Primary-Conrolled High-PF Flyback Converers eliver Consan c Oupu Curren Claudio Adragna SMicroelecronics Via C. Olivei, 2 Agrae Brianza (MB), Ialy el.: +39 / (39) 63597. Fax: +39 / (39) 636564. E-Mail: claudio.adragna@s.com URL: hp://www.s.com Keywords «Converer conrol», «Power facor correcion», «Lighing» Absrac his paper describes a conrol mehod of high-power-facor flyback converers for regulaing heir dc oupu curren using only quaniies available on he primary side. he purpose is o achieve opo-less consan-curren regulaion in isolaed offline drivers of LE lamps for bulb replacemen where a power facor >.9 is required. Inroducion Offline drivers of LE-based lamps for bulb replacemen are ofen required o achieve a power facor greaer han.9 and o provide safey isolaion; a he same ime, for cos reasons, i is desirable o regulae he oupu dc curren required for a proper LE driving wihou closing a feedback loop. In his way, he curren sensing elemen, he volage reference and he error amplifier on he secondary side, as well as he opocoupler ha ransfers he error signal o he conrol circui locaed on he primary side are no longer needed (opo-less regulaion). he high-power-facor (high-pf) flyback converer, whose principle schemaic is shown on he lefhand side of figure 1, is a opology ha mees he requiremens on power facor and isolaion wih a simple and inexpensive power sage. In his converer, like in any high-pf opology, here is no an energy reservoir capacior direcly conneced o he inpu recifier bridge, so ha he volage applied o he power sage is a recified sinusoid. o achieve high-pf, he inpu curren mus rack he inpu volage, hus originaing a ime-dependen inpu-o-oupu power flow. As a resul, he oupu curren ineviably conains a large ac componen a wice he mains frequency. Vac R1 R2 Vin Cf Vou LOA Iou Secondary curren peak envelope I pks ( θ ) Secondary recifier curren Primary curren peak envelope I pkp ( θ ) RZC Primary swich curren I p (,θ ) c oupu curren I ou CONROL EVICE SW Cycle-by-cycle average primary curren C Rs SWICH ON OFF Fig. 1: High-PF flyback converer: principle schemaic (lef) and key curren waveforms (righ)
As of oday, conrol algorihms able o regulae he dc oupu curren of a flyback converer using only quaniies available on is primary side (opo-less consan-curren regulaion) are known in he paen lieraure ([1]-[12]) only when i is operaed wih a subsanially dc inpu volage and oupus a subsanially dc oupu curren. he mehod given in [1] and deeply discussed in [2] is considered he preferred one. All hese mehods, however, do no correcly apply o he high-pf flyback converer, where he inpu volage is a full-wave recified sinusoid and he oupu curren, as previously said, mus have a large ac componen. his paper presens a novel primary conrol mehod able o regulae he dc value of he oupu curren in a high-power-facor flyback converer, hus enabling opo-less consan-curren regulaion in his converer as well. he heory of operaion of he high-power-facor flyback converer is no reaed and he equaions relaed o is operaion are provided direcly. Please refer o [13] for a deailed descripion and explanaion. he same symbolism used in [13] is used whenever possible. o simplify he noaion, all he quaniies depending on he insananeous line volage will be considered as a funcion of he phase angle θ = 2 f L. ime is explicily considered in quaniies varying in a swiching cycle. efiniion of he conrol objecive he primary and secondary currens of a high-power-facor flyback converer conrolled according o he scheme considered in [13] are skeched on he righ-hand side of figure 1 along wih he conducion saus of he primary swich. Assuming θ (, ), according o ha conrol scheme he peak envelope of he primary curren I p (,θ) is given by: = I sin θ I pkp PKp. (1) he inpu curren I in (θ), cycle-by-cycle average of I p (,θ), has a sinusoidal-like shape (see fig. 1), hus a high power facor is achieved. he same preliminary assumpions done in [13] are considered here, excep assumpion 4. We assume valley swiching operaion and in a swiching cycle disinguish he ime (θ) during which curren circulaes on he secondary side and he ime R during which he volage across he primary swich rings (saring jus afer (θ), as he secondary curren has gone o zero), unil he valley of he ringing is reached. he swiching period (θ) is herefore given by: ( ) = ON + R θ +. (2) I is worh reminding ha his scheme resuls in a consan ON-ime of he power swich, ON. he peak envelope of he secondary curren is given by: = n I = I sin θ I pks pkp PKs, (3) where n is he primary-o-secondary ransformer urn raio N 1 /N 2. From (3) and (1) we derive: I PKs = n I PKp. (4) Since he cycle-by-cycle secondary curren, I s (,θ), is he series of ligh blue riangles shown in figure 1, is average value in a swiching cycle is: I o 1 2 = I pks = 1 2 I PKs he dc oupu curren I ou is he average of I o (θ) over a line half-cycle: sin θ. (5) 1 I ou = I o = I PKs sin θ dθ. (6) 2 he conrol objecive is o regulae I ou, (i.e., o make he quaniy on he righ-hand side of (6) consan, independen of he oupu volage V ou, he rms inpu volage V in as well as he swiching frequency f sw (θ) = 1/(θ)), while sinusoidally shaping he envelope of he peak primary curren as per (1) o achieve high power facor and low harmonic disorion of he inpu curren.
he novel conrol mehod he block diagram shown in figure 2 illusraes he basic peak curren conrol loop ha mees he conrol objecive defined in he previous secion. he conrol core is he porion, encircled in he doed box, ha generaes he reference Vcs REF (θ) for he signal Vcs(,θ) represening he primary curren sensed hrough he sense resisor Rs: (, θ ) = Rs I (, θ) Vcs p. (7) he remaining par is a sandard quasi-resonan peak-curren-mode conrol block, where ransformer s demagneizaion (sensed via he R ZC resisor in fig. 1) deermines he urn-on of he power swich (wih an appropriae delay R o achieve valley swiching), while he urn-off is deermined by he curren sense signal Vcs(,θ) reaching he programmed value Vcs REF (θ). Inpu volage sensing ransformer s demag sensing o ransformer s primary winding I CH (θ) ZC ivider A/B Vcs REF(θ) - + elay R S R Q Gae river SW R C Vcs(, θ) I p (, θ) Rs Fig. 2: Block diagram implemening he novel conrol mehod. Figure 3 shows a couple of iming diagrams (a a swiching cycle ime scale on he lef-hand side, a a line cycle ime scale on he righ-hand side) ha help clarify how he circui in figure 2 operaes. Ip(,θ) Is(,θ) Vcs REF (θ)/rs S ON (θ) R B R Vcs REF (θ) Q Ip(,θ) Is(,θ) I ou Fig. 3: iming diagrams (swiching cycle ime-base on he lef-hand side, line cycle ime-base on he righ-hand side) explaining he operaion of he circui in figure 2. he peak primary curren is programmed by he signal Vcs REF (θ) generaed by he divider block A/B ha, on is firs inpu, receives he signal A = K V sinθ P in, pk. (8)
is a porion of he recified inpu volage, whose peak is V in,pk = 2 V in, ypically obained wih a resisor divider (he resisors R 1 and R 2 in fig. 1; K P = R 2 /(R 1 +R 2 ) is he divider raio). On he second inpu, he divider block receives he signal, i.e. he slowly varying dc volage developed across he capacior C by means of is charge/discharge mechanism ha comprises a curren generaor I CH (θ) acive only while curren is circulaing on he secondary side, i.e. during he ime (θ) in which he signal is high, and a resisor R in parallel o C. he curren generaor sources a curren proporional o he signal : = G A = G K V sinθ ICH M M P in, pk. (9) Under seady-sae operaing condiions, he following charge balance holds for C : B R = I CH Solving (1) for and subsiuing (9) yields: B. (1) = GM R KP Vin,pk sinθ. (11) he capacior C is assumed o be large enough so ha he ac componen (a wice he line frequency f L ) of is negligible wih respec o is dc componen B, which is defined as: B GM R KP Vin,pk = B = sin θ d θ. (12) A foriori, he ac componen of a he swiching frequency f sw (θ) caused by he cycle-by-cycle charge/discharge mechanism of C is negligible oo. As a resul, he curren programming reference Vcs REF (θ) is given by: Vcs REF = K A B K A B = K G M R Noe ha he divider gain K is dimensionally a volage. sin θ dθ sin θ. (13) he peak envelope of he primary curren, defined by Vcs REF (θ) / Rs, is herefore sinusoidal, similarly o wha obained wih he conrol scheme considered in [13], and a high power facor is achieved. Combining (13) wih (7), (1) and (4), i is possible o derive: I PKs = n K. (14) Rs GM R sin θ dθ Finally, subsiuing his expression in (6), we find: I n K ou =. (15) 2 Rs GM R his equaion saes ha wih he conrol mehod depiced by he block diagram in figure 2, he dc oupu curren I ou depends only on exernal, user-selecable parameers (n, Rs) and on inernally fixed parameers (G M, R, K ) and does no depend on he oupu volage V ou, nor on he rms inpu volage V in or he swiching frequency f sw (θ) = 1/(θ). herefore, i is possible o conclude ha he proposed mehod, in addiion o providing high power facor and low harmonic disorion of he inpu curren, mees he conrol objecive of providing a regulaed I ou as well.
iscussion of he novel conrol mehod he resul summarized in (15) has been found under some simplifying assumpions. I is expeced ha non-idealiies affecing he real-world operaion cause he acual I ou o deviae from he heoreical value given by (15) and cause dependency on V ou, V in and f sw. heir impac needs o be analyzed. Effec of non-idealiies in he power circui In [2] i is highlighed ha ransformer s imperfec coupling has a major impac on he acual I ou sepoin: due o he leakage inducance, he I pks / I pkp raio - see (4) is lower han he physical urn raio n = N 1 /N 2 and dependen on he operaing condiions. In addiion, here are some oher nonidealiies due o he high-pf naure of he opology. hese effecs are well documened in boos opology [14]-[15] bu no as much in flyback opology, hen hey are addressed here in deails. As wih any high-pf opology, a small region exiss in he converer inpu curren around he line volage zero-crossing where his curren is essenially zero (crossover disorion). Consequenly, such a dead-zone mus exis also for he secondary curren and his secondary dead-zone migh be larger han he primary one. Obviously, hese dead-zones end o lower I ou wih respec o he arge (15). he dead-zone in he primary curren is caused by he absence of ne energy ransiion from he inpu source. In fac, also wih flyback, he primary curren I p (, θ) is negaive during he iniial porion of he swiching period as illusraed in [14] for he boos converer, wih he negaive peak comparable o if no larger han he posiive peak. As a resul, he average curren in hose cycles is essenially zero: energy goes back and forh from he filer capacior C f siuaed jus afer he bridge recifier o he ransformer and vice versa. hus, C f reains a residual volage ha reverse biases he inpu bridge recifier. Addiionally, in his region he demagneizaion signal is so small ha he demagneizaion sensing circui may no properly work, so ha swiching may be sopped. he dead-zone in he secondary curren is caused by he lack of primary-o-secondary energy ransfer near he line volage zero-crossings. I is worh reminding ha a urn-off he energy sored in he ransformer s primary inducance is iniially ransferred o he drain parasiic capaciance unil is volage exceeds V in (θ) + V R and ha curren sars flowing on he secondary side from ha momen on. Around zero-crossings, he peak curren is so low ha he energy sored in he primary inducance a urn-off is no sufficien o charge he parasiic drain capaciance up o and above V in (θ) + V R. he consequence is ha he secondary side does no conduc curren in ha region, and his reducion in he conducion angle of he secondary curren lowers he resuling dc value, as previously said. he lack of primary-o-secondary energy ransfer is expeced o lessen as V ou is reduced and a high line volage. In fac, a lower V ou means a lower V R, and hen less energy is needed o sar conducion on he secondary side. Furher, reducing he inpu curren (which a higher inpu volage and a lower V ou conribue o) he residual volage across C f increases. his enlarges he primary dead-zone bu provides some residual volage o charge he ransformer s primary inducance and make he demagneizaion sensing circui operae properly. Ulimaely, hese phenomena should cause a sligh increase of I ou as he number of LEs is reduced and as V in is increased. Effec of non-idealiies in he conrol circui he circui in figure 2 is supposed o be inegraed in a conrol IC (he CONROL EVICE shown in fig. 1), excep Rs and C : he former because is o be seleced o se I ou a he desired level, he laer because he values required for proper operaion (in he µf) are oo large for inegraion. Some of hese non-idealiies are already exhausively reaed in [2] and are here jus briefly reminded: Propagaion delay in he curren sense circui: during he ime ha elapses from he insan when Vcs(,θ) = Vcs REF (θ) o he insan when he swich SW is urned off he primary curren sill ramps up, so ha i is always I p (, θ) > Vcs REF (θ)/rs emagneizaion deecion delay: any delay in he demagneizaion deecion causes B o increase, hus programming a lower Vcs REF (θ). Addiionally, I ou depends also on he inernal parameers G M, R, K. As o R and G M, he former is an inegraed resisor while he laer is relaed o he value of an inegraed resisor (precisely, i is he
reciprocal of a resisor value). As such, heir individual spread due o producion olerance is high (± 25%) bu he mismach in heir produc can be kep exremely low (< 1%) wih some care in lay ouing he conrol chip. K, he gain of he divider block, is poenially he larges source of error. Is olerance, anyway, can be kep wihin accepable levels wih any of he numerous mehods available o IC echnology. Going ino he deails of his maer is beyond he scope of his paper. esign example and simulaion resuls he proposed conrol mehod has been esed and validaed wih PSIM simulaions on a high-pf flyback designed o mee he specificaion of a ypical low-power driver for high brighness LE. able I summarizes he mos significan elecrical specificaion of he design, able II he significan parameers of he conrol circui used in he simulaion, able III he main elecrical parameers of he power circui deermined using he procedure oulined in [13]. Equaion (15) has been used o deermine he sense resisor Rs. A linearized model has been used for he LE load (see able III). able I: elecrical specificaion of a wide-range-mains, 8.4W high-pf flyback converer Parameer Symbol Value Uni Mains volage range V in,min - V in,max 88-264 V rms Mains frequency f L 5 Hz Regulaed dc oupu curren I ou 7 ma Maximum oupu volage V ou,max 12 V Max. pk-pk oupu curren ripple a 2f L (@V ou,max ) I ou, pk-pk 4 ma Expeced efficiency (@ V in,min, V ou,max ) η 8 % Minimum swiching frequency (@ V in,min, V ou,max ) f sw,min 6 khz Refleced volage (@V ou,max ) V R 12 V Secondary recifier volage drop V f.5 V able II: conrol circui parameers Parameer Symbol Value Uni Inpu volage sensing divider raio K P 4.129 1-3 --- ivider block gain K 1 V Charge generaor ransconducance G M 5 µs ischarge resisor R 1 kω Conrol volage buffer capacior C 2.2 µf Maximum curren reference volage Vcs REF,max 1 V Curren sense resisor Rs 1.3 Ω able III: main power circui parameers Parameer Symbol Value Uni ransformer s primary inducance L p 1.5 mh ransformer s primary leakage inducance L p,lk 45 µh ransformer s primary-o-secondary urn raio n 9.6 --- ransformer s primary-o-auxiliary urn raio n aux 9.6 --- Secondary recifier forward drop V F.5 V Oupu capacior C ou 2x22 µf LE hreshold volage (x LE) V Fh 3.3 V LE dynamic resisance (x LE) R.5 Ω
he diagrams in figures 4 o 6 show he simulaion resuls under differen line and load condiions. Iin(θ) Iin(θ) Ip(,θ) Is(,θ) / 1 Ip(,θ) Is(,θ) / 1 Iou Iou Fig. 4: Simulaion resuls wih 3 LEs (V ou = 1.9 V); @115 Vac (lef), @23 Vac (righ). races (op-down): inpu curren,,, primary and secondary currens, oupu curren. Iin(θ) Iin(θ) Ip(,θ) Is(,θ) / 1 Ip(,θ) Is(,θ) / 1 Iou Iou Fig. 5: Simulaion resuls wih 1 LE (V ou = 3.6 V); @115 Vac (lef), @23 Vac (righ). races (opdown): inpu curren,,, primary and secondary currens, oupu curren. 115 Vac 23 Vac 115 Vac 23 Vac.7 1 LE 1 Iou.695.69 2 LEs 3 LEs PF.99.98 1 LE 3 LEs.685.97 2 LEs.68 2 4 6 8 1 12 Vou.96 2 4 6 8 1 12 Fig. 6: Oupu regulaion characerisic (lef) and PF vs. operaing condiions (righ) In he end, he simulaion has confirmed he viabiliy of he proposed conrol mehod: he resuls are essenially in line wih he heoreical predicions. Also he effecs of non-idealiies have been confirmed, especially hose relaed o he energy ransfer defici near line volage zero-crossings. Low-frequency oupu curren ripple Curren ripple is a concern when supplying LEs. In paricular, a low-frequency ripple, such as ha a 2f L affecing he curren delivered by he high-pf flyback converer, causes a corresponding ripple in he luminous flux ha would be annoying if visible. herefore, he ac componen of he oupu curren I o (θ) superimposed on he regulaed dc value I ou is worh a closer examinaion o undersand how o conrol i. his ac componen is spli beween he oupu capacior and he LE sring, as shown in he circui on he lef-hand side of fig. 7. As apparen in he iming diagrams of fig. 4 and 5, he swiching frequency ripple is, insead, of no concern and his will be confirmed by he following analysis. Vou
V in (θ) I o (θ) I ou + I ou (θ) I in (θ) P in (θ) P ou (θ) P in = P ou C ou I Cou (θ) LE sring m R d m V Fh V ou I o (θ) I ou (θ) V ou (θ) I ou Fig. 7: Equivalen schemaic of he secondary-side of a High-PF flyback regulaor driving a sring of m LEs (lef); idealized key waveforms explaining inpu-o-oupu power balance (righ) I is possible o sae a basic fac: a significan ac componen I o (θ) a 2f L in I o (θ) is unavoidable in a opology wihou inernal energy sorage like he high-pf flyback under consideraion. o jusify his saemen i is useful o refer o he waveforms shown on he righ-hand side of fig. 7. In a high-pf flyback converer, like in all basic opologies operaed wih high PF, here is no means o sore significan energy on a ime scale relevan o a line cycle (he energy sored in he ransformer is significan wihin a swiching cycle bu negligible in a line cycle). herefore, under he simplifying assumpion of 1% efficiency, i is possible o sae ha a a line cycle ime scale he insananeous oupu power P ou (θ) provided o C ou and he load equals he insananeous power P in (θ) drawn from he line. Noe ha in case here was energy sorage he average oupu power P ou would equal he average inpu power P in bu he insananeous values would no. Assuming PF = 1 for simpliciy, he line volage and curren are in-phase sine waves, hus wih obvious symbolism: P in 2 2 = P = V I sin θ = 2 P sin = P ( 1 cos2θ) = P ( 1 cos2θ) ou in,pk in,pk in in ou, (16) i.e. he insananeous value of he oupu power P ou (θ) swings from zero o wice he average value P ou = P in a a frequency 2f L. he oupu capacior C ou is normally large enough o have a subsanially dc oupu volage V ou. As a consequence, he oupu curren I o (θ) is almos proporional o he insananeous oupu power and, hen, pulsaes in he same way a 2f L. Following he same approach used in [13], he fundamenal harmonic of I o (θ) a 2f L is considered. Expanding (5) in Fourier series, i is found ha is peak ampliude is: ( Kv ) ( K ) H 2 Io,pk = 2 Iou, (17) F2 v wih K v = V in,pk / V R, where V R = n (V ou + V F ). he funcions H2(K v ) and F2(K v ) are defined in [13] and heir raio as a funcion of K v is illusraed in fig. 8. his graph shows ha I o,pk ends o slighly decrease a high inpu volage and as he oupu volage (i.e. he number m of LEs) is reduced. Fig. 8: iagram showing he raio H2(K v ) / F2(K v ) as a funcion of K v.
he dc componen of I o (θ), I ou, flows hrough he LE sring only and concurs o deermine he acual dc oupu volage V ou. Assuming he m LEs are all idenical o one anoher: ou ( R I ) V = m V +. (18) Fh ou he ac componen I o (θ) is spli beween he LE sring ( I ou (θ)) and C ou, according o he divider raio of heir admiances 1 / (m R ) and j 4 f L C ou. herefore he peak-o-peak ampliude of I ou (θ) is: ( 4 f m R C ) ( Kv ) Iou ( K ) ( ) 2 Io, pk H 2 Iou, pk pk = 2 = 4. (19) 1+ 2 F2 v 1+ 4 f m R C L ou Equaion (19) shows ha he 2f L ripple curren injeced ino he LE depends on he inpu volage (K v ), he number of LEs (m, K v ), heir characerisics (R ), and he oupu capaciance C ou. Normally, o mee he requiremen on he low frequency ripple curren, C ou is so large (see able III) ha also is ESR is so low ha boh he capaciive and he resisive high frequency ripple are negligible. Operaion wih a chopped ac inpu volage (riac dimming compaibiliy) he conrol circui in fig. 2 makes he flyback converer work as a curren source. herefore, even wih a chopped ac inpu volage which happens in case he converer is operaed hrough a riac dimmer he converer forces he prese dc oupu curren o he load. In ha case, however i would be desirable o reduce he regulaion sepoin depending on he riac firing angle α: he larger α is, he lower he curren sepoin should be. his can be realized by modifying he circui in he doed box in fig. 2 as shown in fig. 9. L ou I CH (θ) Inpu volage sensing o ivider A/B R C Inpu volage sensing + Vh - elay ML EN EN = freezes SW saus Fig. 9: Modificaion of he circui in he doed box in fig. 2 o reduce I ou sepoin proporionally o he firing angle of a riac ha provides a chopped ac inpu volage. he sensed inpu volage is compared o a hreshold V h and, if i says below he hreshold for a ime longer han ML, i is assumed ha he line volage is missing (because he riac is open) and he EN signal goes low. his freezes he sae of he power swich SW (possibly in he ON-sae o help provide he laching curren for he riac when his is fired) and disconnecs boh he curren generaor I CH (θ) and he discharge resisor R. In his way he volage across C is frozen a he value in he insan when he inpu volage goes o zero. he delay ML is needed o preven he circui from being improperly acivaed near he zero-crossings of he line volage when his is no chopped. Noe also ha his delay is unidirecional: as he sensed volage exceeds V h he enable signal EN goes high immediaely. he ne effec of sopping he charge/discharge aciviy of C can be regarded as an average increase of he discharge resisor R and his, according o (15) leads o a reducion of he prese oupu curren I ou. he diagrams of fig. 1 show he simulaion resuls for differen firing angles.
115 Vac 23 Vac 115 Vac 23 Vac 115 Vac 23 Vac.7 Iou.6.5.4.3.2 α = 45 { α = 9 { α = 135 {.1 1 LE 2 LEs 3 LEs 2 4 6 8 1 12 Fig. 1: Regulaion characerisic of he converer defined in ables I-III for differen riac firing angles Conclusion A conrol mehod of high-power-facor flyback converers for regulaing heir dc oupu curren using only quaniies available on he primary side has been proposed. Afer defining he conrol objecive, he circui able o mee his objecive has been provided, is operaing principle explained and is equaions provided. he proposed conrol mehod has been esed and validaed wih PSIM simulaions on a high-pf flyback designed o mee he specificaion of a low-power driver for high brighness LE. he simulaions have confirmed he heoreical predicions and he viabiliy of he mehod. A sligh variaion of he basic conrol circui ha makes he conrol mehod compaible wih riac dimming has been provided. References [1] A. Pavlin, Swiched Curren Regulaor wih Improved Power Swich Conrol Mechanism, US paen #5729443. [2] A. Bailly, Consan Oupu Curren for Flyback Converers wih Viper31, SMicroelecronics, AN173. [3] M. Weirich, Primary side regulaed power supply sysem wih consan curren oupu, US paen #7525259 [4] K.J. Williams, On-ime conrol for consan curren mode in a flyback converer, US paen #755287 [5] S. Huynh e alii, Primary side consan oupu curren conroller, US paen #7388764 [6]. Yang e alii, Primary-side conrolled flyback power converer, US paen #6853563 [7]. Yang e alii, PWM conroller regulaing oupu volage and oupu curren in primary side, US Paen #6721192 [8] A. Ball, Primary side sensing circui for producing a secondary side consan curren, consan volage oupu, US paen #677283 [9]. Lin, Apparaus and mehod for regulaing consan oupu volage and curren on primary side in a flyback converer, US paen applicaion #2973725 [1] Y. Li e alii, Sysem And Mehod For Conrolling A Curren Limi Wih Primary Side Sensing Using A Hybrid PWM and PFM Conrol, US paen applicaion #2959632 [11] M. Gran, Regulaing oupu curren from a primary side power converer by clamping an error signal, Us paen applicaion #28259656 [12] B. Balakrishnan e alii, Mehods and apparaus for mainaining an approximae consan curren oupu characerisic in a swiched mode power supply, US paen applicaion #2735285. [13] C. Adragna, esign Equaions of High-Power-Facor Flyback Converers based on he L6561, SMicroelecronics Applicaion Noe, AN159. [14] L. Huber, B.. Irving, M.M Jovanović, Effec of Valley Swiching and Swiching-Frequency Limiaion on Line-Curren isorions of CM/CCM Boundary Boos PFC Converers, IEEE ransacions on Power Elecronics, Vol. 24, No. 2, February 29, Pages 339-347 [15] C. Adragna, H-opimizer circuis for PFC pre-regulaors, SMicroelecronics Applicaion Noe, AN1616. Vou