The problem with linear regulators

Transcription

1 he problem wih linear regulaors i in P in = i in V REF R a i ref i q i C v CE P o = i o i B ie P = v i o o in R 1 R 2 i o i f η = P o P in iref is small ( 0). iq (quiescen curren) is small (probably). if (feedback curren) is small (probably). ib (base curren) is small (probably). hen, io ic iin. P BJ v CE i o = ( ) i o he vas majoriy of he excess power is dissipaed in he ransisor. As Vin increases and/or io increases, he ransisor ges hoer. EE 333 SMPS 1

2 Swiching he oupu ransisor reduces he power P o = P in = v sw R B = high i C v CE 0.2 V BJ in sauraion 0.2 V i o = i o P o = ( v CE ) i o P BJ v CE i o (0.2 V) i o P o = 0 = 0 i o = 0 v sw R B = low i C = 0 v CE = = 0 i o = 0 BJ is off P o = 0 P BJ = 0 EE 333 SMPS 2

3 Same sory wih NMOS P o = P in = i o = v sw = high i D v DS i o NMOS in ohmic. i o = i D r DS v DS r DS i D (small!) = v DS P o = ( v DS ) i o P MOS = v DS i o (small!) P o = 0 = 0 i o = 0 v sw = low i D = 0 v DS = = 0 i o = 0 NMOS is off. P o = 0 P MOS = 0 EE 333 SMPS 3

4 H H L v sw 0 L Duy cycle D = H ake he raw DC inpu and chop i up. he resul is a square wave wih an average value of D Vin. Add a low-pass filer i o remove he high-frequency pars, leaving only he DC. L = H = D H v sw C L he oupu is a DC volage, lower han he inpu and conrolled by pulse-widh modulaion of he swich. EE 333 SMPS 4

5 Swiched-mode power supply (SMPS) he previous slide gives a very high-level view of an SMPS. aking a DC volage and breaking i up ino pieces seems a lile srange and possibly counerproducive. Bu using he ransisor in a swiched fashion grealy reduces he power dissipaed in i. he advanage in power saving grealy ouweigh he disadvanage of a more complicaed implemenaion. he obvious advanages: Less power wased. Beer for he plane. Beer for baery life. Since he ransisor is dissipaing less power, i can be smaller, which means cheaper and more compac. Less hea being generaed means less hea sinking required, which also means lower cos and lower bulk (size and weigh). here is anoher exremely imporan and non-obvious advanage o swichers : In addiion o he sep-down volage described on he previous slide, i is also possible o sep-up ( > ) and inver ( = ), and more. hese manner in which hese oher conversions work are no a all inuiive and require o look a he operaion of he circuis some wha differenly han he simplified descripion given previously. EE 333 SMPS 5

6 he inducor redeems iself In pas elecronics classes, we were always denigraing he poor inducor. We claimed ha we would no allow inducors in our elecronics circuis, because hey are: bulky (boh size and weigh), cosly (hey have los of aoms), and lossy (due o series resisance). hese all go agains our elecronics manra faser, smaller, cheaper, and lower power. In order o avoid inducors, we even wen o he exreme of making fake inducors using ricky op amp circuis. In our simplified descripion of he SMPS from wo slides back, he inducor was used as par of a 2nd-order low-pass filer. We migh consider rying o use an RC filer (of whaever order) in place of he LC filer. Bu low-pass RC filers have resisors in series and he capacior in shun, meaning ha he oupu curren would have o flow hrough he resisors. An RC circui may do a good job of filering, bu i would be very lossy! We recall describing an inducor as a fancy shor circui, and an ideal inducor would have no loss. So if we can find a good real inducor ha has minimal series resisance, he LC filer will be beer han an RC filer. However, viewing he inducor as simply a filer componen will no give a complee picure of how swiched-mode supplies work. he whole picure is more complicaed and suble. he inducor plays a cenral in he operaion of he circui. We need o view he inducor an energy sorage elemen and hen recall ha he are complicaions when we ry o change he inducor curren rapidly. EE 333 SMPS 6

7 Brief review of inducor properies. v L v L = L d i d L () = An inducor is basically coil of wire, probably wrapped around a core of magneic maerial. I is characerized by he inducance, L. he uni of inducance is henries (H) (= V s/a). he inducance depends on: a) he number of windings, b) diameer of he coil, c) he diameer of he wire, he separaion of he wire beween each urn of he coil, d) he permeabiliy of he core maerial, and oher hings. (I s complicaed.) he curren hrough an inducor canno change insananeously. (Doing so would induce an infiniely large volage and require an infinie amoun of power.) hus, when rying o use an inducor in a swiched applicaion, i will be necessary o provide a means for a coninuous curren o flow. An ideal inducor has no resisance (a fancy shor-circui), bu real inducors, wih all of wire wound ino heir coils, have a series resisance. I can be small a fracion of an ohm or big (10s of ohms for crappy inducors.) I all depends on he diameer of he wire. Good qualiy inducors mus be bigger! An inducors sore energy in he form of a magneic creaed a he cener of he 1 L 0 v ( ) d (0) coil when curren is flowing. he energy is E = 1 2 Li2 L EE 333 SMPS 7

8 Sep-down (buck) configuraion he oupu is a lower volage han inpu, vo < Vin. As a firs sep, we will no ry solving a bunch of differenial equaions. Insead will look he seady operaion of he circui. Here are our assumpions: Nearly ideal componens (MOS has rds = 0, inducor has no series resisance, he diode is ideal wih a urn-on volage of Vdiode = 0. he MOS swich is driven by a PWM square wih period and duy cycle D (= H / ). he inpu is a consan DC wih value Vin and he oupu is also DC wih value vo. L V in C R v L PWM EE 333 SMPS 8

9 1. When he swich is closed (0 < < H) Assume ha he inducor curren is a some value, il(0). Wih he swich closed: L C he lef end of he inducor is a Vin. (According o our assumpions, he righ end will alway be a vo.) hen he volage across he inducor is also consan, vl = Vin vo. he diode is reverse-biased. (So we ignore i.) he inducor curren increases wih ime: () = 1 L ( ) (0) he change in he curren during he on ime is: he inducor energy is increasing wih ime. Δi L = L H v L EE 333 H H H SMPS 9

10 2. When he swich is open ( H < < ) he inducor curren sars a he value il(h). Wih he swich opened: 0 L C here is no longer a pah for curren from he source o he inducor. In order o keep he curren coninuous, he inducor volage mus go sufficienly negaive o urn on he diode, creaing a pah for curren. he lef end of he inducor is now a 0 V. (he diode is ideal.) hen he volage across he inducor is negaive, vl = vo. he inducor curren decreases wih ime: he change in he curren during he off ime is: he inducor energy decreases wih ime. () = L ( H ) ( H ) Δi L = L ( H ) v L H H v H EE 333 o SMPS 10

11 ha complees one full cycle of he PWM conrol signal. If he sysem is in seady-sae, hen he power flowing hrough i mus balance. he energy ha was added o he inducor (coming from source) during he firs phase mus balance he energy ha was removed from inducor (going o he capacior & load) during he second phase. he magniude of he curren increase mus mach he magniude of he curren decrease. L H = L ( H ) = H = D Since D 1 always, he oupu will be less han he inpu sepping down. he source dumps energy ino he inducor when he closed, and inducor dumps he energy o he load when he swich is opened. he capacior helps smooh he volage variaions ha occur due o he swiching. EE 333 SMPS 11

12 Sep-down waveforms v L H H H EE 333 SMPS 12

13 Sep-up (boos) converer he oupu is a higher volage han he inpu. Same assumpions (ideal componens, PWM conrol of he swich, and consan values for Vin and vo wih vo > Vin) and same seady-sae approach as he buck converer. L C Noe ha he boos circui has he same componens as he buck, bu wih a differen configuraion. EE 333 SMPS 13

14 1. he swich is closed ( 0 < < H ) v L i o Assume ha he inducor curren is a some value, il(0). Wih he vpwm high: C he NMOS will be on, and we can rea i as an ideal closed swich. he volage across he inducor will be vl Vin 0. he diode is reverse-biased, effecively disconnecing he inpu from he oupu. he inducor curren increases wih ime: () = 1 L (0) he change in he curren during he on ime is he inducor energy increases wih ime. Δi L = L H v L EE 333 H H H SMPS 14

15 2. he swich is open ( H < < ) he inducor curren sars a he value il(h). When he NMOS is off: v L v D = 0 C i o he inducor curren can no longer flow hrough he NMOS i mus flow hrough he diode. o urn on he diode, he volage on righ end of he inducor mus raise up o vo. he inducor volage becomes vl = Vin vo. Since vo > Vin, he inducor volage is now negaive he inducor curren decreases wih ime: he change in he curren during he off ime is: he inducor energy decreases wih ime. () = L Δi L = L ( H ) ( H ) ( H ) v L H H (v EE 333 o ) H SMPS 15

16 ha complees one full cycle of he PWM conrol signal. As wih he buck converer, if he boos converer is in seady-sae operaion, he power flow mus balance. Energy is added o he inducor when he swich is closed, and ha energy is ransferred o he capacior and load when he swich is open. he magniude of he curren increase in he inducor mus mach he magniude of he curren decrease. L H = L ( H ) = H = 1 D Since he duy cycle is always less han 1, he resul is consisen wih our assumpion ha he oupu would be bigger han he inpu. Again, many deails are missing. Wha values of L & C should be used? Is here ripple? Wha happens if he componens are no ideal. We will look a hese laer. EE 333 SMPS 16

17 Sep-up waveforms H v L ( ) H H EE 333 SMPS 17

18 Buckboos (invering) converer he inpu is posiive and he oupu will be negaive. Same assumpions (ideal componens, PWM conrol of he swich, and consan values for Vin and vo wih vo < 0) and same seady-sae approach as he oher configuraions. V R in v L C L PWM Once again, he same componens, bu wih ye anoher configuraion. EE 333 SMPS 18

19 1. he swich is closed ( 0 < < H ) he inducor curren sars a some value, il(0). Wih he vpwm high v L C ( < 0 ) he NMOS will be on, and we can rea i as an ideal closed swich. he volage across he inducor will be vl Vin. he diode is reverse-biased (vd = vo Vin and vo < 0), effecively disconnecing he inpu from he oupu. he inducor curren increases wih ime: () = 1 L (0) he change in he curren during he on ime is he inducor energy increases wih ime. Δi L = L H v L H H H EE 333 SMPS 19

20 2. he swich is open ( H < < ) v D = 0 he inducor curren sars a he value il(h). When he NMOS is off: v L C ( < 0 ) he inducor curren can no longer flow hrough he NMOS i mus flow hrough he diode. o urn on he diode, he volage on upper end of he inducor mus drop o vo, which is negaive. he inducor volage becomes vl = vo < 0. he inducor curren decreases wih ime: he change in he curren during he off ime is: he inducor energy decreases wih ime. () = L ( H ) ( H ) Δi L = L ( H ) v L H v H H o EE 333 SMPS 20

21 ha complees one full cycle of he PWM conrol signal. I s he same sory he power flow mus balance. Energy is added o he inducor when he swich is closed, and ha energy is ransferred o he capacior and load when he swich is open. he magniude of he curren increase in he inducor mus mach he magniude of he curren decrease. L H = L ( H ) = H H = D 1 D he oupu is always negaive, bu he magniude can be bigger or smaller han Vin. vo = Vin for D = 0.5. vo < Vin for D < 0.5. vo >Vin for D > 0.5. EE 333 SMPS 21

22 Buckboos (inver) waveforms H v L H H EE 333 SMPS 22

23 Ćuk L 1 C 1 L 2 i o C 2 Like buck-boos: = D D 1 Sepic L 1 C 1 i o L 2 C 2 Like buck-boos, bu no invering: = D 1 D EE 333 SMPS 23

24 Flyback Provides isolaion via he flyback ransformer. i o Works jus like buck, bu energy is ransferred hrough he ransformer. EE 333 SMPS 24