6.3. Transformer isolation
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1 6.3. Transformer isolation Objectives: Isolation of input and output ground connections, to meet safety requirements eduction of transformer size by incorporating high frequency isolation transformer inside converter Minimization of current and voltage stresses when a large step-up or step-down conversion ratio is needed use transformer turns ratio Obtain multiple output voltages via multiple transformer secondary windings and multiple converter secondary circuits 32
2 A simple transformer model Multiple winding transformer Equivalent circuit model i 1 n 1 : n 2 i 2 i 1 i M i 1 ' n 1 : n 2 i 2 v 1 v 2 i 3 v 3 v 1 L M v 1 n = v 2 1 n = v 3 2 n = =n 1 i 1 'n 2 i 2 n 3 i 3... : n 3 v 2 i 3 v 3 : n 3 Ideal transformer 33
3 The magnetizing inductance L M Models magnetization of transformer core material Appears effectively in parallel with windings If all secondary windings are disconnected, then primary winding behaves as an inductor, equal to the magnetizing inductance At dc: magnetizing inductance tends to short-circuit. Transformers cannot pass dc voltages Transformer saturates when magnetizing current i M is too large Transformer core B-H characteristic B v 1 dt saturation slope L M H i M 34
4 Volt-second balance in L M The magnetizing inductance is a real inductor, obeying di v 1 =L M M dt integrate: v 1 i M i M (0) = 1 t v L 1 (τ)dτ M 0 Magnetizing current is determined by integral of the applied winding voltage. The magnetizing current and the winding currents are independent quantities. Volt-second balance applies: in steady-state, i M (T s ) = i M (0), and hence i 1 i M L M i 1 ' n 1 : n 2 : n 3 i 2 v 2 i 3 v 3 0= T 1 T s v 1 dt s 0 Ideal transformer 35
5 Transformer reset Transformer reset is the mechanism by which magnetizing inductance volt-second balance is obtained The need to reset the transformer volt-seconds to zero by the end of each switching period adds considerable complexity to converters To understand operation of transformer-isolated converters: replace transformer by equivalent circuit model containing magnetizing inductance analyze converter as usual, treating magnetizing inductance as any other inductor apply volt-second balance to all converter inductors, including magnetizing inductance 36
6 Full-bridge and half-bridge isolated buck converters Full-bridge isolated buck converter Q 3 D 3 i 1 1 : n D 5 i D5 L i v T v s C v Q2 D 2 Q4 D 4 : n D 6 37
7 Full-bridge, with transformer equivalent circuit Q 3 D 3 i 1 i 1 ' i M 1 : n D 5 i D5 i L v T L M v s C v Q2 D 2 Q4 D 4 : n Ideal D 6 i D6 Transformer model 38
8 Full-bridge: waveforms i M v T i v s i D5 I conducting devices: L M 0 0 n i 0 i L M n 0.5 i 0.5 i 0 0 DT s T s T s DT s 2T s D Q 5 2 D 5 Q 4 D Q 6 3 D 6 D 5 D 6 0 t During first switching period: transistors and Q 4 conduct for time DT s, applying voltseconds DT s to primary winding During next switching period: transistors Q 2 and Q 3 conduct for time DT s, applying voltseconds DT s to primary winding Transformer volt-second balance is obtained over two switching periods Effect of nonidealities? 39
9 Effect of nonidealities on transformer volt-second balance Volt-seconds applied to primary winding during first switching period: ( ( and Q 4 forward voltage drops))( and Q 4 conduction time) Volt-seconds applied to primary winding during next switching period: ( (Q 2 and Q 3 forward voltage drops))( Q 2 and Q 3 conduction time) These volt-seconds never add to exactly zero. Net volt-seconds are applied to primary winding Magnetizing current slowly increases in magnitude Saturation can be prevented by placing a capacitor in series with primary, or by use of current programmed mode (Chapter 12) 40
10 Operation of secondary-side diodes : n D 5 i D5 v s L C i v During second (D ) subinterval, both secondary-side diodes conduct v s : n n D 6 n Output filter inductor current divides approximately equally between diodes i D5 conducting devices: i i 0.5 i 0 t 0 DT s T s T s DT s 2T s D Q 5 2 D 5 Q 4 D Q 6 3 D 6 D 5 D 6 0 Secondary amp-turns add to approximately zero Essentially no net magnetization of transformer core by secondary winding currents 41
11 Volt-second balance on output filter inductor : n D 5 i D5 L i i I i v s C v v s n n 0 0 : n D 6 i D5 i 0.5 i 0.5 i 0 t 0 DT s T s T s DT s 2T s V = v s V = nd conducting devices: D Q 5 2 D 5 Q 4 D Q 6 3 D 6 D 5 D 6 M(D) = nd buck converter with turns ratio 42
12 Half-bridge isolated buck converter C a i 1 1 : n D 3 i D3 L i v T v s C v Q2 D 2 C b : n D 4 eplace transistors Q 3 and Q 4 with large capacitors Voltage at capacitor centerpoint is 0.5 v s is reduced by a factor of two M = 0.5 nd 43
13 Forward converter n 1 : n 2 : n 3 D 2 L D 3 C V Buck-derived transformer-isolated converter Single-transistor and two-transistor versions Maximum duty cycle is limited Transformer is reset while transistor is off 44
14 Forward converter with transformer equivalent circuit n 1 : n 2 : n 3 D 2 L i M i 1 ' L M v 1 v 2 v 3 D 3 v D3 C V i 1 i 2 i 3 v Q1 45
15 Forward converter: waveforms v 1 i M n 1 n 2 0 Magnetizing current, in conjunction with diode, operates in discontinuous conduction mode v D3 L M n 1 n 2 n 3 n 1 L M 0 Output filter inductor, in conjunction with diode D 3, may operate in either CCM or DCM 0 0 DT s D 2 T s D 3 T s T s t Conducting devices: D 3 D 2 D 3 46
16 Subinterval 1: transistor conducts i M n 1 : n 2 : n 3 i 1 ' D 2 on L L M v 1 v 2 v 3 v D3 C V i 1 i 2 i 3 on off 47
17 Subinterval 2: transformer reset n 1 : n 2 : n 3 L i M i 1 ' L M v 1 v 2 v 3 D 3 on v D3 C V i 1 i 2 = i M n1 /n2 i 3 off on 48
18 Subinterval 3 n 1 : n 2 : n 3 L i M = 0 L M v 1 i 1 ' v 2 v 3 D 3 on v D3 C V i 1 i 2 i 3 off off 49
19 Magnetizing inductance volt-second balance v 1 0 n 1 n 2 i M L M n 1 n 2 L M 0 v 1 = D D 2 n 1 /n 2 D 3 0 =0 50
20 Transformer reset From magnetizing current volt-second balance: Solve for D 2 : v 1 = D D 2 n 1 /n 2 D 3 0 =0 D 2 = n 2 n 1 D D 3 cannot be negative. But D 3 = 1 D D 2. Hence D 3 =1D D 2 0 D 3 =1 n 2 0 n 1 Solve for D D 1 for n 1 = n 2 : 1 n D n 1 51
21 What happens when D > 0.5 i magnetizing current M waveforms, D < 0.5 for n 1 = n 2 DT s D 2 T s D 3 T s t i M D > 0.5 DT s D 2 T s t 2T s 52
22 Conversion ratio M(D) : n 3 D 2 L D 3 C V v D3 n 3 n DT s D 2 T s D 3 T s T s t v D3 = V = n 3 n 1 D Conducting devices: D 2 D 3 D 3 53
23 Maximum duty cycle vs. transistor voltage stress Maximum duty cycle limited to which can be increased by decreasing the turns ratio n 2 / n 1. But this increases the peak transistor voltage: For n 1 = n 2 D 1 1 n 2 n 1 max v Q1 = 1 n 1 n 2 D 1 2 and max(v Q1 ) = 2 54
24 The two-transistor forward converter D 3 L 1 : n D 4 C V D 2 Q 2 V = nd D 1 2 max(v Q1 ) = max(v Q2 ) = 55
25 Push-pull isolated buck converter v T 1 : n i D1 i L v s C V v T D 2 Q 2 V = nd 0 D 1 56
26 Waveforms: push-pull i M v T i v s i D1 I Conducting devices: L M 0 0 n i 0 i L M n 0.5 i 0.5 i 0 0 DT s T s T s DT s 2T s Q 2 D 2 D 2 D 2 0 t Used with low-voltage inputs Secondary-side circuit identical to full bridge As in full bridge, transformer volt-second balance is obtained over two switching periods Effect of nonidealities on transformer volt-second balance? Current programmed control can be used to mitigate transformer saturation problems. Duty cycle control not recommended. 57
27 Flyback converter buck-boost converter: L V construct inductor winding using two parallel wires: L 1:1 V 58
28 Derivation of flyback converter, cont. Isolate inductor windings: the flyback converter L M 1:1 V Flyback converter having a 1:n turns ratio and positive output: L M 1:n C V Q1 59
29 The flyback transformer i g L M Transformer model i 1:n v L C i C v A two-winding inductor Symbol is same as transformer, but function differs significantly from ideal transformer Energy is stored in magnetizing inductance Magnetizing inductance is relatively small Current does not simultaneously flow in primary and secondary windings Instantaneous winding voltages follow turns ratio Instantaneous (and rms) winding currents do not follow turns ratio Model as (small) magnetizing inductance in parallel with ideal transformer 60
30 Subinterval 1 Transformer model i g i 1:n i C v L = L M v L C v i C = v i g = i CCM: small ripple approximation leads to on, off v L = i C = V i g = I 61
31 Subinterval 2 i g = 0 Transformer model i v L v/n 1:n i/n C i C v v L = v n i C = i n v i g =0 CCM: small ripple approximation leads to off, on v L = V n i C = I n V i g =0 62
32 CCM Flyback waveforms and solution v L Volt-second balance: i C V/n I/n V/ v L = D D' V n =0 Conversion ratio is M(D)= V = n D D' Charge balance: i g V/ I DT s 0 D'T s t i C = D V D' I n V =0 Dc component of magnetizing current is I = D' nv Dc component of source current is I g = i g = DI D' 0 Conducting devices: T s 63
33 Equivalent circuit model: CCM Flyback v L = D D' V n =0 I g I i C = D V D' I n V =0 DI D'V D'I n D n V I g = i g = DI D' 0 1 : D D' : n I g I V 64
34 Discussion: Flyback converter Widely used in low power and/or high voltage applications Low parts count Multiple outputs are easily obtained, with minimum additional parts Cross regulation is inferior to buck-derived isolated converters Often operated in discontinuous conduction mode DCM analysis: DCM buck-boost with turns ratio 65
35 Boost-derived isolated converters A wide variety of boost-derived isolated dc-dc converters can be derived, by inversion of source and load of buck-derived isolated converters: full-bridge and half-bridge isolated boost converters inverse of forward converter: the reverse converter push-pull boost-derived converter Of these, the full-bridge and push-pull boost-derived isolated converters are the most popular, and are briefly discussed here. 66
36 Full-bridge transformer-isolated boost-derived converter i L v L Q 3 1 : n i o v T C v : n Q 2 Q 4 D 2 Circuit topologies are equivalent to those of nonisolated boost converter With 1:1 turns ratio, inductor current i and output current i o waveforms are identical to nonisolated boost converter 67
37 Transformer reset mechanism v T v L i I i o Conducting devices: DT s Q 2 Q 3 Q 4 V/n V/n I/n 0 68 V/n V/n I/n D'T s DT s D'T s T s Q 2 T s Q 4 Q 2 Q 3 Q 4 Q 3 D 2 t As in full-bridge buck topology, transformer voltsecond balance is obtained over two switching periods. During first switching period: transistors and Q 4 conduct for time DT s, applying volt-seconds VDT s to secondary winding. During next switching period: transistors Q 2 and Q 3 conduct for time DT s, applying volt-seconds VDT s to secondary winding.
38 Conversion ratio M(D) v L i I V/n V/n Application of volt-second balance to inductor voltage waveform: v L = D D' V n = 0 Solve for M(D): Conducting devices: DT s Q 2 Q 3 Q 4 D'T s DT s D'T s T s Q 2 T s Q 4 Q 2 Q 3 Q 4 Q 3 D 2 t M(D)= V = n D' boost with turns ratio n 69
39 Push-pull boost-derived converter i o L v T i C v L v T 1 : n V Q 2 D 2 M(D)= V = n D' 70
40 Push-pull converter based on Watkins-Johnson converter 1 : n C V Q 2 D 2 71
41 Isolated versions of the SEPIC and Cuk converter Basic nonisolated SEPIC L 1 C 1 L 2 C 2 v L 1 C 1 1 : n Isolated SEPIC i 1 i p i s C 2 v 72
42 Isolated SEPIC i p i 1 L 1 C 1 i 1 i 2 i p 1 : n i s i 2 L M = L 2 Ideal Transformer model C 2 v i s i 1 0 (i 1 i 2 ) / n I 1 M(D)= V = nd D' i 2 I 2 Conducting devices: DT s T s D'T s t 73
43 Inverse SEPIC 1 Nonisolated inverse SEPIC 2 V Isolated inverse SEPIC 1 : n C 1 L 2 C 2 v 74
44 Obtaining isolation in the Cuk converter L 1 L 2 Nonisolated Cuk converter C 1 Q D 1 1 C 2 v L 1 L 2 Split capacitor C 1 into series capacitors C 1a and C 1b C 1a C 1b C 2 v 75
45 Isolated Cuk converter L 1 L 2 Insert transformer between capacitors C 1a and C 1b C 1a C 1b C 2 v M(D)= V = nd D' 1 : n Discussion Capacitors C 1a and C 1b ensure that no dc voltage is applied to transformer primary or secondary windings Transformer functions in conventional manner, with small magnetizing current and negligible energy storage within the magnetizing inductance 76
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