Cross Regulation in Flyback Converters: ANALYTIC MODEL

Transcription

1 Crss Regulatin in Flybak Cnverters: ANALYTC MODEL Chuanwen Ji and eyue. M. Smedley Det. f Eletrial & Cmuter Engineering University f Califrnia, rvine, CA 9697, USA Abstrat An analytial mdel fr studying rss regulatin amng the multile ututs f flybak nverters is resented in this aer. Bth the mdeling and exerimental results shw that the rss regulatin an be imrved by lwering the lam vltage, whih has nt been reviusly rerted. Many ther fatrs, suh as leakage indutane in rimary and sendary windings, magnetizing indutane, and air ga an als affet the rss regulatin. Detailed analysis and test results are rvided.. NTRODUCTON Amng the variety f swithing-mde wer nverters, the flybak nverter is the favrite hie amng design engineers fr lw wer aliatin due t its lw mnent unt, st-effetive struture as well as its large dynami range. Hwever, a flybak nverter generally suffers frm lw effiieny and r rss regulatin beause f the leakage indutane. n reality, n matter hw t arrange the winding struture inside the transfrmer, the leakage indutane an nt be mletely eliminated. As swithing frequeny reahes megahertz level, the rss regulatin rblem aused by leakage indutanes bemes serius t satisfy its rss regulatin seifiatins. n industrial ratie, a weighted vltage ntrl l is ften used t redue a artiular utut errr by adjusting the weighting fatr. But it des nt redue the ttal utut errr, instead, it nly shifts the errr amng the ututs []. Sme reviusly ublished aers []-[5] have revealed the relatins between leakage indutane and rss regulatin t sme extent. Hwever, quantitative relatinshi desribing the effets f the leakage indutane amng windings n the rss regulatin has nt been rerted s far. Paer [6] has shwn ertain insight int this issue; hwever, it nverts the leakage indutane in rimary winding t sendary side, whih makes the redited results diffiult t be mathed by exeriments. This aer resents an analytial mdel t exlre the rss regulatin mehanism inside a flybak nverter and t investigate the ruial fatrs that affet rss regulatin in a multile utut flybak nverter. The mdel is exerimentally verified. The analytial mdel f rss regulatin is derived in Setin, the analytial reditins and exerimental results are resented in Setin and. A summary is rvided in Setin.. ANALYTCAL MODEL OF CROSS REGULATON N FLYBAC CONERTER A flybak nverter ylially stres energy in its transfrmer frm the inut DC sure when its swith is n and then releases this stred energy int its ututs after the swith is turned ff. By adjusting the amunt f energy stred and released er-yle, the utut vltage an be regulated. Fig. shws a tyial tw-utut flybak nverter tlgy with an RC lam (C, R, and D ) dissiating the energy frm the leakage indutane, L k, eah yle when the swith is turned ff and limiting the vltage stress n the swith. n Fig., the transfrmer is mdeled as an ideal transfrmer with a magnetizing indutane, L m, and equivalent leakage indutanes, L k, L k and L k, rresnding t that f rimary winding, sendary winding, and winding resetively. Cmared with the leakage indutane, the resistane f windings is small enugh t be negleted. g g C C C D C D R R i L k Swith L m L k Swith N - * v m ( b ) * N s * N s L k L k L k L k D D PWM Cntrl D D C C C C feedbak refer Fig.. A tyial flybak nverter f tw ututs, (b) Equivalent transfrmer mdel n the rimary side fr analyzing the rss regulatin. By nverting the sendary sides t the rimary side f the transfrmer, an equivalent iruit is derived as shwn in i i This wrk is surted by Cherkee nternatinal n. and UC MCRO rgram

2 Fig. (b). t is a nsequential latfrm fr quantitative analysis f the rss regulatin in the flybak nverter. f the lad in utut f the nverter shwn in Fig. is lighter than that in utut, the urrent wavefrms in bth ututs an be ltted fr ne swithing yle as shwn in Fig. when erating in disntinuus urrent mde (DCM). n Fig., is urrent flwing t the RC lam and m is equivalent magnetizing urrent. Substitutin f the urrent hanging rates f, i, i and i int () gives m m m m () LP L L C L m m D m i L k i L k D C v m m m i L k - g T L m - m - i i Lk Lk D L m m i Lk D C i (b) T () T T T T Fig.. Equivalent iruits during T, T and T. i i t t t t t Fig.. deal vltage and urrent wavefrms during ne swithing yle. m: magnetizing vltage; : magnetizing urrent; i : urrent int the aaitr f RC lam; i and i : urrents thrugh the utut windings. When the swith is turned n at t, the magnetizing urrent will inrease with a sle f g /(L m L k ), g ( t ) L L m k t At the mment t when the swith is turned ff, a large rtin f the magnetizing urrent will flw int the aaitr C f RC lam due t the leakage indutane in the utut ls. The rresnding equivalent iruit during T is shwn in Fig. where the aaitanes f C, C and C are assumed t be large enugh s that the vltages arss them are nstant during the entire swithing yle and the vltage drs in all dides are negleted. The sum f urrents at nde O equal zer: im i i i () Differentiating f () yields d di di di () dt dt dt dt t () Let L m / L k, L m /L k and L m /L k, slving () fr m yields m (5) During T interval, the urrent flwing int C is m i ( t) t Lk (6) where is magnetizing urrent at the mment when the swith is turned ff. The dide D ndutin time, T, is btained by letting i (t) L m T (7) The urrents f utut and utut during T are ( m ) i( t) t (8) ( m ) i( t) t (9) At t, the end f T, when the urrent in aaitr C drs t zer, the eak urrent in utut is btained by substitutin f (7) int (8) P ( )( m ) ( ) () n similar way, the instantaneus urrent f utut at t an be derived P ( )( m) ( ) ()

3 After the urrent i (t) thrugh aaitr C drs t zer, the dide D is reversely biased. The equivalent iruit during T is redued as shwn in Fig. (b). im i i () Differentiating abve () yields dim di di () dt dt dt Substitutin f the urrent hanging rates f, i and i int () gives m m m () Lk L i.e. m (5) The urrent in utut during T is m i ( t ) t P (6) L k The urrent i (t) will dr t zer befre i (t) des due t its lighter lad and higher vltage at the utut, s that T an be btained by letting i (t) ( )( ) T (7) ( )( ) The urrent f utut during T is m i ( t ) t (8) P L k The instantaneus urrent in utut at time t when the urrent in utut drs t zer an be btained by substitutin f (7) int (8) ( ) P (9) Equatin (9) states that if the tw utut vltages are equal, k, whih means that the tw utut urrents will dr t zer simultaneusly and have similar triangle wavefrm as shwn in Fig.. After t, nly L m and L k have urrent, the equivalent iruit during T is shwn in Fig. (). i ( t) t P () Lk T is btained by letting i (t) ( )( ) T () ( ) i(t) T k T average i(t) k k T T T (b) average Fig.. deal urrent wave frms in the sendary windings. Frm the abve analysis, the urrent in utut and utut, after the swith is turned ff, are alulated and shwn in Fig. and (b) resetively. The average urrent f utut during ne swithing yle is average [ P ( T T )] T ( ) [( )[( ) T]] () and, the average urrent f utut is average [ T P ( P P) T P T] T M T ( )( ) () where M The rati f the tw utut average urrents is btained by dividing () by () average ( ) () average M Equatin () is the base t derive the utut errr exressins. n this aer, tw tyial ases will be disussed. n ase, it is assumed that nly ne utut, say utut, has feedbak ntrl with an infinite l gain t kee its utut nstant n matter hw its lad varies, and the unregulated utut, i.e., utut, has n external lad exet a small re-lad resistr R (whse resistane has been nverted t rimary side in (6). n this ase, the wrst rss regulatin urs at the utut with light lad while the ther has heavy lad. The vltage f utut is assumed t deviate frm utut by an errr. (5) average (6) R Substitutin f (5) and (6) int () gives an exressin resented in the Aendix []. t shws that the errr f utut,, is a funtin with suh variables as (the lam vltage f aaitr), (winding leakage indutane fatr, L m /L k ), (winding leakage indutane fatr, L m /L k ), and R (re-lad resistane in utut ) as well as the lad urrent in the regulated utut. This analytial mdel an be extended t ase where weighted utut ntrl is used. n the steady state, the algrithmi mehanism f the weighted vltage ntrl an be exressed as k k refw (7) where k and k are nstant and refw is the referene vltage f mensatr. Differentiating (7) yields k k (8) Define the weighting fatrs f the tw ututs as w k /(k k ) and w k /(k k ) resetively, thus w w and (8) bemes w w (9)

4 where < w, w <. Sine all eted utut vltages are idential in an ideal multile utut transfrmer, utut errrs, and, an be viewed as their deviatin frm the eted utut vltage, namely, - and -, therefre, w () w () Substitutin f () and () t the basi equatin () yields an exressin as shwn in Aendix [], whih rvides a lse-frm equatin fr analyzing rss regulatin in flybak nverters with weighted utut ntrl. n the next tw setins, the analytial mdel will be verified by exeriments and the analysis results will be resented as well.. RELATON BETWEEN THE CLAMP OLTAGE AND THE OUTPUT OLTAGE CROSS REGULATON Case. One utut is regulated while the ther is en ). The errr f the unregulated utut versus the lad variatin f the regulated utut A flybak nverter used in exeriments has tw ututs, ne f that is fedbak t regulate its utut vltage. ts transfrmer arameters are listed in Table and DC inut vltage is 7. All bxed urves in the figures shwn in this aer are exerimental results. TABLE FLYBAC TRANSFORMER PARAMETERS Turns f rimary 6 Turns f utut Turns f utut 9µH Lk 9.9µH Lk(nverted t rim. side) 9.8µH Lk(nverted t rim. side) 9.8µH R (Pre-lad in utut ) Ω R (Pre-lad in utut ) 66.7Ω ref(utut eted vltage) 6 n the flybak nverter design redure, the lam vltage is seleted t meet the vltage stress requirement f the swith. U t nw, there is n literature rerting the fat that the lam vltage affets the rss regulatin n multile ututs. The study in this wrk has revealed a strng rrelatin between the lam vltage and the rss regulatin. Bth the analytial reditin and exerimental results, as shwn in Fig. 5, indiate that, during heavy lad in the regulated utut, the utut errr in the unregulated utut is redued by erent when dereasing the lam vltage frm 6 t. Furthermre, it is fund that if the lam vltage is designed slightly greater than, but nt equal t, the utut eted vltage, the utut errr in the unregulated utut is minimized. ). The errr f the unregulated utut versus the lad variatin f its wn and the regulated utut The abve setin bserves hw lad variatin in the regulated utut affets the utut errr f the unregulated utut when it has nly a re-lad resistane. t is als imrtant t knw the utut regulatin versus the lad variatin f bth ututs. The utut errr f the unregulated utut rresnding t the variatin f bth lads is shwn by -dimentinal lts in Fig. 6 and (b) fr the lam vltage f 6 and resetively. t is bvius that the errr is dramatially redued by dereasing the lam vltage. Mrever, the extensive flat area in the entral art f the Fig. 6 and (b) indiates that the better rss regulatin urs when bth lad urrents are higher than a ertain level, abve whih the rss regulatin is nt dminantly influened by leakage indutane and ther fatrs () 6 (A). ( a ) (A).85 (A) ( b ) (A).79 Fig. 6. -D lts f the unregulated utut errr: 6, (b) (A) Fig. 5. Bth analyti and exerimental results shw that the errr f the unregulated utut is redued when lwering the lam vltage Case. Outut errrs in flybak nverter with weighted vltage ntrl ( w.8, w.) Based un the mdelling analysis, the utut errr an be analytially redited and ltted as shwn in Fig. 7 fr a lam vltage f 6 and Fig. 8 fr a lam vltage f in terms f the different weighting fatrs. Fig. 7 and Fig. 8 indiate that weighted vltage ntrl by n means

5 redues verall errr but redistributes it amng the ututs. t an redue the artiular utut errr by adjusting the weighting fatr at the st f degrading the thers sine it des nt render a mehanism fr ututs t trak eah ther. Hwever, lwering lam vltage an verall redue the bth utut errrs in the flybak nverter. The analytial utmes an fretell utut errr and hel engineers t make arriate tradeff amng the weighted fatrs, the lam vltage, and re-lad urrents t satisfy the regulatin seifiatin f eah utut..766 by erent when heavy lad is alied t utut mared with the errr in urve a (exerimental) and b (redited). Hwever, its utut vltage will dr mre during light lad in the regulated utut beause the larger indutane in utut auses less energy flw tward its utut. One way t redue the dr and regain its riginal utut is t inrease its re-lad resistane as shwn by urve e in Fig. 9, as a nsequene, the effiieny will be further imrved. n ratie, adding a small indutr in the unregulated ututs an be realized by arrangement f winding struture in the windw f transfrmer re t shift the leakage indutane distributin. Fr instane, a desired larger leakage indutane in the winding f the unregulated ututs an be ahieved by laing it in the uter layer f the re windw..98 (A) (A).59 (A) (b). (A) () e b a Fig. 7. The redited utut errr in a flybak nverter with weighted vltage ntrl where the lam vltage 6, w.8, w.,. the errr at utut ; (b) the errr at utut (A) d 8. Fig. 9. Adding a small indutr in the l f the unregulated utut redues its utut errr. a and b: R 66.7Ω and withut an extra indutr, and d: R 66.7Ω and L extra.6µh, and e: R Ω and L extra.6µh, (A).77 (A) (A) (b) (A) n Fig., bth mdelling reditins and exerimental results shw that larger leakage indutane in rimary winding will result in smaller errr in the unregulated utut. n the exeriment, the added indutane is uh. Fig. 8. The redited utut errr in a flybak nverter with weighted vltage ntrl where the lam vltage, w.8, w.,. the errr at utut ; (b) the errr at utut. () L k 9.9µH. EFFECT OF THE LEAAGE NDUCTANCE ON THE OUTPUT OLTAGE CROSS REGULATON L k 9.9µH A mmnly used methd t redue the errr in the unregulated ututs is t derease its re-lad resistane, whih, hwever, yields mre lss. Analysis shws that adding a small indutr t the unregulated utut redues its utut errr and imrves the rss regulatin as shwn in Fig. 9. n the exeriment as an examle, a.6uh indutr was inserted in series with the winding f the unregulated utut. Curve a and b shw the redited and measured errrs when there is n extra indutr. As shwn by urve (redited) and d (exerimental) in Fig. 9, the errr is redued 6 8 (A) 6 8 Fig.. Larger leakage indutr in rimary side redues the errr f the unregulated utut, where the initial leakage indutane is 9.9µH and an added extra indutr is µh. Magnetizing indutane an be adjusted by varying the air ga between the magneti res, whih des nt hange

6 muh the leakage indutane amng the windings if the fringe effet is nt signifiant. Fig. shws that the rss regulatin is imrved if the magnetizing indutane is inreased by altering the ga while the leakage indutane is assumed t be unhanged. t means that redutin f the ga will imrve the rss regulatin. () a b 6 8 (A) 6 8 Fig.. Larger magnetizing indutane results better rss regulatin, a: LP; b: LP6; : LP; The well mathed exerimental and analytial results, as shwn in Fig. 5, 9 and, demnstrate that the analyti mdel lsely reresents the mehanism f the rss regulatin in flybak nverters.. CONCLUSON The mdel fr analyzing rss regulatin amng the ututs f flybak nverter is resented and verified by exeriments. Bth mdel reditins and exeriment results shw: The rss regulatin f a multi-utut flybak nverter an be signifiantly imrved by lwering the lam vltage, eseially t slightly abve the eted utut vltage. Hwever, it auses mre lss in a traditinal RC lam. Sme slutins fr imrving the rss regulatin with lw lss are rvided and disussed in future ubliatins. Larger leakage indutane in the sendary windings leads t better rss regulatin f that utut when it is lightly laded. Larger leakage indutane in rimary side will be benefiial t imrve the rss regulatin f multile utut flybak nverters. Hwever, it results mre lss in a traditinal RC lam. Reduing re ga t ahieve larger magnetizing indutane in flybak nverter design will imrve rss regulatin. ACNOWLEDGEMENT The authrs wuld like t thank Mr. en ing, ie Exeutive President f Cherkee nternatinal n., Dr. Enri Sant, Senir Engineer f Tesla C., and lleagues in the UC Pwer Eletrnis Labratry fr many valuable disussins. REFERENCES [] Chen, Q.; Lee F.C.; Jvanvi, M.M., Analysis and design f weighted vltage-mde ntrl fr a multile-utut frward nverter, APEC '9, Eighth Annual Alied Pwer Eletrnis Cnferene and Exsitin, San Dieg, CA, USA, 7- Marh 99, [] T. G. Wilsn, Jr., Crss regulatin in an energy-strage DC t DC nverter with tw regulated ututs, EEE Pwer Eletrnis Seialists Cnferene, 977 Rerd [] Je Marrer, mrving rss regulatin f multile utut flybak nverters Offiial Preedings f the Thirty-First nternatinal Pwer Cnversin Eletrnis '95, Lng Beah, CA, USA, 9-5 Set. 995, [] Hamill, D.C.; Ye, T.P.C., Charaterizatin f rss regulatin in DC-DC nverters, NTELEC 9, 5th nternatinal Telemmuniatins Energy Cnferene, New Yrk, NY, USA99,.7-8 [5] Gldman, M.; Witulski, A.F., Prediting regulatin fr a multileutut urrent-mde ntrlled DC-t-DC nverter. APEC '9. Eighth Annual Alied Pwer Eletrnis Cnferene and Exsitin Cnferene,.67- [6] Liu,. H., Effets f leakage indutanes n the rss regulatin in disntinuus-mde flybak nverter, Preedings f th nternatinal Cnferene n High frequeny Pwer Cnversin, May 989, Aendix A lse-frm equatin fr analyzing the rss regulatin f flybak nverters with single vltage feedbak ntrl: S [ ] where R ( S ) A lse-frm equatin fr analyzing the rss regulatin f flybak nverters with weighted vltage ntrl: X [ ] where X ( w w ) Y w w w w and Y w w w w w w w w w w ref w w w ref w w w w w w w w w w w w