Buck ZVS DC-DC Quasi-Resonant Converter: Design, Modeling, Simulation and Experimentation

Transcription

1 hp://dx.doi.og/.5755/j.eee ELEKTRNKA R ELEKTRTECHNKA, N 39-5, VL. XX, N. X, XX Buck ZV C-C Quasi-Resonan Convee: esign, Modeling, imulaion and Expeimenaion Nikolay L. Hinov, Nikolay R. Rangelov epamen of of Powe Eleconics, Technical Univesiy of ofia, Bul Kl. hidski 8, ofia, Bulgaia, hinov@u-sofia.bg, nikan8@gmail.com Absac n he pape wok a expeimenal sudy has been made wih pacical end, of a Buck C C quasi esonan convee, woking wih ZV ( Zeo Volage wiching ). n he wok a mahemaical expessions, fo he paamees, which descibe he wok of he powe pa of he cicui, has been made. Wih hei help a mehod fo designing of a Buck ZV C C quasi esonan convee has been poposed. The advanage of his mehod is he use of simple expessions, which faciliae he designing, bu in he same ime an accepable eo of % is kep, commensuae wih he oleance of he values of he eacive elemens (capacio and induco). The veificaion of hese expessions has been made wih modeling (Malab/imulink), compue simulaions (LTpice) and expeimenal measuemens on a laboaoy sand. ndex Tems Zeo volage swiching, C-C powe convees, of swiching.. NTRUCTN ne of he main mehods fo inceasing he efficiency of convees of elecical enegy is he deceasing of he swiching loses in he powe semiconduco elemens [9,, ]. Theefoe a widely used mehod fo achieving his is he using of a sof swiching shif swiching of he powe elemens on zeo volage o zeo cuen. Fo some convees his is achieved by viue of cicui feaues (fo example esonan invees), and fo ohes by using of a addiional elemens (capacio o induco), which ae conneced paallel o seial o he semiconduco swich. [, 4, 5]. Thus paallel o seial esonan cicuis can be made. These cicuis ae well known in he lieaue wih he name quasi esonan convees. n his pape wok a sudy of a Buck ZV quasi esonan convee has been made. The analysis of hese convees ae in [4, 5, 3], bu hee ae some inaccuacies and incoecly idenified values, and in addiion hese analyses ae no useable fo designing, which is one of he puposes of his wok.. EGN-RENTE ANALY F BUCK ZV QUA-RENANT CNVERTER n figue is shown he cicui of a Buck ZV quasi esonan C-C convee. The cicui consis of ansiso V, diode, file elemens L and C, Load R L esonan Manuscip eceived Apil XX, XX; acceped Apil XX, XX. This eseach was funded by a gan (No.3ПД9-3/3) fom he Reseach Council of he Technical Univesiy of ofia. elemens L и C, which povide he zeo volage swiching. Vin + _ L i W C C Fig.. Cicui of a BUCK ZV convee i The analyze is made unde seady sae and assumpion ha all elemen ae pefec. The cicui is woking in coninuous conducion mode wih negligible ipples hough he file induco. ue o he esonan cicui C -L fo he analysis of he convee some specific aios ae used [4, 5, 9]: - Resonan fequency of he seial L -C cicui fo ideal elemens: = () LC - Raio beween conol fequency and he fequency of he esonan cicui: f s v = () f - Chaaceisic impedance of he esonan cicle: L Z = = L = (3) C C - Nomalized load esisance: RL RL RL CR L R' = = = CR L = = (4) Z L L - Raio beween oupu and inpu volage of he convee ( C volage ansfe funcion ): V = (5) - Nomalized iniial esonan induco and swich cuen when he swich uns on: il () i () L h = = (6) i L C RL

2 ELEKTRNKA R ELEKTRTECHNKA, N 39-5, VL. XX, N. X, XX - uy aio: = on (7) Т The wok of he sudied cicui is shown by he wavefoms on figue (when he value of h=). uing one peiod we can see fou diffeen woking sages: age ( < Т ) The esonan induco accumulae enegy. The swich and he diode ae uned on. uing his sage cuens and volages have he following condiions: V =, L =, C =, V LR = V, and he cuen hough he swiching induco is: U G = L ( ) ( ) L L L + = L + i V d i i () (8) i L i i C u U u L U i u U N 3 FF Fig.. Time wavefoms when he convee is woking. Fo he pupose of he sudy i is convenienly o obain expessions in elaive unis, using he expessions menioned above in he pape wok. Thus he cuen hough he induco L is: il ( ) ( ) ' s is s R = = s+ h (9) The elaionship beween he cuen hough he diode i, and he cuen hough he swich i in he cicui is: i = i = ( i s/ ) () o fo he cuen hough he diode, in elaive unis: i( s) R ' = h () This sage ends when he cuen ough he diode becomes zeo. age ( < ) he diode is uned off. uing his sage he following ems ae execued: V =, CR =, =, is = i LR =, V LR =, и V = V. This sage ends in he momen when he ansiso uns off fom he conol sysem. age 3 ( < Т 3) chaging of he esonan capacio and boh diode and he ansiso ae uned off. uing his sage he following ems ae in effec: i =, =, LR = CR T =, V LR =. The volage ove he capacio is deemined wih he following expession: v = vc = i ( ) ( ) C d vc C + = π, () О V = ( π) = ( π) C CR L Whee VC ( ) s =. Afe ansfomaion fo he volage ove he ansiso and he diode, in elaive unis is: v = ( π) R' (3) v = ( π) R' This ends when he volage ove he diode becomes zeo - v (s 3) =. Fom his em we ge he expession: R ' = π+ M (4) 3 VC age 4 ( 3 < T) in is beginning he diode uns on. By he made assumpions fo pefec elemens in he cicui sas a seial esonan pocess wih he following iniial condiions: LR ( s 3) = и v C ( s 3) = V ( s 3) = V. eemine he cuen in he esonan cicui can be made wih diffeen mehods [4, 5, 9, 3], and in elaive unis i is: il i C 3 = = cos (5) A Fom (5) and () he elaive cuen hough he diode is: i 3 = cos (6) A woking in seady mode he following condiion is execued: il ( π ) = i ( ) L = h (7) Fom is applying in (5) and by using of (4) we deemine: π ( ) R' cos = h (8) The volage ove he esonan induco, duing sage 3 is: dil M VC 3 VL = L = sin (9) d( ) R' The volage ove he swich is: V = VC = i ( ) ( 3) C d vc C + = () 3 VM VC 3 = sin + R ' n elaive unis is: v 3 = sin + () R' Fo achieving ZV mode, he following condiion mus be fulfilled: v ( π ) = v ( ) =. o he elaion beween he used facos is: π ( ) R' R' sin = () Afe igonomeic ansfomaions of (8) and () ges:

3 ELEKTRNKA R ELEKTRTECHNKA, N 39-5, VL. XX, N. X, XX R ' h M = (3) VC Fo he duy aion we ge: = = π + h accosh (4) T π Fo he puposes of he design i is necessay o deemine he elaion beween duy aio and he volage ansfe funcion a consan cuen. niially he aveage value of he inpu cuen is deemined: π ( h) = id s ( s) = (5) π 4π h By assuming fo pefec elemens and lack of losses in he cicui elemens he following elaion is in effec: V =V. Fom he definiion fo he volage ansfe funcion ges: V ( ) h = = = (6) V 4π h n [4, 5, 6, 9, ] ae examined and analyzed he impac of he iniial condiions fo cuen ove he wok of he convee, and he scope of he load esisance fo ZV wok. Fo simplificaion of he calculaions i is ecommended o choose he value h =. Moeove his mode is bes fom he poin of view fo he sess and use of he cicui elemens [4, 5, 3].. METHLGY FR EGNNG The main daa necessay fo designing a Buck ZV convee ae: - npu volage V ; - upu volage V ; - upu cuen ; - Ripple faco fo oupu volage and cuen; - Conol fequency f. Fom he necessay daa menioned above we can see ha hese ae he necessay values fo calculaing andom convees (independenly fom is woking mode is i wih zeo swiching o no). Fo fis sep i begins wih calculaing of he convee wihou esonan cicui (C - L, shown on figue ) sandad Buck convee wih had swiching. Afe ha he values of he esonan elemens mus be deemine. Because he main pupose is o sugges a simple and easy mehod fo designing, a value of h= has been chosen. n his case a simplified kind of he expessions is eceived (3) (4) and (6): R' = M (8) VC 3 π + f f =.99 (9) 4π f f 3π + 3 f f =.9887 (3) 4π f f Excep he eacive componens a suiable semiconduco elemens mus be chosen. This is accomplishing by using he expessions fo hei maximum cuen and volage sess. Fom he pesened analyze he values fo maximum cuen and volage acoss he ansiso is deemined by: M = (3) VM = + V (3) R ' Fo he diode he maximum cuen and volage sess ae: M = (33) VM = V (34) f couse he fequency paamees of he elemens mus be deemined oo duing he design and he pacical ealizaion, because hese cicuis ae woking fo high fequency. [4, 9,, ]. EXAMPLE The necessay daa fo designing is: V i = 3V; V =5V; =ma; f =khz and we choose o wok wih h =. A convenional Buck C C convee wih had swiching is calculaed, by one of he well known design mehods, like he ones in [, 8, 9, ]. Fom he designing we ge he following esuls fo he values of he elemens: L = µh, C= 5µF и R L=75Ω. An induco wih L = 5µH and a capacio wih C= 5,7µF ae chosen. The values of hese file elemens ae deemine so hey can povide a wok in coninuous mode and se values fo he oupu cuen and oupu volage ipple. Afe ha he calculaion of he esonan elemens begins. Fom expession (8) follows ha, M VC=R =,5. Z is deemine by (4) and is value is Z =75/,5=5. Fom (3) afe we eplace he deemined ill now paamees, he value fo he esonan fequency of he seial esonan cicui is f =97775Hz; Wih he deemined esonan fequency he value of he duy aio fom (9) is 54,%; Afe ha he esonan induco mus be deemine fom (4), is value is: L =,73µH; The esonan capacio C is calculaed fom (4) and i is: C =5,3656nF. Fom he deemined values we can see ha he induco and he capacio, in he esonan cicui, ae no wih sandad values. Because of he specificiy of he offeed elemens (hei values ae in sandad ode), a using of a elemens wih sandad values is equied. Thee ae wo possible mehods fo sele his ask, like we can see fom expession (9) and (3). f he values of he esonan capacio and induco ae changed, he duy aio mus be changed oo o he conol fequency. o he values of he elemens poined ou in he assignmen ae kep. The easies way is o change he duy aio (so he woking fequency is kep, which lead o suppession of he elecomagneic inefeence). n his case a sandad values fo he esonan elemens ae se and wih hei new values, he fequency of he esonan cicui mus be calculaed again. o an induco wih L = µh and capacio wih C =6,8nF ae chosen. Afe sandad values ae been used of L and C, hey ae eplaced in (4), he new value of he esonan fequency is - f = 8653Hz. Recalculaion of he duy aio mus be done and he new value is - = 5,6%. Wih hese daa and ceain values he values of he ansiso should be bigge han U M=6V and M=,A, and fo he diode - U M=3V и M=,4A. f couse he elemens should wok wih fequency bigge han khz.

4 ELEKTRNKA R ELEKTRTECHNKA, N 39-5, VL. XX, N. X, XX V. MULATN TUE AN MELNG By he so deemined values of he convee elemens, simulaion eseaches and modeling have been made wih Malab/imulink and LTpice. 3mA 8mA 6mA -6mA -8mA L -3mA 3mA d 35mA -3mA 7V V 3V Fig. 3. Malab/imulink model of a BUCK ZV quasi esonan C-C convee. The pupose of he eseach is checking of he design mehod. n figue 3 is shown he model of he convee in Malab/imulink. n figue 4 he esuls of he modeling ae shown (fom up o down ae cuen ough he ansiso; volage ove he ansiso and he conol signal fo he ansiso). -7V VG 6V 4V V V 8V 6V 4V V V -V.9ms.9ms.93ms.94ms.95ms.96ms.97ms.98ms.99ms 3.ms 3.ms 3.ms Fig. 6. Resuls fom he simulaion of a BUCK ZV quasi esonan C-C convee wih LTpise. Fom he wo simulaion sudies we can see ha he heoeical calculaion and he coecion, elaed o he change of he duy aio, due o using swiching elemens wih sandad values, ae confimed. is impoan o menion ha he condiions fo zeo volage swiching ae fulfilled. Fig. 4. Resuls fom modeling а BUCK ZV quasi esonan C-C convee wih Malab/imulink. n figue 5 is shown he cicui of he sudied convee, which will be simulaed in LTpice. n figue 6 ae shown he esuls of he simulaion (fom up o down ae cuen hough he esonan induco; cuen hough he ansiso; volage ove he ansiso and conol signal fo he ansiso). V. EXPERMENTAL REEARCHE The expeimens ae made on an expeimenal sand, shown on figue 7. The sofwae pa of he conol sysem is implemened wih he sofwae fo visual pogamming LabView, and fo he hadwae pa of he conol sysem a chassis CompacAQ is used wih he conneced modules o i N9 8 inpu AC and N94-8 pogammable TTL inpus/oupus. Fig. 5. imulaion model of a BUCK ZV quasi esonan C-C convee in LTpise Fig. 7. Expeimenal sand By LabView we can achieve a wide ange of vaiaions of he conol fequency and he duy aio, which is vey comfoably fo expeimenal sudies. n figue 8 is shown he block diagam of he pulse geneao.

5 ELEKTRNKA R ELEKTRTECHNKA, N 39-5, VL. XX, N. X, XX C 6.8 nf L uh L 5 uh W C Vin C 5.7uF RL 75Ω Fig.. Powe cicui of he expeimenal sand. Fig. 8. Block diagam of he pulse geneao n he following figues ae shown he esuls fom he measuemens wih he oscilloscope. n figue ae shown he volage ove he ansiso and he conol pulses. Fom he gaphical esuls we can see ha he zeo volage swiching is achieved. Fig. 9. Fon panel of he pulse geneao n figue 9 is shown he fon panel, fom his panel we can change he fequency and he duy aio of he viual insumen. As we can see fom he fon panel i is vey comfoable o se he paamees of he conol pulse fo he ansiso and so we can achieve diffeen woking egimes of he convee. Fo he ealizaion of he powe cicui he following elemens ae used: one MFET ansiso model 6R65, high fequency diode model 6APU4, dive HCPL3 wih inegaed opocouple, esonan induco wih he following value of µh, esonan capacio wih he following value of 6,8nF, file induco wih he following value of 5µH, file capacio wih he following value of 5,7µF and load esiso wih he following value of 75Ω. The cicui of he expeimenal sand of a ZV Busk C-C convee is shown on figue. The measuemens ae done wih oscilloscope model Tekonix T. The volages ae measued wih volage scope wih scale :. The cuens ae measued wih cuen scope. Fig.. Volage acoss he ansiso and conol pulses. n figue ae shown he cuen hough he ansiso and he volage ove i. As we can see when he ansiso uns on we have zeo volage and cuen swiching. These esuls show ha he poposed mehod fo designing is coec, because in he calculaions we have acceped zeo iniial condiion fo he cuen. n figue 3 ae shown he volage ove he swich and he cuen hough he esonan induco and on figue 4 he oupu volage ipples. When woking wih conol fequency of khz allows us he achieving of small ipples (96mV), when he oupu file capacio is wih small value 5,7µF [3, ].

6 ELEKTRNKA R ELEKTRTECHNKA, N 39-5, VL. XX, N. X, XX calculaions esuls, simulaions, mahemaical modeling and expeimens is shown. As we can see hee is a vey good coincidence beween hem (diffeence beween hem no moe han %), despie he assumpions and simplificaions. TABLE. CMPARNG F THE REULT. Paamees LTpice imulink Expeimens Calculaed/ e V (V) (ma) Δ V (mv) V M (V) M (ma) Fig.. Volage ove he ansiso and he cuen hough i. n he ohe side i would be ineesing achieving zeo volage swiching wih possible low value of he volage ove he ansiso. The feaue sudies of he auhos ae dieced in fuhe opimizaions of he design mehod, which will lead o easie way of choosing he elemens of he esonan cicui. All his will lead o a lile volage sess of he powe ansiso. ACKNWLEGMENT This wok is suppoed by he Reseach Council of he Technical Univesiy of ofia unde Conac :3ПД9-3/3 udy of C C convees fo elecical enegy wih low swiching losses. Fig. 3. Volage ove he ansiso and ove he esonan induco. Fig. 4.upu volage ipples.. CNCLUN The made simulaion and expeimenal eseaches of he Buck ZV C C convee check and confimed he poposed, fom he auhos, design mehod. The main pupose in he aicle is finding a comfoable and easy expession fo simple designing of convees, wihou using complicaed calculaions. n able a compaison beween REFERENCE [] Bown M., Powe upply Cookbook, econd Ediion, Elsevie, xfod, UK,. [] Eickson R. W.,. Maksimovic, Fundamenals of Powe Eleconics, econd Ediion, Kluwe Academic Publishes Goup,. [3] Jankovskis J.,. epins, N. Ponomaenko, Effecs of pead pecum on upu File of Buck Convee, cienific Jounal Eleconics and Elecical Engineeing, Vol. 9, No 5, 3, Kaunas, Lihuania, pp [4] Kazimieczuk M. K. and. Czakowski, Resonan Powe Convees, EEE Pess and John Wiley & ons, New Yok, NY nd Ediion, pp. -595, BN ,. [5] Kazimieczuk M. K., Pulse-Widh Modulaed C-C Powe Convees, John Wiley & ons, New Yok, NY, 8, pp. -78, BN-: , BN-3: [6] Kizhanovski V. G.,. V. Chenov, and M. K. Kazimieczuk, Low-volage eleconic ballas based on Class E oscillao, EEE Tans. Powe Eleconics, vol., no. 3, pp , May 7. [7] Lunca E., A. alceanu, Viual nsumenaion Appoach fo Teaching EMC Conceps, cienific Jounal Eleconics and Elecical Engineeing, Vol. 7, No,, Kaunas, Lihuania, pp [8] Mask R., emysifying wiching Powe upplies, Elsevie, xfod, UK, 5. [9] Mohan, Ned; Undeland, Toe M.; Robbins, William P., Powe Eleconics - Convees, Applicaions, and esign (3d Ediion), 3 John Wiley & ons. [] Rashid M. H., Powe Eleconics handbook: devices, cicuis, and applicaions, Academic Pess, 7. [] Rashid M. H., Powe Eleconics: Cicuis, evices and Applicaions, Peason/Penice Hall, 3. [] epins., J. Jankovskis, udy of Fequency Modulaed Boos Convee peaing in isconinuous Conducion Mode, cienific Jounal Eleconics and Elecical Engineeing, Vol., No 6,, Kaunas, Lihuania, pp [3] Zinoviev G., Fundamenals of Powe Eleconics - pa, Novosibisk ae Univesiy, Novosibisk, Russia, 4, (in Russian).