Novel High Step-Up DC-DC Converter with Coupled-Inductor and Voltage-Doubler Circuits

Transcription

1 Novel High SepUp DCDC Converer wih CoupledInducor and olagedoubler Circuis LungSheng Yang, TsorngJuu Liang, Member, IEEE, HauCheng Lee, and JiannFuh Chen, Member, IEEE Absrac In his paper, a novel high sepup DCDC converer wih coupledinducor and volagedoubler circuis is proposed. The converer achieves high sepup volage gain wih appropriae duy raio and low volage sress on he power swiches. Also, he energy sored in he leakage inducor of he coupled inducor can be recycled o he oupu. The operaing principles and he seadysae analyses of he proposed converer are discussed in deail. Finally, a prooype circui of he proposed converer is implemened in he laboraory o verify he performance of he proposed converer. Index Terms Coupledinducor, volagedoubler, high sepup volage gain. I. INTODUCTION The DCDC converer wih high sepup volage gain is widely used for many applicaions, such as fuelcell energyconversion sysems, solarcell energyconversion sysems, and highinensiydischarge lamp ballass for auomobile headlamps. Convenionally, he DCDC boos converer is used for volage sepup applicaions, and in

2 his case his converer will be operaed a exremely high duy raio o achieve high sepup volage gain [1], []. However, he volage gain and he efficiency are limied due o he consraining effec of power swiches, diodes, and he equivalen series resisance (ES) of inducors and capaciors. Moreover, he exremely high duyraio operaion will resul in a serious reverserecovery problem. Some lieraures have researched he high sepup DCDC converers ha do no incur an exremely high duy raio [3][5]. The ransformerless DCDC converers, such as he cascade boos ype [3], he quadraic boos ype [4], he swichedinducor ype [5], [6], he volagelif ype [7], [8], he volage doubler echnique [9][11], he capaciordiode volage muliplier ype [1], and he boos ype ha is inegraed using a swichedcapacior echnique [13]. These converers can provide higher volage gain han he convenional DCDC boos converer. However, he volage gain of hese converers is only moderaely high. If higher volage gain is required, hese converers mus cascade more power sages, which will resul in low efficiency. The DCDC flyback converer is adoped o achieve high sepup volage gain by adjusing he urns raio of he ransformer. This converer has he meris of simple opology, easy conrol, and low cos, bu he fac ha he leakageinducor energy of he ransformer can no be recycled, i resuls in low efficiency and high volage sress on he acive swich. In order o reduce he volage sress, an CD snubber is used [14]. However, his decreases he efficiency. Some aciveclamp echniques are adoped o recycle he leakageinducor energy of he ransformer and o minimize he

3 volage sress on he acive swich, bu his approach requires an addiional swich [15][17]. Some converers, which include he clampmode boos ype, he inegraed boosflyback ype, and he inegraed boossepic ype, are developed o achieve high sepup volage gain by using he coupledinducor echnique [18][]. The leakageinducor energy of he coupled inducor can be recycled and he volage sress on he acive swich is reduced. Much higher volage gain is achieved by using he coupled inducor and he volagemuliplier or volagelif echniques [3][5]. However, he acive swich will suffer high curren sress during he swichon period. A convenional high sepup DCDC converer wih coupledinducor echnique is shown in Fig. 1 [1]. The srucure of his converer is very simple and he leakageinducor energy of he coupled inducor can be recycled o he oupu. However, he volage sresses on swich S 1 and diode D 1, which are equal o he oupu volage, are high. This paper presens a novel high sepup DCDC converer, as shown in Fig.. The coupledinducor and volagedoubler echniques are inegraed in he proposed converer o achieve high sepup volage gain. The feaures of his converer are as follows: 1) The leakageinducor energy of he coupled inducor can be recycled. ) The volage sresses on he swiches are half he level of he oupu volage. Thus, he swiches wih low volage raing and low ONsae resisance DS(ON) can be seleced. 3) The volage gain achieved by he proposed converer is double ha of he convenional high sepup converer. Under he same volage gain and duy raio, he

4 urns raio of he coupled inducor for he proposed converer can be designed o be less han he convenional high sepup converer. 4) The frequency of he magneizinginducor curren for he proposed converer is double of he swiching frequency. Thus, he magneizinginducance of he coupledinducor for he proposed converer can be designed o be less han he convenional high sepup converer under same swiching frequency. II. OPEATING PINCIPLE OF THE POPOSED CONETE Fig. shows he circui configuraion of he proposed converer, which consiss of wo acive swiches S 1 and S, one coupled inducor, four diodes D 1 D 4, and wo oupu capaciors C 1 and C. The simplified circui model of he proposed converer is shown in Fig. 3. The coupled inducor is modeled as a magneizing inducor L m, primary leakage inducor L k1, secondary leakage inducor L k, and an ideal ransformer. Capaciors C S1 and C S are he parasiic capacior of S 1 and S. In order o simplify he circui analysis of he proposed converer, some condiions are assumed as follows: 1) All componens are ideal. ONsae resisance DS(ON) of he acive swiches, he forward volage drop of he diodes, and he ES of he coupledinducor and oupu capaciors are ignored. ) Oupu capaciors C 1 and C are sufficienly large, and he volages across C 1 and C are considered o be consan during one swiching period. Fig. 4 shows some ypical waveforms during one swiching period in coninuous conducion mode (CCM) operaion. The operaing principle is described as follows.

5 1) Mode I [, 1 ]: A =, S 1 and S are urned on. The currenflow pah is shown in Fig. 5(a). The DCsource energy is ransferred o L m and L k1 hrough D 3, S 1, and S, so currens i, i Lk1, and i D3 are increased. The energy sored in L k is released o L m and L k1 hrough D 4, S 1, and S. Thus, i Lk is decreased. Meanwhile, he energy sored in L k is recycled. The energy sored in C S is rapidly and compleely discharged. The energies sored in C 1 and C are discharged o he load. This mode ends when i Lk is equal o zero a = 1. ) Mode II [1, ]: In his mode, S 1 and S are sill urned on. The currenflow pah is shown in Fig. 5(b). The DCsource energy is sill ransferred o L m and L k1. Thus, i and i Lk1 are sill increased. The energies sored in C 1 and C are sill discharged o he load. 3) Mode III [, 3 ]: A =, S 1 is urned off and S is sill urned on. The currenflow pah is shown in Fig. 5(c). The DCsource energy is sill ransferred o L m, L k1, and C S1. Meanwhile, he volage across S 1 is increased rapidly. The energies sored in C 1 and C are sill discharged o he load. 4) Mode I [3, 4 ]: During his ime inerval, S 1 is sill urned off and S is sill urned on. The currenflow pah is shown in Fig. 5(d). The DC source, L m, and L k1 are seriesconneced o ransfer heir energies o L k, C 1, and he load. Thus, i and i Lk1 are decreased and i Lk is increased. Meanwhile, he energy sored in L k1 is recycled o C 1 and he load. The energy sored in C is sill discharged o he load. This mode ends when i Lk1

6 is equal o i Lk a = 4. 5) Mode [4, 5 ]: During his period, S 1 is sill urned off and S is sill urned on. The currenflow pah is shown in Fig. 5(e). The DC source, L m, L k1, and L k are seriesconneced o ransfer heir energies o C 1 and he load. Thus, i, i Lk1, and i Lk are decreased. The energy sored in C is sill discharged o he load. 6) Mode I [5, 6 ]: A = 5, S 1 and S are urned on. The currenflow pah is shown in Fig. 5(f). The DCsource energy is ransferred o L m and L k1 hrough D 3, S 1, and S. So currens i, i Lk1, and i D3 are increased. The energy sored in L k is released o L m and L k1 hrough D 4, S 1, and S. Thus, i Lk is decreased. Meanwhile, he energy sored in L k is recycled. The energy sored in C S1 is rapidly and compleely discharged. The energies sored in C 1 and C are discharged o he load. This mode ends when i Lk is equal o zero a = 6. 7) Mode II [6, 7 ]: During his ime inerval, S 1 and S are sill urned on. The currenflow pah is shown in Fig. 5(g). The DCsource energy is sill ransferred o L m and L k1. Thus, i and i Lk1 are sill increased. The energies sored in C 1 and C are sill discharged o he load. 8) Mode III [7, 8 ]: A = 7, S 1 is sill urned on and S is urned off. The currenflow pah is shown in Fig. 5(h). The DCsource is sill ransferred o L m, L k1, and C S. Meanwhile, he volage across S is increased rapidly. The energies sored in C 1 and C are sill

7 discharged o he load. 9) Mode IX [ 8, 9 ]: During his period, S 1 is sill urned on and S is sill urned off. The currenflow pah is shown in Fig. 5(i). The DC source, L m, and L k1 are seriesconneced o ransfer heir energies o L k, C, and he load. Thus, i and i Lk1 are decreased and i Lk is increased. Meanwhile, he energy sored in L k1 is recycled o C and he load. The energy sored in C 1 is sill discharged o he load. This mode ends when i Lk1 is equal o i Lk a = 9. 1) Mode X [9, 1 ]: In his mode, S 1 is sill urned on and S is sill urned off. The currenflow pah is shown in Fig. 5(j). The DC source, L m, L k1, and L k are seriesconneced o ransfer heir energies o C and he load. Thus, i, i Lk1, and i Lk are decreased. The energy sored in C 1 is sill discharged o he load. This mode ends when S 1 and S are urned on a he beginning of he nex swiching period. III. STEADYSTATE ANALYSIS OF THE POPOSED CONETE (A) olage gain A CCM operaion, he ime duraions of modes I, III, I, I, III, and IX are very shor as compared o one swiching period. Thus, only modes II,, II, and X are considered. A modes II and II, he following equaions can be wrien from Figs. 5(b) and 5(g): v = v = k (1) II II L1 L1 in, II II di di kin = =, () d d L m

8 where couplingcoefficien k of he coupledinducor is equal o L m /(L m L k1 ). A mode, he following equaions are derived from Fig. 5(e): i, Lk1 ilk = (3) i = (1 ni ), (4) Lk1 = v v v v (5), in c1 L1 Lk1 L Lk where urns raio n of he coupledinducor is equal o N /N 1. olage is found o be v Lk dilk dilk1 dilk1 v. Lk = Lk = Lk = nlk1 = nvlk1 (6) d d d Subsiuing (6) ino (5) yields he following equaion: = (1 n) v (1 n ) v. (7) in c1 L1 Lk1 olage v L1 is wrien as di dilk1 v = L1 (1 nl ) m. d = d (8) Thus, di L 1 k v L v v Lk1 k1 Lk1 = k1 = L1 = L1 d (1 n) (1 n) k. (9) Subsiuing (9) ino (7) yields he following equaion: (1 nk ) vl 1 = ( in c 1), 1 nk n di (1 nk ) d nk n L in c1 = 1 m. (1) (11) Similarly, a mode X, he volage across L m is derived from Fig. 5(j) as follows:

9 X (1 nk ) vl 1 = ( in c ), 1 nk n di (1 nk ) d nk n L X in c = 1 m. (1) (13) Using he volsecond balance principle on L m, he following equaion is derived as DTs (1 D) Ts DTs (1 D) Ts II II X L1 L1 L1 L1 v d v d v d v d =. (14) Subsiuing (1), (1), and (1) ino (14), he volage gain is obained as M CCM o n nd n D ndk = = (1 D)(1 n) in (1 ). (15) Thus, he drawing of he volage gain versus he duy raio under various coupling coefficiens of he coupledinducor is shown in Fig. 6. I can be seen ha he volage gain is no very sensiive o he coupling coefficien. If he impac of he leakage inducor of he coupled inducor is negleced, hen coupling coefficien k is equal o 1. Subsiuing k = 1 ino (15), he volage gain becomes M CCM o (1 nd) = =. 1 D in (16) (B) Boundary Operaing Condiion Fig. 7 shows some waveforms of he proposed converer a boundary conducion mode (BCM). When he proposed converer is operaed in BCM, he peak value of he magneizinginducor curren is given as I p kdints =. (17) L m

10 Since he ime duraion [ 1, 3 ] is very shor as compared o one swiching period, his ime duraion is no considered. The average value of i D1 is found o be I D1 1 I p 1 D T s 1 n (1 DI ) p = =. T 4(1 n) s (18) A seady sae, he average value of i D1 is equal o I o. Thus, (1 DI ) p 4(1 n) o = Io =. (19) Then, he normalized magneizinginducor ime consan is defined as τ fs, T = () s where f s is he swiching frequency. Subsiuing (15), (17), and () ino (19), he boundary normalized magneizinginducor ime consan τ B can be derived as τ B = kd(1 D) n nd n D ndk 16(1 ). (1) The curve of τ B is ploed in Fig. 8. If τ is larger han τ B, he proposed converer is operaed in CCM. (C) Efficiency Analysis In order o simplify he efficiency analysis of he proposed converer, he leakage inducors of he coupled inducor are negleced. Thus, he operaing principle is divided ino four modes, he equivalen circuis for which are shown in Fig. 9. r L1 and r L represen he

11 ES of he primary and secondary windings of he coupled inducor. FD1 FD4 and r D1 r D4 are he ONsae forward volage drop and resisance of D 1 D 4. r S1 and r S denoe he ONsae resisance of S 1 and S. When S1 and S are urned on, he equivalen circui is shown in Fig. 9(a). This ime inerval is DT s /. The average values of i c1 and v L1 are obained as I I III o c1 = Ic 1 =, () = = I ( r r r r ), (3) I III L1 L1 in FD3 in( on) L1 D3 S1 S where I in(on) is he average value of he inpu curren in his ime inerval. When S1 is urned off and S is urned on, he equivalen circui is shown in Fig. 9(b). This ime inerval is (1D)T s /. The average values of i c1 and v L1 are derived as I II o c1 = Iin( off ), (4) II L1 in FD 4 FD 1 c1 Iin( off )( rl 1 rd 4 rl rd 1 rs ) =, 1 n (5) where I in(off) he average value of he inpu curren in his ime inerval. When S1 is urned on and S is urned off, he equivalen circui is shown in Fig. 9(c). This ime inerval is (1D)T s /. The average values of i c1 and v L1 are given as I I o c1 =, (6) I L1 in FD 4 c FD Iin( off )( rl 1 rd 4 rl rs 1 rd ) =. 1 n (7) By using he amperesecond balance principle on C 1, he following equaions are obained as

12 DTs (1 D) Ts DTs (1 D) Ts I II III I c1 c1 c1 c1 I d I d I d I d =. (8) Subsiuing (), (4), and (6) ino (8), I in(off) can be compued as I in( off ) o =. (1 D ) (9) Also, I in(on) can be found o be I (1 n ) o = (1 ni ) =. (1 D ) in( on) in( off ) (3) Using he volsecond balance principle on L m yields DTs (1 D) Ts DTs (1 D) Ts I II III I L1 L1 L1 L1 d d d d =. (31) Subsiuing (3), (5), and (7) ino (31), he acual volage gain is derived as o in (1 nd) 1 A1 =, 1 D 4 D(1 n) A A3 1 (1 D) (1 D ) (3) where 1 D (1 nd ) 1 D A1 = (1 nd) 1 nd 1 nd FD1 FD FD3 FD4 ( ), in in in in A r r r r =, L1 D3 S1 S A = r r r r r r r. 3 L1 L D1 D D4 S1 S The inpu power and oupu power of he proposed converer are obained as D D 1 D 1 D Pin = I in in( on) ( ) I in in( off )( ), (33) o Po =. (34)

13 Subsiuing (9) and (3) ino (33), he inpu power can be compued as P (1 nd) =. (1 D ) in in o (35) From (3), (34) and (35), he efficiency of he proposed converer is found o be Po 1 A1 η = =. Pin 4 D(1 n) A A3 1 (1 D) (1 D ) (36) (D) olage and Curren Sresses on Power Devices According o he operaing principle, he volage and curren sresses on power devices are discussed as follows. If he impac of he leakage inducor of he coupled inducor is ignored, he volage sresses on S 1, S, and D 1 D 4 are given as o S1 = S = D1 = D =, n o D3 = ( in), 1 n (37) (38) D4 nin. = (39) From (), he ripple of i can be derived as kdint I = L m s. (4) From (9), (3), and (4), he curren sresses flow hrough S 1, S, and D 1 D 4 are found o be I (1 n) o kdints IS1 = IS = ID 1 = ID = ID3 = Iin( on) =. (1 D ) 4L m (41) I I o kdints = I = (1 n) (1 D ) 4(1 nl ) D4 in( off ) m. (4)

14 I. EXPEIMENTAL ESULTS In order o verify he feasibiliy of he proposed converer, a 5W prooype circui is buil in he laboraory. The circui specificaions and componens are seleced as in = 4, o =, f s = 5 khz, P o = 5 W ( = 16 Ω), and C 1 = C = 47 μf. Also, MOSFET IXFK14NP ( DSS =, DS(ON) = 18 mω) is seleced for S 1 and S, and diode MB15CT ( M = 15, F =.9 ) is seleced for D 1 and D. Subsiuing in = 4 and o = ino (38) and (39), he volage sresses on D 3 and D 4 versus urns raio n of he coupled inducor are ploed in Fig. 1. One can see ha D3 and D4 are increased wih an increase in n. For he volagegain and efficiency analysis, he ES of he coupled inducor, he ONsae forward volage drop and resisance of D 1 D 4, and he ONsae resisance of S 1 and S are considered. Some parameers of hree cases are assumed as follows: 1) Case 1: n = 1, rl1 = r L = r D1 = r D = r D3 = r D4 = 1 mω, r S1 = r S = 18 mω, FD1 = FD =.9, and FD3 = FD4 =.75. ) Case : n =, rl1 = r D1 = r D = r D3 = r D4 = 1 mω, r L = mω, r S1 = r S = 18 mω, FD1 = FD =.9, and FD3 = FD4 =.85. 3) Case 3: n = 3, rl1 = r D1 = r D = r D3 = r D4 = 1 mω, r L = 3 mω, r S1 = r S = 18 mω, FD1 = FD =.9, and FD3 = FD4 =.85. Subsiuing he circui specificaions and parameers ino (3) and (36), he calculaed volage gain and efficiency are ploed in Figs. 11 and 1. Fig. 1 shows ha he calculaed efficiency

15 in case 1 is beer han in cases and 3. Thus, urns raio n of he coupled inducor is chosen as 1. Then, diode SBL6CT ( M = 6, F =.75 ) is seleced for D 3 and D 4. As can be seen from Fig. 11, duy raio D is.634 for case 1. Subsiuing k = 1, n = 1, and D =.634 ino (1), he boundary normalized magneizinginducor ime consan τ B is obained as.16. The proposed converer is operaed in CCM from 5% of he full load, namely = 64 Ω. When τ is larger han τ B, he proposed converer is operaed in CCM. Using (), L m is found by τ fs 5k = = >.16, 64 L > 41 µ H, m L m is seleced o be 48 μh. The circui diagram of he proposed converer wih conrol circui is shown in Fig. 13. Under he operaing condiions in = 4, o =, and P o = 5 W, some experimenal waveforms are shown in Figs Fig. 14 shows some experimenal volage waveforms. I is seen ha v s1, v s, v D1 and v D are equal o half of he oupu volage during he seadysae period. However, he ringing phenomenon of v s1 and v s is caused by he line inducors and parasiic capaciors of S 1 and S when S 1 and S are urned off. Thus, he ringing phenomenon mus be aken ino consideraion for choosing S 1 and S. Fig. 15 shows some experimenal curren waveforms, which agree wih he operaing principle and he seadysae analysis. However, he ringing phenomenon exiss in i D4. One mus consider his phenomenon for

16 choosing D 4. As shown in Fig. 16, he volages across C 1 and C are equal, and hey are also equal o half of he oupu volage. Fig. 17 shows he measured efficiency of he proposed converer and he convenional converer in [1]. The circui componens of he convenional converer are chosen as he urns raio n of he coupled inducor: 3.6, swich S 1 : FDA59N3 ( DSS = 3, DS(ON) = 56 mω), diode D 1 : DSEP33A ( M = 3, F = 1.55 ), and D : DSEP36A ( M = 6, F = 1.6 ). The DS(ON) of he swich and F of diodes in he proposed converer are less han he convenional converer. When he oupu power is over 7 W, he proposed converer has higher efficiency han his convenional converer. Also, he measured efficiency of he proposed converer is 91.1% a he fullload condiion and he maximum efficiency is 9.8% a he halfload condiion.. CONCLUSIONS A novel high sepup DCDC converer is presened in his paper. The coupledinducor and volagedoubler circuis are inegraed in he proposed converer o achieve high sepup volage gain. The energy sored in he leakage inducor of he coupled inducor can be recycled. The volages across he swiches are half he level of he oupu volage during he seadysae period. However, he volages have he ringing phenomenon a he beginning when he swiches are urned off. One mus consider his phenomenon for choosing he swiches. Similarly, since he ringing phenomenon is occurred in he curren hrough diode D 4, his phenomenon is also considered for choosing diode D 4. Finally, a prooype circui for he

17 proposed converer wih 4 inpu volage, oupu volage, and 5W oupu power is buil in he laboraory o verify he feasibiliy. The experimenal resuls show ha high sepup volage gain is achieved. The measured efficiency is 91.1% a he fullload condiion and he maximum efficiency is 9.8% a he halfload condiion. Comparing o he proposed converer and he convenional converer in [1], one can see ha he efficiency is improved. However, since more circui componens are used in he proposed converer, i resuls in higher cos. ACKNOWLEDGMENTS The auhors graefully acknowledge financial suppor from he Naional Science Council of Taiwan under projec NSC E6 8. EFEENCES [1] X. Wu, J. Zhang, X. Ye, and Z. Qian, Analysis and derivaions for a family ZS converer based on a new acive clamp ZS cell, IEEE Trans. Ind. Elecron., vol. 55, no., pp , Feb. 8. [] D. C. Lu, K. W. Cheng, and Y. S. Lee, A singleswich coninuousconducionmode boos converer wih reduced reverserecovery and swiching losses, IEEE Trans. Ind. Elecron., vol. 5, no. 4, pp , Aug. 3. [3] L. Huber and M. M. Jovanovic, A design approach for server power supplies for neworking applicaions, Proc. IEEE APEC, pp ,.

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21 Figure Capions Fig. 1. Circui configuraion of he convenional high sepup DCDC converer. Fig.. Circui configuraion of he proposed converer. Fig. 3. Simplified circui model of he proposed converer. Fig. 4. Some ypical waveforms of he proposed converer a CCM operaion. Fig. 5. Currenflow pah of operaing modes during one swiching period a CCM operaion. Fig. 6. olage gain versus duy raio of he proposed converer a CCM operaion wih n = and various values for k. Fig. 7. Some ypical waveforms of he proposed converer a BCM operaion. Fig. 8. Boundary condiion of he proposed converer wih n = and k = 1. Fig. 9. Equivalen circui of he proposed converer, including ES of he coupled inducor, he ONsae forward volage drop and resisance of he diodes, and he ONsae resisance of he swiches. (a) S 1 and S ON. (b) S 1 OFF and S ON. (c) S 1 ON and S OFF. Fig. 1. olage sresses on D3 and D 4 versus he urns raio of he coupled inducor. Fig. 11. Calculaed volage gain versus duy raio. Fig. 1. Calculaed efficiency versus oupu power. Fig. 13. Circui diagram of he proposed converer wih conrol circui. Fig. 14. Experimenal waveforms. (a) v gs1, v gs, v S1, and v S. (b) v D1, v D, v D3, and v D4.

22 Fig. 15. Experimenal waveforms. (a) i D4, i in, and i D3. (d) i S1 and i D1. Fig. 16. Experimenal waveforms for c1, c, and o. Fig. 17. Measured efficiency of he proposed converer and he convenional converer in [1] wih various oupu power. D 1 in N 1 D N S 1 C o o Fig. 1. Circui configuraion of he convenional high sepup DCDC converer. D 3 N N 1 D 4 D 1 S 1 in C 1 S C c1 o D c Fig.. Circui configuraion of he proposed converer.

23 i in in i D3 v D3 N 1 i D4 D 4 v L i D1 D 1 L i Lk1 L k1 i m vl1 D 3 vlk1 vlk N i Lk L k v D4 i S1 v i c1 D1 S 1 C S1 i S C 1 S v S C C S v S1 v D D i c i D c1 c I o o Fig. 3. Simplified circui model of he proposed converer. v gs1 v gs i i in (i Lk1 ) i D3 i D4 (i Lk ) i S1 i S v S1 v S i D1 i D o / o / DT s DT s (1 DT ) s T s (1 DT ) s Fig. 4. Some ypical waveforms of he proposed converer a CCM operaion.

24 Lk1 D4 D3 N Lk N1 Lk1 D4 D3 N Lk D1 N1 in S1 S D1 CS1 CS D C1 C in S1 S CS1 CS D C1 C (a) Mode I (b) Mode II D3 D3 Lk1 D1 Lk1 D4 N Lk N1 in D4 N Lk S1 S CS1 CS D C C1 N1 in S1 S D1 CS1 CS D C C1 (c) Mode III (d) Mode I D3 D3 Lk1 D4 N Lk N1 in Lk1 D4 N Lk S1 S D1 CS1 CS D C C1 N1 in S1 S D1 CS1 CS D C1 C (e) Mode (f) Mode I D3 D3 N1 Lk1 D4 N Lk D1 Lk1 in S1 S CS1 CS D C1 C N1 in D4 N Lk S1 S D1 CS1 CS D C C1 (g) Mode II (h) Mode III D3 D3 Lk1 D4 N Lk Lk1 D4 N Lk N1 in S1 S D1 CS1 CS D C1 C N1 in S1 S D1 CS1 CS D C1 C (i) Mode IX (j) Mode X Fig. 5. Currenflow pah of operaing modes during one swiching period a CCM operaion.

25 M CCM 16 n =, k = 1 n =, k =.95 n =, k = D Fig. 6. olage gain versus duy raio of he proposed converer a CCM operaion wih n = and various values for k. v gs1 v gs i i in (i Lk1 ) i D3 i D4 (i Lk ) i D1 I p I p I p /(1n) I p /(1n) DT s DT s (1 DT ) s (1 DT ) s T s Fig. 7. Some ypical waveforms of he proposed converer a BCM operaion.

26 τ B.3 CCM..1 DCM D Fig. 8. Boundary condiion of he proposed converer wih n = and k = 1. r L1 I in(on) in L1 r L FD3 r D3 L r S1 r S I c1 I c c1 c I o o (a) I in(off) in r L1 r D4 FD4 L1 r L L r S FD1 r D1 I c1 I c c1 c I o o (b) r L1 r D4 r L FD4 LrS1 I c1 I o I c1 in(off) L1 in I c c r FD D o (c) Fig. 9. Equivalen circui of he proposed converer, including ES of he coupled inducor, he ONsae forward volage drop and resisance of he diodes, and he ONsae resisance of he swiches. (a) S 1 and S ON. (b) S 1 OFF and S ON. (c) S 1 ON and S OFF.

27 () 1 8 D3 D n Fig. 1. olage sresses on D 3 and D 4 versus he urns raio of he coupled inducor. o / in 4 18 Case 1 Case Case D Fig. 11. Calculaed volage gain versus duy raio. Efficieny (%) Case 1 Case Case P o (W) Fig. 1. Calculaed efficiency versus oupu power.

28 D3 in N1 D4 N S1 v gs1 S v gs D1 D C1 C c1 c o 39k 1k 1.5n 1k 16n 1k 5k 1n 4k 1p TL k Y5 Y1 Y Y Y6 15 Y7 Y HCF 417 BE Y9 Y4 Y8 Y Y Y4 Y6 Y8 Y1 Y3 Y5 Y7 Y9 15 1μ 15 1μ 1μ 1μ vgs1 vgs Fig. 13. Circui diagram of he proposed converer wih conrol circui. v gs1 v D1 v gs v D v S v D3 v S1 v D4 v gs1 /v gs : /div, v S1 /v S : 1 /div, Time: 1 μs/div v D1 /v D : 1 /div,v D3 /v D4 : 4 /div, Time: 1 μs/div (a) (b) Fig. 14. Experimenal waveforms. (a) v gs1, v gs, v S1, and v S. (b) v D1, v D, v D3, and v D4. i D4 i S1 i in i D3 i D1 i D4 /i in /i D3 : 1 A/div, Time: 1 μs/div i S1 /i D1 : 1 A/div, Time: 1 μs/div (a) (b) Fig. 15. Experimenal waveforms. (a) i D4, i in, and i D3. (d) i S1 and i D1.

29 o c1 c o / c1 / c : 1 /div, Time: 5 μs/div Fig. 16. Experimenal waveforms for c1, c, and o. Efficiency (%) Proposed converer Converer in [1] 65 P o (W) Fig. 17. Measured efficiency of he proposed converer and he convenional converer in [1] wih various oupu power.