1. DC-DC Converter
Functional block diagram

3. Stepping Down a DC Voltage
Avg. output voltage is controlled by controlling the switch on-off duration. If constant switching freq. is employed, the output voltage can be varied by varying switch ‘on’ duration. The method is termed as PWM switching and duty ratio, D is defined as ton/ Tswitching
A simple approach that shows the evolution

7. Pulse-Width Modulation in DC-DC Converters

8. Step-Down/Buck DC-DC Converter
Pulsating input to the low-pass filter

9. Step-Down DC-DC Converter: Waveforms
Switch closed
Switch open
Steady state; inductor current flows continuously, CCM

10. Note: D’ = 1 – D = 1 - ton/Ts = turn off duration/Switching time

11. CCM, continuous conduction mode; DCM, discontinuous conduction mode

12. Critical current below which inductor current becomes discontinuous
Step-Down DC-DC Converter: Waveforms at the boundary of Cont./Discont. Conduction
Assuming ideal ckt., Po= Pin, Therefore, Vo/Vd = Id/Io = 1/D
ILB = ½ (Vd-Vo).DTs/L = ½ (1-D)Ts.Vo/L = D.D’.Ts.Vd/2L & ILBmax = Ts.Vd/8L
At, D= 0.5
Critical current below which inductor current becomes discontinuous

14. Step-Down DC-DC Converter: Discontinuous Conduction Mode
(Vd-Vo).DTs + (-Vo)Δ1Ts = 0, Therefore, Vo/Vd = D/(D+Δ1); where, D+Δ1 < 1
iLpk = (Vo/L).Δ1Ts, Therefore,
Io = iLpk.(½ .D+Δ1)
= ½Vo.Ts (D+Δ1).Δ1/L
= ½Vd.Ts D.Δ1/L
= 4ILBmax.D.Δ1, Therefore,
Δ1 = Io/(4.ILBmax.D)
Vo/Vd = D2/[D2 +Io/(4.ILBmax)]
Steady state; inductor current discontinuous

16. The duty-ratio of 0.5 has the highest value of the critical current
Step-Down DC-DC Converter: Limits of CCM/DCM
Note: Vd = Vg = Vin
The duty-ratio of 0.5 has the highest value of the critical current

17. Step-Down DC-DC Converter: Limits of CCM/DCM
ILB = (1-D).Ts.Vo/2L
ILBmax = Ts.Vo/2L , at D=0
ILB = (1-D). ILBmax
D=(Vo/Vd )[(Io/ILBmax)/(1-Vo/Vd )]1/2
Output voltage is kept constant

18. ESR is assumed to be zero
Step-Down Converter: Output Voltage Ripple
Pk to pk voltage ripple is given by
ΔV0 = ΔQ/C = ½ .1/C. ΔIL/2. Ts/2
During toff
ΔIL = (1-D).Ts. Vo/L
ΔVo = ΔIL .Ts/8C
ΔVo/Vo = Ts2.(1-D)/8LC
= [π2.(1-D)/2] .(fc/fs)2
Where, fs = 1/Ts & fc = 1/(2π√LC)
fc<< fs
ESR is assumed to be zero

24. Step-Up DC-DC Converter
Vd.ton + (Vd-Vo).toff = 0
dividing both sides by Ts
Vo/Vd = 1/(1-D)
Output voltage must be greater than the input

25. Step-Up DC-DC Converter Waveforms
Continuous current conduction mode, CCM

32. Step-Up DC-DC Converter: Limits of Cont./Discont. Conduction (CCM/DCM)
The output voltage is held constant
ILB = ½ iLpk = ½ (Vd/L).ton = ½ [(Ts.Vo)/L ].D.(1-D)
IoB = ½ [(Ts.Vo)/L ].D.(1-D)2 & ILBmax = Ts.Vo/8L
IoBmax at D=1/3, IoBmax (2/27).(Ts.Vo/L)

33. Step-Up DC-DC Converter: DCM
occurs at light loads
Vd.DTs+(Vd-Vo). Δ1.Ts)= 0, Therefore, Vo/Vd = (D+Δ1)/ Δ1; where, D+Δ1 < 1
iLpk = (Vo/L).Δ1Ts, Therefore,
Io/Id = Δ1/(D+Δ1), (since Po=Pd)
Id = (Vd/2L).DTs(D+Δ1)
Io=Ts (Vd/2L)D. Δ1

34. Step-Up DC-DC Converter: Limits of CCM/DCM
The output voltage Vo is held constant

35. Step-Up DC-DC Converter: Effect of Parasitics
The duty-ratio is generally limited before the parasitic effects become significant

36. Step-Up DC-DC Converter Output Ripple
Assuming constant Io
ΔV0 = ΔQ/C = Io.D.Ts/C
= (V0/R).(D.Ts/C)
ΔVo/Vo = D.Ts/RC
= D.Ts/τ
Where, τ = RC time constant
ESR is assumed to be zero

37. Step-Down/Up DC-DC Converter (Buck-Boost)
Vd.DTs+(-Vo).(1-D).Ts = 0,
Therefore, Vo/Vd = D/ (1-D);
Io/Id = (1-D)/D, (since Po=Pd)
The output voltage can be higher or lower than the input voltage

38. Step-Up/down DC-DC Converter: CCM Waveforms
With Vo as constant
ILB = ½ ILpeak = Ts.Vd.D/2L
Io = IL- Id
Therefore, ILB = Ts.Vo.(1-D)/2L
and IoB = Ts.Vo.(1-D)2/2L
ILBmax = Ts.Vo/2L and IoBmax = Ts.Vo/2L Therefore,
ILB = ILBamx (1-D) and
IoB = IoBmax (1-D)2

39. Step-Up/Down DC-DC Converter: Limits of CCM/DCM
The output voltage is held constant

40. Discontinuous conduction mode
Vd.DTs+(-Vo). Δ1Ts = 0, Therefore, Vo/Vd = D/Δ1 Io/Id = Δ1/D, (since Po=Pd)
IL = (Vd/2L).DTs(D+Δ1)

41. Step-Up/Down dc-dc Converter: Limits of CCM/DCM conduction
The output voltage Vo is held constant

42. Step-Up/Down dc-dc Converter: Effect of Parasitics
The duty-ratio is limited to avoid these parasitic effects from becoming significant

43. Step-Up/Down DC-DC Converter: Output Voltage Ripple
ESR is assumed to be zero

44. Cük DC-DC Converter
The output voltage can be higher or lower than the input voltage

45. Cük DC-DC Converter: Waveforms, CCM
Assuming Vc1 to be constant
L1: Vd.DTs + (Vd- Vc1)(1-D)Ts = 0, Therefore,
Vc1 = (1/1-D).Vd
L2: (Vc1-Vo).DTs + (-Vo)(1-D)Ts = 0, Therefore,
Vc1 = Vo/D
So, Vo/Vd = D/(1-D) & Io/Id = (1-D)/D
IL1(1-D)Ts =IL2.DTs
or IL2/IL1 = (1-D)/D = Io/Id
and , Vo/Vd = D/(1-D)

54. Converter for DC-Motor Drives
Four quadrant operation is possible

55. Converter Waveforms
Bi-polar voltage switching

56. Converter Waveforms
Uni-polar voltage switching

59. Output Ripple in Converters for DC-Motor Drives
bi-polar and uni-polar voltage switching

60. Switch Utilization in DC-DC Converters
It varies significantly in various converters

61. Equivalent Circuits in DC-DC Converters
Step-up
Step-down
Cϋk
Step-down/step-up
Full-bridge
inductors and capacitors replaced by current and voltage sources, respectively

62. Reversing the Power Flow in DC-DC Conv.
For power flow from right to left, the input current direction should also reverse