Series-Resonant Converter with Reduced- Frequency-Range Control

Transcription

1 Series-Resonan Converer wih Reduced- Frequency-Range Conrol Yungaek Jang, Milan M. Jovanović, Juan M. Ruiz, and Gang Liu 1, Power Elecronics Laboraory, Dela Producs Corporaion, 511 Davis Drive, Research Triangle Park, NC, USA 1 Elecrical Engineering, Fudan Universiy, Shanghai 433, People s Republic of China Dela Power Elecronics (Shanghai) Co. Ld, 19, People s Republic of China Absrac In his paper, a conrol mehod ha improves performance of series-resonan converers ha operae wih a wide inpu-volage and/or oupu-volage range by subsanially reducing heir swiching-frequency range. The swichingfrequency-range reducion is achieved by conrolling he oupu volage wih a combinaion of variable-frequency and delayime conrol. Variable-frequency conrol is employed o conrol he primary swiches, while delay-ime conrol is used o conrol secondary-side recifier swiches provided in place of diode recifiers. The performance evaluaion of he proposed conrol was done on a 69-W prooype operaing in a -45-V inpuvolage range and delivering a 13.8-V oupu volage. The prooype circui exhibis he maximum full-load efficiency of 95.8% wih a swiching frequency variaion from 48 khz o 7 khz over he enire inpu-volage range. I. INTRODUCTI Resonan converers use a resonan-ank circui o shape swich volage and/or curren waveform o minimize swiching losses and allow high-frequency operaion while mainaining high conversion efficiencies. As a resul, resonan converers are exensively used in sae-of-he-ar power supplies ha offer he highes power densiies and efficiencies [1]-[5]. Generally, resonan converers operae wih variable swiching-frequency conrol. When operaing above he resonan frequency, resonan converer operaes wih zero volage-swiching (ZVS) of he primary swiches. Generally, variable swiching-frequency conrol is seen as a drawback of a resonan converer especially in applicaions wih a wide inpu-volage and/or oupu-volage range. Specifically, as he inpu or oupu volage range increases, he conrol frequency range also increases so ha driving and magneic componen losses also increase, hereby reducing conversion efficiency. Furhermore, in many applicaions, converers are resriced o operae wihin a relaively limied frequency range o avoid inerfering wih oher pars of he sysem. While resonan converers can operae a a consan frequency ( clamp-mode operaion) [6], such an operaion is no desirable because he increased circulaing energy in he resonan ank circui significanly degrades conversion efficiency. As a resul, here have been several aemps o improve performance of resonan converers operaing in a wide inpu-volage range and/or a wide oupu-volage range by reducing he swiching frequency range by adding range windings and/or swiches o effecively change he urns raio of he ransformer [7]-[1]. While hese approaches have been proven o improve performance, heir major downsides are addiional cos and complexiy. In his paper a new conrol mehod ha improves he performance of resonan converers ha operae wih a wide inpu-volage range and/or a wide oupu-volage range by subsanially reducing heir swiching-frequency range is inroduced. Reducion in he swiching frequency range is achieved by conrolling he oupu volage wih a combinaion of variable-frequency feedback conrol and open-loop delayime conrol. Variable-frequency conrol is used o conrol he primary swiches of an isolaed resonan converer, while delay-ime conrol is used o conrol secondary-side recifier swiches provided in place of diode recifiers. The secondaryside conrol is implemened by sensing he secondary curren and/or he primary curren and by delaying he urning-off of he corresponding secondary swich(es) wih respec o he zero crossings of he secondary or he primary curren. Generally, he delay ime is deermined by he inpu volage and/or he oupu volage and is se o properly adjus he volage gain. Since delay-ime conrol increases he energy in he resonan ank circui and makes he series resonan converer exhibi a boos characerisic, he delay-ime conrol is ypically designed o supplemen he variable-frequency feedback conrol a low inpu and/or high oupu volages. The evaluaion of he proposed delay-ime conrol was performed on a 69-W prooype operaing in he inpuvolage range from V o 45 V. II. SERIES-RESANT CVERTER WITH REDUCED- FREQUENCY-RANGE CTROL Figure 1 illusraes he proposed conrol mehod in a series-resonan converer wih a full-bridge secondary synchronous recifier. However, i should be noed ha he described conrol mehod is also applicable o he cener-ap secondary implemenaion. As illusraed in Fig. 1, oupu volage regulaion is achieved using a combinaion of variable-frequency feedback conrol and open-loop delayime conrol. Specifically, variable-frequency conrol is applied o primary swiches S P1 -S P4, and delay-ime conrol is applied o secondary-side swiches S S1 -S S4. Figures (a) and (b) show waveforms of primary swiches S P1 -S P4, secondary swiches S S1 -S S4, and resonan inducor curren for wo secondary side conrol mehods; one wih asymmeric gaing and he oher wih symmeric gaing. As shown in Figs. (a) and (b), in boh implemenaions, all same-leg pairs of /15/$ IEEE 1453

2 SP1 SP S P1 SP CR SP4 S P3 SP3 SP4 N 1 TR N1 n= N N SS1 SS SS4 SS3 CO S S1 S S S S3 S S4 L O V O A - D S S P1 S P3 Ts P S P4 S S1 S S sensing & scaling DRIVER f S VCO V EA VIN(scld) ZCD ERORR AMPLIFIER w/ COMPENSATI CTROL DELAY-TIME CTROL VE V O(scld) - V O(REF) DRIVER V O(scld) VIN(scld) sensing & scaling V O S S3 S S4 Fig. 1. Series-resonan converer wih proposed secondary-side-swich delay-ime conrol. swiches operae in a complemenary fashion wih a small dead ime beween heir commuaions o achieve ZVS. In Fig. (a), he delay-ime conrol is implemened by delaying he urn-off of swiches S S and S S3 wih respec o corresponding zero crossings of resonan curren so ha boh swiches S S and S S3 are urned on during delay-ime inervals [T -T 1 ] and [T 3 -T 4 ] shoring he secondary of ransformer TR. This conrol mehod is easy o implemen since i requires modulaion of only wo secondary-side swiches. As illusraed in Fig. (a), swiches S S and S S3 are modulaed o provide necessary ime delay, while swiches S S1 and S S4 are operaed wih complimenary gae signals o ha of swiches S S and S S3, respecively. Because swiches S S1 and S S4 are no acively modulaed, hey can be replaced by diode recifiers, which furher simplifies he circui and may be beneficial in some applicaions. However, since in his asymmerical-gaing conrol implemenaion, swiches S S and S S3 operae wih a greaer duy cycle compared o swiches S S1 and S S4, hey also carry greaer average currens and, consequenly, exhibi increased hermal sress compared o swiches S S1 and S S4 and require beer hermal design. The uneven hermal sress of he secondary-side swiches can be eliminaed by implemening a symmericgaing conrol shown in Fig. (a). In his implemenaion, all secondary-side swiches operae wih he same duy cycle of 5%. The delay-ime conrol is implemened by delaying he urn-off of swiches S S1 and S S wih respec o corresponding zero crossings of resonan curren so ha swiches S S and S S3 are urned on during he delay-ime inerval [T -T 1 ] and swiches S S1 and S S4 are urned on during he delay-ime inerval [T 3 -T 4 ] shoring he secondary of ransformer TR. In his implemenaion, if advanageous, swiches S S3 and S S4 can be replaced by diode recifiers. To faciliae explanaion of operaion, Fig. 3 shows he opological sages of he converer wih he proposed delayime conrol during a half of he swiching period. The converer exhibis hree opological sages. In he firs S P1 S P3 T T 1 T T 3 T 4 (a) S P4 S P S S1 S S S S3 S S4 Ts T T 1 T T 3 T 4 (b) Fig.. Swich-gaing and resonan-inducor curren waveforms of seriesresonan converer wih proposed delay-ime conrol: (a) asymmeric gaing and (b) symmeric gaing. opological sage, shown in Fig. 3(a), ha occurs during he delay-ime period [T -T 1 ], he secondary of he ransformer is shored. As a resul, no energy is ransferred from he -C R resonan ank o he oupu and he resonan ank is driven by inpu volage only. The second opological sage, shown in Fig. 3(b), occurs during he [T 1 -T ] period. Since during his sage he resonan curren flows o he oupu, resonanank energy is ransferred o he load. During his sage he volage driving he resonan ank is given by he difference beween inpu volage and primary-refleced oupu volage nv O, i.e., by -nv O. In he hird opological sage ha occurs during he [T -T 3 ], shown in Fig. 3(c), he resonan-ank energy coninues o be delivered o he oupu. However, since during his sage he inpu-volage polariy is negaive because of he commuaion of primary swiches a =T, a par of he resonan-ank energy is reurned o he 1454

3 C R v - CR C R v - CR C R v - CR (a) [T -T 1] (b) [T 1-T ] (c) [T -T 3] Fig. 3. Topological sages of series-resonan converer wih proposed delay-ime conrol during half of swiching period when resonan inducor curren is posiive [T -T 3]. inpu. In fac, his circulaing energy is used o achieve ZVS of he primary swiches. During his sage he volage driving he resonan ank is given by he difference beween he negaive inpu volage and primary-refleced oupu volage nv O, i.e., by - -nv O. As seen from Fig. 3(a), because in his opological sage he secondary of he ransformer is shored, he volage across resonan ank C R - during delay-ime inerval [T -T 1 ] is insead of nv O which is he case wih no delayime conrol. Therefore, wih he delay-ime conrol, a higher volage is applied across resonan inducor ank and, consequenly, a higher amoun of energy is sored in resonan inducor. Therefore, a he same inpu volage and swiching frequency, secondary-side delay-ime conrol provides a higher oupu volage compared o he convenional frequency conrol. This boos characerisic makes opimizing circui performance possible by enabling selecion of a higher urns raio in he ransformer o reduce he primary conducion losses and a larger magneizing inducance o reduce he circulaing (i.e., magneizing) curren loss. Because of is boos characerisic, he proposed delay-ime conrol is mos effecive when applied in a low inpu-volage range or in a high oupu-volage range. Specifically, he maximum delay ime, which is nv O nv O approximaely T S /4, where T S is he swiching period, is se a he minimum inpu volage or he maximum oupu volage. This delay ime is progressively reduced for higher inpu volage or lower oupu volage. In ypical applicaions, he delay-ime conrol is no used a he middle and high inpu volages, or nominal and low oupu volages. The proposed conrol mehod can be implemened by eiher analog or digial echnique, or heir combinaion. A microconroller- or DSP-based implemenaion is preferred since he delay ime ha depends on inpu or oupu volage can be easily programmed. III. DERIVATI OF DC VOLTAGE CVERSI RATIO To provide ools for design opimizaion of he seriesresonan converer wih he proposed delay-ime conrol, is dc-conversion raio M=nV O / is derived using he normalized sae-plane analysis. The normalizaion was done wih he following base parameers: Base volage Base impedance Base curren Base ime Base frequency V BASE = Z BASE = Z O = I BASE = = π Base angular frequency ω The normalized variables are defined as: Normalized inpu volage _ 1 Normalized oupu volage _ Normalized resonan-capacior volage v CR_N = Normalized peak resonan-capacior volage Normalized oupu curren I O_N = Normalized resonan inducor curren Normalized delay ime v CR_PK_N = _ Normalized swiching frequency _ = 1455

4 Oher variables and parameers used are defined as: Transformer urns raio n = VCR VCR_PK Qualiy facor -ime sage (Fig. 3(a)) angle α = ω O [T -T 1 ] Energy-delivery sage (Fig. 3(b)) angle β = ω O [T 1 -T ] Energy-circulaing sage (Fig. 3(c)) angle γ = ω O [T -T 3 ] Half swiching period angle λ = α β γ = ω = π Figure 4, shows he normalized sae rajecory of he converer during one half of a swiching half cycle. Since he proposed converer exhibis hree opological sages during a half swiching cycle, rajecory consiss of hree corresponding arcs, as shown in Fig. 4. I should be noed ha he ceners of hese arcs are on he v CR_N axis wih he disances from he origin ha are equal o he respecive normalized volage across resonan ank -C R. Since according o Figs. 3(a)-(c), he resonan ank volages during he hree opological sages are, -nv O, and -nv O, respecively, he ceners of he corresponding arcs in he normalized v CR_N _N sae plane are a (, 1), (, 1-M), and (,-1-M). To be able o complee he consrucion of he sae-plane rajecory in Fig. 4, i is necessary o deermine radius R 1 of he arc ha corresponds o he sage in Fig. 3(a) which is he firs sage in he half cycle. To faciliae his derivaion, Fig. 5 shows resonan volage v CR and curren waveforms x V CR_PK_N M _N = M M -V CR_PK_N α β β p γ V CR_N R R 3 R h R 1 _N Fig. 4. Sae plan represenaion for one half of swiching cycle [T -T 3] where v CR_N and _N are normalized resonan capacior C R volage and resonan inducor curren, respecively. -VCR_PK Fig. 5. Seady-sae waveforms of resonan-capacior volage V CR and resonan-inducor curren during half swiching period where resonan-inducor curren is posiive (>). during a half swiching cycle when resonan-inducor curren is posiive. As can be seen from Fig. 5, during he shown half swiching period, he posiive resonan-inducor curren coninuously charges he resonan capacior so ha he volage across resonan capacior increases from is negaive o is posiive peak, i.e., changes for V CR_PK. The relaionship beween he resonan-capacior volage change and sored charge during he half swiching cycle is given by Area 1 Area T T 1 T T 3 _ (1) or 1 _, () where Area1 and Area are defined in Fig. 5. Since during he delay-ime opological sage shown in Fig. 3(a), i.e., during he [T -T 1 ] inerval, he resonan-inducor curren is given by sin _ sin, (3) where, as shown in Fig. 5, iniial capacior volage V CR ()=V CR_PK, Area1 can be calculaed as 1 _ sin. (4) Area can be calculaed by recognizing ha he oupu (load) curren refleced o he primary is he average of he resonan inducor curren over a half swiching period. Since flows hrough he oupu only during he inerval [T 1 -T 3 ], he refleced oupu curren a he primary side is given by T / S (5) From equaions ()-(5), i follows ha I O n Area = T / S 1456

5 _ sin _, (6) which afer normalizaion wih replacing 1 and assuming ha =T = can be wrien as 1 sin θ θ λ. (7) Finally, from (7), normalized peak resonan-capacior volage can be solved as λ _. (8) From he normalized sae-plane diagram in Fig. 4, i follows ha radii R 1, R, and R 3 are relaed o V CR_PK_N as R 1 = V CR_PK_N 1, (9) R = =, (1) R 3 = V CR_PK_N M 1. (11) By using he law of cosine for he riangle ha is formed by radii R and R 3, as well as angles ββ P and γ, dc-conversion raio M of he series-resonan converer wih he proposed delay-ime conrol can be derived as cos π, (1) where. (13) Since λ = α β γ, Eq. (1) can be rewrien as 4 cos π λ, (14) Using Eqs. (9), (1), and (11), Eq. (14) can be expressed as V CR_PK_N 1 M MV CR_PK_N 11cosα) V 1M V CR_PK_N 1 M MV CR_PK_N 1cosα cos λ α β P. (15) Because an explici soluion for dc-conversion raio M = nv O / given by Eq. (15) is no available, i is numerically calculaed for a given qualiy facor Q and normalized delay ime _N =α/(λ)= /T S. As examples, Figs 6(a) and (b) show he plos of dc conversion raio M as funcion of normalized swiching frequency and normalized delay ime _N as a parameer for Q=1 and Q=., respecively. When delay ime is zero (α=, =), he converer characerisic is he same as ha of a convenional series resonan converer. As delay ime increases, dc gain M increases and exhibis a boos characerisic. To illusrae he effeciveness of he delay-ime conrol o reduce conrol-frequency range, Figs. 7 (a) and (b) show, respecively, he conrol-frequency range of he LLC converer and he proposed series-resonan converer wih delay-ime conrol designed for -45-V inpu-volage range and 13.8-V oupu. For comparison, magneizing inducance L M was chosen o be four imes larger han he resonan inducance in he case of LLC resonan converer, whereas magneizing inducance L M of he proposed series-resonan converer is assumed infinie. For boh converers urns raio of he ransformer is n=n 1 /N =1. Operaing poins marked A, B, and C in Figs. 7(a) and (b) represen operaing poins when he converers deliver full power from inpu volage V, 3 V, and 45 V, respecively. As can be seen from Figs. 7(a) and (b), he series-resonan converer wih he proposed delay-ime conrol exhibis a significanly narrower frequency range compared o ha of he LLC converer. Specifically, he frequency range of he converer wih delay-ime conrol is from 1.5 (operaing A) o 1.6 (operaing poin C), whereas he corresponding range for he convenional LLC is from.67 o 1.71, i.e., he proposed delay-ime conrol reduces he range for more han eigh imes (1.4/.1 8.7). M = =.35 =.15 = =.3 (a) (b) Q = =. = M = =.15 =.35 = =.3 Q = = 1 = Fig. 6. Calculaed dc-volage conversion raio characerisics of seriesresonan converer wih proposed delay-ime conrol for Q-facor: (a) Q=.; (b) Q=

6 M = BI-DIRECTIAL POWER FLOW A = 4 Q = SP1 SP4 SS1 SS4 1 TR V 1 CF1 CF C R C R1 V B M = A B.1 C (a) Q=. Q=.45 Q=1.1 (b) Fig. 7. Comparison of conrol-frequency ranges of: (a) convenional LLC resonan converer; (b) proposed series-resonan converer wih delay-ime conrol. Poins A, B, and C represen operaing poins when converers deliver full power from inpu volage V, 3 V, and 45 V, respecively. Oupu volage of boh converers is V O=13.8 V and heir ransformer s urns raio is n=n 1/N =1. IV. BI-DIRECTIAL IMPLEMENTATI Because he series-resonan converer wih proposed delay-ime conrol exhibis buck-boos characerisics, i is very suiable for bidirecional power applicaions. However, o enable a proper bidirecional implemenaion, he power sage needs o be slighly modified. As shown in Fig. 8, he modificaion consiss of making he power sage symmerical by placing resonan inducor 1 and capacior C R1 on he primary side and resonan inducor and capacior C R on he secondary side. By having he resonan capaciors in series wih boh primary and secondary windings of ransformer TR, any dc-bias curren a he primary side as well as he secondary side of he ransformer is blocked, i.e., sauraion of ransformer TR is prevened. A microconroller- C Q = Q=., =.165 Q=.45, =.75 Q=1.1, = or DSP-based implemenaion is preferred since he roles (funcions) of he primary swiches and he secondary swiches can be easily configured based on he power-flow direcion. V. EXPERIMENTAESULTS The performance of he proposed converer wih he delay-ime conrol was evaluaed on a 69-W prooype designed o operae from he -45-V inpu-volage range and deliver a nominal oupu volage of 13.8-V. Because he specified full load power is relaively low (<1 kw), he halfbridge opology is seleced, as shown in Figure 9. The resonan frequency of he prooype was se a f O =4 khz. To make dc volage conversion raio M equal o 1 when he inpu volage is approximaely 6 V, 9:1 urns raio of ransformer TR is chosen. As a resul, he delay ime of he secondary-side swiches is se o zero when he converer operaes from 75-V o 45-V inpu, i.e., when M<1, so ha in his range he proposed converer operaes as a convenional series-resonan converer. However, when he inpu volage drops below 75 V, he conroller sars monoonically increasing he delay ime o provide he boos characerisics necessary o mainain he oupu volage - V 1 S P1, SP PQ35/35-DMR S S1 - SS4 IPW65R41CFD Liz.1mmx3 BSB8NELX 8T, 79 uh C R1 C R S P C R1, C R 1nF/ 94C1P1K S P1 SP S P3 S P1 S P S P3 S P4 S S1 S S S S3 S S4 Fig. 8. Implemenaion of bidirecional series-resonan converer wih proposed delay-ime conrol. CTROLLER N 1 TR TR ETD59/8-3C94 Primary: Liz.1mmx3, 9 urns Secondary: 4 mils 9mm widh Copper foil, 1 urn Lm=8 uh Fig. 9. Experimenal prooype circui. N SS SS1 i S SS SS3 SS4 SS3 C O V C O 45 x uf MLCC-5V V O

7 regulaion wih he seleced urns raio of ransformer TR. As shown in Fig. 9, he prooype is buil using IPW65R41CFD MOSFET (V DS = 65 V, R DS =.41 Ω, C OSS =4 pf, Q rr =1.9 μc) from Infineon for each swich. To obain he desired inducance of resonan inducors of approximaely 79 μh and also o achieve high efficiency a ligh-load, each inducor was buil using a pair of ferrie cores (PQ-35/35, DMR9) wih 8 urns of Liz wire (Φ.1mm, 3 srands) and approximaely 5 mm gap. Liz wire was used o reduce he fringing-effec-induced winding loss near he gap of he inducor core. Transformer TR was buil using a pair of ferrie cores (ETD-59/8, 3C94) wih 9 urns of Liz wire (Φ.1mm, 3 srands) for he primary winding [1 A/div] = V, V O =13.8 V, P O =69 W, f S =51 khz [5 A/div] [5 A/div] =35 V, V O =13.8 V, P O =69 W, f S =59 khz (d) =45 V, V O =13.8 V, P O =69 W, f S =7 khz (a) =4 V, V O =13.8 V, P O =69 W, f S =5 khz (e) Fig. 1. Measured full-load primary-curren and gae-volage waveforms of secondary swiches S S3 and S S4 for inpu volage: (a) = V; (b) = 4 V; (c) = 75 V (d) = 35 V; and (e) = 45 V. scale is 5 μs/div. [5 A/div] [5 A/div].1 (b) =75 V, V O =13.8 V, P O =69 W, f S =48 khz (c) and 1 urns of copper foil (4 mils hickness, 9 mm widh) for he secondary winding. The measured magneizing and leakage inducances a he primary winding are 8 μh and.5 μh, respecively. A film capacior (1 nf, 1 VDC) was used for each resonan capacior, C R1 and C R. Fory-five parallel conneced ceramic capaciors ( μf, 5 VDC) were used for oupu capacior C O. The oupu-volage regulaion ha employs variable-frequency conrol ogeher wih openloop (preprogrammed) delay-ime conrol was implemened by a TMS3F87 microconroller wih 3-bi CPU from TI. Figures 1(a)-(e) show he measured waveform of primary curren and he gae waveforms of secondary swiches S S3 and S S4 of he experimenal circui when i delivers full power from -V, 4-V, 75-V, 35-V, and 45-V inpu, respecively. As shown in Fig. 1(a), a he - V inpu, normalized delay ime _N is approximaely.18. As i can be seen from he gae waveforms, secondary-side swiches S S3 and S S4 operae in complimenary fashion wih a small dead ime beween heir commuaions. The urn-off momen of swich S S3 is delayed afer he zero crossing of primary curren which coincides wih ha of secondary curren i S because he magneizing curren of he ransformer is small due o a relaively high magneizing inducance. 1459

8 EFFICIENCY [%] = 35 V = 75 V = 4 V = V = 45 V V O = 13.8 V OUTPUT CURRENT [A] Fig. 1, he delay-ime conrol reduces he swiching frequency range by limiing he minimum swiching frequency. V. SUMMARY In his paper, a conrol mehod ha offers improved performance of series-resonan converers ha operae wih a wide inpu- and/or oupu-volage range by subsanially reducing heir swiching-frequency range has been inroduced. Reducion in he swiching frequency range is achieved by regulaing he oupu volage wih a combinaion of closed-loop variable-frequency conrol of primary-side swiches and open-loop delay-ime conrol of secondary-side swiches. The performance of he proposed conrol was evaluaed on a 69-W prooype operaing from he -45-V inpuvolage range and providing a nominal 13.8-V oupu. The measured efficiency of he proposed recifier in he 5-1% load range is approximaely beween 91% and 96%. Over he enire inpu-volage range, he full-load swiching frequency varies from 48 khz o 7 khz. Fig. 11. Measured efficiency of experimenal prooype as funcion of oupu curren for differen inpu volages. When he converer operaes from inpu volage of 4 V, _N is decreased o.1, as shown in Fig. 1(b). A inpu volages greaer han 75 V, _N is se o zero, as shown in Figs. 1(c)-(e). Figure 11 shows measured efficiency of he prooype as a funcion of load curren for differen inpu volages. As can be seen from Fig. 11, he converer exhibis he maximum full-load efficiency of 95.8% a 75-V inpu. Figure 1 shows he measured full-load swiching frequency of he experimenal prooype as funcion of inpu volage. The measured full-load swiching frequencies are in he 48-7 khz range over he enire inpu-volage range. As seen from SWITCHING FREQUENCY [khz] P O = 69 W V O = 13.8 V =.18 4 khz 5 = = OUTPUT VOLTAGE [V] Fig. 1. Measured full-load swiching frequency of experimenal prooype as funcion of inpu volage. REFERENCES [1] B. Yang, R. Chen, and F.C. Lee, "Inegraed magneics for LLC Resonan Converer," in IEEE Applied Power Elecronics Conf. Rec., pp [] B. Lu, W. Liu, Y. Liang, F.C. Lee, and J.D. Van Wyk, "Opimal design mehodology for LLC resonan converer," in IEEE Applied Power Elecronics Conf. Rec. 6, pp [3] R. Beiranvand, B. Rashidian, M.R. Zolghadri, S.M.H. Alavi, A design procedure for opimizing he LLC resonan converer as a wide oupu range volage source, IEEE Transacions on Power Elecronics, vol. 7, No. 8, pp , Augus 1. [4] F. Musavi, M. Cracium, D.S. Guaam, W. Eberle, and W.G. Dunford, An LLC resonan DC-DC converer for wide oupu volage range baery charging applicaions, IEEE Transacions on Power Elecronics, vol. 8, No. 1, pp , December 13. [5] J. Deng, S. Li, S. Hu, C.C. Mi, and R. Ma, Design Mehodology of LLC Resonan Converers for Elecric Vehicle Baery Chargers, IEEE Transacions on Vehicular Technology, vol. 63, No. 4, pp , May 14. [6] F.S. Tsai, P. Maeru, and F.C. Lee, Consan-frequency clamped-mode resonan converers, IEEE Transacions on Power Elecronics, vol. 3, No. 4, pp , Ocober [7] B. Yang, P. Xu, and F.C. Lee, Range winding for wide inpu range fron end DC/DC converer, in IEEE Applied Power Elecronics Conf. Rec. 1, pp [8] B.C. Kim, K.B. Park, and G.W. Moon, Asymmeric PWM conrol scheme during hold-up ime for LLC resonan converer, IEEE Transacions on Indusrial Elecronics, vol. 59, no. 7, pp , July 1. [9] I.H. Cho, Y.D. Kim, and G.W. Moon, A half-bridge LLC resonan converer adoping boos PWM conrol scheme for hold-up sae operaion, IEEE Transacions on Power Elecronics, vol. 9, No., pp , February 14. [1] T. LaBella, W. Yu, J. Lai, M. Senesky, D. Anderson, A bidirecionalswich-based wide-inpu range high-efficiency isolaed resonan converer for phoovolaic applicaions, IEEE Transacions on Power Elecronics, vol. 9, No. 7, pp , July