Current-mode one-cycle control applied to linear–assisted DC/DC converters

Cu en -Mode One-Cycle Con ol Applied o Linea –Assis ed DC/DC Con e e s He minio Ma ínez-Ga cía, Membe , IEEE, An oni G au-Saldes, Membe , IEEE Yolanda Bolea-Mon e, Membe , IEEE, and Juan Gámiz-Ca o Abs ac This a icle shows he p oposal o an cu en -mode one-cycle con ol o linea -assis ed DC/DC con e e s. Linea -assis ed DC/DC con e e s a e s uc u es ha allow o ake ad an ages o he wo classic al e na i es in he design o powe supply sys ems: ol age linea egula o s (classic NPN opology o LDO –low d opou –) and swi ching DC/DC con e e s. The cu en -mode one-cycle con ol echnique is p oposed in o de o ob ain he du y cycle o he linea -assis ed con e e swi ch. The p oposed s uc u e can p o ide an ou pu wi h sui able load and line egula ions. The pape shows he design and simula ion esul s o he p oposed cu en -mode one-cycle linea - assis ed con e e . I. INTRODUCTION Linea -assis ed DC/DC con e e s (also known as linea -swi ching hyb id con e e s) a e ci cui al s uc u es ha p esen an inc easing in e es o he implemen a ion o powe supply sys ems ha equi e wo demanding design speci ica ions: (1) high slew- a e o he ou pu cu en and (2) high cu en consump ion by he ou pu load. This i is he case o he sys ems based on he mode n mic op ocesso s and DSPs, whe e bo h equi emen s con e ge [1], [2]. These linea -swi ching hyb id con e e s a e able o combine he well-known ad an ages o he wo exis ing ypical al e na i es o he implemen a ion o DC/DC ol age egula o s o con e e s, diminishing as well hei disad an ages. These wo al e na i es a e known la gely: (1) he use o ol age se ies linea egula o s (classic s anda d NPN –o nMOS– opologies and LDO) ha e been widely used o some decades [3]-[5], and (2) he DC/DC swi ching con e e s, hanks o which high cu en powe supply sys ems can be ob ained [6]-[8]. Linea -assis ed DC/DC con e e s can be implemen ed on p in ed ci cui s using disc e e componen s. Ne e heless, hey a e also an a ac i e al e na i e suscep ible o be in eg a ed in on-chip powe supply sys ems as a pa o powe managemen sys ems. An impo an pa o hese con e e s is hei con olle . Some al e na i es a e p esen [9]-[12]. Howe e , he nonlinea con ol echnique known as one-cycle con ol ([13], [14]) is p oposed in cu en a icle. One-cycle con ol akes ad an age o he pulsed and nonlinea na u e o swi ching con e e s and achie es ins an aneous dynamic con ol o he a e age alue o a swi ched a iable; mo e speci ically, i akes only one swi ching cycle o he a e age alue o he swi ched a iable o each a new s eady s a e a e a ansien . The e is no s eady-s a e e o o dynamic e o be ween he con ol e e ence and he a e age alue o he swi ched a iable. This echnique p o ides as dynamic esponse, excellen powe sou ce dis u bance ejec ion, obus pe o mance, and au oma ic swi ching e o co ec ion. Though one-cycle con ol has so many ad an ages, i is in i mness o load dis u bance. Howe e , he inclusion in he linea - assis ed con e e o a ol age linea egula o p o ides he sui able load egula ion hank o a second loop included in he linea egula o block. II. BASIC TOPOLOGY OF A LINEAR-ASSISTED DC/DC CONVERTER The basic scheme o a single ou pu linea -assis ed con e e is shown in igu e 1 [11], [12]. This s uc u e consis s, mainly, o a ol age linea egula o in pa allel wi h a s ep-down swi ching DC/DC con e e . In his ype o con e e s, he alue o he ou pu ol age, supposed cons an , is ixed wi h good p ecision by he ol age linea egula o . The cu en lowing h ough his linea egula o is cons an ly sensed by he cu en sense elemen Rm. Based on i s alue, he con olle ac i a es o no he ou pu o compa a o CMP1 ha , as well, leads o he swi ch elemen o he DC/DC swi ching con e e . The e o e, no ice ha he cu en h ough he linea egula o cons i u es a measu emen o he e o o he powe supply sys em. The powe s age ( ha is, he swi ching con e e ) injec s in he ou pu he necessa y cu en o o ce o a minimum alue (no necessa ily ze o) he cu en lowing h ough he linea egula o . As a consequence, i is ob ained, al oge he , a powe supply sys em whe e he swi ching equency comes ixed, among o he pa ame e s (such as he possible hys e esis o he analog compa a o ), by he alue o he cu en h ough he linea egula o . On he o he hand, he ou pu ol age alue is ixed by he ol age linea egula o . Manusc ip ecei ed June 1s , 2011. This wo k was suppo ed in pa by he p ojec TEC2010-15765 (subp og ama MIC) om he Spanish MCYT and EU FEDER unds. He minio Ma ínez-Ga cía is wi h he College o Indus ial Enginee ing o Ba celona (EUETIB), Depa men o Elec onics Enginee ing, Technical Uni e si y o Ca alonia (UPC). C/ Com e d’U gell, nº 187. 08036 - Ba celona. SPAIN (co esponding au ho o p o ide phone: 34-93-413-7290; ax: 34- 93-4137400; e-mail: he minio.m[email p o ec ed]). An oni G au-Saldes is wi h he Depa men o Au oma ic Con ol (ESAII), Technical Uni e si y o Ca alonia (UPC). C/ Pau Ga gallo, nº 5. 08028 - Ba celona. SPAIN (e-mail: [email p o ec ed]du). Yolanda Bolea-Mon e is wi h he Depa men o Au oma ic Con ol (ESAII), Technical Uni e si y o Ca alonia (UPC). C/ Pau Ga gallo, nº 5. 08028 - Ba celona. SPAIN (e-mail: y[email p o ec ed]). Juan Gámiz-Ca o is wi h he College o Indus ial Enginee ing o Ba celona (EUETIB), Depa men o Au oma ic Con ol (ESAII), Technical Uni e si y o Ca alonia (UPC). C/ Com e d’U gell, nº 187. 08036 - Ba celona. SPAIN (e-mail: juan.ga[email p o ec ed]). ! ! 48 IV Semina o Ad anced Indus ial Con ol Applica ions In he linea -assis ed con e e in igu e 2, in which he swi ching con e e is a s ep-down ype [11], [12], he linea egula o consis s o a push-pull ou pu s age ( ansis o s Q2a and Q2b). In his s a egy, he main objec i e o he DC/DC swi ching con e e is o p o ide almos all he load cu en in s eady-s a e condi ions ( o ob ain a good e iciency o he whole sys em). Thus, in s eady s a e, he linea egula o p o ides a li le pa o he load cu en , main aining he ou pu ol age o an accep able cons an alue. Vou Vin I eg Iou IL VC CMP1 L1 IQ Rm RL Vol age Linea Regula o V e + – + – D i e DC-DC Swi ching Con e e Cu en Sensing Vou Vin Iou IL VC L1 D1 Q1 Vin CMP1 Q2a Q2b I eg Vin VZ OA1 Rm R L V e + – + – R3 R1 R2 Vol age Linea Regula o + – Cu en Sensing Fig. 1. Block diag am o he p oposed linea -assis ed con e e . Fig. 2. Basic s uc u e o he p oposed linea -assis ed DC/DC con e e . As a ma e o ac , i he cu en demanded by he load Iou is in e io o a maximum alue o cu en , which we will denomina e swi ching h eshold cu en , Iγ, he ou pu o compa a o CMP1 will be a low le el, disabling he DC/DC swi ching con e e and, hus, he cu en lowing h ough induc o L1 will be ze o ( igu e 3). The e o e, he ol age linea egula o supplies he load RL, p o iding all he ou pu cu en (I eg=Iou ). Howe e , when he cu en demanded by he load o e passes his cu en limi Iγ, au oma ically he ou pu o he compa a o will pass o high le el, causing ha he cu en h ough he induc ance L1 g ows linea ly app oxima ely acco ding o: 1 1 () ( ) in ou LL VV i I L    (1) In his exp ession, he conduc ion collec o -emi e ol age o ansis o Q1 is igno ed. IL(τ1) is he ini ial alue o he cu en h ough induc o L1 a he ime ins an in which L1 s a s conduc ion (TON). Conside ing ha he ou pu cu en Iou =I eg+IL, and is assumed o be cons an (equal o Vou /RL), he linea egula o cu en I eg will dec ease linea ly, un il becoming sligh ly smalle han Iγ. A his momen , he compa a o will change i s ou pu o low le el, cu ing he ansis o Q1 and causing ha he cu en ough he induc o dec eases acco ding o equa ion (2) 2 1 () ( ) ou LL V i I L    (2) In his exp ession i is conside ed ha he diode D1 is ideal (wi h ze o di ec ol age). IL(τ2) is he maximum alue eached by he cu en lowing h ough he induc o (jus a he beginning o he in e al TOFF). When he induc o cu en dec eases o a alue in which I eg>Iγ, he compa a o changes i s s a e o high le el, epea ing he cycle again. Wi hou hys e esis in he compa a o , he swi ching poin o he DC/DC swi ching con e e is gi en by he swi ching h eshold cu en , Iγ, o he linea egula o . This one can be adjus ed o a alue hanks o he gain o he cu en sensing elemen , Rm, and he e e ence ol age V e , acco ding o he exp ession: e m V IR   (3) In case o a compa a o wi hou hys e esis, in insic delays o he elec onic ci cui s de e mine a small hys e esis ha limi s he maximum alue o he linea -assis ed con e e swi ching equency. Howe e , wi h he objec i e o ixing his swi ching equency o a p ac ical alue (in o de no o inc ease signi ican ly losses by he swi ching p ocess), i is impo an o add he a o emen ioned hys e esis o he compa a o CMP1 ( igu e 2). Deno ing VH and VL as he supe io and in e io le els swi ching o his compa a o ( igu e 3), he alue o his equency can be de e mined as: ! ! IV Semina o Ad anced Indus ial Con ol Applica ions 49 lim 1 1 ou ou HL in VV R LV V V     (4) I is impo an o emphasize ha , educing he alue o he powe dissipa ed in he pass ansis o o he linea egula o inc eases he e iciency o he se , e en wi h signi ican ou pu cu en s. The e o e, i is impo an o ix he cu en limi Iγ o a commi men alue be ween he minimum necessa y o ope a e he linea -assis ed con e e p ope ly bu wi hou penalizing i s good cha ac e is ics o egula ion. Thus, conside ing comme cial model o ol age linea egula o s, his alue is a ound ew mA. Wha is mo e, wi h he pu pose o ob aining a good egula ion o he ou pu , wi hou signi ican ipple, i is manda o y ha he cu en p o ided by he linea egula o does no each ze o. In ac , in igu e 4 we can app ecia e he ou pu cu en and he cu en lowing h ough he induc o and he linea egula o when he swi ching h eshold cu en Iγ is adjus ed o 50 mA. In his simula ion he e e ence ol age VZ=5 V. T ansien esponse o he con e e can be obse ed wi h Vin=10 V. I is also shown he ci cui esponse o a s ep o he con e e inpu ol age om 10 V o 13 V a =20 µs, as well as he ansien om a educ ion o he load esis ance o he 100%, om 5 Ω o 2.5 Ω a =40 µs. No ice ha he egula ion o he ou pu ol age is excellen . The e o e, he swi ching cu en h eshold mus be a alue such ha :  I signi ican ly does no inc ease he powe dissipa ion o he pass ansis o in he linea egula o and does no diminish excessi ely he e iciency o he egula o .  I does no signi ican ly de e io a e he egula ion o he ou pu ol age. iL( ) i eg( ) I TON TOFF Linea block enabled Swi ching block disabled Bo h linea and swi ching blocks enabled 0 IH IL I (A) Iou IL Iou I eg Vin Vou Time 0s 10us 20us 30us 40us 50us 60us I(L1) I(RL1) IC(Q1) 0A 1.0A 2.0A S EL>> V(VCC) V(VOUT) 0V 5V 10V 1 4V Fig. 3. P inciple o ope a ion o he p oposed linea -assis ed DC/DC con e e . Fig. 4. Response o he con e e shown in igu e 2 wi h Vin=10 V. In addi ion, i can be seen he ci cui esponse o a s ep o he inpu ol age om 10 V o 13 V a he ime ins an =20 µs, and a a ia ion in he load esis ance om 5 Ω o 2.5 Ω a =40 µs. The swi ching h eshold cu en Iγ has been adjus ed o 50 mA. Thus, we can denomina e his ype o con ol as a s a egy con ol wi h nonnull a e age linea egula o cu en . A e some simula ions i can be concluded ha , o load cu en s lowe han 10 A, he sui able alue o Iγ ha ul ills he wo p e ious condi ions is ound o be be ween 10 mA and 50 mA, app oxima ely. III. ONE-CYCLE CONTROL CONCEPT One cycle con ol was p oposed by Keyue M. Smedley in 1991 and ealized ini ially in buck PWM con e e [13]-[15]. DC/DC swi ching con e e s wi h one-cycle con ol ejec inpu pe u ba ions in only one swi ching cycle and ollow he con ol e e ence ins an ly. I is said ha one-cycle con ol is uni e sal and can be applied di ec ly o swi ching con e e s in ei he PWM o quasi esonan modes [15], [16]. F om hen on, wi h one-cycle con ol, boos con e e , Cûk con e e , h ee- phase PFC con e e and h ee-phase boos ec i ie ha e been p esen ed. Du ing his pe iod, a gene al-pu pose eed odwa d one cycle con olle was also ad anced. One-cycle con ol heo y is shown in igu e 5, and i s ope a ing wa e o ms a e shown in igu e 6. The swi ch unc ion d( ), a bina y unc ion, can be desc ibed by: 1 o 0 () 0 o ON ON S T d T T       (6) In each cycle, he swi ch is on o a ime du a ion TON and is o o a ime du a ion TOFF, whe e TON+TOFF=TS is he swi ching pe iod. The du y- a io, equal o he a e age alue o d( ), ha is  ()d , is gi en by:  () ()/ ON S d T T (7) F om igu e 5 and equa ion (6), we know: ! ! 50 IV Semina o Ad anced Indus ial Con ol Applica ions () () () y d x  (8) The a e age o he swi ched a iable is [14]:   1() () () () () ON ON TT oo SS x y x d d x d TT   (9) OA1 y( ) CMP1 x( ) – + Ci Ri in ( ) ese – + One-cycle con olled cons an equency swi ch Con olle REF( ) Clock cmp( ) x( ) y( ) in ( ) REF( ) clock cmp( ) Fig. 5. Basic scheme o one-cycle con ol. Fig. 6. Typical wa e o ms o one-cycle con ol. I he du y- a io o swi ch is modula ed such ha he in eg a ion o he swi ched a iable a he swi ch ou pu is exac ly equal o he in eg a ion o he con ol e e ence in each cycle, ha is: () () ON S TT REF oo x d d   (10) Then:  11 () () () () ON S TT REF REF oo SS y x d d TT    (11) Wi h one-cycle con ol, he e ec i e ou pu signal o he swi ch (i.e., he a e age alue o he swi ched a iable) is:  () () REF y  (12) The key componen o one-cycle con ol echnique is he in eg a o and he ese e . The in eg a ion s a s he momen when he swi ch is u ned on by he ix equency clock pulse. The in eg a ion alue is gi en by: in () () is cons an o kx d k (13) When he in eg a ion alue eaches he con ol e e ence, he con olle sends a command o he swi ch o change i om he on s a e o he o s a e. The du y- a io o he p esen cycle is de e mined by he ollowing equa ion: () () S dT REF o kx d   (14) The a e age alue o he swi ched a iable a he swi ch ou pu is gua an eed o be:  11 () () () S dT REF o SS y x d TkT   (15) in each cycle. Figu e 6 shows he ope a ing wa e o ms o he ci cui when REF( ) is cons an . Acco ding o he one-cycle con ol he adjus ing is comple ed in one swi ching cycle o ejec he powe sou ce dis u bance. So i is excellen o powe sou ce dis u bance ejec ion. Howe e , al hough one-cycle con ol is excellen o ejec ion he powe sou ce dis u bance, i is in i mness o load dis u bance. The pape p oposes a new con ol echnique, imp o ed one-cycle con ol echnique ha can o e come his sho coming. IV. TOPOLOGY OF THE CURRENT-MODE ONE-CYCLE LINEAR-ASSISTED DC/DC CONVERTER Based on he linea -assis ed DC/DC con e e , he s uc u e o he p oposed linea -assis ed DC/DC con e e wi h cu en - mode one-cycle con ol s a egy is shown in igu e 7. In his igu e we can obse e he linea egula o , he swi ching DC/DC con e e and he con ol loop ha ixes he du y cycle o he swi ch elemen Q1. ! ! IV Semina o Ad anced Indus ial Con ol Applica ions 51 Compa ing igu es 7 and 5, he basic idea o he p oposed con ol is o achie e an a e age induc o cu en du ing he ime in e al TON equal o he ou pu cu en . Thus, ha ing in o accoun ha : () () L eg ou i i I   (16) he a e age alue p o ided by he linea egula o block will end o be ze o. In addi ion, no ice ha he main di e ence wi h one-cycle con ol is ha he linea egula o ixes he ou pu ol age. In ac , he ou pu ol age is gi en (and ixed) by he linea egula o . The e o e, acco ding o be o e de ailed, he new p oposed echnique can ejec no only powe dis u bances, bu load dis u bances oo. Vou Vin Iou iL( ) VC D1 Q1 CMP1 L1 i eg( ) Q2a Q2b VZ OA1 OA1 VC Rm=–1 Rm=–1 MUL1 RL + – D i e RS Flip–Flop R S Q VCLK /Q   ()d Vol age Linea Regula o + – – + Ci Ri in ( ) Low Pass Fil e ese Cu en Sensing Cu en Sensing mul ( ) Swi ching DC/DC Con e e cmp( ) i( ) y( ) in ( ) REF( )=  () () mul ou d I clock cmp( ) Fig. 7.- Basic s uc u e o a cu en -mode one-cycle linea -assis ed DC/DC con e e . Fig. 8. Typical wa e o ms o he p oposed linea -assis ed con e e wi h cu en -mode one-cycle con ol. The main idea o he p oposed con ol is o achie e ha he a e age alue o he cu en lowing ac oss he induc o du ing he ime in e al TON (=  () S d T) equals o he a e age alue o he cu en h ough he load du ing his in e al. The e o e, conside ing ha he ou pu cu en is gi en by Iou =I eg+IL, he a e age cu en lowing h ough he linea egula o will end o ze o. On he one hand, he low-pass il e ex ac he a e age alue o he du y cycle,  ()d , ha mul iplied by he ou pu cu en Iou (conside ed cons an ), p o ides a measu e o he a e age alue o he cu en lowing h ough he load du ing he in e al TON. Thus, conside ing he gain ac o o he cu en sensing elemen Rm=1, we ha e:  () () mul ou d I (17) On he o he hand, he analog in eg a o p o ides he measu e o he a e age alue o he cu en lowing ac oss he induc o du ing he ime in e al TON, conside ing ha he ime cons an is gi en by: ii S RC T  (18) The e o e: in 11 () () () LL oo ii S i d i d RC T   (19) whe e he gain ac o o he cu en sensing elemen Rm=–1 ( he nega i e sign compensa es he addi ional in e sion p o ided by he in eg a o ). The a e age alue o he swi ched a iable a he swi ch ou pu is gua an eed o be:  1() () S dT L ou o S i d d I T  (20) in each cycle. Figu e 8 shows he ope a ing wa e o ms o he ci cui when REF( ) is cons an . V. SIMULATION RESULTS OF THE CURRENT-MODE ONE-CYCLE LINEAR-ASSISTED DC/DC CONVERTER In o de o alida e he p esen ed s uc u e o he cu en -mode one-cycle linea -assis ed DC-DC con e e in igu e 7, simula ion esul s ha e been ob ained om a sys em ha p o ides 5.0 V a he ou pu Vou . The alue o he induc o is L=100 H. Figu e 9 shows he ci cui he s a -up ansien wa e o ms when he cu en -mode one-cycle linea -assis ed DC/DC con e e p o ides 2 A a he ou pu Vou . No ice ha he one-cycle con ol loop assu es a alue o he a e age cu en lowing h ough he linea s age nea ze o. ! ! 52 IV Semina o Ad anced Indus ial Con ol Applica ions Figu e 10 shows he ansien esponse o he linea -assis ed DC/DC con e e o a s ep when he e e ence ol age inc eases om 5 V o 8 V a 500 µs. Time 0s 50us 100us 150us 200us 250us 300us 350us 400us I(Rsens) I(RL1) I(L1) -1.0A 0A 1.0A 2.0A 3.0A Time 0s 50us 100us 150us 200us 250us 300us 350us 400us V(Vou ) 0V 2.0V 4.0V 6.0V Iou IL( ) I eg( ) Vou Time 0s 100us 200us 300us 400us 500us 600us 700us 800us V(Vou ) 0V 5.0V 10.0V Time 0s 100us 200us 300us 400us 500us 600us 700us 800us I(Rsens) I(RL1) I(L1) 0A 2.0A 4.0A -1.0A Iou IL( ) I eg( ) Vou Fig. 9. S a -up ansien wa e o ms when he cu en -mode one-cycle linea - assis ed DC/DC con e e p o ides 2 A a he ou pu Vou . No ice ha he one- cycle con ol loop assu es a alue o he a e age cu en lowing h ough he linea s age nea ze o. Fig. 10. T ansien esponse o he linea -assis ed DC/DC con e e o a s ep when he e e ence ol age inc eases om 5 V o 8 V a 500 µs. VI. CONCLUSIONS In he p esen ed pape , he design and simula ion o a cu en -mode one-cycle con ol linea -assis ed DC/DC con e e has been ca ied ou . The a icle has shown ha linea -assis ed DC/DC con e e s a e sui able s uc u es ha allow o ake ad an ages o he wo classic al e na i es in he design o powe supply sys ems ( ol age linea egula o s and swi ching DC/DC con e e s). In addi ion, s a ing om his linea -assis ed opology, and hanks o he gene al idea o one-cycle con ol, a cu en -mode one cycle linea -assis ed DC/DC con e e has been p oposed. As a whole, he p oposed DC/DC con e e p o ides a good line egula ion, hanks o he excellen powe sou ce dis u bance ejec ion shown by he one-cycle con ol loop, a sui able load egula ion hanks o he excellen load dis u bance shown by he linea egula o and, inally, high e iciency shown by he swi ching con e e . ACKNOWLEDGMENT This wo k has been pa ially unded by p ojec TEC2010-15765 (subp og ama MIC) om he Spanish MCYT and EU FEDER unds. REFERENCES [1] X. Zhou, P. L. Wong, P. Xu, F. C. Lee, A. Q. Huang. “In es iga ion o Candida e VRM Topologies o Fu u e Mic op ocesso s”. 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