research article study on a novel high-efficiency...

Research ArticleStudy on a Novel High-Efficiency Bridgeless PFC Converter

Cao Taiqiang1 Chen Zhangyong2 Wang Jun1 Sun Zhang1 Luo Qian3 and Zhang Fei2

1 School of Electric Information Xihua University Chengdu 610039 China2 School of Electrical Engineering Southwest Jiaotong University Chengdu 610031 China3 Information Technology Branch The Second Research Institute of General Administration of Civil Aviation of ChinaChengdu 610042 China

Correspondence should be addressed to Cao Taiqiang ctq815163com

Received 24 January 2014 Accepted 18 June 2014 Published 4 August 2014

Academic Editor Gongnan Xie

Copyright copy 2014 Cao Taiqiang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In order to implement a high-efficiency bridgeless power factor correction converter a new topology and operation principles ofcontinuous conduction mode (CCM) and DC steady-state character of the converter are analyzed which show that the converternot only has bipolar-gain characteristic but also has the same characteristic as the traditional Boost converter while the voltagetransfer ratio is not related with the resonant branch parameters and switching frequency Based on the above topology a novelbridgeless Bipolar-Gain Pseudo-Boost PFC converter is proposed With this converter the diode rectifier bridge of traditional AC-DC converter is eliminated and zero-current switching of fast recovery diode is achievedThus the efficiency is improved Next wealso propose the one-cycle control policy of this converter Finally experiments are provided to verify the accuracy and feasibilityof the proposed converter

1 Introduction

A great number of harmonic currents which are caused bynonlinear loads connected to grid aremain pollution sourcesof power system and important factors in the safe operationof the grid In order to reduce the harmonic pollution theactive power filter (APF) and power factor correction (PFC)are required which are applied to control the harmonic andreactive current generated from rectifier loads PFC convertercan realize the AC input current control and DC outputvoltage control at the same frequency and phase with ACvoltage and thus it is widely used in server power [1ndash8]charger UPS and so on Traditional PFC converter includesa front-end bridge rectifier which increases conductionloss and greatly affects the efficiency of the PFC converterMoreover more serious loss is generated under low inputvoltage and light load particularly [5 9ndash13]

In order to improve efficiency of the traditional PFCconverter an effective method named as bridgeless PFCtechnology without front-end bridge rectifier is proposed[3 14 15] Then the bridgeless PFC converter is proposed in[1ndash18] which uses two switches instead of the uncontrolled

diodes When AC input voltage is in positive half-cyclethe front bridge leg of the converter operations while ACinput voltage is in negative half-cycle the rear bridge legoperations The papers report that the bridgeless PFC con-verter adopts the same two DC-DC converters to implementthe power conversion for positive and negative half-cycleof AC input voltage respectively Another bridgeless PFCconverter makes the input voltage greater than zero at firstand then obtains steady output voltage through the DC-DC converter All of these bridgeless PFC converters havea higher cost require complex topology and may lead toserious electromagnetic inference (EMI) [3 13ndash18]

In this paper we research a novel Pseudo-Boost converterwhich has bipolar-gain characteristic that is no matter ifthe input voltage is positive or negative the output voltageis always positive and the converter also has the samecharacteristic as the traditional Boost converter Althoughthe converter has a resonant branch the difference fromthe traditional resonant converter is that the voltage transferratio is not relevant to the resonant branch parameters andswitching frequency it only depends on the switching dutycycle Based on the Bipolar-Gain Pseudo-Boost converter

Hindawi Publishing CorporationJournal of Applied MathematicsVolume 2014 Article ID 514281 8 pageshttpdxdoiorg1011552014514281

2 Journal of Applied Mathematics

iL + minus

L+

+

minus

minus

+

minus

+

minus

+

minus

L

S

CrLr

s D1 D1

D2 ic

Co R

Iominus D2 +c119903

iL119903

oin

Figure 1 The topology of Bipolar-Gain Pseudo-Boost converter

a bridgeless Bipolar-Gain Pseudo-Boost PFC converter incontinuous conduction mode (CCM) is investigated Theconverter adopts one bidirectional controllable switch andtwo fast-recovery diodes instead of bridge rectifier andthe zero-current switching of the fast-recovery diodes isachieved Therefore the efficiency of the converter isimproved Meanwhile the one-cycle control technology isadopted to control the Bipolar-Gain Pseudo-Boost PFCconverter

2 Operation Principle of Bipolar-GainPseudo-Boost Converter

The topology of the Bipolar-Gain Pseudo-Boost converterconsists of switch 119878 two recovery diodes119863

1and119863

2 resonant

capacitor 119862119903 and resonant inductor 119871

119903 as in Figure 1 When

the input voltage is positive or negative the output voltageof traditional Boost converter is the corresponding polarityCompared with the traditional one the output voltage ofBipolar-Gain Pseudo-Boost converter is just positive that isthe Bipolar-Gain Pseudo-Boost has bipolar-gain characteris-tic To simplify the analysis of the operation of the Bipolar-Gain Pseudo-Boost converter the following assumptions aremade

(a) All of the switches diodes inductors and capacitorsare ideal

(b) Output capacitor 119862119900is large enough to make the

output voltage keep constant in a switching cycle(c) Resonant inductor 119871

119903and resonant capacitor 119862

119903

are much smaller than the inductor 119871 and outputcapacitor 119862

119900 respectively

(d) The converter operates in CCM

21 Positive Input Voltage The operation modes of Bipolar-Gain Pseudo-Boost converter operate in CCM with positiveinput voltage (Figure 2) The corresponding key waveformsof the converter are shown in Figure 3 At the beginning ofeach switching cycle the resonant inductor current 119894

119871119903

is zeroand the initial value of resonant capacitor voltage V

119888119903

is ΔV119888119903

where V

119888gt ΔV119888119903

gt 0 exists(1) Mode 1 [119905

0sim 1199051] as shown in Figures 2(a) and 3

at 119905 = 1199050 the switch 119878 is turned on The voltage across the

inductor 119871 is equal to input voltage Vin whichmakes inductorcurrent increase linearly The resonant capacitor voltage V

119888119903

makes diode 1198631turn on and the reverse voltage across 119863

2

makes it turn off Resonant capacitor voltage V119888119903

and resonantinductor current 119894

119871119903

are given as

V119888119903

= ΔV119888119903

cos120596119903(119905 minus 1199050)

119894119871119903

= minusΔV119888119903

119885119899

sin120596119903(119905 minus 1199050)

(1)

where 119885119899= radic119871

119903119862119903 120596119903= 1radic119871

119903119862119903

(2) Mode 2 [1199051sim1199052] as shown in Figures 2(b) and 3 at 119905 =

1199051= 1199050+ 1198791199032 resonant inductor current 119894

119871119903

is equal to zeroand diode119863

1gets zero-current turn-off where 119879

119903= 2120587120596

119903is

the resonant period At this moment the resonant capacitoris equal to minusΔV

119888119903

Due to V119888gt ΔV119888119903

the diode1198632is still turned

off with reverse voltage ΔV119888119903

minus V119888 The voltage across diode119863

1

is equal to V1198631

= minusV119888119903

= ΔV119888119903

while the voltage across diode1198632is equal to V

1198632= V119888minus ΔV119888119903

(3) Mode 3 [119905

2sim 1199053] as shown in Figures 2(c) and 3 at

119905 = 1199052 the switch 119878 is turned off Because the inductor current

119894119871does not change suddenly the diode 119863

2is turned on to

provide the path for the inductor current 119894119871 The diode 119863

1is

reversely biased and the voltage across it is equal to minusV119888 and

the inductor 119871 is then discharged and capacitor119862119900is charged

As 119871119903≪ 119871 119871

119903can be ignored So during 119905

2sim1199053 the resonant

capacitor voltage can be expressed as

V119888119903

= minusΔV119888119903

+119894119871

119862119903

(119905 minus 1199052) (2)

When the resonant capacitor voltage rises to ΔV119888119903

theconverter begins to enter the next switch cycle

22 Negative Input Voltage Figure 4 shows the operationmodes of Bipolar-Gain Pseudo-Boost converter operated inCCM with negative input voltage The corresponding keywaveforms of the converter are shown in Figure 5 At thebeginning of each switching cycle the resonant inductorcurrent 119894

119871119903

is zero and the initial value of resonant capacitorvoltage V

119888119903

= minusV119888minus ΔV119888119903

where V119888gt ΔV119888119903

gt 0(1) Mode 4 [119905


at 119905 = 1199054 the switch 119878 is turned on The voltage across

the inductor 119871 is equal to input voltage minusVin which makesinductor current decrease linearlyThe diode119863

2is turned on

by the opposite voltage ΔV119888119903

and the diode 1198631is reversely

biased The resonant branch begins to resonate the resonantcapacitor voltage V

119888119903

and resonant inductor current 119894119871119903

aregiven as

V119888119903

= minusV119888minus ΔV119888119903

cos120596119903(119905 minus 1199054)

119894119871119903

=ΔV119888119903

119885119899

sin120596119903(119905 minus 1199054)

(3)

where 119885119899= radic119871

119903119862119903 120596119903= 1radic119871

119903119862119903

(2) Mode 5 [1199055sim 1199056] as shown in Figures 4(b) and 5 at

119905 = 1199055 the resonant inductor current 119894

119871119903

is equal to zero anddiode119863


5minus 1199054= 1198791199032 and

119879119903= 2120587120596

119903is the resonant period The resonant capacitor is

equal to minusV119888+ ΔV119888119903

the diode 1198631is still reversely biased and

Journal of Applied Mathematics 3

iL + minus

L+

+

minus

minus

+

minus

+

minus

L Cr Lr

D1D1

D2

Co R

IominusD2+c119903

iL119903

in c

(a) Mode 1

iL + minus

L+

+

minus

minus

+

minus

+

minus

L CrLr

D1 D1

D2

Co R

IominusD2+c119903

iL119903

oin

(b) Mode 2

iL + minus

L+

+

minus

minus

+

minus

+

minus

+

minus

L

Cr Lr

D1D1

D2

Co R

IominusD2+

S s

c119903iL119903

oin

(c) Mode 3

Figure 2 Equivalent circuit of operation mode of the converter with positive input voltage

st

D1

D2

iL

t0 t1 t2(DTs) t3(Ts)

Δc119903

c119903Δc119903

minusΔc119903

minusΔc119903Zn

iL119903

c + Δc119903

c

c

c minus Δc119903

c minus Δc119903

c

Figure 3 The key waveform of the converter with positive inputvoltage

the voltage across it is equal to V1198631

= minusV119888119903

= V119888minus ΔV119888119903

Thevoltage across diode 119863

2is equal to ΔV

119888119903

(3) Mode 6 [119905




1is turned on to


2is

reversely biased and the inductor 119871 is then discharged andcapacitor119862

119900is charged During 119905

6sim1199057 the resonant capacitor

voltage can be given as

V119888119903

= minusV119888+ ΔV119888119903

minus119894119871

119862119903

(119905 minus 1199056) (4)

When the resonant capacitor voltage decreases to minusV119888minus

ΔV119888119903

the converter begins to enter the next switch cycle

3 The Steady-State Analysis of Bipolar-GainPseudo-Boost Converter

There are four state variables in Bipolar-Gain Pseudo-Boostconverter One is the energy storage state variable (V

119888 119894119871)

in which the natural frequency is much lower than theswitching frequency The other one is the resonant statevariables (V

119888119903

119894119871119903

) in which the natural frequency is closeto the switching frequency According to the generalizedstate space averaging (GSSA) approach the GSSA equationof the converter can be established which chooses V

119888 119894119871as

state variables Based on the GSSA equation the steady-statecharacteristic can be analyzed

31 Positive Input Voltage For positive input voltage fromFigures 2(a) and 2(b) when the switch 119878 is turned on the statedifferential equations are

119871d119894119871

d119905= Vin

119862119900

dV119888

d119905= minus

V119888

119877

(5)

From Figure 2(c) when the switch 119878 is turned off thecorresponding state differential equations are

(119871 + 119871119903)d119894119871

d119905= Vin minus V

119888minus V119888119903

119862119900

dV119888

d119905= 119894119871minusV119888

119877

(6)


iL + minus

L+

+

minus

minus

+

minus

+

minus

LCr

Lr

D1D1

D2

Co R

IominusD2+c119903

iL119903

minusin c

(a) Mode 4

iL + minus

L+

+

minus

minus

+

minus

+

minus

LCr

Lr

D1D1

D2

Co R

IominusD2+c119903

iL119903

minusin c

(b) Mode 5

iL + minus

L+

+

minus

minus

+

minus

+

minus

LCr

Lr

D1D1

D2

Co R

IominusD2+

+

minus

S s

c119903iL119903

minusin c

(c) Mode 6

Figure 4 Equivalent circuit of operation mode of the converter with negative input voltage

s

t

D1

D2

iL


Δc119903Zn

iL119903

Δc119903 minus cminusc

minusc minus Δc119903

Δc119903 minus c

minusc


Δc119903

c119903

c minus Δc119903

c

c

Figure 5 The key waveform of the converter with negative inputvoltage

The above analysis shows that the resonant capacitorvoltage satisfies (2) when the switch 119878 is turned off FromFigure 3 at the end of switching cycle the resonant capacitorvoltage is equal to ΔV

119888119903

meanwhile the integration of theresonant capacitor voltage is zero

The matrix representation of the state variables is x =

[119894119871

V119888]119879 according to (5) and (6) the state space equation

is

x = 119860119894x + 119861119894u 119894 = 1 2 (7)

where

1198601= [

[

0 0

0 minus1

119877119862119900

]

]

1198611= [

[

Vin119871

0

]

]

1198602=

[[[

[

0 minus1

119871 + 119871119903

1

119862119900

minus1

119877119862119900

]]]

]

1198612= [

[

Vin minus V119888119903

119871 + 119871119903

0

]

]

(8)

According to GSSA approach for positive input voltagethe GSSA equation of the Bipolar-Gain Pseudo-Boost con-verter can be obtained as

dd119905

[119894119871

V119888

] =[[[

[

0 minus(1 minus 119889)

119871 + 119871119903

(1 minus 119889)

119862119900

minus1

119877119862119900

]]]

]

[119894119871

V119888

] + [

[

Vin119871

0

]

]

(9)

where 119889 is the transient state switching duty cycleThe equation (dd119905) [ 119894119871V

119888

] = 0 is founded at steady statebecause 119871 ≫ 119871

119903 so 119871 + 119871

119903asymp 119871 From (9) there are

Vin = (1 minus 119863) V119888 119868

119871=

V119888

119877 (1 minus 119863) (10)

where 119863 is the steady state switching duty cycle and 119868119871is the

steady state inductor current

32 Negative Input Voltage For negative input voltage fromFigure 4(a) when the switch 119878 is turned on the statedifferential equations are

119871d119894119871

d119905= minusVin

119862119900

dV119888

d119905= 119894119871119903

minusV119888

119877

(11)


From Figure 4(b) when the switch 119878 is turned on thecorresponding state differential equations are

119871d119894119871

d119905= minusVin

119862119900

dV119888

d119905= minus

V119888

119877

(12)


(119871 + 119871119903)d119894119871

d119905= minusVin minus V

119888119903

119862119900

dV119888

d119905= minus

V119888

119877

(13)

According to the above analysis it can be seen that theresonant capacitor voltage satisfies (4) when the switch 119878 isturned off From Figure 5 at the end of switching cycle theresonant capacitor voltage is equal to ΔV

119888119903

minus V119888 thus the

integration of the resonant capacitor voltage isminusV119888in the time


[119894119871

V119888]119879 according (11) (12) and (13) the state space equa-

tion isx = 119860

119894x + 119861119894u 119894 = 1 2 3 (14)

where

1198601= [

[

0 0

0 minus1

119877119862119900

]

]

1198611=

[[[

[

minusVin119871

119894119871119903

119862119900

]]]

]

1198602= [

[

0 0

0 minus1

119877119862119900

]

]

1198612= [

[

minusVin119871

0

]

]

1198603= [

[

0 0

0 minus1

119877119862119900

]

]

1198613= [

[

minusVin minus V119888119903

119871 + 119871119903

0

]

]

(15)

Therefore for negative input voltage the GSSA equationof the Bipolar-Gain Pseudo-Boost converter can be obtainedas

dd119905

[119894119871

V119888

] = [

[

0 0

0 minus1

119877119862119900

]

]

[119894119871

V119888

] +[[[

[

minusVin119871

+V119888

119871(1 minus 119889)

119894119871(1 minus 119889)

119862119900

]]]

]

(16)

The equation (dd119905) [ 119894119871V119888


119903 so 119871 + 119871


Vin = (1 minus 119863) V119888 119868

119871=

V119888

119877 (1 minus 119863) (17)

According to (10) and (17) no matter if the input voltageis positive or negative the voltage transfer ratios of Bipolar-Gain Pseudo-Boost converter keep the same The converterhas the same Boost characteristic as the traditional Boostconverter In addition the voltage transfer ratio does not relyon the resonant branch parameters and switching frequencywhich is determined only by the switching duty cycle

iL

+ minus

L

+ minus

+

minus

+

minus

L

CrLr

D1 D1

D2

Co R

IominusD2+

+

minus

s

icG

S1

S2

c119903iL119903

in c

Figure 6 The topology of bridgeless Bipolar-Gain Pseudo-BoostPFC converter

4 The Implementation of BridgelessBipolar-Gain Pseudo-Boost Converter

The voltage transfer ratio of traditional DC-DC converteris unipolar which means that it only makes positive andnegative input voltage transfer to positive output voltageHowever the PFC converter belongs to AC-DC converterwhich makes AC input voltage transfer to DC output voltageHence the traditional DC-DC converter cannot be usedas PFC converter To realize PFC the most direct wayis combining a front-end bridge rectifier with a DC-DCconverter Assume that the voltage transfer ratio of DC-DCconverter is bipolar that is no matter if the input voltageis positive or negative the output voltage is always positiveThis DC-DC converter can realize AC-DC transformationwhich eliminates the bridge of traditional AC-DC converterand improves the efficiency of the converter

According to the steady state characteristic of Bipolar-Gain Pseudo-Boost converter it is shown that the converterhas bipolar-gain characteristic So the Bipolar-Gain Pseudo-Boost converter can be used as PFC converter From Figure 6the bridgeless PFC converter can be achieved by using bidi-rectional switch 119878

1combined with 119878

2instead of controllable

switching 119878 of the Bipolar-Gain Pseudo-Boost converter Theconverter has some advantages such as simple topology highefficiency and simple controlled circuit Compared with thedouble bridge-leg bridgeless PFC converter researched inpaper [3 14ndash16] the converter has reduced the EMI dueto common-grounded input and output Compared withthe bridgeless PFC converter proposed in paper [3 13ndash17]the Bipolar-Gain Pseudo-Boost converter has improved theutilization ratio and reduced the costs

From the preceding analysis the achievement conditionsof bridge Pseudo-Boost PFC converter are as follows

(1) From Figures 3 and 5 a two-way switch is neededbecause the switch 119878 should suffer positive and neg-ative voltage

(2) The choice of inductor 119871 to guarantee that theconverter operates in CCM the inductor 119871 mustsatisfy

Vinpmax

119871119863max119879119904 le 2119868inp (18)

The input current effective value is 119868inp = radic2119875119900

120578VinRMS where VinRMS is the input voltage effective


iL

+ minus

L

+ minus

+

minus

+

minus

L

CrLr

D1D1

D2

CoR

minusD2+

+

minus

sG

S1

S2

R1

R2

PIQ

Q

R

S

Clock

Drivers G

minus

minus

+

minus

+

+

v2 Resetintegrator

v1

vm

Control circuit

Rs|iL|

Rs

c119903iL119903

in c

ref

Figure 7 Block diagram of one-cycle control bridgeless Bipolar-Gain Pseudo-Boost PFC converter

value Vinpmax is the maximum input voltage peakvalue 119875

119900is the output power and 120578 is the efficiency

of the converter In addition 119863max is the maximumduty cycle and 119879

119904is the switching cycle

(3) The choice of resonant branch parameters from (2)(4) and the operation figure it can be obtained as

ΔV119888119903

=119868119871

2119862119903

(119879119904minus 119863119879119904) =

V119888

2119877119862119903

119879119904 (19)

From (19) the choice of ΔV119888119903

has nothing to do withresonant inductor 119871

119903 ΔV119888119903

is too large to increase the switchvoltage stress so larger resonant 119862

119903and smaller switching

period 119879119904should be chosen with the condition that resonant

capacitor 119862119903is much smaller than output capacitor 119862

119900

However the resonant capacitor 119862119903is too small to result in

zero-crossing distortion and it must satisfy V119888gt ΔV119888119903

gt 0moreover

119863min119879119904 gt119879119903

2 (20)

where the minimum duty cycle is 119863min = 1 minus VinpmaxV119888and the resonant period is 119879

119903= 2120587radic119871

119903119862119903 Thus a suitable

resonant inductor 119871119903should be chosen with respect to (19)

when the resonant inductor 119871119903is much smaller than the

Boost inductor 119871

5 One-Cycle Control Bridgeless Bipolar-GainPseudo-Boost Converter

Figure 7 is the principle scheme of bridgeless Pseudo-Boost PFC converter based on one-cycle control technologyThe main circuit topology employs a bidirectional switchcomposed of 119878

1and 119878

2 Dotted part of Figure 7 is the one-

cycle control circuit which consists of an integrator withreset function a comparator a RS trigger and a clock signalgenerator

The output voltage V119888is sampled in each period and

comparedwith a reference voltage119881refThe compared result iscompensated by PI regulator and then the modulation signal

T

1

4

2

iin (5Adiv)

in (100Vdiv)

o (100Vdiv)

Figure 8 Waveforms of DC output voltage V119888 AC input voltage Vin

and AC input current 119894119871

V119898

is obtained At each clock pulse coming the two-wayswitch is turned on Meanwhile the modulation signal V

119898

begins to be integrated by the reset integrator The differencevalues V

1between V

119898and119877

119904|119894119871| are compared with the output

signal V2from reset integrator when V

2= V1 and the output

level of the comparator is flipped and the switch is turned offwhile the reset integrator resets to zero until the next clockpulse arrives

According to the principle of one-cycle control it can beobtained that

V119898

minus 119877119904

10038161003816100381610038161198941198711003816100381610038161003816 =

1

119879119904

int

119879119904

0

119863V119898d119905 (21)

where V119898

= V119888119877119904119877119890and 119877

119890is the equivalent input resistor of

the bridgeless Bipolar-Gain Pseudo-Boost PFC converter and119877119904is the sampling resistor of inductor currentWhen (21) is applied at each switching cycle the output

voltage of the bridgeless Bipolar-Gain Pseudo-Boost PFCconverter is steady moreover the input current that is 119894

119871will

maintain sinusoidal and thus the purpose of PFC is achieved

6 Experiment Verification

In order to verify the accuracy of the theoretical analysis aset of experiments are designed According to (18)ndash(20) theparameters of experiment circuit are as follows 119875

119900= 100W

VinRMS = 50V V119888= 100V 119862 = 470 120583F 119891line = 50Hz 119891 =

50 kHz 119871 = 25mH 119871119903= 78 120583H and 119862

119903= 330 nF

Figure 8 shows the input voltage input current andoutput voltage waveforms of bridgeless Bipolar-Gain Pseudo-Boost PFC converter with 119875

119900= 100W It can be observed

from Figure 8 that the output voltage of the converter V119888is

constant and the input current 119894in closely follows the inputvoltage Vin to realize power factor correction

Figure 9 shows the efficiency curve of bridgeless Pseudo-Boost PFC converter with V

119888= 100V It can be seen that the

proposed converter has relatively high efficiencyFigures 10(a) and 10(b) show the switch voltage diode

voltage and inductor current waveforms for the positive


099

098

097

096

095

120578

50 100 150 200

Po (W)

Figure 9 Efficiency of the converter with 100V DC output voltage

M

1

4

2

T

Mode 2Mode 1Mode 3

s (100Vdiv)

D1 (100Vdiv)

D2 (100Vdiv)

t = 4 (120583div)

iL119903(2Adiv)

(a)

M

1

4

2T

Mode 5Mode 4Mode 6

s (100Vdiv)D1 (100Vdiv)

D2 (100Vdiv)

t = 4 (120583div)

iL119903(2Adiv)

(b)

Figure 10 The key operation waveforms of the converter (a) with positive input voltage and (b) with negative input voltage

0

5

10

15

20

25

30

35

3 5 7 9 11 13 15

IEC 61000-3-2 class C

Harmonic (n)

Bridgeless PFC converter

Har

mon

ic cu

rren

tinp

ut cu

rren

t (

)

Figure 11 Measured harmonic contents of the proposed converter

input voltage and negative voltage It is seen that the exper-iment waveforms are consistent with the theoretical analysiswaveforms and the diodes119863

1and119863

2can realize zero-current

switchingThe measured harmonic contents of the line current at

100V AC input voltage are shown in Figure 11 together withthe limits of IEC61000-3-2 class D standard It is shown that

85 95 105

1

115 125 135

0995

0990

0985

0980

PF

in (V)

Figure 12 Measured PF value at full load of the proposed converteras the function of input voltage

the input current harmonics of proposed converter can meetthe IEC61000-3-2 standard In addition Figure 12 illustratesthe measured PF value at full load of the proposed converteras the function of input voltage

7 Conclusion

In this paper we research the Bipolar-Gain Pseudo-Boostconverter and the topology and operation principles in


CCM and DC steady-state character of this converter areanalyzed Based on this topology a novel bridgeless Bipolar-Gain Pseudo-Boost PFC converter is proposed In additionthe implement condition of the bridgeless PFC and controltechnology of the converter is studiedThe experiments showthat the proposed converter is capable of achieving the PFCbetter and zero-current switching of the fast recovery diodeis achieved Moreover the reverse-recovery loss of the diodeis reduced and the efficiency of the converter is improved

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the Applied Basic ResearchPrograms of Technology Department under Foundationof Sichuan Province of China (no 2012JY012012209596)Technology Support Programs of Technology Departmentof Sichuan Province (no 2013GZ0130) the EducationalCommission of the Sichuan Province of China (no11ZA00311209435) the Key Programs of Xihua University(no Z1120940) and Key Laboratory of University Projectof Sichuan Provincial (application promotion and solartechnology integration)

References

[1] QChen J-P Xu Z Y Chen and F Zhang ldquoResearch on bridge-less DCM pseudo boost PFC converter with high efficiencyrdquoPower Electronic Technology vol 46 no 11 pp 53ndash62 2012

[2] Q Chen J-P Xu Z-Y Chen and X-S Liu ldquoResearch onbipolar gain Boost converterrdquoAdvanced Technology of ElectricalEngineering and Energy vol 32 no 4 pp 44ndash48 2013

[3] A J Sabzali E H Ismail M A Al-Saffar and A A FardounldquoNew bridgeless DCM sepic and Cuk PFC rectifiers withlow conduction and switching lossesrdquo IEEE Transactions onIndustry Applications vol 47 no 2 pp 873ndash881 2011

[4] W Wang and D D C Lu ldquoA bridgeless DIVM buck PFCrectifier with digital control and voltage doubler configurationrdquoInternational Journal of Power Electronics vol 5 no 2 pp 125ndash144 2013

[5] A A Fardoun E H Ismail A J Sabzali and M A Al-SaffarldquoNew efficient bridgeless cuk rectifiers for PFC applicationsrdquoIEEE Transactions on Power Electronics vol 27 no 7 pp 3292ndash3301 2012

[6] M Mahdavi and H Farzanehfard ldquoBridgeless SEPIC PFCrectifierwith reduced components and conduction lossesrdquo IEEETransactions on Industrial Electronics vol 58 no 9 pp 4153ndash4160 2011

[7] Z Chen J Xu G Zhou and F Zhang ldquoAnalysis of bridgelesspseudo-boost PFC converterrdquo in Proceedings of the 21st IEEEInternational Symposium on Industrial Electronics (ISIE rsquo12) pp189ndash193 IEEE Hangzhou China May 2012

[8] T Jiang P Mao and S-J Xie ldquoDistortion issue on input currentof OCC-PFC converter and its solutionrdquo Proceedings of theChinese Society of Electrical Engineering vol 31 no 12 pp 51ndash562011

[9] B Liu J J Wu J Li and J Y Dai ldquoA novel PFC controllerand selective harmonics suppressionrdquo International Journal ofElectrical Power amp Energy Systems vol 44 no 1 pp 680ndash6872013

[10] D Bortis L Fassler and J W Kolar ldquoComprehensive analysisand comparative evaluation of the isolated true bridgeless Cuksingle-phase PFC rectifier systemrdquo in Proceedings of the IEEE14th Workshop on Control and Modeling for Power Electronics(COMPEL rsquo13) pp 1ndash9 2013

[11] M N M Hussain M F M Idris I Intan Rahayu et alldquoDevelopment of PI controller for battery charger using PFCrectifierrdquo in Proceedings of the IEEE International Symposiumon Power Electronics Electrical Drives Automation and Motion(SPEEDAM rsquo10) pp 1099ndash1101 June 2010

[12] WWang and D Dah-Chuan Lu ldquoA bridgeless DIVM buck PFCrectifier with digital control and voltage doubler configurationrdquoInternational Journal of Power Electronics vol 5 no 2 pp 125ndash144 2013

[13] D Bortis L Fassler and J W Kolar ldquoComprehensive analysisand comparative evaluation of the isolated true bridgeless Cuksingle-phase PFC rectifier systemrdquo in Proceedings of the IEEE14th Workshop on Control and Modeling for Power Electronics(COMPEL rsquo13) pp 1ndash9 IEEE Salt Lake City Utah USA June2013

[14] Y Chen J Zhou W P Dai et al ldquoApplication of improvedbridgeless power factor correction based on one-cycle controlin electric vehicle charging systemrdquo Electric Power Componentsand Systems vol 42 no 2 pp 112ndash123 2014

[15] K H Wu J H Chiu and Y K Lo ldquoA single-stage high power-factor bridgeless AC-LED driver for lighting applicationsrdquoInternational Journal of CircuitTheory and Applications vol 42no 1 pp 96ndash109 2014

[16] A Karaarslan and I Iskender ldquoAnalysis and comparison ofcurrent control methods on bridgeless converter to improvepower qualityrdquo International Journal of Electrical Power andEnergy Systems vol 51 pp 1ndash13 2013

[17] E H Ismail ldquoBridgeless SEPIC rectifier with unity power factorand reduced conduction lossesrdquo IEEETransactions on IndustrialElectronics vol 56 no 4 pp 1147ndash1157 2009

[18] Y Jang and M M Jovanovic ldquoBridgeless high-power-factorbuck converterrdquo IEEE Transactions on Power Electronics vol 26no 2 pp 602ndash611 2011

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


iL + minus

L+

+

minus

minus

+

minus

+

minus

+

minus

L

S

CrLr

s D1 D1

D2 ic

Co R

Iominus D2 +c119903

iL119903

oin

Figure 1 The topology of Bipolar-Gain Pseudo-Boost converter

a bridgeless Bipolar-Gain Pseudo-Boost PFC converter incontinuous conduction mode (CCM) is investigated Theconverter adopts one bidirectional controllable switch andtwo fast-recovery diodes instead of bridge rectifier andthe zero-current switching of the fast-recovery diodes isachieved Therefore the efficiency of the converter isimproved Meanwhile the one-cycle control technology isadopted to control the Bipolar-Gain Pseudo-Boost PFCconverter

2 Operation Principle of Bipolar-GainPseudo-Boost Converter

The topology of the Bipolar-Gain Pseudo-Boost converterconsists of switch 119878 two recovery diodes119863

1and119863

2 resonant

capacitor 119862119903 and resonant inductor 119871

119903 as in Figure 1 When

the input voltage is positive or negative the output voltageof traditional Boost converter is the corresponding polarityCompared with the traditional one the output voltage ofBipolar-Gain Pseudo-Boost converter is just positive that isthe Bipolar-Gain Pseudo-Boost has bipolar-gain characteris-tic To simplify the analysis of the operation of the Bipolar-Gain Pseudo-Boost converter the following assumptions aremade

(a) All of the switches diodes inductors and capacitorsare ideal

(b) Output capacitor 119862119900is large enough to make the

output voltage keep constant in a switching cycle(c) Resonant inductor 119871

119903and resonant capacitor 119862

119903

are much smaller than the inductor 119871 and outputcapacitor 119862

119900 respectively

(d) The converter operates in CCM

21 Positive Input Voltage The operation modes of Bipolar-Gain Pseudo-Boost converter operate in CCM with positiveinput voltage (Figure 2) The corresponding key waveformsof the converter are shown in Figure 3 At the beginning ofeach switching cycle the resonant inductor current 119894

119871119903

is zeroand the initial value of resonant capacitor voltage V

119888119903

is ΔV119888119903

where V

119888gt ΔV119888119903

gt 0 exists(1) Mode 1 [119905


at 119905 = 1199050 the switch 119878 is turned on The voltage across the

inductor 119871 is equal to input voltage Vin whichmakes inductorcurrent increase linearly The resonant capacitor voltage V

119888119903

makes diode 1198631turn on and the reverse voltage across 119863

2

makes it turn off Resonant capacitor voltage V119888119903

and resonantinductor current 119894

119871119903

are given as

V119888119903

= ΔV119888119903

cos120596119903(119905 minus 1199050)

119894119871119903

= minusΔV119888119903

119885119899

sin120596119903(119905 minus 1199050)

(1)

where 119885119899= radic119871

119903119862119903 120596119903= 1radic119871

119903119862119903

(2) Mode 2 [1199051sim1199052] as shown in Figures 2(b) and 3 at 119905 =

1199051= 1199050+ 1198791199032 resonant inductor current 119894

119871119903

is equal to zeroand diode119863


119903= 2120587120596

119903is

the resonant period At this moment the resonant capacitoris equal to minusΔV

119888119903

Due to V119888gt ΔV119888119903

the diode1198632is still turned

off with reverse voltage ΔV119888119903

minus V119888 The voltage across diode119863

1

is equal to V1198631

= minusV119888119903

= ΔV119888119903

while the voltage across diode1198632is equal to V

1198632= V119888minus ΔV119888119903

(3) Mode 3 [119905




2is turned on to


1is

reversely biased and the voltage across it is equal to minusV119888 and

the inductor 119871 is then discharged and capacitor119862119900is charged

As 119871119903≪ 119871 119871

119903can be ignored So during 119905

2sim1199053 the resonant

capacitor voltage can be expressed as

V119888119903

= minusΔV119888119903

+119894119871

119862119903

(119905 minus 1199052) (2)

When the resonant capacitor voltage rises to ΔV119888119903

theconverter begins to enter the next switch cycle

22 Negative Input Voltage Figure 4 shows the operationmodes of Bipolar-Gain Pseudo-Boost converter operated inCCM with negative input voltage The corresponding keywaveforms of the converter are shown in Figure 5 At thebeginning of each switching cycle the resonant inductorcurrent 119894

119871119903

is zero and the initial value of resonant capacitorvoltage V

119888119903

= minusV119888minus ΔV119888119903

where V119888gt ΔV119888119903

gt 0(1) Mode 4 [119905


at 119905 = 1199054 the switch 119878 is turned on The voltage across

the inductor 119871 is equal to input voltage minusVin which makesinductor current decrease linearlyThe diode119863

2is turned on

by the opposite voltage ΔV119888119903

and the diode 1198631is reversely

biased The resonant branch begins to resonate the resonantcapacitor voltage V

119888119903

and resonant inductor current 119894119871119903

aregiven as

V119888119903

= minusV119888minus ΔV119888119903

cos120596119903(119905 minus 1199054)

119894119871119903

=ΔV119888119903

119885119899

sin120596119903(119905 minus 1199054)

(3)

where 119885119899= radic119871

119903119862119903 120596119903= 1radic119871

119903119862119903

(2) Mode 5 [1199055sim 1199056] as shown in Figures 4(b) and 5 at

119905 = 1199055 the resonant inductor current 119894

119871119903

is equal to zero anddiode119863


5minus 1199054= 1198791199032 and

119879119903= 2120587120596

119903is the resonant period The resonant capacitor is

equal to minusV119888+ ΔV119888119903

the diode 1198631is still reversely biased and


iL + minus

L+

+

minus

minus

+

minus

+

minus

L Cr Lr

D1D1

D2

Co R

IominusD2+c119903

iL119903

in c

(a) Mode 1

iL + minus

L+

+

minus

minus

+

minus

+

minus

L CrLr

D1 D1

D2

Co R

IominusD2+c119903

iL119903

oin

(b) Mode 2

iL + minus

L+

+

minus

minus

+

minus

+

minus

+

minus

L

Cr Lr

D1D1

D2

Co R

IominusD2+

S s

c119903iL119903

oin

(c) Mode 3


st

D1

D2

iL


Δc119903

c119903Δc119903

minusΔc119903

minusΔc119903Zn

iL119903

c + Δc119903

c

c

c minus Δc119903

c minus Δc119903

c



= minusV119888119903

= V119888minus ΔV119888119903


2is equal to ΔV

119888119903

(3) Mode 6 [119905




1is turned on to


2is





V119888119903

= minusV119888+ ΔV119888119903

minus119894119871

119862119903

(119905 minus 1199056) (4)


ΔV119888119903




119888 119894119871)


119888119903

119894119871119903


119888 119894119871as



119871d119894119871

d119905= Vin

119862119900

dV119888

d119905= minus

V119888

119877

(5)


(119871 + 119871119903)d119894119871


119888minus V119888119903

119862119900

dV119888

d119905= 119894119871minusV119888

119877

(6)


iL + minus

L+

+

minus

minus

+

minus

+

minus

LCr

Lr

D1D1

D2

Co R

IominusD2+c119903

iL119903

minusin c

(a) Mode 4

iL + minus

L+

+

minus

minus

+

minus

+

minus

LCr

Lr

D1D1

D2

Co R

IominusD2+c119903

iL119903

minusin c

(b) Mode 5

iL + minus

L+

+

minus

minus

+

minus

+

minus

LCr

Lr

D1D1

D2

Co R

IominusD2+

+

minus

S s

c119903iL119903

minusin c

(c) Mode 6


s

t

D1

D2

iL


Δc119903Zn

iL119903



Δc119903 minus c

minusc


Δc119903

c119903

c minus Δc119903

c

c



119888119903



[119894119871


is

x = 119860119894x + 119861119894u 119894 = 1 2 (7)

where

1198601= [

[

0 0

0 minus1

119877119862119900

]

]

1198611= [

[

Vin119871

0

]

]

1198602=

[[[

[

0 minus1

119871 + 119871119903

1

119862119900

minus1

119877119862119900

]]]

]

1198612= [

[

Vin minus V119888119903

119871 + 119871119903

0

]

]

(8)


dd119905

[119894119871

V119888

] =[[[

[


119871 + 119871119903

(1 minus 119889)

119862119900

minus1

119877119862119900

]]]

]

[119894119871

V119888

] + [

[

Vin119871

0

]

]

(9)


119888


119903 so 119871 + 119871


Vin = (1 minus 119863) V119888 119868

119871=

V119888

119877 (1 minus 119863) (10)




119871d119894119871

d119905= minusVin

119862119900

dV119888

d119905= 119894119871119903

minusV119888

119877

(11)



119871d119894119871

d119905= minusVin

119862119900

dV119888

d119905= minus

V119888

119877

(12)


(119871 + 119871119903)d119894119871


119888119903

119862119900

dV119888

d119905= minus

V119888

119877

(13)


119888119903




[119894119871


tion isx = 119860

119894x + 119861119894u 119894 = 1 2 3 (14)

where

1198601= [

[

0 0

0 minus1

119877119862119900

]

]

1198611=

[[[

[

minusVin119871

119894119871119903

119862119900

]]]

]

1198602= [

[

0 0

0 minus1

119877119862119900

]

]

1198612= [

[

minusVin119871

0

]

]

1198603= [

[

0 0

0 minus1

119877119862119900

]

]

1198613= [

[


119871 + 119871119903

0

]

]

(15)


dd119905

[119894119871

V119888

] = [

[

0 0

0 minus1

119877119862119900

]

]

[119894119871

V119888

] +[[[

[

minusVin119871

+V119888

119871(1 minus 119889)

119894119871(1 minus 119889)

119862119900

]]]

]

(16)

The equation (dd119905) [ 119894119871V119888


119903 so 119871 + 119871


Vin = (1 minus 119863) V119888 119868

119871=

V119888

119877 (1 minus 119863) (17)


iL

+ minus

L

+ minus

+

minus

+

minus

L

CrLr

D1 D1

D2

Co R

IominusD2+

+

minus

s

icG

S1

S2

c119903iL119903

in c











Vinpmax

119871119863max119879119904 le 2119868inp (18)




iL

+ minus

L

+ minus

+

minus

+

minus

L

CrLr

D1D1

D2

CoR

minusD2+

+

minus

sG

S1

S2

R1

R2

PIQ

Q

R

S

Clock

Drivers G

minus

minus

+

minus

+

+

v2 Resetintegrator

v1

vm

Control circuit

Rs|iL|

Rs

c119903iL119903

in c

ref







ΔV119888119903

=119868119871

2119862119903

(119879119904minus 119863119879119904) =

V119888

2119877119862119903

119879119904 (19)



119903 ΔV119888119903





119900



gt 0moreover

119863min119879119904 gt119879119903

2 (20)


119903= 2120587radic119871

119903119862119903 Thus a suitable






1and 119878





T

1

4

2

iin (5Adiv)

in (100Vdiv)

o (100Vdiv)



V119898


119898


1between V

119898and119877






V119898

minus 119877119904

10038161003816100381610038161198941198711003816100381610038161003816 =

1

119879119904

int

119879119904

0

119863V119898d119905 (21)

where V119898

= V119888119877119904119877119890and 119877




119871will




119900= 100W


50 kHz 119871 = 25mH 119871119903= 78 120583H and 119862

119903= 330 nF










099

098

097

096

095

120578

50 100 150 200

Po (W)


M

1

4

2

T

Mode 2Mode 1Mode 3

s (100Vdiv)

D1 (100Vdiv)

D2 (100Vdiv)

t = 4 (120583div)

iL119903(2Adiv)

(a)

M

1

4

2T

Mode 5Mode 4Mode 6


D2 (100Vdiv)

t = 4 (120583div)

iL119903(2Adiv)

(b)


0

5

10

15

20

25

30

35

3 5 7 9 11 13 15


Harmonic (n)


Har

mon

ic cu

rren

tinp

ut cu

rren

t (

)



1and119863




85 95 105

1

115 125 135

0995

0990

0985

0980

PF

in (V)



7 Conclusion






Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










iL + minus

L+

+

minus

minus

+

minus

+

minus

L Cr Lr

D1D1

D2

Co R

IominusD2+c119903

iL119903

in c

(a) Mode 1

iL + minus

L+

+

minus

minus

+

minus

+

minus

L CrLr

D1 D1

D2

Co R

IominusD2+c119903

iL119903

oin

(b) Mode 2

iL + minus

L+

+

minus

minus

+

minus

+

minus

+

minus

L

Cr Lr

D1D1

D2

Co R

IominusD2+

S s

c119903iL119903

oin

(c) Mode 3


st

D1

D2

iL


Δc119903

c119903Δc119903

minusΔc119903

minusΔc119903Zn

iL119903

c + Δc119903

c

c

c minus Δc119903

c minus Δc119903

c



= minusV119888119903

= V119888minus ΔV119888119903


2is equal to ΔV

119888119903

(3) Mode 6 [119905




1is turned on to


2is





V119888119903

= minusV119888+ ΔV119888119903

minus119894119871

119862119903

(119905 minus 1199056) (4)


ΔV119888119903




119888 119894119871)


119888119903

119894119871119903


119888 119894119871as



119871d119894119871

d119905= Vin

119862119900

dV119888

d119905= minus

V119888

119877

(5)


(119871 + 119871119903)d119894119871


119888minus V119888119903

119862119900

dV119888

d119905= 119894119871minusV119888

119877

(6)


iL + minus

L+

+

minus

minus

+

minus

+

minus

LCr

Lr

D1D1

D2

Co R

IominusD2+c119903

iL119903

minusin c

(a) Mode 4

iL + minus

L+

+

minus

minus

+

minus

+

minus

LCr

Lr

D1D1

D2

Co R

IominusD2+c119903

iL119903

minusin c

(b) Mode 5

iL + minus

L+

+

minus

minus

+

minus

+

minus

LCr

Lr

D1D1

D2

Co R

IominusD2+

+

minus

S s

c119903iL119903

minusin c

(c) Mode 6


s

t

D1

D2

iL


Δc119903Zn

iL119903



Δc119903 minus c

minusc


Δc119903

c119903

c minus Δc119903

c

c



119888119903



[119894119871


is

x = 119860119894x + 119861119894u 119894 = 1 2 (7)

where

1198601= [

[

0 0

0 minus1

119877119862119900

]

]

1198611= [

[

Vin119871

0

]

]

1198602=

[[[

[

0 minus1

119871 + 119871119903

1

119862119900

minus1

119877119862119900

]]]

]

1198612= [

[

Vin minus V119888119903

119871 + 119871119903

0

]

]

(8)


dd119905

[119894119871

V119888

] =[[[

[


119871 + 119871119903

(1 minus 119889)

119862119900

minus1

119877119862119900

]]]

]

[119894119871

V119888

] + [

[

Vin119871

0

]

]

(9)


119888


119903 so 119871 + 119871


Vin = (1 minus 119863) V119888 119868

119871=

V119888

119877 (1 minus 119863) (10)




119871d119894119871

d119905= minusVin

119862119900

dV119888

d119905= 119894119871119903

minusV119888

119877

(11)



119871d119894119871

d119905= minusVin

119862119900

dV119888

d119905= minus

V119888

119877

(12)


(119871 + 119871119903)d119894119871


119888119903

119862119900

dV119888

d119905= minus

V119888

119877

(13)


119888119903




[119894119871


tion isx = 119860

119894x + 119861119894u 119894 = 1 2 3 (14)

where

1198601= [

[

0 0

0 minus1

119877119862119900

]

]

1198611=

[[[

[

minusVin119871

119894119871119903

119862119900

]]]

]

1198602= [

[

0 0

0 minus1

119877119862119900

]

]

1198612= [

[

minusVin119871

0

]

]

1198603= [

[

0 0

0 minus1

119877119862119900

]

]

1198613= [

[


119871 + 119871119903

0

]

]

(15)


dd119905

[119894119871

V119888

] = [

[

0 0

0 minus1

119877119862119900

]

]

[119894119871

V119888

] +[[[

[

minusVin119871

+V119888

119871(1 minus 119889)

119894119871(1 minus 119889)

119862119900

]]]

]

(16)

The equation (dd119905) [ 119894119871V119888


119903 so 119871 + 119871


Vin = (1 minus 119863) V119888 119868

119871=

V119888

119877 (1 minus 119863) (17)


iL

+ minus

L

+ minus

+

minus

+

minus

L

CrLr

D1 D1

D2

Co R

IominusD2+

+

minus

s

icG

S1

S2

c119903iL119903

in c











Vinpmax

119871119863max119879119904 le 2119868inp (18)




iL

+ minus

L

+ minus

+

minus

+

minus

L

CrLr

D1D1

D2

CoR

minusD2+

+

minus

sG

S1

S2

R1

R2

PIQ

Q

R

S

Clock

Drivers G

minus

minus

+

minus

+

+

v2 Resetintegrator

v1

vm

Control circuit

Rs|iL|

Rs

c119903iL119903

in c

ref







ΔV119888119903

=119868119871

2119862119903

(119879119904minus 119863119879119904) =

V119888

2119877119862119903

119879119904 (19)



119903 ΔV119888119903





119900



gt 0moreover

119863min119879119904 gt119879119903

2 (20)


119903= 2120587radic119871

119903119862119903 Thus a suitable






1and 119878





T

1

4

2

iin (5Adiv)

in (100Vdiv)

o (100Vdiv)



V119898


119898


1between V

119898and119877






V119898

minus 119877119904

10038161003816100381610038161198941198711003816100381610038161003816 =

1

119879119904

int

119879119904

0

119863V119898d119905 (21)

where V119898

= V119888119877119904119877119890and 119877




119871will




119900= 100W


50 kHz 119871 = 25mH 119871119903= 78 120583H and 119862

119903= 330 nF










099

098

097

096

095

120578

50 100 150 200

Po (W)


M

1

4

2

T

Mode 2Mode 1Mode 3

s (100Vdiv)

D1 (100Vdiv)

D2 (100Vdiv)

t = 4 (120583div)

iL119903(2Adiv)

(a)

M

1

4

2T

Mode 5Mode 4Mode 6


D2 (100Vdiv)

t = 4 (120583div)

iL119903(2Adiv)

(b)


0

5

10

15

20

25

30

35

3 5 7 9 11 13 15


Harmonic (n)


Har

mon

ic cu

rren

tinp

ut cu

rren

t (

)



1and119863




85 95 105

1

115 125 135

0995

0990

0985

0980

PF

in (V)



7 Conclusion






Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










iL + minus

L+

+

minus

minus

+

minus

+

minus

LCr

Lr

D1D1

D2

Co R

IominusD2+c119903

iL119903

minusin c

(a) Mode 4

iL + minus

L+

+

minus

minus

+

minus

+

minus

LCr

Lr

D1D1

D2

Co R

IominusD2+c119903

iL119903

minusin c

(b) Mode 5

iL + minus

L+

+

minus

minus

+

minus

+

minus

LCr

Lr

D1D1

D2

Co R

IominusD2+

+

minus

S s

c119903iL119903

minusin c

(c) Mode 6


s

t

D1

D2

iL


Δc119903Zn

iL119903



Δc119903 minus c

minusc


Δc119903

c119903

c minus Δc119903

c

c



119888119903



[119894119871


is

x = 119860119894x + 119861119894u 119894 = 1 2 (7)

where

1198601= [

[

0 0

0 minus1

119877119862119900

]

]

1198611= [

[

Vin119871

0

]

]

1198602=

[[[

[

0 minus1

119871 + 119871119903

1

119862119900

minus1

119877119862119900

]]]

]

1198612= [

[

Vin minus V119888119903

119871 + 119871119903

0

]

]

(8)


dd119905

[119894119871

V119888

] =[[[

[


119871 + 119871119903

(1 minus 119889)

119862119900

minus1

119877119862119900

]]]

]

[119894119871

V119888

] + [

[

Vin119871

0

]

]

(9)


119888


119903 so 119871 + 119871


Vin = (1 minus 119863) V119888 119868

119871=

V119888

119877 (1 minus 119863) (10)




119871d119894119871

d119905= minusVin

119862119900

dV119888

d119905= 119894119871119903

minusV119888

119877

(11)



119871d119894119871

d119905= minusVin

119862119900

dV119888

d119905= minus

V119888

119877

(12)


(119871 + 119871119903)d119894119871


119888119903

119862119900

dV119888

d119905= minus

V119888

119877

(13)


119888119903




[119894119871


tion isx = 119860

119894x + 119861119894u 119894 = 1 2 3 (14)

where

1198601= [

[

0 0

0 minus1

119877119862119900

]

]

1198611=

[[[

[

minusVin119871

119894119871119903

119862119900

]]]

]

1198602= [

[

0 0

0 minus1

119877119862119900

]

]

1198612= [

[

minusVin119871

0

]

]

1198603= [

[

0 0

0 minus1

119877119862119900

]

]

1198613= [

[


119871 + 119871119903

0

]

]

(15)


dd119905

[119894119871

V119888

] = [

[

0 0

0 minus1

119877119862119900

]

]

[119894119871

V119888

] +[[[

[

minusVin119871

+V119888

119871(1 minus 119889)

119894119871(1 minus 119889)

119862119900

]]]

]

(16)

The equation (dd119905) [ 119894119871V119888


119903 so 119871 + 119871


Vin = (1 minus 119863) V119888 119868

119871=

V119888

119877 (1 minus 119863) (17)


iL

+ minus

L

+ minus

+

minus

+

minus

L

CrLr

D1 D1

D2

Co R

IominusD2+

+

minus

s

icG

S1

S2

c119903iL119903

in c











Vinpmax

119871119863max119879119904 le 2119868inp (18)




iL

+ minus

L

+ minus

+

minus

+

minus

L

CrLr

D1D1

D2

CoR

minusD2+

+

minus

sG

S1

S2

R1

R2

PIQ

Q

R

S

Clock

Drivers G

minus

minus

+

minus

+

+

v2 Resetintegrator

v1

vm

Control circuit

Rs|iL|

Rs

c119903iL119903

in c

ref







ΔV119888119903

=119868119871

2119862119903

(119879119904minus 119863119879119904) =

V119888

2119877119862119903

119879119904 (19)



119903 ΔV119888119903





119900



gt 0moreover

119863min119879119904 gt119879119903

2 (20)


119903= 2120587radic119871

119903119862119903 Thus a suitable






1and 119878





T

1

4

2

iin (5Adiv)

in (100Vdiv)

o (100Vdiv)



V119898


119898


1between V

119898and119877






V119898

minus 119877119904

10038161003816100381610038161198941198711003816100381610038161003816 =

1

119879119904

int

119879119904

0

119863V119898d119905 (21)

where V119898

= V119888119877119904119877119890and 119877




119871will




119900= 100W


50 kHz 119871 = 25mH 119871119903= 78 120583H and 119862

119903= 330 nF










099

098

097

096

095

120578

50 100 150 200

Po (W)


M

1

4

2

T

Mode 2Mode 1Mode 3

s (100Vdiv)

D1 (100Vdiv)

D2 (100Vdiv)

t = 4 (120583div)

iL119903(2Adiv)

(a)

M

1

4

2T

Mode 5Mode 4Mode 6


D2 (100Vdiv)

t = 4 (120583div)

iL119903(2Adiv)

(b)


0

5

10

15

20

25

30

35

3 5 7 9 11 13 15


Harmonic (n)


Har

mon

ic cu

rren

tinp

ut cu

rren

t (

)



1and119863




85 95 105

1

115 125 135

0995

0990

0985

0980

PF

in (V)



7 Conclusion






Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119871d119894119871

d119905= minusVin

119862119900

dV119888

d119905= minus

V119888

119877

(12)


(119871 + 119871119903)d119894119871


119888119903

119862119900

dV119888

d119905= minus

V119888

119877

(13)


119888119903




[119894119871


tion isx = 119860

119894x + 119861119894u 119894 = 1 2 3 (14)

where

1198601= [

[

0 0

0 minus1

119877119862119900

]

]

1198611=

[[[

[

minusVin119871

119894119871119903

119862119900

]]]

]

1198602= [

[

0 0

0 minus1

119877119862119900

]

]

1198612= [

[

minusVin119871

0

]

]

1198603= [

[

0 0

0 minus1

119877119862119900

]

]

1198613= [

[


119871 + 119871119903

0

]

]

(15)


dd119905

[119894119871

V119888

] = [

[

0 0

0 minus1

119877119862119900

]

]

[119894119871

V119888

] +[[[

[

minusVin119871

+V119888

119871(1 minus 119889)

119894119871(1 minus 119889)

119862119900

]]]

]

(16)

The equation (dd119905) [ 119894119871V119888


119903 so 119871 + 119871


Vin = (1 minus 119863) V119888 119868

119871=

V119888

119877 (1 minus 119863) (17)


iL

+ minus

L

+ minus

+

minus

+

minus

L

CrLr

D1 D1

D2

Co R

IominusD2+

+

minus

s

icG

S1

S2

c119903iL119903

in c











Vinpmax

119871119863max119879119904 le 2119868inp (18)




iL

+ minus

L

+ minus

+

minus

+

minus

L

CrLr

D1D1

D2

CoR

minusD2+

+

minus

sG

S1

S2

R1

R2

PIQ

Q

R

S

Clock

Drivers G

minus

minus

+

minus

+

+

v2 Resetintegrator

v1

vm

Control circuit

Rs|iL|

Rs

c119903iL119903

in c

ref







ΔV119888119903

=119868119871

2119862119903

(119879119904minus 119863119879119904) =

V119888

2119877119862119903

119879119904 (19)



119903 ΔV119888119903





119900



gt 0moreover

119863min119879119904 gt119879119903

2 (20)


119903= 2120587radic119871

119903119862119903 Thus a suitable






1and 119878





T

1

4

2

iin (5Adiv)

in (100Vdiv)

o (100Vdiv)



V119898


119898


1between V

119898and119877






V119898

minus 119877119904

10038161003816100381610038161198941198711003816100381610038161003816 =

1

119879119904

int

119879119904

0

119863V119898d119905 (21)

where V119898

= V119888119877119904119877119890and 119877




119871will




119900= 100W


50 kHz 119871 = 25mH 119871119903= 78 120583H and 119862

119903= 330 nF










099

098

097

096

095

120578

50 100 150 200

Po (W)


M

1

4

2

T

Mode 2Mode 1Mode 3

s (100Vdiv)

D1 (100Vdiv)

D2 (100Vdiv)

t = 4 (120583div)

iL119903(2Adiv)

(a)

M

1

4

2T

Mode 5Mode 4Mode 6


D2 (100Vdiv)

t = 4 (120583div)

iL119903(2Adiv)

(b)


0

5

10

15

20

25

30

35

3 5 7 9 11 13 15


Harmonic (n)


Har

mon

ic cu

rren

tinp

ut cu

rren

t (

)



1and119863




85 95 105

1

115 125 135

0995

0990

0985

0980

PF

in (V)



7 Conclusion






Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










iL

+ minus

L

+ minus

+

minus

+

minus

L

CrLr

D1D1

D2

CoR

minusD2+

+

minus

sG

S1

S2

R1

R2

PIQ

Q

R

S

Clock

Drivers G

minus

minus

+

minus

+

+

v2 Resetintegrator

v1

vm

Control circuit

Rs|iL|

Rs

c119903iL119903

in c

ref







ΔV119888119903

=119868119871

2119862119903

(119879119904minus 119863119879119904) =

V119888

2119877119862119903

119879119904 (19)



119903 ΔV119888119903





119900



gt 0moreover

119863min119879119904 gt119879119903

2 (20)


119903= 2120587radic119871

119903119862119903 Thus a suitable






1and 119878





T

1

4

2

iin (5Adiv)

in (100Vdiv)

o (100Vdiv)



V119898


119898


1between V

119898and119877






V119898

minus 119877119904

10038161003816100381610038161198941198711003816100381610038161003816 =

1

119879119904

int

119879119904

0

119863V119898d119905 (21)

where V119898

= V119888119877119904119877119890and 119877




119871will




119900= 100W


50 kHz 119871 = 25mH 119871119903= 78 120583H and 119862

119903= 330 nF










099

098

097

096

095

120578

50 100 150 200

Po (W)


M

1

4

2

T

Mode 2Mode 1Mode 3

s (100Vdiv)

D1 (100Vdiv)

D2 (100Vdiv)

t = 4 (120583div)

iL119903(2Adiv)

(a)

M

1

4

2T

Mode 5Mode 4Mode 6


D2 (100Vdiv)

t = 4 (120583div)

iL119903(2Adiv)

(b)


0

5

10

15

20

25

30

35

3 5 7 9 11 13 15


Harmonic (n)


Har

mon

ic cu

rren

tinp

ut cu

rren

t (

)



1and119863




85 95 105

1

115 125 135

0995

0990

0985

0980

PF

in (V)



7 Conclusion






Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










099

098

097

096

095

120578

50 100 150 200

Po (W)


M

1

4

2

T

Mode 2Mode 1Mode 3

s (100Vdiv)

D1 (100Vdiv)

D2 (100Vdiv)

t = 4 (120583div)

iL119903(2Adiv)

(a)

M

1

4

2T

Mode 5Mode 4Mode 6


D2 (100Vdiv)

t = 4 (120583div)

iL119903(2Adiv)

(b)


0

5

10

15

20

25

30

35

3 5 7 9 11 13 15


Harmonic (n)


Har

mon

ic cu

rren

tinp

ut cu

rren

t (

)



1and119863




85 95 105

1

115 125 135

0995

0990

0985

0980

PF

in (V)



7 Conclusion






Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra













Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article study on a novel high-efficiency...

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