1. DC-DC PWM Converters
Lecture Note 5

2. DC Choppers. The converters that achieve the voltage regulation by varying the on–off or time duty ratio of the switching element using a control technique called Pulse Width Modulation PWM.

3. Objective – to efficiently reduce DC voltage!
Objective – to efficiently reduce DC voltage
The DC equivalent of an AC transformer
Iin
Iout
DC−DC Converter +
Vin − +
Vout −
Lossless objective: Pin = Pout, which means that VinIin = VoutIout and

4. Linear Conversion + Vin − Vout R1 R2 The load
If Vin = 39V, and Vout = 13V, efficiency η is only 0.33
Unacceptable except in very low power applications

5. Linear Conversion
From what explained above, it is clear that a DC conversion by a voltage divider presents some drawbacks:
A DC voltage higher than the input voltage cannot be obtained;
The output voltage depends on the load, in general;
The efficiency is very poor.

6. Linear Conversion only a step down conversion is possible
the output voltage is given by:
only a step down conversion is possible
the efficiency remains low because all the power supplied by the source that it is not utilized by the load have to be dissipated by the power BJT.

7. Switching Conversion
𝑉 𝑜𝐴𝑉 = 𝑉 𝑖𝑛 𝑡 𝑜𝑛 𝑡 𝑜𝑛 + 𝑡 𝑜𝑓𝑓 = 𝑉 𝑖𝑛 𝑡 𝑜𝑛 𝑇 = 𝑉 𝑖𝑛 𝐷
Duty Cycle

8. Switching Conversion Transistor is operated in switched-mode:
Switch closed: Fully on (saturated)
Switch opened: Fully off (cut-off)
When switch is open, no current flow in it
When switch is closed no voltage drop across it.
Since P=V.I, no losses occurs in the switch.
Power is 100% transferred from source to load.
Power loss is zero (for ideal switch):
Switching regulator is the basis of all DC-DC converters

9. Pulse Width Modulation
The output DC voltage of DC chopper can be varied by controlling the width period (ton)
with constant switching/chopping frequency fs. This method is called PWM method

10. Pulse Width Modulation

11. Choppers Types
Two of the most popular categories of DC-DC converters are:
Transformerless DC-DC Converters
Insulated DC-DC Converters.
Three basic types of non-isolated DC–DC converters are
Step-down converter
Step-up converter
Step-up-down converter

12. DC−DC Buck Converter Step-Down Converter Buck Chopper

13. On-State
Off-State

14. Switch is turned on (closed)
• Diode is reversed biased.
• Switch conducts inductor current
• This results in positive inductor voltage, i.e:
• It causes linear
increase in the
inductor current

15. Switch turned off (opened)
• Because of inductive
energy storage, iL continues to flow.
• Diode is forward biased
• Current now flows (freewheeling) through the diode.
• The inductor voltage can be derived as:

16. Analysis

17. Analysis

18. Steady-state Operation
Unstable
Steady-state

19. Since the average voltage across L is zero!
Since the average voltage across L is zero
The input/output equation becomes
From power balance,
, so
Note – even though iin is not constant (i.e., iin has harmonics), the input power is still simply Vin • Iin because Vin has no harmonics

20. Output Voltage Ripple

21. Output Voltage Ripple

22. Examine the inductor current

23. Examine the inductor current
Switch closed,
Switch open,
From geometry, Iavg = Iout is halfway between Imax and Imin iL
Imax
Iavg = Iout ΔI
Periodic – finishes a period where it started
Imin DT
(1 − D)T T

24. Examine the inductor currentiL
Imax ΔI
Periodic – finishes a period where it started
Imin DT
(1 − D)T
Taking the derivative of above equation with respect to D and setting it to zero shows that ΔI is maximum when D = 0.5

25. Examine the inductor current
The boundary of continuous conduction is when ΔiLmin = 0, as shown below:
The maximum required value of Lboundary occurs when D → 0. Therefore, the value of L
will guarantee CCM for all D.

26. Effect of raising and lowering L while holding Vin, Vout, Iout and f constant
Lower L
Raise L
Lowering L increases ΔI and moves the circuit toward discontinuous operation

27. Effect of raising and lowering f while holding Vin, Vout, Iout, and L constant
Lower f
Raise f
Slopes of iL are unchanged
Lowering f increases ΔI and moves the circuit toward discontinuous operation

28. the rms value inductor current:
the ripple + =
the minimum value

29. the rms value inductor current:
Define

30. the rms value inductor current:
Recognize that Or

31. Component Ratings
Inductor current rating
Capacitor current rating
MOSFET and diode currents ratings
Voltage ratings

32. Inductor current rating
Max impact of ΔI on the rms current occurs at the boundary of continuous/discontinuous conduction, where ΔI =2Iout iL
2Iout
Iavg = Iout ΔI
Use max

33. Capacitor current ratingL
out L C
(iL – Iout)
iC = (iL – Iout)
Note – raising f or L, which lowers ΔI, reduces the capacitor current
Iout ΔI
−Iout
Max rms current occurs at the boundary of continuous/discontinuous conduction, where ΔI =2Iout
Use max

34. MOSFET and diode currents and current ratingsL
out in L C
(iL – Iout)
2Iout
Iout
2Iout
Iout
Use max
Take worst case D for each

35. Voltage ratings i i I L + V V C i – i I L + V V C i – C sees Vout
Switch Closed L + V V in C
out i C –
Diode sees Vin
MOSFET sees Vin i I L
out
Switch Open L + V V in C
out i C –
Diode and MOSFET, use 2Vin
Capacitor, use 1.5Vout

36. There is a 3rd state – discontinuous!
There is a 3rd state – discontinuous I
MOSFET
out + L V V in C
out
DIODE I
out –
Occurs for light loads, or low operating frequencies, where the inductor current eventually hits zero during the switch-open state
The diode opens to prevent backward current flow
The small capacitances of the MOSFET and diode, acting in parallel with each other as a net parasitic capacitance, interact with L to produce an oscillation
The output C is in series with the net parasitic capacitance, but C is so large that it can be ignored in the oscillation phenomenon
vL = (Vin – Vout)
Switch closed
vL = –Vout
Switch open
 650kHz. With L = 100µH, this corresponds to net parasitic C = 0.6nF

37. ! Impedance matching Iout = Iin / D Iin DC−DC Buck Converter + +
Vin − +
Vout = DVin −
Source
Iin +
Vin −
Equivalent from source perspective
So, the buck converter makes the load resistance look larger to the source

38. Example 1: Step-Down DC-DC Converter supplied by 230V DC voltage
Example 1: Step-Down DC-DC Converter supplied by 230V DC voltage. The load resistance equal to10Ω. Voltage drop across the chopper when it is ON equal to 2V. For a duty cycle of 0.4, calculate:
Average and RMS values of output voltage
Power delivered to the load and
Chopper efficiency.

39. DC−DC Boost Converter Step-Down Converter Boost Chopper

40. Buck converter Boost converter i + v – I i + V V C i – i + v – I i + VL
+ v – I i
out
Buck converter in + V V in C
out i C – i L
+ v – I
out
Boost converter i in + V V in C
out i C –

41. Boost (step-up) converter

42. Boost Analysis: Switch Closed

43. Boost Analysis: Switch Opened

44. Average Output voltage Expression
The net energy in the inductor is should be equal to zero over T period
Average voltage across inductor is 0
toff
ton

45. Output CharacteristicsVo
Infinity Vs D 1

46. Output CharacteristicsIo Is D 1

47. As 1 → D , the width of the ΔQ area increases to fill almost the entire cycle, and the maximum peak-to-peak ripple becomes

48. Examine the inductor current
Switch closed,
Switch open,
Iavg = Iin is half way between
Imax and Imin iL
Imax
Iavg = Iin ΔI
Imin DT
(1 − D)T T

49. Continuous current in LiL
2Iin
Iavg = Iin
(1 − D)T
Then, considering the worst case (i.e., D → 1),
use max
guarantees continuous conduction
use min

50. Inductor current rating
Max impact of ΔI on the rms current occurs at the boundary of continuous/discontinuous conduction, where ΔI =2Iin iL
2Iin
Iavg = Iin ΔI
Use max

51. MOSFET and diode currents ratings
+ v L – i i I i L D
out in L + V V in C
out i C –
2Iin
2Iin
Use max
Take worst case D for each

52. Capacitor current and current ratingL
out i D in L + V V in C
out i C –
iC = (iD – Iout)
2Iin −Iout
−Iout
Max rms current occurs at the boundary of continuous/discontinuous conduction, where ΔI =2Iout
Use max

53. Voltage ratings i I i L + V V C – i I i L + V V C – Diode sees Vout
C sees Vout L + V V in C
out – i I
out i L in L + V V in C
out –
MOSFET sees Vout
Diode and MOSFET, use 2Vout
Capacitor, use 1.5Vout

54. Impedance matching Iin DC−DC Boost Converter + + Vin − − Source Iin +
Equivalent from source perspective

55. Example 2: A boost chopper has input voltage of 20 V with switching frequency equal to 1 kHz. Calculate:
The required duty cycle that can be applied to the switch to boost the input voltage to 60V.
The ON and OFF period for the constant switching frequency operation.
Output current if the resistance load equal to 10 Ω.
Average input inductor current.
The maximum and minimum currents via the input inductor if the inductance is 10mH.