Exclusive Technology Feature. Current-Loop Control In Switching Converters Part 6: Slope Compensation. Slope Compensation. ISSUE: February 2012

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1 : Fbruary Currn-oop Conro n wchng Convrr Par 6: op Copnaon By nn Fuch, nnovaa aboraor, Cayo, B h a nan of h arc prnd a rfnd od of currn-od conro ha provd a dpr unfcaon of h qua-ac or ow-frquncy currn-oop bhavor wh h apng apc by drvng h dynac quaon for ranfr funcon fro h avrag currn varab rahr han h vay currn Hr n par 6 of h r, h ffc of op copnaon ncudd n h rfnd od pcfcay, w anay h pac of hr dffrn op-copnaon ch on h rfnd od, nong ar and dffrnc n h y wavfor quaon W ao no how h rfnd od wh op copnaon copar o arr od of currn-od conro Fnay, w xan h pcaon of h anay n r of abhng gudn for convrr dgn ha nur oop aby op Copnaon op copnaon a dynac copnaon chnqu by whch h op of h fdbac nducor currn odfd by h addon of a rap o ru n h nd currn n h con, h ncrna oupu varab xprd a, o ncud h op-copnaon funcon, h op-copnad wavfor npu o h PWM crcu a h nd currn,, a hown n h boc dagra op copnaon ch dffr n how addd o and h uaon rqur an addona ung boc, a hown n h ch of h dagra, h uaon occur whn h forward pah wh h rror quany C and h copnaon funcon, ; C h wo ohr pob ocaon for h uaon of ar n h npu pah and n h fdbac pah For h npu pah, h npu, ffcvy bco : A ur n h fdbac pah ubrac fro hn h copnad rror quany,, h nd fdbac currn ubracd fro h npu o for h rror quany: HowPowr A rgh rrvd Pag of 3

2 Bcau addon aocav and couav, and wh no addona procng bwn uaon, h hr an of cobnng h hr quan coprng ar quvan Conquny, w can condr h ffc of o b ha of an addon o h coandd npu, houd hrfor b pob o ubu no h uncopnad cod-oop for and drv h copnad nducor-currn wavfor quaon hough vnuay w wan h ncrna od a hown n h boc dagra, h drvaon bgn wh h oa varab By addng h oa a a copnang wavfor o h oop rror, h cau o b ard, a vau ach cyc drnd by h F boc F conan no ony h coparaor apng funcon f abd PWM bu ao a ung boc prcdng whch oupu h nd wavfor, op copnaon affc h nd wavfor a an addon o h rror quany, C h nd currn C h rung G h uncopnad cod-oop wavfor quaon of and ar affcd by op copnaon n ha now drnd by F Howvr, h op of ran h uncopnad op bcau hy ar drnd by convrr crcu parar, no by F h op and off of aon ar odfd by h forward-pah rananc, G, howvr, an ncrna ranfr funcon and h oa-varab / nonnar and can vary bwn on- and off- of h cyc h copca h drnaon of F n ha u b nard G d arady nar h corrc vau for a nard F addrd n a ar con By ubung for no h uncopnad cod-oop quaon, h copnad quaon for ru; G G G G G G whr G/ G h unfd-od uncopnad cod-oop ranfr funcon of / h copnad hrfor h uncopnad wh h addd rpon o op copnaon,, by h a oop Rurnng o h oa varab and ubung no h uncopnad dcr- wh a addona npu, Whn an xpron for ubud, w f conan ncud and r, whch odfy h coffcn of h nd currn can b xprd or gnray n ady-a by appyng h op quaon; h apng nan a whn h cyc or n oa drnd by F accordng o h conro aw: h gnra for of dcrbng h apng vn of cyc HowPowr A rgh rrvd Pag of 3

3 HowPowr A rgh rrvd Pag 3 of 3 whr h quaon dcrb h nd currn a h apng, h aby of w, of cour, affc oop aby bcau drn oop aby anay hrfor can b an anay of h aby of h conro aw,, drn and can b ovd for whn ubud no Rurnng o h gnra quaon for, h xpron n ha h for of C xcp ha of h prvou cyc For ady-a opraon, h wavfor ab and ubung fro h op quaon for, hn -a ady off V h uua hod of anay drv h oa cod-oop wavfor quaon fro h wavfor gory undr ady-a rpon, and hn dffrna or prurb h o produc h ncrna quaon h approach an hr wh dncon anand bwn and and wh h addona donraon ha h wavfor quaon ar quvan o h uncopnad quaon wh h addon of o, hu ocang op copnaon n h od o F h oa-varab vay-currn wavfor w b drvd for copn and ud o how h ocaaon of o F h oa and ncrna vay-currn wavfor quaon w b hown o b quvan for h gvn op-copnaon ch wh dffr wh h avrag-currn wavfor ar ao drvd op w b hd conan for h anay Fr op-copnaon ch o h oa-varab oop rror C addd a ngav-op copnaon rap of op whr c, and a wchng h op,, ran unchangd by op copnaon and a h nd of h off-, For h up-op gn, h op of ran h unard and h conro-aw quaon A h apng pon, h nducor-currn pa vau ovng for,

4 HowPowr A rgh rrvd Pag 4 of 3 ubung h no, ubung h pa vau no h off- quaon, h rung copnad oa vay nducor currn Coparng h op-copnad o h uncopnad, wha ha changd ar h coffcn whch con of op xpron woud appar ha ha caud o hav changd op bu h woud b a adng nrpraon of h copnad xpron A ha copnaon ha affcd a chang n a xprd n op h convrr crcu parar hav no changd and hy drn op h dcr- coffcn ar rao of op and ar dpndn ony on Conquny, houd b pob o xpr n obrvab crcu op, odfd ony by h nroducon of a h oop npu o how ha h oa can b wrn wh ocaaon of a addd o, ar wh h uncopnad and add o : ubung for, h bco ubung h ohr of h wo uncopnad wavfor quan, hn

5 HowPowr A rgh rrvd Pag 5 of 3 Afr o agbra, h rduc o h a a drvd abov Conquny, h ffc of copnaon n h wavfor quaon can b ocad o h npu rror ur a addd o n h gnra uncopnad wavfor quaon h op xpron can b rpacd by h pr duy-rao xpron for ady-a wavfor conan fro charg baanc Appyng h wavfor quaon of for ady-a rpon, off on h foowng convron forua appy o a a hr ch fa ou of h conran: ubung fro h xpron, h oa op-copnad vay nducor currn n n, h quaon h a a for h uncopnad wavfor Ony whn h coffcn ar xprd n op hr a dffrnc Conquny, h ffc of op copnaon nry conand whn ffc on op copnaon odf h unodfd wavfor by addng o a copnaon rap o ha h nd addon ru n h drd h odfd op of affc how drnd wh h nducor-currn wavfor connu o b dcrbd by h a quaon n ubung no, h oa quaon for a h nd of h cyc h pf o h ha h a for a h gnra bu wh dffrn op xpron f wrn n, howvr, Whn ubud n h gnra wrn n, h ru h a op copnaon chang h op-rao coffcn a dd for, and hy ar h a n a h uncopnad rao h conan r, whch rad o, ran unchangd ang h dffrna of h oa currn, h copnad ncrna vay nducor currn

6 HowPowr A rgh rrvd Pag 6 of 3 h uncopnad ncrna vay currn, affcd ony by an addon o of : h ncrna a funcon of h uncopnad d, d h uncopnad d ud n bcau h d conn wh h uncopnad h ffc of o odfy h uncopnad wavfor quaon by ffc on h uncopnad oop ubung d, d ubung no h uncopnad and pfyng, h a ncrna ru a drvd abov fro h copnad oa-varab xpron for h ncrna can b found by ang h dffrna of h oa ; h can b corroborad wh h ocaaon propry by ubung havng h uncopnad d no hn Cocng r, h ru quvan o h prvou quaon:

7 HowPowr A rgh rrvd Pag 7 of 3 For avrag oa nducor currn, h dcr- or ubung for fro h gnra wavfor quaon n coffcn and rducng, ndr ady-a opraon and wh conan op, h cyc vay currn vau ar V hn V V whr h avrag ovr a cyc A ngav ha h ffc of rducng and caung o b han ha of h uncopnad oop h ncrna of h uncopnad ady-a wavfor By ubung, no d wh conan convrr npu and oupu voag whrby v OFF V off, hn / V v d off OFF ubung d no,

8 HowPowr A rgh rrvd Pag 8 of 3 d Wh addd o, bco ubung for and afr o agbra, h rduc o a cond-ordr dffrnc quaon: cond op-copnaon ch For h cond ch, copnang op,, addd o boh up-op and down-op gn of h oop rror h accophd by ubracng fro h a copnang rap a n h fr ch, h ru hn ubracd fro, o ha C h quvan o h fr ch, hough pa a wh h on- op of pr bcau of addon of h wo ffc canc, rung n h a h wavfor quaon ar drvd fro h wavfor gory A h ap, hn h dnca o h fr ch urng h off-, connu o hav addd o h op, and a, ubung for and pfyng,

9 HowPowr A rgh rrvd Pag 9 of 3 Copard o h fr ch, h wo xpron for ar qua n h fr ch, copard o wh n h cond ch, hy ar cobnd bfor bng copard o ro Y h dynac of h cobnaon of a hr wavfor ha drn h aby of and h vau of, whhr hy ar addd bfor or a h npu of h coparaor h coparaor rpond o h dffrnc bwn npu, and ha conu h copon of h uaon n n h fr ch, hr no ng crcu wavfor a n h cond, hough can b rgardd a xng a h coparaor npu h abracd and no hr coparaor npu wavfor ha rvan o h anay of h fr ch and whch a quvan o h cond ch h coparaor oupu h gn or poary of h coparaor opraon of h PWM boc ar quvan bwn ch ovng for by ubung h a a n h fr ch no h a uncopnad quaon produc h a ru: h avrag nducor currn for h cond copnaon ch h a a h fr; h wavfor quaon ar dnca and h avrag currn u ao b h a ndr ady-a opraon, V and V V hn ang h ady-a avrag currn fro h fr ch and dvopng furhr by ubung V, V h quaon for and u b h a a ho of h fr ch bcau h wavfor and avragng quaon fro whch hy ar drvd ar h a hrd op-copnaon ch h hrd ch found n Rdy and hhan dffr fro h prvou ch n ha h copnang rap non-ro ony durng h on- Whn a cyc,, h nd currn a h ap pon hn and ov for ; h quaon h a a for h fr wo ch a u b; h condon durng on- ar h a h nducor currn w hrfor hav h a wavfor quaon a h prvou ch:

10 HowPowr A rgh rrvd Pag of 3 Bcau h op copnaon dffrn, dffr fro h prvou ch For h off- gn, ubung no h nd currn, vau a h nd of h cyc h bco h nd vay currn; h nd vay currn ha h a for a of h prvou ch bu h op-rao coffcn ar no h a n ady-a, and h op rao ar rad o by h foowng forua: hn n, h ady-a h a a h prvou ch h avrag nducor currn quaon h a a for h prvou ch, hough can arnavy b drvd for h hrd ch fro afr nad h quaon do no ncud hough h ffc of on ar pc n ncrna Avrag nducor Currn Wh op Copnaon h oa and ncrna wavfor quaon for h hr op-copnaon ch condrd ar quvan whhr h coffcn ar xprd a op rao or duy-rao hu h nducor currn quaon ndpndn of op copnaon ch, and ary, h ncrna ndpndn of op-copnaon ch and

11 HowPowr A rgh rrvd Pag of 3 h -ranfor of xprd a a vay-currn-gan ranfr funcon n h -doan, CV and ab whn / < or < ½ h h cod-oop quaon of h apd-oop od of Rdy quvan o ha of h unfd od of an whch ap concdn wh h currn-oop ranfr funcon ffcvy h a a ha ud n h unfd od of an bad on h a wavfor dffrnc quaon and conquny hr a dcrpancy n h od bwn vay-currn apng and avrag-currn drvaon of F h ru n a od ha do no fuy unfy h avrag currn wh h apng ffc of h apd-oop od h rfnd od ap o a a fu unfcaon by drvng F a a conqunc of ung avrag n h wavfor quaon of h currn-oop ranfr funcon h nd currn,, h a for h fr and cond ch and dffr fro h hrd ch ony n how op rao ar rad o xprd n, hy ar quvan: h dffrnc quaon dpndn on and ndpndn of copnaon ch; h cond-ordr quaon n h -doan can b wrn a h cod-oop ranfr funcon,

12 HowPowr A rgh rrvd Pag of 3 ng A/, h rduc o C : C n norad for, h frquny-occurrng and h pa-o-pa PWM currn rap h condon ofn chon for opa dynac rpon whch ru n h abov xpron rducd o n h raur, h pron o gvn ha can xcd 5 n a ab oop bcau of Howvr, h ffc of o rduc h vau of o ha whn h ab nrva Conquny, h drc hod of oop copnaon o dgn h oop o opra whn an accpab rpon rang of by cng urn rao and ohr rvan parar o p whn accpab dynac-rpon bound Howvr, ao ha an ffc on F and hu frquncy rpon, bu h affc connuou-fdbac aby nvovng oop gan and no h aby rad o dcr- ffc n h nx and fna con of h arc, par 7, w w rurn o a coparon of h poran PWM facor, F n h currn oop and how ha h rfnd od copab wh h ajor xng od whn rducd o accooda hr ng aupon Fnay, w cop h nghy proc of odng h currn-oop wh h rgng of wavfor-bad and crcu-bad odng Abou h Auhor nn Fuch ha bn nvovd n powr cronc for 5 yar, dgnng oordrv and powr convrr H ha an nrun bacground fro ronx, whr h dgnd and aurn qupn and dd rarch n ab H ha ay bn dong currn-oop convrr odng and convrr opaon

13 For or on currn-od conro hod, h HowPowr gn Gud, c h Advancd arch opon, go o arch by gn Gud Cagory, and c Conro Mhod n h gn Ara cagory HowPowr A rgh rrvd Pag 3 of 3