Resonant CLL Non-Inverting Buck-Boost Converter

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1 Jounal of Powe Electonics, ol. 3, No., Januay 203 JPE Resonant CLL Non-Inveting Buck-Boost Convete Masoud Jabbai, Saead Shaifi *, and Ghazanfa Shahgholian * * Depatment of Electical Engineeing, Najafabad Banch, Islamic Azad Univesity, Isfahan, Ian Abstact This pape pesents a esonant non-inveting buck-boost convete in which all switches opeate unde ZCS conditions. In a symmetic configuation, a CLL esonant tank along with an invete am and a ectifying diode ae employed. The diode is tuned off at ZCS and hence the poblem of its evese ecovey is obviated also. As a esult switching losses and EMI ae educed and switching fequency can be inceased. The convete can wok at DCM and CCM depend on the switching fequency and the load-cuent. Expeimental esults fom a 200W/200KHz laboatoy pototype veify opeation of the poposed convete and the pesented theoetical analysis. Key wods: Non-inveting buck-boost, Resonant powe convesions, Soft-switching, ZCS, Powe supply. NOMENCLATURE i, v esonant cuent/voltage. Z chaacteistic impedance. R, load/nomalized esistance. α inductance atio. L esonant inductance. C, C esonant /output capacito. f, w esonant fequency. A DC voltage gain. o DC output voltage. s DC input voltage. ZCS zeo-cuent switching. ZS zeo-voltage switching. ZCT zeo-cuent tansition. ZT zeo-voltage tansition. EMI electomagnetic intefeence. PBBC positive buck-boost convete. RC esonant convete. QRC quasi-esonant convete. DCM discontinuous conduction mode. CCM continuous conduction mode I. INTRODUCTION Buck-boost convete with non-inveting voltage gain is employed in many applications such as battey-backup Manuscipt eceived Jun. 8, 202; evised Oct. 2, 202 Recommended fo publication by Associate Edito Sangshin Kwak. Coesponding Autho: jabbai.masoud@gmail.com Tel: , Najafabad Banch, Islamic Azad Univesity * Depatment of Electical Engineeing, Najafabad Banch, Islamic Azad Univesity, Ian utilities, voltage stabilizes, fuel-cell systems, sola panels, potable appaatus, RF powe amplifies and PFC convetes due to the ability of poviding a wide ange of voltage egulation []-[0]. The basic PWM non-inveting buck-boost convetes ae positive buck-boost convete (PBBC), SEPIC, and Zeta convete. In PBBC two switches and two diodes should be employed while SEPIC and Zeta convete possess two inductos and one coupling capacito []-[]. In [7], a new topology is poposed which includes one inducto and one coupled inducto plus two switches, two diodes and one exta capacito which impoves the instability of PBBC. Howeve, despite of employing additional powe elements all these convetes ae had-switching. To enhance powe density and efficiency, and educe electomagnetic intefeence (EMI) soft-switching techniques ae successfully developed. Soft-switching conditions ae attained by switching unde zeo-voltage (ZS) and/o zeo-cuent (ZCS) []-[26]. In Quasi-Resonant Convetes (QRC), by adding a esonant netwok to the basic PWM S Q Q 2 i i 2 + v - Fig.. Poposed non-inveting buck-boost convete. C i d i D L L 2 C R + v O

2 2 Jounal of Powe Electonics, ol. 3, No., Januay 203 convete soft-switching conditions ae povided []-[4]. This method is simple; howeve, thee ae disadvantages such as highe voltage/cuent stesses and loosing soft-switching conditions at tansient-states. The family of ZT/ZCT convetes ae deived by using a esonant netwok along with auxiliay switch(es) and diode(s). In these convetes the esonances ae unde moe contol and theeby the convete behavio is impoved, howeve the element numbe is inceased [5]-[7]. Classically, a soft-switching non-inveting buck-boost convete can be deived by applying the auxiliay netwok of QRC o that of ZT/ZCT convetes to PBBC, SEPIC, and Zeta convete []-[7]. Howeve, the esult is a topology with many powe elements. Since PBBC has two switches, poviding soft-switching conditions fo both switches needs moe elements. E.g., in a ZCT PBBC, if by employing only one auxiliay cell soft-switching conditions can be povided fo both main switches, the deived convete includes thee switches and thee diodes (to the best knowledge of authos such topology has not been epoted yet). O, SEPIC/Zeta QRC possesses at least thee inductos. In QRCs, the convete main inducto(s) is taken lage enough so that its cuent is assumed constant duing one switching cycle []-[4]. Similaly, in ZT/ZCT techniques the convete main inducto is still a bulky component since the PWM opeation must be held. In Resonant Convetes (RC), soft-switching conditions ae attained by using a esonant netwok as the medium of powe tansfe. A majo advantage is that in RCs no bulky inducto is equied and hence the convete volume and size ae educed [8]-[26]. RCs with high-ode esonant tank such as LLC, LCC, LCT, ae developed to attain/impove the expected featues [2]-[26]. Howeve, almost all RCs ae isolated topologies whee even by omitting the tansfome no common gound is found between input and output teminals. A esonant non-inveting buck-boost convete is pesented in this pape (Fig. ). The poposed topology includes only two switches in a well-known bidge stuctue along with a CLL esonant tank in a symmetic configuation. Both switches commutate at soft-switching conditions as ZCS tun-on and ZCS/ZZCS tun-off. As a esult switching losses and EMI ae consideably educed and switching fequency can be inceased. The ectifying diode at the output is tuned off at ZCS and theeby the poblem of evese ecovey of the FAST diode is popely obviated. Both inductos ae esonant type and hence no bulky inducto is employed. Since two inductos ae employed, anothe degee of feedom is povided in design pocedue. Simila to Cuk, SEPIC, and Zeta convete, the capacito C povides magnetic isolation between input and output teminals []. Moe significantly, C is also a pat of the esonant netwok and possesses a small value. Expeimental esults fom a 200W/200KHz laboatoy pototype veify opeation of the poposed convete and its pesented theoetical analysis. II. PROPOSED CONERTER ANALYSIS The convete can opeate at thee conditions: Discontinuous Conduction Mode (DCM), Continuous Conduction Mode (CCM), and deep-ccm. At deep-ccm, daining powe fom the input voltage souce and supplying load ae pefomed simultaneously which esults in educing cuent stesses and enegy ciculation. Simila to the most of RCs, the DC voltage gain is contolled by adjusting switching fequency. In a pope design, by deceasing the output cuent fom full-load to no-load, the convete opeating state moves fom deep-ccm to DCM. At full-load and at the minimum of the input voltage (the wost conditions), the convete is designed to opeate at deep-ccm; o in othe wods, sets at its maximum powe handling capability. By deceasing the load, o inceasing the input voltage, the convete switching fequency is deceased to peseve the output voltage constant. Reduction in switching fequency leads to CCM opeation. Futhe decease of load o incease of input voltage esults in DCM opeation. The convete opeating conditions (DCM, CCM and deep-ccm) ae defined consideing the wavefom of L 2 cuent (i ). It is assumed that all elements ae ideal and the output capacito is lage enough so that its voltage is constant duing one switching cycle. The following quantities ae defined: L L + L 2 () L a 2 L + L 2 w w, f L C T 2p (2) (3) Z L C (4) R Z (5) A o s (6) A. DCM Opeation Impotant wavefoms and equivalent cicuit of each opeating mode ae illustated in Figs. 2(a) and 2(b). Mode I (t -t 2 ): Pio to t, all semiconducto devices ae OFF. At t, Q is tuned-on at ZCS (i (t )0) and the ectifying diode D stats conducting at ZCS (i d (t )0). The capacito C chages though a esonance with L, L 2. The input voltage souce S supplies the output via L and inceases the enegy stoed in the esonance tank via L 2. At the end of this mode the diode cuent i d becomes zeo.

3 Jounal of Powe Electonics, ol. 3, No., Januay Q L Q L C S C Mode I Mode II Q L Q L S C S C Mode III Mode I Q L Q L S C S C Mode Mode I (a) (b) Fig. 2. (a) Wavefoms of DCM opeation, and (b) Opeating modes. ( ) v ( t) év ( t ) - + a cos w ( t - t ) + é -a ë s o û ë s o û ( w ) ( -a) i ( t) - év ( t) - + a sin ( t - t) Z ë s o û w a( -a) + o ( t - t ) Z Mode II (t 2 -t 3 ): At t 2 the diode is tuned off at ZCS but Q is still conducting until at t 3 the esonant cuent i eaches zeo. Then Q tuns off at t 3 unde the ZCS conditions. é- ( -a) év ( t2) - S ê ë û i ( t) i ( t2) é ê Z ê ê êv ( t) - ë s û ê i ( t2). Z ê v ( t2) - S ê ( a) ë - û ésin( w ( -a)( t - t2)) ê ê cos( w ( -a)( t - t2)) ë û Z i ( t ) t3 - t2 w ( -a) ( -a) v ( t2) - s - 2 tan ( ) (7) (8) (9) (0) Mode III (t 3 -t 4 ): Since i has eached zeo at the end of pevious inteval, by setting the gate of Q 2 at t 3, this switch is tuned ON at ZCS. At the end of this mode the esonant voltage v eaches O. v ( t) v ( t3)cos( w ( -a)( t - t3)) () - ( -a) ( 3) ( ) v t i t sin( w ( -a)( t - t3)) (2) Z - - t4 - t3 cos o w ( -a) v ( t3) (3) é - êp - cos o w ( -a) ê v ( t3) ë û Mode I (t 4 -t 5 ): The diode D tuns on and the enegy stoed in L 2 stats deliveing to the output via L. At t 5 the magnitude of L 2 cuent becomes equal to that of L and thus Q 2 is tuned off at ZCS. v ( t) év ( t ) + a cos( w ( t - t )) -a 4 O 4 ë û o (4) -a i ( t) é v ( t4) + ao sin( w ( t - t4)) Z ë û w a( -a) o (5) + ( t - t4) + i ( t4) Z æ -Z i ( t 4) ö - t5 - t4 sin (6) ç ( -a) O è ø Mode (t 5 -t 6 ): The magnitudes of esonant cuent and diode cuent decease linealy until at t 6 each zeo. At this time D is tuned off at ZCS. v ( t) v ( t ) cte (7) 5

4 4 Jounal of Powe Electonics, ol. 3, No., Januay 203 Fig. 3. CCM opeation. Fig. 4. Opeation at deep-ccm. w a( -a) i ( t) ( t - t5) + i ( t5) (8) Z o -Z i ( t5) t6 - t 5 w a( -a) O (9) Mode I (t 6 -t 7 ): The output capacito C supplies the load. Duation of this inteval is detemined by the contolle so that pope voltage egulation is attained (dead-time contol). by A m. Mode I (t -t 2 ): At t, Q tuns on at ZCS while the diode D is conducting. The capacito C is chaged though a esonance with L and L 2. At the end of this mode the cuent of Q has passed a sinusoidal cycle and again has eached zeo. Hence, Q is tuned off at t 2 unde the ZCS conditions. ( ) v ( t) év ( t) - + a cos w ( t - t) + é -a ë s o û ë s o û (22) B. CCM Opeation By tuning Q on pio to t 6, CCM opeation with highe powe handling capability than DCM is achieved. The key wavefoms ae depicted in Fig. 3. Except mode I, all othe opeating modes ae exactly the same as those of DCM. Fo mode I the equations ae as follows. ( ) ( w ) v ( t) év ( t) - + a cos w ( t - t) + é -a ë s o û ë s o û ( -a) i ( t) - év ( t) - + a sin ( t - t) Z ë s o û w a( -a) + o ( t - t ) + i ( t 6) Z C. Deep CCM Opeation (20) (2) By futhe inceasing switching fequency the convete lies in deep-ccm opeation as shown in Fig.4. Conside the shaded aea in Fig. 4. This Aea shows an inteval in which Q is conducting. At deep-ccm this inteval completely lies in the middle of conduction inteval of D. Thus, simultaneously enegy is dained fom the input voltage souce and load is fed by the enegy stoed in the esonant tank. The convete DC voltage gain at deep-ccm is denoted ( w ) ( -a) i ( t) - év ( t) - + a sin ( t - t) Z ë s o û w a( -a) + o ( t - t ) + i ( t 6) Z (23) p ( t2 - t) w (24) Mode II (t 2 -t 3 ): The diode is conducting until at t 3 its cuent becomes zeo and tuns off at ZCS. v ( t) v ( t ) v ( t ) 2 2 c s o w a( -a) i ( t) ( t - t2) + i ( t2) (26) Z o a (25) -Z i ( t2) t3 - t 2 w a( -a) O (27) Mode III- (t 3 -t 6 ): All othe opeating modes ae exactly the same as those of DCM.

5 Jounal of Powe Electonics, ol. 3, No., Januay ααmax α 0.5 α 0.35 α 0.55 α 0.75 α 0.9 A 3 2 A 0. A Fig. 5. A vesus α max. 0 α 0.5 α 0.35 α 0.55 α 0.75 α 0.9 α A 0.05 Deep CCM CCM Deep CCM α αmax /π Fig. 7. DC voltage gain at deep-ccm vs. /π DCM and CCM bounday DCM /π Fig. 6. DC voltage gain at the DCM-CCM bounday vs. /π. 0. /π Fig. 8. Convete voltage gain behavio fo α0.85. III. DESIGN As pesented by (28), deep-ccm opeation can be attained if the duation of Q conduction is less than o equal to the conduction time of diode D. By numeical solving of (28), a maximum value fo α (α max ) is obtained as a function of the convete DC voltage gain. DC voltage gain at αα max is sketched in Fig. 5. E.g. fo A2, α max 0.34 is obtained which means by choosing α 0.34 the convete can be set at deep-ccm fo A 2. p ( t7 - t6) ( t8 - t5) Þ ( t8 - t5) (28) w By using numeical analysis, DC voltage gain at the bounday of DCM-CCM and deep-ccm ae obtained as Figs. 6 and 7. The design is easily accomplished by using Figs. 5-7 based on the equiements. As an example, conside a 200W voltage egulato fo S 200±0% to O 60±% and f 200KHz. TABLE I SOFT-SWITCHING OPERATION Mode I II III I Step-) Detemining α: By applying AA max 60/80 in Fig. 5, α max is obtained; then α0.85 is selected. Fig. 8 shows the convete behavio and its opeating egions s. the nomalized load (/π). The aea between DCM and deep-ccm detemines the CCM egion. Step-2) Detemining Z : By applying A m A max in Fig. 6, 2.4 is obtained. Then with 20% ovedesign, Z is calculated as Z 602/200W/2.4/ W. Step-3) Detemining L, L 2 : By using α0.85 and f200khz then L 35.24µH and C 8nF ae obtained. Then L 4µH and L 2 235µH ae calculated. Step-4) Detemining C: In ode to have peak-to-peak output voltage ipple equal to fo the wost conditions (almost zeo-load), simulation shows that the value of the output capacito should be C47µF. Soft-switching conditions fo all thee opeating modes ae pesented in TABLE I. DCM CCM Deep CCM Q ZCS on ZCS off off off off ZCS on ZCS D on ZCS off ZCS on Q ZCS on ZCS off off off off ZCS on ZCS D on ZCS off ZCS on Q ZCS ZCS off off off off off ZCS on ZCS D on on ZCS ZCS on

6 6 Jounal of Powe Electonics, ol. 3, No., Januay 203 Buck-Boost j,max (µwb) j 2,max (µwb) TABLE II COMPARISON OF THE Z ETA CONERTER AND PROPOSED CONERTER Cuent oltage Non-Inveting stess (A) stess () C (nf) Q max (µc) Q Q 2 Q Q 2 Poposed Zeta N/A 370 N/A I. EALUATION The poposed convete povides soft-switching conditions fo both switches at tun-on and tun-off switching instants independent fom the load-cuent and opeating voltages. Also, ZCS tun-off condition fo the output diode obviates the poblem of evese-ecovey. The passive components constitute a high-fequency esonant CLL tank with a elatively small size. Non-inveting step-down/up voltage gain is attainable fom DCM to deep-ccm. In Table II, the designed convete is compaed with an ideal PWM Zeta convete. The Zeta convete is chosen since in both convetes an inducto exists at the output and the numbe of passive components is equal. The Zeta convete is designed to have the same opeating conditions as 200W, 00KHz, and voltage gain of 60/200. The switching losses ceated due the had-switching opeation of Zeta convete ae neglected and it is supposed this convete can opeate at 00KHz popely. The inductos of the Zeta convete ae also set the same as those of the poposed convete but in ode to povide acceptable opeating conditions its coupling capacito is ascetained to have less than 5% voltage ipple. Accoding to Table II, the sum of cuent stesses of Q and Q 2 in the poposed convete ae almost equal to the cuent stess of the switch of Zeta convete. Hence, it can be supposed that the switch cuent stess of the Zeta convete is shaed between the switches of the poposed convete. It implies no additional enegy ciculation is ceated in the poposed esonant convete and thus no additional conduction losses ae ceated too. The maximum magnetic flux j max L I max and maximum electic chage Q max C max detemine the size of inducto and capacito espectively. Accoding to Table II, the size of inductos in the poposed convete and the ideal Zeta convete ae almost the same. Howeve, anothe advantage of the poposed convete it that the size of its coupling capacito is 20 times less which is due its esonant opeation. The disadvantage of poposed convete is that the voltage stess of Q 2 is slightly highe (the additional voltage stesses of the Zeta convete ceated due to the had switching opeation ae neglected).. EXPERIMENTAL RESULTS The employed switches ae IRF840 (500, 4A, R DS(ON) 0.85Ω) in seies with MUR860 (600). The ectifying diode is MUR860 in paallel with a 500pF ceamic capacito fo deceasing its voltage inging. This small capacito does not have any consideable effect on the convete opeation. The passive elements ae C 8nf (Metallized Polypopylene (MKP) type), L 4µH (Coe: Feite 3F3, EI, 3 tuns) and L 2 235µH (Coe: Feite 3F3, EI, 30 tuns). Soft-switching opeation of Q, Q 2 and diode ae pesented in Fig. 9. The spiky cuents appeaed at tun-on instants ae due to the output capacitance of the switches. This is a well-known phenomenon of ZCS bidge stuctues and can be eliminated easily [27]. Q is tuned off at ZCS and Q 2 is tuned off at ZZCS. By esetting the gate signal of Q, its output capacitance is chaged though a esonant with L which esults in a small evese cuent at its tun-off instant. The esonance voltage (v ) and the ipple of output voltage ae pesented in Fig. 0. Fig. pesents the tajectoy of the state vaiables in state-plane. The closed fom of tajectoy shows the convete has a stable opeation. The convete efficiency and its switching fequency vaiations vs. output powe ae illustated in Fig. 2. Accoding to this figue, by inceasing output powe the switching fequency is inceased to hold the output voltage constant and thus the convete opeation state moves fom DCM to Deep-CCM. At DCM the convete efficiency is almost constant about 93% and vaiations of switching fequency vs. output powe ae almost linea. At CCM and Deep-CCM incease of efficiency is expected because the peak-to-aveage of switches cuent is educed. This featue is seen at the beginning of the CCM egion; howeve, a small eduction in efficiency is seen aound the full-load which is the esult of incease of the switches R DS(ON) due to incease of the switches junction tempeatue. I. CONCLUSIONS A non-inveting esonant buck-boost convete with a few numbe of element is pesented. ZCS conditions ae achieved fo all semiconducto devices independent fom the load-cuent and opeating voltages. Expeimental esults fom a laboatoy pototype veified the pesented opeation and theoetical analysis of the poposed convete.

7 Jounal of Powe Electonics, ol. 3, No., Januay ZCS tun-off ZCS tun-on IQ 40 DCM CCM 94 Q Switching fequency (KHz) Efficiency 92 9 Switching fequency (KHz) 90 Deep-CCM Output powe (w) Efficiency (%) ZCS tun-on ZZCS tun-off I Fig. 2. Switching fequency and efficiency vesus output powe. REFERENCES Fig. 9. Soft-switching opeation of Q, Q 2, D, and esonant voltage (2.5 µs/div), 6.67A/div, 200 /div. Fig. 0. Ripple output voltage 2/div (2.5 µs/div). ZCS tun-off I ZS tun-on out Fig.. Tajectoies of state vaiables in the phase plane: i and v (left), i d and v (ight), 6.67A/div, 200 /div. I Id d [] B. Sahu and G. A. Rincon-Moa, A low voltage, dynamic, non-inveting, synchonous buck-boost convete fo potable applications, IEEE Tans. Powe Electon., ol. 9, No.2, pp , Ma [2] W.-C. Lee, S.-J. Jang, S.-S. Kim, S.-W. Lee, and C.-Y. Won, A fuel cell geneation system with a new active clamp sepic-flyback convete, Jounal of Powe Electonics, ol. 9, No., pp , Jan [3] C. Jingquan, D. Maksimovic, and R. W. Eickson, Analysis and design of a low-stess buck-boost convete in univesal-input PFC applications, IEEE Tans. Powe Electon., ol. 2, No. 2, pp , Ma [4] M. Jabbai and H. Fazanehfad, New soft switching step-down/up convete with inheent PFC pefomance, Jounal of Powe Electonics, ol. 9, No. 6, pp , [5] M. Gaboiault and A. Notman, A high efficiency, non-inveting, buck-boost Dc-Dc convete, Applied Powe Electonics Confeence and Exposition, pp. 4-45, [6] R. Paul and D. Maksimovic, Smooth tansition and ipple eduction in 4-switch non-inveting buck-boost powe convete fo WCDMA RF powe amplifie, IEEE ISCAS, pp , [7] C. Restepo, J. Calvente, A. Cid, A. El Aoudi, and R. Gial, A non-inveting buck-boost DC-DC switching convete with high efficiency and wide bandwidth, IEEE Tans. Powe Electon., ol. 26, No. 9, pp , Sep. 20. [8] P.-C. Huang, W.-Q. Wu, H.-H. Ho, and K.-H. Chen, Hybid buck-boost feedfowad and educed aveage inducto cuent techniques in fast line tansient and high-efficiency buck-boost convete, IEEE Tans. Powe Electon., ol. 25, No. 3, pp , Ma [9] Y.-J. Lee, A. Khaligh, and A. Emadi, A compensation technique fo smooth tansitions in a non-inveting buck-boost convete, IEEE Tans. Powe Electon., ol. 24, No. 4, pp , Ap [0] Y.-J. Lee, A. Khaligh, A. Chakaboty, and A. Emadi, Digital combination of buck and boost convetes to contol a positive buck-boost convete and impove the output tansients, IEEE Tans. Powe Electon., ol. 24, No. 5, pp , May [] N. Mohan, T. M. Undeland, and W. P. Robbins, Powe Electonics: Convetes, Applications, and Design, 3d ed. Hoboken, NJ: Wiley, [2] B. T. Lin, Y. S. Lee, A unified appoach to modeling, synthesizing, and analyzing quasi-esonant convetes, IEEE Tans. Powe Electon., ol. 2, No. 6, pp , Nov. 997.

8 8 Jounal of Powe Electonics, ol. 3, No., Januay 203 [3] D. Maksimovic and S. C uk, A geneal appoach to synthesis and analysis of quasi-esonant convetes, IEEE Tans. Powe Electon., ol. 6, No., pp , Jan. 99. [4] K.-H. Liu, R. Ouganti, and F.C. Lee, Quasi esonant convetes-topologies and chaacteistics, IEEE Tans. Powe Electon., ol. 2, No., pp. 62-7, 987. [5] E. Adib, H. Fazanehfad, Zeo-voltage-tansition PWM convetes with synchonous ectifie, IEEE Tans. Powe Electon., ol. 25, No., pp. 05-0, Jan [6] E. Adib, H. Fazanehfad, Family of zeo-voltage tansition pulse width modulation convetes with low auxiliay switch voltage stess, IET Powe Electon., ol. 4, No. 4, pp , Ap. 20. [7] E. Adib and H. Fazanehfad, Family of zeo cuent zeo voltage tansition PWM convetes, IET Powe Electon., ol., No. 2, pp , Jun [8] M. Jabbai and H. Fazanehfad, Family of soft switching esonant DC-DC convetes, IET Powe Electon., ol. 2, No. 2, pp. 3-24, Ma [9] M. Jabbai, Uni ed analysis of switched-esonato convetes, IEEE Tans. Powe Electon., ol. 26, No.5, pp , May 20. [20] M. Jabbai and H. Fazanehfad, New esonant step-down/up convetes, IEEE Tans. Powe Electon., ol. 25, No., pp , Jan [2] S.-K. Kwon, B. Saha, S.-P. Mun, K. Nishimua, and M. Nakaoka, Seies esonant ZCS-PFM DC-DC convete using high fequency tansfome paasitic inductive components and lossless inductive snubbe fo high powe micowave geneato, Jounal of Powe Electonics, ol. 9, No., pp. 8-25, Jan [22] S.-S. Hong, S.-H. Cho, C.-W. Roh, and S.-K. Han, Pecise analytical solution fo the peak gain of llc esonant convetes, Jounal of Powe Electonics, ol. 0, No. 6, pp , Nov [23] H.-S. Choi, Design consideation of half-bidge llc esonant convete, Jounal of Powe Electonics, ol. 7, No., pp. 3-20, Jan [24] F. Dianbo, F. C. Lee, Q. Yang, and F. Wang, A novel high-powe-density thee-level LCC esonant convete with constant-powe-facto-contol fo chaging applications, IEEE Tans. Powe Electon., ol. 23, No. 5, pp , Sep [25] D. Fu, Y. Liu, F. C. Lee, and M. Xu, A novel diving scheme fo synchonous ectifies in LLC esonant convetes, IEEE Tans. Powe Electon., ol. 24, No. 5, pp , May [26] M. Jabbai, H. Fazanehfad, and G. Shahgholian, Isolated Topologies of Switched-Resonato Convetes, Jounal of Powe Electonics, ol. 0, No. 2, pp. 25-3, Ma [27] G. Ivensky, I. Zeltse, A. Kats, and S. Ben-Yaakov, Reducing IGBT losses in ZCS seies esonant convetes, IEEE Tans. Ind. Electon., ol. 46, No., pp , Feb Masoud Jabbai (S 08 M 0) was bon in Isfahan, Ian, in 979. He eceived the B.S. degee fom Kashan Univesity, Kashan, Ian, in 200, and, the M.S. and Ph.D. degees fom Isfahan Univesity of Technology, Isfahan, Ian, in 2003 and 2009, espectively, all in electical engineeing. His eseach inteests include soft-switching techniques in high-fequency high-powe convetes, powe-facto coections, and active powe filtes. Besides, he has vast studies on moden physics, especially on quantum mechanics. One of his eseaches is the family of switched-esonato convetes in powe-electonics. Saead Shaifi was bon in Najafabad, Isfahan, Ian, in 985. He eceived the B.S. and M.S. degees in electical engineeing fom Islamic Azad Univesity, Isfahan, in 2008 and 202, espectively. His cuent eseach inteests include soft switching techniques in dc dc convetes. Ghazanfa Shahgholian was bon in Isfahan, Ian, on Decembe 7, 968. He gaduated with a degee in Electical Engineeing fom the Isfahan Univesity of Technology (IUT), Isfahan, Ian, in 992. He eceived his M.Sc and PhD in Electical Engineeing fom Tabiz Univesity, Tabiz, Ian in 994 and fom the Islamic Azad Univesity, Science and Reseach Banch, Tehan, Ian, in 2006, espectively. He is now an Associate Pofesso in the Depatment of Electical Engineeing, Faculty of Engineeing, Islamic Azad Univesity, Najaf Abad Banch. His teaching and eseach inteests include the application of contol theoy to powe system dynamics, powe electonics and powe system simulation.