Reduction of a Boost Inductanceusing a Switched Capacitor DC-DC Converter
Jun-ichi Itoh1, Koichi Matsuura1, and Koji Orikawa1
1

Nagaoka University of Technology, 1603-1 Kamitomioka-cho Nagaoka City, Niigata, Japan

Abstract-- The loss analysis of a switched capacitor
converter (SCC) with a boost reactor is discussed in thispaper. The proposed SCC can deliver an output voltage
independent from the circuit structure comparing to othervoltage control methods. The main feature of this circuit isthat most of the energy for the boost up function istransferred from a flying capacitor which results theinductance of the input reactor can be reduced. The reactor
size of the proposed SCC is smaller than that of theconventional boost converters. A 1000 W 3-level SCC
prototype has been built and tested. The efficiency of 97.8%
is achieved at 1000 W when the boost up ratio is three times.
Moreover, the loss analysis shows the main loss of the
proposed SCC is the diode conduction loss.
Index Terms-- DC/DC converter, Switched capacitor
converter, Boost converter

I. INTRODUCTION
High power DC-DC converters are required forelectric vehicles and photovoltaic systems recently.
However, conventional DC-DC converters need a big
inductance because the charge energy of a reactor mustbe large enough for the reactor current to operatecontinuously. As a result, the circuit size is large due tothe bulky input reactor.
On the other hand, switched capacitor converters(SCCs) have attracted attention because SCC only uses
capacitor to boost-up the input voltage [1]-[4]. Since the
SCC does not require a magnetic component, this type of
converter has the lowest weight among other DC-DC
converters. Due to the light weight advantage, SCCs arewisely applied in the low power application. However,the SCC has known problems. One of the problems isthat a large peak inrush current occurs at the flying
capacitor. Therefore the efficiency decreases and life timeof flying capacitor becomes short. Another problem isthat the output voltage is unable to control. In addition,
the maximum output voltage is depending on the circuit
structure. The output voltage can be increased by adding
the number of level n. However, the output voltage is
impossible to output over (n–1) Vin,. This problem limits
the application of this circuit.
Recently, the applications of SCCs into the high power
converter have been actively studied. Especially, resonant
switched capacitor converters (RSCC) have shown to bean effective circuit [5]-[10]. The RSCC uses an additional
inductor in series to the capacitor in order to suppress alarge peak current and leads to the soft switching
operation. Varies methods have been proposed to control

the output voltage of RSCCs by using the phase shift, theduty ratio and the switching frequency. However each of
the methods has not been reported in term of the output
voltage control. These proposed methods had a similar
problem on the control of the output voltage because thevoltage control is depending on the circuit structure.
This paper proposes a SCC with the use of small boost
reactor in the input side which enables the control of
output voltage. The proposed SCC can control the output
voltage if the input current is in continuous mode.
Moreover, a large peak current will not occur because themaximum current through circuit is limited by the input
current.
One of features in the proposed SCC is that most of
the boost-up energy is transferred from the flying
capacitor. Therefore, the input reactor can be composedby a smaller inductor compared to the conventional boost
converter. (A conventional boost converter is consistingof two switching devices and a boost reactor.) Anotheradvantage of the proposed SCC is to increase the circuit
level by adding two more switches and one more flying
capacitor. The reduction of the input inductance is shown
to be more effective in a multi-level connection.
Although the switching devices are increased in proposed
SCC, the total loss can be reduced for using low-voltage
devices.
Firstly, a basic principle of the SCC and the proposed
SCC are described. Secondly, design method of the boost
reactor is discussed. The design method shows that theinductance used in the proposed SCC is 75% smaller thanthat of the conventional boost chopper. After that, an
input reactor core volume is compared. As a result, theinput reactor is successfully reduced by 35%. Finally,
experimental results are shown in order to demonstrate
the advantages of the proposed SCC. The efficiency is
97.8 % at 1000 W. From these results, the validity of the
proposed SCC is confirmed. In addition, the multi-level
SCC with a boost-up reactor will be discussed in order toconsider suitable number of the level.
II. PRINCIPLE
A. Switched capacitor dc-dc converter
Figure 1 shows a circuit configuration of a 3-level
SCC. The output voltage Vout is twice of the input voltage
Vin by controlling the charging and discharging operationin the capacitor C. Since the SCC does not use a magnetic
component, this converter is small size and lightweight.
Figure 2 (a) shows the switching pattern and Fig. 2 (b)shows the operation mode of the SCC at 50 % duty ratio.
The operation modes are classified as follows; (I) charge
mode from the input voltage Vin and (II) discharge modeto the load. In mode (I), the capacitor C is charged by
input voltage Vin, and then MOSFET S2 and S4 are in ON
state. In mode (II), the energy of capacitor C istransferred to the load. Therefore, the maximum output
voltages are obtained from Eq. (1). Equation (1) mentions
that the maximum output voltage is limited by the circuit
structure.
Vout = 2Vin ............................................................... (1).
In order to solve this problem, a RSCC is connecting
to a resonant reactor in series to the capacitor C and its
control methods have been proposed. However, thelimitation on the voltage control is still remaining.
B. Voltage control type 3-level SCC
Figure 3 shows a circuit configuration of the proposed
3-level SCC with the functionality of controlling theoutput voltage. This circuit combines a SCC with a boost
reactor. The output voltage can be controlled
independently from the circuit construction since thestandard boost reactor is utilized in this circuit. Therefore
the output range of the voltage is wide comparing to aconventional control method. The relationship between
the input voltage and the output voltage is obtained from1
Vout =
Vin ....................................................... (2),1− λwhere λ is the duty ratio (λ=Ton/T).
Figure 4 shows the switching patterns of the proposed
3-level SCC with the uses of two triangle carriers in the
carrier comparison. In addition, these triangle carriers
have phase difference mutually. In the proposed 3-level
SCC, a 180 degrees phase shift is needed because electriccharges of charge and discharge time must be balanced in
one switching period. The charge time of an input reactor
is determined from the crossover time of two switchingpulses; particularly the boost ratio is two times and higher.
Figure 5 illustrates the operation mode of the output
voltage control type SCC. If the boost ratio α is smaller
than 2, then this circuit operates in mode (I), (II) and (III).
If α is larger than 2, then this circuit operates in mode (I),(II) and (IV).

Fig. 1. Boost type 3 level switched capacitor converter.

(a) Switching pattern.

(b) Equivalent circuits.
Fig. 2. Operation mode of the 3-level switched capacitor
converter.

Fig. 3. 3-level output voltage control SCC.

III. DESIGN OF THE INPUT REACTOR
A. Design method
A design of the input reactor is dominated by the
maximum input current ripple. In order to simplify thederivation, the following conditions are assumed:(a) Output voltage and flying capacitor voltage areconstant i.e. the voltage ripple on flying capacitor can beneglected.
(b) On state resistance of the switching devices anddead time are ignored.
First of all, the ripple of the input current at the input
reactor charging time is discussed. The input current

Fig. 4. Switching pattern of the 3-level SCC.

ripple ∆I is obtained from Eq. (3).
∆I = VL

TL................................................................. (3),Lwhere TL is the charge time of input reactor and VL is
input reactor voltage. Equation (3) shows that input
current ripples become maximum if the product VL and TL
are maximum.
An inductance is obtained by Eq. (4) using Eq. (3) in aconventional boost chopper. Equation (4) is designed

from the maximum point of the current ripple.
LChopper =Vout T 1
× ×............................................... (4),2
2 ∆I

where Vout is the output voltage and T is switching
period. In the conventional boost chopper, if a boost ratio
is 2, then the ripple current is at the maximum. Therefore,a reactor voltage and switching period is half. As a result,the charge and discharge times are the same.
Figure 6 shows the relationship between a boost ratio
and voltage time products (VLTL) of the reactor in the
proposed SCC. It should be noted that 1.0 p.u. is the
maximum point of the current ripple. In the proposed 3level SCC, at the maximum point of the current ripple,
the boost ratio is either 1.33 or 4. The inductance L canbe obtained fromV
T
1
LSCC = out ××......................................... (5).
2 × 2 2 × 2 ∆I
In the proposed 3-level SCC, the reactor voltage ishalf of a conventional boost chopper. Moreover, the input
current frequency of the proposed 3-level SCC isapproximately twice of the conventional boost chopper.
Therefore the charge time of input reactor TL is half of theconventional boost chopper.
Figure 7 shows the inductance of the conventional
boost chopper and the proposed 3-level SCC with a boost
reactor. The calculation conditions are follows; output
power Pout=1000 W, output voltage Vout=500 V,
switching frequency fs=100 kHz and current ripple is
30% of a maximum input current. This graph shows thatthe required inductance of the proposed 3-level SCC witha boost reactor is approximately 25% of that for theconventional boost chopper. Due to the reason, theinductance is proportional to the number of turn of thereactor, the copper loss is reduced.

Fig. 5. Operation mode of 3 level SCC with input reactor.

Fig. 6. Relation between the volte time products and boost ratio in the
proposed circuit.

B. Comparing of the volume of input reactor
In this section, the core volume of an input reactor is
discussed. The core volume of the proposed 3-level SCC
and the conventional boost chopper are compared by
Area Product concept [10].
Area Product is a quantitative estimation method of acore. According to Area Product, the core volume isobtained by.
3

 2W  4 .............................................. (6),
Vol = K v 
 K u Bm J w 
where Kv is the constant related to volume factor, W is
the maximum energy of the reactor, Ku is the window
utilization factor of the core, Bm is the maximum flux
density and Jw is the current density in wire. A core
volume is proportional to the three-fourth power of the
maximum energy of the reactor.
The needed inductance for the proposed 3-level SCC
is approximately 25 % of a conventional boost chopper,
which can be clarified by the following equations. Theenergy for the standard boost converter and the proposed
3-level SCC are obtained from Eq. (7) and Eq. (8),Fig. 7. Comparing of inductance between a conventional .boost chopperand a proposed 3-leve SCC.

respectively.
1
LChopper I 2 ............................................... (7),21
1 L
WSCC = LSCC I 2 = × Chopper I 2 ........................... (8).
22
4
If the same core is used in both circuits, the core
volume ratio can be obtained from Eq. (9).
WChopper =33

 Lchopper  4 1 4........................... (9).
 ==vol _ 3levelSCC  Lchopper 4 
4vol _ chopperAs a result, the core volume for the proposed 3-level
SCC is 65 % smaller than that of the conventional boost
chopper.
IV. SIMULATION RESULTS
Figure 8 shows operation waveforms by simulation
when the boost ratio is 1.33. The inductance is 174 µH
from Eq. (5) and the design value of the input current
ripple is 1.8 A. It is confirmed that the input current is 1.7
A, which is within the design value. Moreover, thereactor voltage is similar to the conventional boost
chopper. However, the input current ripple may be
increased due to unbalance of flying capacitor voltage.
V. EXPERIMENTAL RESULTS

Fig. 8. Operation waveforms by simulation at the boost ratio of 1.33.
Table 1. Experiment condition.

The proposed 3-level SCC was tested in an order toconfirm the basic operation and also to analyze the circuit
losses. Table 1 shows the experimental conditions. The
circuit is assumed to apply in a PV system. Note that
MOSFET S1 and S2 are replaced with Fast Recovery
Diode because only single power flow requires in the PV
system applications.
A. Basic operation waveforms
Figure 9 shows the experimental waveforms between
the input current and the input reactor voltage, at 1000 W
with boost ratio α = 1.33. In this case, the input current
ripple is set to the maximum, which is 1.6 A according to
the design. Those results agree well with that of thesimulation results in Fig. 8.
Figure 10 shows the experimental waveforms among
the input current, the flying capacitor current and input
reactor voltage, at 1000 W with boost ratio α = 3. The
flying capacitor current is suppressed by the peak valueof the input current. Therefore, the result confirms thatthe large peak current does not occur in the circuit.

Fig. 9. Operation waveforms (1.33-times boost and 1000W).

B. Boost ratio vs. input current ripple characteristic
Figure 11 shows the input current characteristic
between the boost ratio and the input current ripple. It
should be noted that the design value is within 1.0 p.u..
When the boost ratio is 1.33, the input current ripple is0.87 p.u, which is the maximum value. The graph showsthat the design method is valid.
C. Output power characteristic
Figure 12 shows the output power characteristic. The
output voltage is 500 V constant and the boost ratio is 3
in this experiment. High efficiency 97.7 % is obtained
over half of the rated output power. The maximum
efficiency is 97.8 % at 650 W. The efficiency decreases
at high load areas because the conduction loss of the
MOSFET increases.
D. Boost ratio characteristic
Figure 13 shows the relationship between theefficiency and the boost ratio. The output voltage is 500
V constant and the output power is 1000 W constant in

Fig. 10. Operation waveforms (3-times boost and 1000W).

this experiment. The maximum efficiency is obtained
98.7% at 1.33 boost ratio. The efficiency decreases as theboost ratio increases. If the boost ratio is low, the input
voltage is high. Then the input current is low. Therefore,
the losses on the MOSFET and diode are not dominant.
On the other hand, if the boost ratio is high, the input
current is high. As a result, the efficiency decreases.

E. Loss analysis based on the output load
In this section, partition of the loss is discussed inorder to clarify the circuit loss. The conduction losses ofthe following devices are calculated in this loss analysis;
MOSFETs, diodes, a flying capacitor and wire resistances.
Other kinds of calculations involve of the switching lossof the MOSFETs, the recovery loss of the diode and thecopper loss of the reactor.
Figure 14 shows the loss partition of the proposed
SCC based on the output power. Others in the figure
include of a no-load loss, a ringing loss and an iron loss.
The 100 % loss on the y-axis shows the total loss of a 1kW. The conduction loss of the flying capacitor is small
because a film capacitor is used as the flying capacitor in
the circuit, due to the small ESR (Equivalent Series
Resistance). Moreover, the proposed 3-level SCC uses asmall inductance, which only requires small numbers ofturning due to low inductance. As a result, the copper loss
becomes small. In this proposed 3-level SCC, the major
loss is from the conduction loss of diodes, which isapproximately 40 % of the total losses. The largest
increase is conduction loss of MOSFETs because theinput current increases by increasing output power. The
loss at 1 kW is 3.7 times of the loss at 550 W.
F. Loss partition based on the boost ratio
Figure 15 shows the loss partition of the proposed 3level SCC depending on the boost ratio. The input current
changes accordingly to the boost ratio. The conduction
loss increases largely if the boost ratio is high. However,the conduction loss of the diodes remains unchanged
even the boost ratio increased. Even the diode current
increases at high boost ratio, but the conduction period isshort, which results the conduction loss of the diodes issmall.
If a boost ratio is high, diodes current is high. On theother hand, conduction times of diodes are short.
Therefore a change of the conduction loss of the diodes islittle. However, the conduction loss of diodes is dominant
in total loss. Moreover, the largest increase of the loss is aconduction loss of MOSFETs because the input current
increases by increasing boost ratio.
G. Discussion of power devices
In this section, differences of power devices arecompared and selected in order to improve the efficiency.
By using a low voltage drop of the diode, the conduction
loss of the diode can be reduced such as a schottky diode.
Moreover, a synchronous rectification by MOSFET iseffective for reduction of the conduction loss. It should be
noted that the recovery loss by the body diode in
MOSFET, increases the total loss in a synchronousrectification.
In order to reduce the loss happens at the heavy load
and the high boost ratio, a low on-resistance MOSFET isselected. The on-resistance can be decreased byconnecting the MOSFETs in parallel connection.
Therefore, the overall efficiency can be improved by

Fig. 11. Input current ripple characteristics.

Fig. 12. Output load characteristics.

Fig. 13. Boost ratio characteristics.

Fig. 14. Loss separation of output load characteristics.

using low voltage drop diodes and low on-resistance
MOSFETs.

VI. EXTENSION TO MULTI-LEVEL SCC
The proposed voltage control type SCC can increase
the number of level by adding switches and flying
capacitors. The inductance of the boost-up reactor can be
decreased by increasing the level of a SCC. According toincrease the numbers of level, low on-resistance
MOSFETs are used in the circuit because the device
voltage becomes lower and lower. As a result, it ispossible to reduce the total loss. In this section, therelation between the inductance and the loss reduction are
discussed with multi-level circuit structure in a SCC.
A.

n-level voltage control type SCC
Figure 16 shows the circuit configuration of the
proposed n-level voltage control type SCC. The
relationship between the input voltage and the output
voltage is obtained from Eq. (2), which is similarly to 3level circuit. The flying capacitor voltages are

Fig. 15. Loss separation of boost ratio characteristics.

1
Vout ，n −1

2
n−2
Vout ，…，Vout from the nearest input voltage.
n −1
n −1

In the control method of n-level SCC, a triangle wave
carrier increase according to the number of level. These
triangle wave carriers need to shift their phase. The
number of the carrier and phase shift angle are obtained
from Eq. (10) and Eq. (11).
M = n − 1 .................................................................. (10),2πθ=...................................................................... (11).
M

B. Inductance reduction by multi-level
The design method of the inductance based on the nlevel is discussed in this section. A design method is
explained when MOSFETs of below the neutral point are
on state in Fig. 16.
The inductance is calculated from Eq. (12). The
inductance is the product of a reactor voltage and acharge time of reactor.
T
L = VL L ................................................................ (12).
∆I
Then, using boost-up ratio α, the reactor voltage is
obtained by
V
VL = Vin = out ......................................................... (13).

αThe reactor voltage is difference between the reactor
input side and output side. The input side of the reactor isconnected to the input voltage and output side of thereactor is connected to ground. Therefore reactor voltage
becomes equal to an input voltage.
The charge time of the reactor is obtained by  1 T − (n − 1)1 − 1 − T
T − (n − 1)Toff  α  ... (14),
TL =
=
n −1
n −1
where Toff is the off time of MOSFETs below theneutral point. The charge time of the reactor is between
the switching period and the charge/ discharge time of theFig. 16. n-level switched capacitor converter.

flying capacitor. The total charge and discharge times ofthe flying capacitor is obtained by (n-1)Toff.. The reactor
charge time is (n-1)th in per switching period. For
example, the reactor charge time is two times in a 3-level
circuit. Therefore, a single charge time of the reactor is
obtained by dividing the total reactor charge times with(n-1).
As a result, the inductance is obtained by Eq. (15)from Eq. (13) and Eq. (14).
V
1 − (n − 1){1 − (1 − 1 α )}1............ (15).
L = out ×
T×
α
n −1
∆I
A current ripple is obtained by.
V
1 − (n − 1){1 − (1 − 1 α )}1
∆I = out ×T × .............. (16).
n −1LαThe boost ratio can be obtained by Eq. (17) using
differential of Eq. (15).
α = 2(n − 1) ................................................................ (17).

If the number of level n is 2 at a boost chopper, theninput current ripple becomes maximum as the boost-up
ratio is 2 from Eq. (17). Similarly 3-level, it is confirmed
the ripple current is the maximum as the boost ratio is 4
times boost.
The inductance at where the input current ripple is the
maximum can be obtained by Eq. (18) using Eq. (15) andEq. (17).
LchopperVout
T
1
Ln−level =××=......... (18).
2(n − 1) 2(n − 1) ∆I (n − 1)2
The inductance is reduced in proportional to 1/(n-1)2

in a multi-level circuit structure.
Figure 17 shows the relationship between the
inductance and the number of level of the SCC. The
inductance can be reduced by approximately 1/16 of thatof the standard boost chopper under a 5-level SCC circuit
structure. The result shows multi-level SCC is possible toachieve compact size.
C. Loss reduction by multi-level
The proposed voltage control type SCC uses lowvoltage MOSFETs in a multi-level circuit structure.
Generally, low-voltage MOSFETs have low on-resistancecharacteristics, and the conduction loss is low. Moreover,under a multi-level structure, the copper loss of a reactor
is small because the numbers of turnings is low. However,a trade-off relationship is shown at the devices, between alow on-resistance and a high speed switching
characteristics. This section only discusses the conduction
loss at rated power of 1 kW.
Figure 18 shows the MOSFET characteristics between
a voltage rating and an on-resistance. These MOSFET’sdata are collected from Renesas Electronics Co. Note thatthe current rating of MOSFET is selected as five times ofthe maximum input current (6 A). Two 500 V MOSFETs
are connected in series in order to test on the range ofover 1000 V. If the MOSFETs which has twice ofterminal voltage are selected, the on-resistance of
MOSFETs used at 5-level is 1/10 of that of 2 level.
Therefore, the conduction loss per a device reduces 1/10.
However, it is necessary to fulfill condition for reductionof total conduction loss.
Figure 19 shows the comparison on the conduction
loss among the devices A, B and C from Fig. 18. In thisanalysis, device A is used in the boost chopper, device B
is used in the 3-level SCC and device C is used in the 5level SCC. The 1.0 p.u represents the total conduction
loss of the boost converter. From the analysis, multi-levelstructure is shown to reduce the conduction loss.
However, the total conduction loss increases due to theincrement of the number of switching devices.
Therefore, in order to reduce total conduction loss, thedecrease rate of on-resistance has to be more thanincrease rate of the number of switches. In order toreduce the total conduction loss under a 5-level SCC, thedevice which has under 1/4 on-resistance of conventional
boost chopper must be selected because switches increaseby four times.
Next, the copper loss of the input reactor is discussed.
In the proposed SCC, if the core size is same among all
the level, the numbers of turning are decreased in order toreduce the inductance value. Therefore, the copper loss is
reduced subsequently. The copper loss is obtained byPcopper = I L2 RL ............................................................. (19),where IL is the circuit current and RL is the wire
resistance of the input reactor. RL considers the skin effectas shown in Eq. (20).

Fig. 17. Relationship between the number of level and inductance.

Fig. 18. Drain-source voltage v.s. on-resistance.

Fig. 19. Comparing to the conduction loss by multi-level.

RL =Nl mean.............................................................. (20),σS AC

where N is the number of turns, lmean is the mean
length of on turn, σ is the electrical conductivity ofcopper and SAC is the sectional area considered skin effect.
The wire resistance is proportional to the lmean and 1/SAC.
The numbers of turning are expressed as
N=

LchopperAL (n − 1)

2

=

1

(n − 1)

LchopperAL......................... (21),where, Lchopper is the inductance of a boost chopper, n
is the number of level and AL is the AL value of core.
Therefore, the numbers of turning are proportional to1/(n-1).
On the other hand, sectional area considered skineffect is obtained by
π 2
2
S AC =r − (r − δ ) ............................................. (22),2{}where, r is the wire radius and d is the skin depth
obtained by
δ=

2

ϖµσ

=

1

πf n −level µσ........................................ (23),where, µ is the magnetic permeability and fn-level is thefrequency of the input current at each level. The
relationship between the fn-level and the switchingfrequency fsw is obtained by
f n − level = (n − 1) f sw ..................................................... (24).

Therefore the skin effect is more significant if the fnlevel is increased under the multi-level structure.
The SAC is approximated by Eq. (25) provided that theskin depth is shorter comparing to the wire radius.
S AC ≅ πrδ =Fig. 20 Comparing to the copper loss by multi-level.

πr.......................................... (25).
f n −level µσ
2

The wire resistance is given by Eq. (26) using Eq. (21)and Eq. (25).
l
RL = meanr

Lchopper f sw µ

1

σπAL

n −1

................................. (26).

As a result, the copper loss is proportional to

1

n −1

under a multi-level structure.
Figure 20 shows the copper loss comparison. The total
copper loss of the boost chopper is equivalent to 1.0 p.u.
It is confirmed that the copper loss is able to reduce byconnecting a multi-level structure.
Figure 21 shows the percentage of reduction in term of
total loss by connecting a multi-level structure. In thisanalysis, it is assumed that the iron loss of the boost
reactor and the switching loss are constant. 5-level SCC
shows a higher efficiency than the boost chopper.
VII. CONCLUSION
This paper discussed a Switched Capacitor Converterwith the use of a boost reactor for controlling the output
voltage.
The following subjects have been discussed in thispaper; (a) The design method of an input reactor, (b)confirmation of the fundamental operation, (c) loss
analysis, and (d) reduction in term of inductance value
and loss which is based on the multi-level structure.
The experimental results are obtained as follows;(1) The efficiency of the rated output power is 97.7%.
(2) The maximum efficiency is 97.9% at 600W withthe boost ratio 3 times boost.
(3) The maximum efficiency is 98.7% at 1kW withboost ratio 1.33
(4) The total loss of 5-level proposed SCC is 70% of
the conventional boost chopper.
The future work will be the optimization design
method based on the loss analysis results.
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Fig. 21. Reduction of total loss by multi-level.

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