Lecture 13 - Boost DC-DC Converters. Step-Up or Boost converters deliver DC power from a lower voltage DC level (V d ) to a higher load voltage V o.

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1 ecture 13 - Bt C-C Cnverter Pwer Electrnic Step-Up r Bt cnverter eliver C pwer frm a lwer vltage C level ( ) t a higher la vltage. i i i + v i c T C (a) + R (a) v 0 0 i 0 R1 t n t ff + t T i n T t ff = (1-)T + v - C + R i + v - C R Circuit uring t n Circuit uring t ff Figure (a) The baic bt cnverter uring t n & t ff ecture 13 C-C (Bt) Cnverter 13-1 F. Rahman

2 Pwer Electrnic Analyi f the bt cnverter with cntinuu cnuctin me f inuctr current (CCM) Frm T i(t) vt i0 (13.1) 0 i(0) t n + ( 0 )t ff = 0 (13.) 1 1 (13.3) that > fr thi cnverter. Theretically, when = 1. Auming the cnverter t be lle P = = R(1) R(1 ) (13.4) (13.5) Nte that fr the bt cnverter, the average inuctr current an the average input current (nt the average utput current a in the buck cnverter) are the ame. ecture 13 C-C (Bt) Cnverter 13- F. Rahman

3 Bunary between cntinuu/icntinuu cnuctin Pwer Electrnic v i max i t n t ff t T Figure 13. nuctr current an vltage wavefrm with cntinuu cnuctin (CCM) f inuctr current. When cnuctin i jut cntinuu, 1 i 1 t B max n 1 T (1 )T (13.6) The inuctr current fr peratin at the bunary f CCM an CM a a functin f i pltte in figure ecture 13 C-C (Bt) Cnverter 13-3 F. Rahman

4 Pwer Electrnic Bmax Bmax Figure Cntinuu-icntinuu bunary fr the bt cnverter. Frm (13.4) OB = T (1 ) (13.7) t can be hwn that B an B becme maximum fr = 1 an 1 3. The crrepning maximum value are: an B max B max T 8 T 7 (13.8) (13.9) ecture 13 C-C (Bt) Cnverter 13-4 F. Rahman

5 Frm 13.5 i i max Pwer Electrnic i T R( 1 ) (13.10) i T R( 1 ) (13.11) min At the bunary f cntinuu an icntinuu cnuctin, imin 0 T R( 1 ) f (13.1) f (1 ) R fr peratin at the bunary f CCM an CM peratin f inuctr current. ecture 13 C-C (Bt) Cnverter 13-5 F. Rahman

6 Pwer Electrnic CM peratin with cntant v i t n 1T T Figure 13.4 nuctr current an vltage wavefrm with icntinuu cnuctin. Frm T i(t) vt i0 0 i(0) T T (13.13) Becaue P = P, (13.14) The average inuctr current i al the average input current, thu ecture 13 C-C (Bt) Cnverter 13-6 F. Rahman

7 Pwer Electrnic T ( 1) (13.15) Frm (13.14), T (13.15a) 0 1 Uing (13.13), (13.15a) an (13.9) B max 1 (13.16) The range f require variatin in t keep cntant at a pecifie level when the inuctr current i icntinuu i inicate in figure = cntant Bmax, Amp Figure 13.5 characteritic with la; fr cntant an variable. ecture 13 C-C (Bt) Cnverter 13-7 F. Rahman

8 Pwer Electrnic Nte that uring icntinuu cnuctin, the energy 1 i max tre in the inuctr at the en f each t n, i.e.,, i tranferre t the la circuit which inclue the capacitr C. f the la i nt able t abrb thi energy, the capacitr vltage mut rie, leaing pibly t t high capacitr vltage. Thi can be avie if i cntrlle (i.e., regulate) uring every witching cycle (T ). Output ltage Ripple uring t n, the ie current i zer. The la current i maintaine by the capacitr. Auming cntinuu cnuctin f la current an al auming that the average la current i, which i al the average ie current, the change in the la vltage,, uring t n i given by Q T T C C RC (13.17) T RC (13.18) The abve analyi i vali nly fr cntinuu cnuctin me an when i min r ecture 13 C-C (Bt) Cnverter 13-8 F. Rahman

9 Pwer Electrnic = 0 i Q Q t n t ff T (1-)T t T Figure 13.6 Wavefrm f utput vltage, capacitr current an ie current ripple. ecture 13 C-C (Bt) Cnverter 13-9 F. Rahman

10 Example: eign f a bt cnverter i i Pwer Electrnic + v T i c C + R a 0 i 0 0 R 0 t n t ff tn t ff = (1-)T T Given, = 1 ; = 30 ; R = 50 ; f = 5 khz (i) Fin that peratin i in CCM fr the la pecifie. What wul yu che fr CM peratin up t the maximum (pecifie) la? (ii) Fin i (iii) Fin C fr / < 10% T (iv) Sketch the vltage an current wavefrm f the witch an the ie. ecture 13 C-C (Bt) Cnverter F. Rahman

11 Slutin: Pwer Electrnic 1 1 ; = 0.6 T 6 1 f At the cntinuu /icntinuu bunary, f min ( 1 ) R max = 96 H Alternatively, the C utput current B = 30/50 = 0.6A. B 1 T ; frm A Fr peratin in CCM with B = 0.6A, = 96µH Nrmally, we che < 96 H, ay, 85 µh, t enure CM fr the maximum (50Ω in thi example) la. With = 96µH, (ii) T 3A (iii) T 0.6 C 48 F R fr ecture 13 C-C (Bt) Cnverter F. Rahman

12 Pwer Electrnic (vi) 1 R 1 R1 1.5A T max 1.5 3A T &min 1.5 0A Sketch f i T, v T, i an v are left fr yu a an exercie. Bt Cnverter Gain Nte that fr a bt cnverter, 1 1 With cntinuu cnuctin, apprache a 1. Thi e nt happen in practice becaue paraitic element, uch a the witch, ie an inuctr reitance an the capacitr ESR, prevent the rie f when apprache unity. Nte al that a 1, i apprache. ecture 13 C-C (Bt) Cnverter 13-1 F. Rahman

13 1 1 With cnt. cnuctin With ic. cnuctin Pwer Electrnic Figure 13.7 Bt cnverter gain characteritic. The ign f practical bt cnverter gain becme negative a apprache unity. Becaue f thi an the ther prblem mentine abve, the bt cnverter i nrmally perate with uty cycle le than 0.85 r. Al, the mall-ignal tranfer functin f the bt cnverter in CCM exhibit a zer in the right-half -plane. Thi make it ifficult t btain g cle-lp perfrmance an tability. Becaue f thee rean, the bt cnverter i ften perate in CM t enure table peratin an fat ynamic f cntrl. ecture 13 C-C (Bt) Cnverter F. Rahman

14 Buck-Bt Cnverter Pwer Electrnic The utput C vltage f a buck-bt cnverter can be lwer r higher than the input C vltage, with revere plarity with repect t the input C vltage. T i C i R i + Figure 13.8 Buck-bt cnverter circuit Operatin with cntinuu inuctr current 0 v i T t = + 0 t n = T t ff i i + v _ C i + R + v _ C i + R uring t n uring t ff Figure 13.8 Buck-bt cnverter perating me ecture 13 C-C (Bt) Cnverter F. Rahman

15 T (1 0 )T 0 Pwer Electrnic 0 1 (13.19) Frm pwer balance: (13.0) (13.1) Bunary between cnt/ic cnuctin v,,max i, = B 0 t n = T (1-)T t T Figure nuctr vltage an current wavefrm B 1 T i max (13.) ecture 13 C-C (Bt) Cnverter F. Rahman

16 Becaue the average capacitr current i zer Pwer Electrnic 0 (13.3) Uing an 13. B T (1 ) (13.4) Uing 13.0 an 13.3 an 13.4 B T 1 (13.5) Frm (4) an (5), B,max an B,max ccur fr = 0, hence, B,max T (13.6) an B,max T (13.7) Al frm (4) an (5), 1 B B B,max (13.8) 1 B,max (13.9) ecture 13 C-C (Bt) Cnverter F. Rahman

17 Pwer Electrnic = cntant B,/ B,max B / B,max B / B,max B,/ B,max Figure Cntinuu-icntinuu bunarie fr an fr cntant. 1 Nw (13.30) 1 0 / (13.31) Al (frm 31) 0 R Frm R R( 1 ) (13.3) Nw i max i ecture 13 C-C (Bt) Cnverter F. Rahman

18 Pwer Electrnic R 1 T (13.33) T i R 1 min (13.34) Fr imin 0 f (13.35) R( 1 ) (1 ) R f min (13.36) fr peratin at the bunary f CCM an CM. ecture 13 C-C (Bt) Cnverter F. Rahman

19 Operatin with icntinuu cnuctin Pwer Electrnic v i 0 t n = T T 1 T t ff = (1-)T Figure nuctr current an vltage wavefrm with icntinuu cnuctin. Frm 0 T vt0, T T 0 1 that (13.37) 1 an frm P = P 1 (13.38) Frm the abve figure T 1 (13.39) ecture 13 C-C (Bt) Cnverter F. Rahman

20 Pwer Electrnic Uing 13.3, 13.37, an it can be hwn that, with icntinuu me f peratin, a a functin f an i given by B,max (13.40) where Bmax i given by 13.7 an. R When i kept cntant, the require range f variatin f when the inuctr current i icntinuu i inicate in the figure = cntant ½ B,max B,max 13.1 Buck-bt cnverter characteritic fr cntant. ecture 13 C-C (Bt) Cnverter 13-0 F. Rahman

21 Buck-Bt Cnverter Gain Pwer Electrnic A fr the bt cnverter, the vltage-gain f thi cnverter remain cntant fr lw an it increae harply a 1. T high a gain i prevente by the paraitic element in the witch an the inuctr Figure ecture 13 C-C (Bt) Cnverter 13-1 F. Rahman

22 Output ltage Ripple Pwer Electrnic = 0 Q i t n Q t ff T (1-)T t T Figure Output vltage an ie current ripple an capacitr current Auming cntinuu cnuctin an cniering that the ripple current in i flw thrugh the capacitr, the utput vltage ripple i fun frm Q T T C C R C (13. 34) T T RC (13.35) where = RC = time-cntant f the capacitr-la circuit. ecture 13 C-C (Bt) Cnverter 13- F. Rahman