1. DC-DC Switch-Mode Converters
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
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Chapter 7 DC-DC Switch-Mode
Converters

2. Block Diagram of DC-DC Converters
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Chapter 7 DC-DC Switch-Mode
Converters

3. Stepping Down a DC Voltage
switching at constant frequency:
pulse-width modulation (PWM) switching vo
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Chapter 7 DC-DC Switch-Mode
Converters

4. 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
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Chapter 7 DC-DC Switch-Mode
Converters

5. Pulse-Width Modulation (2)
switch duty-cycle D is
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Chapter 7 DC-DC Switch-Mode
Converters

6. Chapter 7 DC-DC Switch-Mode
Step-Down (Buck) DC-DC Converter (1)
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Chapter 7 DC-DC Switch-Mode
Converters

7. Step-Down (Buck) DC-DC Converter (2)
average output voltage Vo
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Chapter 7 DC-DC Switch-Mode
Converters

8. Chapter 7 DC-DC Switch-Mode
R L C low-pass filter
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Chapter 7 DC-DC Switch-Mode
Converters

9. Continuous conduction mode (1)
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Chapter 7 DC-DC Switch-Mode
Converters

10. Continuous conduction mode (2)
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Chapter 7 DC-DC Switch-Mode
Converters

11. 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
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Chapter 7 DC-DC Switch-Mode
Converters

12. Edge of Cont./Discont. Conduction
Critical current below which inductor current becomes discontinuous:
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Chapter 7 DC-DC Switch-Mode
Converters

13. Discontinuous Conduction Mode
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Chapter 7 DC-DC Switch-Mode
Converters

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

15. Discontinuous Conduction Mode (3)
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Chapter 7 DC-DC Switch-Mode
Converters

16. 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
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Chapter 7 DC-DC Switch-Mode
Converters

17. 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
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Chapter 7 DC-DC Switch-Mode
Converters

18. Discont. Conduction mode with constant Vo
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Chapter 7 DC-DC Switch-Mode
Converters

19. Step-Down Conv.: Output Voltage Ripple (1)
Peak-peak voltage ripple:
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Chapter 7 DC-DC Switch-Mode
Converters

20. Step-Down Conv.: Output Voltage Ripple (2)
Computing :
During toff:
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Chapter 7 DC-DC Switch-Mode
Converters

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

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

23. Step-Up DC-DC Converter Waveforms (1)
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Chapter 7 DC-DC Switch-Mode
Converters

24. Chapter 7 DC-DC Switch-Mode
Effect of Parasitics
The duty-ratio is generally limited before the parasitic effects become significant
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Chapter 7 DC-DC Switch-Mode
Converters

25. 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
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Chapter 7 DC-DC Switch-Mode
Converters

26. Edge of Cont./Discont. Conduction (1)
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Chapter 7 DC-DC Switch-Mode
Converters

27. 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
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Chapter 7 DC-DC Switch-Mode
Converters

28. Edge of Cont./Discont. Conduction (3)
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Chapter 7 DC-DC Switch-Mode
Converters

29. Chapter 7 DC-DC Switch-Mode
Discont. Conduction (1)
Occurs at light loads
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Chapter 7 DC-DC Switch-Mode
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30. Chapter 7 DC-DC Switch-Mode
Discont. Conduction (2)
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Chapter 7 DC-DC Switch-Mode
Converters

31. Chapter 7 DC-DC Switch-Mode
Discont. Conduction (3)
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Chapter 7 DC-DC Switch-Mode
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32. Chapter 7 DC-DC Switch-Mode
Discont. Conduction (4)
Solving Io in order to 1
Substituting above
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Chapter 7 DC-DC Switch-Mode
Converters

33. Edge of Cont./Discont. Conduction with Vd constant
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Chapter 7 DC-DC Switch-Mode
Converters

34. Discont. Conduction with constant Vo (5)
substituting IoB,max
We get
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Chapter 7 DC-DC Switch-Mode
Converters

35. Discont. Conduction with Vo constant (6)
Solving for D
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Chapter 7 DC-DC Switch-Mode
Converters

36. Boost Converter Output Ripple (1)
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Chapter 7 DC-DC Switch-Mode
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37. 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)
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Chapter 7 DC-DC Switch-Mode
Converters

38. Step-Down/Up (Buck-Boost) Converter
The output voltage can be higher or lower than the input voltage
The output voltage is negative
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Chapter 7 DC-DC Switch-Mode
Converters

39. 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:
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Chapter 7 DC-DC Switch-Mode
Converters

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

41. Limits of Cont./Discont. Conduction (2)
Maximum values obtained when D=0
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Chapter 7 DC-DC Switch-Mode
Converters

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

43. Discontinuous Conduction Mode (2)
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Chapter 7 DC-DC Switch-Mode
Converters

44. Limits of Cont./Discont. Conduction;
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Chapter 7 DC-DC Switch-Mode
Converters

45. Limits of Cont./Discont. Conduction with Vo constant
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Chapter 7 DC-DC Switch-Mode
Converters

46. Buck-Boost Converter: Effect of Parasitics
The duty-ratio is limited to avoid these parasitic effects from becoming significant
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Chapter 7 DC-DC Switch-Mode
Converters

47. Buck-Boost Converter: Output Voltage Ripple
(where =RC is the time const)
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Chapter 7 DC-DC Switch-Mode
Converters

48. Chapter 7 DC-DC Switch-Mode
Cuk DC-DC Converter
The output voltage can be higher or lower than the input voltage
The output voltage is negative
Capacitor C1 stores and transfers energy
in steady state average inductor voltages VL1, VL2 are zero
VC1 is larger than Vd and Vo:
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Chapter 7 DC-DC Switch-Mode
Converters

49. Cuk DC-DC Converter: Waveforms (1)
when switch T is off
VL1=Vd-VC1
VL2=-Vo
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Chapter 7 DC-DC Switch-Mode
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50. Cuk DC-DC Converter: Waveforms (2)
when switch T is on
VL1=Vd
VL2=VC1-Vo
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Chapter 7 DC-DC Switch-Mode
Converters

51. Cuk DC-DC Converter: Waveforms (3)
equating the integral voltages of L1, L2 over one period:
thus
and since Po=Pd
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Chapter 7 DC-DC Switch-Mode
Converters

52. Cuk DC-DC Converter: pros and cons
Advantages
input current and output current have small ripple
Disadvantages
requirement of capacitor C1 with large ripple current capability
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Chapter 7 DC-DC Switch-Mode
Converters

53. 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
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Chapter 7 DC-DC Switch-Mode
Converters

54. Bipolar voltage switching
thus
ton of switch pair (TA+,TB-) is
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Chapter 7 DC-DC Switch-Mode
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55. Bipolar voltage switching (2)
Duty-rate of pair (TA+,TB-)
Duty-rate of pair (TA-,TB+)
noting that
D1 can vary between 0 and 1
Vo can vary between -Vd and +Vd
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Chapter 7 DC-DC Switch-Mode
Converters

56. unipolar voltage switching
Duty-rate of switch TA+
Duty-rate of switch TB+
noting that
D1 can vary between 0.5 and 1
Vo can vary between 0 and Vd
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Chapter 7 DC-DC Switch-Mode
Converters

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

58. Chapter 7 DC-DC Switch-Mode
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
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by Jose Bastos
Chapter 7 DC-DC Switch-Mode
Converters