressed asin which the possible range for αT is1
1≤ 𝑇 ≤ ,.
ftx =fMAX TCLK
fmin TCLK
αT TCLK
1(5)(4)

and fformin arethe maximum and minimum values of the switching frequency,
In thetheabove,
fMAXrangein which
possibleαT isrespectively. By turning a signal on when the counter reaches the upper limit (αT) and off when the
1
1to generate rectangular waveforms withcounter reaches half of the upper limit (αT/2),
it≤isαpossible
.
(5)
T ≤
f
T
f
TCLK
a frequency corresponding to αT and aMAX
dutyCLK
cycle of 0.5. minThissignal is designated as the G1′ signal.

Figure4.
4.Principle
Principleof
ofField
FieldProgrammable
ProgrammableGate
GateArray
ArrayPWFC
PWFCfunction.
function.
FigureIn the G1′
above,
fMAX and G3′
fmin isaregenerated
the maximum
and minimumof the switching frequency,
Whileis generated,by a comparisonof αvaluesδ and the sawtooth wave counter.
respectively.
Byonturningsignalon whenthe counter
upper
limit
(αT ) and
offwhenwhen thethe
Byturning G3′
when athesawtoothwaves
become reaches
smaller thethanαδ andturning
it offcounterreaches
half
of
the
upper
limit
(α
),
it
is
possibletogenerate
rectangular
waveforms
with
T/2
same amount of time since G1′ was turned on has elapsed, G3′ becomes a signal that isa
0 signal.
frequency corresponding
dutyrange
cycleofofδ0.5.
Thisthesignalis designatedas the G1
T and a thephase-shiftedfrom G1′ byto
δ. αBecause
wherecontrolholds is between
0° and180°,
0 is generated, G30 is generated by a comparison of α and the sawtooth wave counter.
While
G1
δ
the possible range of αδ is
By turning G30 on when the sawtooth wavesbecome smaller than αδ and turning it off when the same𝑇≤  ≤ G3
𝑇 .0 becomes a signal that is phase-shifted from(6)
amount of time since G10 was turned on haselapsed,◦ and 180◦ , the possible range ofG10 byBecause therangeG1′of δtowhere
theobtained
control holds
is between
Theδ.switching
signals
G4′ areby expressing
the0 inverted
signals of G1′ and G3′
αδG2′
is and G4′, respectively. As illustrated in Figure 4, Vtxp,’ which is on the primary side voltage ofasαT≤α
T .tx) change according to the input values (6)the transformer generated by G1′ to G4′, Dtx 2andTδtx ≤(=α1/fofWorld Electric Vehicle Journal 2020, 11, 72

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The switching signals G10 to G40 are obtained by expressing the inverted signals of G10 and G30
as G20 and G40 , respectively. As illustrated in Figure 4, Vtxp ,’ which is on the primary side voltage ofthe transformer generated by G10 to G40 , Dtx and Ttx (=1/ftx ) change according to the input values of
αT and αδ . However, although ftx is determined uniquely by αT , Dtx is not determined uniquely by αδ ,because the sawtooth shape determined by αT is calculated by comparison with the counter.
3. Verification of Proposed Method Using Actual Circuit
3.1. Circuit Specifications
The specifications, circuit diagram and outer appearance of the actual circuit created to verify
the proposed control method are presented in Table 1 and Figure 5, respectively. The output powerof the Vout1 and Vout2 sides are expressed as Pout1 and Pout2 , respectively. The maximum value of thetotal output power, Pout1 + Pout2 , was set to 1 kW and the maximum value of Pout2 was set to 500 W.
The input voltage Vin was set to 300 V, whereas the target values of the output voltages Vout1 and Vout2
were set to 48 V and 12 V, respectively. The minimum and maximum switching frequencies, fmin and
fMAX , were set to 50 kHz and 100 kHz, respectively and the FPGA used was a XC7K70T-1FBG484C
with a clock frequency (fCLK ) of 200 MHz (TCLK = 5 ns). When substituting the values of fmin , fMAX andTCLK into Equation (5), αT can take values between 2000 and 4000. As αT is an integer, ftx and |Zout2 |could take 2001 possible values under the verification control conditions. Proportional gains and time
constants of PI1 and PI2 were K1 = 2.5, K2 = 0.5, τ1 =3 µs, τ2 = 8 µs, respectively.
Table 1. Specifications of experimental circuit.
Parameter

Value

Pout1 + Pout2 (MAX)
Pout2 (MAX)
Vin
Vout1
Vout2
fswminfswMAXFPGA
fCLK (TCLK )
K1
K2
τ1
τ2
Cin
S1, S2, S3, S4
D11, D12, D13, D14, D21, D22, D23, D24
Transformer turn ratio
Lsr
Csr
Lout1
Lout2
Cout1
Cout2
f0

1 kW
500 W
300 V
48 V
12 V
50 kHz
100 kHzXC7K70T-1FBG484C
200 MHz (5 ns)
2.5
0.5
3 µs
8 µs
330 µF
SCT3030AL (ROHM)
FFSH4065A (ON Semiconductor)
N1:N2 = 20:5
4.5 µH560 nF7.3 µH7.0 µH
44 µF
188 µF100.3 kHzfmin and fMAX, were set to 50 kHz and 100 kHz, respectively and the FPGA used was a
XC7K70T-1FBG484C with a clock frequency (fCLK) of 200 MHz (TCLK = 5 ns). When substituting thevalues of fmin, fMAX and TCLK into Equation (5), αT can take values between 2000 and 4000. As αT is an
integer, ftx and |Zout2| could take 2001 possible values under the verification control conditions.
Proportional gains and time constants of PI1 and PI2 were K1 = 2.5, K2 = 0.5, τ1 =3 µs, τ2 = 8 µs,
World Electric
Vehicle Journal 2020, 11, 72
7 of 20
respectively.

(a)

(b)

(c)

Figure
5. Experimental
circuitdiagram
diagramandand setup:
setup: (a)diagram,(b) (b)Main
circuitwith with
Figure
5. Experimental
circuit(a)Main
Maincircuit
circuitdiagram,Main
circuitcontrol circuit; (c) Main circuit without control circuit.
control circuit; (c) Main circuit without control circuit.

The input capacitor Cin was an aluminum electrolytic capacitor of 330 µF, the switching devicesof the primary side H-bridge circuit (S1 to S4) were SiC MOSFET (SCT3030AL, ROHM) and theeight diodes of the secondary side diode bridge were SiC Schottky barrier diodes (FFSH4065A,
ON Semiconductor). Because this circuit was designed to verify the proposed control method,
the breakdown voltage and current capacity of these devices were substantially larger than necessary.
The turn ratio of the transformer was 20:5. The parameters of the elements of the series resonant filter,
Lsr and Csr , were 4.5 µH and 560 nF, respectively. The output smoothing inductors were Lout1 = 7.3 µH
and Lout2 = 7.0 µH, the output capacitor Cout1 was 88 µF with four ceramic capacitors of 22 µF in
parallel and Cout2 was 188 µF with four ceramic capacitors of 47 µF in parallel. The values of Cin ,Cout1 and Cout2 are nominal values and the values of Lsr , Lout1 and Lout2 are calculated by using thefollowing equation:di

L = dt .
(7)
V
In the above, di/dt is the rate of current change and V is the voltage across the inductor. Both di/dt
and V are obtained by the experimental measurement. The data range both parameters are constant isused for the calculation.
The resonant frequency of the series resonant filter, f 0 , could be calculated as 100.3 kHz according
to the following equation:
1
f0 =
.
(8)
√
2π Lsr Csr
Each value of Table 1 was substituted into Equations (1) and (2) to calculate Zsr and Zsm , which werethen substituted into Equation (3). The result is presented in Figure 6. In this case, it was assumed that
Rout2 → ∞. As indicated in Figure 6, the resonant frequency of the Vout2 -side circuit was approximately
100 kHz. It can be observed that this value was the resonant frequency of the resonant filter and it
was not affected by the output smoothing LC filter. This is because the resonant frequency of theWorld Electric Vehicle Journal 2020, 11, x
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8 of 20
World
Electric
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x
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21
was far from 100.3 kHz. Moreover, the Q value of the output smoothing LC filter was less than of
10%of the Q value of the series resonant filter (assuming that both filters had the same line resistance).
outputfilter(Lout2 , Cthe
) wasapproximately
kHz, which
was farfromwas
far smoothingfrom 100.3 LC
kHz.
Moreover,valueof the output4.4
smoothing
LC filterwas
less100.3
than kHz.
10%
out2Q
As the resonant frequency requiredfor control was approximately 100 kHz, in the operating
Moreover,the Qofvalueof theresonant
output smoothing
LC filter
waslessfilters
than 10%theQ valuethe seriesofthe Q value
the series
filter (assuming
that
both
hadof
the
same
line ofresistance).
frequency range between 50 kHz and 100 kHz, the impedance of the Vout2-side circuit decreased
resonant
filter (assuming
thatrequired
both filters
the sameline resistance).100
As kHz,the resonantAs
the resonant
frequency
for hadcontrol
was approximately
in the frequency
operatingmonotonically as the frequency of the transformer voltage (ftx) increased, which enabled Vout2 to berequired forcontrol
was approximately
100 kHz,
kHz, thein theoperatingof
frequency
rangecircuit
between
50 kHzfrequency
range
between
50 kHz and 100
impedance
the Vout2-side
decreased
controlled by ftx, as mentioned previously. The reason for the monotonic decrease instead of an
and
100
kHz,
the
impedance
of
the
V
-side
circuitdecreased
monotonicallyasthefrequency
monotonically as the frequency of thetransformer voltage (ftx) increased, which enabled Vout2 ofto thebeout2increase is that the volume of Lout1 andLout2 could be reduced with higher frequency when a largetransformerby
voltagewhich enabledby ftx , asmentioned
previously.
controlled
ftx, as (fmentioned
previously.
The Vreason
forcontrolled
the monotonic
decreaseinsteadof antx ) increased,out2 to be
current passed (Zout2 was small).
The reason
for theinsteadof an beincreaseis thatthehigher
volumeof Lout1 andLout2a could
increaseis thatthemonotonic
volume ofdecrease
Lout1 andLout2 could
reducedwithfrequency
when
large
be reducedwith(Zhigher
when a large current passed (Zout2 was small).
current
passedout2 wasfrequency
small).
30
Impedance(Ω) (Ω)Impedance

25
30
20
25
15
20
10
15
5
10
0
50

25

50

75

100

125

150

0
0

25

50

75

100

125

150

Frequency (kHz)

Figure 6. Zout2–f characteristics
of Vout2-side circuit.
Frequency (kHz)

Figure6.6.ZZout2–f characteristics
characteristics of
of V
Vout2
-sidecircuit.
circuit.
Figureout2–fout2
As described above, thechangerateof impedanceby-sidethe frequencychange and resonant
frequencycanbecalculatedusing
Equation(3)
andFigure6.
Theresonant
frequencyis thefrequency
upper orAs describedchangeraterateof impedanceby thebyfrequencychange andresonantAs
describedabove,
above,thethechangeof impedance
the frequencychangeand resonant
lowerof the using
operatingfrequency.
theresonant
number frequencyof possibleis frequency
valuesiscan belimit
calculated
Equation(3) andFurthermore,
FigureThe
the upper
or lowerfrequency
can be calculatedusing Equation(3) and6.Figure
6. The resonant
frequencyis the upperordefinedbyEquation
(5).
If
the
operatingfrequency
is
too
high,
the
core
lossesandswitchinglosseslimit oflimit
the operating
frequency.
Furthermore,
the numberof possible
frequency
values isvalues
definedlowerof the operating
frequency.
Furthermore,
the numberof possible
frequencyisincrease,
whereasifthe
it isoperating
too low, frequency
the volumeisoftoo
thehigh,magnetic
core
increases.
Moreover,if theincrease,changebyEquation
(5).
If
the
core
lossesandswitchinglossesdefined by Equation (5). If the operating frequency is too high, the core losses and switching losses
rateof theimpedance
relativeto the frequencychange increases.
is excessively
high andanchange
FPGA rate
withoutawhereasifwhereasitis tooiflow,
the magnetic
Moreover,if theof theincrease,
it isthetoovolume
low, theofvolumeof the coremagnetic core increases.
Moreover,if the change
high
clock
frequency
is
used,
the
impedance
values
that
it
can
take
are
not
continuousandthe
impedance
relative to relative
the frequency
is excessively
high and an
FPGAa highclock
rateof the impedance
to the change
frequencychange is excessively
highandwithout
an FPGA
withoutacontrol
resolution
decreases.
However,ifthechangerateofthe
impedance
relativetothefrequency
frequency
used, the impedance
that it cantakethat
are not
continuous
control resolution
highclockisfrequency
is used, thevalues
impedance
valuesit cantake areandnot thecontinuousand thechangeis excessively
the control
increases
but ifthe
thefrequency
operatingchange
frequency
range isdecreases.
However,
ifsmall,the change
rate ofifresolution
therelativeis excessively
control
resolution
decreases.
However,theimpedancechange rateof the toimpedance
relative to thefrequency
notexpanded,
the
power
range
that
can
be
controlledbytheV
out2-side circuit becomes narrower.
small, thecontrol resolution
butresolution
if the operating
frequencyrange
is not expanded,powerchangeis excessively
small, increases
the control
increases
but if theoperatingfrequencythe
range
isTherefore,
forthe
proposedcontrolmethodtowork
asintended,itisnecessarytoselect
the
most
range
that
can
be
controlled
by
the
V
-side
circuitbecomesnarrower.
Therefore,
forthe
proposedout2
not expanded, the power range that can be controlled by the Vout2-side circuit becomes narrower.
appropriate
resonant
frequency,
operatingfrequency
range,
characteristics
control method
to work
as intended,
it is necessary
to selectthefrequency–impedance
mostTherefore,
for theproposedcontrol method
to work
as intended,
it appropriate
is necessaryresonant
to selectfrequency,
the most
andFPGA.
operating frequency
frequency–impedance
characteristics
and FPGA.
appropriate
resonantrange,
frequency,
operating frequency
range, frequency–impedance
characteristics
and
FPGA.
3.2.
3.2. Static
Static Characteristics
Characteristics

VoltageVoltage(V) (V)
Output Output
CurrentCurrent(A) Output(A) Output

Figurepresents thetheoutput
outputvoltages
voltagesVVout1
out1 andand VVout2
out2 and
output currents
currents IIout1
out1 andout2, , with
3.2. Static
Characteristics
Figure77 presents
and output
and IIout2
with aa
total
of 1,037
1,037 W
W (P(Pout1out1 =
=
576
W),
from
power-up
until
reachingasteadystate.
total output
output of
=461
461W
W and
and PPout2
=
576
W),
from
power-up
until
reachingasteadystate.
Figure 7 presents the output voltages out2
Vout1 and Vout2 and output currents Iout1 and Iout2, with aThemeasurement
devicesusedinthe
actualverificationarelistedin
Table
2.
The measurement devices used in the actual verification are listed in Table 2.
total output of 1,037 W (Pout1 = 461 W and Pout2 = 576 W), from power-up until reaching a steady state.
The measurement devices used60in the actual verification are listed in Table 2.
50
40
60
30
50
20
40
10
30
0
20
10
60
0
50
40
60
30
50
20
40
10
30
2000.0
10
0
0.0

Vout1
Vout2

Vout1
Vout2

Iout1
Iout2
Iout1
Iout2

0.2

0.4

0.6

0.8

1.0

0.6

0.8

1.0

Time (s)0.2

0.4

Figure 7. Dual
Dual port
port
outputwaveforms.
outputwaveforms.
Time
(s)

Figure 7. Dual port output waveforms.

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Table 2. Measuring
Measuring instruments.
instruments.
Table

Instrument
Instrument
Oscilloscope
Oscilloscope
Voltage differential
differentialprobe
probe
Voltage
Current
probe
(<30
A)
Current probe (<30 A)
Currentprobe
probe(>30(>30 A)A)
Current
Deskew calibration
calibration source
sourceDeskew

Model
ModelNumber
Number
HDO6104A-MS (TELEDYNE)HDO6104A-MS (TELEDYNE)
700924700924(YOKOGAWA)(YOKOGAWA)
TCP312A
TCP312A(Tektronix)(Tektronix)
TCP303
TCP303(Tektronix)(Tektronix)
DCS025
DCS025(TELEDYNE)(TELEDYNE)

The voltage and current of both outputs were adjusted to constant values and steady operation
The voltage and current of both outputs were adjusted to constant values and steady operation
was established within 0.5 s following power-up. The averages of the adjusted voltages Vout1 andwas established within 0.5 s following power-up. The averages of the adjusted voltages Vout1 and Vout2
Vout2 were 48.0 V and 12.0 V, respectively, as per the target values. The ripple voltages in the steadywere 48.0 V and 12.0 V, respectively, as per the target values. The ripple voltages in the steady state,state, Vout1 and Vout2, were both ±0.6 V, whereas the ripple currents, Iout1 and Iout2, were ±0.2 A and ±0.8
Vout1 and Vout2 , were both ±0.6 V, whereas the ripple currents, Iout1 and Iout2 , were ±0.2 A and ±0.8 A,
A, respectively. The ripple current Iout2 was larger because the resolution of TCP303 used to measure
respectively. The ripple current Iout2 was larger because the resolution of TCP303 used to measure Iout2
Iout2 was lower than that of the TCP312A used to measure Iout1. These results indicate that thewas lower than that of the TCP312A used to measure Iout1 . These results indicate that the proposed
proposed control method can produce an output of 1 kW in an actual circuit.
control method can produce an output of 1 kW in an actual circuit.
The manner in which the voltage and current increased in this experiment was not a result of
The manner in which the voltage and current increased in this experiment was not a result of
the proposed control method but rather, because of the voltage increase slew rate of the DC power
the proposed control method but rather, because of the voltage increase slew rate of the DC power
supply ZX-1600H used in the verification. Furthermore, the control parameters of the proposed
supply ZX-1600H used in the verification. Furthermore, the control parameters of the proposed
method (proportional gain of the time constant of the PI calculation part) were only optimized formethod (proportional gain of the time constant of the PI calculation part) were only optimized forthe disturbance response, which is detailed later. This is because, if this circuit is used as designed,
the disturbance response, which is detailed later. This is because, if this circuit is used as designed,load changes will occur more frequently than power increases. The control of a circuit with a power
load changes will occur more frequently than power increases. The control of a circuit with a power
supply voltage applied from the start is a topic for future research.
supply voltage applied from the start is a topic for future research.
3.3.
3.3. Operation
Operation Points
PointsThe
The circuit
circuit operation
operation points
points used
used inin thethe simulation
simulation andand verification
verificationare
are illustrated
illustratedin
inFigure
Figure8.8.
Six
operation
points
of
154
W,
285
W,
456
W,
568
W,
740
W
and
853
W
were
preparedon
Pout1
Six operation points of 154 W, 285 W, 456 W, 568 W, 740 W and 853 W were prepared on the Pthe
out1 side
side
using
inductive
resistance,
whereasfour
operation
points
of
142
W,
268
W,
394
W
and
499
W
using inductive resistance, whereas four operation points of 142 W, 268 W, 394 W and 499 W were
were
preparedon thePout2 side using non-inductive resistance. The tests and analysis werepreparedon the P
out2 side using non-inductive resistance. The tests and analysis were conducted at aconducted
at
a
total
of
18
where power
the total
output(Pout1
Pout2)1000
was W,
lesswhichthan were1000
total of 18 locations wherelocations
the total output
Ptotal(Pout1power+ Pout2P)total
was
less+ than
W,
which
were
definedasoperation
points.
In
theSections
3.4–3.6,
4.2,
and
4.3,
the
numbers
defined as operation points. In the Section 3.4, Section 3.5, Section 3.6, Section 4.2, and Section 4.3,
indicated
in Figure
8 areinused
to 8denotethe tooperation
points.
the numbers
indicated
Figureare useddenote theoperation points.
600

#16

#17

#18

#12

#13

#14 #15

300

#7

#8

#9

#10

#11

200

#1

#2

#3

#4

#5

Pout2 (W)

500
400

#6

100
0
0

100 200 300 400 500 600 700 800 900 1000

Pout1 (W)
Figure 8.
8. Measured
Measured operation
operation points.
points.
Figure3.4. Analysis
Analysis ofof SteadySteady Operation
Operation
3.4.
In thethe simulation,
simulation, thethe waveform
waveform ofof eacheach part
part ofof thethe circuit
circuit inin steadysteady operation
operation was
was calculated
calculated
In
and
an
analysiswasperformedoneach
operation
point.
PSIM(v.
12.04)
was
used
for
the
simulation.
and an analysis was performed on each operation point. PSIM (v. 12.04) was used for the
Table 3 lists Table
the specificationsof simulation circuit.
The values
displayedin Table
3 were sameas thesimulation.
3 lists the specificationsof simulation
circuit.
The values
displayedin Table
3
experimental
listedspecificationsin Table 1 except
for theswitchingdevices.
All ofthe switching
devicesweresame asspecifications
the experimental
listedin Table
1 except
for theswitchingdevices.
AllWorldElectric Vehicle
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20

of the switching devices and the transformer were ideal and there were no parasitic resistance,
and the transformer
were ideal
andsimulation
there werecircuit.
no parasitic resistance, inductance and capacitance ininductanceand capacitancein thethe simulation circuit.
Table 3. Specifications of simulation circuit.
Table 3. Specifications of simulation circuit.
Parameter
Value
Parameter
Value
Vin
300
V
48
VinVout1
300VV
Vout1Vout2
1248VVVout2
V
fswmin
50 12
kHz
fswmin50
kHz
100 kHz
fswMAX
fswMAX
100 kHz
200 MHz
(5 ns)fCLK (TCLK)
K1 )
2.5 (5 ns)
fCLK (TCLK
200 MHz
K1 K2
2.5
0.5
K 2 τ1
0.5
3 µs
τ1 τ2
µs
83µs
τ2 Cin8µs
330 µFCin
330 µFS1, S2, S3, S4
Ideal devices
S1, S2, S3, S4
Ideal devices
D11, D12, D13, D14, D21, D22, D23, D24
Ideal devices
D11, D12, D13, D14, D21, D22, D23, D24
Ideal devices
Transformer turn ratio
N1:N2 = 20:5
Transformer turn ratio
N1:N2 = 20:5
sr
4.5
L
Lsr
4.5µH
µH
sr
560
C
Csr
560nF
nF
7.3
Lout1Lout1
7.3µH
µH
7.0
Lout2Lout2
7.0µHµH
Cout1Cout1µF
4444µF
Cout2Cout2
188µF
µF
188

These
refer toto thethe operation
operation mode
mode ofof thethe secondary
secondary side
side circuit
circuitwhen
whenPPout2
out2 wasThese analysis
analysis results
results referwasmaintained
constant
and
P
out1
was
changed(operation
points
#01,
#02,
#03,
#04,
#05
and
#06)
maintained constant and Pout1 was changed (operation points #01, #02, #03, #04, #05 and #06) and
and
when
Pout1
out1 waswaschanged(operation
points
#01,
#07,
#12
and
#16).
when P
wasmaintained
maintainedconstantconstantand
andPPout2
waschanged(operation
points
#01,
#07,
#12
and
#16).
out2
Figuredefine thethe operation
operation
Figure 99 indicatesindicates thethe voltage
voltage andand current
current direction
direction ofof eacheach part
part used
used toto definemodes,
whereas
Table
4
lists
the
operation
modes
of
the
secondaryside
circuitinthehalfmodes, whereas Table 4 lists the operation modes of the secondary side circuit in the half cycle
cycle inin aa
steadystatebased
basedonon
voltagecurrent
directionsof Figure
9. As in
shown
Table
4, thesteady state
thethevoltageandandcurrent
directionsof Figure
9. As shown
Table in4, theoperation
operation
modes
were
definedby
thesecondaryside
voltageandcurrentofthetransformer
txs
modes were defined by the secondary side voltage and current of the transformer (Vtxs and I(Vtxs ),
andItxs), thefrom
current
from the transformer
the diodebridgeon theVout1-side
(I),
recA
and
IrecB),
the current
the transformer
to the diodetobridgeon theVout1 -side
circuit(IrecA circuit
and IrecB
thecurrent
thecurrent
of
L
out1
(I
Lout1
),
the
returncurrent
of
the
V
out1
-side
circuit
(I
ret1
),
the
currents
oftheseriesof Lout1 (ILout1 ), the return current of the Vout1 -side circuit (Iret1 ), the currents of the series resonant
resonant
srA and IsrB), the current of Lout2 (ILout2), the return current of the Vout2-side circuit (Iret2)
filters (IsrAfilters
and I(IsrB ), the current of Lout2 (ILout2 ), the return current of the Vout2 -side circuit (Iret2 ) and theandthe circulating
current(Icir) thatflowedthe
betweenGNDof bothoutputs.
Inrepresents
Table 4, “+”circulating
current (Icir) that flowed
between
GND ofthe
both
outputs.
In Table4, “+”
therepresents
thepositive
direction,“−”
denotesthenegative
direction
and
“0”
is
the
conditionofpositive direction, “−” denotes the negative direction and “0” is the condition of no voltage appliedno
orvoltageappliedor no current flowing.
no current
flowing.

Figure 9.
9. Definition
Definition ofof voltage
voltage andand current
current directions.
directions.
FigureWorld Electric Vehicle Journal 2020, 11, 72

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Table 4. Definition of operation modes.
Voltage/Current

1

2

3

4

5

6

7

8

9

10

11

Vtxs
Itxs
IrecA
IrecB
ILout1
Iret1
IsrA

+
+
+
−
+
+
+

+
+
+
−
+
+
+

+
+
+
−
+
+
+

+
+
+
−
+
+
+

+
+
+
−
+
+
−

0
+
+
−
+
+
+

0
+
+
−
+
+
−

0
+
+
−
+
+
−

0
−
+
−
+
+
−

0
−
+
−
+
+
−

0
−
+
0
+
0
−

IsrB
ILout2
Iret2
Icir

−
+
+
−

−
+
+
+

+
+
+
+

+
+
0
+

+
+
+
+

+
+
+
+

+
+
+
+

+
+
+
−

+
+
+
+

+
+
+
−

+
+
+
−

There were a total of 11 operation modes for the operation points of the analysis. Table 5 lists thepossible operation modes for each operation point as indicated in Table 5, for each operation point,
several modes were used and others were not, which created a large variety of current paths. As an
example, Figure 10 depicts the simulation waveform of Vtxs and each current at operation points #04
and #12. The both waveforms of #04 and #12 are divided into 8 modes based on the definition of
Table 4, respectively. The operation modes 3, 6 and 9 were not used at operation point #04 and themodes 4, 5 and 8 were not used at #12 as shown in Table 5. Therefore, it is difficult to explain thecircuit operation by the 11 operation modes. However, by focusing on the charging condition of Lout1 ,the 11 operation modes could be categorized into three groups (A, B and C). The changes in Dtx and ftx
caused by the changes in the operation points can be explained by these three operation modes.
Table 5. Operation modes and measurement points.
Operation Point
#01
#02
#03
#04
#05
#06
#07
#12
#16

•

Operation Mode
1
#
#
#
#
#
#
#

2

3

#
#
#
#
#
#
#
#
#

#

#
#
#

4
#
#
#
#
#

5

6
#

#
#
#

#
#

7
#
#
#
#
#
#
#
#
#

8

#
#
#

9

10

11

#
#
#

#
#
#
#
#
#
#
#
#

#
#
#
#
#
#
#
#
#

Group A: Lout1 is charged (modes 1 to 5)

In this mode, Vtxs is positive. As an example, Figure 11a presents the current path in mode 2.
The transformer voltage works as the voltage source and Lout1 is charged by the following path:
Transformer → D11 → Zsm1 → D14 → Transformer.
•

Group B: Lout1 discharges (modes 6 to 10)

In this mode, Vtxs is zero and Iret1 is flowing. As an example, the current path in mode 7 isillustrated in Figure 11b. When Lout1 is discharged, its discharge current returns along the following
path: Zsm1 → D14 → Transformer → D11 →Zsm1 .

#04 and the modes 4, 5 and 8 were not used at #12 as shown in Table 5. Therefore, it is difficult to
explain the circuit operation by the 11 operation modes. However, by focusing on the charging
World Electric Vehicle Journal 2020, 11, x
12 of 21
condition of Lout1, the 11 operation modes could be categorized into three groups (A, B and C). Thechanges in Dtx and ftx caused
by 5.
the
changesmodesin theandoperation
pointspoints.
can be explained by these three
Table
Operationmeasurement
World
Electricmodes.
Vehicle Journal 2020, 11, 72
12 of 20
operation
Operation Point

Vtxp (V), Itxs (A)

80

1

40
0
-40

IrecA, IrecB (A)

-80
40
20
0
-20

2

4

operation mode#01
5 7 8 10
#02
#03
#04
#05
#06
#07
#12
#16

1

2
○
11
○ ○
○ ○
○ ○
○ ○
○ ○
○
○ ○
○ ○

Operation Mode
4 5 6 7 8 9 10 11mode○ 3 6 7operation
○
○
1
2
9 10
11
○
○ ○
○
○
Vtxs
○
○
○
Itxs ○
○ ○
○ ○
○
○
○ ○
○ ○
○
○
○
○
○
○
○
○
IrecA
○ ○
○
○IrecB
○ ○
○
○ ○
○ ○
○
○
○
○ ○
○

3
○

Vtxs
Itxs

IrecA
IrecB

-40
40
30
Group A:
Lout1 is charged (modes 1 to 5)
ILout1, Iret1 (A)•20

ILout1
Iret1

ILout1Iret1

10
In this mode,
Vtxs is positive. As an example, Figure 11a presents the current path in mode 2.
0
The transformer
voltageworks as the voltage Isource and Lout1 is charged by the following path:
50
I
Transformer25→ D11 → Zsm1 → D14 → Transformer.

•

IsrA, IsrB (A)

srA
srB

IsrA
IsrB

0

Group B:
Lout1 discharges (modes 6 to 10)
-25
-50

50
In this mode,
Vtxs is zero and Iret1 is flowing. As an example, the current path in mode 7 isI
40
I
illustrated in30Figure 11b. When Lout1 is discharged,
its discharge current returns along
the followingI
20
I
path: Zsm1 → 10D14 → Transformer → D11 →Zsm1.
ILout2, Iret2 (A)

Lout2

•

ret2

Lout2
ret2

0
20

Group C: The charge/discharge of Lout1 depends on the resonant filter voltage (mode 10)
10

Icir (A)Figure 11c
depicts the current path of mode 10. In this mode, Iret1 and IrecB are zero. The return0
current from-10Zsm1 becomes a circulating current (Icir) and moves around the return current of the Vout2-20 circulating current Icir flows because the GND of the Vout1-side and Vout2-side circuits
side (Iret2). This
0
2
4
6
8
0
1
2
3
4
5
6
are common and the return pathof the Vout2-side circuit contains ZsrA Timeor (μs)
ZsrB. The circulating current
Time (μs)
of this mode flows according(a)to the state of ZsrA and ZsrB. The current path(b) involved in Lout1 is Zsm1 →D22 →ZsrA → D11 →Zsm1. When the both-end voltage of ZsrA (VsrA) exhibits the relationship of VsrA >FigureWaveforms
halfmeasurement
Figure10.
Waveformsofoffor
halfperiod:
period:(a)measurementpoints
points#04;#04;(b)(b)measurement
measurementpoints
points#12.
#12.
Vout1, Lout1
is10.
chargedby ZsrAfor
andwhen
VsrA(a)<V
out1, Lout1 discharges.

(a)

(b)

(c)

Figure 11.
11. Current
Current path
pathofofexperimental
experimentalcircuit
circuiteach
operationmode
red indicatesline indicates
the
in in
each
operationmode(the(thered line
the pathpath
relatedto ):Lout1):(a) Mode2; (b) Mode7; (c) Mode10.
relatedto Lout1(a) Mode2; (b) Mode7; (c) Mode
10.

•

Group
charge/dischargeof Ltimeon the resonant
filter voltage(mode
out1 depends
Figure C:
12 Thepresents
the occupancy
and corresponding
frequenciesof thesethree10)modes ateach Figure
operation
Pout2 wasconstant
andout1 changed (Figure 12a), the time occupied by
11c point.
depictsWhen
the current
pathof mode10.PInthis mode, Iret1 and IrecB are zero. The returnmode
A
increased(Dtx increased) and ftx decreased (Ttx increased) as Pout1 increased. The increase incurrent from Zsm1 becomes a circulating current (Icir ) and moves around the return current of the Vout2
D
tx was caused by the increase in Pout1 and the decrease in ftx occurred to prevent an increase in theside(Iret2 ). This circulating current Icir flows because the GND of the Vout1 -side and Vout2 -side circuits
power
supplythereturnVout2-side
circuitby the increase in Dtx. However, when Pout1 wasare common
andtothepath ofthe Vcaused
out2 -side circuit contains ZsrA or ZsrB . The circulating current
constant
andP
out2 changed (Figure 12b), Pout2 increased as Ttx decreased (ftx increased) but few
of this mode flows according to the state of ZsrA and ZsrB . The current path involved in Lout1 is Zsm1
changes occurred in the percentages of the three operation modes (changes in Dtx), regardless of the→ D22 →ZsrA → D11 →Zsm1 . When the both-end voltage of ZsrA (VsrA ) exhibits the relationship ofchanges in Pout2. This indicates that the impedance change of the Vout2-side circuit caused by the
VsrA > Vout1 , Lout1 is charged by ZsrA and when VsrA < Vout1 , Lout1 discharges.
frequency change played a dominant role in the changes in Pout2.
Figure 12 presents the occupancy time and corresponding frequencies of these three modes at each
operation point. When Pout2 was constant and Pout1 changed (Figure 12a), the time occupied by modeWorld Electric Vehicle Journal 2020, 11, 72

13 of 20A increased (Dtx increased) and ftx decreased (Ttx increased) as Pout1 increased. The increase in Dtx wascaused by the increase in Pout1 and the decrease in ftx occurred to prevent an increase in the power
supply to the Vout2 -side circuit caused by the increase in Dtx . However, when Pout1 was constant andPout2 changed (Figure 12b), Pout2 increased as Ttx decreased (ftx increased) but few changes occurredin the percentages of the three operation modes (changes in Dtx ), regardless of the changes in Pout2 .
This indicates that the impedance change of the Vout2 -side circuit caused by the frequency change
World Electric Vehicle Journal 2020, 11, x
13 of 21
playeda dominant role in the changes in Pout2 .
group A

500

Pout1

250

group B

Frequency (kHz)
167
125
100

83

71

Pout2

63

#01 (154W)

group B

group C

500

250

Frequency (kHz)
167
125
100

83

71

63

1

2

3

6

7

8

#01 (140W)#02 (282W)

load conditionload conditiongroup A

group C

#03 (463W)#04 (570W)#07 (283W)#12 (427W)#05 (747W)#16 (581W)#06 (854W)
0

1

2

3

4
5
Time (μs)

6

7

8

(a)

0

4
5
Time (μs)(b)

Figure 12. Occupied time and frequency of three operation modes: (a) Pout1changesfrom
from 154
154 W
W to
out1changes
=
142
W);
(b)
P
out2
changes
from
140
W
to
581
W
(P
out2
=
154
W).
853 W (Pout2
=
142
W);
(b)
P
changes
from
140
W
to
581
W
(P
=
154
W).
out2
out2
out2

3.5. Comparative
Comparative Evaluation
Evaluation ofof Simulation
Simulation andand Measured
Measured Results
Results
3.5.
Figure 13
13 depicts
depicts thethe measured
measured andand simulation
simulation waveforms
waveforms ofof eacheach part
part at
at operation
operation points
points #01,
#01,
Figure#06 andand #16
From thethe top,top, Figure
Figure 13
13 presents
presents thethe voltages
voltages ofof the#06#16 inin steadysteady operation.
operation. Fromthe primaryprimary andandsecondary
sides
of
the
transformer
(V
and
V
),
the
currents
oftheprimary
andsecondarysides
txpand Vtxstxs
secondary sides of the transformer (Vtxp), the currents of the primary and secondary sidesofof thetransformer
the both-end
voltagesof and
D11 D12and (V
D12(Vd11Vd12and
Vd12L),
the Lout1
txp andtxs ), both-end
thetransformer(Itxp(IandItxs), Ithevoltagesof D11
d11 and), theout1 current
current
and current
output current(ILout1
series resonant
filter currents
andseries
IsrB ), theseriesout1 ), thesrA
andoutput(ILout1 andIout1),and
theIseries
resonant
filter currents(IsrA and (IIsrB), theresonant
resonant
filtervoltages
(V
and
V
),
the
both-end
voltages
of
D21
and
D22
(V
and
V
),
the
Lout2
srB
filter voltages (VsrA and VsrAsrB), the both-end
voltages of D21 and D22 (Vd21 andd21
Vd22), thed22
Lout2 current
current
and output(ILout2
Iout2the) andthe circulating
current(Icir ). According
to Figure13,
andoutputcurrentcurrent(ILout2 andIout2and) andcirculating
current(Icir). According
to Figure13, thethemeasuredandsimulation
waveforms
of
#01,
#06
and
#16
were
all
very
close,
which
confirms
thatmeasured and simulation waveforms of #01, #06 and #16 were all very close, which confirms thatthe verification
The errors
errors inand ftx,, thethe voltage
voltage surge
surge thatthat only
only
theverification circuit
circuit operated
operated asas designed.
designed. The
in D
Dtx
tx and ftx
appeared inin thethe measured
waveforms andand thethe ringing
ringing resulting
resulting fromfrom itit werewere allappearedmeasured waveforms
all caused
caused byby wiringwiringresistance,parasitic
inductanceandfloating
capacitance,
which
were
not
includedinthesimulation.
resistance, parasitic inductance and floating capacitance, which were not included in the
Figures 14 and 15 present the relationships between Dtx and Pout1 and ftx and Pout2 , respectively,
simulation.
in steady operation for the measurement and simulation. In addition, the difference between theexperimental results and the simulation results for Figures 14 and 15 are depicted in Figure 16.
Figures 14–16 indicate the experimental tests are operated by larger Dtx and lower ftx than thesimulation tests under all load conditions. The reason for the larger Dtx is that Dtx compensates for
Vout1 decreased by the conduction losses of parasitic resistance in the actual circuit and the reason forthe lower ftx is that ftx controls increasing Vout2 with increasing Dtx . Although these errors appeared,
it can be observed that the values of Dtx and ftx at all operation points in steady operation wereclose to the simulation results. Therefore, the verification circuit also operated as per the simulation
analysis at other operation points that are not shown in the waveforms of Figure 13. This is a further
demonstration of the efficacy of the proposed control method.

Vd12

Itxs

Vd11

Vd12

txp

300
150
0
-150
-300

60
30
0
-30
-60
200
160
120
80
40
0

Icir (A)

24
18
12
6
0
60
30
0
-30
-60
240
160
80
0
-80

Lout1

out1

IsrA

Iout1

IsrA

IsrB

VsrA

Vtxp
VtxsVsrB

IsrB

Vtxp
VsrA Vtxs

Itxp

240
180
120
60
0
48
36
24
12
0
10

VsrB

Itxp

Itxs

Vd21

Vd11

IsrA

IsrB

5

10

15

0

Iout1

IsrA

IsrB

20

Time (μs)
VsrA#01 VsrB

5

Vd11

Vd12

ILout1

Iout1

IsrA

IsrB

VsrA

Vtxp
VVtxs
srB

Itxp

Itxs

Vd21

Vd22

Vd11

Vd12

I ILout2
Lout1

IIout2

IsrA

IsrB

Iout2

ILout1

00

Vd12

ILout2

Iout2

Iout1

Vd22

Vd11

Vd12

ILout1

Itxs

Vd21

Vd22

ILout2-10-20

ILout1

10

15

20

0

Time
VsrA (μs)
VsrB
#01

5

10

out1

15

20

Time
(μs) V
VsrA
srB
#16

(a)

240
180
120
60
0
48
36
24
12
0
10

Itxs

Itxp

Itxs

Vd11

Vd12

Vd11

Vd12

24
18
12
6
0
60
30
300
0
150
-30
0
-60
-150
240
-300
160
80
60
30
0
-800

ILout1

Iout1

IsrA

IsrB

VsrA

VsrBVtxs

240
-60
180
200
120
160
60
120
0
80
48
40
360
24
24
12
18
0
12
106

Vd21

60
30
0
-30
-60
200
160
120
80
40
0

Vd21

Vd22

Vtxp

Itxp

-30

ILout1

Iout1

IsrA

IsrB

Vd21

Iout2

Iout1

IsrA

IsrB

15

20

-30
-60
240 Time (μs)
VsrA
160
#01
80
0
-80

I
14 of 20
14 of 21

5

10

15

Time (μs)
VsrA
#01

VsrB

d21

d22

d22

Vtxp
Vtxs
Itxs

Vd22

Vd12

Iout2

ILout1

Iout1

Iout1
IsrA

IsrB

20

0

VsrB

5

10

15

IsrB

20

Time (μs)VsrA
#01

VsrB

(b)

d21

120
60
0
48
36
24
12
0
10

VsrB

Itxp

Vd11

240
V
V of proposed circuit: (a) Experimental
V results;
V
V
Vresults.
Figure13. Waveforms(b) Simulation
V
180

Vd21

IsrB

Iout2

IsrA

0

out1

Vd21

Vd12

ILout1

10

ILout1

ILout2

00

5

Vd12

VsrA

Vd22

ILout2

ILout1

Vd11

Itxs

Vd11

Vd12

ILout2

-10
60

30
-20
0

VsrB Vtxs

Itxp

Vd22

txs

IsrA

Vtxp

VsrA

Itxs

Vd11

txp

d22

d21

d22

Vd21

Vd22

Figures 14 and 15 present the relationships between Dtx and Pout1 and ftx and Pout2, respectively,
I
I
I
I
I
I
I
I
in steady
operation
for the measurement and simulation. In addition, the difference between theIIIexperimental results and the simulationI resultsfor Figures 14 and 15 are depicted in Figure 16.
Figures 14–16 indicate the experimental tests are operated by larger Dtx and lower ftx than thesimulation
tests under all load conditions. The reason 0for the larger Dtx is that Dtx compensates for
0
-10
-10
Vout1 decreased by the conduction losses of parasitic resistancein the actual circuit and the reason
-20
-20
0
5
10
15
20
0
5
10
15
20
0
5
10
15
20
0
5
10
15
20
0
5
10
15
20
0
5
10lower
15
20 ftx is that ftx controls increasing Vout2 with increasing Dtx. Although these errors
fortheappeared,at allin steady operation
Time (μs) it can be observedTime (μs) that the values
Time (μs)of Dtx and ftxTime(μs)operation points
Time (μs)
Time (μs)
#01
#16
#01
were#01close to the simulation
results. Therefore,
the verification
circuit also#01operated as per#01the(a)at other operation points that are not shown in the waveforms(b)simulation analysisof Figure 13. Thisis a further demonstration of the efficacy of the proposed control method.
Figure13.
13.Waveforms
Waveformsof
of proposed
proposed circuit:
circuit: (a)Figure(a) Experimental
Experimentalresults;
results;(b)(b)Simulation
Simulationresults.
results.
Lout2

Lout2

out2

out2

Lout2

out2

Lout2

out2

Lout2

out2

Lout2

out2

Icir (A)

Icir (A)

ILout2, Iout2 (A) Vd21, Vd22 (V) Vsr1, Vsr2 (V) Isr1, Isr2 (A) ILout1, Iout1 (A) Vd11, Vd12 (V) Itxp, Itxs (A)Vtxp, Vtxs (V)World Electric
VehicleJournal2020, 11, 72
I
I24
World Electric
Vehicle Journal 2020, 11, x
18
12
6
0
60
30
0
-30
-60
240
160
80
0
-80

Itxp

txs

Itxp, Itxs (A)

Vd11

Itxp

ILout1, Iout1 (A) Vd11, Vd12 (V)Itxs, Vsr2 (V)ILout2, Iout2V(A)Vd21(V), Vd22 (V)ILout1, Iout1(A)
Vtxp, IVsr1txs, I(V)Itxp, IVtxssr1(A)Isr1, Isr2 (A)Icir (A)sr2 (A)d11, Vd12

Itxp

ILout2, Iout2 (A) Vd21, Vd22 (V) Vsr1, Vsr2 (V)ILout2, Iout2 (A) Vd21, Vd22 (V) Vsr1, Vsr2 (V) Isr1, Isr2 (A) ILout1, Iout1 (A) Vd11, Vd12 (V) Itxp, Itxs (A)

60
30
0
-30
-60
200
160
120
80
40
0

Duty of transformer voltage (%)

Duty of transformer voltage (%)

Figures 14 and 15 present the relationships between Dtx and Pout1 and ftx and Pout2, respectively,
65
65#6 between thein steady operation for the measurement#6 and simulation.
In addition, the difference
60
#5
60
#5
experimental
results and the simulation results for Figures
14 and 15 are depicted in Figure 16.
55
55
#4
#4
#11 tests are operated
50
Figures 14–16
indicate the#3 experimental
by larger
lower ftx than the#3 Dtx#10and #11
50
#10
#9
45for the larger Dtx#9is #15
simulation45tests underall
load
conditions.
The
reasonthatD
tx compensates for
#15
#2
#2
#14
40
Pout2 ≈ 140W
#1440
#8 conduction
Pout2 of
≈ 140W
Vout1 decreasedbythelossesparasitic
resistanceintheactualcircuitand the reason
#1
#8
#18
#1
Pout2 ≈ 283W
#
#18
35
P
≈
283W
#7
# out235 #7#13
for the lower ftx is that
increasing
Dtx. Althoughthese errors#13 ftx controls increasing Vout2 with
Pout2 ≈ 427W
Pout2 ≈ 427W
30 #12#1730 #12#17≈ 581W
Pout2 ≈ 581W
appeared, it canof Dtx and25ftx#16
at all operation points inPout2
steadyoperation#16 be observed that the values
25
0 100 200 300 400 500 600 700 800 900 1000
0 100 200 300 400 500 600 700 800 900 1000
were
close
to
the
simulation
results.
Therefore,
theverification
circuit
also
operatedas
per the
P
(W)
out1
Pout1
World Electric Vehicle Journal 2020,
11,(W)x
15 of 21
simulation analysis at other operation points that are not shown in the waveforms of Figure 13. This(a)(b) (b) Simulation results.
is a further
demonstrationtheefficacyof thepoint:
proposedcontrol method.
Figure14. Results of Dtxof
for
each
measurement(a) Experimental
results;

95

60

90

55
50
45
40

#7
#8
#9 #4

85

#3

80
75

70
#1
35 #7
65
30 #12
60
#16

25
0

95

#12
#13
#14

#1
#2#2
#3#8
#4
#5 #13
#6

#9
#10

100

300

#10

#11

#15

#14
#18

#17
200

400

#5

#6 #16#17#18#15#11
Pout1 ≈ 154W
Pout1 ≈ 282W
Pout1 ≈ 463W
Pout2
P#out1≈≈140W
570W#Pout2
Pout1≈≈283W
747W
Pout2
Pout1≈≈427W
854W
P500
out2 ≈ 581W
600

Frequency voltage(kHz) (%)
Duty of transformer

65

Frequency (kHz)

Duty of transformer voltage (%)

Figure 14. Results of Dtx for each measurement point: (a) Experimental results; (b) Simulation results.
#7
#8
#9

8555
8050
7545
7040
6535
6030

Pout2 600
(W) 700 800 900 1000
100 200 300 400 500

#12
#13
#14

65

9060

25
0

Pout1 (W)

(a)

#1
#2
#3
#1
#4
#5
#7
#6

#12
#16
100

#2
#8
#13
#17

200

#15

#5

#16
#6
#17
#18

#4
Pout1 ≈ 154W
#3
#10 P #11
out1 ≈ 282W
#10
#11 #9 #15 Pout1 ≈ 463W
#14
P#out1 ≈Pout2
570W≈ 140W#18
Pout1#≈Pout2
747W≈ 283W
300

400

Pout1 ≈Pout2
854W≈ 427W
Pout2600≈ 581W

500

out2 (W)
100 200 300 P
400
500 600 700 800 900 1000

Pout1 (W)

(b)

(a)

(b)

Figure 15. Results of ftx for each measurement point: (a) Experimental results; (b) Simulation results.

5

-5

4

-4

3

(kHz)

r voltage (%)

Figure 15. Results of ftx for each measurement point: (a) Experimental results; (b) Simulation results.

-3

60

100

200

300

400

Pout2 (W)

500

100

600

200

(a)

300

400

Pout2 (W)

500

600

(b)

5

-5

4

-4

Frequency (kHz)

Duty of transformer voltage (%)

World Figure
Electric Vehicle
Journalof2020,11,each72 measurement point: (a) Experimental results; (b) Simulation results.15 of 20
15. Results
ftx for

3
2
1
0

-3
-2
-1
0

#1 #2 #3 #4 #5 #6#7 #8 #9#10#11#12#13#14#15

Measurement points(a)#16#17#18#1 #2 #3 #4 #5 #6#7 #8 #9#10#11#12#13#14#15#16#17#18

Measurement points(b)

Figurethesimulation
simulationresults
resultsfrom
fromthetheexperimental
results
each
Figure 16.
16. Results
Results of subtract theexperimental
results
forforeachmeasurementtx; f(b)measurement
point:of Dofpoint: (a) resultsof D(a)(b) results
tx ;results
tx . results of ftx.

3.6. Dynamic
DynamicCharacteristics
Characteristics
3.6.
Figures 17
thetheoutputvoltage,measuredcurrent
waveformand simulation
results
Figures
17 andand1818present
present
outputvoltage,measuredcurrent
waveformand simulation
when
P
was
maintained
constant
at
140
W
and
P
was
switched
between285
W
and568568W
out2 Pout2 was maintained constant at 140 W and
out1Pout1 was switched between 285 W andresults when(#02
andand#04 #04
werewereswitched)
and whenPout1 wasconstant
at 286 Watand
was PswitchedW(#02
switched)
and whenPout1maintained
was maintained
constant
286Pout2
W andout2 wasbetween
270
W
and
393
W
(#08
and
#13
were
switched),
respectively.
Under
any
conditionof condition
Figures 17
switched between 270 W and 393 W (#08 and #13 were switched), respectively. Under any
and18, within
8 ms
the8output
power
was switched,bothswitched,of the output
were voltages
adjustedofFigures
17 and18,afterwithinms afterthe output
power wasboth voltagesof the output
to theirrespective
valuesprior to values
the switch.
of Figure17, an overshootwere
adjusted
to theirrespective
priorIntothe
themeasured
switch. Inwaveforms
the measured
waveformsof Figure
with
a
peak
value
of
around2
V
appearedin
both
outputvoltages
V
and
V
anand
error
of
out1
out2 and17, an overshoot with a peak value of around 2 V appeared in both output
voltages
Vout1
Vout2
approximately
0.5 V occurred 0.5
in thesteady value
Vout1 value
in the ofmeasured
waveformofwaveform
Figure 18.
andan error of approximately
V occurredin theofsteadyVout1 in themeasured
However,overall,themeasuredandsimulation
waveforms
werevery
close,
confirming
World
Electric 18.
VehicleJournal 2020,overall,
11, x
16
ofthe
21
of
FigureHowever,the measured and simulation waveforms were verythat
close,
dynamic
characteristics
ofthe
proposedcontrolmethodwerevalid.
confirming that the dynamic characteristics of the proposed control method were valid.

(a)

(b)

Figure 17. Results
Resultsofof
Pout1
dynamic
responsewhen= 140
W: (a) Experimental
results;
Pout1
dynamic
response
test test
when
Pout2 =Pout2
140 W:(a) Experimental
results; (b)(b)
Simulation
results.
Simulation
results.

(a)

(b)

Figure 17. Results of Pout1 dynamic response test when Pout2 = 140 W: (a) Experimental results; (b)Simulation
results.
World Electric
Vehicle Journal
2020, 11, 72
16 of 20(a)(b)

World Electric Vehicle Journal 2020, 11, x

17 of 21

FigureResultsofofPPout2
out2 dynamic
Pout1
= 286
results;(b)
Figure18.18.Results
dynamicresponse
responsetest
testwhen
when
Pout1
= W:
286(a)
W:Experimental(a) Experimental
results;(b)Simulation
Simulationresults.
results.

4. Evaluation of Efficiency and Losses
4. Evaluation of Efficiency and Losses
4.1. Measurement Method
4.1. Measurement Method
To evaluate the efficiency and losses of the verification circuit, the input/output power (Pin, Pout1
evaluatethe efficiency
andof theverification
circuit,the input/output
powerand(Pin ,current
Pout1 andand ToPout2) was measured
witha losses
WT1800power
analyzer.
Furthermore,
the voltageofPthe) was measured
withsidea WT1800
power
Furthermore,
the transformer
voltage and secondary
current of sidetheprimary(Vtxp, Itxp), the analyzer.
voltage andcurrent of theout2transformer
transformer
primaryside (Vand), the voltage
currentof theItxs )(Vtxs, Itxs) andthe voltage
currentof the andresonant
filterof transformer
each series secondary(VsrA, VsrB, side
IsrA, (V
IsrBtxs) ,weretxp , Itxpandthe voltageof the resonant, VsrB , IsrA , IsrB )areweremeasuredmeasuredusingandthecurrent
instruments
listed in filter
Tableof2.each
Theseries
points(Vofillustratedin
srAmeasurement
using
Figurethe19.instruments listed in Table 2. The points of measurement are illustrated in Figure 19.

FigureFigure19.
19.Points
Pointsandandloss
losspositions
positionsof
ofexperimental
experimentaltest.
test.

The efficiency η of the measured power was calculated according to the following equation:=

Pout1 + Pout2
.
Pin

(9)

For the measured voltage and current, the power of the primary side of the transformer (Ptxp),
power of the secondary side of the transformer (Ptxs) and power of the resonant filters (PsrA and PsrB)
were calculated using the following equation:

World Electric Vehicle Journal 2020, 11, 72

17 of 20

The efficiency η of the measured power was calculated according to the following equation:η=

Pout1 + Pout2
.
Pin

(9)

For the measured voltage and current, the power of the primary side of the transformer (Ptxp ),power of the secondary side of the transformer (Ptxs ) and power of the resonant filters (PsrA and PsrB )were calculated using the following equation:
40T

P=

1 X
v(t)i(t)∆T
40Tn = 6, 7, 8, 9.

(10)

0

In the above, n is the number of cycles contained in the 100 µs measured, T is the length of acycle, v(t) and i(t) are the measured voltage and current, respectively and ∆T is the time interval of
the oscilloscope of 0.1 ns. Owing to the conditions of the measuring system, each series of data was
obtained with three or four measurements, which could produce errors in the measurement results.
4.2. Efficiency Characteristics
Figure 20 depicts the efficiency at each operation point with Pout1 on the x-axis. The lowest
efficiency of 68.3% was registered at point #16, where Pout1 was the minimum and Pout2 was the
maximum. Meanwhile, the maximum efficiency was 88.9% at point #06, where Pout1 was the maximum
and Pout2 was the minimum. When Pout2 was constant, the efficiency increased along with Pout1 ,regardless of the value of Pout2 , indicating that the load losses caused by Pout2 and other fixed losses
were larger than the load losses related to Pout1 . However, when Pout1 was constant, the overall
efficiency decreased as Pout2 increased, regardless of the value of Pout1 . This indicates that the load
losses related to Pout2 were larger than those caused by Pout1 and other fixed losses. Therefore, the load
World
VehicleJournal2020, 11, x impact on the efficiency of this circuit.
18 of 21
lossesElectricof Pout2
hada significant

Total efficiency (%)

90
85

#3
#2

80
75
70
65
0

#9

#1

#8

#14

#7

#13

#18

#12

#17

#5

#4
#10

#6

#11

#15
Pout2 ≈ 142W
P#out2 ≈ 268W
Pout2 ≈ 394W
Pout2 ≈ 499W

#16

100 200 300 400 500 600 700 800 900 1000

Pout1 (W)

Figure 20.
20. Results
Results ofof efficiency
efficiency measurements.
measurements.
Figure4.3. Loss Analysis
4.3. Loss Analysis
To analyze the loss points, loss separation was performed when the ratio of P
to the total
To analyze the loss points, loss separation was performed when the ratio of Pout1
out1 to the total
output power (Pout1 + Pout2 ) was the maximum (#06), when the ratio of Pout2 was the maximum (#16)
output power (Pout1 + Pout2) was the maximum (#06), when the ratio of Pout2 was the maximum (#16)
and under intermediate conditions (#10). For the power at each part obtained by the measurement andand under intermediate conditions (#10). For the power at each part obtained by the measurement
calculation, the losses at the inverter (Winv ), transformer (Wtx ), series resonant filter (Wsr ) and rectifierand calculation, the losses at the inverter(Winv), transformer (Wtx), series resonant filter (Wsr) andcircuit (Wrec ), as well as the total loss (Wtotal ), were calculated using the equation shown in Table 6.
rectifier circuit(Wrec), as well as the total loss (Wtotal), were calculated using the equation shown in
The results are illustrated in Figure 21. The left axis indicates the losses and the right axis represents
Table 6. The results are illustrated in Figure 21. The left axis indicates the losses and the right axis
the ratio of Pout2 to the total output power.
represents theratio of Pout2 to the total output power.
Table 6. Loss calculations.
Part
Total loss
Inverter loss
Transformer loss

Symbol
WtotalWinv
Wtx

Equation
Pin − (Pout1 + Pout2)
Pin − Ptxp
Ptxp − Ptxs

World Electric Vehicle Journal 2020, 11, 72

18 of 20

Table 6. Loss calculations.
Part
Total loss
Inverter loss
Transformer loss
Resonant filter loss
Rectifier circuit loss
World Electric Vehicle Journal 2020, 11, x
400
300
250

100
50
0

Wtotal
Winv
Wtx
Wsr
Wrec

Pin − (Pout1 + Pout2 )Pin − Ptxp
Ptxp − Ptxs
Pr1 + Pr2
Wtotal − (Winv + Wtx + W sr )

132

72

51.1

45.5
34.4
46.1

#06

#10

80
60

→
24.4
25.4
43.6

19 of 21100

Rectifier circuit loss
Resonant filter loss
Transformer loss
Inverter loss

200
150

Equation

125

40

41.1

20

rate of Pout2 (%)

Power loss (W)350

Symbol

62.1
#16

0

Measurement points
Figure 21. Loss analysis results.

As
indicated
inand
Figurethe(whichWtotal values
at thepoints were
144 Wfor(#06),
198
W
Given
that Winv
Wtx 21,
at #06
exhibitedthe operation
highest efficiency)
accounted
more
than
(#10)
and
360, itWis(#16),
whereasthe ratios
Pout2 wereefficiency
14.4% (#06),
(#10)
and
76.7%
half of
Wtotalpossibleto increase
theofmaximumby 32.5%
reducing
WinvandWtx.(#16).
It is
Therefore,W
increased
as
the
ratio
of
P
increased.
Figure15
demonstrates
that,
as
the ratioa
out2the operation specifications to reduce Winv, whereas
totalnecessary to selectswitching devices that suitof
Pout2
increased,also increased
and,simultaneously,
the impedance
the Vout2 sidedecreased
core
withlow lossftxshould
be selected
andthe core structureneeds to beofoptimized
to reduce
Wtx.
and
the
value
of
the
filtercurrent
increased.
Asaresult,thecurrents
oftheinverter,transformer
andHowever, as the efficiency was the lowest when the ratio of Pout2 was the maximum (#16), Wsr andrectifiercircuitincreased,
did thelosseseachpart. increased,
Moreover,limited
the switchinglossesWrec, which
were
producedaswhen
theconduction
current of the
Vout2of-side
circuitthe efficiencyofandrectifiercircuit increased,
did twothe corelossesthe transformerandof thethe inverter
proposedcircuit.
Therefore,
reducing as
thesevaluescanof
effectively
improvetheinductor.
overall
Therefore,asfincreased,
thelossesofallparts
increased;
however,
the
fact
that
the
increase
ratio
of
tx
efficiency of the circuit. Decreasing the peak value of the resonant filter current has been suggested
W
and
W
was
larger
than
that
of
W
and
W
and
the
total
outputpower
decreased
as
the
ratio
of
rec means of reducing the Qinv
assra possible
value oftxthe series resonant filter but decreasing the Q valueP
indicatesthat thereofwaschangechanges
in Winv andWtxfrequency, whereas changes.
Wsr and W
increasedout2 increased,means
decreasing
the sensitivity
the little
impedance
to theInrecthiscase, it
at
the
three
operation
points,as
illustratedin
Figure21.
will be necessary to expand the operating frequency range to offset the amount of impedance
Giventhat Winvifand(which exhibitedthe highest efficiency)
accounted
more
thantx at #06
change.
However,
the W
range
is expanded
to the high-frequency
side, anincreasedforloss
will
be
half
of
W
,
it
is
possibletoincreasethemaximum
efficiency
byreducing
W
and
W
.
It
is
necessary
tx
total
inv
caused by the higher frequencies, as mentioned previously. Furthermore, if it is expanded to thetoselect switching
devicesthat suitof
thea operation
specifications
reduceWinv, whereas a corelow
low-frequencyside,
the problem
volume increasein thetocoreof thetransformer
and with
inductorloss
be selecteditandthe core structureneeds
be optimized
to reduce Wtx . However, as thewill should
occur. Therefore,
is necessary
to determine
thetooptimal
conditions.
efficiency was the lowest when the ratio of Pout2 was the maximum (#16), Wsr and Wrec , which were
produced
when the current of the Vout2 -side circuit increased, limited the efficiency of the proposed
5. Conclusions
circuit. Therefore, reducing these two values can effectively improve the overall efficiency of the circuit.
This paper has presented a new method to control isolated single-input, dual-output DC/DC
Decreasing the peak value of the resonant filter current has been suggested as a possible means ofconverters that are designed to be installed in EVs, PHVs and FCVs. The proposed method involves
reducing the Q value of the series resonant filter but decreasing the Q value means decreasing thedual voltage control by the duty cycle and frequency, which is realized by inserting parts withsensitivity of the impedance changes to the frequency changes. In this case, it will be necessary tofrequency-impedance characteristics into the circuit. To verify its efficacy, the proposed control
expand the operating frequency range to offset the amount of impedance change. However, if the range
method was applied to an actual circuit in which a series resonant filter was inserted in one of theis expanded to the high-frequency side, an increased loss will be caused by the higher frequencies,
diode bridge smoothing circuits that were connected in parallel to the secondary side of theas mentioned previously. Furthermore, if it is expanded to the low-frequency side, the problem of atransformer.
volume increase in the core of the transformer and inductor will occur. Therefore, it is necessary to
The results of the static characteristics indicate that two output voltages were adjusted to theirdetermine the optimal conditions.
respective target values 48 V and 12 V for the maximum output power 1037 W (Pout1 = 461 W, Pout2 =576Conclusions
W). The dynamic characteristics results show that when switching each output power, it
5.
recovered to a steady state within 8 ms after the switching of the operation point. The circuit
This paper has presented a new method to control isolated single-input, dual-output DC/DC
behaviors at the different load conditions are analyzed by the simulation of the ideal circuit and theconverters that are designed to be installed in EVs, PHVs and FCVs. The proposed method involves
simulation waveforms were close to the experimental waveforms. These results demonstrated thevalidity of the proposed control method.
The efficiency of the circuit varied between 68.3% and 88.9%. The loss separation analysis
indicated that the losses in the series resonant filter and diode bridge smoothing circuit account for
71% of the total loss and restricted the efficiency. The maximum efficiency of the circuit can beWorld Electric Vehicle Journal 2020, 11, 72

19 of 20

dual voltage control by the duty cycle and frequency, which is realized by inserting parts withfrequency-impedance characteristics into the circuit. To verify its efficacy, the proposed control method
was applied to an actual circuit in which a series resonant filter was inserted in one of the diode bridgesmoothing circuits that were connected in parallel to the secondary side of the transformer.
The results of the static characteristics indicate that two output voltages were adjusted to theirrespective target values 48 V and 12 V for the maximum output power 1037 W (Pout1 = 461 W,
Pout2 = 576 W). The dynamic characteristics results show that when switching each output power,
it recovered to a steady state within 8 ms after the switching of the operation point. The circuit
behaviors at the different load conditions are analyzed by the simulation of the ideal circuit and thesimulation waveforms were close to the experimental waveforms. These results demonstrated thevalidity of the proposed control method.
The efficiency of the circuit varied between 68.3% and 88.9%. The loss separation analysis indicatedthat the losses in the series resonant filter and diode bridge smoothing circuit account for 71% of
the total loss and restricted the efficiency. The maximum efficiency of the circuit can be effectively
increased by reducing the losses in the inverter and transformer because these losses constitute 66% of
the total loss.
Our goal for future research is to examine the following points that were not covered in this study:
controlling the circuit with a power supply voltage applied; improving the efficiency by considering
modifications in the main circuit; and selecting the parts and designing the layout with the aimof miniaturization.
Author Contributions: Conceptualization, K.S., T.N.; methodology, K.S., Y.M. and T.N.; software, Y.M.; validation,
Y.M., T.N.; formal analysis, Y.M.; investigation, Y.M.; data curation, Y.M.; writing—original draft preparation,
Y.M.; writing—review and editing, Y.M., T.N.; supervision, T.N.; project administration, N.T., M.I. All authors
have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Conflicts of Interest: The authors declare no conflict of interest.

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