Magamp application and limitation for multiwinding flyback converter

Transcription

1 Mgmp ppliion nd limiion for muliwinding flyk onverer C.-C. Wen nd C.-L. Chen Asr: A new mgmp ehnique for muliwinding flyk onverers is proposed. Idel opering priniple nd nlysis re presened. he pril irui operion is limied due o he nonidel omponen hrerisis. An nlyil model for sudying he phenomenon is provided. Bsed on he model, he mehnism of he oundry ondiion h uses he onverer o e ou of regulion is explored. Experimenl verifiions on W wo-oupu flyk onverer re ondued. hey illusre he effeiveness of he proposed mgmp pproh nd he ury of he presened nlyil model. Lis of symols C C I MA I MPi,, i pine of RC lmp snuer insnneous urren of verge urren of pek urren of he end of he ih ime inervl insnneous urren of L KP, L K1 nd L K, respeively I PA, I 1A, I A verge urrens of L KP, L K1 nd L K, respeively I PPi, I 1Pi, I Pi pek urrens of L KP, L K1 nd L K, respeively he end of he ih ime inervl I iniil urren of he eginning of 1 ime inervl K P, K 1, K indune fors where K p ¼ /L KP, : L SR N 1, N n P, n 1, n K 1 ¼ /L K1 nd K ¼ /L K N L SR mgneising indune of rnsformer sured indune of surle reor SR urn rios of rnsformer where N 1 ¼ n p /n 1 nd N ¼ n p /n swihing period winding urns of rnsformer for primry winding, seondry winding 1 nd seondry winding, respeively i ih ime inervl where i is 1 5 V C volge ross C C inpu DC volge R C resisne of RC lmp snuer V Mi volge ross during he ih ime inervl V 1, V oupu volge 1 nd where V 1 ¼ N 1 V O1, V ¼ N V O r IEE, 5 IEE Proeedings online no. 489 doi:1.149/ip-ep:489 Pper firs reeived 1h Jnury nd in revised form rd June 4 he uhors re wih he Grdue Insiue of Eleronis Engineering nd Deprmen of Eleril Engineering, Nionl iwn Universiy, ipei, iwn L KP, L K1, L K 1 Inroduion lekge indunes of rnsformer for primry winding, seondry winding 1 nd seondry winding, respeively Among he vriey of swihing-mode power onverers, he flyk onverer is fvourie hoie: for design engineers in low power ppliions. he mjor meris of he flyk onverer re: low pr oun, effeive os, quik dynmi response nd simple muli-oupu sruure. In indusril design of he muli-oupu flyk onverer, weighed volge onrol sheme is ofen used o minin regulion for ll oupus. However, i does no redue he ol oupu error y djusing he weighing fors. I only shifs he error o he oher oupus [1]. Anoher disdvnge is h i is hrd o rrnge he rnsformer sruure o mke he oupu volge e in he enre of regulion. Some previous ppers [, ] hve improved he ross-regulion of he muli-oupu flyk onverer. However, in some ppliions, suh s he onord power supply of F-LCD monior, sringen regulion is required o preven he inerferene effe on he disply pnel. A posregulor is dded o mee he regulion requiremens. Among he differen posregulion pprohes, he mgnei mplifier (mgmp) regulor hs een populr for yers. Compred wih oher posregulion shemes, he mgmp posregulor is one of he mos relile, effiien nd os-effeive soluions. In reen dedes, he mgmp pproh hs mosly een pplied in forwrd-ype onverers. Reserh on he use of he mgmp for forwrd onverers hs lso een widely repored, inluding: reseing mehods, design guidelines nd limiions [4 6]. here hs een lile reserh on he use of he mgmp for flyk onverers. A mgmp ehnique for he flyk onverer is presened in [7]. he min drwk is h he min oupu for he PWM feedk is resried o he oupu wih higher volge, even wih ligh red oupu urren. In his pper, new mgmp ehnique for flyk onverers wih muliple oupu windings is proposed [8]. he feedk loop nd winding urn rio n e hosen. his feure provides IEE Pro.-Eler. Power Appl., Vol. 15, No., My 5 517

2 more freedom o hieve opimum performne. For pril design, he opering ondiion is limied due o he nonidel hrerisis of he omponens. Bsi operion priniple Figure 1 shows he digrm of he muliwinding flyk onverer wih mgmp oupu. For simpliiy, wooupu flyk onverer is presened. As we know, in forwrd onverer, he seondry oupus of he min rnsformer n e viewed s volge soures nd rnsfer energy o eh oupu simulneously. However, in he flyk onverer, he opering priniple is ompleely differen. he flyk rnsformer n e viewed s urren soure. he urren ime-shring ehnique is pplied. Figure shows some wveforms in oninuous urren mode ssuming idel omponens. he si operions re desried s follows. V V P g Fig. 1 oupu V S V SR i n P S 1 PWM onrol D 1 V S1 V 1 C 1 n 1 V S n SR V SR D i 1 I 1 V A D mgmp onrol i I C V Digrm of muliwinding flyk onverer wih mgmp d d 1 V A d Fig. Some key wveforms in flyk onverer wih mgmp regulor Inheimeperiodd, he min swih S 1 is on nd he inpu volge hrges he mgneising indune, where d is he urn-on duy yle nd is he swihing period. In he flyk onverer, he min rnsformer is no only ommon rnsformer u lso n induor o supply he energy o he oupus. A his period, he surle reor SR is rese y he volge differene eween he reverse seondry winding volge V S nd he mgmp onrolled volge V A. During he ime period d 1, he swih is urned off nd he energy in he mgneising indune is relesed o he oupu V O1. In his period, he diode D 1 is on nd he seondry winding volge V S1 is lmped he oupu volge V O1. he surle reor SR is in he loking se nd is se wih he volge differene eween he seondry winding volge V S nd he oupu volge V O. Idelly he sored energy in he min rnsformer is only supplied o he oupu V O1. As soon s he surle reor SR is sured, he diode D omes on nd he seondry winding V S is lmped he oupu volge V O. Sine he refleed volge on he winding volge V S1 is lower hn he oupu volge V O1, he diode D 1 eomes reverse is nd is urned off. As resul, idelly he sored energy of he min rnsformer is only rnsferred o he oupu V O during he ime period d. A he end of he swihing period, he min swih is urned on gin nd he surle reor SR is rese redy for nex swihing period. Aording o he ove desripions, he following equion is needed o e sisfied o ensure he mgmp se operion: V O1 4 V O ð1þ n 1 n For he vol se nd lne rule of he min rnsformer, we my hve d ¼ n P V O1 d 1 þ n P V O d ðþ n 1 n d þ d 1 þ d ¼ 1 ðþ where n P, n 1 nd n re winding urns for primry winding, oupu winding 1 nd oupu winding, respeively. o hieve oninuiy of mgneising urren when he urren flowing hrough oupu V O1 is swihed o V O,he following equion is sisfied: I O1 n 1 n P d 1 ¼ IO n n P þ 1 d d ð4þ where I O1 nd I O re he verge urren of oupu 1 nd oupu, respeively. Susiuing () nd () ino (4) yields d þ p d þ q d þ r ¼ where p ¼ ð V 1 þv 1 þ V þv Þ q ¼ ðv V 1 Þ V 1 V þ ð þ V 1 Þð þ V Þ r ¼ I 1 þ I þ V þ V 1 ðv V 1 ÞðI 1 V 1 þ I V Þ ð þ V 1 Þð þ V Þ V 1 ¼ n P V O1 ; V ¼ n P V O ; n 1 n I 1 ¼ n 1 I O1 ; I ¼ n I O n P n P ð5þ 518 IEE Pro.-Eler. Power Appl., Vol. 15, No., My 5

3 o solve he roo d of he hird-order (5), one my follow he proedure in he Appendix (Seion 7). As soon s d is found, i would e esy o find d 1 nd d from () nd (). Figure shows he relions of duy yles versus lod ondiions h re pplied o he exmple in Seion 4. Sine i is hrd o find roo of he hird-order equion or higher-order equion, pproximion ould e mde y ssuming h he urren ripples re negligile. he pproxime equion n e oined from (4) y negleing he ls iem I P d ¼ I 1 ¼ I ¼ I MA ð6þ d 1 d where I MA is he verge mgneising urren of rnsformer. From (6), we find h he relions eween duies nd inpu/oupu depend on he verge urrens. his is very ineresing feure. In mos opologies of swihing mode power supplies, he relions re domined y volges rher hn urrens. I 1, A I 1, A d...1 d I, A I, A Anlyil model wih nonidel hrerisis of omponens In pril design, he performne of he flyk onverer wih mgmp ppliion is limied y he nonidel hrerisis of he omponens. Sine he energy delivery for eh oupu depends on he urren shring priniple, some prsii prmeers suh s lekge indune nd sured indune my limi he re of urren flow. hese will no only onsrin he numer of oupus, u lso he opering re under exreme lod ondiions. An nlyil model is now proposed o explore he inernl mehnism nd o invesige he riil fors h ffe proper operion..1 Cirui nlysis of proposed nlyil model o simplify he nlysis, some resonle ssumpions re mde: firs, when he min swih nd he diodes re urned on, hey re onsidered s shor iruis. he volge drop of onresisne (Rds,on) of he min swih is negligile ompred wih he inpu volge. In he low oupu volge ppliion, he drops of he diodes ould e lumped wih he oupu volges. Under he off se, hey re represened s n open irui. Seondly, he min rnsformer n e represened s n idel rnsformer wih mgneising indune nd equivlen lekge indunes, L KP, L K1 nd L K, orresponding o primry winding, seondry winding 1 nd seondry winding, respeively. he volge drops of he winding resisnes re smll enough ompred wih he inpu volge nd oupu V O1 nd V O. hey re negleed in he model. hirdly, he oupu pines C 1, C nd he pine of he lmp snuer C C re suffiienly lrge h he volges ross hese pines ould e onsidered o e onsn during he swihing yle. Finlly, he ehviour of he surle reor SR n e modelled s n indune L SR when sured. During lok operion, i ould e viewed s n open irui. he ore loss due o he hyseresis hrerisis is suffiienly smll so h i n e negleed. he equivlen irui model of Fig. 1 is shown in Fig. 4 where ll seondry quniies hve een referred o he primry side. A ypil RC lmp snuer irui is dded on he primry side o preven high volge sress due o he energy sored in he lekge indune L KP. d.6.4. R C C C D C V C L KP V M LM L K1 C 1 N 1 D 1 V 1 S 1 L K i SR C V N I 1, A I, A Fig. Duy yles ploed gins lod ondiions ¼ V, V O1 ¼. V, V O ¼ 5V, I O1 ¼ A, I O ¼ A duy d duy d 1 duy d N L SR Fig. 4 Equivlen irui model of Fig. 1 Figure 5 shows he key wveforms h re simuled y he proposed equivlen model in norml oninuous urren mode. I would e esy o indie h some urren rnsiion periods re insered mong every duy period in he previous idel se. In priulr, he ime D IEE Pro.-Eler. Power Appl., Vol. 15, No., My 5 519

4 V M ime inervl: A he eginning of he 1 ime inervl, he min swih S 1 is urned off. he mgneising urren srs o hrge oupus 1 nd. A he sme ime he energy sored in he lekge indune L KP is sored y he pior of he RC lmp snuer. he equivlen irui during he 1 inervl is represened sh showninfig. 6. hus, one n oin he following equions: ¼ þ þ i ð7þ ðþ¼ V M1 þ I ð8þ ðþ ¼ ðv M1 V C ÞK P þ I ð9þ ðþ ¼ ðv M1 V 1 ÞK 1 ð1þ i i ðþ ¼ ðv M1 V ÞK ð11þ Susiuing (8) (11) ino (7), we oin V M 1 V M V M V M1 ¼ðV M1 V C ÞK P þðv M1 V 1 ÞK 1 þðv M1 V ÞK ð1þ V M I V M 4 V M 5 D C V C V M 1 L K 1 V I PP 4 I PP 5 =I L KP L K i SR N L SR D 1 D V I 1P 1 V M V 1 V M L K 1 L K 1 i IP 1 I P IP L K i SR D 1 V L K SR V i Fig. 5 Key wveforms h re simuled y he proposed equivlen model norml ondiion oundry ondiion inervl in whih diodes D 1 nd D re on is he mos eviden in rel ppliions nd deserves enion. As he lod of oupu inreses he duy for oupu lso inreses u he loking ime of he surle induor dereses. Under he exreme lod ondiion, he loking ime eomes minimum. Sine he urren rise ime is limied y he lekge indune nd he sured indune, oupu nno oin enough energy nd eomes nonoperionl. Figure 5 shows he key wveforms under exreme lod ondiions. N L SR V M 4 D L KP L K SR V S 1 S 1 i d N L SR D N L SR Fig. 6 Equivlen irui for differen ime inervls 1 ime inervl ime inervl ime inervl d 4 ime inervl e 5 ime inervl e L KP D V MS 5 IEE Pro.-Eler. Power Appl., Vol. 15, No., My 5

5 Solving (1) for V M1 yields V M1 ¼ K 1V 1 þ K V þ K P V C ð1þ 1 þ K 1 þ K þ K P A he end of he 1 inervl, 1 is oined from (9) y leing ( 1 ) ¼. 1 ¼ I 1 þ K 1 þ K þ K P ð14þ K P V C þ K 1 V C þ K V C K 1 V 1 K V Susiuing 1 nd V M1 ino (1) nd (11), he pek urrens of nd i he end of 1 re, respeively I 1P1 ¼ K 1 K P K V þ K P V C V 1 K V 1 K P V 1 V C þ K 1 V C þ K V C K 1 V 1 K V I ð15þ I P1 ¼ K K 1V 1 þ K P V C V K 1 V K P V I ð16þ K P V C þ K 1 V C þ K V C K 1 V 1 K V In his period, he energy sored in he lekge L KP hd een rnsferred o he RC lmp snuer. Assuming he volge V C is onsn, he energy will e dissiped y he resisne R C. he ol power loss of snuer n e derived s follows: P RC ¼ 1 Z 1 V C ðþd ¼ I ð1 þ K 1 þ K þ K P ÞV C K P ðv C þ K 1 V C þ K V C K 1 V 1 K V Þ ¼ V C R C ð17þ Solving (17), he volge of he snuer pior C C is qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V C ¼ ðk 1V 1 þ K V Þþ ðk 1 V 1 þ K V Þ þ LM RCI ð1þk1þkþkp Þð1þK1þKÞ K P ð1 þ K 1 þ K Þ ð18þ.1. ime inervl: As he urren of L KP dereses o zero, he diode D C is reverse ised nd he operion eners he ime inervl. he equivlen irui model is given in Fig. 6. Similrly, he following equions n e oined: ¼ þ i ð19þ ðþ¼ V M þ I 1P1 þ I P1 ðþ ðþ ¼ ðv M V 1 ÞK 1 þ I 1P1 ð1þ i ðþ ¼ ðv M V ÞK þ I P1 ðþ Similrly, V M n e found s V M ¼ K 1V 1 þ K V ðþ 1 þ K 1 þ K is lso oined from (1) y leing ( ) ¼. ¼ I K P 1 þ K 1 þ K V 1 þ K V 1 K V K V þ K P V C V 1 K V 1 K P V 1 ð4þ V C þ K 1 V C þ K V C K 1 V 1 K V Susiuing (16), () nd (4) ino (), we n oin he pek urren IP I P ¼ K ðv 1 V Þ V 1 þ K V 1 K V I ð5þ.1. ime inervl: When he urren of diode D deys o zero, he ime inervl egins. Only nd L K hve urren hrough i. he equivlen irui model during is shown in Fig. 6. Similrly o he 1 nd inervls, we hve ¼ i ð6þ ðþ¼ V M þ I P ð7þ i ðþ¼ ðv M V ÞK þ I P ð8þ Solving (6) (8), V M n e derived s V M ¼ K V ð9þ 1 þ K Susiuing (5) nd (9) ino (8), he pek urren of i he end of is I P ¼ K V ð1 þ K Þ þ K ðv 1 V Þ I ðþ V 1 þ K V 1 K V ime inervl: A he eginning of he 4 inervl, he min swih urns on gin nd hen he inpu srs o hrge.figure6d shows he equivlen irui model in he 4 inervl. As in he previous proess, we hve ¼ þ i ð1þ ðþ¼ V M4 þ I P ðþ ðþ ¼ ðv M4 þ ÞK P ðþ i ðþ¼ ðv M4 V ÞK þ I P ð4þ Solving (1) (4), V M4 is V M4 ¼ K V K P ð5þ 1 þ K þ K P 4 is oined from (4) y leing i ( 4 ) ¼. 4 ¼ 1 þ K þ K P K V ð K V þ K P V þ K P ð1 þ K Þ þ K ðv 1 V Þ I Þ ð6þ V 1 þ K V 1 K V And he pek urren of he end of 4 n e found y susiuing (5) nd (6) ino () I PP 4 ¼ K P þ K þ K V K V ð K V þ K P V þ K P ð1 þ K Þ þ K ðv 1 V Þ I Þ V 1 þ K V 1 K V ð7þ ime inervl: As long s he urren i drops o zero, he diode D is off nd he urren loop hrough nd L KP only exiss on he primry side. he equivlen irui model is presened in Fig. 6e. Similrly, one my oin ¼ ð8þ ðþ¼ V M5 þ I PP 4 ð9þ IEE Pro.-Eler. Power Appl., Vol. 15, No., My 5 51

6 ðþ ¼ ðv M5 þ ÞK P þ I PP 4 ð4þ Solving (8) (4) for V M5 yields V M5 ¼ K P ð41þ 1 þ K P Susiuing (7) nd (41) ino (4), he pek urren I PP5 is expressed y K P I PP 5 ¼ ð1 þ K P Þ 5 þ K P þ K þ K V K V þ K P V þ K P K V ð1 þ K Þ þ K ð4þ ðv 1 V Þ I V 1 þ K V 1 K V Due o he oninuiy of he induor urren in sedy se operion, he following equion is sisfied: I PP 5 ¼ I ð4þ Susiuing (4) ino (4), one n oin 5 A ¼ B I ð44þ where A ¼ V ð1 þ K P Þð þ K þ K V Þ ð1 þ K ÞðV þ K P V þ K P Þ B ¼ V ð1 þ K P ÞðV 1 þ K V 1 K V þ K P V 1 þ K P Þ K P ðv þ K P V þ K P ÞðV 1 þ K V 1 K V Þ For swihing period, wehve ¼ 1 þ þ þ 4 þ 5 ð45þ Susiuing (14), (4) nd (6) ino (45) yields 5 þ C ¼ D I ð46þ where C ¼ K P ð þ K þ K V Þ ð1 þ K ÞðV þ K P V þ K P Þ D ¼ ðv 1 þ K V 1 K V þ K P V 1 þ K P Þ ðv þ K P V þ K P ÞðV 1 þ K V 1 K V Þ nd 5 n e oined y solving (44) nd (46) ð1 þ K Þ ¼ ð1 þ K Þ þ K þ K V K P ðv 1 þ K V 1 K V þ K P V 1 þ K P Þ ð þ K þ K V ÞðV 1 þ K V 1 K V Þ I ð47þ 5 ¼ V ð1 þ K P Þ V þ K P V þ K P ð48þ. Anlyil expression of oundry ondiion Bsed on he ove nlysis, he verge urrens of oupus 1 nd under he oundry ondiion re luled s follows: I 1A ¼ 1 I 1P1 ð 1 þ Þ ¼ K 1 I K P ðk V þ K P V C V 1 K V 1 K P V 1 Þ ðv C þk 1 V C þk V C K 1 V 1 K V ÞðV 1 þk V 1 K V Þ ð49þ I A ¼ 1 ½ I P1ð 1 þ ÞþI P ð þ ÞþI P ð þ 4 ÞŠ ¼E I 1A þ 1 ½ I Pð þ ÞþI P ð þ 4 ÞŠ ð5þ where K ðk 1 V 1 þ K P V C V K 1 V K P V Þ E ¼ K 1 ðk V þ K P V C V 1 K V 1 K P V 1 Þ he soluion of (5) n e oined esily y susiuing eh individul iem h hs lredy een derived efore. However, i is rivil nd oo omplex o nlysis he relion eween I 1A nd I A. o oin n nlyil expression of he oundry ondiion, some resonle ssumpions ould e mde. Firs, sine nd 4 re rnsiion periods, hey ould e negleed ompred wih. Seondly, he mgneising indune is lrge enough, so h he n dey n e negleed during, i.e. I P EI P EI. Finlly, he lekge indunes L K1, L K, L KP nd he sured indune L SR re muh smller hn he mgneising indune, suh h K 1, K nd K P 441. Equion (5) n e pproximed y I A E I 1A þ I Equion (47) n e lso pproximed y þ V L KP I þ ðl K þ N L SRÞð þ V 1 Þ þ V ðv 1 V Þð þ V Þ Susiuing (5) ino (51) yields I A E I 1A þ I þ V I L KP þ ðl K þ N L SRÞð þ V 1 Þ þ V ðv 1 V Þð þ V Þ ð51þ ð5þ ð5þ Equion (5) will help us o undersnd he fors h ffe he oundry ondiion in Seion 4. 4 Experimenl resuls o illusre he effeiveness of he previous nlysis, some experimenl resuls re given elow. A W wo-oupu flyk onverer is onsrued hving he following prmeers: inpu rnge V oupu V O1 : V = A oupu V O 5 V = A swihing period 1 ms urn numer n P =n 1 =n 1==8 lekge indune L KP =L K1 =L K :95=:96=:94 mh mgneising indune 7 mh sured indune L SR :45 mh he ore numer of he min rnsformer is EI from DK orporion. he surle reor hs eigh urns nd he ore numer is MP156 from Allied Signl. he ommon used urren rese sheme is pplied o rese surle reor. he lmp snuer pine nd resisne re.1 uf nd 1kO, respeively. he oupu diode D 1 isshokydiode SBL84 from rnsys Eleronis Limied nd he diode D is fs diode SF14G from iwn Semionduor 5 IEE Pro.-Eler. Power Appl., Vol. 15, No., My 5

7 Co. Ld. Sine oh oupu volges re low, he volge drops of diodes re ken ino oun in he simulions. he volge drops of D 1 nd D under oundry lod ondiions re.1 V nd.9 V, respeively. Figure 7 shows some experimenl wveforms under: () hlf lod; () full lod; () oundry lod ondiions. In Fig. 7, V P is he volge ross he primry winding of he rnsformer s shown in Fig. 1 nd i O1, i O re he insnneous urrens of oupus 1 nd, respeively. Figure 8 shows he oundry ondiion for he verge oupu urrens I O1 nd I O wih oh he nlyil model nd experimenl resuls. I is ovious h he experimenl resuls re in good greemen wih he proposed nlyil model. We n find he oundry ondiions when he oupu urren I O is hevy lod nd I O1 is ligh lod. On he lef side of he oundry line, oupu eomes ou of regulion. he resuls lso verify he effeiveness of (5). However, (5) is omplex nd rivil. he simplified (5) is more omprehensive nd nlyil. In (5), oupu urrens I 1A nd I A re funion of I whih depends on he lod ondiion. he only nonidel fors h ffe he oundry (5) re he lekge indunes L KP, L K nd i O 1 i O 1 i O i O 1 i O i O V p, V /div i O, A /div i O 1, 5A /div, A /div V p, V /div i O, A /div i O 1, 5 A /div, A /div V p, V /div i O, A /div i O 1, 5 A /div, A /div Fig. 7 Some experimenl wveforms ime sle is 1 ms/div hlf lod: ¼ V, I O1 ¼ A, I O ¼ A full lod: ¼ V, I O1 ¼ 1.5 A, I O ¼ 1A oundry lod: ¼ V, I O1 ¼.49 A, I O ¼ A I, A I, A I, A I, A I 1, A I 1, A I 1, A prediion 1 experimen I 1, A Fig. 8 Experimenl resuls wih differen design ondiions under ¼ V, ¼ 1 ms ndn ¼ 8 ondiion: 1 L SR ¼.45 mh, L SR ¼.7 mh, L SR ¼ 1 mh under ¼ V, ¼ 1 ms ndl SR ¼.45 mh ondiion: 1 n ¼ 8, n ¼ 7, n ¼ 6 under ¼ V, ¼ 1 ms ndl SR ¼.45 mh ondiion: 1 n ¼ 8, n ¼ 7, n ¼ 6 d under ¼ V, ¼ 6.67 ms ndl SR ¼.45 mh ondiion: 1 n ¼ 8, n ¼ 7, n ¼ 6 d IEE Pro.-Eler. Power Appl., Vol. 15, No., My 5 5

8 he sured indune L SR. he urren rise ime is limied y hese fors. Hene, he mgneising indune nno supply enough energy o oupu eyond he oundry. he oher fors of (5) re designed prmeers suh s he swihing period, inpu volge, oupu volges V 1, V,urnrioN nd he urns of he surle reor. Figure 8 d show he effeiveness of he designed fors wih differen vlues ompred o he originl design. In Fig. 8, hree differen urns of surle reor re provided: ondiion 1 is he originl vlue: 8 urns nd L SR ¼.45 mh, ondiion is 1 urns nd L SR ¼.7 mh nd ondiion is 1 urns nd L SR ¼ 1 mh. I n e seen h he oundry lines move owrd he righ wih inresing urns of he surle reor. his omplies wih he onlusion of (5) h he lrger he lekge indunes nd he sured indune re, he worse he oundry ondiion is. I seems h fewer urns of he surle reor re preferred. However, he side effes should e onsidered o redue he sured indune. More rese urren from he onroller is needed when he urns of he surle reor re deresed. On he oher hnd, i redues he vol seond loking rnge of he surle induor. Sine he oupu volges V O1 nd V O re defined y he speifiion, he ul designed fors re he urn rios for V 1 nd V. he urn rio N 1 for he min oupu V 1 n e designed y he rdiionl pproh. However, he urn rio N for he mgmp oupu V eomes riil for ffeing he oundry. Figure 8 shows he effe wih hree differen urns for winding i.e. ondiion 1 is he originl vlue: n ¼ 8 urns, ondiion : n ¼ 7 urns nd ondiion : n ¼ 6 urns. As he winding urns of oupu derese, he volge differene eween V 1 nd V will e redued. I n e oserved from (5) h he hird iem in he righ-hnd side of he equion will e inresed nd he oundry lines re shifed o he righ. he mjor reson is h reduing he volge differene V 1 V ross L K will inrese he urren rise ime. his for eomes signifin when he volge differene is oo smll. o preven his, one should inrese he winding urns. However, his will inrese he volge sress on he oupu diode. As he inpu volge is hnged o high line volge ( ¼ V), ll he oundry lines wih he sme ondiions s in Fig. 8 re shifed o he lef. his is euse higher inpu volge n speed up he urren rise ime. he effe isshowninfig.8. his lso mens h he worse se ondiion is under he low line ondiion. In Fig. 8d, he swihing frequeny is inresed o 15 khz, i.e. he swihing period ( ¼ 6.67 ms) eomes wo-hirds of he originl vlue. he oundry lines wih he sme ondiions s in Fig. 8 re moved furher owrds he righ. his is euse he ime period for he urren disriuion is furher limied. his n e lso explined y (5), h deresing he swihing period will lso e inrese he hird iem. From he ove disussions, he design eomes rdeoff prolem. One should design he prmeers refully o oin he opimum performne. However, under ny ondiion, he minimum lod requiremen on oupu 1 is neessry o keep regulion. A simple nd os effeive wy o solve his issue is o dd prelod on oupu 1. In his exmple, 1 W prelod is pled o mee he 1% regulion requiremen. Figure 9 shows he ross-regulion of oupu V O1 ndv O (wihou nd wih mgmp, respeively). Oupu V O1 is onrolled y he PWM feedk loop. he ross-regulion of oupu V O1 mees I 1, A I 1, A I 1, A I 1, A he 1% (..%) regulion requiremen for wih nd wihou mgmp ondiion. On he oher hnd, he rossregulion of oupu V O wihou mgmp onrol is vried from %. As he surle reor is dded nd he mgmp feedk loop is enled, he ross-regulion of oupu V O is well under 1% (.4.4%) regulion requiremen. 5 Conlusions V 1 V 1 % 5. We hve invesiged he operion of he mgmp posregulor in flyk onverers wih muliple oupu V % V 1 V 1 V 1 % V V % I, A.5 5. I, A I, A I, A Fig. 9 Cross-regulion of oupu V O1,V O oupu V O1 wihou mgmp oupu V O wihou mgmp oupu V O1 wih mgmp d oupu V O wih mgmp d 54 IEE Pro.-Eler. Power Appl., Vol. 15, No., My 5

9 windings. he irui of he mgmp regulor looks similr o h of he forwrd onverers. Bu he opering priniple is olly differen. he oupu of he min rnsformer in he flyk onverer is viewed s urren soure. he energy is supplied o eh oupu winding y he ime-shring pproh. Due o he lekge indunes nd he sured indune, he urren rise ime is limied so h some rnsiion periods re insered. he proposed nlyil model effeively explins he mehnism of he regulion oundry. he experimenl resuls mhed he predied oundry ondiions. A simple nlyil expression is derived o explin he fors h ffe he oundry lines, suh s: lekge indune, sured indune, swihing frequeny nd inpu volge. o minin he regulion, minimum lod is required. Finlly, he experimenl exmple shows he effeive of pplying he mgmp in he flyk onverer. Boh oupu regulions re exellen wih 1 W prelod on oupu 1. 6 Referenes 1 Chen, Q., Lee, F.C., nd Jovnovi, M.M.: Anlysis nd design of weighed volge-mode onrol for muliple-oupu forwrd onverer. APEC, Sn Diego, CA, USA, 199, pp Mksimovi, D., nd Erikson, R.: Modeling of ross regulion in muliple-oupu flyk onverers. APEC, Dlls, X, USA, 1999, pp Ji, C., Smih, K.M., Smedley, K.M., nd King, K.: Cross regulion in flyk onverer: nlyi model nd soluion, IEEE rns. Power Eleron., 1, 16, (), pp Kolrewsky, P.: Beyond he limiion of rese onrol nd squre loop of merils for mg-mp pos regulors. High Frequeny Power Conversion Conferene, orono, Cnd, 1991, pp Lee, J., Chen, D.Y., nd Jmerson, C.: Mgmp pos regulorsfpril design onsiderions o llow operion under exreme loding ondiions, IEEE rns. Power Eleron., 199, 5, (1), pp edder, R.M.: Effes of onverer ype, rese mehod nd ore meril on mgmp regulor performne. APEC, Blimore, MD, USA, 1989, pp Nelson, O.N.: ime shre mg mp. High Frequeny Power Conversion Conferene, Sn Diego, CA, USA, 1988, pp Wen, C.C., Chen, C.C., Chen, W., nd Jing, J.: Mgmp pos regulion for flyk onverer. PESC, Vnouver, Cnd, 1, pp. 8 7 Appendix For ui equion d þ p d þ q d þ r ¼ ð54þ One my redue (54) o he form y susiuing for d wih he vlue, x p/. x þ x þ ¼ ð55þ where ¼ (1/)(q p )nd ¼ (1/7)(p 9pq7r). Equion (54) wih n e lwys solved y rnsforming i o he rigonomeri ideniy. Le x ¼ m os y, hen x þ x þ ¼ m os y þ m os y þ ¼ 4os y osy osðyþ¼ Hene 4 m ¼ osðyþ ¼ m from whih i follows h: rffiffiffiffiffiffiffi m ¼ ð56þ ð57þ ð57þ osðyþ ¼ ð58þ m Any soluion y 1, whih sisfies (59), will lso hve he soluions y 1 þ p nd y 1 þ 4p he roos of (55) re rffiffiffiffiffiffiffi rffiffiffiffiffiffiffi os y 1 ; os y 1 þ p ; rffiffiffiffiffiffiffi os y 1 þ 4p Hene, he roos of (54) re rffiffiffiffiffiffiffi os y 1 p rffiffiffiffiffiffiffi ; os y 1 þ p p rffiffiffiffiffiffiffi ; os y 1 þ 4p p IEE Pro.-Eler. Power Appl., Vol. 15, No., My 5 55