Basic Principle of Buck-Boost

Transcription

1 Bac Prncple of Buck-Boot he buck-boot a popular non-olated nvertng power tage topology, ometme called a tep-up/down power tage. Power upply degner chooe the buck-boot power tage becaue the requred output nverted from the nput voltage, and the output voltage can be ether hgher or lower than the nput voltage. he nput current for a buck-boot power tage dcontnuou, or pulatng, becaue the power wtch Q current that pule from zero to every wtchng cycle. he output current for a buck-boot power tage alo dcontnuou or pulatng becaue the output dode only conduct durng a porton of the wtchng cycle. Fgure how a mplfed chematc of the buck-boot power tage. nductor and capactor make up the effectve output flter. he capactor equvalent ere retance E,, and the nductor dc retance,, are ncluded n the analy. etor repreent the load een by the power upply output. he dode uually called the catch dode, or freewheelng dode. Fgure. Buck Power tage chematc urng normal operaton of the buck-boot power tage, Q repeatedly wtched on and off wth the on- and off-tme governed by the control crcut. h wtchng acton gve re to a tran of pule at the juncton of Q,, and. Although the nductor,, connected to the output capactor,, only when conduct, an effectve / output flter formed. t flter the tran of pule to produce a output voltage.

2 Fgure. Buck Power tage tate he nductor current ncreae durng the on tate gven by: he quantty + the nductor rpple current. he nductor current decreae durng the off tate gven by: he quantty - alo the nductor rpple current. n teady condton, the current ncreae, + and the current decreae - mut be equal. olvng for :... N Q FF d d Q FF FF N d FF N Q

3 A common mplfcaton to aume Q, d, and are mall enough to gnore. ettng Q, d, and to zero, the above equaton mplfe conderably to: Unlke the buck power tage, the average of the nductor current not equal to the output current. o relate the nductor current to the output current, referrng to Fgure and 3, note that the nductor delver current to the output only durng the off tate of the power tage. h current averaged over a complete wtchng cycle equal to the output current becaue the average current n the output capactor mut be equal to zero. Fgure 3. M Buck Power tage Waveform 3

4 FF Avg Avg 5 Fgure 4. Boundary Between ontnuou and contnuou Mode Further reducton n output load current put the power tage nto dcontnuou current conducton modem. he dcontnuou mode power tage nput-to-output relatonhp qute dfferent from the contnuou mode. Fgure 5. contnuou urrent Mode he duraton of the on tate N, where the duty cycle et by the control crcut. he duraton of the off tate FF. he dle tme the remander of the wtchng cycle and gven a -N-FF 3. hee tme are hown wth the waveform n Fgure 5. he nductor current ncreae durng the on tate gven by: + N PK 6 he rpple current magntude, +, alo the peak nductor current, pk, becaue n dcontnuou mode. he current tart at zero each cycle. 4

5 he nductor current decreae durng the off tate gven by: FF 7 A n the contnuou conducton mode cae, the current ncreae, +, durng the on tme and the current decreae durng the off tme, -, are equal. o, N FF 8 Fgure 6. contnuou Mode Buck Power tage Waveform 5

6 6 Now calculate the output current. t the average over one wtchng cycle of the nductor current durng the tme when conduct*. Now olve two equaton, and equaton 8 and 0, the dcontnuou conducton mode buck voltage converon relatonhp gven by: Where K defned a: 9 PK avg 0 K K K M M

7 rtcal nductance he prevou analye for the buck-boot power tage have been for contnuou and dcontnuou conducton mode of teady-tate operaton. he conducton mode of a power tage a functon of nput voltage, output voltage, output current, and the value of the nductor. A buck-boot power tage can be degned to operate n contnuou mode for load current above a certan level uually 5 to 0% of full load. Uually, the nput voltage range, output voltage, and load current are defned by the power tage pecfcaton. h leave the nductor value a the degn parameter to mantan contnuou conducton mode. he mnmum value of nductor to mantan contnuou conducton mode can be determned by the followng procedure. Frt, defne B a the mnmum output current to mantan contnuou conducton mode, normally referred to a the crtcal current. h value hown n Fgure 4. n boundary between M and M, B B Q N 3 n Boundary: o 4 d B N FF 5 M: mn max Q B N mn B o max max 6 7

8 utput apactor n wtchng power upply power tage, the functon of output capactor to tore energy. he output capactance for a boot power tage generally elected to lmt output voltage rpple to the level requred by the pecfcaton. he ere mpedance of the capactor and the power tage output current determne the output voltage rpple. he three element of the capactor that contrbute to t mpedance and output voltage rpple are equvalent ere retance E, equvalent ere nductance E, and capactance. he voltage varaton due to the nductor current flow n the output capactor approxmately: For M Mode: PK + d N max f max For M Mode max f o 8

9 he above equaton baed on the aumpton that all nductor rpple current flow through the capactor and the E zero. Now, aumng that the capactor very large, the E needed to mt the rpple to max : For M Mode: E max For M Mode: Max max + max PK E max max PK *he output flter capactor hould be rated at leat 0~0 tme the calculated capactance and 30 to 50 percent lower than the calculated E. he M value of the rpple current flowng n the output capactancem gven by: M 9

10 0 Buck-Boot / onverter mall gnal Model ranfer Functon: Z G H U load g g ref gan loop G G H M d

11 For M Mode: G d + wz wz + + w0q w0 g Q + w0 w Z w Z *wo Pole f, ne Zero f E for Gd and ne ght-half-plane zero From a practcal vew, at HP zero frequency, the loop gan tart ncreang at a 0dB/decade rate but the loop phae decreae by 45 degree n a normal, HP zero, the loop phae wll ncreae by +45 degree. h mpoe the retrcton that the gan be rolled off to 0dB before encounterng the HP zero. he output nductor, capactor and the capactor E mut be elected o that the double pole occur frt and then the output capactor zero and then the HP zero. h aure that the loop gan croe 0dB at a lope that frt order 0dB/decade and that the ntablty nherently aocated wth the HP zero crcumvented by crong 0dB before the HP zero frequency occur. ompenate rule: 3 4. ecreae the double pole nfluence. f Z compenator f 4 5. roover frequency f f < f E f ~ f ecreae the HP zero nfluence f << f Z HP 6

12 For M Mode: G d g + w P w P

13 3 Applcaton Example of Buck-Boot rcut max max mn max mn o B N B Q

14 N5, o-8,o00ma, foc500khz 8 6.5% 8 5. nductor : he condton of becaue of a contnuou current n the range of the ue voltage 6 max mn.83µ B o max H elect µh, oad current value whch become contnou current condton. 6 max B mn o max ma f B, the peak value of the nductor peak peak + t + N peak A P-MFE ran urrent: Peak value he peak value of the dran current of P-MFE hould be n the rated current value of P-MFE. he peak current of P-MFE aumed to be, obtaned by the followng formula peak A

15 P Q N + o tr + t f f + QGate G f Where t r and t f are the MFE turn-on and turn-off wtchng tme Q Gate the MFE gate-to-ource capactance 3.ode : he peak value of dode current FM FM peak A he Average urrent F F 0. A he repetton peak revere voltage of the dode M M 5

16 Bac Prncple of Flyback he flyback converter baed on the buck-boot converter. t dervaton llutrated n Fg.7. Fgure 7a depct the bac buck-boot converter, wth the wtch realzed ung a MFE and ode. n Fg. 7b, the nductor wndng contructed ung two wre, wth a : turn rato. he bac functon of the nductor unchanged, and the parallel wndng are equvalent to a ngle wndng contructed of larger wre. 6

17 n Fg. 7c, the connecton between the two wndng are broken. ne wndng ued whle the Q conduct, whle the other wndng ued when dode conduct. he total current n the two wndng unchanged from crcut of Fg. 7b; the current now dtrbuted between the wndng dfferently. he magnetc feld nde the nductor n both cae are dentcal. Although the two-wndng magnetc devce repreented ung the ame ymbol a the tranformer, a more decrptve name two-wndng nductor. h devce ometme alo called a flyback tranformer. Fg. 7d llutrate the uual confguraton of the flyback converter. Fgure 7. ervaton of the flyback converter 7

18 Fgure 8. Flyback converter wth tranformer equvalent crcut model he behavor of mot tranformer-olated converter can be adequately undertood by modelng the phycal tranformer wth a mple equvalent crcut contng of an deal tranformer n parallel wth the magnetzng nductance. he magnetzng nductance mut then follow all of the uual rule for nductor; n partcular, voltecond balance mut hold when the crcut operate n teady-tate. h mple that the average voltage appled acro every wndng of the tranformer mut be zero. 8

19 he magnetzng nductance M functon n the ame manner a nductor of the orgnal buck-boot converter of Fg. 7a. When Q conduct, energy from the tored n M. When the dode conduct, th tored energy tranferred to the load, wth the nductor voltage and current caled accordng to the :n turn rato. urng on tate, whle Q conduct, the converter crcut model reduce to Fg. 8a. he nductor voltage, capactor current, and the ource current, are gven by v g v 7 Wth the aumpton that the converter operate wth mall nductor current rpple and mall capactor voltage rpple, the magnetzng current and the output capactor voltage v can be approxmated by ther dc component, and, repectvely. Equaton 7 then become v g 8 urng off tate, the equvalent crcut of Fg. 8b obtaned. he prmary-de magnetzng nductance voltage v, capactor current, and the ource current, are gven by v g n 0 v n v 9 Upon makng the mall-rpple approxmaton, one obtan 9

20 v g n 0 v n 0 he v t, t, and t waveform are ketched n Fg. 9. Fgure 9. Flyback converter waveform, M mode Applcaton of the prncple of volt-econd balance to the prmary-de magnetzng nductance yeld v v + n 0

21 oluton for the converon rato then lead to M n o the converon rato of the flyback converter mlar to that of the buck-boot converter, but contan an added factor of n. Applcaton of the prncple of charge balance to the output capactor lead to + n 3 oluton for yeld n 4 h the dc component of the magnetzng current, referred to yhe prmay. he dc component of the ource current 5 Fgure 0. Flyback converter equvalent crcut model

22 An equvalent crcut whch model the dc component of the flyback converter waveform can be contructed. he reultng dc equvalent crcut of the flyback converter gven n Fg. 0. t contan a : buck-type converon rato, followed by a -: boot-type converon rato, and an added factor of :n, arng from the flyback tranformer turn rato.

23 Effect of tranformer leakage nductance he peak MFE voltage equal to the dc nput voltage plu the reflected load voltage /n; n practce, addtonal voltage oberved due to rngng aocated wth the tranformer leakage nductance. A nubber crcut may be requred to clamp the magntude of th rngng voltage to a afe level that wthn the peak voltage ratng of the MFE. eakage nductance e effectvely n ere wth MFE Q e nduce voltage pke accordng to et de t e t e dt f the peak magntude of the voltage pke exceed the voltage ratng of the MFE, the Q wll fal. 3

24 nubber provde a path for e to flow after Q ha turned off Energy tored n e W tranferred to and then dpated by. W e e e oltage re untl power dpated by equal to average power tranferred from e P W f chooe uch that acceptably low. 4

25 Ue large, o that t ha neglgble rpple: >> t Note that e depend on wndng geometry, and not known untl tranformer wound. meaure e on hort crcut tet, or gue t value n a good, carefully wound tranformer, t may be poble to acheve e3% of M. 5

26 Fgure. Flyback converter M waveform he mplfed voltage converon relatonhp for the flyback power tage operatng n M gven by: n 6

27 Fgure. Flyback converter M waveform he mplfed voltage converon relatonhp for the flyback power tage operatng n M gven by: n K K E 7

28 8 Flyback / onverter mall gnal Model ranfer Functon: Z G H U load g g ref gan loop G G H M d

29 For M Mode: G d n + wz wz + + w0q w0 g Q E w 0 E + E w Z Z E w *wo Pole f, ne Zero f E for Gd and ne ght-half-plane zero From a practcal vew, at HP zero frequency, the loop gan tart ncreang at a 0dB/decade rate but the loop phae decreae by 45 degree n a normal, HP zero, the loop phae wll ncreae by +45 degree. h mpoe the retrcton that the gan be rolled off to 0dB before encounterng the HP zero. he output nductor, capactor and the capactor E mut be elected o that the double pole occur frt and then the output capactor zero and then the HP zero. h aure that the loop gan croe 0dB at a lope that frt order 0dB/decade and that the ntablty nherently aocated wth the HP zero crcumvented by crong 0dB before the HP zero frequency occur. ompenate rule: 3. ecreae the double pole nfluence. f Z compenator f 4. roover frequency f f < f E f ~ f ecreae the HP zero nfluence f << f Z HP 6 9

30 For M Mode: G d g n E + w P w P 30