Analysis, Design, and Performance Evaluation of Asymmetrical Half-Bridge Flyback Converter for Universal-Line-Voltage-Range Applications

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1 Analysis, Design, Pefomance Evaluation of Asymmetical Half-Bidge Flyback Convete fo Univesal-ine-Voltage-Range Applications aszlo Hube Milan M. Jovanović Delta Poducts Copoation P.O. Box Davis Dive Reseach Tiangle Pak, NC 7709, USA Abstact The asymmetical half-bidge (AHB) flyback convete is an attactive topology fo opeation at highe switching fequencies because it can opeate with zeo-voltage switching of the pimay-side switches zeo-cuent switching of the seconday-side ectifie. In this pape, a detailed analysis design pocedue of the AHB flyback convete fo the univesalline-voltage-ange applications is pesented. The pefomance of the AHB flyback convete is evaluated by loss analysis based on the simulation wavefoms obtained in Simplis expeimentally veified on a laboatoy pototype of a 65-W (19.5-V, 3.33-A) univesal-line-voltage-ange adapte. I. INTRODUCTION The inceasing dem fo size eduction of today s extenal powe supplies such as adaptes/chages fo laptops, tablets, mobile devices, game consoles, pintes, etc., has continued to dive substantial development eseach effots in highefficiency high-powe-density powe convesion. As the silicon-based devices appoach thei theoetical pefomance limit, thei ability to impove the pefomance of the next geneation of powe supplies is diminished. The emeging wide-b-gap devices, such as GaN-based devices, will inevitably bing about futue significant incemental efficiency impovements. Geneally, GaN MOSFETs have consideably lowe gate chage lowe output capacitance than Si MOSFETs, theefoe, they have a good potential fo opeation at highe switching fequencies, consequently, fo size eduction of the powe supplies [1]-[4]. In low-powe offline applications, the flyback topology is the mostly used topology due to its simplicity low cost. To achieve high efficiency at highe switching fequencies, the cicuit paasitic components, such as the leakage inductance of the flyback tansfome, should be exploited to play an active ole in the cicuit opeation. Two flyback topologies enable efficient ecycling of the leakage enegy in the flyback tansfome: the active-clamp (AC) flyback [5]-[10] the asymmetical half-bidge (AHB) flyback [11]-[16]. Both AC AHB flyback topologies can opeate with zeo-voltage switching (ZVS) of the pimay-side switches zeo-cuent switching (ZCS) of the seconday-side ectifie (diode ectifie o synchonous ectifie). Design pefomance evaluation of the AC flyback convete fo the univesal line-voltage ange (90-64 Vms) wee aleady epoted in the liteatue [7]-[9]. Howeve, design evaluation of the AHB flyback convete wee pesented only at constant input voltages [11]- [14] o at naow line-voltage anges [15], [16]. In this pape, a detailed analysis design pocedue of the AHB flyback convete fo the univesal line-voltage ange is povided. The analysis of opeation is illustated by simulation wavefoms obtained in Simplis. Detailed deivation of design equations is also povided. The pefomance of the AHB flyback convete is evaluated on a laboatoy pototype of a 65-W (19.5-V, 3.33-A) univesal-line-voltage-ange adapte. II. ANAYSIS OF OPERATION The cicuit diagam of the AHB flyback convete is shown in Fig. 1. It should be noted that in ac/dc applications the AHB convete in Fig. 1 is poceeded by the font-end stage consisting of the line-voltage ectifie also powe-factocoection (PFC) cicuit, if necessay. In Fig. 1, the esonant inducto includes the leakage inductance of the flyback tansfome T. It should be noted that the cicuit afte the half bidge that is connected in paallel to the bottom switch of the half bidge can also be connected in paallel to the uppe switch of the half bidge. In both cases, the opeation of the cicuit is identical. Key wavefoms that illustate the opeation of the cicuit in Fig. 1 ae shown in Fig.. It can be ecognized that the opeation of the cicuit in one switching cycle T sw can be divided in seven subintevals, as shown in Figs. -4. The coesponding subtopologies ae pesented in Fig. 5. It should be noticed that seconday-side ectifie SR conducts only duing subintevals [T 3 T 4] [T 4 T 5]. A new switching cycle stats at instant t = T 0, when switch S 1 is tuned on. Duing subinteval [T 0 T 1], fom the cicuit equations di ( m ) (1) dv C C i, () the esonant-inducto cuent i esonant capacito voltage can be detemined as [17], V in S 1 Coss1 SR S HB C oss i v m i m m N:1 Fig. 1. Cicuit diagam of AHB flyback convete. T i SR C O V O /17/$ IEEE 481

Fig.. Key wavefoms that illustate opeation of AHB flyback convete.

(6) C Taking into account that i (T 0) 0 (see Fig. 1), (3) (4) can be simplified as V v ( T ) in C 0 sin[ 1( t T0 )] (7) Z1 ( t) [ ( T0 )] cos[ 1( t T0 )].

(9) With appoximation in (9), the appoximated esonantinducto cuent i can be diectly obtained fom (1) as V (1 D) in ( t T0 ). (10) m Fig. 3. Wavefoms fom Fig. 1 exped between instants T 1 T 4.

At instant t = T 1, switch S 1 tuns off. Duing subinteval [T 1 T ], voltage = v DS linealy deceases fom V in to zeo, i.e., i ( T ) v ( t) v ( ) 1 t V HB DS in ( t T1 ), (11) Coss1 Coss voltage v m becomes negative, i.

2 Fig.. Key wavefoms that illustate opeation of AHB flyback convete. V v ( T ) i ( T ) cos[ ( )] t T in C 0 sin[ 1( t T0 )] (3) Z1 ( t) [ ( T0 )] cos[ 1( t T0 )] Z1i ( T0 ) sin[ 1( t T0 )],(4) whee 1 1 (5) ( m ) C m Z 1. (6) C Taking into account that i (T 0) 0 (see Fig. 1), (3) (4) can be simplified as V v ( T ) in C 0 sin[ 1( t T0 )] (7) Z1 ( t) [ ( T0 )] cos[ 1( t T0 )]. (8) Equations (7) (8) can be futhe simplified if esonant capacito voltage is appoximated with its aveage value duing a switching cycle, i.e., t), avg( T vhb avg T DV sw), ( sw) in (. (9) With appoximation in (9), the appoximated esonantinducto cuent i can be diectly obtained fom (1) as V (1 D) in ( t T0 ). (10) m Fig. 3. Wavefoms fom Fig. 1 exped between instants T 1 T 4. Duing subinteval [T 0 T 1], the pimay voltage of tansfome T, v m, is positive (see Fig. 1), i.e., the seconday voltage of the tansfome is negative, theefoe, the seconday-side ectifie does not conduct. At instant t = T 1, switch S 1 tuns off. Duing subinteval [T 1 T ], voltage = v DS linealy deceases fom V in to zeo, i.e., i ( T ) v ( t) v ( ) 1 t V HB DS in ( t T1 ), (11) Coss1 Coss voltage v m becomes negative, i.e., the seconday voltage of the tansfome becomes positive, but lowe than output voltage V o. Theefoe, the seconday-side ectifie does not conduct. At instant t = T, the body diode of switch S stats to conduct. Duing subinteval [T T 3], voltage slightly inceases, consequently, the seconday voltage of tansfome inceases, but it is still smalle than output voltage V o the seconday-side ectifie does not conduct. At instant t = T 3, the seconday voltage of the tansfome inceases to the output voltage V o the seconday-side ectifie stats to conduct. Theefoe, the pimay voltage of the tansfome becomes v m = -NV o. Duing subinteval [T 3 T 4], fom the cicuit equations di NVo (1) dv C C i, (13) the esonant-inducto cuent i esonant capacito voltage can be detemined as [17], 48

(17) C Equations (14) (15) can be futhe deived as i ( t) I, m sin[ ( t T3 ) ] (18) ( t) NVo VC, m cos[ ( t T3 ) ], (19) whee NV ( 3),m [ ( 3)] o T I i T, (0) Z V, (1) C, m Z I,m Z ( ) tan( ) i T 3.

3 S 1 i V in v m m C OSS1 + ( T 1 ) C OSS I (a) i (b) D S v m m (c) i i D S NV o S NV o Fig. 4. Wavefoms fom Fig. 1 exped between instants T 5 T 7. NV v ( T ) i ( T ) cos[ ( )] 3 3 t T o C 3 sin[ ( t T3 )] (14) Z ( t) NVo [ NVo ( T3 )] cos[ ( t T3 )], (15) Z i ( T3 ) sin[ ( t T3 )] whee 1 C (16) Z. (17) C Equations (14) (15) can be futhe deived as i ( t) I, m sin[ ( t T3 ) ] (18) ( t) NVo VC, m cos[ ( t T3 ) ], (19) whee NV ( 3),m [ ( 3)] o T I i T, (0) Z V, (1) C, m Z I,m Z ( ) tan( ) i T 3. () NVo ( T3 ) C OSS1 C OSS + ( T 5 ) (f) (d) I At instant t = T 4, switch S tuns on with ZVS. Duing subinteval [T 4 T 5], the wavefom of esonant-inducto cuent i esonant capacito voltage follows Eqs. (18) (19), espectively. At instant t = T 5, the seconday-side ectifie cuent deceases to zeo the ectifie tuns off with ZCS. As a esult, at t = T 5, i = i m. At the same instant t = T 5, switch S tuns off. It should be noted that if the seconday-side ectifie is a synchonous ectifies SR, the conduction angle of SR is slightly smalle than the inteval [T 3 T 5]. To bette illustate the opeation of the cicuit duing the conduction inteval of the seconday-side ectifie, [T 3 T 5], the wavefoms of the esonant-inducto cuent i esonant capacito voltage ae edawn with moe details in Fig. 6. Duing subinteval [T 5 T 6], voltage = v DS linealy inceases fom zeo to V in, i.e., i ( T ) v ( t) v ( ) 5 t HB DS ( t T5 ), (3) Coss1 Coss wheeas, voltage v DS1 linealy deceases fom V in to zeo. D S1 V in i v m m Fig. 5 Equivalent subtopologies coesponding to subintevals (a) [T 0-T 1], (b) [T 1-T ], (b) [T -T 3], (d) [T 3-T 4], (e) [T 4-T 5], (f) [T 5-T 6], (g) [T 6-T 7]. (g) (e) 483

4 At instant t = T 6, the body diode of switch S 1 stats to conduct. Shotly afte t = T 6, at instant t = T 7, switch S 1 tuns on with ZVS the new switching cycle stats. It should be noted that the implementation of the opeation of the AHB flyback convete fo a wide input-voltage ange equies opeation with vaiable switching fequency. In simulations, the contol cicuit with vaiable switching fequency is implemented with voltage-mode contol by sensing the zeo cossing of the seconday-side ectifie cuent. III. DESIGN AND IMPEMENTATION The design pocedue is illustated on the example of a 65- W (19.5-V, 3.33-A) adapte fo the univesal line-voltage ange (90-64 Vms). Assuming a 10-µF bulk capacito 96% full-load efficiency of the AHB flyback dc/dc convete, the Vms line-voltage ange coesponds to the ectified voltage ange at the input of the AHB flyback convete fom V in,min = 87.5 V to V in,max 375 V. In this design, it is assumed that the minimum switching fequency that occus at the minimum input voltage full load is 00 khz. Design equations ae deived stating fom the volt-second balance of the flyback tansfome, ( 1 D) T NV m sw o m ( ). (4) DT sw whee, N = N P/N S is the tuns atio of the tansfome. The ight-h side of (4) can be futhe expessed as m V m in D D D m 1 ) DT m (, (5) sw whee, it is taken into account that the aveage voltage duing DT sw is appoximately equal to the aveage voltage duing T sw, as it can be obseved in Fig., i.e.,, avg( DT avg T D T sw), ( sw) sw. (6) D It follows fom (4) (5) that the duty cycle D is m NVo NV D o, if m. (7) m The voltage stess on the seconday-side ectifie is (1 D) V V V in V in SR o. (8) N N The fist design step is the selection of tansfome tuns atio N. Fo lowe voltage stess on the seconday-side ectifie, N should be as lage as possible. Howeve, N is limited by maximum duty cycle D max at V in,min. In fact, as the seconday-side cuent flows only duing the (1-D)T sw inteval, D max has to be limited, typically, below 0.7 to 0.8. Fo D max = 0.7 D max = 0.8, N = 3.14 N = 3.59, espectively. In this design, N = 3.5 is selected, which esults in D max = 0.78 V SR,max = 107 V. The second design step is the selection of the magnetizing inductance m of the tansfome. Fom the wavefom of the magnetizing cuent i m in Fig., the peak valley values of i m duing a switching cycle can be obtained as Im NV I o m, peak Im,avg (1 D) (9) N m Im NV I o m, valley Im,avg (1 D), (30) N m espectively. The aveage value of i m duing a switching cycle, I m,avg = I o/n in (9) (30), can be deived as follows. isr N ( im i ) N im i N Im,avg, (31) whee, it is taken into account that the aveage value of the esonant cuent i duing a switching cycle is equal to zeo. Fo ZVS tun-on of switch S 1, the valley value of the magnetizing cuent has to be negative, I m,valley < 0. Theefoe, using (30), the magnetizing inductance is obtained as N V (1 max ) o D m 39.4H. (3),max fsw Afte a few iteations of Simplis simulations fo ZVS tun-on of switch S 1, m = 36 µh is selected. The thid design step is the selection of the components of the seies esonant cicuit -. Duing the conduction inteval of the seconday-side ectifie, the wavefoms of the esonant-inducto cuent i esonant capacito voltage, shown in Fig. 6, ae detemined by Eqs. (16)-(). Accoding to the cuent wavefoms in Fig. 6, the aveage value of cuent i SR duing a switching cycle can be expessed as isr N ( im i ), (33) i (,m 3) ( ) T T I T N im i N 4 (1 D) T sw Fig. 6. Wavefoms of esonant-inducto cuent i esonant-capacito voltage duing conduction inteval of seconday-side ectifie. 484

5 whee, it is ecognized that the aea enclosed by the diffeence of cuents i m-i in inteval (1-D)T sw can be appoximated as the sum of a tiangle a half sine wave. In (0) (), cuent i (T 3) is equal to the peak value of the magnetizing cuent detemined by (9), wheeas, cuent I,m can be obtained fom (18) as i ( T ) I 3,m. (34) sin( ) Angle in (34) can be obtained by obseving Fig. 6 as T 1 (1 D ) sw. (35) T Combining (33)-(35), the following elationship can be obtained i ( T3 ) I T i ( T3 ) o sw. (36) T 1 N T 4 sin (1 D) sw T Using (36), esonant peiod T is obtained as T = µs. The value of is typically 1%-% of m. Fo example, selecting = % of m, i.e. = 0.7 µh, is obtained as T C 133 nf 4. (37) Afte ZVS design optimization in Simplis, = 180 nf is selected. The tansfome is implemented by using plana coe EQ5/PT (3C96) with 6-laye PCB winding (7 pimay tuns swiched between seconday tuns. The measued leakage inductance of the tansfome is lk = 1.4% of m, i.e. = 0.5 µh, which is smalle than the value of = 0.7 µh used in the simulations. Theefoe, esonant capacito is implemented with an inceased capacitance of 70 nf. The pimay-side switches ae implemented with TPH306 (600V, 150 mω) GaN HEMT devices fom Tansphom the seconday-side ectifie is implemented with BSC093N15 (150V, 9.3 mω) MOSFET fom Infineon. IV. OSS ANAYSIS The loss analysis includes the conduction gate-dive losses of pimay-side switches seconday-side ectifie, winding coe losses of the tansfome, ESR-loss of the output filte capacito at full load. Due to ZVS-tun-on of pimay-side switches, geneally, low tun-off switching loss of GaN devices [4], the switching losses of pimay-side switches can be neglected. Due to ZCS, the switching losses of seconday-side ectifie can be also neglected. All conduction losses ae calculated by using ms values of elevant cuents obtained with Simplis simulations. The coe loss of the tansfome is calculated by using the coe-loss calculation softwae fom Feoxcube [18], [19]. The cicuit vaiables elevant fo the loss calculations ae summaized in Table I. In addition to the ms cuents of pimay-side switches S 1 S, seconday-side synchonous ectifie SR, esonant inducto, output-filte capacito C o, Table I also includes the peak-to-peak value of the magnetizing inducto cuent, ΔI m, the peak-to-peak value of the esonant capacito voltage, ΔV C, the peak-to-peak value of the magnetic flux density of the flyback tansfome, ΔB, duty cycle D, switching fequency f sw. As shown in Table I, the switching fequency ange fo the input-voltage ange of V at full load is khz. The beakdown of losses is summaized in Table II. It should be noted in Table II that the coe loss of the flyback tansfome significantly inceases at highe input voltages. The calculated dc-dc efficiency fom the output of the linevoltage ectifie to the load is also included in Table II plotted in Fig. 7. It can be seen in Fig. 7 that the dc-dc efficiency deceases at highe input voltages, which is the esult of the inceased coe loss of the tansfome. TABE I CIRCUIT VARIABES REEVANT FOR OSS CACUATION V in [V dc ] I S1,ms [A] I S,ms [A] I,ms [A] I SR,ms [A] I Co,ms [A] I m [A] V c [V] f sw [khz] D B[mT] TABE II BREAKDOWN OF OSSES V in [V dc ] P S1,cond [mw] P S,cond [mw] P S1+S,Qg [mw] P SR,cond [mw] P SR,Qg [mw] P Co,es [mw] P coe [mw] P cu,p [mw] P Cu,S [mw] P loss, T [W] P loss, DC-DC [W] η DC-DC [%]

97 DC-DC [%] 96 95 94 93 87.5 170 35 375 V in [V] Fig. 7 Calculated (solid line) measued (dashed line) DC-DC efficiency at full load. V. EXPERIMENTA RESUTS Key measued wavefoms at V in=87.

These wavefoms nicely illustate the ZVS tun-on of the pimay-side switches, except at V in,max = 375 V, whee switch S 1 tuns on with a small voltage.

8, the seconday-side synchonous ectifie cuent i SR also contains cuent spikes at the tun-on tunoff instants of the seconday-side ectifie, which is the esult of the chaging dischaging of the

6 97 DC-DC [%] V in [V] Fig. 7 Calculated (solid line) measued (dashed line) DC-DC efficiency at full load. V. EXPERIMENTA RESUTS Key measued wavefoms at V in=87.5 V, 170 V, 35 V, 375 V, full load ae pesented in Fig. 8. These wavefoms nicely illustate the ZVS tun-on of the pimay-side switches, except at V in,max = 375 V, whee switch S 1 tuns on with a small voltage. The ZCS opeation of the seconday-side synchonous ectifie can be also obseved in Fig. 8. Howeve, as shown in Fig. 8, the seconday-side synchonous ectifie cuent i SR also contains cuent spikes at the tun-on tunoff instants of the seconday-side ectifie, which is the esult of the chaging dischaging of the seconday-side ectifie paasitic capacitance, which was neglected in the simulations. DC-DC efficiency measuements ae shown in Fig. 7. The measued efficiency is in excellent ageement with the calculated efficiency at 170-V 35-V input voltages. At V in,min = 87.5 V, the measued efficiency is lowe than the measued efficiency due to the additional conduction losses in the tansfome windings teminations, which wee neglected in the simulations. Finally, at V in,max = 375 V, the measued efficiency is slightly lowe than the calculated efficiency, which is the esult of the tun-on of switch S 1 with non-complete ZVS as shown in Fig. 8(d). Fig. 8(b) Measued wavefoms at V in=170v full load Fig. 8(c) Measued wavefoms at V in=35v full load. Fig. 8(a) Measued wavefoms at V in=87.5v full load. Fig. 8(d) Measued wavefoms at V in=375v full load. 486

7 The contol cicuit is implemented in open loop by geneating the gate signals fo the pimay-side switches the seconday-side synchonous ectifie though a DSP a coesponding GUI softwae. VI. SUMMARY In this pape, a detailed analysis design pocedue of the AHB flyback convete fo the univesal line-voltage ange is povided. The analysis of opeation is illustated by simulation wavefoms obtained in Simplis. It is shown that the pimayside switches opeate with zeo-voltage switching (ZVS), wheeas, the seconday-side ectifie opeates with zeocuent switching (ZCS), esulting in significantly educed switching losses. The implementation of opeation of the AHB flyback convete fo a wide input-voltage ange equies opeation with vaiable switching fequency. In simulations, the contol cicuit is implemented with voltage-mode contol by sensing the zeo cossing of the seconday-side ectifie cuent. Detailed deivation of design equations is also povided. The pefomance of the AHB flyback convete is evaluated by loss analysis based on simulation wavefoms obtained in Simplis. The coe loss of the tansfome is calculated by using the coe-loss calculation softwae fom Feoxcube [18]. It is shown that at highe input voltages, the coe loss of the tansfome significantly inceases, esulting in educed efficiency. Expeimental wavefoms efficiency measuements obtained on a 65-W (19.5-V, 3.33-A) laboatoy pototype of the AHB flyback convete fo the univesal-linevoltage ange ae also pesented. The expeimental contol cicuit is implemented in open loop by geneating the gate signals fo the pimay-side switches the seconday-side synchonous ectifie though a DSP a coesponding GUI softwae. VII. ACKNOWEDGMENT The authos appeciate the help of M. Haibin Song fom the Delta Shanghai Design Cente fo building the laboatoy pototype of the expeimental cicuit. REFERENCES [1] M.A. Khan, G. Simin, S.G. Pytel, A. Monti, E. Santi, J.. Hudgins, New development in Gallium Nitide the impact on powe electonics, Poc. Powe Electonics Specialists Conf. (PESC), Jun. 005, pp [] N. Ikeda, Y. Niiyama, H. Kambayashi, Y. Sato, T. Nomua, S. Kato, S Yoshida, GaN powe tansistos on Si substates fo switching applications, Poc. IEEE, vol. 98, no. 7, pp , Jul [3] X. Huang, Z. iu, Q. i, F.C. ee, Evaluation application of 600 V GaN HEMT in cascode stuctue, IEEE Tans. Powe Electonics, vol. 9, no 5, pp , May 014. [4] X. Huang, Z. iu, F.C. ee, Q. i, Chaacteization enhancement of high-voltage cascode GaN devices, IEEE Tans. Electon Devices, vol. 6, no, pp , Feb [5] K. Yoshida, T. Ishii, N. Nagagata, Zeo voltage switching fo flyback convetes, Poc. Int l Telecom. Enegy Conf. (INTEEC), pp , Oct [6] R. Watson, F.C. ee, G. Hua, Utilization of an active-clamp cicuit to achieve soft switching in flyback convetes, IEEE Tans. Powe Electonics, vol. 11, no 1, pp , Jan [7] P. Alou, O. Gacia, J.A. Cobos, J. Uceda, M. Rascon, Flyback with active clamp: a suitable topology fo low powe vey wide input voltage ange applications, Poc. Applied Powe Electonics Conf. (APEC), pp. 4-48, Ma. 00. [8] J. Zhang, X. Huang, X. Wu, Z. Qian, A high efficiency flyback convete with new active clamp technique, IEEE Tans. Powe Electonics, vol. 5, no 7, pp , Jul [9] X. Huang, J. Feng, W. Du, F.C. ee, Q. i, Design consideations of MHz active clamp flyback convete with GaN devices fo low powe adapte applications, Poc. Applied Powe Electonics Conf. (APEC), pp , Ma [10] J.J. Zhang D.M. Kinze, Zeo voltage soft switching scheme fo powe convetes, U.S. Patent 9,379,60, Jun. 8., 016. [11] D.H. Seo, O.J. ee, S.H. im, J.S. Pak, Asymmetical PWM flyback convete, Poc. Powe Electonics Specialists Conf. (PESC), pp , Jun [1] T.M. Chen C.. Chen, Analysis design of asymmetical half bidge flyback convete, IEE Poc. Elect. Powe Appl., vol. 149, no 6, pp , Nov. 00. [13] X. Xu, A.M. Khambadkone, R. Ouganti, An asymmetical half bidge flyback convete with zeo-voltage zeo-cuent switching, Poc. Industial Electonics Conf. (IECON), pp , Nov [14].M. Wu C.Y. Pong, A half bidge flyback convete with ZVS ZCS opeations, Poc. Int l Conf. Powe. Electonics, pp , Oct [15] J. Cho, J. Kwon, S. Han, Asymmetical ZVS PWM flyback convete with synchonous ectification fo ink-jet pinte, Poc. Powe Electonics Specialists Conf. (PESC), pp , Jun [16] S. Buso, G. Spiazzi, F. Sichiollo, Study of the asymmetical half-bidge flyback convete as an effective linefed solid-state lamp dive, IEEE Tans. Ind. Electonics, vol. 61, no 1, pp , Dec [17] N. Mohan, T.M. Undel, W.P. Robbins, Powe Electonics: Convetes, Applications, Design. Ney Yok, NY: John Wiley & Sons, [18] Feoxcube Softwae Design Tool, SFDT 010 [Online]. Available: sign/action.do?action=gotopage&pagetype=_en&pagename= design-1 [19] M. Albach, T. Dubaum, A. Bockmeye, Calculating coe losses in tansfomes fo abitay magnetizing cuents a compaison of diffeent appoaches, Poc. Powe Electonics Specialists Conf. (PESC), pp , Jun

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