Design Methods of Inductor and Flying Capacitor for
Multi-level Flying Capacitor Boost Converter
Asmarashin Ponniran*

Koji Orikawa*

Jun-ichi Itoh**Nagaoka University of Technology
1. Introduction
Flying capacitor boost converters (FCBC) can be widely usedin photovoltaic (PV) systems and electric vehicle (EV)applications [1]. Generally, a DC-DC boost converter in highpower-capacity applications typically demands high conversion
efficiency with low weight and small volume. A typical two-level
conventional DC-DC boost converter (CBC) requires a large
boost inductor for continuous current mode (CCM) operation andconsequently it suffers from bulkiness of the input inductor.
In this paper, the designs of a boost inductor and flying
capacitors in the n-level FCBC are clarified in order to achieve
passive components design optimization in terms of size
reduction [2]. First, a general principle of the n-level FCBC
circuit configuration is explained. Then, the design principles ofthe boost inductor L and the flying capacitor are described.
Finally, the experimental results for the three-level FCBC areclarified for the design methods validation.

Vfc1(n−level) =1
Voutn −1

Vfc2(n−level) =2
Vout V fcx(n−level ) = (n − 2) Voutn −1n −1Fig. 1. n-level FCBC.

1.0

1
Vout =
Vin ........................................................................ (1)
1− D

3. Boost Inductor Design
The boost inductor L in the n-level FCBC can be designed
based on an inductor current ripple ∆IL. Generally the inductor
current ripple is expressed as follows:∆I L =VL
TL ............................................................................. (2)L

where TL is the charging time of the inductor and VL is theinductor voltage. From Eq. (2), when the inductor voltage-time
product at maximum point, a maximum inductor current ripple∆IL is obtained.
Fig. 2 shows the relationship between the inductor voltagetime product (VL × TL), and the duty ratio D of the two-level CBC,a three-level FCBC, a five-level FCBC and a seven-level FCBC.
In the three-level FCBC, the maximum inductor current ripples
are achieved at duty ratios D of 0.25 and 0.75, respectively as
shown in Fig 2. On the other hand, a charging time of the input
inductor L becomes quarter of a switching period T and theinductor voltage VL become quarter of an output voltage Vout.
Thus the boost inductor L(three-level FCBC) in the three-level FCBC isexpressed as follows:L( three −level FCBC ) =Vout T1............................ (3)2 × 2 2 × 2 ∆I L ( three−level FCBC )Meanwhile, the boost inductor L(n-level FCBC) in the n-level

TL (p.u.)

Fig. 1 shows the n-level FCBC consists of diodes (upper arms),
switches (bottom arms), a boost inductor L at the input side, aflying capacitors Cfc, and an output capacitor Cout at the output
side. Principally, the boost inductor is used in order to control
independently the output voltage by controlling the duty ratio D.
Thus, the relationship between the input voltage Vin and theoutput voltage Vout is expressed as follows:

0.8
0.4

VL

2. n-level FCBC

0.2
0.0
0.0

0.2

0.4

0.6

0.8

1.0

Fig. 2. Relationship between VL × TL (p.u.) and duty ratio D for the twolevel CBC, three-level FCBC, five-level FCBC and seven-level FCBC.

FCBC is generalized as follows:
VoutT
1..................... (4)L( n−level FCBC ) =2 × (n − 1) 2 × (n − 1) ∆I L ( n−level FCBC )4. Flying Capacitor Design
Theoretically the average flying capacitor voltage Vfc in thethree-level FCBC is half of the output voltage Vout. Hence, themaximum voltage stress on each switch is equal to the maximum
flying capacitor voltage and it is expressed as follows:VS 1(three−level )−max = VS 2 (three−level )−max = V fc (three−level )−max ..................... (5)Thus, the maximum voltage across each switch, VS1(three-level)-maxand VS2(three-level)-max can be expressed as follows:VS 1(three−level )−max = VS 2 (three−level )−max =Vout 1
Pin D+2
2 C fc ( three−level )−minVin f sw................................................................................................. (6)where Pin in the input power, fsw is the switching frequency. Inaddition, the minimum capacitance of the flying capacitor Cfc(threelevel)-min in the three-level FCBC is expressed as follows:
C fc (three −level )−min =(2 V (Pin Dfc three −level )− max)

− Vout Vin f sw..................... (7)Meanwhile the maximum voltage stress on switching devices

Capacitance Cfc-min ( F)

1.2

Seven-level

Vout = 350 V
fsw = 100 kHz
Pout = 1 kW

1.0
Five-level

0.8
0.6

Vfc =0.4

Vfc =30%

0.2

15%Three-level
Cfc = 0.1 F∆I L−max =Vfc =55%

Vout4(n −1) L f sw
2?

0.050

100

150

200

250Maximum voltage stress on switching devices Vsw(n-level)-max (V)Fig. 3. Switching device voltage stresses with regard to the capacitancesof the flying capacitor.

Vsw(n-level)-max for the n-level FCBC is generalized as follows:
Pin D11
Vsw(n−level )−max =Vout +.................. (8)(n − 1)
2 Vin C fc1( n−level)−min f sw
Fig. 3 shows the relationship between switching device
voltage stresses and capacitances of the flying capacitor whereby
the voltage stress is reduced when higher level is considered.
Figs. 4(a) and 4(b) show the design procedures of the boost
inductor L and the flying capacitor Cfc, respectively in the n-level
FCBC. In addition, the IL-min must always be a positive value for
CCM operation. Meanwhile the designed Vfc-max must be lower
than the Vsw-max specification of a switching device for surge
voltage condition consideration. Besides, in the seven-level
FCBC, the flying voltage ripple becomes small compared to thethree-level FCBC; consequently the maximum switching device
voltage stress is also reduced.

5. Experimental Results
A three-level FCBC prototype is constructed andexperimented in order to confirm the design methods of theinductor and the flying capacitor. Table 1 shows the experimental
specifications of the prototype circuit.
Figs. 5(a) and (b) show the experimental waveforms of theflying capacitor voltage ripple (∆Vfc = 100 V) and the maximum
switch voltage (VS2-max = 230 V, without surge voltage),respectively when the capacitance of the flying capacitor 0.1 µF
is used. The experimental value of the maximum switch voltage
agrees with the calculated value as expressed by Eqs. (5) and (6).
Thus, estimation of the maximum switching devices voltage
stress based on flying capacitor voltage ripple is confirmed in thethree-level FCBC as shown in Fig. 3. In Fig. 3, the variation ofswitching device voltage stresses with regard to the capacitancesof the flying capacitor is also depicted. Besides, the maximuminductor current ripple ∆IL-max is designed at 1.1 A, as expressedby Eq. (3). Meanwhile, Fig. 5 shows the experimental result of
the inductor current ripple agrees with the designed value. Thus,
the inductor current ripple design is experimentally confirmed.
Fig. 6 shows the efficiency of the several flying capacitor
values with respect to the several output powers. In addition, themaximum efficiency is 98.5% when the output power is 1 kW
and the flying capacitors are 1.1 µF and 0.6 µF.
6. Conclusion
This paper presented the design method of the boost inductor
and the flying capacitor in the n-level FCBC. The inductor isdesigned based on the maximum inductor voltage-time product.
Meanwhile, the flying capacitor is designed based on themaximum voltage stress on switching devices. The design

Fig. 4. Optimization design procedures.
Table 1. Specifications of the experimental prototype circuit.

Switch Voltage VS2 (V)Output Voltage Ripple (V)0( Vout)(20 V/div)

VoutVfc

VVS2-maxV(without surge)

V

Flying Capacitor Voltage (V)
0Vfc(50 V/div)0(IL)(2A/div)0(VS2)(100 V/div)

Inductor Current (A)Inductor Current (A)
LA

L

0(IL)
(2A/div)

4 ( s/div)(a)
Cfc = 0.1 F, L = 200 H

A

T = 10 s(b)Cfc = 0.1 F, L = 200 H

Fig. 5. Experimental waveforms of the output voltage ripple, the flying
capacitor voltage ripple, the inductor current ripple, and the switch
voltage in the three-level FCBC (L = 200 µH and Cfc = 0.1 µF).

10098969492902504506508501050Fig. 6. The converter efficiency characteristic.

methods are confirmed by the experimental results for theinductor and the flying capacitor in the three-level FCBC. The
achieved maximum efficiency is 98.5% at the output power of 1kW.
Reference[1] Zhang Fan, et al., "A New Design Method for High-Power HighEfficiency Switched-Capacitor DC-DC Converters". IEEE
Transactions on Power Electronics, 23(2): p. 832-840. (2008).
[2] A. B. Ponniran, et al., “Size Reduction of DC-DC Converter using
Flying Capacitor Topology with Small Capacitance”, IEEJ Journal ofIndustry Applications, Vol.3, No.6, pp.446-454 (2014).