energies

Article A New Combined Boost Converter with Improved Gain as a Battery-Powered Front-End Interface for Automotive Audio Amplifiers

Ching-Ming Lai 1 ID , Yu-Huei Cheng 2,* ID , Jiashen Teh 3 ID and Yuan-Chih Lin 4

1 Department of Vehicle Engineering, National Taipei University of Technology, 1, Sec. 3, Chung-Hsiao E. Road, Taipei 106, Taiwan; [email protected] 2 Department of Information and Communication Engineering, Chaoyang University of Technology, Taichung 41349, Taiwan 3 School of Electrical and Electronic Engineering, Universiti Sains Malaysia, USM Engineering Campus, Nibong Tebal, Seberang Perai Selatan 14300, Penang, Malaysia; [email protected] 4 Department of Electrical Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei 106, Taiwan; [email protected] * Correspondence: [email protected]; Tel.: +886-4-2332-3000 (ext. 7712)

Received: 18 April 2017; Accepted: 28 July 2017; Published: 1 August 2017

Abstract: High boost DC/DC voltage conversion is always indispensable in a power electronic interface of certain battery-powered electrical equipment. However, a conventional boost converter works for a wide duty cycle for such high voltage gain, which increases power consumption and has low reliability problems. In order to solve this issue, a new battery-powered combined boost converter with an interleaved structure consisting of two phases used in automotive audio amplifier is presented. The first phase uses a conventional boost converter; the second phase employs the inverted type. With this architecture, a higher boost voltage gain is able to be achieved. A derivation of the operating principles of the converter, analyses of its topology, as well as a closed-loop control designs are performed in this study. Furthermore, simulations and experiments are also performed using input voltage of 12 V for a 120 W circuit. A reasonable duty cycle is selected to reach output voltage of 60 V, which corresponds to static voltage gain of five. The converter achieves a maximum measured conversion efficiency of 98.7% and the full load efficiency of 89.1%.

Keywords: automotive audio amplifier; battery-powered; combined boost converter; voltage gain

1. Introduction High boost DC/DC ( to direct current) voltage conversions are indispensable in a power electronic interface of certain low-voltage DC-powered electrical devices, including audio amplifiers [1–7], high intensity discharge (HID) lamps [8–14], uninterruptible power supplies (UPS) [15–19], and systems [20–32]. For such high voltage gain application, the conventional boost converter have to works for extremely wide duty cycle which increases power consumption and has low reliability problems [32,33]. In order to overcome these problems, several high boost converter DC/DC topologies have been presented. Franceschini et al. presented a DC/DC boost converter topology that is a full-bridge architecture using a three-phase transformer and is well suitable for high-power applications with battery supplies [5]. Zhao and Lee proposed a series of high efficiency, high boost DC/DC converters that apply diodes and coupling windings instead of active switches to achieve similar functions to active clamps [9,10]. In [11], Yang et al. presented a transformerless DC/DC converter that consists of a boost converter paralleled with an inverting boost and a floating diode- output rectifier. Though the voltage gain of the converter is

Energies 2017, 10, 1128; doi:10.3390/en10081128 www.mdpi.com/journal/energies Energies 2017, 10, 1128 2 of 20 improved with the relative low-cost components, the input current ripple is large owing to the fact that the activeEnergies switches 2017, 10, 1128 are controlled simultaneously by using one control signal. Divakar et al. introduced2 of 20 a circuit that can eliminate one auxiliary winding and can reduce the voltage on the primary side improved with the relative low-cost components, the input current ripple is large owing to the fact switch. Furthermore, with this circuit, the selection of switches with a lower rating is permitted [12]. that the active switches are controlled simultaneously by using one control signal. Divakar et al. Shahinintroduced et al. proposed a circuit that a cascade can eliminate DC/DC one converter auxiliary winding including and interleaved can reduce boostthe voltage converters on the with two phasesprimary and side three switch. level Furthermore, series boost with converters this circuit, [23 the]. Theselection efficiency of switches and reliabilitywith a lower of rating this solution is are low.permitted In [24 ],[12]. a cascaded Shahin et boostal. proposed converter a cascade regulated DC/DC the reasonableconverter including voltage gaininterleaved with aboost common pulse-widthconverters modulation with two (PWM)phases control.and three However, level seri if aes high boost voltage converters gain has[23]. to The be offered, efficiency more and power switchesreliability and capacitorsof this solution are actually are low. necessary. In [24], a cascaded In addition, boost although converter exceeding regulated dutythe reasonable cycles can be prevented,voltage the gain input with current a common ripple pulse-width is large because modulation of its (PWM) single-phase control. operationHowever, if makes a high the voltage converter not suitablegain has forto highbe offered, current more and power low rippleswitches applications. and In are order actually to further necessary. decrease In addition, the voltage although exceeding duty cycles can be prevented, the input current ripple is large because of its stress on active switches and electromagnetic interference (EMI), Lai presented a high boost converter single-phase operation makes the converter not suitable for high current and low ripple consisting of three-phase circuits by an auxiliary forward circuit [19]. However, the circuit structure applications. In order to further decrease the voltage stress on active switches and electromagnetic of thisinterference particular (EMI), topology Lai presented is costly a and high complex. boost converter Lai et consis al. alsoting proposed of three-phase a modular circuits interleaved by an boostauxiliary converter forward that integrates circuit [19]. a However, forward energy-deliveringthe circuit structure circuitof this particular with a voltage-doubler topology is costly to and realize a highcomplex. voltage gain,Lai et the al. reducedalso proposed switch a modular voltage andinterleaved high efficiency boost converter for DC-microgrid that integrates applications a forward [31]. The characteristicenergy-delivering low circuit ripple with of the a voltage-doubler interleaved boost to realize converter a high is responsiblevoltage gain, forthe thereduced attention switch placed on investigationsvoltage and high into efficiency this technology for DC-microgrid [28–31]. applic Althoughations many [31]. The DC/DC characteristic converters low ripple offer highof the boost voltageinterleaved gain, they boost have converter the disadvantage is responsible of either for requiringthe attention a complex placed circuiton investigations structure or into considerable this highertechnology costs for [28–31]. the bill Although of material many (BOM). DC/DC It converters is therefore offer difficult high boost to manufacturevoltage gain, they these have circuits the in disadvantage of either requiring a complex circuit structure or considerable higher costs for the bill a batch manner [32,33]. of material (BOM). It is therefore difficult to manufacture these circuits in a batch manner [32,33]. To provide an appropriate solution, in this study, we introduce a combined boost converter To provide an appropriate solution, in this study, we introduce a combined boost converter topology.topology. While While the the low low ripple ripple characteristics characteristics thatthat benefit benefit from from interleaved interleaved structures, structures, this thissimpler simpler and lowerand lower cost cost topology topology can can also also give give an an improved improved voltage gain gain when when comparing comparing to a toconventional a conventional interleavedinterleaved boost boost converter converter with with two two phases. phases. A A pa partialrtial study study and and analysis analysis of a of battery-powered a battery-powered combinedcombined boost boost converter converter for automotivefor automotive audio audio amplifiers amplifiers was was presented presented in [in7], [7], but but only only a brief a brief concept was describedconcept was therein. described By contrast,therein. By this contrast, paper this introduces paper introduces a detailed a detailed analysis analysis of the operation of the operation of this new topologyof this and new simulated topology and and simulate experimentedd and experimented results for results all its modesfor all its of modes operation. of operation. Figure Figure1 shows 1 the studiedshows audio the amplifierstudied audio architecture. amplifier architecture. In today's automotive In today's automotive framework, framework, galvanic galvanic isolation isolation is no longer is no longer required in automotive audio applications because the head unit of the amplifier’s required in automotive audio applications because the head unit of the amplifier’s signal and the signal and the power supply of the amplifier share a power ground [4]. As with the post-amplifier, power supply of the amplifier share a power ground [4]. As with the post-amplifier, the pre-amplifier the pre-amplifier is connected to a full-bridge class-D amplifier, which can output any voltage is connectedwaveform to to a supply full-bridge the load. class-D In the amplifier, audio amplifier which architecture can output studied, any voltage the loads waveform are primarily to supply the load.speakers. In the The audio battery amplifier is connected architecture to the studied, combined the loadsboost areconverter, primarily which speakers. is subsequently The battery is connectedconnected to the to combinedthe full-bridge boost class-D converter, amplifier. which Finally, is subsequently the full-bridge connected class-D amplifier to the full-bridge is connected class-D amplifier.to the Finally,load. the full-bridge class-D amplifier is connected to the load.

FigureFigure 1. 1.Illustration Illustration of ofthe the studiedstudied audio audio amplifier amplifier architecture. architecture.

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2. Converter Topology and Operation Principles 2. Converter Topology and Operation Principles The proposed converter is used as an automotive battery-powered interface. The converter topologyThe proposedfor the new converter combined is usedboost as converter an automotive contains battery-powered two-phase circuits, interface. as shown The in converter Figure 2. topology for the new combined boost converter contains two-phase circuits, as shown in Figure2. One is the boost circuit, which involves inductor L1, capacitor C1, active switch S1 and diode D1. The One is the boost circuit, which involves inductor L , capacitor C , active switch S and diode D . other is the inverted boost circuit, which contains 1inductor L2, capacitor1 C2, active1 switch S2, and1 The other is the inverted boost circuit, which contains inductor L , capacitor C , active switch S , diode D2. The inductors L1 and L2 are amount to L, and the capacitors2 C1 and C2 are2 amount to C. Co 2is and diode D . The inductors L and L are amount to L, and the capacitors C and C are amount to C. the common2 output capacitor,1 Vi is the2 supply voltage, Vo is the output voltage,1 and2 Ro is the output Cloado is theresistance. common output capacitor, Vi is the supply voltage, Vo is the output voltage, and Ro is the output load resistance.

FigureFigure 2.2. Proposed combinedcombined boostboost converterconverter topology.topology.

TheThe followingfollowing fourfour assumptionsassumptions areare mademade in analyzinganalyzing the proposed combined boost converter. (1)(1) ForFor simplicity,simplicity, it it isis assumedassumed thatthat allall thethe componentscomponents inin FigureFigure2 2 are are idealized; idealized; (2) (2) All All voltages and and currentscurrents inin thethe circuitcircuit areare periodic periodic in in steady-state steady-state conditions; conditions; (3) (3) For For high high boost boost conversion,conversion, thethe dutyduty cyclecycle ofof thethe majormajor switchswitch isis exceedexceed 50%,50%, whichwhich isis presentedpresented asas DD,, andand thethe switchingswitching periodperiod isis denoteddenoted asasT Ts;s; (4) (4) The The converter converter works works in continuous in continuous conduction conduction mode (CCM).mode (CCM). In the combined In the combined boost converter, boost allconverter, working all modes working and modes their equivalent and their circuitsequivalent corresponding circuits corresponding to the ON/OFF to the status ON/OFF of the status active of switchesthe active have switches been illustrated have been in illustrated Figure3. The in steady-stateFigure 3. The waveforms steady-state of the waveforms combined of boost the convertercombined areboost demonstrated converter are in Figuredemonstrated4. The working in Figure modes 4. The can beworking described modes clearly can as be follows. described clearly as follows. (1) Mode 1 [t0–t1] and Mode 3 [t2–t3]: In these two modes, the active switches S1 and S2 are switched (1) Mode 1 [t0–t1] and Mode 3 [t2–t3]: In these two modes, the active switches S1 and S2 are switched on while the diodes, D1 and D2 are reverse-bias. The current in the inductors, iL1 and iL2, increase on while the diodes, D1 and D2 are reverse-bias. The current in the inductors, iL1 and iL2, increase to store energy in L1 and L2, respectively. The output power for the back-end amplifier is provided to store energy in L1 and L2, respectively. The output power for the back-end amplifier is by capacitor Co. The total current iLt and inductor currents of L1 and L2 are expressed below. provided by capacitor Co. The total current iLt and inductor currents of L1 and L2 are expressed below. iLt = iL1 + iL2 (1) = + iLt diiL1 iLV2 (1) L1 = i (2) dt L1 diL1 = Vi diL2 V i (2) dt =L1 (3) dt L2

(2) Mode 2 [t1–t2]: The active switch S1 remainsdiL2 conducting= Vi and S2 is switched off. D1 is reverse-bias (3) and D2 is forward-bias. While the current dtiL1 increaseL2 to store energy in L1, the energy stored in inductor L2 is now released through D2, C2, C1, and Co to the output. The total current iLt and (2) Mode 2 [t1–t2]: The active switch S1 remains conducting and S2 is switched off. D1 is reverse-bias inductor currents of L1 and L2 can be expressed as follows: and D2 is forward-bias. While the current iL1 increase to store energy in L1, the energy stored in inductor L2 is now released through D2, C2, C1, andiL C2 o to the output. The total current iLt and iLt = iL1 + (4) inductor currents of L1 and L2 can be expressed as follows:2

=diL1 + i LV2 i iLt iL1 = (4)(5) dt 2L1

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diL1 = Vi (5) dt L Energies 2017, 10, 1128 1 4 of 20

di V − V V − V L2 = i C2 = C1 o di V − V V − V (6) L2 dt= i LC22 = C1L2 o (6) dt L2 L2 (3) Mode 4 [t3–t4]: S2 is switched on and S1 is switched off. D2 is reverse-bias and D1 is forward-bias. (3) Mode 4 [t –t ]: S is switched on and S is switched off. D is reverse-bias and D is forward-bias. The energy3 4 stored2 in L1 is released 1through D1 to charge2 capacitor C1 and Co1. The total current iLt The energy stored in L is released through D to charge capacitor C and C . The total current i and inductor currents1 of L1 and L2 can be 1expressed as follows: 1 o Lt and inductor currents of L1 and L2 can be expressed as follows: i i = i + L1 (7) Lt L2 i 2 i = i + L1 (7) Lt L2 2 di V − V V − V L1 = i C1 = C2 o diL1 Vi − VC1 VC2 − Vo (8) dt= L1 = L1 (8) dt L1 L1 di V diL2L2 = Vi i = (9)(9) dtdt LL2 2

(a)

(b)

(c)

FigureFigure 3. Working 3. Working modes modes and and equivalent equivalent circuits circuits of the of combinedthe combined boost boost converter. converter. (a) Mode (a) Mode 1 and 1 and ModeMode 3, (b )3, Mode (b) Mode 2, and 2, (andc) Mode (c) Mode 4. 4.

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FigureFigure 4. Depicted 4. Depicted steady-state steady-state waveforms waveforms of the of the combined combined boost boost converter. converter.

3. Analysis3. Analysis of ofSteady-State Steady-State In Inthis this section, section, the the voltage voltage gain, gain, voltage voltage stress stress on on the the switches, andand inductorinductor currentcurrent ripple ripple of of the thecombined combined boost boost converter converter working working in in the the steady steady state state are are analyzed. analyzed.

3.1.3.1. Voltage Voltage Gain Gain UsingUsing Figures Figures 3 and3 and Figure4, the 4, corresponding the corresponding state equationstate equation for each for modeeach mode can be can obtained. be obtained. These Theseillustrations illustrations enable enable the observation the observation that thethat weighting the weighting factors factors in the fourin the working four working modes whichmodes are which(D− 1/2),are (D (1−−1/2),D), (1 (D−−D1/2),), (D− and1/2), (1 and−D ).(1 The−D). EquationsThe Equations (10) and(10) (11) and are (11) obtained are obtained using theusing inductor the inductorvoltage-second voltage-second balance balance principle principle on L1 and on L12 andas follows: L2 as follows: V = i Vi VCV1 = (10)(10) C1 1 −1 D− D

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V V = i (11) C2 1−V V = iD (11) C2 1 − D The C1 and C2 capacitors are connected in series with the supply voltage, and the equation of outputThe voltageC1 and ofC the2 capacitors converter areis expressed connected as: in series with the supply voltage, and the equation of output voltage of the converter is expressed as: = + − Vo VC1 VC 2 Vi (12) Vo = VC1 + VC2 − Vi (12) By combining (10)–(12), the static voltage gain can be derived by: By combining (10)–(12), the static voltageV gain1 can+ D be derived by: o = 1− (13) VVi 1 +DD o = (13) The static voltage gain of the conventionalVi boost1 − converterD is expressed as:

The static voltage gain of the conventionalVo boost= 1 converter is expressed as: (14) V 1− D V i 1 o = (14) Figure 5 shows a comparison of the voltageVi gains1 − D produced by the proposed combined boost converter, the interleaved boost converter with two-phase and the conventional boost converter. Figure5 shows a comparison of the voltage gains produced by the proposed combined boost From Figure 5, we observe that the converter has a higher voltage gain than the two-phase converter, the interleaved boost converter with two-phase and the conventional boost converter. interleaved converter and the conventional boost converter. From Figure5, we observe that the converter has a higher voltage gain than the two-phase interleaved converter and the conventional boost converter.

Figure 5. The comparison of the voltage gains produced by the proposed combined boost converter, theFigure conventional 5. The comparison boost converter, of the voltage and the gains interleaved produced boost by converterthe proposed with combined two-phases. boost converter, the conventional boost converter, and the interleaved boost converter with two-phases. 3.2. Voltage Stress of the Switches 3.2. Voltage Stress of the Switches The open circuit voltage stress on switches S1 and S2 can be obtained by the aforementioned The open circuit voltage stress on switches S1 and S2 can be obtained by the aforementioned analyses of operations. The relevant expression is written as (15). analyses of operations. The relevant expression is written as (15).

Vi VS1,max ==VS2,max == Vi (15) VS1,max VS2,max − (15) 11− DD 3.3. Inductor Current Ripples 3.3. Inductor Current Ripples Using Equations (1)–(9), the total current ripple in the proposed combined boost converter can be representedUsing Equations by: (1)–(9), the total current ripple in the proposed combined boost converter can V T be represented by: ∆i = i s (2D − 1) (16) Lt L

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V T Δi = i s (2D −1) (16) Lt L

EnergiesThe2017 current, 10, 1128 ripples of the inductors L1 and L2, in the proposed combined boost converter7 ofcan 20 thus be expressed as:

The current ripples of the inductorsΔ =L1Δand=LΔ2, in= theViT proposeds combined boost converter can i i 1 i 2 D (17) thus be expressed as: L L L L V T ∆i = ∆i = ∆i = i s D (17) The variation of the duty cycle of theL totalL1 currentL2 rippleL to inductor current ripple as a function of theThe duty variation cycle is of displayed the duty in cycle Figure of the 6. totalThe proposed current ripple converter to inductor has the current same performance ripple as a function as the two-phaseof the duty interleaved cycle is displayed boost converter, in Figure 6and. The that proposed is superior converter to the conventional has the same boost performance converter. as the two-phase interleaved boost converter, and that is superior to the conventional boost converter.

Figure 6. Figure 6. TheThe ratioratio between between the the total total current current ripple ripple and and the the inductor inductor current current ripple ripple versus versus the duty the cycle.duty cycle. 3.4. The Mode for Boundary Conduction 3.4. The Mode for Boundary Conduction The boundary normalized inductor time constant τL,B is expressed as:

The boundary normalized inductor time constant τL,B is expressed as: L f τ = sw (18) L,B LfR τ = sw (18) L,B R where fsw is the switching frequency. whereThe fsw outputis the switching current during frequency. boundary conduction mode (BCM) is indicated by: The output current during boundary conduction mode (BCM) is indicated by: ViTs iO = V T (1 + D) (19) i = Li s (1+ D) (19) O L Therefore, the boundary normalized time constant is represented by: Therefore, the boundary normalized time constant is represented by:

τL,B == 1 − D (20) L,B 1 D (20) Figure7 shows a plot of the boundary normalized inductor time constant curve. When τ is Figure 7 shows a plot of the boundary normalized inductor time constant curve. When τL is planned to be higher than the boundary curve of τ , the converter operates in continuous conduction planned to be higher than the boundary curveL,B of τL,B, the converter operates in continuous conductionmode (CCM). mode Conversely, (CCM). Conversely, the proposed the converter proposed works converter in discontinuous works in discontinuous conduction mode conduction (DCM) when τ is chosen to be smaller than the boundary curve of τ . mode (DCM)Lb when τLb is chosen to be smaller than the boundaryLb,B curve of τLb,B.

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Figure 7. Normalized boundary inductance-time constant curve.

3.5. Component Stress and Loss The equations for analyzing the component stress of thethe combinedcombined boost converterconverter are summarized inin TableTable1 1.. In In addition, addition, equations equations for for loss loss analysis analysis are are shown shown in in Table Table2. 2.

Table 1.1. The results forfor stressstress analysisanalysis inin steady-state.steady-state.

ItemsItems State State = RMS current stress on S1 (iS1) I I D√ S1(RMS) =L2(RMS) RMS current stress on S1 (iS1) IS1(RMS) IL2(RMS)√D 2 S2 I = I D RMSRMS current current stress stress on S2 on(iS 2S) (i ) SIS2(RMS)2(RMS) =L1(RMS)IL1(RMS) D s  ∆i2 2 RMS current stress on L (i ) 2  Δ  L1 1 L1 IL1(RMS) = (IL21)+ + iL1 √ RMS current stress on L1 (iL1) IL1(RMS) (IL1)  2 3 s 2 3    2 2 ∆iL2 RMS current stress on L2 (iL2) I = (I ) + √ L2(RMS) L2 Δ 2 = 2 +  iL2  3 RMS current stress on L2 (iL2) IL2(RMS) s (IL2)   2 3 i 2 L i  2 ∆ L2 RMS current stress on t ( Lt) ILt(RMS) = (IL1 + IL2) + √ 4 3 √Δ 2 RMS current stress on D (i ) I = =+I 2 +  1i−L2 D RMS current stress1 onD L1 t (iLt) ILt(RMS)D1(RMS()IL1 LI2L(2RMS) )√   4 3  RMS current stress of D2 (iD2) ID2(RMS) = IL1(RMS)  1 − D v I u = I r2 1− D RMS current stress on D1 (iD1) D1(RMS)u +L2(RMS) C i t D ∆I I RMS current stress of 1 ( C1) = = 12 = − = o RMS current stress of D2 (iD2) IC1(RMS) ID2I(RMS)o IL1(RMS), r 1 D, I f t 1 − D If t 1 − D v u 2 r2 u D+ +r RMS current stress of C (i ) tD Δ ∆I Io RMS current stress2 ofC C2 1 (iC1) 12 12 I Io IC2I(RMS) === IIo , r ,=r = , I ,=If t = C1(RMS) o −1 − D Ifft t − 1 − D 1 D I ft 1 D r D RMS current stress of Co (iCo) ICo(RMS) =2 Io + r 1 + D D Δ RMS current stress of C2 (iC2) I I I == I 12 , r = , I = o C2(RMS) o − ft − 1 D I ft 1 D D RMS current stress of Co (iCo) I = I Co(RMS) o 1+ D

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Energies 2017, 10, 1128 9 of 20 Table 2. The equations of loss in steady-state. Table 2. The equations of loss in steady-state.

ItemsItems State State V 1 ( 1 )I×1 I 1 (T )1 ×fTr1 ×VSf1sw(DS 2) VIS1((D2) )T×f1 I fsw( ) × Tf 1 × fsw SS1(DSDS)1 S (DS1) D1r sw  + S1 DS2 S1 D2 + TotalTotal loss loss of S of S1 2 2 2 2 1 h i2 R  I 2  Q V  f DS1(ON )  SR1(RMSDS1()ON ) ×g1 IS1GS(RMS1 )sw + Qg1 × VGS1 × fsw VVS2(DS( 1) )IS×2(DI1) ( Tr2) ×fswTr2 ×VSf2sw(DS 2) VIS2(D2) )T×f 2I f(sw ) × T × fsw S2 DS1 S2 D1  + S2 DS2 S2 D2 f 2 + TotalTotal loss loss of S of2 S2 2 2 2 2 R 2 × I 2 + Q × V × f RDS 2(ON )  IS2(RMSDS)2(ONQ)g2 VSGS2(2RMS fsw) g2 GS2 sw h i2 Conduction loss of L1 r × I2 Conduction loss of L1 rL1 ILL1(1RMS)  L 1(RMS) h i2 Conduction loss of L 2 Conduction loss of2 L2 rL2  IrLL2(2RMS× ) IL 2(RMS)

TotalTotal loss loss of D of1 D1 VF1VF1Io×KIo×0.5K+VR0.51 T×RRV1R1f×sw TRRIRR11× fsw × IRR1 Total loss of D2 VF2 × Io × K + 0.5 × VR2 × TRR2 × fsw × IRR2 Total loss of D2 VF2 Io K  0.5VR2 TRRh 2  fsw IiRR2 2 Conduction loss of C1 rC1 × 2IC1(RMS) Conduction loss of C1 r I  C1 C1(RMS)h i2 Conduction loss of C2 rC2 × I2 ( ) Conduction loss of C2 rC2 IC2(RMS) C 2 RMS h i2 Conduction loss of C 2 Conduction loss ofo Co rCo IrCoCo(RMS)× ICo (RMS)

※ QQgg represents the total charge on the gategate ofof thethe metal-oxide-semiconductormetal-oxide-semiconductor field-effectfield-effect transistor (MOSFET). (TheMOSFET rise time). TheTr isrise the time time Tr it is takes the time to complete it takes chargingto complete the charging gate of the the MOSFET gate of the after MOSFET the threshold after the voltage VGS(th) has been reached. The fall time, Tf, is the time it takes to reach the threshold voltage following the MOSFET’s threshold voltage VGS(th) has been reached. The fall time, Tf, is the time it takes to reach the threshold switch-off delay time [34]. VF represents the forward voltage drop of the diode. K is the time of the conduction voltage following the MOSFET’s switch-off delay time [34]. VF represents the forward voltage drop period of the diode. VR represents the reverse voltage of the diode. IR is the reverse leakage current of the diode [35]. of the diode. K is the time of the conduction period of the diode. VR represents the reverse voltage of the diode. IR is the reverse leakage current of the diode [35]. 4. Converter Control Strategy 4. ConverterAs described Control in Strategy the preceding paragraphs, the combined boost converter is dominated by the specificAs described duty ratio in of the switches precedingS1 paragraphsand S2. By, appropriatelythe combined boost adjusting converter duty is ratio, dominate the outputd by the voltage can bespecific flexible. duty The ratio circuit of switches model S is1 and established S2. By appropriately by PSIM© simulationadjusting duty software ratio, the (Powersim output voltage Inc., Rockville, MD,can be USA) flexible under. The the circuit later suppositions model is establish to deviseed by the PSIM closed-loop© simulation controller software and (Powersim reduce the Inc., mathematics forRockville, the converter. MD, USA) The under suppositions the later supposition includes (1)s to power devise switchesthe closed and-loop diodes controller are ideal;and reduce (2) equivalent seriesthe mathematics resistances for (ESRs) the converter of all the. The inductors supposition ands capacitorsincludes (1) of power the converter switches and are diodes thought are to acquire ideal; (2) equivalent series resistances (ESRs) of all the inductors and capacitors of the converter are a comparatively precise dynamic model; (3) the converter works in under CCM. The taken circuit thought to acquire a comparatively precise dynamic model; (3) the converter works in under CCM. parameters are L1 = L2 = 250 µH, C1 = C2 = 10 µF, Co = 1000 µF, output resistance R = 30 Ω, and ESRs The taken circuit parameters are L1 = L2 = 250 μH, C1 = C2 = 10 μF, Co = 1000 μF, output resistance R = r = r = r = r = 100 mΩ. 30L1 Ω, andL2 ESRC1s rL1 =C 2rL2 = rC1 = rC2 = 100 mΩ. Figure 88 illustratesillustrates thethe block block diagram of of the combined boost boost converter converter by by measuring measuring the the output voltageoutput voltage feedback feedback signal into signal the into controller the controller for control. for control. Figure 8Figure illustrates 8 illustrates the developed the developed control system forcontrol the combinedsystem for the boost combined converter. boost It converter. can be seen It can that be theseen output that the voltage output voltage (Vo) is sensed(Vo) is sensed and compared withand compared the reference with (theVo, refreference). The output (Vo, ref). voltageThe output controller voltage producescontroller produce those twos those inductor two inductor current reference current reference (iL1,ref, iL2, ref) for the entire system, and the equal current sharing between the two (iL1,ref , iL2,ref) for the entire system, and the equal current sharing between the two interleaved phases interleaved phases can be also acquired. Furthermore, during the system startup, using a soft start can be also acquired. Furthermore, during the system startup, using a soft start system (Vconss) is used system (Vconss) is used to avoid the capacitor charge surge current causing damage to the converter to avoid the capacitor charge surge current causing damage to the converter components. components. The Block diagram of the closed-loop control scheme is shown in Figure9. In the inner current The Block diagram of the closed-loop control scheme is shown in Figure 9. In the inner current F G G controlcontrol loop, loop, FM Mis theis the constant constant gain gainof the ofPWM the generator; PWM generator; Gi1d and Gi2di 1isd theand transferi2d is function the transfer from function fromthe duty the dutyratio to ratio the totwo the different two different inductor inductor current; current; Ci1 and CCii12 andindicateCi2sindicates the transfer the function transfer of function of currentcurrent controllers controllers;; and and Hi1H andi1 and Hi2 Harei2 theare sensing the sensing gains gainsof the ofcurrent the current sensor. In sensor. the outer In the voltage outer voltage controlcontrol loop, loop, GGvdvd is isthe the transfer transfer function function from from the duty the dutyratio to ratio the tooutput the outputvoltage; voltage; Cv indicateCvs indicatesthe the transfertransfer function function of of output output voltage voltage controller; controller; and H andv indicateHv indicatess the sensing the sensinggain of the gain voltage of the sensor. voltage sensor.

EnergiesEnergies 20172017, 10,, 101128, 1128 10 of10 20 of 20 Energies 2017, 10, 1128 10 of 20

iL1 L1 D1 iL1 L 1 S1 D1 Vi C1 S1 Vi C1 To supply a audio amplifier CO VO R To supply a with a pure audio amplifier CO VO R resistivewith a pureload resistive load S2 C2 Hi1 S2 C2 Hi1

i L2 D2 H v H L2 i2 iL2 L2 D2 H v Hi2

i 1 L1, ref vcon1 iL, ref i 1 L1, ref KP1 vcon1 iL, ref K P1 0 S1 0 S1 v KI1  conssv KI1  conss

i 1 L2, ref i 1 vcon2 L2, ref K vcon2 P2 KP2 0 0 S2S2 K vconssv I2 KI2   conss CurrentCurrent Control Control Loop Loop

Vo, ref Vo, ref K iL, ref KP3 P3 iL, ref

K KI3  I3  VoltageVoltage Control Control Loop Loop

Figure 8. The developed control system for the combined boost converter. FigureFigure 8. The 8. The developed developed control control system system for forthe thecombined combined boost boost converter. converter.

~ i ~ ~ L1 ~ iL1 vcon1 ~ d1 ~ ~ vo vcon1 d1 ~ vo ~ ~ ~ v~ i con2 d2 L2 iL, ref ~ ~ ~ v~ i con2 d2 L2 iL, ref

Vo ,ref Vo,ref Figure 9. Block diagram for the closed-loop control scheme. Figure 9. Block diagram for the closed-loopclosed-loop control scheme. From Figure 9, we can derive open the loop gain of the voltage and current loops of the proposed converter by the following equations. FromFrom Figure Figure 9,9 ,we we can derivederive open open the the loop loop gain gain of the of voltagethe voltage and currentand current loops ofloops the proposedof the = proposedconverter converter by the followingby the following equations. equations.Ti1(s) FmHi1Gi1d(s)Ci1(s) = (21) Ti2=(s) FmHi2Gi2d(s)Ci2(s) Ti1(s) FmHi1Gi1d(s)Ci1(s) T (s) = Fm H G (s)C (s) i1 = i1 i1d i1 (21) (21) TTi2(s()s) =FmHF i2HGi2Gd(s)C(si2)(Cs) (s) i2 m i2 i2d i2

Energies 2017, 10, 1128 11 of 20

T (s) 1 T (s) 1 Energies 2017, 10, 1128 T (s) = H G (s)C (s) ⋅( i1 ⋅ + i2 ⋅ ) 11 of 20 v v vd v + + (22) 1 Ti1(s) Hi1 1 Ti2(s) Hi2 where, FM = 1/100, Hi1 = Hi2 = Hv = 1. Ti1(s) 1 Ti2(s) 1 Tv(s) = HvGvd(s)Cv(s) · ( · + · ) (22) The small-signal transfer from the duty ratio1 + toTi 1those(s) Hinductori1 1 + currentTi2(s) GHi1di2 and Gi2d and the duty ratio to output voltage Gvd can be shown below. where, FM = 1/100, Hi1 = Hi2 = Hv = 1. The small-signal transfer from the duty ratio to those inductor current Gi1d and Gi2d and the duty G 2DRC ratio to output voltage vd can be shown below. s 1 +1 2V + G (s) = G (s) = o 1 D i1d i2d − 2 2LDRCC (23) (1 D) R s2 s 1 1 1 +11 2Vo −+ 2 G (s) = G (s) = D(11 DD) (23) i1d i2d 2 2L C (1 − D) R 2 1 1 + s 2 1  − D2 (1 − D) − L1 1 D  + 1 s   (srCoCo 1) 1− " 2R1+ D  2# = ( D)R  L1 1 − D  (24) Gvd (s) − ( + ) 2 1 s RC srCoCo 1 (1 − D)R 2R s1 + Do +1 Gvd(s) = 2 (24) 2 RCo s + 1 2 A uncomplicated type-II controller that comprise one-zero, one-pole, and another one-pole at the originA uncomplicated is employed type-IIfor the controllercurrent loop that compensation comprise one-zero, to offer one-pole, sufficient and DC another gain, bandwidth, one-pole at gain/phasethe origin ismargins employed for the for system. the current In addition, loop compensation a proportional-integral to offer sufficient (PI) controller DC gain, that bandwidth, contain one-zerogain/phase and margins one-pole for at theorigin system. is applied In addition, for the voltage a proportional-integral loop compensation. (PI) controller that contain one-zeroThe corresponding and one-pole at current/voltage origin is applied controllers for the voltage of the loopconverter compensation. are selected as follows: The corresponding current/voltage controllers of the converter are selected as follows: +  = =  s 6280   Ci1(s) Ci2 (s) 21.29     s +s 6280  C (s) = C (s) = 21.29  i1 i2 + s (25)  =  s 1570  (25) Cv (s) 10 s + 1570  Cv(s) = 10  s   s

FigureFigure 1010aa shows the frequency response of the loop gain for compensated current current loop, loop, under under thethe full-loadfull-load conditions.conditions. This This work work leads leads to ato phase a phase margin margin of 55 degreesof 55 degrees and the crossoverand the crossover frequency frequencyis approximately is approximately 8 kHz. 8 kHz. FigureFigure 1010bb shows the frequency response of the loop gain for compensated voltage voltage loop, loop, under under thethe full-loadfull-load conditions.conditions. This This work work leads leads to ato phase a phase margin margin of 45 degreesof 45 degrees and the crossoverand the crossover frequency frequencyis approximately is approximately 800 Hz. 800 Hz.

f = 0.8kHz fC = 8kHz C

0 dB

0 dB

PM=55 Deg. -180º -180º PM=45 Deg.

(a) (b)

FigureFigure 10.10. FrequencyFrequency responses responses of theof loopthe gain.loop ( a)gain compensated. (a) compensated current loop current and ( b)loop compensated and (b) compensatedvoltage loop. voltage loop.

5. Simulated and Experimented Results

Energies 2017, 10, 1128 12 of 20

EnergiesEnergies 2017 2017, ,10 10, ,1128 1128 1212 of of 20 20 5.Energies Simulated 2017, 10,and 1128 Experimented Results 12 of 20

InIn order orderorder to to confirmto confirmconfirm the performancethethe performanceperformance of the combinedofof thethe combinedcombined boost converter, boostboost converter, simulationsconverter, simulationssimulations and experiments andand In order to confirm the performance of the combined boost converter, simulations and wereexperimentsexperiments conducted werewere based conductedconducted on the test basedbased setup onon shown thethe intesttest Figure setupsetup 11 shown.shown Figure in12in FigureshowsFigure a11.11. three-view FigureFigure 12 photograph12 showsshows aa experiments were conducted based on the test setup shown in Figure 11. Figure 12 shows a ofthree-viewthree-view the realized photographphotograph boost converter ofof thethe realized prototype.realized boostboost Figure converconver 13 showsterter prototype.prototype. the realized FigureFigure test 1313 bench, showsshows which thethe realizedrealized consists testtest of three-view photograph of the realized boost converter prototype. Figure 13 shows the realized test anbench,bench, oscilloscope, whichwhich consistsconsists a power ofof an source,an oscilloscope,oscilloscope, an electronics aa powerpower load, source,source, a PWM anan electronics generator,electronics andload,load, the aa PWMPWM proposed generator,generator, combined andand bench, which consists of an oscilloscope, a power source, an electronics load, a PWM generator, and boostthethe proposedproposed converter combinedcombined prototype. boostboost converterconverter prototype.prototype. the proposed combined boost converter prototype.

FigureFigure 11.11. Block Block diagram diagram ofof thethe experimentalexperimental testtest setup.setup. Figure 11. Block diagram of the experimental test setup.

((aa)) ((bb)) ((cc)) (a) (b) (c) FigureFigure 12. 12. Realized Realized combined combined boost boost converter converter prototype. prototype. ( (aa)) Top Top view; view; ( (bb)) Front Front view; view; ( (cc)) Side Side view. view. Figure 12. Realized combined boost converter prototype. ( a)) Top Top view; (b) Front view; ((c)) SideSide view.view.

FigureFigure 13.13. RealizedRealized testtest benchbench systemsystem (the(the oscilloscope,oscilloscope, powerpower source,source, electronicselectronics load,load, pulse-widthpulse-width Figure 13.13. RealizedRealized testtest benchbench systemsystem (the(the oscilloscope,oscilloscope, powerpower source,source, electronicselectronics load,load, pulse-widthpulse-width modulationmodulation (PWM) (PWM) generator, generator, and and the the proposed proposed co combinedmbined boost boost converter converter prototype prototype are are labeled). labeled). modulation (PWM) generator, andand thethe proposedproposed combinedcombined boostboost converterconverter prototypeprototype areare labeled).labeled).

TheThe specificationsspecifications andand parametersparameters ofof thethe compcomponentsonents takentaken inin thethe converterconverter prototypeprototype areare The specifications and parameters of the components taken in the converter prototype are providedprovided inin TablesTables 33 andand 4,4, respectively.respectively. provided in Tables 3 and 4, respectively.

Energies 2017, 10, 1128 13 of 20

The specifications and parameters of the components taken in the converter prototype are provided in Tables3 and4, respectively.

Table 3. Specifications of Converter Prototype.

Specification Value

Input Voltage, Vi 12 V Output Voltage, Vo 60 V Duty Cycle, D 0.67 Switching Frequency, fsw 40 kHz Output power, Po 120 W

Table 4. Parameters of Components.

Specification Value MOSFET IPP080N06NG Diode STPS8H100 Load Resistance, R 30 Ω Inductors, L1 and L2 250 µH Filter Capacitors, C1 and C2 10 µF Output Capacitor, Co 1000 µF

For input voltage of 12V and duty cycle of 66.7%, output voltage of 60 V can be obtained using (13). The voltages on the capacitors of C1 and C2 are calculated using (10) and (11). The values across both C1 and C2 are calculated to be about 36 V (i.e., VC1 = VC2 = 36 V). PSIM© simulation software (Powersim Inc., Rockville, MD, USA) is used to confirm the feasibility of the combined boost converter. Figures 14 and 15 indicate the simulated and experimented waveforms of the combined boost converter for gate driving signals VGS1 and VGS2 and two-phase inductor currents iL1 and iL2, respectively. Figure 16 shows the simulated and experimented waveforms of the combined boost converter for the cross voltages across S1 and S2, respectively. Figure 17 shows the simulated and experimented waveforms of the combined boost converter for the cross voltages across D1 and D2, respectively. Figure 18 shows the simulated and experimented waveforms of the combined boost converter for the voltages across the C1 and C2 capacitors. The results verify the feasibility of the converter. Figure 19 shows the transient response because of a step load current change between 120 W and 60 W for the combined boost converter prototype. As can be seen from Figure 19, the output voltage can be stably regulated to be 60 V under the load current variation between 1 A and 2 A. Figure 20 shows the measured conversion efficiency of the combined boost converter, the interleaved boost converter with a two-phases and the conventional converter. The conversion efficiency is measured via precise digital power meter equipment, Yokogawa WT310 (Yokogawa Electric Corporation, Tokyo, Japan). Using the proposed combined boost converter, we obtain the maximum conversion efficiency is 98.7%, as well as the conversion efficiency with a full load is 89.2%. The proposed combined boost converter owns higher efficiency under full load conditions because the conduction loss can be cut down through applying the low-voltage-rated devices. The calculated interleaved boost converter power loss distribution at the rated load condition, obtained using the equations in Table2, is listed in Table5 to expound the measured conversion efficiency. Furthermore, the resulting loss breakdown charts are depicted in Figure 21. Energies 2017, 10, 1128 14 of 20 Energies 2017, 10, 1128 14 of 20 Energies 2017, 10, 1128 14 of 20

(a) (a)

(b) (b)

Figure 14. Waveforms of the combined boost converter for gate driving signals Vgs1 and Vgs2 and Figure 14. Waveforms of the combined boost converter for gate driving signals V and V and Figuretwo-phase 14. inductorWaveforms current of the iL1 .combined (a) Simulated boost waveforms; converter (forb) Experimentedgate driving signalswaveforms. Vgs1gs1 and Vgs2 and two-phase inductor current i .(a) Simulated waveforms; (b) Experimented waveforms. two-phase inductor current iLL11. (a) Simulated waveforms; (b) Experimented waveforms.

(a) (a)

(b) (b)

Figure 15. Waveforms of the combined boost converter for gate driving signals VGS1 and VGS2 and Figure 15. Waveforms of the combined boost converter for gate driving signals VGS1 and VGS2 and two-phase inductor current iL2.(a) Simulated waveforms; (b) Experimented waveforms. Figuretwo-phase 15. inductorWaveforms current of the iL 2.combined (a) Simulated boost waveforms; converter for(b) Experimentedgate driving signals waveforms. VGS1 and VGS2 and two-phase inductor current iL2. (a) Simulated waveforms; (b) Experimented waveforms.

Energies 2017, 10, 1128 15 of 20 Energies 2017, 10, 1128 15 of 20 Energies 2017, 10, 1128 15 of 20

(a) (a)

(b) (b)

Figure 16. Waveforms of the combined boost converter for the cross voltages across S1 and S2. (a) Figure 16. Waveforms of the combined boost converter for the cross voltages across S1 and S2. SimulatedFigure 16. waveforms; Waveforms ( bof) Experimentedthe combined waveforms.boost converter for the cross voltages across S1 and S2. (a) (a) Simulated waveforms; (b) Experimented waveforms. Simulated waveforms; (b) Experimented waveforms.

(a) (a)

(b) (b)

Figure 17. Waveforms of the proposed combined boost converter for the cross voltages across D1 and Figure 17. Waveforms of the proposed combined boost converter for the cross voltages across D1 and D2.(a) Simulated waveforms; (b) Experimented waveforms. DFigure2. (a) Simulated 17. Waveforms waveforms; of the proposed(b) Experimented combined waveforms. boost converter for the cross voltages across D1 and D2. (a) Simulated waveforms; (b) Experimented waveforms.

Energies 2017, 10, 1128 16 of 20 Energies 2017, 10, 1128 16 of 20 Energies 2017, 10, 1128 16 of 20

(a) (a)

(b) (b)

Figure 18. Waveforms of the combined boost converter for the cross voltages across C1 and C2. (a) Figure 18. Waveforms of the combined boost converter for the cross voltages across C1 and C2. Figure 18. Waveforms of the combined boost converter for the cross voltages across C1 and C2. (a) (Simulateda) Simulated waveforms; waveforms; (b) (Experimentedb) Experimented waveforms. waveforms. Simulated waveforms; (b) Experimented waveforms.

(a) (a)

(b) (b)

Figure 19. Waveforms of transient response in the load period steps from 120 W to 60 W and then back toFigure 120 W.19. ( aWaveforms) Simulated of waveforms; transient response (b) Experimented in the load waveforms. period steps from 120 W to 60 W and then Figureback to 19.120 Waveforms W. (a) Simulated of transient waveforms; response (b) Experimentedin the load period waveforms. steps from 120 W to 60 W and then back to 120 W. (a) Simulated waveforms; (b) Experimented waveforms.

EnergiesEnergies2017 2017, 10, ,10 1128, 1128 1717 of of 20 20 Energies 2017, 10, 1128 17 of 20

FigureFigure 20. 20. TheThe measured conversion conversion efficiency efficiency for for th thee proposed proposed combined combined boost boost converter, converter, the Figure 20. The measured conversion efficiency for the proposed combined boost converter, the theconventional conventional boost boost converter, converter, and and the the inte interleavedrleaved boost boost converter converter with with two-phase. two-phase. conventional boost converter, and the interleaved boost converter with two-phase.

TableTable 5. 5.Parameters Parameters of of Components. Components. Table 5. Parameters of Components. Results Results ItemsItems Results (50%Results Load) ResultsResults (100% Load) Items (50% Load) (100% Load) (50% Load) (100% Load) Switching lossSwitching of S1 loss of S1 0.049 0.049W W 0.059 0.059 W W Switching loss of S1 0.049 W 0.059 W Switching lossSwitching of S2 loss of S2 0.049 0.049W W 0.059 0.059 W W Switching loss of S2 0.049 W 0.059 W Conduction loss of L1 and L2 0.64 W 3.2 W ConductionConduction loss of L1 lossand ofL2 L1 and L2 0.64 0.64 W W 3.2 W 3.2 W Conduction loss of D1 and D2 0.0384 W 0.23 W ConductionConduction loss of D1 lossand ofD D2 1 and D2 0.0384 0.0384 W W 0.23 0.23W W Conduction loss of C1 and C2 0.196 W 1.02 W Conduction loss of C1 and C2 0.196 W 1.02 W Conduction lossConduction of C1 and Closs2 of Co 0.196 0.035W W 0.075 1.02 W W Conduction loss of Co 0.035 W 0.075 W Conduction lossTotal of C losses 0.035 1.8828 W W 9.134 0.075 W W Total losseso 1.8828 W 9.134 W Calculated Efficiency 98.5% 92.4% TotalCalculated losses Efficiency 1.8828 98.5% W 92.4% 9.134 W Measured Efficiency 97.3% 89.1% CalculatedMeasured Efficiency Efficiency 98.5% 97.3% 89.1% 92.4%

Measured Efficiency 97.3% 89.1%

(a) (b) (a) (b) Figure 21. The losses breakdown charts. (a) half load and (b) rated load conditions. FigureFigure 21.21. TheThe losseslosses breakdownbreakdown charts.charts. ((aa)) halfhalf loadload andand ((bb)) ratedrated loadload conditions.conditions. For the sake of verifying the performance of the proposed combined boost converter, the other For the sake of verifying the performance of the proposed combined boost converter, the other three converters published in [11,19,24] are used for comparison here, as shown in Table 6. It can be three converters published in [11,19,24] are used for comparison here, as shown in Table 6. It can be

Energies 2017, 10, 1128 18 of 20

For the sake of verifying the performance of the proposed combined boost converter, the other three converters published in [11,19,24] are used for comparison here, as shown in Table6. It can be observed that the amounts of passive components in [19] exceed the requirement in the converter. It will lead to an increase in manufacturing costs. The voltage gain of the former converter [11] is equal to the proposed one presented in this work, Although the former converter in [11] has the relatively low-cost components, the input current ripple is large because of the active switches being controlled simultaneously by using one control signal. The voltage gain of the previous converter in [24] is slightly larger than that of the proposed converter in this study; however, the input current ripple is large owing to the single-phase operation makes this converter not suitable for high current and low ripple applications. From the point view of the cost–performance ratio, the proposed combined boost converter really carries out the higher conversion efficiency and also lower input current ripple under 120 W power rating than other existing works [11,19,24]. Based on its features, this converter can be as a suitable candidate for 12 V battery-powered front-end stage for supplying an automotive audio amplifier.

Table 6. Performance comparisons among other existing converters.

Topology Items This Converter [11][19][24] Switching control structure two-phase single-phase three-Phase single-phase Input current ripple Low High Low Medium Voltage gain (1 + D)/(1 − D) (1 + D)/(1 − D) (3+ nD − D2 )/(1 − D) 1/(1 − D)2 High-side voltage 60 V 60 V 200 V 62.5 V Low-side voltage 12 V 12 V 24 V 10 V Number of main power devices 4 3 8 4 Number of storage components 5 4 8 5 Maximum efficiency 98.7% 92.1% 92.3% 92.5% Realized prototype power rating 120 W 40 W 100 W 100 W BOM Cost Low Low High Medium Remark-n represents the turns ratio for coupled inductor [19].

6. Conclusions A modified interleaved boost converter with two-phase is presented as a battery-powered front-end interface for automotive audio amplifiers. The combined boost converter is created based on a two-phase structure by combining the conventional boost converter with its inverted type. As well as the existing characteristics that benefit from interleaved converters, the converter provides the more advantages in extending the duty cycle than the conventional boost and the interleaved boost converters. Furthermore, it also prevents working with a wide duty cycle. The operating principles, steady-state analyzes, as well as the closed-loop control designs of the converter are explored in this study. Simulations and experiments are also performed using input voltage of 12 V for a 120 W circuit. A reasonable duty cycle of 0.67 is selected to reach output voltage of 60 V, which corresponds to static voltage gain of five. The converter achieves a maximum measured conversion efficiency of 98.7%. According to its characteristics, the combined boost converter is highly suitable for use as a front-end converter in powering automotive audio amplifiers.

Acknowledgments: This work is partly supported by the Ministry of Science and Technology (MOST) in Taiwan under grants MOST 105-2221-E-027-096, MOST 105-2221-E-324-02, MOST 105-2221-E-324-026, and MOST 106-2218-E-027-010. The authors would like to express their appreciation to the student Chao-Wei Ku (NTUT) for the experimental bench setup. Author Contributions: Ching-Ming Lai substantially contributed to examination and interpretation of the results, development of the overall system, and review and proofreading of the manuscript. Yu-Huei Cheng substantially contributed to control strategy design, production and analysis of the results, and preparation and revision of the manuscript. Jiashen Teh substantially contributed to the review and proofreading of the manuscript. Energies 2017, 10, 1128 19 of 20

Yuan-Chih Lin substantially contributed to literature search, control strategy design, and production and analysis of the results. Conflicts of Interest: The authors declare no conflict of interest.

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