Lecture 17 Push-Pull and Bridge DC-DC converters Push-Pull Converter (Buck Derived) Centre-tapped primary and secondary windings
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1 ecture 17 Push-Pull and Bridge DC-DC converters Push-Pull Converter (Buck Derived) Centre-tapped primary and secondary windings 1 2 D 1 i v 1 v 1s + v C o R v 2 v 2s d 1 2 T 1 T 2 D 2 Figure 17.1 v c ( 2 / 1 ) d T 1 T 2 T 1 o DT s T s /2 i Ts I o i D1 T 1 & T 2 Both off ; D 1 & D 2 on T 1 & T 2 Both off; D 1 & D 2 on Figure 17.2 ecture 17 Push-pull DC-DC Converters 17-1 F. Rahman
2 ote that the following analysis assumes that two PWM cycles constitute one switching period T s. T 1 and T 2 are O alternately with on-time (or D) obtained by comparing the control voltage v c with triangular or sawtooth waveforms of switching frequency given by 2/T s. The parasitic diodes across switches (shown dotted) allow energy of the leakage flux to return to the DC source when T 1 and T 2 are both off. When T 1 is O, v 1 = d, v 1s = 2 d 1 (17.1) and v 2 d o 1 (17.2) 2 d o 1 i DTs (17.3) ote that D is now defined somewhat differently from previous sections. ote also that at maximum, D = 0.5. When T 2 is O, v 2 d o 1 and i 2 d 1 o DT s ecture 17 Push-pull DC-DC Converters 17-2 F. Rahman
3 When both T 1 and T 2 are off diodes D 1 and D 2 both conduct and share i equally. is then zero during this period. v 0 (17.4) From T s / 2 0 v dt 0 2 d s 1 DT DTs D 0 2 d 1 (17.5) Using the analysis of the buck converter, it can be shown that 1 2D Cfs (17.6) ecture 17 Push-pull DC-DC Converters 17-3 F. Rahman
4 Half-bridge converter This converter uses the centre-tap of the DC supply (created by two equal capacitors C 1 and C 2 connected in series). The potential of the centre-tap is d /2 with respect to the ve DC link. d C 1 T 1 d /2 + v D 1 i D1 i I o + + v C o R C 2 T 2 1 D 2 Figure 17.3 v c ( 2 / 1 ) d /2 T 1 T 2 T 1 o DT s T s /2 i Ts I o i D1 T 1 & T 2 Both off D 1 & D 2 on T 1 & T 2 Both off D 1 & D 2 on Figure 17.4 ecture 17 Push-pull DC-DC Converters 17-4 F. Rahman
5 During t on, v 2 d 2 1 (17.7) During t on < t < t on +, v (17.8) o The waveforms repeat in T s /2. By integrating v over T s /2, D o 2 d 1 (17.9) where D = t on /T s and 0 < D < 0.5. Full-bridge Converter D s1 i d T 1 T 4 T 3 D 1 D 3 + v 1 1 D T 2 4 D v 1s v 2s + v C o I o R D s2 Figure 17.5 ecture 17 Push-pull DC-DC Converters 17-5 F. Rahman
6 v c ( 2 / 1 ) d o T 1 & T 2 T 3 & T 4 T 1 & T 2 DT s T s /2 i T s I o i D1 All switches are off. D 3 & D 4 on All switches are off. D 1 & D 2 on Figure 17.6 Switch pairs T 1 -T 2 and T 3 -T 4 are O alternately. When either pair is O, v for 0 < t < t on (17.10) v 2 oi d o 1 (17.11) o By integrating v over T s /2, and recognising that ecture 17 Push-pull DC-DC Converters 17-6 F. Rahman
7 Ton D T and 0 < D < 0.5, s 2 D (17.11) o 2 d 1 Diodes D1-D4 (could be parasitic) allow energy trapped in the leakage inductance of the transformer to return to the DC source when a switch pair is turned off. ote that the switch current for the full-bridge converter is half of the half-bridge converter for the same output, because the transformer primary voltage swing is the full DC source voltage with both positive and polarity. Thus I THB 2ITFB. (17.12) ecture 17 Push-pull DC-DC Converters 17-7 F. Rahman
8 Transformer core selection For ferrites (3C8), B max 0.35 T, B r = T B 2 d 1 o Bmax DT s T s o Figure B variation in core with unidirectional field, e.g., a forward converter. B B max DT s T s /2 Figure B variation in core with bidirectional field, e.g., a bridge converter. ecture 17 Push-pull DC-DC Converters 17-8 F. Rahman
9 B T = 25C T = 100C H Figure Field variations with temperature For D=0.5 and for triangular B variation (rather than sinusoidal) 4 A f B for D=0.5 (17.13) d 1 c s max B max (Bm B r ) (17.14) for unidirectional core excitation (e.g. forward converter to be studied later) and B max 2B m for bidirectional core excitation (e.g. push-pull or bridge converters). B r should be as low as practicable (the air-gap is used to reduce the B r ). ecture 17 Push-pull DC-DC Converters 17-9 F. Rahman
10 air gap Figure Core cross-section with air-gap. The core loss in a transformer (or inductor) is given by P c = n 2 2 n s max e s max K f B K f ( B ) (17.15) P c 1 mw/cm 3 50 H z f s, KHz Figure Core loss with switching frequency Magnetic cores with ceramic (ferrites) and powdered-iron materials reduce the core loss when switching high frequency is used. ecture 17 Push-pull DC-DC Converters F. Rahman
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