ResearchonDual-CarrierPulse-Train-Controlled BuckConverter

Research ArticleResearch on Dual-Carrier Pulse-Train-ControlledBuck Converter

Ming Qin and Shiwei Li

School of Electrical Engineering Zhengzhou University Zhengzhou 450001 China

Correspondence should be addressed to Ming Qin qinmingzzueducn

Received 18 June 2019 Accepted 24 August 2019 Published 10 September 2019

Academic Editor Daniel Morinigo-Sotelo

Copyright copy 2019 Ming Qin and Shiwei Li -is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

In order to solve the low-frequency oscillation of pulse-train- (PT-) controlled switching converter operating in a continuousconduction mode (CCM) a dual-carrier pulse-train (DCPT) control technique is proposed in this paper With the CCM buckconverter as an example the operational principle pulse control law and output voltage ripple of the DCPT-controlled converterare studied-e experimental results are provided to verify the theoretical analysis and simulation results Compared with the PT-controlled converter the DCPT-controlled CCM buck converter enjoys much better operating characteristics and smaller outputvoltage ripple

1 Introduction

With the development of electronic technology the steady-state performance and transient response of power suppliesare very important in many electronic devices However forpulse-width modulation (PWM) switching DC-DC con-verters with the disadvantages of slow transient responseand complicated compensational network it is hard to meetthe requirements of modern electronic equipments [1ndash4]

In order to get a great transient response a pulse-train(PT) control technique for DC-DC converter was proposed[5] When the PT-controlled switching converter operates indiscontinuous conduction mode (DCM) the output voltagewill increase during each high-energy pulse PH and decreaseduring each low-energy pulse PL which improves thetransient characteristic of the converter Qin and Xu [6]proposed a multiple pulse-train (MPT) control technique bysetting several duty cycle pulses to get better output char-acteristics Qin and Xu [7] introduced a current-referencedpulse-train (CRPT) control technique to enlarge the loadrange and improve the voltage accuracy of the converterConsidering the spectrum of the switching converter the bi-frequency pulse-train (BFPT) control technique was pro-posed [8] However all the control techniques mentioned

above were used in DCM converters which limited theapplications

Wang et al [9] applied the PT control technique to abuck converter operating in the continuous conductionmode (CCM) and indicated that the low-frequency oscil-lation existed at this time which confused the pulse controllaw and enlarged the output voltage ripple In order to solvethis problem several control techniques have been pro-posed By limiting the valley value of the inductor currentthe valley current mode PT (VCM-PT) controlled buckconverter eliminated the low-frequency oscillation but itlimited the output power range at the same time [10] Bydetecting the load current the sliding current valley PT(SCV-PT) controlled buck converter changed the valleyvalue of the inductor current adaptively and improved theoutput power range of the converter [11] However loadcurrent inductor current and output voltage were detectedat the same time for SCV-PT control which is quite com-plicated Sha et al [12] indicated that by limiting the peakvalue of the capacitor current within one switching cycle thelow-frequency oscillation could be eliminated although thecontrol parameters were complicated to design By con-trolling the leading edge of the pulse the pulse phase shift-based PT (PPS-PT) control was proposed [13] Although the

HindawiJournal of Control Science and EngineeringVolume 2019 Article ID 7514621 9 pageshttpsdoiorg10115520197514621

PPS-PT-controlled buck converter could eliminate the low-frequency oscillation it weakened the transient character-istic In [14] the PT control technique was applied to boostconverter operated in the pseudo continuous conductionmode (PCCM) -is converter enjoyed wide power rangewithout low-frequency oscillation but the efficiency of theconverter was poor due to the freewheeling phase In ad-dition by improving the topology of the converter the low-frequency oscillation could be suppressed but it wascomplicated to the integration of the switching converter[15ndash20]

In this paper a dual-carrier pulse-train (DCPT) controltechnique is proposed and studied in detail In the DCPT-controlled CCM buck converter the capacitor current islimited to the preset valley current by a carrier signal at thebeginning of each switching cycle -e output voltage willincrease during one PH switching cycle and decrease duringeach PL switching cycle which indicates that the low-fre-quency oscillation did not exist in the DCPT-controlledconverter -e theoretical analysis simulation and experi-mental results verify that the DCPT-controlled CCM buckconverter enjoys small output ripple and fast transientresponse

2 Operational Principle

For a buck converter when the switch S is on the inductorcurrent will increase with a slope of (Vin minus Vo)L when S isoff the inductor current will decrease with a slope of VoLSince the capacitor current reflects the ripple of the inductorcurrent completely the slope of the capacitor current is also(Vin minus Vo)L or VoL when the switch is on or off re-spectively If a control signal vsaw with a slope of VoL isapplied to the capacitor current the capacitor current willmove along with the trajectory of vsaw after the switch turnsoff

Figure 1(a) shows the schematic diagram of the DCPT-controlled buck converter In the controller a comparator isused to compare the output voltage of the switching converterwith a reference value a sense resistor connected to the outputcapacitor and its auxiliary circuit are employed to obtain thecapacitor current and two DA converters are acquired togenerate the carrier signals Besides that there is no extracompensational network in the controller which indicates theDCPT-controlled converter enjoys convenient design processand fast response -e main working waveforms includingcapacitor current ic control pulse control signal vp andoutput voltage vo are shown in Figure 1(b)-e carrier signalsvsawH and vsawL generated by the controller have the samevalley current Iv and slope VrefL However the frequency ofvsawH or vsawL is different which is fH or fL respectivelyBecause the control pulse is generated by comparing thecapacitor current with the carrier signal in the DCPT con-troller the switching frequency of the converter is also fH or fLcorrespondingly

-e working principle of the DCPT-controlled buckconverter is as follows -e carrier signal vsaw is chosenbetween vsawH and vsawL When vsaw decreases to the valleycurrent Iv the switch S turns on immediately and the output

voltage is compared with the reference voltage Vref Ifvo ltVref the carrier signal vsawH is selected as vsaw When thecapacitor current icgt vsawH the switch S turns off which isrecorded as a high-energy pulse PH Similarly if vo geVref atthe time when vsaw decreases to Iv the carrier signal vsawLwill be selected When icgt vsawL S turns off which isrecorded as the low-energy pulse PL When the converteroperates in a steady state the DCPTcontroller will generate apulse train which consists of PH and PL to stabilize theoutput voltage

3 Steady-State Analysis

31 Design of Control Parameters In order to avoid low-frequency oscillation the output voltage should be increasedduring PH and decreased during PL Based on this principlethe control parameters the frequencies of the carrier signalsand the valley current can be designed properly

Figure 2 shows the capacitor current waveform of theDCPT-controlled buck converter within one switching cy-cle For the switching converter with a low output voltagethe on-state voltage of the diode has a significant influenceon the process of control law analysis When the on-statevoltage VD of the diode is considered the rising or fallingslope of the capacitor current is (Vin minus Vo)L or (Vo +VD)Lrespectively

During t1 or t2 the peak value of the capacitor current Ipcan be expressed as

Ip Vin minus Vo

Lt1 (1)

Ip Vo + VD

Lt2 (2)

By combining equations (1) and (2) we have

t1 + t2 LIp Vin + VD( 1113857

Vin minus Vo( 1113857 Vo + VD( 1113857 (3)

Based on Figure 2 and equation (3) the area of thetriangle ABC can be written as

SΔABC 12

t1 + t2( 1113857Ip Vin + VD( 1113857LI2p

2 Vin minus Vo( 1113857 Vo + VD( 1113857 (4)

-e area of the quadrangle BCED within one switchingperiod T is

SBCED minus12

t1 + t2 + T( 1113857Iv minusVin + VD( 1113857LIvIp

2 Vin minus Vo( 1113857 Vo + VD( 1113857minus12

IvT

(5)

Similarly the areas of the triangle BOD and the triangleCFE can be expressed as

SΔBOD + SΔCFE SOFED minus SBCED minus12

IvT

+Vin + VD( 1113857LIvIp

2 Vin minus Vo( 1113857 Vo + VD( 1113857

(6)

2 Journal of Control Science and Engineering

According to equation (6) the charge variation of theoutput capacitor during one switching cycle T can be cal-culated asΔq SΔABC minus SΔBOD + SΔCFE( )

Vin + VD( )LI2p

2 Vin minus Vo( ) Vo + VD( )+12IvT minus

Vin + VD( )LIvIp2 Vin minus Vo( ) Vo + VD( )

(7)

During the conduction time of the switch Ip can bewritten as

Ip Iv +Vin minus Vo

LDT Iv +

Vin minus Vo( ) Vo + VD( )L Vin + VD( )

T

(8)

By combining equations (7) and (8) it is available that

Δq IvT +Vin minus Vo( ) Vo + VD( )

2L Vin + VD( )T2 (9)

erefore the variation of the output voltage within oneswitching cycle can be calculated as

Δvo ΔqCIvCT +

Vin minus Vo( ) Vo + VD( )2LC Vin + VD( )

T2 (10)

By choosing dierent TH or TL the variation of theoutput voltage within PH or PL can be obtained as

ΔvHo IvCTH +


T2H

ΔvLo IvCTL +


T2L

(11)

Based on equation (11) the output voltage iterativeequation of the DCPT-controlled buck converter can beexpressed as

von+1

von +IvCTH +


T2H von ltVref

von +IvCTL +


T2L von geVref

(12)

According to the principle of the DCPT control tech-nique ΔvHo gt 0 and ΔvLo lt 0 should be guaranteed ereforeit is available that

minusVin minus Vo( ) Vo + VD( )2LC Vin + VD( )

TH lt Iv lt minusVin minus Vo( ) Vo + VD( )

2L Vin + VD( )TL

(13)

e control parameter Iv can be determined by the presetinput voltage range of the converter Since the falling slope ofthe carrier signals vsawH and vsawL isVref L the peak value ofthe carrier signals can be calculated when the frequencies ofthe carrier signals fH and fL and the valley current Iv are

Vin

S L

D

iL ic

RE

VoDriverC

Rvp

Vref

vsawH

vsawL

FPGA

DAconverter

DAconverter

vsaw

R2 R1

R3R4

ic

(a)

tIv

0

t0

vsawH

vsawL

ic

vp

Vref

vo

PH PHPL PL PL

(b)

Figure 1 Working principle diagram of the DCPT-controlled buck converter (a) Schematic diagram (b) Working waveforms

IvD

t1 t2

Ip

OB

A

C

E

Ft

ic

Figure 2 Capacitor current of the DCPT-controlled buckconverter

Journal of Control Science and Engineering 3

determined Based on the analysis above the parameters ofthe researched the DCPT-controlled buck converter arelisted in Table 1

From equation (12) it can be known that the outputvoltage variations ΔvHo and ΔvLo vary with the input voltageVin In order to achieve ΔvHo gt 0 and ΔvLo lt 0 Vin would belimited within a valid range

Assuming the output voltage variation is zero in one PHswitching cycle (ΔvHo 0) the lower boundary of the inputvoltage for the DCPT-controlled buck converter will becalculated as

Vinmin Vo + VD( )2TH

Vo + VD( )T minus 2LIvminus VD (14)

Similarly assuming the output voltage variation is zeroin one PL switching cycle (ΔvLo 0) the upper boundary ofthe input voltage will be

Vinmax Vo + VD( )2TL


Substituting the parameters of Table 1 into equation (14)the operating range of the input voltage can be calculatedwhich is [811V 19V] When the input voltage varies in thisrange the output voltage will increase during each PH anddecrease during each PL thus the low-frequency oscillationcan be avoided

By using equation (12) the relationship between theoutput voltage variation ΔvHo gt 0 and minus ΔvLo lt 0 and the inputvoltage Vin can be obtained as shown in Figure 3 It can beseen that with the increasing input voltage the variation ofthe output voltage ΔvHo gt 0 increases and minus ΔvLo lt 0 decreases

32AnalysisofPulseControlLaw According to the principleof charge balance the variation of the output voltage is zeroin a whole pulse train that is

μHΔvHo + μLΔv

Lo 0 (16)

By combining equations (12) and (16) it can be obtainedthat

μHμL minus

Vin minus Vo( ) Vo + VD( )T2L minus 2LIvTL Vin + VD( )

Vin minus Vo( ) Vo + VD( )T2H minus 2LIvTH Vin + VD( )

(17)

Substituting the parameters shown in Table 1 intoequation (17) the relationship between the pulse ratio μHμLand the input voltage Vin can be obtained as shown inFigure 4 It can be known that the pulse ratio μHμL de-creases gradually with the increase of Vin which is caused bythe increase of ΔvHo gt 0 and the decrease of minus ΔvLo lt 0erefore the proportion of the high-energy pulse PH in thepulse train gradually decreases with the increase in the inputvoltage

According to equation (17) the typical pulse train of theDCPT-controlled buck converter in the condition of dif-ferent input voltages can be obtained as listed in Table 2

33 Analysis of the Output Voltage Ripple To analyse theoutput voltage variation the capacitor current ic and outputvoltage vo of the DCPT-controlled buck converter withinone switching cycle are shown in Figure 5

During [0 ton] the capacitor current ic (t) and the outputvoltage of the converter can be written as

Table 1 Parameters of the DCPT-controlled buck converter

Parameters ValueRated input voltage Vin 12 VReference voltage Vref 5 VInductor L 100 μHCapacitor C 560 μFEquivalent series resistance RE 30mΩFrequency fL of carrier vsawL 40 kHzFrequency fH of carrier vsawH 20 kHzValley current Iv minus 05 A

∆νoH

ndash∆νoL

109 11 12 13 14 15Vin (V)

0

5

10

15

20

Δνo (

mV

) 25

30

35

40

Figure 3 Output voltage variation versus input voltage of theDCPT-controlled buck converter

109 11 12 13 14 15Vin (V)

0

05

1

15

2

μ H (μ

L)

25

3

35

Figure 4 Pulse ratio versus input voltage of the DCPT-controlledbuck converter


ic(t) Iv +Vin minus Vo

Lt (18)

vo(t) 1Cintt

0ic(t)dt + ic(t)RE

IvCt

+Vin minus Vo

2LCt2 +

Vin minus Vo

LREt

(19)

By taking the derivation of equation (19) one obtains

dvo(t)dt

IvC+Vin minus Vo

2LCt +

Vin minus Vo

LCRE (20)

Substituting the parameters listed in Table 1 intoequation (20) it can be known that the output voltage risesto the maximum at the time tonerefore it is available that

ΔvHpp IvCton +

Vin minus Vo

2LCt2on +

Vin minus Vo

LREton (21)

For the DCPT-controlled buck converter the outputvoltage ripple is closely related to the pulse train Taking thepulse train 2PH-1PL as an example the capacitor current icand the output voltage vo are shown in Figure 6(a) Obvi-ously the output voltage ripple of the converter is Δvo ΔvHpp + ΔvHo at this time

In general when the pulse train is nPH-1PL the outputvoltage ripple of the converter is

Δvo (n minus 1)ΔvHpp + ΔvHo (22)

When the pulse train is 1PH-nPL the capacitor current icand the output voltage vo are shown in Figure 6(b) Ap-parently the output voltage ripple on this condition is

Δvo ΔvHpp (23)

By using equations (21)ndash(23) the output voltage rippleΔvo of the DCPT-controlled buck converter can be calcu-lated as listed in Table 3 For the DCPT-controlled buckconverter the output voltage ripple increases gradually withthe increase of the input voltage

4 Simulation and Experimental Results

41 SimulationResults To verify the theoretical analysis thesimulation results are provided in Figure 7 which includecarrier signal vsaw control pulse vp capacitor current ic andoutput voltage vo

As shown in Figure 7(a) when the input voltage equals to868V the pulse train is 2PH-1PL the pulse ratio is μHμL 2and the output voltage ripple is 40mV which are consistentwith the theoretical analysis Similarly as shown inFigures 7(b)ndash7(d) when the input voltage equals to 92V1083V or 12V the pulse train is 1PH-1PL 1PH-3PL or 1PH-5PL the pulse ratio is 1 13 or 15 and the output voltageripple is 40mV 55mV or 60mV respectively

According to Figure 7 the following conclusion of theDCPT-controlled buck converter can be obtained as theinput voltage Vin increases μHμL decreases gradually iethe proportion of PH in the pulse train decreases which isconsistent with the theoretical analysis in Section 32

In addition the value of the capacitor current at thebeginning of each switching cycle is equal to the preset valleycurrent Iv due to the traction of the carrier signals Since thecapacitor current reects the ripple of the inductor currentthe value of the inductor current is constant at the beginningof each switching cycle erefore the variation of theoutput voltage is only inuenced by the control pulse PH orPL which indicates that the low-frequency oscillation doesnot exist in the DCPT-controlled buck converter

42 Experimental Results In order to verify and test theproposed technique a prototype of the DCPT-controlledbuck converter is designed with the parameters in Table 1 Inthe prototype the control scheme is achieved by an FPGAdevice with a type of EP4CE15F17C8 An operationalamplicenter OPA228 and a 10mΩ sense resistor connectedwith the output capacitor are employed to obtain the ca-pacitor current Two DA DAC0808 converters are appliedto generate the carrier signals and an analogue multiplexerCD4051 is used to select the carrier signal between vsawH andvsawL Besides the type of the comparators in this prototypeis LM393

When the input voltage equals to 868V the experi-mental waveforms are shown in Figure 8(a) e pulse trainis 2PH-1PL and the output voltage ripple is 40mV ap-proximately Similarly when the input voltage equals to92V 1083V or 12V the pulse train is 1PH-1PL 1PH-3PL

Iv

ton

O t

ic

t

vo

O

ΔνHpp

T

Figure 5 Capacitor current and output voltage of the DCPT-controlled buck converter

Table 2 Pulse train of the DCPT-controlled buck converter atdierent voltages

Vin (V) μHμL Pulse train849 3 3PH-1PL868 2 2PH-1PL92 1 1PH-1PL1083 13 1PH-3PL12 15 1PH-5PL


or 1PH-5PL and the output voltage ripple is 40mV 50mV or60mV respectively

According to the principle of DCPT control the controlpulse is generated by comparing the capacitor current with thecarrier signals It can be seen from Figure 8 that the combi-nation of the carrier signals changes with the variation of the

input voltage which causes the variation of the pulse trainBased on the experimental results it can be known that theDCPT-controlled buck converter can operate in a steady stateby adjusting the pulse train when the input voltage changes

In order to study the transient response of the DCPTcontrol method the experimental transient waveforms are

2PH-1PL

40mV5045

10

1

2

85 86 87t (ms)

88 89 9

v o (V

)i c

(A)

v p (V

)v s

aw (V

)

Iv

Iv

(a)

85 86 87t (ms)

88 89 9

5045

10

1

2

v o (V

)i c

(A)

v p (V

)v s

aw (V

)

Iv

Iv

1PH-1PL

40mV

(b)

85 86 87t (ms)

88 89 9

5045

10

1

2

v o (V

)i c

(A)

v p (V

)v s

aw (V

)

Iv

Iv

1PH-3PL

55mV

(c)

85 86 87t (ms)

88 89 9

5045

10

1

2

v o (V

)i c

(A)

v p (V

)v s

aw (V

)

Iv

Iv

1PH-5PL

60mV

(d)

Figure 7 Simulation waveforms of the DCPT-controlled buck converter (a) Vin 868V (b) Vin 92 V (c) Vin 1083V (d) Vin 12V

ic

vo

Vref

Iv

2PH-1PL

ΔvHPP

ΔvHo

Δvo

(a)

1PH-3PL

ΔvHPP

ic

vo

Vref

Iv

(b)

Figure 6 Output voltage ripple of the DCPT-controlled buck converter (a) -e case of 2PH-1PL (b) -e case of 1PH-3PL

Table 3 -e output voltage ripple of the DCPT-controlled buck converter

Vin (V) ΔvHo (mV) ΔvHpp (mV) Δvo (mV)

849 33 343 409868 49 363 41292 89 415 4151083 191 522 52212 248 577 577


provided in Figure 9 When the load current increases from2A to 3A two high-energy pulses are generated successivelyby the controller to stabilize the output voltage and thisconverter enjoys excellent transient response Consideringthe parasitic parameters such as the on-state resistor of theMOSFET when the load current increases the input voltageof the inductor will decrease slightly which causes theproportion of PH in the pulse train to increase

In order to verify the suppression effect on the low-frequency oscillation the comparative experimental resultsare provided in Figure 10 -e control parameters of

traditional PT-controlled buck converter are as followsDH 06 DL 03 and T 25 μs

As shown in Figure 10(a) the pulse train is 1PH-5PL forthe DCPT-controlled CCM converter and the output voltageripple is 60mV In contrast the pulse train of the PT-controlled buck converter is 4PH-4PL and the output voltageripple is 120mV as shown in Figure 10(b) -is phenom-enon of successive several high-energy pulses followed bysuccessive several low-energy pulses indicates that the low-frequency oscillation exists in the PT-controlled CCMconverter -e low-frequency oscillation has not occurred in

2PH-1PL vsaw [2Vdiv]

Time [50μsdiv]

vp [2Vdiv]ic [1Adiv]

vo [50mVdiv]

4

3

2

1

lt2HzF

(a)


Time [50μsdiv]


vo [50mVdiv]

4

3

2

1

lt2HzF

(b)


Time [50μsdiv]


vo [50mVdiv]273306kHz

4

3

2

1

F

(c)


Time [50 μsdiv] 331936kHzF

4

3

2

1


vo [50 mVdiv]

(d)

Figure 8 Experimental waveforms of the DCPT-controlled buck converter (a)Vin 868V (b)Vin 92V (c)Vin 1083V (d)Vin 12V

2PH

lt2HzFTime [100μsdiv]

vp [2Vdiv]

ic [1Adiv]

vo [50mVdiv]

Io [1Adiv]

2

3

14

Figure 9 Experimental transient waveforms of the DCPT-controlled buck converter while load changes


the DCPT-controlled CCM buck converter e proposedDCPT control technique enjoys much better output char-acteristics compared with the traditional PT controltechnique

5 Conclusions

In this paper a dual-carrier pulse-train control technique isproposed With the CCM buck converter as an example theoperational principle is analysed in detail Based on theoutput voltage variation of the DCPT-controlled buckconverter within one switching cycle the pulse control lawand the output voltage ripple are analysed e simulationand experimental results verify the theoretical analysis andindicate that there is no low-frequency oscillation in theDCPT-controlled CCM buck converter Compared with thetraditional PTcontrol technique the DCPT-controlled buckconverter enjoys better control characteristics and muchsmaller output voltage ripple

Data Availability

e data used to support the centndings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that there are no conicts of interestregarding the publication of this paper

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (51507155) and the Key ResearchProgram of Hersquonan Higher Education (16A470014)

References

[1] C Y-F Ho B W-K Ling Y Yan-Qun Liu P K-S Tam andK Kok-Lay Teo ldquoOptimal PWM control of switched-ca-pacitor DC-DC power converters via model transformationand enhancing control techniquesrdquo IEEE Transactions on

Circuits and Systems I Regular Papers vol 55 no 5pp 1382ndash1391 2008

[2] C Duan and D Wu ldquoNonlinear voltage regulation algorithmfor DC-DC boost converter with centnite-time convergencerdquoJournal of Control Science and Engineering vol 2019 ArticleID 6761784 5 pages 2019

[3] X Zhang Q-C Zhong and W-L Ming ldquoStabilization ofcascaded DCDC converters via adaptive series-virtual-im-pedance control of the load converterrdquo IEEE Transactions onPower Electronics vol 31 no 9 pp 6057ndash6063 2016

[4] S Kennedy M R Yuce and J-M Redoute ldquoFully integratedswitched-capacitor DCDC converters with clock slope EMIcontrolrdquo IEEE Transactions on Electromagnetic Compatibilityvol 60 no 6 pp 2073ndash2075 2018

[5] M Telefus A Shteynberg M Ferdowsi and A Emadi ldquoPulsetrain control technique for yback converterrdquo IEEE Trans-actions on Power Electronics vol 19 no 3 pp 757ndash764 2004

[6] M Qin and J Xu ldquoMultiduty ratio modulation technique forswitching DC-DC converters operating in discontinuousconduction moderdquo IEEE Transactions on Industrial Elec-tronics vol 57 no 10 pp 3497ndash3507 2010

[7] M Qin and J Xu ldquoImproved pulse regulation controltechnique for switching DC-DC converters operating inDCMrdquo IEEE Transactions on Industrial Electronics vol 60no 5 pp 1819ndash1830 2013

[8] J Xu and J Wang ldquoBifrequency pulse-train control techniquefor switching DC-DC converters operating in DCMrdquo IEEETransactions on Industrial Electronics vol 58 no 8pp 3658ndash3667 2011

[9] J Wang J Xu G Zhou and B Bao ldquoPulse-train-controlledCCM buck converter with small ESR output-capacitorrdquo IEEETransactions on Industrial Electronics vol 60 no 12pp 5875ndash5881 2013

[10] J Sha S Liu S Zhong and J Xu ldquoValley current mode pulsetrain control technique for switching DC-DC convertersrdquoElectronics Letters vol 50 no 4 pp 311ndash313 2014

[11] L Wang D Yu R Xu Z Ye and P Wang ldquoSliding current-valley based pulse train control for buck converterrdquo in IECON2017mdash43rd Annual Conference of the IEEE Industrial Elec-tronics Society pp 4978ndash4981 Beijing China October-No-vember 2017

[12] J Sha D Xu Y Chen J Xu and B W Williams ldquoA peak-capacitor-current pulse-train-controlled buck converter withfast transient response and a wide load rangerdquo IEEE

Time [100μsdiv]lt2HzF

vp [2Vdiv]

ic [1Adiv]

vo [100mVdiv]

Io [1Adiv]2

1

3

4

1PH-5PL

(a)

2

Time [100μsdiv]

vp [2Vdiv]

ic [1Adiv]

vo [100mVdiv]

Io [1Adiv]

4PH-4PL

13

4

F 398217kHz

(b)

Figure 10 Experimental waveforms(a) DCPT-controlled buck converter (b) PT-controlled buck converter


Transactions on Industrial Electronics vol 63 no 3pp 1528ndash1538 2016

[13] D Yu Y Geng H H C Iu T Fernando and R Xu ldquoPulsephase shift based low-frequency oscillation suppression forPT controlled CCM buck converterrdquo IEEE Transactions onCircuits and Systems II Express Briefs vol 65 no 10pp 1465ndash1469 2018

[14] G Zhou W Tan S Zhou Y Wang and X Ye ldquoAnalysis ofpulse train controlled PCCM boost converter with low fre-quency oscillation suppressionrdquo IEEE Access vol 6pp 68795ndash68803 2018

[15] D Yu LWang Y Geng CMa Z Ye and Y Liu ldquoPulse traincontrolled buck converter with coupled inductorsrdquo IET PowerElectronics vol 10 no 10 pp 1231ndash1239 2017

[16] R Xu Y Zhang S Lu G Chen D Yu and L Wang ldquoPulsetrain-controlled CCM boost converter with suppression oflow-frequency oscillationrdquo IET Power Electronics vol 10no 8 pp 957ndash967 2017

[17] X Jin L Wang D Yu Y Geng and R Xu ldquoPulse traincontrolled single-input dual-output buck converter withcoupled inductorsrdquo IEEE Access vol 6 pp 41504ndash415172018

[18] J Sha J Xu S Zhong S Liu and L Xu ldquoControl pulsecombination-based analysis of pulse train controlled DCMswitching DC-DC convertersrdquo IEEE Transactions on In-dustrial Electronics vol 62 no 1 pp 246ndash255 2015

[19] S Kapat ldquoConfigurable multimode digital control for lightload DC-DC converters with improved spectrum and smoothtransitionrdquo IEEE Transactions on Power Electronics vol 31no 3 pp 2680ndash2688 2016

[20] K Muppala Kumar and K Anbukumar ldquoPulse train con-trolled quadratic buck converter operating in discontinuousconduction moderdquo IET Circuits Devices amp Systems vol 12no 4 pp 486ndash496 2018


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PPS-PT-controlled buck converter could eliminate the low-frequency oscillation it weakened the transient character-istic In [14] the PT control technique was applied to boostconverter operated in the pseudo continuous conductionmode (PCCM) -is converter enjoyed wide power rangewithout low-frequency oscillation but the efficiency of theconverter was poor due to the freewheeling phase In ad-dition by improving the topology of the converter the low-frequency oscillation could be suppressed but it wascomplicated to the integration of the switching converter[15ndash20]

In this paper a dual-carrier pulse-train (DCPT) controltechnique is proposed and studied in detail In the DCPT-controlled CCM buck converter the capacitor current islimited to the preset valley current by a carrier signal at thebeginning of each switching cycle -e output voltage willincrease during one PH switching cycle and decrease duringeach PL switching cycle which indicates that the low-fre-quency oscillation did not exist in the DCPT-controlledconverter -e theoretical analysis simulation and experi-mental results verify that the DCPT-controlled CCM buckconverter enjoys small output ripple and fast transientresponse

2 Operational Principle

For a buck converter when the switch S is on the inductorcurrent will increase with a slope of (Vin minus Vo)L when S isoff the inductor current will decrease with a slope of VoLSince the capacitor current reflects the ripple of the inductorcurrent completely the slope of the capacitor current is also(Vin minus Vo)L or VoL when the switch is on or off re-spectively If a control signal vsaw with a slope of VoL isapplied to the capacitor current the capacitor current willmove along with the trajectory of vsaw after the switch turnsoff

Figure 1(a) shows the schematic diagram of the DCPT-controlled buck converter In the controller a comparator isused to compare the output voltage of the switching converterwith a reference value a sense resistor connected to the outputcapacitor and its auxiliary circuit are employed to obtain thecapacitor current and two DA converters are acquired togenerate the carrier signals Besides that there is no extracompensational network in the controller which indicates theDCPT-controlled converter enjoys convenient design processand fast response -e main working waveforms includingcapacitor current ic control pulse control signal vp andoutput voltage vo are shown in Figure 1(b)-e carrier signalsvsawH and vsawL generated by the controller have the samevalley current Iv and slope VrefL However the frequency ofvsawH or vsawL is different which is fH or fL respectivelyBecause the control pulse is generated by comparing thecapacitor current with the carrier signal in the DCPT con-troller the switching frequency of the converter is also fH or fLcorrespondingly

-e working principle of the DCPT-controlled buckconverter is as follows -e carrier signal vsaw is chosenbetween vsawH and vsawL When vsaw decreases to the valleycurrent Iv the switch S turns on immediately and the output

voltage is compared with the reference voltage Vref Ifvo ltVref the carrier signal vsawH is selected as vsaw When thecapacitor current icgt vsawH the switch S turns off which isrecorded as a high-energy pulse PH Similarly if vo geVref atthe time when vsaw decreases to Iv the carrier signal vsawLwill be selected When icgt vsawL S turns off which isrecorded as the low-energy pulse PL When the converteroperates in a steady state the DCPTcontroller will generate apulse train which consists of PH and PL to stabilize theoutput voltage

3 Steady-State Analysis

31 Design of Control Parameters In order to avoid low-frequency oscillation the output voltage should be increasedduring PH and decreased during PL Based on this principlethe control parameters the frequencies of the carrier signalsand the valley current can be designed properly

Figure 2 shows the capacitor current waveform of theDCPT-controlled buck converter within one switching cy-cle For the switching converter with a low output voltagethe on-state voltage of the diode has a significant influenceon the process of control law analysis When the on-statevoltage VD of the diode is considered the rising or fallingslope of the capacitor current is (Vin minus Vo)L or (Vo +VD)Lrespectively

During t1 or t2 the peak value of the capacitor current Ipcan be expressed as

Ip Vin minus Vo

Lt1 (1)

Ip Vo + VD

Lt2 (2)

By combining equations (1) and (2) we have

t1 + t2 LIp Vin + VD( 1113857

Vin minus Vo( 1113857 Vo + VD( 1113857 (3)

Based on Figure 2 and equation (3) the area of thetriangle ABC can be written as

SΔABC 12

t1 + t2( 1113857Ip Vin + VD( 1113857LI2p

2 Vin minus Vo( 1113857 Vo + VD( 1113857 (4)

-e area of the quadrangle BCED within one switchingperiod T is

SBCED minus12

t1 + t2 + T( 1113857Iv minusVin + VD( 1113857LIvIp

2 Vin minus Vo( 1113857 Vo + VD( 1113857minus12

IvT

(5)

Similarly the areas of the triangle BOD and the triangleCFE can be expressed as

SΔBOD + SΔCFE SOFED minus SBCED minus12

IvT

+Vin + VD( 1113857LIvIp

2 Vin minus Vo( 1113857 Vo + VD( 1113857

(6)



Vin + VD( )LI2p



(7)


Ip Iv +Vin minus Vo

LDT Iv +


T

(8)



2L Vin + VD( )T2 (9)


Δvo ΔqCIvCT +


T2 (10)


ΔvHo IvCTH +


T2H

ΔvLo IvCTL +


T2L

(11)


von+1

von +IvCTH +


T2H von ltVref

von +IvCTL +


T2L von geVref

(12)




2L Vin + VD( )TL

(13)


Vin

S L

D

iL ic

RE

VoDriverC

Rvp

Vref

vsawH

vsawL

FPGA

DAconverter

DAconverter

vsaw

R2 R1

R3R4

ic

(a)

tIv

0

t0

vsawH

vsawL

ic

vp

Vref

vo

PH PHPL PL PL

(b)


IvD

t1 t2

Ip

OB

A

C

E

Ft

ic














μHΔvHo + μLΔv

Lo 0 (16)


μHμL minus



(17)







∆νoH

ndash∆νoL

109 11 12 13 14 15Vin (V)

0

5

10

15

20

Δνo (

mV

) 25

30

35

40


109 11 12 13 14 15Vin (V)

0

05

1

15

2

μ H (μ

L)

25

3

35




Lt (18)

vo(t) 1Cintt

0ic(t)dt + ic(t)RE

IvCt

+Vin minus Vo

2LCt2 +

Vin minus Vo

LREt

(19)


dvo(t)dt

IvC+Vin minus Vo

2LCt +

Vin minus Vo

LCRE (20)


ΔvHpp IvCton +

Vin minus Vo

2LCt2on +

Vin minus Vo

LREton (21)





Δvo ΔvHpp (23)









Iv

ton

O t

ic

t

vo

O

ΔνHpp

T









2PH-1PL

40mV5045

10

1

2

85 86 87t (ms)

88 89 9

v o (V

)i c

(A)

v p (V

)v s

aw (V

)

Iv

Iv

(a)

85 86 87t (ms)

88 89 9

5045

10

1

2

v o (V

)i c

(A)

v p (V

)v s

aw (V

)

Iv

Iv

1PH-1PL

40mV

(b)

85 86 87t (ms)

88 89 9

5045

10

1

2

v o (V

)i c

(A)

v p (V

)v s

aw (V

)

Iv

Iv

1PH-3PL

55mV

(c)

85 86 87t (ms)

88 89 9

5045

10

1

2

v o (V

)i c

(A)

v p (V

)v s

aw (V

)

Iv

Iv

1PH-5PL

60mV

(d)


ic

vo

Vref

Iv

2PH-1PL

ΔvHPP

ΔvHo

Δvo

(a)

1PH-3PL

ΔvHPP

ic

vo

Vref

Iv

(b)




849 33 343 409868 49 363 41292 89 415 4151083 191 522 52212 248 577 577







Time [50μsdiv]


vo [50mVdiv]

4

3

2

1

lt2HzF

(a)


Time [50μsdiv]


vo [50mVdiv]

4

3

2

1

lt2HzF

(b)


Time [50μsdiv]



4

3

2

1

F

(c)



4

3

2

1


vo [50 mVdiv]

(d)


2PH


vp [2Vdiv]

ic [1Adiv]

vo [50mVdiv]

Io [1Adiv]

2

3

14




5 Conclusions


Data Availability




Acknowledgments


References















vp [2Vdiv]

ic [1Adiv]

vo [100mVdiv]

Io [1Adiv]2

1

3

4

1PH-5PL

(a)

2

Time [100μsdiv]

vp [2Vdiv]

ic [1Adiv]

vo [100mVdiv]

Io [1Adiv]

4PH-4PL

13

4

F 398217kHz

(b)















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Vin + VD( )LI2p



(7)


Ip Iv +Vin minus Vo

LDT Iv +


T

(8)



2L Vin + VD( )T2 (9)


Δvo ΔqCIvCT +


T2 (10)


ΔvHo IvCTH +


T2H

ΔvLo IvCTL +


T2L

(11)


von+1

von +IvCTH +


T2H von ltVref

von +IvCTL +


T2L von geVref

(12)




2L Vin + VD( )TL

(13)


Vin

S L

D

iL ic

RE

VoDriverC

Rvp

Vref

vsawH

vsawL

FPGA

DAconverter

DAconverter

vsaw

R2 R1

R3R4

ic

(a)

tIv

0

t0

vsawH

vsawL

ic

vp

Vref

vo

PH PHPL PL PL

(b)


IvD

t1 t2

Ip

OB

A

C

E

Ft

ic














μHΔvHo + μLΔv

Lo 0 (16)


μHμL minus



(17)







∆νoH

ndash∆νoL

109 11 12 13 14 15Vin (V)

0

5

10

15

20

Δνo (

mV

) 25

30

35

40


109 11 12 13 14 15Vin (V)

0

05

1

15

2

μ H (μ

L)

25

3

35




Lt (18)

vo(t) 1Cintt

0ic(t)dt + ic(t)RE

IvCt

+Vin minus Vo

2LCt2 +

Vin minus Vo

LREt

(19)


dvo(t)dt

IvC+Vin minus Vo

2LCt +

Vin minus Vo

LCRE (20)


ΔvHpp IvCton +

Vin minus Vo

2LCt2on +

Vin minus Vo

LREton (21)





Δvo ΔvHpp (23)









Iv

ton

O t

ic

t

vo

O

ΔνHpp

T









2PH-1PL

40mV5045

10

1

2

85 86 87t (ms)

88 89 9

v o (V

)i c

(A)

v p (V

)v s

aw (V

)

Iv

Iv

(a)

85 86 87t (ms)

88 89 9

5045

10

1

2

v o (V

)i c

(A)

v p (V

)v s

aw (V

)

Iv

Iv

1PH-1PL

40mV

(b)

85 86 87t (ms)

88 89 9

5045

10

1

2

v o (V

)i c

(A)

v p (V

)v s

aw (V

)

Iv

Iv

1PH-3PL

55mV

(c)

85 86 87t (ms)

88 89 9

5045

10

1

2

v o (V

)i c

(A)

v p (V

)v s

aw (V

)

Iv

Iv

1PH-5PL

60mV

(d)


ic

vo

Vref

Iv

2PH-1PL

ΔvHPP

ΔvHo

Δvo

(a)

1PH-3PL

ΔvHPP

ic

vo

Vref

Iv

(b)




849 33 343 409868 49 363 41292 89 415 4151083 191 522 52212 248 577 577







Time [50μsdiv]


vo [50mVdiv]

4

3

2

1

lt2HzF

(a)


Time [50μsdiv]


vo [50mVdiv]

4

3

2

1

lt2HzF

(b)


Time [50μsdiv]



4

3

2

1

F

(c)



4

3

2

1


vo [50 mVdiv]

(d)


2PH


vp [2Vdiv]

ic [1Adiv]

vo [50mVdiv]

Io [1Adiv]

2

3

14




5 Conclusions


Data Availability




Acknowledgments


References















vp [2Vdiv]

ic [1Adiv]

vo [100mVdiv]

Io [1Adiv]2

1

3

4

1PH-5PL

(a)

2

Time [100μsdiv]

vp [2Vdiv]

ic [1Adiv]

vo [100mVdiv]

Io [1Adiv]

4PH-4PL

13

4

F 398217kHz

(b)















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia













μHΔvHo + μLΔv

Lo 0 (16)


μHμL minus



(17)







∆νoH

ndash∆νoL

109 11 12 13 14 15Vin (V)

0

5

10

15

20

Δνo (

mV

) 25

30

35

40


109 11 12 13 14 15Vin (V)

0

05

1

15

2

μ H (μ

L)

25

3

35




Lt (18)

vo(t) 1Cintt

0ic(t)dt + ic(t)RE

IvCt

+Vin minus Vo

2LCt2 +

Vin minus Vo

LREt

(19)


dvo(t)dt

IvC+Vin minus Vo

2LCt +

Vin minus Vo

LCRE (20)


ΔvHpp IvCton +

Vin minus Vo

2LCt2on +

Vin minus Vo

LREton (21)





Δvo ΔvHpp (23)









Iv

ton

O t

ic

t

vo

O

ΔνHpp

T









2PH-1PL

40mV5045

10

1

2

85 86 87t (ms)

88 89 9

v o (V

)i c

(A)

v p (V

)v s

aw (V

)

Iv

Iv

(a)

85 86 87t (ms)

88 89 9

5045

10

1

2

v o (V

)i c

(A)

v p (V

)v s

aw (V

)

Iv

Iv

1PH-1PL

40mV

(b)

85 86 87t (ms)

88 89 9

5045

10

1

2

v o (V

)i c

(A)

v p (V

)v s

aw (V

)

Iv

Iv

1PH-3PL

55mV

(c)

85 86 87t (ms)

88 89 9

5045

10

1

2

v o (V

)i c

(A)

v p (V

)v s

aw (V

)

Iv

Iv

1PH-5PL

60mV

(d)


ic

vo

Vref

Iv

2PH-1PL

ΔvHPP

ΔvHo

Δvo

(a)

1PH-3PL

ΔvHPP

ic

vo

Vref

Iv

(b)




849 33 343 409868 49 363 41292 89 415 4151083 191 522 52212 248 577 577







Time [50μsdiv]


vo [50mVdiv]

4

3

2

1

lt2HzF

(a)


Time [50μsdiv]


vo [50mVdiv]

4

3

2

1

lt2HzF

(b)


Time [50μsdiv]



4

3

2

1

F

(c)



4

3

2

1


vo [50 mVdiv]

(d)


2PH


vp [2Vdiv]

ic [1Adiv]

vo [50mVdiv]

Io [1Adiv]

2

3

14




5 Conclusions


Data Availability




Acknowledgments


References















vp [2Vdiv]

ic [1Adiv]

vo [100mVdiv]

Io [1Adiv]2

1

3

4

1PH-5PL

(a)

2

Time [100μsdiv]

vp [2Vdiv]

ic [1Adiv]

vo [100mVdiv]

Io [1Adiv]

4PH-4PL

13

4

F 398217kHz

(b)















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Lt (18)

vo(t) 1Cintt

0ic(t)dt + ic(t)RE

IvCt

+Vin minus Vo

2LCt2 +

Vin minus Vo

LREt

(19)


dvo(t)dt

IvC+Vin minus Vo

2LCt +

Vin minus Vo

LCRE (20)


ΔvHpp IvCton +

Vin minus Vo

2LCt2on +

Vin minus Vo

LREton (21)





Δvo ΔvHpp (23)









Iv

ton

O t

ic

t

vo

O

ΔνHpp

T









2PH-1PL

40mV5045

10

1

2

85 86 87t (ms)

88 89 9

v o (V

)i c

(A)

v p (V

)v s

aw (V

)

Iv

Iv

(a)

85 86 87t (ms)

88 89 9

5045

10

1

2

v o (V

)i c

(A)

v p (V

)v s

aw (V

)

Iv

Iv

1PH-1PL

40mV

(b)

85 86 87t (ms)

88 89 9

5045

10

1

2

v o (V

)i c

(A)

v p (V

)v s

aw (V

)

Iv

Iv

1PH-3PL

55mV

(c)

85 86 87t (ms)

88 89 9

5045

10

1

2

v o (V

)i c

(A)

v p (V

)v s

aw (V

)

Iv

Iv

1PH-5PL

60mV

(d)


ic

vo

Vref

Iv

2PH-1PL

ΔvHPP

ΔvHo

Δvo

(a)

1PH-3PL

ΔvHPP

ic

vo

Vref

Iv

(b)




849 33 343 409868 49 363 41292 89 415 4151083 191 522 52212 248 577 577







Time [50μsdiv]


vo [50mVdiv]

4

3

2

1

lt2HzF

(a)


Time [50μsdiv]


vo [50mVdiv]

4

3

2

1

lt2HzF

(b)


Time [50μsdiv]



4

3

2

1

F

(c)



4

3

2

1


vo [50 mVdiv]

(d)


2PH


vp [2Vdiv]

ic [1Adiv]

vo [50mVdiv]

Io [1Adiv]

2

3

14




5 Conclusions


Data Availability




Acknowledgments


References















vp [2Vdiv]

ic [1Adiv]

vo [100mVdiv]

Io [1Adiv]2

1

3

4

1PH-5PL

(a)

2

Time [100μsdiv]

vp [2Vdiv]

ic [1Adiv]

vo [100mVdiv]

Io [1Adiv]

4PH-4PL

13

4

F 398217kHz

(b)















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






2PH-1PL

40mV5045

10

1

2

85 86 87t (ms)

88 89 9

v o (V

)i c

(A)

v p (V

)v s

aw (V

)

Iv

Iv

(a)

85 86 87t (ms)

88 89 9

5045

10

1

2

v o (V

)i c

(A)

v p (V

)v s

aw (V

)

Iv

Iv

1PH-1PL

40mV

(b)

85 86 87t (ms)

88 89 9

5045

10

1

2

v o (V

)i c

(A)

v p (V

)v s

aw (V

)

Iv

Iv

1PH-3PL

55mV

(c)

85 86 87t (ms)

88 89 9

5045

10

1

2

v o (V

)i c

(A)

v p (V

)v s

aw (V

)

Iv

Iv

1PH-5PL

60mV

(d)


ic

vo

Vref

Iv

2PH-1PL

ΔvHPP

ΔvHo

Δvo

(a)

1PH-3PL

ΔvHPP

ic

vo

Vref

Iv

(b)




849 33 343 409868 49 363 41292 89 415 4151083 191 522 52212 248 577 577







Time [50μsdiv]


vo [50mVdiv]

4

3

2

1

lt2HzF

(a)


Time [50μsdiv]


vo [50mVdiv]

4

3

2

1

lt2HzF

(b)


Time [50μsdiv]



4

3

2

1

F

(c)



4

3

2

1


vo [50 mVdiv]

(d)


2PH


vp [2Vdiv]

ic [1Adiv]

vo [50mVdiv]

Io [1Adiv]

2

3

14




5 Conclusions


Data Availability




Acknowledgments


References















vp [2Vdiv]

ic [1Adiv]

vo [100mVdiv]

Io [1Adiv]2

1

3

4

1PH-5PL

(a)

2

Time [100μsdiv]

vp [2Vdiv]

ic [1Adiv]

vo [100mVdiv]

Io [1Adiv]

4PH-4PL

13

4

F 398217kHz

(b)















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







Time [50μsdiv]


vo [50mVdiv]

4

3

2

1

lt2HzF

(a)


Time [50μsdiv]


vo [50mVdiv]

4

3

2

1

lt2HzF

(b)


Time [50μsdiv]



4

3

2

1

F

(c)



4

3

2

1


vo [50 mVdiv]

(d)


2PH


vp [2Vdiv]

ic [1Adiv]

vo [50mVdiv]

Io [1Adiv]

2

3

14




5 Conclusions


Data Availability




Acknowledgments


References















vp [2Vdiv]

ic [1Adiv]

vo [100mVdiv]

Io [1Adiv]2

1

3

4

1PH-5PL

(a)

2

Time [100μsdiv]

vp [2Vdiv]

ic [1Adiv]

vo [100mVdiv]

Io [1Adiv]

4PH-4PL

13

4

F 398217kHz

(b)















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



5 Conclusions


Data Availability




Acknowledgments


References















vp [2Vdiv]

ic [1Adiv]

vo [100mVdiv]

Io [1Adiv]2

1

3

4

1PH-5PL

(a)

2

Time [100μsdiv]

vp [2Vdiv]

ic [1Adiv]

vo [100mVdiv]

Io [1Adiv]

4PH-4PL

13

4

F 398217kHz

(b)















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia














RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Documents

ResearchonDual-CarrierPulse-Train-Controlled BuckConverter