ELEC-E8417 Switched-Mode Power Supplies Exam

Transcription

1 ELE-E847 Swiche-Moe Power Supplies Exa Quesion. n sep-up converer (Boos) he oupu volage o = 48 V an supply volage changes beween 0 V 5 V. upu power P o 5 W an swiching frequency ƒ s = 0 khz, = 47 F. alculae he neee inucance so ha he operaion is always in coninuous conucion oe. alculae he oupu volage ripple o when his inucance value is use. Quesion. n a Flyback-converer urns raios N :N = 5:, oupu volage o = V, supply volage = 48 V, oupu power P o = 60 W an swiching frequency ƒ s = 00 khz. The agneizing inucance of he agneic core is 0, H an converer operaes in coninuous area, i.e. he agneizaion of he core is always higher han zero. Derive equaions for he axiu curren an volage raings of he swich use in he converer an calculae heir nuerical values Quesion. The recifier of a swiche-oe power supply is equippe wih an acive power facor correcion circui. has been realize wih a single-phase ioe brige an sep-up converer. RMS value of he supply volage is 0 V an frequency 50 Hz. The recifier is loae wih 000 W an he c-volage is 70 V an filering capacior is 00 F. a) Draw he equivalen circui of he recifier an explain is operaing principle shorly. b) alculae he ac coponen in he oupu c-volage of he recifier. The oupu curren can be assue o be ieal c, efficiency of he recifier 00 % an he swiching frequency of he sep-up converer large. TRN THE PAGE

2 Quesion 4. Transforer of a full-brige converer is buil using ferrie aerial, which agneizing an loss wavefors are shown below (Örse = /(4π) 0 A/). Supply volage = 80 V, uy cycle D = 0,5, ƒs = 00 khz, B ax = 0, T (Wb/ ) = 000 Gauss an he easure peak value of he agneizing curren is 0,5 A. alculae he losses of he ransforer core when eperaure is 5. nucance of he agneic circui can be calculae fro L N R N A l where N is nuber of urns, pereabiliy of he ferrie, A surface area of he core, an l average lengh of he agneic circui. Quesion 5. Why feeback conrol is neee in swiche-oe power supplies? Wha basic principles nee o be aken ino accoun when esigning feeback conrol?

3 QESTN. + V L + - v L i L i o R V o - v L il i Lpeak L = LB on off T s n M D (.) 5 0 D... 0, , onverer is assue o be lossless D, (.) A he bounary of M an DM. LB ilpeak TS N D( D) (.) L L Base on his an Eq. (.) oupu curren a bounary is TS B LB ( D) D( D). (.4) L Duy cycle when his curren is a axiu is obaine by erivaion.

4 B D D TS L ( D) D( D) 0 4 4D 0 D 6 6 (.5) Eli aksii saaaan ohjaussuheella /. When obax is equal o he iniu of oupu curren, converer operaes always in M. T T L (.6) S S B ax in in 7 L 7 in Tarviavan kurisien arvo saaaan laskeua lähövirran iniiarvon avulla. Lähöieoina on anneu; lähöeho P o 5 W ja lähöjännie o = 48 V => o 5/48 A. 48V T S L 00kHz in 0,H 7 oin 7 5/ 48V (.7) Wih he values of he quesion, Lin is 0,044 H. f L is higher han his, operaion is always in M. However, in his quesion D = 0,687. 0,79 an / is ou fro his. Therefore, L can be even saller han above. Wih D = 0,687 T L D D (.8) S in ( ) 5, 6μH B The value is 5,6 H. D = 0,79 woul give even a saller value for L bu his canno be use as operaion wih oher D:s woul be in DM. i D Q Q D = o on off v o V o V o

5 Q DTS DTS (.9) R 5 A 0,79 Q DTS 48 00kHz 5,8 V ˆ 0,% (.0) 47μF Wih he values of he quesion he resul is 5,96 V, which is equal o 0,0 %. Quesion a) v V N N V o on off T s 0 i D o Peak value of he flux is a he en of conucion perio

6 ˆ = on = on N n seay sae inegral of he volage is zero o T s = ˆ T s on = on T s on = 0 N N o N an herefore o = N D D N N o D 0, 058 N o o when he urns raio is 5/ he resul is 0,8 Afer urn-on of he swich, curren in he priary increases linearly an i is equal o he agneizing curren. Peak value of he curren is ˆ = Îsw = on L When swich is urne off, seconary volage o is seen in he priary when uliplie by he urns raio. urren ecreases linearly i = Î o N N on on T s L This coul also be use o erive he volage raio shown alreay above. The ioe curren is equal o he agneizing curren when ransferre o he seconary, i.e. i D = N i = N N o N N Î on on T s N L Peak value of his curren can be calculae when he oupu curren is known. The average value of he ioe curren is equal o he oupu curren o = Po/o = 0 A. Base on his we obain he peak value as ˆ = = Îsw N N N D o DT s N L o, 5 A 70,65 A, A Wih he values of he quesion he resul is 5,5 A + 4,8 A = 5,9 A This is obaine by calculaing he ioe curren a he en of a cycle an wih help of his calculaing he area of shown in he figure. urren coprises of wo ers. The firs one epens on he oupu curren seen in he priary. The laer par shows he effec of he agneizing curren. Volage over he swich, when i is no conucing is N u sw = o = N D 48 V V 5 V

7 Quesion. a) Deaile explanaion is in he book b) n PF circui inpu volage an curren can be assue o be in phase p sin sin cos i (.) in s s s s s s an furher 00 % efficiency has been assue. D-curren conains a c-coponen an an ac coponen flowing hrough he capacior ss ss i i cos cos (.) Base on his capacior curren is s s i cos cos (.) an volage ripple over capacior can be inegrae u, ripple i cos (.4) P 000 Average value of he c curren is A an ripple volage is hus 70 uˆ, ripple 4 V (.5)

8 Quesion 4. Magneizaion in full-brige is wo-irecional, an Bax = 0, T = Gaussia is he highes flux. Fro he core loss curve a 00 khz i can be seen ha loss ensiy is 400 W/c. We nee o calculae he volue of he corev A l in orer o obain he losse.. When resisive volage rops are ignore, supply volage is equal o he flux change ore area is hus B N NA NA B ax (.6) DTS A DT S (.7) NBax 4NBax f s Nuber of wining urns is sill unknown. Magneizing curren iˆ DT DT S S L (.8) L ˆ i Magneizing inucance epens on core area an lengh of he flux pah L Fro his we obain L N R (.9) DT N A l N A N A S l iˆ (.0) ˆ i l DTS ore volue can now be calculae, when we use he core are in (4.) wo ies N A ˆ i V A l i NA N B f DT B D ˆ 4 ax s S 4 ax iˆ iˆ N 4 N B f 4 B D 4B Df ax s ax ax For he nuerical calculaion, pereabiliy of he ferrie is neee. can be esiae fro he given B-H loop. As flux ensiy is less han 0, T operaing area is quie linear. We use he higher 5 slope when he volue an also losses are highes. Then s

9 core volue V 000G 0,T 5,0*0 (0,5 0,5)örse 0,5 0 A/ 4π ˆ i (4B Df ax ) s 80*5,0*0 **0,5 8,c 4*0, *00*0 *0,5 Vs A losses P v V 400W/c *8,c,W Quesion 5. Soe require aspecs,. -Accurae an conrolle oupu volage wih goo ynaic alhough supply volage or oupu curren changes => uning of conrollers an oel of he syse -Sae-space averaging, soe basic escripion of his, only vali on frequencies below half of he swiching frequency -M an DM area, ransfer funcions are ifferen -npu volage feeforwar -urren oe conrol, inner curren loop is faser han he slower ouer volage loop, liis peak curren, auoaic inpu volage feeforwar, ransfer funcions are sipler han in VM, ifferen curren conrol ehos (consan frequency, hyseresis), slope copensaion neee when uy cycle is larger han 0,5 More eaile in he exbook