Lecture 12 - Non-isolated DC-DC Buck Converter

Transcription

1 ecture 12 - Non-iolated DC-DC Buck Converter Step-Down or Buck converter deliver DC power from a higher voltage DC level ( d ) to a lower load voltage o. d o ene ref + o v c Controller Figure 12.1 The baic buck converter The witch T connect the output terminal of the converter to d and for time T on in each witching period which remain contant (i.e., T i witched at a contant witching frequency, f ). The output DC voltage o i normally proportional to T on. For DC power upplie with contant output voltage o, the turn-on time T on i normally controlled in cloed-loop in order to maintain o at a fixed level. For application where o may be variable, T on i varied accordingley. ecture 12 - DC-DC Buck Converter 12-1 F. Rahman

2 ˆ ST v c t on t off t on t off T d v o v o ton vc Duty cycle, D ; T f ˆ Figure 12.2 Pule-width modulated (PWM) witching and output voltage waveform. ST 1 T o f 2f 3f 4f 5f Figure 12.3 Frequency pectrum of v o ecture 12 - DC-DC Buck Converter 12-2 F. Rahman

3 T d C o oad Controller Figure 12.4 Implementation of the buck converter circuit The impedance of the capacitor C for f mut be mall compared to the impedance of the load. ecture 12 - DC-DC Buck Converter 12-3 F. Rahman

4 The Power Tranitor BJT and Darlington h fe < 1 for the BJT CEat 1-2 volt Turn off time a few hundred nec to about 6 ec. BD up to 14 B E n + = 1 19 /cm 3 p = 1 16 /cm 3 1 m 5-2 m n - = 1 14 /cm 3 n + = 1 19 /cm m 25 m C Figure 12.5 ertical cro ection of a npn power BJT ecture 12 - DC-DC Buck Converter 12-4 F. Rahman

5 Figure 12.6 vertical cro ection of a npn BJT. Courtey: N. Mohan, Undeland & Robin Figure 12.7 BJT (a) Symbol, (b) v-i characteritic, (c) idealized characteritic ecture 12 - DC-DC Buck Converter 12-5 F. Rahman

6 MOSFET ery fat, t off 5 nec - 5 nec. R don increae with a 5, 15A device 2.6 BD ; typically, R d 4 m for Turned-on and -off by GS 5-2 Thee device are eaily connected in parallel. S G n + n + n + n + p (body) p (body) n n + D Figure 12.8 ertical ection of an n-channel Power MOSFET ecture 12 - DC-DC Buck Converter 12-6 F. Rahman

7 Figure 12.9 N-Channel MOSFET (a) Symbol, (b) v-i characteritic, (c) Idealied characteritic. IGBT (Inulated Gate Bipolar Tranitor) at 2-3 A t q 1 ec G Rating up to 3,, 3A K Figure 12.1 ertical cro ection of an IGBT and IGBT ymbol ecture 12 - DC-DC Buck Converter 12-7 F. Rahman

8 Figure 12.1 Static characteritic of an IGBT. GS < 2 max. ecture 12 - DC-DC Buck Converter 12-8 F. Rahman

9 Average voltage and current of capacitor In ome power electronic circuit, capacitor act a reervoir of energy. Conider the circuit of figure in which a contant amplitude of current pule i aumed to charge the capacitor for time t. + v c i c C v c i c t = Figure t The capacitor voltage v c i given by 1 v(t) c idt v C t C 12.1 The capacitor voltage will rie linearly with time. In figure 12.14, a capacitor i connected between two circuit. Circuit 1 charge the capacitor with a contant amplitude of current during T on while Circuit 2 dicharge the capacitor, alo with contant amplitude of current during time toff. The average voltage acro the capacitor remain contant over the witching period T t t. on off ecture 12 - DC-DC Buck Converter 12-9 F. Rahman

10 Circuit 1 i c Circuit 2 dc t on v o t off i c A B Fig If v C at the end of a period i the ame a at the beginning, the average current through the capacitor mut be zero. In other word, Area A = Area B in figure Average voltage and current in inductor In ome circuit, inductor act a reervoir of energy. Conider the circuit of figure in which a contant amplitude voltage i applied acro the inductor. + v i i t = t Figure The inductor voltage i given by v di o that, dt 1 i dt i t 12.2 ecture 12 - DC-DC Buck Converter 12-1 F. Rahman

11 In figure 12.14, an inductor i connected between two circuit. Circuit 1 applie a contant amplitude voltage to ; i increae linearly with time during t on. During t off, a negative but contant amplitude voltage i applied acro the inductor, o that i decreae linearly with time. The average current through the inductor remain contant around a mean (DC) value over the witching period. Ckt 1 Ckt 2 i i I dc A B Figure If i at the end of a period i the ame a at the beginning, the average voltage acro the inductor mut be zero. In other word, Area A = Area B in figure ecture 12 - DC-DC Buck Converter F. Rahman

12 Analyi of the Step-Down (Buck) Converter in CCM i d T i i o d + v oi + v D C v o o R (oad) Figure The baic buck converter topology During < t < t on, voltage acro the inductor i d - o ; i rie to I max. During t on < t < T, voltage acro the inductor i - o, and i fall to I min. In the teady-tate, the inductor current mut return to I min at the end of the witching period T, and the integral of the inductor voltage (i.e., the DC voltage upported acro the inductor) mut be zero. In the following we aume that the output voltage ripple i negligible. We alo aume that the inductor current i continuou throughout the witching period T. Thi i the o-called continuou conduction mode (CCM) of operation. The voltage acro the inductor i v di dt (12.3) Over one witching period T, T i (T ) vdt di (12.4) i () ecture 12 - DC-DC Buck Converter F. Rahman

13 i d T i i o d + v oi + v D C v o o R (oad) v d - o o t d v oi t on T t off t i I = I o I d i d Figure Buck converter waveform ecture 12 - DC-DC Buck Converter F. Rahman

14 Ton d o t 1 T dt o dt on Ton T d odt odt (12.5) t t T t on d on on (12.6) on d t T D (12.7) Alo, Pd P or I d d I (12.8) I I d d D (12.9) Note that the DC inductor current equal the DC output or load current for a buck converter. Thi follow from the aumption of contant o. Note alo I = I o i not the cae with other DC-DC converter to be tudied later. The waveform of figure are for continuou conduction of current in the inductor, the o called CCM (continuou conduction mode) of operation. If the inductor current i become dicontinuou during t off, equation do not hold, leading to a few problem. ecture 12 - DC-DC Buck Converter F. Rahman

15 Boundary between Continuou-Dicontinuou Conduction d - v i max I B = I ob i T - t on = DT (1-D)T Figure Inductor voltage and current waveform; with jut continuou operation. From figure 12.17, 1 1 I i t I 2 2 d B max on ob (d ) d Dd (12.1) DT DT T dd 1 D (12.11) ecture 12 - DC-DC Buck Converter F. Rahman

16 I B become maximum when D. 5 (thi i found by differentiating I B with repect to D and equating the derivative to zero). For D =.5, I B max T d 8 (12.12) And IB 4IBmax D(1 D) (12.13) D I B locu I Bmax I o Figure 12.2 Converter characteritic with duty-cycle and load During normal operation, I B hould be maller than the lowet load current, o that the converter operate in continuou conduction mode (i.e., in the linear mode with o = D d ). The minimum inductance and the witching frequency f for thi condition of operation are obtained from the following conideration: ecture 12 - DC-DC Buck Converter F. Rahman

17 From v dt di T i(t ) i() (12.14) d o o DT (1 D)T (12.15) The firt term in (12.15) i i (rie) and the econd term i i (fall). For a given load reitance R, i imax 1 DT R 2 R 2 o o o (12.16) i i 1 D T R 2 R 2 o o o and min (12.17) At the boundary of continuou-dicontinuou conduction, i min =, o that f min 1 D R 2 (12.18) for operation at the boundary of CCM and DCM operation of inductor current. 1 D R f (12.19) for operation with CCM. 2 ecture 12 - DC-DC Buck Converter F. Rahman

18 DCM Operation with contant d In ome application, the output DC voltage i variable while the input DC voltage i maintained contant. If Io IB, then i i dicontinuou. v d i A DT 1 T B 2 T T Figure v and i waveform with dicontinuou conduction. (d )DT 1T (12.2) o D D (12.21) d 1 where D1 1 Now i max 1T (12.22) and DT T I i i /T max max ecture 12 - DC-DC Buck Converter F. Rahman

19 i max (D 1 ) 2 D 1 1T 2 (uing 22) (12.23) D D D 2 (uing 21) d 1 1T 1 2 d TD 1 (12.24) 4IBmaxD1 (uing 12) (12.25) 1 4I I B max D (12.26) d D 2 1 D (I / I Bmax ) 4 2 (uing 21) (12.27) Equation how that with DCM, the converter output o ha a non linear relationhip with D. ecture 12 - DC-DC Buck Converter F. Rahman

20 o d d = contant I B locu D = 1. D =.75 D =.5 D =.25 I Bmax Figure Converter characteritic with dicontinuou conduction. Note that with DCM operation, fall harply with load when the inductor current i dicontinuou. Note alo that with dicontinuou conduction, o / d ratio become higher than D, implying lo of voltage gain of the converter. Converter gain with continuou and dicontinuou conduction ( d = contant). The voltage gain, G c, of the buck converter i normally expreed a I o G c d o dd d (12.28) ecture 12 - DC-DC Buck Converter 12-2 F. Rahman

21 G c remain contant (= d ) when the inductor current i continuou. It fall a the inductor current become more and more dicontinuou. G c d Dic. cond. Cont. conduction I ob I o Figure ariation of converter gain with cont & dic conduction. DCM operation with contant o In many application, uch a power upplie, o i kept contant (by regulating the duty cycle D), when d varie over ome range. From (12.11), at the boundary of continuou-dicontinuou conduction, I B T dd 1 D T o 1 D 2 2 (12.29) The average inductor current at the boundary of continuou-dicontinuou conduction varie linearly with D a indicated by the dotted line of figure It i maximum for D = and zero for D = 1. ecture 12 - DC-DC Buck Converter F. Rahman

22 I B max T o 2 (12.3) D o = contant d / o = 1. d / o = 1.25 d / o = 2 d / o = 4 T IBmax = o 2 I o or I Figure Converter duty-cycle and load characteritic for contant o and variable d in cont and dic conduction. (d )DT 1T (12.31) o D D (12.32) d 1 where D1 1 Now i max 1T (12.33) and DT T I i i /T max max ecture 12 - DC-DC Buck Converter F. Rahman

23 i max (D 1 ) 2 D 1 1T 2 (uing 12.32) (12.34) T D 2 (uing 12.33) o d 1 o I D ob max 1 d o (12.35) 1 I I D ob max o d (12.36) Thu, when o i kept contant, o I o / IBmax D 1 / (12.37) d o d Figure alo indicate the range of variation of D required for maintaining o contant for varying d and I o, when the inductor current become dicontinuou. ecture 12 - DC-DC Buck Converter F. Rahman

24 Output voltage ripple of the buck converter (approximate analyi) The following analyi aume continuou conduction. I /2 Q i max I R T /2 T Figure Inductor current waveform For contant DC level of o, the filter capacitor can not carry any DC current. Thu, I c =, and I =I. i ripple = i c (12.38) Q 1 1 I T IT C C C (12.39) I (1 D)T (From 12.15) (12.4) T (1 D ) T 8C (12.41) ecture 12 - DC-DC Buck Converter F. Rahman

25 2 (1 D)T 8 C (12.42) o o 2 T (1 D) 8 C (12.43) 2 fc 1D 2 f 2 (12.44) where fc filter. 1 2 C, i the cut-off frequency of the C Therefore, it i deirable to have f f c! Deign conideration of the buck converter High f reduce the ize of and C. The core of inductor not to aturate for i max. Sufficient to maintain continuou conduction for the lowet load current. C to limit, typically, to le than 1%. ecture 12 - DC-DC Buck Converter F. Rahman