Chapter 7 DCDC SwitchMode Converters dcdc converters for

Chapter 7 DC-DC Switch-Mode Converters • dc-dc converters for switch-mode dc power supplies and dc-motor drives • these dc-dc converters are studied: • step-down (buck) • step-up (boost) • step-up/ step-down (buck-boost) • Cúk • Full-bridge 7 -1

Block Diagram of DC-DC Converters 7 -2

Stepping Down a DC Voltage • switching at constant frequency: • pulse-width modulation (PWM) switching vo 7 -3

Pulse-Width Modulation (1) • signal-level control voltage vcontrol generated by amplifying the difference between actual output voltage and desired output voltage • switch control signal generated by comparing vcontrol with repetitive waveform 7 -4

Pulse-Width Modulation (2) • switch duty-cycle D is 7 -5

Step-Down (Buck) DC-DC Converter (1) 7 -6

Step-Down (Buck) DC-DC Converter (2) • average output voltage Vo 7 -7

R L C low-pass filter 7 -8

Continuous conduction mode (1) 7 -9

Continuous conduction mode (2) 7 -10

Continuous conduction mode (3) • input power equals output power: • step-down converter is equivalent to a dc transformer where the turns ratio is in the range 0 -1 7 -11

Edge of Cont. /Discont. Conduction • Critical current below which inductor current becomes discontinuous: 7 -12

Discontinuous Conduction Mode 7 -13

Discontinuous Conduction Mode (2) • Vo/Vd in the discontinuous mode • integrating the inductor voltage over one time period, • From the figure, 7 -14

Discontinuous Conduction Mode (3) 7 -15

Limits of Cont. /Discont. Conduction with constant D • The duty-ratio of 0. 5 has the highest value of the critical current • The boundary between the cont/discont mode is shown by the dashed curve 7 -16

Discont. Conduction mode with constant Vo • in regulated dc power supplies Vo is kept constant by adjusting the duty ratio D • since Vd=Vo/D the average inductor current at the edge of cont/discont mode is • when D=0 the maximum ILB, max is 7 -17

Discont. Conduction mode with constant Vo 7 -18

Step-Down Conv. : Output Voltage Ripple (1) Peak-peak voltage ripple: 7 -19

Step-Down Conv. : Output Voltage Ripple (2) Computing : During toff: 7 -20

Step-Down Conv. : Output Voltage Ripple (3) • ripple can be minimized by making fc of the low pass filter fc << fs 7 -21

Step-Up (Boost) DC-DC Converter • Output voltage is greater than the input • main application: regulated dc power supplies 7 -22

Step-Up DC-DC Converter Waveforms (1) 7 -23

Effect of Parasitics • The duty-ratio is generally limited before the parasitic effects become significant 7 -24

Step-Up DC-DC Converter Waveforms (2) • Assuming a lossless circuit Pd=Po Thus: • power remains the same • voltage increases • current decreases • equivalent to a DC transformer 7 -25

Edge of Cont. /Discont. Conduction (1) 7 -26

Edge of Cont. /Discont. Conduction (2) • recognizing that the inductor current IL and the input current Id are the same Id= IL • and • highest ILB at D=0. 5 • highest IOB at D=1/3 7 -27

Edge of Cont. /Discont. Conduction (3) 7 -28

Discont. Conduction (1) • Occurs at light loads 7 -29

Discont. Conduction (2) 7 -30

Discont. Conduction (3) 7 -31

Discont. Conduction (4) Solving Io in order to 1 Substituting above 7 -32

Edge of Cont. /Discont. Conduction with Vd constant 7 -33

Discont. Conduction with constant Vo (5) substituting Io. B, max We get 7 -34

Discont. Conduction with Vo constant (6) Solving for D 7 -35

Boost Converter Output Ripple (1) 7 -36

Boost Converter Output Ripple (2) • the ripple current flows through the capacitor and the average through R idiode Io (where =RC is the time const) 7 -37

Step-Down/Up (Buck-Boost) Converter • The output voltage can be higher or lower than the input voltage • The output voltage is negative 7 -38

Buck-Boost DC-DC Converter: Waveforms • equating the integral of inductor voltage over one period: • D>0. 5 means Vo>Vd • D<0. 5 means Vo<Vd • power is conserved Pd=Po: 7 -39

Limits of Cont. /Discont. Conduction (1) • The average inductor current is • Noting that average capacitor current is zero: re-arranging: Substituting: 7 -40

Limits of Cont. /Discont. Conduction (2) • Maximum values obtained when D=0 7 -41

Discontinuous Conduction Mode (1) • integrating the inductor voltage over one period • and since Pd=Po • This occurs at light loads 7 -42

Discontinuous Conduction Mode (2) 7 -43

Limits of Cont. /Discont. Conduction ; 7 -44

Limits of Cont. /Discont. Conduction with Vo constant 7 -45

Buck-Boost Converter: Effect of Parasitics • The duty-ratio is limited to avoid these parasitic effects from becoming significant 7 -46

Buck-Boost Converter: Output Voltage Ripple (where =RC is the time const) 7 -47

Cuk DC-DC Converter • The output voltage can be higher or lower than the input voltage • The output voltage is negative • Capacitor C 1 stores and transfers energy • in steady state average inductor voltages VL 1, VL 2 are zero • VC 1 is larger than Vd and Vo: 7 -48

Cuk DC-DC Converter: Waveforms (1) • when switch T is off • VL 1=Vd-VC 1 • VL 2=-Vo 7 -49

Cuk DC-DC Converter: Waveforms (2) • when switch T is on • VL 1=Vd • VL 2=VC 1 -Vo 7 -50

Cuk DC-DC Converter: Waveforms (3) • equating the integral voltages of L 1, L 2 over one period: • thus • and since Po=Pd 7 -51

Cuk DC-DC Converter: pros and cons Advantages • input current and output current have small ripple • Disadvantages • requirement of capacitor C 1 with large ripple current capability 7 -52

Full-Bridge DC-DC Converter • Four quadrant operation is possible • (TA+, TB-) (TA-, TB+) are switch pairs • bipolar voltage switching: switches in each pair are activated simultaneously • unipolar voltage switching: switches are activated independently 7 -53

Bipolar voltage switching thus ton of switch pair (TA+, TB-) is 7 -54

Bipolar voltage switching (2) • Duty-rate of pair (TA+, TB-) • Duty-rate of pair (TA-, TB+) • noting that • D 1 can vary between 0 and 1 • Vo can vary between -Vd and +Vd 7 -55

unipolar voltage switching • Duty-rate of switch TA+ • Duty-rate of switch TB+ • noting that • D 1 can vary between 0. 5 and 1 • Vo can vary between 0 and Vd 7 -56

Output Ripple in full-bridge DC converters • unipolar voltage switching vs bipolar voltage switching: • switching frequency is doubled • ripple is reduced ripple bipolar unipolar • better frequency response • better output voltage • more complex switch control 7 -57

Converter Comparison • Buck, Boost, Buck-Boost, Cuk transfer energy in only one direction • full-bridge is capable of bi-direccional power flow • in Buck, Boost, switch utilization is good • in Buck-Boost, Cuk, full-bridge switch utilization is poor CONCLUSION • Prefer Buck, Boost converters • If higher and lower voltages needed, use Buck-Boost, Cuk • If four-quadrant operation needed, use full-bridge 7 -58