Download Journal of Applied Science and Agriculture

Journal of Applied Science and Agriculture, 9(11) Special 2014, Pages: 148-157
AENSI Journals
Journal of Applied Science and Agriculture
ISSN 1816-9112
Journal home page: www.aensiweb.com/JASA
Design and Analysis of Positive/Negative Boost Converters Combined with a CockcroftWalton Voltage Multiplier
1
Kei Eguchi, 2Ichirou Oota, 3Kuniaki Fujimoto, 1Ya Nan Zhan, 3Hirofumi Sasaki
1
Faculty of Engineering, Department of Information Electronics, Fukuoka Institute of Technology, Japan.
Department of Information, Communication and Electronic Engineering, Kumamoto National College of Technology,Japan.
3
Graduate School of Science and Technology, Electrical Engineering and Electronics, Tokai University, Japan.
2
ARTICLE INFO
Article history:
Received 25 June 2014
Received in revised form
8 July 2014
Accepted 10 August May 2014
Available online 30 August 2014
Keywords:
Switching converters
DC-DC converters
High step-up gain
Boost converter
Cockcroft-Walton voltage multiplier
Positive/negative outputs
ABSTRACT
Background: DC voltage power supplies are used in various types of electronic
devices. To provide stepped-up DC voltages, a boost converter has been widely used,
because the boost converter can realize a simple circuit configuration. However, the
boost converter is difficult to utilize for high voltage applications, because the boost
converter requires a large duty cycle to generate a high voltage. For this reason, several
types of high step-up DC-DC converters have been proposed to provide high voltages
without a large duty cycle. However, most of the conventional converters are bulky and
expensive due to high frequency transformers or coupled inductors. Objective: For
high DC voltage applications, positive/negative boost converters combined with a
Cockcroft-Walton voltage multiplier (CWVM) are proposed in this paper. The features
of the proposed converter are as follows: (1) Owing to the combination of the boost
converter and the CWVM, a high voltage can be generated without a large duty cycle;
(2) Easy circuit control can be provided, because the proposed converter has only one
active switch; and (3) Owing to the circuit configuration without transformers and
coupled inductors, a small circuit scale can be achieved. Results: The simulation
program with integrated circuit emphasis (SPICE) simulation showed the following
results: (1) The output voltage of the proposed positive converter was about three times
of that of the boost converter. On the other hand, the output voltage of the proposed
negative converter was about two times of that of the buck-boost converter. (2) The
power efficiency of the proposed positive converter was 82.6% when the duty cycle is
0.5 and the output load is 500Ω. On the other hand, the power efficiency of the
proposed negative converter was 84.8%. In continuous mode, the characteristics of the
proposed converters were also clarified by the theoretical analysis considering the onresistance of transistor switches and the ripple loss of inductors. Furthermore,
concerning the laboratory prototype of the proposed converter, the validity of circuit
topology was confirmed by experiments. Conclusion: For high voltage applications,
positive/ negative boost converters combined with a CWVM have been proposed in this
paper. The conclusion of this research is as follows: (1) The proposed converters can
achieve high step-up gain without a large duty cycle, (2) High frequency transformers
and coupled-inductors are not required to design the proposed converters, and (3) The
obtained theoretical formulas will be helpful to estimate the maximum power efficiency
and the maximum output voltage of the proposed converters.
© 2014 AENSI Publisher All rights reserved.
To Cite This Article: Kei Eguchi, Ichirou Oota, Kuniaki Fujimoto, Ya Nan Zhan, Hirofumi Sasaki, Design and Analysis of
Positive/Negative Boost Converters Combined with a Cockcroft-Walton Voltage Multiplier. J. Appl. Sci. & Agric., 9(11): 148-157, 2014
INTRODUCTION
DC voltage power supplies are used in various types of electronic devices. For example, high-intensity
discharge lamps (HID) for automobile require a 100V DC voltage from the typical 12V battery voltage, and
servers for data processing in a telecommunication industry require a 380V DC voltage from a 48V telecom
power supply. To provide high voltages for above-mentioned applications, step-up DC-DC converters have been
proposed. For example, Amir et al. (2013), Iqbal (2013), and Sun et al. (2000) designed the transformer based
high step-up converter. These transformer based converters can achieve a high voltage gain, but it is bulky and
expensive due to the high frequency transformer. Abutbul et al. (2003) proposed an integration of a switchedcapacitor (SC) converter within a boost converter (Wester et al. (1973)), where the output voltage of the seriesparallel type SC DC-DC converter is stepped-up by the boost converter. However, the circuit control of the
Abutbul’s converter is complex, because five active switches must be controlled to generate a high voltage.
Corresponding Author: Kei Eguchi, Faculty of Engineering, Department of Information Electronics, Fukuoka Institute of
Technology, Fukuoka. Japan.
Tel: +81-92-606-3137 E-mail: [email protected]
149
Kei Eguchi et al, 2014
Journal of Applied Science and Agriculture, 9(11) Special 2014, Pages: 148-157
Chen et al. (2011), Van de Sype et al. (2005), and Zhao et al. (2010) proposed a high step-up converter with a
coupled inductor and a switched capacitor circuit. These coupled-inductor based converters can provide a high
voltage without a large duty cycle. However, extra inductor is required.
In this paper, positive/negative boost converters combined with a Cockcroft-Walton voltage multiplier
(CWVM) (Lamantia et al. (1990)) are proposed. Owing to the combination of the boost converter and the
CWVM, the proposed converters can provide a high voltage without a large duty cycle. Unlike the conventional
converter of Abutbul et al. (2003), the high stepped-up voltage is generated by controlling only one active
switch. Therefore, the proposed converters can achieve simple circuit control. Compared with transformer based
converters (Amir et al. (2013), Iqbal (2013), and Sun et al. (2000)) and coupled-inductor based converters
(Chen et al. (2011), Van de Sype et al. (2005), and Zhao et al. (2010)), the proposed converter can achieve a
small circuit scale. Because the proposed converters is consists of an inductor, an active switch, capacitors, and
diodes. Furthermore, unlike conventional converters (Abutbul et al. (2003), Amir et al. (2013), Chen et al.
(2011), Iqbal (2013), Sun et al. (2000), Van de Sype et al. (2005), and Zhao et al. (2010)), not only positive
circuit topology but also negative circuit topology is proposed to generate a high voltage. By combining these
positive/negative voltages, the proposed converter can achieve a high step-up gain.
The rest of this paper is organized as follows. In Section 2, the structure of the conventional converter and
the proposed converter are presented. In Section 3, the characteristic of the proposed converter is analyzed
theoretically. Simulation results and experimental results are shown in Section 4 and 5, respectively. Finally,
conclusion and future work are drawn in Section 6.
Circuit configuration:
Cockcroft-Walton Voltage Multiplier:
Figure 1 shows the circuit configuration of the Cockcroft-Walton voltage multiplier (CWVM) (Lamantia et
al. 1990) with N stages (N=1, 2, … ). The CWVM of Figure 1 provides a positive DC output by converting an
AC input. The output DC voltage of the conventional CWVM is expressed as
Vout  2 N Vac ,
(1)
where Vac is the maximum value of an AC input voltage and N is the number of stages. As Figure 1 shows,
the CWVM can be constructed without magnetic components. However, as (1) shows, the CWVM requires
many circuit components to achieve a high step-up gain, because the number of circuit components increases
according to the number of stages N. Furthermore, due to the electrical impedance of capacitors in lower stages,
the output voltage begins to sag according to the increase of the number of stages. To avoid these problems, a
boost converter is combined with the CWVM.
Fig. 1: Cockcroft-Walton voltage multiplier.
Boost Converter:
Figure 2 shows the circuit configuration of the boost converter (Wester et al. (1973)). Unlike the CWVM of
Figure 1, the boost converter of Figure 2 provides a positive DC output by converting a DC input. In continuous
mode, the output DC voltage is expressed as
 1 
Vout  
Vin ,
1 D 
(2)
where Vin is the DC input voltage and D is the duty cycle of the clock pulse. As (2) shows, the boost
converter of Figure 2 can change the step-up ratio by controlling the duty cycle D (=T1/T). However, due to the
limit of clock speed, the boost converter is difficult to achieve a high step-up gain.
150
Kei Eguchi et al, 2014
Journal of Applied Science and Agriculture, 9(11) Special 2014, Pages: 148-157
Fig. 2: Boost converter.
(a)
(b)
(c)
Fig. 3: Proposed boost converter combined with a Cockcroft-Walton voltage multiplier; (a) Positive converter,
(b) Negative converter, and (c) Block diagram of the bipolar structure.
Proposed Boost Converters Combined with a Cockcroft-Walton Voltage Multiplier:
Figure 3 shows the proposed positive/negative boost converters combined with a Cockcroft-Walton voltage
multiplier. Figure 3 (a) shows the proposed positive converter and Figure 4 (b) shows the proposed negative
converter. The output voltages of the proposed converters are expressed as
 N 1
 N 
V po  
Vin and Vno  
Vin ,
 1 D 
1 D 
(3)
where Vpo is the output voltage of the proposed positive converter and Vno is the output voltage of the
proposed negative converter. Furthermore, by combining these proposed voltage multipliers as shown in Figure
3 (c), the proposed voltage multiplier can provide the following high stepped-up voltage:
151
Kei Eguchi et al, 2014
Journal of Applied Science and Agriculture, 9(11) Special 2014, Pages: 148-157
  N    2N  1 
 N 1
Vout  
Vin   
Vin   
Vin .
 1 D 
 1 D    1 D 
(4)
Compared with the boost converter of Figure 2, the proposed converter can achieve higher step-up gain (see
(2), (3), and (4)).
Fig. 4: Equivalent circuit used in the theoretical analysis.
Steady-state analysis:
To analyze steady-state behavior of the proposed converters, theoretical analysis is performed concerning
the simplest example of the proposed converters. In the theoretical analysis discussed in Abutbul et al. (2003),
Chen et al. (2011), Van de Sype et al. (2005), Wester et al. (1973), and Zhao et al. (2010), the on-resistance of
transistor switches and the ripple loss of inductors were not considered. To consider these factors, the equivalent
circuit of the proposed converter is expressed as Figure 4 (Tsubomi et al. (2013)). In Figure 4, m is the ratio of
an ideal transformer, Rac is the resistance to express the ripple loss of reactors, Ro is the resistance to express the
output resistance, and RL is the output load.
To save space, concerning the proposed converter operating in continuous mode, the theoretical analysis
will be discussed in the following subsections.
(a)
(b)
Fig. 5: Instantaneous equivalent circuits of the proposed positive converter in the case of N=1; (a) State-T1 and
(b) State-T2
Fig. 6: Inductor current in a steady state.
Positive Converter:
Figure 5 shows the instantaneous equivalent circuits of the proposed positive converter in the case of N=1,
where Ron is the on-resistance of the transistor switch, Rd is the on-resistance of the diode switch, Rl is the
resistance of the inductor, and L is the ideal inductor. When the proposed positive converter operates in
continuous mode, the current through the inductor L is expressed as shown in Figure 6. In Figure 6, the inductor
currents in State-T1 and State-T2 are expressed as
152
Kei Eguchi et al, 2014
Journal of Applied Science and Agriculture, 9(11) Special 2014, Pages: 148-157
 i  
i 
iL ,T1 t    L t   I in  L 
2 
 T1  
 i  
 2T  T  
and
iL ,T2 t    L t   I in   1 2 iL  ,
 T2  
 2T2  
T1  DT and T2  1  D T .
where
(5)
(6)
In (5) and (6), ΔiL is the variation of the inductor current (see Figure 6). Using (5) and (6), the variation of
the inductor current in State-T1 is given by
iL  iL ,T1 T1   iL,T1 0 
Vin
T1 .
L
(7)
On the other hand, the variation of the inductor current in State-T2 is given by
iL  iL,T2 T1   iL,T2 T1  T2  
VL  Vin
T2 ,
L
(8)
where VL denotes the voltage of the inductor on output side (see in Fig.3 (a)). From (7) and (8), we have the
following relations:
VL 
Vin
1 D
and
I L  1  D I in ,
(9)
where IL is the average inductor current and Iin is the average input current.
In State-T1, the differential values of electric charges in VL and Vpo, ΔqT1,VL and ΔqT1,Vpo, are expressed as
qT1 ,VL  0
(10)
qT1 ,Vpo  q ,
po
T1
and
(11)
qTp11  qTp1 2 ,
where
In (10) and (11), ΔqT1pj denotes the differential value of the electric charge in the capacitor Cpj (j= 1, 2, o).
On the other hand, in State-T2, the differential values of electric charges in VL and Vpo, ΔqT2,VL and ΔqT2,Vpo, are
expressed as
qT2 ,VL  qTp21  qTp22
(12)
qT2 ,Vpo  qTp22  qTpo2 .
and
(13)
In the steady-state, the deferential value of the electric charge satisfies the following conditions:
qTp11  qTp21  0 , qTp1 2  qTp22  0 , and qTpo
 qTpo2  0 .
1
(14)
Using (11)-(15), the average inductor current and the average output current can be obtained as
IL 
and
qT1 ,VL  qT2 ,VL
I po
2qTp11

T
T
qT1 ,V po  qT2 ,V po qTp11


.
T
T
(15)
153
Kei Eguchi et al, 2014
Journal of Applied Science and Agriculture, 9(11) Special 2014, Pages: 148-157
Substituting (15) into (9), we have the relation between the input and the output as follows:
I in  
2
I  m p I po
1  D  po
mp 
where
Vin 
and
1  D V
2
po

1
V po ,
mp
(16)
2
.
1 D
Next, let us consider the consumed energy in one period. Using (5) and (6), the consumed energy in StateT1 and State-T2, WT1 and WT2, can be expressed as

2
0

and
T1
2
T1 T2
WT2  
T1
2

 qTp11 
qTp1 2 


 RT
Ron iL,T1 t  
dt  


 T  d 1
T
1 

 1 
WT1   Rl iL,T1 t  dt  
T1
0
2
2
 qTp21 
 qTp22 


 RT .
Rl iL,T2 t  dt 
R T 
 T  d 2  T  d 2
 2 
 2 


(17)
2
(18)
Therefore, using (5), (6), (10), (11), (12), (13), (14), (17), and (18), the total consumed energy in one period,
WT, is obtained as
WT  WT1  WT2
(19)
2
  2 2
 1  D  Rd
2Rd 
 Rl  Ron D 
2
2


R
D


I po  T .
iL  T   Rl 


on 
12
D 1  D 


  1  D 
 D1  D 
From Figure 4, the consumed energy of the general equivalent circuit can be defined as
WT : Rac  Ro I out  T
2
 Ro I out  T  Rac
2
mL2 iL 2 T .
T1 2 RL  Ro 2
(20)
Using (19) and (20), Rac and Ro of the proposed positive converter are obtained as
1  D   R 1  D 
 2 
Ro  Rl 
  Ron
d
2
D1  D 
D1  D 
1 D 
2
and
Rac
2
2
2

DT  RL  Ro 
R

12m p L 
2
l
 DRon  .
(21)
(22)
Therefore, we have the output voltage Vpo and the power efficiency ηp as follows:
 RL  2 

Vpo  
  Vin
 RL  Ro  1  D 
RL
p 
and
.
RL  Ro  Rac
(23)
(24)
154
Kei Eguchi et al, 2014
Journal of Applied Science and Agriculture, 9(11) Special 2014, Pages: 148-157
(a)
(b)
Fig. 7: Instantaneous equivalent circuits of the negative voltage multiplier in the case of N=1; (a) State-T1 and
(b) State-T2.
Negative Voltage Multiplier:
Figure 7 shows the instantaneous equivalent circuits of the negative voltage multiplier in the case of N=1.
In the same way, the relation between IL and Iin is obtained as (9), because the inductor current of the negative
voltage multiplier can be expressed by (5) and (6). In State-T1, the differential values of electric charges in VL
and Vno, ΔqT1,VL and ΔqT1,Vno, are expressed as
qT1 ,VL  0
(25)
qT1,Vno  qTno1  qTn11  qTn12 .
and
(26)
On the other hand, in State-T2, the differential values of electric charges in VL and Vno, ΔqT2,VL and ΔqT2,Vno,
are expressed as
qT2 ,VL  qTn21
(27)
qT2 ,Vno  qTn22  qTno2 .
and
(28)
In the steady-state, the deferential value of the electric charge satisfies the following conditions:
qTn11  qTn21  0 , qTn12  qTn22  0 , and qTno1  qTno2  0 .
(29)
Using (25)-(29), the average inductor current and the average output current can be obtained as
IL 
and
qT1 ,VL  qT2 ,VL

qTn11
T
T
qT1 ,Vno  qT2 ,Vno
qTn11
I no 

.
T
T
(30)
Substituting (30) into (9), we have the relation between the input and the output as follows:
1
I  mn I no
1  D  no
1
mn  
where
.
1  D 
I in 
and
Vin  1  D V po 
1
V po ,
mn
(31)
Next, let us consider the consumed energy in one period. Using (5) and (6), the consumed energy in StateT1 and State-T2, WT1 and WT2, can be expressed as
155
Kei Eguchi et al, 2014
Journal of Applied Science and Agriculture, 9(11) Special 2014, Pages: 148-157

2

WT1   Rl iL,T1 t  dt  
T1
0
T1
2
0
2

 qTn11 
qTn11 
 dt  
 RT
Ron  iL,T1 t  


 T  d 1
T
1
1




(32)
2
and
 qTn21 
 R  Rd T2 .
WT2  
 T  l
 2 
(33)
Therefore, using (5), (6), (25), (26), (27), (28), (29), (32), and (33), the total consumed energy in one period,
WT, is obtained as
WT  WT1  WT2

(34)

DRl  Ron 
D
R
R  Rd 
iL 2 T   Rl D 2  Ron
I no 2 T .
 d  l

2
12
D1  D D 1  D 
 1  D 
Using (20) and (34), we have Rac and Ro as follows:
 1 




1
1
Ro  Rl 
 Ron 
 Rd 

2
2
 D1  D 
 1  D  
 D1  D  
2
2
DDT  RL  Ro 
Rl  Ron  .
and
Rac 
2
12mn L 
(35)
(36)
From (23) and (24), the output voltage Vno and the power efficiency ηn can be obtained in the same way.
(a)
(b)
Fig. 8: Simulated output voltage; (a) Positive converter and (b) Negative converter.
Simulation:
To clarify the characteristics of the proposed converters, simulation program with integrated circuit
emphasis (SPICE) simulations are performed under conditions that Vin=10V, Cp1= … = Cp4= 10μF, Cpo= 50μF,
Rl=0.45Ω, Ron=1Ω, Rd=0.1Ω, T=10μs, and N=2. Figure 8 shows the simulated output voltages of the proposed
converters as a function of output load RL. Figure 8 (a) shows the output voltage of the proposed positive
converter, and Figure 8 (b) shows the output voltage of the proposed negative converter. In Figure 8, the duty
cycle was set to D=0.5. Therefore, in continuous mode, the ideal output voltages of the positive converter and
the negative converter are 60V and 40V, respectively. On the other hand, the ideal output of the boost converter
is 20V (see (2)). As Figure 8 shows, the proposed positive/negative converters can achieve higher step-up gain
than the conventional boost converter. Furthermore, unlike conventional converters, negative output can be
provided by the proposed converter. Figure 9 shows the power efficiency of the proposed converters as a
function of the load. In continuous mode, the power efficiency of the positive converter is 82.6% when the
output load is RL=1kΩ at f=1MHz. On the other hand, the power efficiency of the negative converter is 84.8%
when the output load is RL=500Ω.
156
Kei Eguchi et al, 2014
Journal of Applied Science and Agriculture, 9(11) Special 2014, Pages: 148-157
(a)
(b)
Fig. 9: Simulated power efficiency; (a) Positive converter and (b) Negative converter.
Experiment:
To confirm the validity of the circuit topology, experimental circuits were built with commercial available
components on a breadboard. Figure 10 shows the laboratory prototype of the proposed converter. In the
experiments, the proposed converters with two stages (N=2) were assembled with diode switch 1N4007,
MOSFET 2SK2382, electrolytic capacitor 10μF, and inductor 10μH. Figure 11 shows the measured output
voltage of the proposed positive/negative converters. The experiment of Figure 11 was performed under
conditions that Vin=3V, Cp1= … = Cp4=10μF, Cn1= … = Cn4=10μF, Cpi=Cpo=100μF, Cni=Cno=100μF, D=0.5, and
RL=510Ω, Cpi and Cni denote the capacitors connected to the input terminals. From Figure 11, the validity of
circuit topology can be confirmed.
Fig. 10: Laboratory prototype of the proposed voltage multiplier.
(a)
(b)
Fig. 11: Measured output voltage of the experimental circuits; (a) Positive converter and (b) Negative converter.
157
Kei Eguchi et al, 2014
Journal of Applied Science and Agriculture, 9(11) Special 2014, Pages: 148-157
Conclusion:
For high voltage applications, positive/negative boost converters combined with a Cockcroft-Walton
voltage multiplier (CWVM) have been proposed in this paper. Furthermore, the analysis method considering the
on-resistance of transistor switches and the ripple loss of inductors is proposed to clarify the characteristics of
the proposed converter. Concerning the simple example of the proposed converter, SPICE simulations,
theoretical analysis, and experiments were performed.
The results of the SPICE simulation showed the following results: (1) By controlling only one active switch,
the proposed converters can provide a higher stepped-up voltage than conventional converters and (2) In
continuous mode, more than 82% power efficiency was achieved when the duty cycle was 0.5 and the output
load was 500Ω. Through theoretical analysis, handy theoretical formulas were obtained to estimate output
voltage and power efficiency. Furthermore, the laboratory prototype of the proposed converter was fabricated on
a breadboard. Through experiments, the validity of the circuit topology was confirmed.
REFERENCES
Abutbul, O., A. Gherlitz., Y. Berkovich and A. Ioinovici, 2003. Step-up switching-mode converter with
high voltage gain using a switched-capacitor circuit. IEEE Trans. Circuits and Systems-I, 50(8): 1098-1102.
Amir, A., S, Taib., and S, Iqbal., 2013. Voltage multiplier-based continuous conduction LCCL series
resonant inverter fed high voltage DC-DC converter. Proc. of IEEE Symp. on Industrial Electronics and
Applications: pp: 105-110.
Chen, S.M., T.J., Liang., L.S., Yang, J.F., Chen and K.C., Juang, 2011. A quadratic high step-up DC-DC
converter with voltage multiplier. Proc. of IEEE Int. Electric Machines & Drives Conf, pp: 1025-1029.
Eguchi, K. and I. Oota, 2014. Design and analysis of a high-speed bipolar voltage multiplier for nonthermal food processing. Proc. of the 3rd Int. Conf. on Electronics Engineering and Grid System, pp: 130-135.
Iqbal, S., 2012. A multi power band high voltage DC-DC converter. Proc. of IET Int. Conf. on Power
Electronics, Machines and Drives, pp: 1-6.
Lamantia, A., P. Maranesi and L. Radrizzani, 1990. The dynamics of the Cockcroft-Walton voltage
multiplier. Proc. of IEEE Power Electronics Specialists Conf., pp: 485-490.
Sharma, R. and A. Vivek, 2013. A high gain dc-dc converter with voltage multiplier. Proc. of IEEE ECCE
Asia Downunder, pp: 1310-1314.
Sun, J., H., Konishi, Y. Ogino and M. Nakaka, 2000. Series resonant high-voltage ZCS-PFM DC-DC
converter for medical power electronics. Proc. of Power Electronics Specialists Conf, 1247-1252.
Tsubomi, K., S. Terada, K. Eguchi and I. Oota, 2013. An analysis of steady-state characteristic for
switching power supply (in Japanese). Proc. of the 26th Workshop on Circuits and Systems in Awaji, pp: 385390.
Van de Sype, D.M., K.D. Gusseme, W.R. Ryckacert, A.P. Van de Bossche and J.A. Melkebeek, 2005. A
single switch buck-boost converter with a high conversion ratio. Proc. of European Conf. on Power Electronics
and Applications, pp: 1-10.
Wester, G.W. and R.D. Middlebrook, 1973. Low-frequency characterization of switched dc-dc converters.
IEEE Trans. Aerospace and Electronic Systems, AES, 9(3): 376-385.
Zhao, Y., W. Li., Y. Deng, X. He., S. Lambert and V. Pickert, 2010. High step-up boost converter with
coupled inductor and switched capacitor. Proc. of 5th IET Int. Conf. on Power Electronics, Machines and Drives,
pp: 1-6.