Clarification of Relationship between Current Ripple
and Power Density in Bidirectional DC-DC Converter
Hoai Nam Le, Koji Orikawa, and Jun-ichi Itoh
Department of Electrical engineering
Nagaoka University of Technology, NUT
Niigata, Japanlehoainam@stn.nagaokaut.ac.jp
Abstract— This paper clarifies the relationship between thecurrent ripple and the power density in bidirectional DC-DC
converters. In the conventional power density design method, inorder to obtain the pareto-front curve of the power density andthe efficiency, the current ripple is designed as constant value,
whereas the switching frequency is varied. As a result, thepossibilities of higher power density or higher efficiency at
different current ripple are not considered. Therefore, in thispaper, the current ripple is also varied in order to evaluate all thedesignable power density. Specifically, a design flow chart isintroduced to show step-by-step how to express all the losses andthe volume of the converter as functions of the current ripple.
Several 1-kW prototypes are constructed in order to confirm thevalidity of the design flow chart. By varying the current ripple,
the highest power density of 10.1 kW/dm3 with the efficiency of
98.55% is achieved at the current ripple of 60%. Furthermore,
the maximum error between the calculated and experimental
power density and efficiency are 19.5% and 0.22 pt. respectively.
Keywords—pareto-front curve; power density; current ripple

I.

INTRODUCTION

In recent years, non-isolated bidirectional DC-DC
converters are widely applied to battery systems in HybridElectric Vehicles (HEVs), or Uninterruptible Power Supplies.
This DC-DC converter is required to have small size and highefficiency. The minimization of converters provides not only
the material cost reduction but also the easy implementation for
applications which requires space-saving power system.
Because the passive components such as inductors andcapacitors account for the majority of the volume of DC-DC
converters, the miniaturization of these passive components
leads to compact DC-DC converter. Many minimization
methods have been proposed such as high frequency switching,or resonant circuit [1]-[2]. However, higher switchingfrequency leads to the increase of switching loss, noise level,
and also requires high-speed controller [3]-[4].
The boost inductor is one of the components which
contributes mainly to the converter volume. By reducing theinductance, the volume of the boost inductor can be reduced.
Instead of increasing the switching frequency, the inductancecan be reduced by increasing the current ripple with interleaved
topology [5]. In the interleaved topology, the total current
ripple can still be maintained at small value despite that thecurrent ripple in each phase is increased. This avoids thecomplexity of the input filter design in the applications where
the current ripple is strictly limited [6]. However, many
challenges arise when the current ripple is increased such as thehigh flux density ripple, which increases the core loss. Besides,
the high current ripple increases the effective current for thesame average current. This leads to higher conduction loss inthe semiconductor devices, the boost inductor, and higher
current rating for the capacitors, which result in larger volumeof the heatsink and the capacitors. Therefore, the increase of
the current ripple introduces the tradeoff relationship among
the volume of the boost inductor, the power conversion
efficiency and the volume of other components in the circuit. In
order to design the converter at the high power density with theacceptable power conversion efficiency, the relationshipbetween the current ripple and the power density is necessary
to be clarified. According to the knowledge of the author, thisrelationship has not been researched thoroughly yet.
In this paper, the relationship between the current ripple
and the power density of the bidirectional DC-DC converter isclarified by the pareto-front curve of the power density and theefficiency. Specifically, a flow chart is introduced to show
step-by-step how to obtain the pareto-front curve when thecurrent ripple is varied. First, the semiconductor devices’ losses
are calculated in order to design the heatsink volume. Second,
the method is explained to design the capacitor volume withthe condition that both the current ripple and the voltage ripple
are satisfied. One of the most difficult challenges is the designof the inductor. When the inductance is reduced by increasing
the current ripple, the winding loss decreases due to thedecrease of the winding turns. However, the core loss increases
due to the high flux density ripple. This results in anothertradeoff relationship between the winding loss and the core loss
in the inductor design step. Therefore, the method to achieve
the smallest volume of the inductor with the lowest loss is
explained. Finally, several 1-kW prototypes are constructed inorder to verify the validity and the effectiveness of the
proposed power density design flow chart.
II.

CIRCUIT TOPOLOGY

Fig. 1 shows the circuit of the non-isolated bidirectional
DC-DC converter. In order to achieve the high power densitywith the acceptable power conversion efficiency, the analysisof the relationship between losses and volume is conducted. In
this circuit, four main kinds of loss occur; the conduction loss

and the switching loss due to the on-resistance and the nonideal switching of the semiconductor devices (Pcond, Psw), thecore loss and the winding loss of the boost inductor (Pcore,
Pwind). On the other hand, there are three factors which
contribute to the volume; the heatsink of the semiconductor
devices VolH, the boost inductor VolL and the capacitor VolC.
By varying both the switching frequency and the current ripple,
every possibilities of the designable power density can beevaluated. This paper limits to the one-phase DC-DC converter.
However, the optimal phase for the interleaved topology can becalculated simply with the proposed power density design
method.
III.

Fig. 1. Non-isolated bidirectional DC-DC with simple buck-boost
topology. The losses and volume is calculated in order to design the power
density and the power conversion efficiency.

FLOWCHART OF POWER DENSITY DESIGN METHOD

Fig. 2 shows the flowchart to design the power density
when both the switching frequency and the current ripple arevaried. The main contribution of the paper to the conventional
power density design method is to consider the current ripple
as a variable. First, the range of the switching frequency fsw andthe current ripple ΔI are selected.
Fig. 3 shows the definition of the boost inductor current
ripple ΔI and the output voltage ripple ΔVp-p. In this paper, theswitching frequency fsw is kept constant at 50 kHz, whereas thecurrent ripple ΔI is varied in 10%~200%, because the design ofthe power density by varying the switching frequency fsw at theconstant current ripple ΔI is considered as the conventional
design method. It should be noted that, when the current ripple
is larger than 100%, the DC-DC converter can be operated ineither Continuous Current Mode (CCM) or Discontinuous
Current Mode (DCM). Second, at certain (fsw,ΔI), the variables
such as the inductance L, the capacitance C, and the maximum
current Imax are calculated. Then, the heatsink volume VolH is
calculated from the semiconductor device losses Pcond and Psw.
After that, the effective value of the capacitor current IC_rms is
calculated. The capacitor volume is designed in the condition
that both the capacitance C and the allowable effective current
are satisfied.
Next, from the inductance L and the maximum current Imax,
the required storage energy in the boost inductor is calculated
in order to select the core size. Because the high power density
is preferred, the minimum designable core size is selected.
With certain core size, the evaluation range of the air gap isselected. Next, at certain air gap, the winding turns N is
calculated and decided whether this design can be
implemented. In case that all the windings can be fit into thewindow area of the core, the inductor volume VolL, and theinductor loss Pcore, Pwind are calculated. After that, the length of
the air gap is increased in order to find another combination of
Pcore and Pwind. In case that all the windings cannot be fit into
the window area of the core, the current ripple and theswitching frequency are varied in order to evaluate the losses
and the volumes at the next combination of (fsw,ΔI).
A. Design of heatsink
The volume of the heatsink changes according to the loss
from the semiconductor devices. The estimation of the heatsinkvolume is conducted based on the Cooling System
Performance Index (CSPI) [7]. CSPI is defined as the inverse
factor of the thermal resistance per unit volume. Furthermore,

Fig. 2. Flowchart to design power density when both switching frequency
and current ripple are varied. By this method, every possibilities of thedesignable power density can be evaluated.

ΔI =I max − I avg
I avg

×100

ΔV p − p =Vmax − Vmin
× 100
Vavg

Fig. 3. Definition of boost inductor current ripple and output voltage
ripple. By increasing the current ripple, the inductance of the boost
inductor is decreased. This leads to the size reduction of the boost
inductor.

the higher CSPI becomes, the more effective the heat isdissipated through the heatsink.
First, the conduction loss Pcond and the switching loss Psw ofthe semiconductor devices are derived as follows. In this paper,
MOSFET is chosen as the semiconductor devices. The
conduction loss Pcond is calculated by the effective current
flowing through MOSFET and the on-resistance of MOSFET,
T

Pcond =⎛
1 sw 2
ΔI 2 ⎞
2⎟
iin Ron dt =Ron ⎜⎜ I avg +
∫
Tsw 0
3 ⎟⎠
⎝

(1)

Where, Tsw is the switching period, Ron is the on-resistance of
MOSFET, and iin, Iavg, ΔI are the instantaneous value, theaverage value and the ripple of the boost inductor current
respectively as shown in Fig. 3.
Fig. 4 shows the pattern of the switching losses when thecurrent ripple is varied. When the current ripple is smaller than
100%, the DC-DC converter is operated in only CCM.
However, when the current ripple is larger than 100%, the DCDC converter is operated in either CCM or DCM. The turn-on
loss Psw_on is calculated by,t

Psw _ on =1 r
vds ids dt = f sw K swVo t r ( I avg − ΔI )Tsw ∫0(2)

Where, vds is the voltage applied to MOSFET, ids is the current
flowing through MOSFET, Ksw is the coefficient derived fromthe switching waveform [9], Vo is the output voltage, and tr is
the rise time of the MOSFET current ids. Similarly, the turn-off
loss Psw_off is calculated by,a) Switching losses in CCM.
Tsw
Gate Signal
SW1ON

⎡I
⎤
Psw _ re cov ery = f swVo ⎢ rrm | I avg − ΔI | +Qrr ⎥⎢⎣ k Ifall⎥⎦(4)

Where, Irrm is the peak value of the reverse recovery current,
kIfall is the current decrease rate, and Qrr is the reverse recovery
charge. The total switching loss of MOSFET changes
corresponding to the current ripple, and is classified as shownin Fig. 4,

ΔI < 100%(CCM) : Psw = Psw1 _ on + Psw1 _ off + Psw1_ re cov ery
ΔI ≥ 100%(CCM) : Psw = Psw1 _ off + Psw2 _ off
ΔI ≥ 100%(DCM) : Psw = Psw1_ off

(5)

SW1ON

SW2ON

Switching Losses when ΔI≧100%
DIODE2
conducts
FET1
conducts
Psw_off(3)

Where, tf is the fall time of the MOSFET current ids. On theother hand, the reverse recovery loss in the parasitic diodePsw_recovery is calculated by [8],Deadtime

0

tf

1
Psw _ off =vds ids dt = f sw K swVo t f ( I avg + ΔI )Tsw ∫0

Deadtime

FET2
conducts
ZVS

FET1
conducts
ZCS

iin

0

b) Switching losses in DCM.
Fig. 4. Pattern of switching losses when current ripple is varied. When thecurrent ripple is smaller than 100%, the reverse recovery, which results inhigh switching loss, occurs in the parasitic diode. When the current ripple
is larger than 100%, the DC-DC can be operated in either CCM or DCM.

Fig. 5 shows the relationship between the current ripple andthe MOSFET loss. When the current ripple is increased, theeffective current also increases. This leads to the increase in the
conduction loss. On the other hand, when the current ripple issmaller than 100%, the reverse recovery, which results in highswitching loss, occurs in the parasitic diode. Furthermore,when the current ripple is larger than 100%, by applying DCM,
not only the switching loss but also the conduction loss are
reduced due to the decrease in the effective current. However,the control method for DCM becomes complex due to thenonlinearity in DCM [10].
From (1)-(5), the required thermal resistance between theheatsink and the ambience Rth(s-a) is calculated by [11],Rth ( s − a ) =T j − TaPcond + Psw− Rth ( j − s )(6)Where, Tj is the junction temperature of the MOSFET, Ta is theambient temperature, and Rth(j-s) is the thermal resistance
between the junction and the heatsink. Next, the volume of theheatsink VolH is estimated by [7],Vol H =

1
Rth ( s − a ) CSPI

(7)

Where, CSPI is the coefficient which depends on the coolingmethods such as natural cooling or water cooling. CSPI can beextracted from the datasheet of the heatsink or can be obtainedin optimal heatsink design [7].
B. Design of capacitor
The volume of the capacitor depends on the capacitance C,
the allowable effective current, and the type of theimplemented capacitors. There are three main types of thecapacitor; the electrolytic capacitor, the film capacitor, and theceramic capacitor. The film capacitor and the ceramic capacitor
are evaluated to have longer life time than the electrolytic
capacitor in high temperature environment such as HEVs.
Moreover, with the same required capacitance, the ceramic
capacitor volume is smaller than the film capacitor volume dueto the high dielectric coefficient of the ceramic capacitor.
Therefore, in this paper, the ceramic capacitor is applied. First,
the capacitance C is calculated as a function of the desiredpeak-to-peak voltage ripple ΔVp-p,
C=

I avg

1
D1 (1 − D1 )0.5ΔV p − p f sw

(8)

Where, D1 is the duty ratio of SW1. Then, the effective current
IC_rms flowing to the capacitor is calculated by,⎡ (I − I )2⎤
= D1 ⎢ max min + ( I max − I o )( I min − I o )⎥ + (1 − D1 ) I o2
3⎣⎦

Fig. 6. Relationship between capacitance change rate due to DC bias
voltage from Murata Manufacturer. When the DC bias voltage is applied
to the ceramic capacitor, the effective capacitance decreases [12].
Therefore, when applying the ceramic capacitor, the capacitor is necessary
to be designed based on the DC bias voltage characteristic in thedatasheet.

Cdesign = C

Tsw

1
I C _ rms =iC2 dtTsw ∫0Fig. 5. Relationship between current ripple and MOSFET loss. When thecurrent ripple is increased, the conduction loss increases. On the other
hand, when the current ripple is set as 100%, the DC-DC converter isoperated in Boundary Conduction Mode. In this mode, the switching loss
reaches the smallest value. When the current ripple is larger than 100%,by applying DCM, not only the switching loss but also the conduction loss
are reduced due to the decrease in the effective current [10].

(9)Where iC is the instantaneous value of the capacitor current,
and Io is the average output current as shown in Fig. 1.
Fig. 6 shows the relationship between the capacitancechange rate due to DC bias voltage from Murata Manufacturer.
When the DC bias voltage is applied to the ceramic capacitor,
the effective capacitance decreases [12]. Therefore, when
applying the ceramic capacitor, the capacitor is necessary to be
designed based on the DC bias voltage characteristic in thedatasheet. The actual designed capacitance Cdesign is calculatedby the capacitance change rate due to DC bias voltage KDCbias
and the required capacitance C,

100
100 + K DCbias(10)

Fig. 7 shows the ratio between the capacitance and theallowable effective current from the datasheet [12]. It isnecessary to make the capacitor current below the allowableeffective current. The method to satisfy both the allowableeffective current and the actual designed capacitance is toconnect capacitors in parallel. However, this might increase thecapacitor volume. Therefore, the procedure to achieve thesmallest designable capacitor volume is applied. First, thedashed line which shows the designable capacitors in Fig. 7, iscalculated by,
I rms _ data
Cdata

≥

I C _ rms
C design(11)

Where, Irms_data and Cdata are the allowable effective current andthe capacitance for each series of capacitor in the datasheet
respectively. From Fig. 7, it is understood that, by connecting

the capacitors with high ratio between the allowable effective
current and the capacitance, the allowable effective current is
simply satisfied. Then, from the designable capacitors, thecapacitor which achieves the smallest volume is selected.
Fig. 8 shows the relationship between the capacitor volume
and the actual designed capacitance. It is understood that, thecapacitor with the highest ratio between the allowable effective
current and the capacitance does not always achieve thesmallest volume. By this procedure of capacitor design, thesmallest volume of capacitor is achieved with the satisfactionof both the allowable effective current and the actual designed
capacitance.
C. Design of boost inductor
1) Estimation of inductor volume
In this section the design of the boost inductor to achieve
the smallest volume and lowest loss is explained. First, theinductance L is calculated from the boost inductor current
ripple ΔI,
L=

1 Vi (Vo − Vi )f sw ΔI
2Vo

Fig. 7. Relationship between allowable current ripple and capacitancefrom Murata Manufacturer [12]. The higher the ratio between theallowable effective current and the capacitance becomes, the more simply
the allowable effective current is satisfied.

(12)

Where, Vi is the input voltage. The inductor volume VolL is
calculated by Area Product [13],32⎛ LI max⎞4⎟
Vol L = K V ⎜⎜⎟⎝ K u Bmax J ⎠(13)

Where, KV is the coefficient which depends on the shape of thecore [13], Ku is the window utilization factor, Bmax is the
maximum flux density of the core, and J is the current density.
By substituting (12) into (13), the equation of the inductor
volume is rewritten as the function of the current ripple ΔI andthe switching frequency fsw,

Fig. 8. Relationship between capacitor volume and capacitance. From thedesignable capacitors shown in Fig. 7, the capacitor which achieves thesmallest volume is selected. It should be noted that the capacitor with thehighest ratio between the allowable effective current and the capacitance,
does not always achieve the smallest volume.

3⎡ Vi (Vo − Vi ) I avg 1 ⎛1 ⎞⎤ 4⎟⎟⎥⎜⎜ ΔI +
Vol L = K V ⎢ΔI ⎠⎥⎦⎣⎢ 2 K u Bmax JVo f sw ⎝(14)

It is clearly understood from (14) that, the inductor volume
depends on both the switching frequency fsw and the current
ripple ΔI. Therefore, in case only the switching frequency isvaried, the smallest designable inductor volume might beunconsidered.
Fig. 9 shows the relationship between the current ripple andthe volume of the DC-DC converter. Because the heatsinkvolume depends on the MOSFET loss as shown in (6), and (7),the dependence of the heatsink volume on the current ripple issimilar to the relationship between the MOSFET loss and thecurrent ripple as shown in Fig. 5. Besides, the capacitor volume
is relatively small because the ceramic capacitor with the highdielectric coefficient is applied. On the other hand, the inductor
volume reaches the smallest value when the current ripple isdesigned at 100%. When the current ripple is increased over
100%, the required storage energy in the inductor can be noFig. 9. Relationship between current ripple and converter volume. By
varying the current ripple, the smallest volume of the converter isachieved at current ripple of 60%.

longer decreased due to the increase of the current peak Imax asshown in (13) and (14). In order to achieve the highest power
density, the smallest core size which satisfies (15) is selected[13].

Ae Aw ≥

2
LI max
JBmax K u

(15)

Where Ae, and Aw are the cross-sectional area, and the window
area of the core.
2) Calculation of winding turns
With selected core, the air gap is varied in order to achieve
the smallest inductor loss. This section explained the method
to calculate the required winding turns at certain air gap lg.
The winding turns N is calculated by,

N = L( Rg + Rc )(16)

Where, Rg and Rc are the reluctance of the gap and the core. In
the case that the air gap is applied to avoid the flux saturation,
the fringing flux near the gap is necessary to be consider inorder to calculate the winding turns accurately. Specifically,
the conventional and improved equations to calculate thereluctance of the gap are as follows respectively,

Rg _ conv =1 lg
Ae μ o(17)

Rg _ impr =σ xσ y l g
Ae μo

(18)

Where, μo is the relative permeability of the core material, andσx, σy are the fringing factors considering the fringing effects
in the x-direction and y-direction respectively. The procedure
to calculate the fringing factor σx and σy with certain air gap
shape has been explained thoroughly in [14].
3) Calculation of winding loss
The method to calculate the winding loss considering theskin effect is explained in this section. First, the effective
cross-sectional area of the winding wire Swind which considers
the skin effect is calculated by,
2

r
⎡
− ⎞⎤
⎛
⎢r − δ ⎜⎜1 − e δ ⎟⎟⎥⎢⎝⎠⎥⎦S wind = 4πδ ⎣r−⎞
δ⎛r − ⎜⎜1 − e 2δ ⎟⎟
2⎝
⎠

(19)

Where, r is the radius of the winding wire, and δ is the skindepth at certain switching frequency [13]. Then, the winding
loss Pwind is calculated by the effective value of the boost
inductor current and the resistance of the winding wire Rwind,
TPwind =

ΔI 2
1 sw 2
1 l wind
2
=
I
+
(
)
i
R
dt
in
wind
avg
σ S wind3
Tsw ∫0(20)

Where, lwind is the length of the winding wire, and σ is theelectrical conductivity of the winding material. In this paper,
because the switching frequency is limited up to 50 kHz, theproximity effect is considered to be small enough to be
negligible.

Fig. 10. LOSS MAP under DC bias conditions (ferrite PC40). By
increasing the winding turn, the flux density ripple is reduced. However,
because the premagnetization HDC is increased, the core loss reduction is
not effective.

4) Calculation of core loss
When the current ripple is increased, the flux density ripple
becomes high, which leads to the high core loss. The core loss
Pcore is calculated by the improved Generalized Steinmetz
Equation (iGSE),

'
e i

α

Pcore = V k f sw ΔB

β ' −αα⎡ ΔB α
⎤
ΔB
⎢
D1 +
D2 ⎥
D2
⎢⎣ D1
⎥⎦

(21)

where Ve is the effective core volume, ΔB is the flux density
ripple and D2 is the duty ratio of SW2, ki’, α, β’ are the iGSE
parameters. The calculation of the core loss is conducted asfollowing steps:i) The LOSS MAP, which is the measured core losses of
the triangular flux waveforms at different DC bias conditions,is obtained [15]-[16]. In this paper, the LOSS MAP is
obtained at 3 different values of ΔB.
ii) The iGSE parameters ki’, α, β’ are derived from the
LOSS MAP in order to be able to calculate the core loss invarious conditions [17].
Fig. 10 shows the LOSS MAP of PC40 (Ferrite) at 25oC. It
is understood from Fig. 10 that, in case that the impact of DC
bias to core losses cannot be negligible as in ferrite PC40, thereduction of ΔB is not always a good solution to reduce thecore loss. Specifically, by increasing the winding turns, ΔB
can be reduced from point A to point B; however, thisincreases the premagnetization HDC, which increases the coreloss. As the result, the increase in the winding turns cannot
reduce the core loss but only increases the winding loss.
IV.

EXPERIMENTAL RESULTS

Table 1 shows the experimental condition and theparameters of the semiconductor devices and the inductor.
Fig. 11 shows one of the prototypes which are constructedin order to verify the validity of the proposed power density
design method. In this paper, both the highest power density of
10.1 kW/dm3 and the highest efficiency of 98.55% areachieved at the current ripple of 60%. By the waveform of the
input current, it is confirmed that the core do not saturate at
rated power.

Table 1. Experimental and Design Parameters.

H = 40 mm

Inductance L [ H](a) Inductance with 10 turns.

L = 59 mm

W = 42 mm(b) Inductance with 50 turns.
Fig. 12. Inductance design with/without consideration of fringing flux
around gap. By considering the fringing effect, the desired inductance isdesigned accurately. The winding turn design step is crucial to the
inductor loss design.

(a) Prototype Layout.

Fig. 13. Relationship between current ripple and inductor loss. The tradeoff relationship between the winding loss and the core loss requires the
optimal design of both the current ripple and the air gap.

(b) Operation Waveform.
Fig. 11. 1-kW non-isolated DC-DC converter with power density of 10.1
kW/dm3 and efficiency of 98.55%.

Fig. 13 shows the relationship between the inductor loss
and the current ripple. By increasing the air gap, the winding
turns can be increased without making the core become
saturated. However, the core loss does not always decrease byincreasing the winding turns as explained above. The
calculation of the winding loss by (20) still results with error ofabove 10% due to the inconsideration of the proximity effect.

Fig. 12 shows the calculated and experimental inductancewhen the fringing flux is unconsidered/considered. When the
air gap increases from 0.5 mm to 1.25 mm, the error between
the calculated and experimental inductance increases from 34%
to 79%. Furthermore, when the fringing flux is considered, theerror is reduced from 79% to 6%.

Fig. 14 shows the experimental and calculated total loss.
The experimental results agree to the calculated results with theerror smaller than 10%. For simplicity, the air gap is designed
at constant value (1.25 mm). However, as mentioned above,
the air gap should be varied in order to find the lowest inductor
loss. By calculating accurately the total loss, the efficiency canbe designed simply.

the proposed power design method. The highest power densityof 10.1 kW/dm3 was achieved with the efficiency of 98.55% at
the current ripple at 60%.
In the future, the consideration of the losses from theproximity effect and the fringing flux will be conducted in casethat those losses cannot be neglected. Furthermore, the input
filter will also be considered in order to satisfy the regulationsof the noises.
REFERENCES[1]

Fig. 14. Experimental and calculated results of total loss. By calculating
the total loss accurately, the efficiency can be designed simply.

Fig. 15. η-ρ pareto front with current ripple as variable. The proposed
power density design method enables to evaluate every possibilities ofthe designable power density.

Fig. 15 shows the pareto-front curves of the proposed
design with the varied current ripple. The maximum errors in
the power density and the efficiency are 19.5% and 0.22 pt.,
respectively. The error of the power density occurs because theair space between the devices is not considered in the proposed
power density design method, whereas the errors of theefficiency occurs due to the inconsideration of the proximity
effect and the fringing flux loss. However, the experimental
power density without the air space almost agrees with thecalculated value. This result confirms the validity of the
proposed design. Furthermore, in this consideration, the highest
power density can be reached with the highest efficiency.
However, the parameters such as the switching frequency andthe core material should be varied in order to find the optimum
point of the power density or the efficiency.
V.

CONCLUSION

In this paper, the relationship between the current ripple
and the power density of the bidirectional DC-DC converter
was clarified. The flowchart which was used to draw every
possibilities of the designable power density in the pareto-front
curve was introduced. Furthermore, the method to calculate theceramic capacitor with condition that both the effective
capacitor current and the capacitance are satisfied was
explained. Besides, the method to design the smallest inductor
with the lowest loss was also explained. Several 1-kW
prototypes were constructed in order to verify the validity of

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