Analysis of Energy Transmission Modes of Flyback Converter

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1 Senr & Tranducer l. 177 ue 8 Auut Senr & Tranducer 014 by FSA Publihin S.. htt:// Analyi f Enery Tranmiin Mde f Flyback Cnverter 1 GONG Shu GONG Ren-Xi 3 WANG Kuan Cllee f Electrical Enineerin Guanxi Univerity Nannin Guanxi China Tel.: @qq.cm rxn@xu.edu.cn @qq.cm Received: 1 March 014 /Acceted: 31 July 014 /Publihed: 31 Auut 014 Abtract: t i f inificance t invetiate enery tranmiin mde f a flyback cnverter fr it timum dein. n thi aer the ETM f a flyback cnverter are divided int three mde which are cntinuu cnductin mde-cmlete inductr uly mde cntinuu cnductin mde-incmlete inductr uly mde and dicntinuu cnductin mde-incmlete inductr uly mde reectively. A dee analyi f the eratin i made a reductin f the bundary cnditin between the mde i cnducted and a cmarin f current tre tranfrmer AP and utut rile vltae between the mde i erfrmed. A 30W rttye i develed and it exeriment i dne. The exeriment reult are in areement with the theretical analyi quite well. Cyriht 014 FSA Publihin S.. Keywrd: Enery tranmiin mde Flyback cnverter Cntinuu cnductin mde-cmlete inductr uly mde Cntinuu cnductin mde-incmlete inductr uly mde icntinuu cnductin mdeincmlete inductr uly mde. 1. ntrductin A flyback cnverter ha been widely ued in the lw-wer rate wer ulie becaue f it imle tructure lw ct and eay imlementatin f multile utut etc. [1-4]. By cmarin the current thruh the rectifyin dide with utut current the enery tranmiin mde (ETM) f C/C cnverter can be divided int: 1) Cntinuu cnductin mde (M) and dicntinuu cnductin mde (CM) ) Cmlete inductr uly mde (CSM) and incmlete inductr uly mde (SM). The frmer i ractical fr invetiatin the wer circuit [5-8] while the latter i ueful fr analyzin the utut rile vltae [9 10]. A a matter f the fact the enery tranmiin rce f a flyback cnverter can nt be cmletely decribed by any f them. n rder t rereent the cnverter cmrehenively the enery tranmiin mde (ETM) f a flyback cnverter are red t be divided int M-CSM M-SM and CM- SM in thi aer. An analyi f the eratin and bundary cnditin i made and a cmarin f current tre tranfrmer AP and utut rile vltae between the mde i erfrmed.. efinitin f the Three Enery Tranmiin Mde The tly f a flyback cnverter i hwn in Fi. 1 f which n S C R are rimary inductr ecndary inductr turn rati which i defined a n the main witch the rectifyin dide mthin caacitr and lad reitance htt:// 177

Senr & Tranducer l. 177 ue 8 Auut 014. 177-183 reectively. urin the erid when the witch S i n and the dide i ff the enery will be tred in the tranfrmer.

reectively and i the rati f cnductin time f the witch S t witchin erid. n' c f (6) A reult f 1 the fllwin relatinhi can be btained: k c k (1) Eq.

2 Senr & Tranducer l. 177 ue 8 Auut reectively. urin the erid when the witch S i n and the dide i ff the enery will be tred in the tranfrmer. The rile current and eak current f rimary current i (t) can be exreed a and Δ f Δ + (1) () where f and are the witchin frequency the averae value f utut vltae and the averae value f utut current reectively and i the rati f cnductin time f the witch S t witchin erid. n' c f (6) A reult f 1 the fllwin relatinhi can be btained: k c k (1) Eq. (5) t (7) indicate that the ETM f a flyback cnverter deend n the rimary inductr and can be reciely defined a fllw: 1) A flyback cnverter erate in M-CSM if k. ) A flyback cnverter erate in M-SM if c k. 3) A flyback cnverter erate in CM-SM if c. The key wavefrm f three ETM are hwn in Fi.. Fi. 1. Tly f flyback cnverter. urin the erid when the witch S i ff while the dide i n the enery i releaed by the tranfrmer. The minimum current thruh i iven a (a) M-CSM ' min n f (3) where ' i defined a the rati f cnductin time f t witchin erid. n M + ' 1. Accrdin t the relatinhi f the vltaeecnd balance the fllwin exrein can be btained: n' (4) (b) M-SM f the min equal at the end f a witchin erid the bundary rimary inductr between M-CSM and M-SM i btained by ubtitutin Eq.()-(4) int Eq. (1) k n' (5) f f the min equal zer at the end f a witchin erid the bundary rimary inductr between M-SM and CM-SM i derived by ubtitutin Eq.() (3) and (4) int Eq.(1) (c) CM-SM Fi.. Key wavefrm f flyback cnverter. 178

3 Senr & Tranducer l. 177 ue 8 Auut Fi. hw that nly C ulie R with wer durin the interval [t 1 -t ] f the n-tate f S while the enery f R i ulied by r C durin the interval [t 0 -t 1 ] f the ff-tate f S. The enery tranmiin rcee durin the ff-tate f S are decribed in detail: 1) M-CSM: a flyback tranfrmer cntinuuly ulie R with wer and chare C u durin the interval [t 0 -t 1 ]. ) M-SM: a flyback tranfrmer ulie R and C with enery durin the interval [t 0 -t c ] then bth tranfrmer and C uly R with enery durin the interval [t c -t 1 ]. 3) CM-SM: the enery tranmiin rce i ame a that f M-SM durin the interval [t 0 -t ]. Hwever the enery f R i lely ulied by C durin the interval [t -t 1 ] which i becaue the tranfrmer ha releaed all the tred enery. 3. Analyi and Cmarin f the Three Enery Tranmiin Mde 3.1. Branch Current Nw emetric analyi arach i ued t make the cmarin f the branch current. Primary current f a flyback tranfrmer i hwn in Fi. 3 where / i the le f i (t) the traezid ABC rereent the bundary wavefrm between M- CSM and M-SM and the trianle ABE rereent the bundary wavefrm between M- SM and CM-SM. Accrdin t enery cnervatin thery the wavefrm area huld be equal t the variatin f. 1 T Kr rm i ( t) dt ( Kr + 1) (10) T 0 3 where 0 1 and K r i defined a K r K r Δ (11) The RMS current f the trianle wavefrm ABE divided by the RMS current f traezid wavefrm ABC yield: Kr α 1 K 3K + 3) r r (1) where α i the mntnuly decreain functin f K r at the rane [0 1]. n term f Eq. (8) and (9) the relatinhi f K r amn the three mde can be exreed a K r_ Kr_ C K (13) r_ Cnequently the relatinhi f rm amn three mde can be derived a: rm_ rm_ C (14) rm_ The RMS value f i (t) can be exreed a 1 T Kr i ( t) dt n '( Kr + 1) (15) rm T ' T 3 Similarly the fllwin relatinhi can be achieved by cmarin the eak and RMS current f i (t): C (16) rm_ rm_ C _ (17) rm_ The RMS value f i c (t) can be exreed a Fi. 3. Primary current wavefrm f flyback tranfrmer. The relatinhi f the eak current and the rile current f i (t) between the three ETM are clearly hwn in the Fi. 3. Δ Δ Δ (8) C C (9) _ where C and in ubcrit are the abbreviatin f M-CSM M-SM and CM- SM reectively. The RMS value f i (t) can be exreed a c rm rm Frm Eq.(17) and (18) we et (18) c rm_ c rm_ C 3.. AP alue f Tranfrmer (19) c rm_ The effective cr-ectinal area A e can be frmulated by A e N ΔBf (0) 179

4 Senr & Tranducer l. 177 ue 8 Auut where N i the rimary turn and ΔΒ i the manetic flux denity win which i defined a 0.4πN Δ Δ B l + lm / μr (1) where l l m and u r are the aira lenth effective manetic ath lenth and relative ermeability reectively. Similarly the imum f manetic flux denity win can be written by B 0.4πN l + l / μ Frm Eq.(18) and (19) we have m r () Slvin frm Eq.(4)ne btain: n + n Subtitutin f Eq.(9) int Eq.(8) yield n Δ C f C ( + n ) (9) (30) Eq.(30) hw that Δ i indeendent n. C A hwn in Fi. (b) and Fi. (c) C i chared by tranfrmer thruh durin the interval [t 0 -t c ]. The charin time Δt and charin current i c (t) can be exreed a ΔB B Δ K r (3) Δ t tc t0 ( n ) (31) n additin the cre windw area i A N rm w JK K u (4) where J K and K u are the cer current denity rimary turn area cefficient and the windw effective area cefficient reectively. Frm Eq.(1) (3) and (4) the AP value f the tranfrmer can be derived a: AP rm Ae Aw (5) JK KuKrB f The rati f the AP value crrendin t the trianle wavefrm ABE t that f the traezid wavefrm ABC yield ( Kr) Kr β 1 K 3K + 3) r r (6) where β i the mntnuly incremental functin f K r at the interval [0 1]. Frm Eq. (5) and (6) the relatinhi f the value AP f the tranfrmer amn three mde can be written a: AP > AP > AP (7) 3.3. Outut Rile ltae C A hwn in Fi. (a) the increment f (t) at the interval [t 0 t 1 ] huld be equal t the decrement f (t) at [t 1 t ]. The utut rile vltae in M-CSM can be derived a i c ( t) n t (3) The utut rile vltae in M-SM and CM-SM can be derived a 1 t ΔC ic ( t) dt ( n ) C Δ 0 C (33) n M-SM can be lved frm Eq.(1) and () + f (34) By ubtitutin Eq.(34) and n int Eq.(33) the utut rile vltae in M-SM can be exreed a 1 Δ C C + ( ) C f n (35) The firt rder and ecnd rder f artial derivative f Δ C with reect t are reectively made then the fllwin exrein can be btained: Δ C 1 ( ) ( ) n f C Δ C 4 f C 3 (36) > 0 (37) T 1 T Δ C dt C 0 C (8) By lettin the riht ide f Eq.(36) be zer an nly tanatin int can be btained: 180

5 Senr & Tranducer l. 177 ue 8 Auut n' n f( n ) f k (38) tranfrmer and utut rile vltae vary with. The cmarin amn three ETM i made in the Table 1. where Δ i the mntnuly direive functin C f at the interval [ c k ] ince the ecnd rder f artial derivative i reater than zer. n CM-SM equal Δ i. By ubtitutin Eq.(1) and n int Eq.(33) the utut rile vltae in CM-SM can be exreed a ( n f ) Δ C (39) C n f Eq. (39) hw that Δ C i inverely rrtinal t. U t nw the utut rile vltae have been derived under the aumtin that the mthin caacitr C i ideal. n ractice the equivalent erie reitr (ESR) R er f the mthin caacitr can nt be nelected in the rile vltae analyi. n any ETM the rile vltae acr R er can be exreed a Δ n R (40) R er The ttal utut rile vltae i Δ Δ C + Δ R (41) Subtitutin Eq.(1) (30) (33) (35) (39) and (40) int (41) we btain the utut rile vltae f three ETM with ESR f the mthin caacitr cnidered n Δ + nrer ( + ) C f + n ) f ( 1 Δ C + ( ) + nrer( + ) C f n f ( n f ) nrer Δ + Cn f f 4. Exeriment Reult (4) (43) (44) A rttye i made t verify the theretical analyi. The key arameter f the cnverter are a fllw: A R 4.8 Ω f 66 khz n8.5 J4 A/mm K 0.4 K u 0.3 B 0.3 T C 000 μf R er 0 mω. Subtitutin the relative arameter int Eq.(5) and (6) we et: k 1.8 mh and c 0.64 mh. A we knw all the branch current the AP value f the Table 1. Cmarin between the three ETM. Δ (A) rm rm (A) (mh) (A) (A) (A) crm AP Δ C Δ R Δ (mh) (A) (mm ) (m) (m) (m) The key exerimental wavefrm are hwn in Fi. 4. The exerimental reult are arximately in areement with the theretical calculatin. But tw difference huld be inted ut: 1) A hwn in Fi. 4(a) and Fi. 4(c) the meaured rile and eak current f i (t) are a little reater than the calculated value ince the cnverin efficiency i le than 1 due t the exitence f the araitic cmnent [11-14]. ) Frm Fi. 4(b) and Fi. 4(d) it can be een that the AC cmnent f v (t) are cmed f rile and nie. The witchin nie i caued by the araitic cmnent and it i ften deirable t add a t C filter t ure it. 5. Cncluin An invetiatin f the enery tranmiin mde f a flyback cnverter i made and a cmarin f the three mde red i erfrmed. A 30 W rttye i develed and teted. The exerimental reult aree with the theretical analyi. Accrdinly the fllwin cncluin can be drawn: 1) The current tre i mallet and the AP value f tranfrmer i biet in M-CSM bth current tre and the AP value f tranfrmer i medium in M-SM and current tre i biet and the AP value f tranfrmer i mallet in CM-SM. ) f the ESR f the mthin caacitr i nelected the rile vltae in M-CSM i mallet and i indeendent n that in M-SM i medium and i inverely rrtinal t and that in CM-SM i biet and vary inverely with. Thi cncluin i imilar t the reference [9] in which the ETM f bt cnverter are analyzed. f the ESR f the mthin caacitr i cnidered the rile vltae decreae with increaed in any ETM. 181

Senr & Tranducer l. 177 ue 8 Auut 014. 177-183 (a) (b) (c) (d) Fi. 4. Key exerimental wavefrm: (a) CH1 CHi(t) when 1.7 mh (b) CH1 CH when 1.7 mh (c) CH1 CH i(t) when 0.9 mh

010GXNSFA01303) and Nannin Scientific Reearch & evelment Fundatin f Guanxi China (Grant N. 01105). Reference [1].

Jn-Jae ee Jun-Min Kwn Eun-H Kim et al Sinle-tae inle-witch PFC flyback cnverter uin a ynchrnu rectifier EEE Tranactin n ndutrial Electrnic l. 55 ue 3 008. 135-1365. [3]. H.

[4]. Ki-Bum Park Chn-Eun Kim Gun-W Mn et al PWM renant inle-witch ilated cnverter EEE Tranactin n Pwer Electrnic l. 4 ue 8 009. 1876-1886. [5]. J. Sun. M. Mitchell M. F. Greuel P. T. Krein et al Averaed mdelin f PWM cnverter eratin in dicntinuu cnductin mde EEE Tranactin n Pwer Electrnic l.

6 Senr & Tranducer l. 177 ue 8 Auut (a) (b) (c) (d) Fi. 4. Key exerimental wavefrm: (a) CH1 CHi(t) when 1.7 mh (b) CH1 CH when 1.7 mh (c) CH1 CH i(t) when 0.9 mh (d) CH1 CH when 0.9 mh. Acknwledement The reearch wa urted by Guanxi Natural Science Fundatin f China (Grant N. 010GXNSFA01303) and Nannin Scientific Reearch & evelment Fundatin f Guanxi China (Grant N ). Reference [1]. Hin-Fu iu n-ku Chan Flexible and lw ct dein fr a flyback AC/C cnverter with harmnic current crrectin EEE Tranactin n Pwer Electrnic l. 0 ue []. Jn-Jae ee Jun-Min Kwn Eun-H Kim et al Sinle-tae inle-witch PFC flyback cnverter uin a ynchrnu rectifier EEE Tranactin n ndutrial Electrnic l. 55 ue [3]. H. M. Pan P. M. H. Bryan A tability iue with current mde cntrl flyback cnverter drivin E in Prceedin f EEE 6 th nternatinal Pwer Electrnic and Mtin Cntrl Cnference Wuhan China 17-0 May [4]. Ki-Bum Park Chn-Eun Kim Gun-W Mn et al PWM renant inle-witch ilated cnverter EEE Tranactin n Pwer Electrnic l. 4 ue [5]. J. Sun. M. Mitchell M. F. Greuel P. T. Krein et al Averaed mdelin f PWM cnverter eratin in dicntinuu cnductin mde EEE Tranactin n Pwer Electrnic l. 16 ue [6]. Nikla P. Paaniklau Emmanuel C. Tataki Active vltae clam in flyback cnverter eratin in M mde under wide lad variatin EEE Tranactin n ndutrial Electrnic l. 51 ue [7]. Tzuen-ih Chern i-hian iu Pin-un Pan et al Sinle-tae flyback cnverter fr cntant current utut E driver with wer factr crrectin in Prceedin f nternatinal Cnference n ndutrial Electrnic and Alicatin Xi an China 5-7 May

Senr & Tranducer l. 177 ue 8 Auut 014. 177-183 [8].

iu Shulin iu Jian Yan Yinlin et al Enery tranmiin mde and utut rile vltae f Bt cnverter Prceedin f the CSEE l. 6 ue 5 006. 119-14. [10].

-P. Keradec J.-P. Ferrieux et al Cer le f flyback tranfrmer: earch fr analytical exrein EEE Tranactin n Manetic l. 39 ue 3 003. 1745-1748. [1]. A. Hren J.

Haiyan u Jianu Zhu S. Y. R. Hui Exerimental determinatin f tray caacitance in hih frequency tranfrmer EEE Tranactin n Pwer Electrnic l. 18 ue 5 003. 1105-111.

7 Senr & Tranducer l. 177 ue 8 Auut [8]. Yuan-Chil Chan Chan-Min iaw ein and cntrl fr a chare-reulated flyback witch-mde rectifier EEE Tranactin n Pwer Electrnic l. 4 ue [9]. iu Shulin iu Jian Yan Yinlin et al Enery tranmiin mde and utut rile vltae f Bt cnverter Prceedin f the CSEE l. 6 ue [10]. iu Shulin iu Jian Ku ei et al Analyi f utut rile vltae f Buck C/C cnverter and it alicatin Tranactin f China Electrtechnical Sciety l. ue [11]. C. aruci J.-P. Keradec J.-P. Ferrieux et al Cer le f flyback tranfrmer: earch fr analytical exrein EEE Tranactin n Manetic l. 39 ue [1]. A. Hren J. Krelic M. Milanvic RC-RC clam circuit fr rinin le reductin in a flyback cnverter EEE Tranactin n Circuit and Sytem l. 53 ue [13]. Haiyan u Jianu Zhu S. Y. R. Hui Exerimental determinatin f tray caacitance in hih frequency tranfrmer EEE Tranactin n Pwer Electrnic l. 18 ue [14]. Himanhu K. Patel ltae tranient ike urein in flyback cnverter uin diiative vltae nubber in Prceedin f the nternatinal Cnference n ndutrial Electrnic and Alicatin Sinare 3-5 June Cyriht nternatinal Frequency Senr Aciatin (FSA) Publihin S.. All riht reerved. (htt:// 183

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